LMFDB - Embedded newform 446.2.c.d.39.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [446,2,Mod(39,446)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(446, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("446.39"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 446 = 2 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	446.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,14,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.56132793015$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 16 x^{12} - 12 x^{11} + 175 x^{10} - 149 x^{9} + 1070 x^{8} - 1093 x^{7} + 4783 x^{6} + \cdots + 13689 $ x^14 + 16x^12 - 12x^11 + 175x^10 - 149x^9 + 1070x^8 - 1093x^7 + 4783x^6 - 4593x^5 + 12718x^4 - 12011x^3 + 23362x^2 - 15327x + 13689
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			39.7
Root			$1.18397 - 2.05069i$ of defining polynomial
Character	$\chi$	$=$	446.39
Dual form			446.2.c.d.183.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.48752 - 2.57645i) q^{3} +1.00000 q^{4} +(0.877575 + 1.52000i) q^{5} +(1.48752 - 2.57645i) q^{6} -2.19386 q^{7} +1.00000 q^{8} +(-2.92540 - 5.06695i) q^{9} +(0.877575 + 1.52000i) q^{10} +(-1.63202 - 2.82675i) q^{11} +(1.48752 - 2.57645i) q^{12} +3.36793 q^{13} -2.19386 q^{14} +5.22162 q^{15} +1.00000 q^{16} +1.99023 q^{17} +(-2.92540 - 5.06695i) q^{18} +(-0.398184 + 0.689676i) q^{19} +(0.877575 + 1.52000i) q^{20} +(-3.26340 + 5.65238i) q^{21} +(-1.63202 - 2.82675i) q^{22} +(-1.46461 + 2.53678i) q^{23} +(1.48752 - 2.57645i) q^{24} +(0.959725 - 1.66229i) q^{25} +3.36793 q^{26} -8.48124 q^{27} -2.19386 q^{28} +(5.23651 + 9.06990i) q^{29} +5.22162 q^{30} +(-4.75889 + 8.24264i) q^{31} +1.00000 q^{32} -9.71064 q^{33} +1.99023 q^{34} +(-1.92528 - 3.33468i) q^{35} +(-2.92540 - 5.06695i) q^{36} +(-0.231543 - 0.401045i) q^{37} +(-0.398184 + 0.689676i) q^{38} +(5.00985 - 8.67731i) q^{39} +(0.877575 + 1.52000i) q^{40} -1.73875 q^{41} +(-3.26340 + 5.65238i) q^{42} +(-4.01628 + 6.95640i) q^{43} +(-1.63202 - 2.82675i) q^{44} +(5.13452 - 8.89325i) q^{45} +(-1.46461 + 2.53678i) q^{46} +(-4.74219 - 8.21371i) q^{47} +(1.48752 - 2.57645i) q^{48} -2.18697 q^{49} +(0.959725 - 1.66229i) q^{50} +(2.96050 - 5.12773i) q^{51} +3.36793 q^{52} +(4.33812 + 7.51385i) q^{53} -8.48124 q^{54} +(2.86445 - 4.96136i) q^{55} -2.19386 q^{56} +(1.18461 + 2.05181i) q^{57} +(5.23651 + 9.06990i) q^{58} -5.81887 q^{59} +5.22162 q^{60} +(5.10860 - 8.84835i) q^{61} +(-4.75889 + 8.24264i) q^{62} +(6.41793 + 11.1162i) q^{63} +1.00000 q^{64} +(2.95561 + 5.11927i) q^{65} -9.71064 q^{66} +(1.22354 - 2.11924i) q^{67} +1.99023 q^{68} +(4.35726 + 7.54700i) q^{69} +(-1.92528 - 3.33468i) q^{70} +(-4.30442 + 7.45548i) q^{71} +(-2.92540 - 5.06695i) q^{72} +(5.35953 + 9.28299i) q^{73} +(-0.231543 - 0.401045i) q^{74} +(-2.85521 - 4.94537i) q^{75} +(-0.398184 + 0.689676i) q^{76} +(3.58043 + 6.20149i) q^{77} +(5.00985 - 8.67731i) q^{78} +(-3.32743 - 5.76328i) q^{79} +(0.877575 + 1.52000i) q^{80} +(-3.83977 + 6.65067i) q^{81} -1.73875 q^{82} +(0.728309 + 1.26147i) q^{83} +(-3.26340 + 5.65238i) q^{84} +(1.74658 + 3.02516i) q^{85} +(-4.01628 + 6.95640i) q^{86} +31.1575 q^{87} +(-1.63202 - 2.82675i) q^{88} +(5.66550 - 9.81293i) q^{89} +(5.13452 - 8.89325i) q^{90} -7.38877 q^{91} +(-1.46461 + 2.53678i) q^{92} +(14.1578 + 24.5221i) q^{93} +(-4.74219 - 8.21371i) q^{94} -1.39775 q^{95} +(1.48752 - 2.57645i) q^{96} +(-4.71440 - 8.16558i) q^{97} -2.18697 q^{98} +(-9.54866 + 16.5388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} - 3 q^{3} + 14 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} + 14 q^{8} - 18 q^{9} - 6 q^{10} - 5 q^{11} - 3 q^{12} + 14 q^{13} - 6 q^{14} - 8 q^{15} + 14 q^{16} - 18 q^{18} - 4 q^{19} - 6 q^{20}+ \cdots - 43 q^{99}+O(q^{100}) $ 14 * q + 14 * q^2 - 3 * q^3 + 14 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 + 14 * q^8 - 18 * q^9 - 6 * q^10 - 5 * q^11 - 3 * q^12 + 14 * q^13 - 6 * q^14 - 8 * q^15 + 14 * q^16 - 18 * q^18 - 4 * q^19 - 6 * q^20 - 15 * q^21 - 5 * q^22 + 2 * q^23 - 3 * q^24 - 23 * q^25 + 14 * q^26 + 12 * q^27 - 6 * q^28 + 2 * q^29 - 8 * q^30 - 11 * q^31 + 14 * q^32 + 4 * q^33 + 9 * q^35 - 18 * q^36 - 5 * q^37 - 4 * q^38 + 11 * q^39 - 6 * q^40 + 44 * q^41 - 15 * q^42 - 14 * q^43 - 5 * q^44 - 3 * q^45 + 2 * q^46 - 13 * q^47 - 3 * q^48 + 24 * q^49 - 23 * q^50 + 13 * q^51 + 14 * q^52 + 17 * q^53 + 12 * q^54 + 3 * q^55 - 6 * q^56 - 5 * q^57 + 2 * q^58 + 20 * q^59 - 8 * q^60 + 24 * q^61 - 11 * q^62 + 21 * q^63 + 14 * q^64 - q^65 + 4 * q^66 - 10 * q^67 - 8 * q^69 + 9 * q^70 - 18 * q^71 - 18 * q^72 + 28 * q^73 - 5 * q^74 - 14 * q^75 - 4 * q^76 - 35 * q^77 + 11 * q^78 - 7 * q^79 - 6 * q^80 + 17 * q^81 + 44 * q^82 - 15 * q^83 - 15 * q^84 + 9 * q^85 - 14 * q^86 + 38 * q^87 - 5 * q^88 + 8 * q^89 - 3 * q^90 - 20 * q^91 + 2 * q^92 - 4 * q^93 - 13 * q^94 - 24 * q^95 - 3 * q^96 + 24 * q^98 - 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/446\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.48752	−	2.57645i	0.858817	−	1.48752i	−0.0142404	−	0.999899i	$-0.504533\pi$
$3$	1.48752	−	2.57645i	0.858817	−	1.48752i	0.873058	−	0.487617i	$-0.162134\pi$
$4$	1.00000			0.500000
$5$	0.877575	+	1.52000i	0.392463	+	0.679767i	0.992774	−	0.120001i	$-0.0382896\pi$
$5$	0.877575	+	1.52000i	0.392463	+	0.679767i	−0.600310	+	0.799767i	$0.704956\pi$
$6$	1.48752	−	2.57645i	0.607276	−	1.05183i
$7$	−2.19386			−0.829201			−0.414601	−	0.910003i	$-0.636079\pi$
$7$	−2.19386			−0.829201			−0.414601	+	0.910003i	$0.636079\pi$
$8$	1.00000			0.353553
$9$	−2.92540	−	5.06695i	−0.975135	−	1.68898i
$10$	0.877575	+	1.52000i	0.277514	+	0.480668i
$11$	−1.63202	−	2.82675i	−0.492074	−	0.852296i	0.507885	−	0.861425i	$-0.330428\pi$
$11$	−1.63202	−	2.82675i	−0.492074	−	0.852296i	−0.999958	+	0.00912861i	$0.997094\pi$
$12$	1.48752	−	2.57645i	0.429409	−	0.743758i
$13$	3.36793			0.934096			0.467048	−	0.884232i	$-0.345318\pi$
$13$	3.36793			0.934096			0.467048	+	0.884232i	$0.345318\pi$
$14$	−2.19386			−0.586334
$15$	5.22162			1.34822
$16$	1.00000			0.250000
$17$	1.99023			0.482702			0.241351	−	0.970438i	$-0.422410\pi$
$17$	1.99023			0.482702			0.241351	+	0.970438i	$0.422410\pi$
$18$	−2.92540	−	5.06695i	−0.689524	−	1.19429i
$19$	−0.398184	+	0.689676i	−0.0913498	+	0.158222i	−0.908079	−	0.418798i	$-0.862451\pi$
$19$	−0.398184	+	0.689676i	−0.0913498	+	0.158222i	0.816730	+	0.577021i	$0.195785\pi$
$20$	0.877575	+	1.52000i	0.196232	+	0.339883i
$21$	−3.26340	+	5.65238i	−0.712133	+	1.23345i
$22$	−1.63202	−	2.82675i	−0.347949	−	0.602665i
$23$	−1.46461	+	2.53678i	−0.305392	+	0.528955i	−0.977349	−	0.211636i	$-0.932121\pi$
$23$	−1.46461	+	2.53678i	−0.305392	+	0.528955i	0.671956	+	0.740591i	$0.265454\pi$
$24$	1.48752	−	2.57645i	0.303638	−	0.525916i
$25$	0.959725	−	1.66229i	0.191945	−	0.332458i
$26$	3.36793			0.660506
$27$	−8.48124			−1.63222
$28$	−2.19386			−0.414601
$29$	5.23651	+	9.06990i	0.972395	+	1.68424i	0.688276	+	0.725449i	$0.258368\pi$
$29$	5.23651	+	9.06990i	0.972395	+	1.68424i	0.284119	+	0.958789i	$0.408299\pi$
$30$	5.22162			0.953334
$31$	−4.75889	+	8.24264i	−0.854721	+	1.48042i	0.0221818	+	0.999754i	$0.492939\pi$
$31$	−4.75889	+	8.24264i	−0.854721	+	1.48042i	−0.876903	+	0.480667i	$0.840395\pi$
$32$	1.00000			0.176777
$33$	−9.71064			−1.69041
$34$	1.99023			0.341322
$35$	−1.92528	−	3.33468i	−0.325431	−	0.563663i
$36$	−2.92540	−	5.06695i	−0.487567	−	0.844491i
$37$	−0.231543	−	0.401045i	−0.0380655	−	0.0659314i	0.846365	−	0.532603i	$-0.178786\pi$
$37$	−0.231543	−	0.401045i	−0.0380655	−	0.0659314i	−0.884430	+	0.466672i	$0.845453\pi$
$38$	−0.398184	+	0.689676i	−0.0645940	+	0.111880i
$39$	5.00985	−	8.67731i	0.802218	−	1.38948i
$40$	0.877575	+	1.52000i	0.138757	+	0.240334i
$41$	−1.73875			−0.271547			−0.135773	−	0.990740i	$-0.543352\pi$
$41$	−1.73875			−0.271547			−0.135773	+	0.990740i	$0.543352\pi$
$42$	−3.26340	+	5.65238i	−0.503554	+	0.872181i
$43$	−4.01628	+	6.95640i	−0.612477	+	1.06084i	0.378344	+	0.925665i	$0.376493\pi$
$43$	−4.01628	+	6.95640i	−0.612477	+	1.06084i	−0.990822	+	0.135177i	$0.956840\pi$
$44$	−1.63202	−	2.82675i	−0.246037	−	0.426148i
$45$	5.13452	−	8.89325i	0.765409	−	1.32573i
$46$	−1.46461	+	2.53678i	−0.215945	+	0.374028i
$47$	−4.74219	−	8.21371i	−0.691720	−	1.19809i	−0.971274	−	0.237964i	$-0.923520\pi$
$47$	−4.74219	−	8.21371i	−0.691720	−	1.19809i	0.279555	−	0.960130i	$-0.409813\pi$
$48$	1.48752	−	2.57645i	0.214704	−	0.371879i
$49$	−2.18697			−0.312425
$50$	0.959725	−	1.66229i	0.135726	−	0.235084i
$51$	2.96050	−	5.12773i	0.414553	−	0.718026i
$52$	3.36793			0.467048
$53$	4.33812	+	7.51385i	0.595887	+	1.03211i	0.993421	+	0.114519i	$0.0365327\pi$
$53$	4.33812	+	7.51385i	0.595887	+	1.03211i	−0.397534	+	0.917587i	$0.630134\pi$
$54$	−8.48124			−1.15415
$55$	2.86445	−	4.96136i	0.386242	−	0.668990i
$56$	−2.19386			−0.293167
$57$	1.18461	+	2.05181i	0.156906	+	0.271768i
$58$	5.23651	+	9.06990i	0.687587	+	1.19094i
$59$	−5.81887			−0.757552			−0.378776	−	0.925488i	$-0.623655\pi$
$59$	−5.81887			−0.757552			−0.378776	+	0.925488i	$0.623655\pi$
$60$	5.22162			0.674109
$61$	5.10860	−	8.84835i	0.654089	−	1.13292i	−0.328032	−	0.944666i	$-0.606386\pi$
$61$	5.10860	−	8.84835i	0.654089	−	1.13292i	0.982121	−	0.188249i	$-0.0602811\pi$
$62$	−4.75889	+	8.24264i	−0.604379	+	1.04682i
$63$	6.41793	+	11.1162i	0.808583	+	1.40051i
$64$	1.00000			0.125000
$65$	2.95561	+	5.11927i	0.366599	+	0.634967i
$66$	−9.71064			−1.19530
$67$	1.22354	−	2.11924i	0.149480	−	0.258906i	−0.781556	−	0.623836i	$-0.785574\pi$
$67$	1.22354	−	2.11924i	0.149480	−	0.258906i	0.931035	+	0.364929i	$0.118907\pi$
$68$	1.99023			0.241351
$69$	4.35726	+	7.54700i	0.524552	+	0.908552i
$70$	−1.92528	−	3.33468i	−0.230115	−	0.398570i
$71$	−4.30442	+	7.45548i	−0.510841	+	0.884802i	0.489080	+	0.872239i	$0.337333\pi$
$71$	−4.30442	+	7.45548i	−0.510841	+	0.884802i	−0.999921	+	0.0125635i	$0.996001\pi$
$72$	−2.92540	−	5.06695i	−0.344762	−	0.597146i
$73$	5.35953	+	9.28299i	0.627286	+	1.08649i	0.988094	+	0.153851i	$0.0491677\pi$
$73$	5.35953	+	9.28299i	0.627286	+	1.08649i	−0.360808	+	0.932640i	$0.617499\pi$
$74$	−0.231543	−	0.401045i	−0.0269164	−	0.0466205i
$75$	−2.85521	−	4.94537i	−0.329691	−	0.571042i
$76$	−0.398184	+	0.689676i	−0.0456749	+	0.0791112i
$77$	3.58043	+	6.20149i	0.408028	+	0.706725i
$78$	5.00985	−	8.67731i	0.567254	−	0.982512i
$79$	−3.32743	−	5.76328i	−0.374365	−	0.648419i	0.615867	−	0.787850i	$-0.288806\pi$
$79$	−3.32743	−	5.76328i	−0.374365	−	0.648419i	−0.990232	+	0.139431i	$0.955473\pi$
$80$	0.877575	+	1.52000i	0.0981158	+	0.169942i
$81$	−3.83977	+	6.65067i	−0.426641	+	0.738963i
$82$	−1.73875			−0.192013
$83$	0.728309	+	1.26147i	0.0799423	+	0.138464i	0.903225	−	0.429168i	$-0.141193\pi$
$83$	0.728309	+	1.26147i	0.0799423	+	0.138464i	−0.823283	+	0.567632i	$0.807860\pi$
$84$	−3.26340	+	5.65238i	−0.356066	+	0.616725i
$85$	1.74658	+	3.02516i	0.189443	+	0.328124i
$86$	−4.01628	+	6.95640i	−0.433087	+	0.750128i
$87$	31.1575			3.34044
$88$	−1.63202	−	2.82675i	−0.173974	−	0.301332i
$89$	5.66550	−	9.81293i	0.600542	−	1.04017i	−0.392197	−	0.919881i	$-0.628285\pi$
$89$	5.66550	−	9.81293i	0.600542	−	1.04017i	0.992739	−	0.120288i	$-0.0383817\pi$
$90$	5.13452	−	8.89325i	0.541226	−	0.937431i
$91$	−7.38877			−0.774554
$92$	−1.46461	+	2.53678i	−0.152696	+	0.264478i
$93$	14.1578	+	24.5221i	1.46810	+	2.54282i
$94$	−4.74219	−	8.21371i	−0.489120	−	0.847180i
$95$	−1.39775			−0.143406
$96$	1.48752	−	2.57645i	0.151819	−	0.262958i
$97$	−4.71440	−	8.16558i	−0.478675	−	0.829089i	0.521026	−	0.853541i	$-0.325549\pi$
$97$	−4.71440	−	8.16558i	−0.478675	−	0.829089i	−0.999701	+	0.0244516i	$0.992216\pi$
$98$	−2.18697			−0.220918
$99$	−9.54866	+	16.5388i	−0.959676	+	1.66221i
$100$	0.959725	−	1.66229i	0.0959725	−	0.166229i
$101$	−3.11261	+	5.39120i	−0.309716	+	0.536444i	−0.978300	−	0.207192i	$-0.933567\pi$
$101$	−3.11261	+	5.39120i	−0.309716	+	0.536444i	0.668584	+	0.743637i	$0.266901\pi$
$102$	2.96050	−	5.12773i	0.293133	−	0.507721i
$103$	−3.47073			−0.341981			−0.170990	−	0.985273i	$-0.554697\pi$
$103$	−3.47073			−0.341981			−0.170990	+	0.985273i	$0.554697\pi$
$104$	3.36793			0.330253
$105$	−11.4555			−1.11794
$106$	4.33812	+	7.51385i	0.421356	+	0.729809i
$107$	−0.779898	−	1.35082i	−0.0753955	−	0.130589i	0.825863	−	0.563871i	$-0.190689\pi$
$107$	−0.779898	−	1.35082i	−0.0753955	−	0.130589i	−0.901258	+	0.433282i	$0.857355\pi$
$108$	−8.48124			−0.816108
$109$	−5.98146	−	10.3602i	−0.572920	−	0.992326i	−0.996264	−	0.0863573i	$-0.972477\pi$
$109$	−5.98146	−	10.3602i	−0.572920	−	0.992326i	0.423344	−	0.905969i	$-0.360856\pi$
$110$	2.86445	−	4.96136i	0.273114	−	0.473048i
$111$	−1.37770			−0.130765
$112$	−2.19386			−0.207300
$113$	−0.174842	+	0.302836i	−0.0164478	+	0.0284884i	−0.874132	−	0.485688i	$-0.838569\pi$
$113$	−0.174842	+	0.302836i	−0.0164478	+	0.0284884i	0.857684	+	0.514177i	$0.171902\pi$
$114$	1.18461	+	2.05181i	0.110949	+	0.192169i
$115$	−5.14122			−0.479421
$116$	5.23651	+	9.06990i	0.486198	+	0.842119i
$117$	−9.85256	−	17.0651i	−0.910870	−	1.57767i
$118$	−5.81887			−0.535670
$119$	−4.36629			−0.400257
$120$	5.22162			0.476667
$121$	0.173000	−	0.299644i	0.0157272	−	0.0272404i
$122$	5.10860	−	8.84835i	0.462511	−	0.801092i
$123$	−2.58641	+	4.47980i	−0.233209	+	0.403930i
$124$	−4.75889	+	8.24264i	−0.427361	+	0.740210i
$125$	12.1447			1.08625
$126$	6.41793	+	11.1162i	0.571755	+	0.990308i
$127$	0.216387	−	0.374794i	0.0192013	−	0.0332576i	−0.856265	−	0.516537i	$-0.827221\pi$
$127$	0.216387	−	0.374794i	0.0192013	−	0.0332576i	0.875466	+	0.483279i	$0.160554\pi$
$128$	1.00000			0.0883883
$129$	11.9486	+	20.6955i	1.05201	+	1.82214i
$130$	2.95561	+	5.11927i	0.259224	+	0.448990i
$131$	7.35630	−	12.7415i	0.642723	−	1.11323i	−0.342100	−	0.939664i	$-0.611138\pi$
$131$	7.35630	−	12.7415i	0.642723	−	1.11323i	0.984822	−	0.173565i	$-0.0555286\pi$
$132$	−9.71064			−0.845203
$133$	0.873561	−	1.51305i	0.0757474	−	0.131198i
$134$	1.22354	−	2.11924i	0.105698	−	0.183074i
$135$	−7.44292	−	12.8915i	−0.640585	−	1.10953i
$136$	1.99023			0.170661
$137$	7.69713	−	13.3318i	0.657610	−	1.13901i	−0.323622	−	0.946186i	$-0.604901\pi$
$137$	7.69713	−	13.3318i	0.657610	−	1.13901i	0.981233	−	0.192828i	$-0.0617660\pi$
$138$	4.35726	+	7.54700i	0.370915	+	0.642443i
$139$	−2.91155	+	5.04294i	−0.246954	+	0.427737i	−0.962679	−	0.270645i	$-0.912763\pi$
$139$	−2.91155	+	5.04294i	−0.246954	+	0.427737i	0.715725	+	0.698382i	$0.246096\pi$
$140$	−1.92528	−	3.33468i	−0.162716	−	0.281832i
$141$	−28.2163			−2.37624
$142$	−4.30442	+	7.45548i	−0.361219	+	0.625650i
$143$	−5.49654	−	9.52029i	−0.459644	−	0.796127i
$144$	−2.92540	−	5.06695i	−0.243784	−	0.422246i
$145$	−9.19085	+	15.9190i	−0.763259	+	1.32200i
$146$	5.35953	+	9.28299i	0.443558	+	0.768265i
$147$	−3.25316	+	5.63464i	−0.268316	+	0.464737i
$148$	−0.231543	−	0.401045i	−0.0190327	−	0.0329657i
$149$	−10.4423	−	18.0866i	−0.855465	−	1.48171i	−0.876213	−	0.481924i	$-0.839938\pi$
$149$	−10.4423	−	18.0866i	−0.855465	−	1.48171i	0.0207477	−	0.999785i	$-0.493395\pi$
$150$	−2.85521	−	4.94537i	−0.233127	−	0.403788i
$151$	−5.86579	−	10.1598i	−0.477351	−	0.826796i	0.522312	−	0.852754i	$-0.325070\pi$
$151$	−5.86579	−	10.1598i	−0.477351	−	0.826796i	−0.999663	+	0.0259584i	$0.991736\pi$
$152$	−0.398184	+	0.689676i	−0.0322970	+	0.0559401i
$153$	−5.82223	−	10.0844i	−0.470699	−	0.815275i
$154$	3.58043	+	6.20149i	0.288519	+	0.499730i
$155$	−16.7051			−1.34179
$156$	5.00985	−	8.67731i	0.401109	−	0.694741i
$157$	−18.7214			−1.49413			−0.747064	−	0.664752i	$-0.768537\pi$
$157$	−18.7214			−1.49413			−0.747064	+	0.664752i	$0.768537\pi$
$158$	−3.32743	−	5.76328i	−0.264716	−	0.458502i
$159$	25.8121			2.04703
$160$	0.877575	+	1.52000i	0.0693784	+	0.120167i
$161$	3.21315	−	5.56534i	0.253232	−	0.438610i
$162$	−3.83977	+	6.65067i	−0.301680	+	0.522526i
$163$	−0.592601			−0.0464161			−0.0232080	−	0.999731i	$-0.507388\pi$
$163$	−0.592601			−0.0464161			−0.0232080	+	0.999731i	$0.507388\pi$
$164$	−1.73875			−0.135773
$165$	−8.52181	−	14.7602i	−0.663422	−	1.14908i
$166$	0.728309	+	1.26147i	0.0565277	+	0.0979089i
$167$	16.8713			1.30554			0.652768	−	0.757558i	$-0.273607\pi$
$167$	16.8713			1.30554			0.652768	+	0.757558i	$0.273607\pi$
$168$	−3.26340	+	5.65238i	−0.251777	+	0.436090i
$169$	−1.65704			−0.127464
$170$	1.74658	+	3.02516i	0.133956	+	0.232019i
$171$	4.65940			0.356313
$172$	−4.01628	+	6.95640i	−0.306239	+	0.530421i
$173$	−5.83318	+	10.1034i	−0.443489	+	0.768145i	−0.997946	−	0.0640674i	$-0.979593\pi$
$173$	−5.83318	+	10.1034i	−0.443489	+	0.768145i	0.554457	+	0.832213i	$0.312926\pi$
$174$	31.1575			2.36205
$175$	−2.10550	+	3.64684i	−0.159161	+	0.275675i
$176$	−1.63202	−	2.82675i	−0.123018	−	0.213074i
$177$	−8.65565	+	14.9920i	−0.650599	+	1.12687i
$178$	5.66550	−	9.81293i	0.424647	−	0.735510i
$179$	12.3440	+	21.3804i	0.922633	+	1.59805i	0.795324	+	0.606184i	$0.207301\pi$
$179$	12.3440	+	21.3804i	0.922633	+	1.59805i	0.127309	+	0.991863i	$0.459366\pi$
$180$	5.13452	−	8.89325i	0.382705	−	0.662864i
$181$	−8.58932	+	14.8771i	−0.638439	+	1.10581i	0.347337	+	0.937741i	$0.387086\pi$
$181$	−8.58932	+	14.8771i	−0.638439	+	1.10581i	−0.985775	+	0.168068i	$0.946247\pi$
$182$	−7.38877			−0.547692
$183$	−15.1982	−	26.3241i	−1.12349	−	1.94593i
$184$	−1.46461	+	2.53678i	−0.107972	+	0.187014i
$185$	0.406393	−	0.703894i	0.0298786	−	0.0517513i
$186$	14.1578	+	24.5221i	1.03810	+	1.79805i
$187$	−3.24810	−	5.62588i	−0.237525	−	0.411405i
$188$	−4.74219	−	8.21371i	−0.345860	−	0.599047i
$189$	18.6067			1.35344
$190$	−1.39775			−0.101403
$191$	22.6991			1.64245			0.821224	−	0.570606i	$-0.193291\pi$
$191$	22.6991			1.64245			0.821224	+	0.570606i	$0.193291\pi$
$192$	1.48752	−	2.57645i	0.107352	−	0.185939i
$193$	−14.7243			−1.05988			−0.529940	−	0.848035i	$-0.677785\pi$
$193$	−14.7243			−1.05988			−0.529940	+	0.848035i	$0.677785\pi$
$194$	−4.71440	−	8.16558i	−0.338474	−	0.586254i
$195$	17.5861			1.25936
$196$	−2.18697			−0.156212
$197$	22.1406			1.57745			0.788726	−	0.614745i	$-0.210741\pi$
$197$	22.1406			1.57745			0.788726	+	0.614745i	$0.210741\pi$
$198$	−9.54866	+	16.5388i	−0.678593	+	1.17536i
$199$	13.8449	−	23.9800i	0.981436	−	1.69990i	0.324621	−	0.945844i	$-0.394763\pi$
$199$	13.8449	−	23.9800i	0.981436	−	1.69990i	0.656814	−	0.754052i	$-0.271904\pi$
$200$	0.959725	−	1.66229i	0.0678628	−	0.117542i
$201$	−3.64008	−	6.30480i	−0.256751	−	0.444706i
$202$	−3.11261	+	5.39120i	−0.219002	+	0.379323i
$203$	−11.4882	−	19.8981i	−0.806311	−	1.39657i
$204$	2.96050	−	5.12773i	0.207276	−	0.359013i
$205$	−1.52588	−	2.64290i	−0.106572	−	0.184588i
$206$	−3.47073			−0.241817
$207$	17.1383			1.19119
$208$	3.36793			0.233524
$209$	2.59938			0.179803
$210$	−11.4555			−0.790506
$211$	−2.42987	+	4.20866i	−0.167279	+	0.289736i	−0.937462	−	0.348087i	$-0.886831\pi$
$211$	−2.42987	+	4.20866i	−0.167279	+	0.289736i	0.770183	+	0.637823i	$0.220165\pi$
$212$	4.33812	+	7.51385i	0.297943	+	0.516053i
$213$	12.8058	+	22.1803i	0.877438	+	1.51977i
$214$	−0.779898	−	1.35082i	−0.0533127	−	0.0923403i
$215$	−14.0983			−0.961499
$216$	−8.48124			−0.577075
$217$	10.4403	−	18.0832i	0.708736	−	1.22757i
$218$	−5.98146	−	10.3602i	−0.405115	−	0.701681i
$219$	31.8896			2.15490
$220$	2.86445	−	4.96136i	0.193121	−	0.334495i
$221$	6.70296			0.450890
$222$	−1.37770			−0.0924650
$223$	7.27564	+	13.0409i	0.487213	+	0.873283i
$223$	7.27564	+	13.0409i	0.487213	+	0.873283i
$224$	−2.19386			−0.146583
$225$	−11.2303			−0.748689
$226$	−0.174842	+	0.302836i	−0.0116303	+	0.0201443i
$227$	3.37265			0.223851			0.111925	−	0.993717i	$-0.464298\pi$
$227$	3.37265			0.223851			0.111925	+	0.993717i	$0.464298\pi$
$228$	1.18461	+	2.05181i	0.0784528	+	0.135884i
$229$	−5.45349	+	9.44573i	−0.360377	+	0.624191i	−0.988023	−	0.154308i	$-0.950685\pi$
$229$	−5.45349	+	9.44573i	−0.360377	+	0.624191i	0.627646	+	0.778499i	$0.284019\pi$
$230$	−5.14122			−0.339002
$231$	21.3038			1.40169
$232$	5.23651	+	9.06990i	0.343794	+	0.595468i
$233$	1.75202	+	3.03459i	0.114779	+	0.198802i	0.917691	−	0.397294i	$-0.130051\pi$
$233$	1.75202	+	3.03459i	0.114779	+	0.198802i	−0.802913	+	0.596097i	$0.796717\pi$
$234$	−9.85256	−	17.0651i	−0.644082	−	1.11558i
$235$	8.32325	−	14.4163i	0.542949	−	0.940416i
$236$	−5.81887			−0.378776
$237$	−19.7984			−1.28605
$238$	−4.36629			−0.283024
$239$	2.07786			0.134406			0.0672029	−	0.997739i	$-0.478593\pi$
$239$	2.07786			0.134406			0.0672029	+	0.997739i	$0.478593\pi$
$240$	5.22162			0.337054
$241$	−0.990128	−	1.71495i	−0.0637797	−	0.110470i	0.832372	−	0.554217i	$-0.186982\pi$
$241$	−0.990128	−	1.71495i	−0.0637797	−	0.110470i	−0.896152	+	0.443747i	$0.853649\pi$
$242$	0.173000	−	0.299644i	0.0111208	−	0.0192618i
$243$	−1.29844	−	2.24897i	−0.0832951	−	0.144271i
$244$	5.10860	−	8.84835i	0.327044	−	0.566458i
$245$	−1.91923	−	3.32421i	−0.122615	−	0.212376i
$246$	−2.58641	+	4.47980i	−0.164904	+	0.285622i
$247$	−1.34106	+	2.32278i	−0.0853295	+	0.147795i
$248$	−4.75889	+	8.24264i	−0.302190	+	0.523408i
$249$	4.33348			0.274623
$250$	12.1447			0.768096
$251$	26.1184			1.64858			0.824288	−	0.566170i	$-0.191575\pi$
$251$	26.1184			1.64858			0.824288	+	0.566170i	$0.191575\pi$
$252$	6.41793	+	11.1162i	0.404292	+	0.700253i
$253$	9.56111			0.601102
$254$	0.216387	−	0.374794i	0.0135773	−	0.0235166i
$255$	10.3922			0.650787
$256$	1.00000			0.0625000
$257$	−17.1234			−1.06813			−0.534065	−	0.845443i	$-0.679336\pi$
$257$	−17.1234			−1.06813			−0.534065	+	0.845443i	$0.679336\pi$
$258$	11.9486	+	20.6955i	0.743885	+	1.28845i
$259$	0.507974	+	0.879836i	0.0315640	+	0.0546704i
$260$	2.95561	+	5.11927i	0.183299	+	0.317484i
$261$	30.6378	−	53.0662i	1.89643	−	3.28472i
$262$	7.35630	−	12.7415i	0.454474	−	0.787171i
$263$	−6.90213	−	11.9548i	−0.425604	−	0.737167i	0.570873	−	0.821038i	$-0.306605\pi$
$263$	−6.90213	−	11.9548i	−0.425604	−	0.737167i	−0.996477	+	0.0838712i	$0.973272\pi$
$264$	−9.71064			−0.597649
$265$	−7.61405	+	13.1879i	−0.467728	+	0.810128i
$266$	0.873561	−	1.51305i	0.0535615	−	0.0927712i
$267$	−16.8550	−	29.1938i	−1.03151	−	1.78663i
$268$	1.22354	−	2.11924i	0.0747398	−	0.129453i
$269$	−0.908781	+	1.57406i	−0.0554094	+	0.0959718i	−0.892400	−	0.451246i	$-0.850980\pi$
$269$	−0.908781	+	1.57406i	−0.0554094	+	0.0959718i	0.836990	+	0.547218i	$0.184313\pi$
$270$	−7.44292	−	12.8915i	−0.452962	−	0.784553i
$271$	−11.4336	+	19.8036i	−0.694543	+	1.20298i	0.275792	+	0.961217i	$0.411060\pi$
$271$	−11.4336	+	19.8036i	−0.694543	+	1.20298i	−0.970335	+	0.241766i	$0.922273\pi$
$272$	1.99023			0.120675
$273$	−10.9909	+	19.0368i	−0.665200	+	1.15216i
$274$	7.69713	−	13.3318i	0.465001	−	0.805405i
$275$	−6.26517			−0.377804
$276$	4.35726	+	7.54700i	0.262276	+	0.454276i
$277$	−6.56234			−0.394293			−0.197146	−	0.980374i	$-0.563167\pi$
$277$	−6.56234			−0.394293			−0.197146	+	0.980374i	$0.563167\pi$
$278$	−2.91155	+	5.04294i	−0.174623	+	0.302456i
$279$	55.6867			3.33387
$280$	−1.92528	−	3.33468i	−0.115057	−	0.199285i
$281$	−9.91792	−	17.1783i	−0.591653	−	1.02477i	−0.994010	−	0.109290i	$-0.965142\pi$
$281$	−9.91792	−	17.1783i	−0.591653	−	1.02477i	0.402357	−	0.915483i	$-0.368191\pi$
$282$	−28.2163			−1.68026
$283$	−18.8395			−1.11989			−0.559945	−	0.828530i	$-0.689178\pi$
$283$	−18.8395			−1.11989			−0.559945	+	0.828530i	$0.689178\pi$
$284$	−4.30442	+	7.45548i	−0.255420	+	0.442401i
$285$	−2.07917	+	3.60123i	−0.123159	+	0.213318i
$286$	−5.49654	−	9.52029i	−0.325017	−	0.562947i
$287$	3.81457			0.225167
$288$	−2.92540	−	5.06695i	−0.172381	−	0.298573i
$289$	−13.0390			−0.766999
$290$	−9.19085	+	15.9190i	−0.539706	+	0.934797i
$291$	−28.0510			−1.64438
$292$	5.35953	+	9.28299i	0.313643	+	0.543246i
$293$	−12.9709	−	22.4663i	−0.757770	−	1.31250i	−0.943986	−	0.329986i	$-0.892956\pi$
$293$	−12.9709	−	22.4663i	−0.757770	−	1.31250i	0.186216	−	0.982509i	$-0.440378\pi$
$294$	−3.25316	+	5.63464i	−0.189728	+	0.328619i
$295$	−5.10649	−	8.84470i	−0.297311	−	0.514958i
$296$	−0.231543	−	0.401045i	−0.0134582	−	0.0233103i
$297$	13.8416	+	23.9743i	0.803170	+	1.39113i
$298$	−10.4423	−	18.0866i	−0.604905	−	1.04773i
$299$	−4.93271	+	8.54370i	−0.285266	+	0.494095i
$300$	−2.85521	−	4.94537i	−0.164846	−	0.285521i
$301$	8.81116	−	15.2614i	0.507867	−	0.879651i
$302$	−5.86579	−	10.1598i	−0.337538	−	0.584633i
$303$	9.26011	+	16.0390i	0.531979	+	0.921415i
$304$	−0.398184	+	0.689676i	−0.0228374	+	0.0395556i
$305$	17.9327			1.02682
$306$	−5.82223	−	10.0844i	−0.332834	−	0.576486i
$307$	−2.18053	+	3.77678i	−0.124449	+	0.215552i	−0.921518	−	0.388337i	$-0.873050\pi$
$307$	−2.18053	+	3.77678i	−0.124449	+	0.215552i	0.797068	+	0.603889i	$0.206383\pi$
$308$	3.58043	+	6.20149i	0.204014	+	0.353363i
$309$	−5.16276	+	8.94216i	−0.293699	+	0.508702i
$310$	−16.7051			−0.948787
$311$	1.39938	+	2.42380i	0.0793518	+	0.137441i	0.902970	−	0.429703i	$-0.141382\pi$
$311$	1.39938	+	2.42380i	0.0793518	+	0.137441i	−0.823619	+	0.567144i	$0.808048\pi$
$312$	5.00985	−	8.67731i	0.283627	−	0.491256i
$313$	−14.6562	+	25.3852i	−0.828415	+	1.43486i	0.0708666	+	0.997486i	$0.477424\pi$
$313$	−14.6562	+	25.3852i	−0.828415	+	1.43486i	−0.899281	+	0.437371i	$0.855910\pi$
$314$	−18.7214			−1.05651
$315$	−11.2644	+	19.5106i	−0.634679	+	1.09930i
$316$	−3.32743	−	5.76328i	−0.187183	−	0.324210i
$317$	−16.1589	−	27.9881i	−0.907576	−	1.57197i	−0.817422	−	0.576039i	$-0.804598\pi$
$317$	−16.1589	−	27.9881i	−0.907576	−	1.57197i	−0.0901535	−	0.995928i	$-0.528736\pi$
$318$	25.8121			1.44747
$319$	17.0922	−	29.6046i	0.956980	−	1.65754i
$320$	0.877575	+	1.52000i	0.0490579	+	0.0849708i
$321$	−4.64044			−0.259004
$322$	3.21315	−	5.56534i	0.179062	−	0.310144i
$323$	−0.792478	+	1.37261i	−0.0440947	+	0.0763742i
$324$	−3.83977	+	6.65067i	−0.213320	+	0.369482i
$325$	3.23229	−	5.59849i	0.179295	−	0.310548i
$326$	−0.592601			−0.0328211
$327$	−35.5900			−1.96813
$328$	−1.73875			−0.0960063
$329$	10.4037	+	18.0197i	0.573575	+	0.993461i
$330$	−8.52181	−	14.7602i	−0.469110	−	0.812523i
$331$	−12.5600			−0.690358			−0.345179	−	0.938537i	$-0.612182\pi$
$331$	−12.5600			−0.690358			−0.345179	+	0.938537i	$0.612182\pi$
$332$	0.728309	+	1.26147i	0.0399711	+	0.0692320i
$333$	−1.35472	+	2.34644i	−0.0742379	+	0.128584i
$334$	16.8713			0.923154
$335$	4.29500			0.234661
$336$	−3.26340	+	5.65238i	−0.178033	+	0.308362i
$337$	−5.95873	−	10.3208i	−0.324593	−	0.562211i	0.656837	−	0.754033i	$-0.271894\pi$
$337$	−5.95873	−	10.3208i	−0.324593	−	0.562211i	−0.981430	+	0.191821i	$0.938561\pi$
$338$	−1.65704			−0.0901310
$339$	0.520161	+	0.900945i	0.0282513	+	0.0489326i
$340$	1.74658	+	3.02516i	0.0947213	+	0.164062i
$341$	31.0665			1.68234
$342$	4.65940			0.251952
$343$	20.1549			1.08826
$344$	−4.01628	+	6.95640i	−0.216543	+	0.375064i
$345$	−7.64764	+	13.2461i	−0.411735	+	0.713146i
$346$	−5.83318	+	10.1034i	−0.313594	+	0.543161i
$347$	6.96499	−	12.0637i	0.373900	−	0.647614i	−0.616261	−	0.787542i	$-0.711354\pi$
$347$	6.96499	−	12.0637i	0.373900	−	0.647614i	0.990162	+	0.139927i	$0.0446869\pi$
$348$	31.1575			1.67022
$349$	−11.1497	−	19.3119i	−0.596832	−	1.03374i	−0.993285	−	0.115689i	$-0.963092\pi$
$349$	−11.1497	−	19.3119i	−0.596832	−	1.03374i	0.396453	−	0.918055i	$-0.370241\pi$
$350$	−2.10550	+	3.64684i	−0.112544	+	0.194932i
$351$	−28.5642			−1.52465
$352$	−1.63202	−	2.82675i	−0.0869871	−	0.150666i
$353$	16.3468	+	28.3136i	0.870054	+	1.50698i	0.861939	+	0.507011i	$0.169250\pi$
$353$	16.3468	+	28.3136i	0.870054	+	1.50698i	0.00811483	+	0.999967i	$0.497417\pi$
$354$	−8.65565	+	14.9920i	−0.460043	+	0.796817i
$355$	−15.1098			−0.801945
$356$	5.66550	−	9.81293i	0.300271	−	0.520084i
$357$	−6.49492	+	11.2495i	−0.343748	+	0.595388i
$358$	12.3440	+	21.3804i	0.652400	+	1.12999i
$359$	−2.13668			−0.112770			−0.0563849	−	0.998409i	$-0.517957\pi$
$359$	−2.13668			−0.112770			−0.0563849	+	0.998409i	$0.517957\pi$
$360$	5.13452	−	8.89325i	0.270613	−	0.468716i
$361$	9.18290	+	15.9052i	0.483310	+	0.837118i
$362$	−8.58932	+	14.8771i	−0.451444	+	0.781925i
$363$	−0.514679	−	0.891450i	−0.0270136	−	0.0467890i
$364$	−7.38877			−0.387277
$365$	−9.40679	+	16.2930i	−0.492374	+	0.852816i
$366$	−15.1982	−	26.3241i	−0.794424	−	1.37598i
$367$	13.2396	+	22.9317i	0.691102	+	1.19702i	0.971477	+	0.237133i	$0.0762079\pi$
$367$	13.2396	+	22.9317i	0.691102	+	1.19702i	−0.280375	+	0.959891i	$0.590459\pi$
$368$	−1.46461	+	2.53678i	−0.0763481	+	0.132239i
$369$	5.08654	+	8.81014i	0.264795	+	0.458638i
$370$	0.406393	−	0.703894i	0.0211274	−	0.0365937i
$371$	−9.51724	−	16.4843i	−0.494110	−	0.855824i
$372$	14.1578	+	24.5221i	0.734050	+	1.27141i
$373$	2.22803	+	3.85906i	0.115363	+	0.199815i	0.917925	−	0.396754i	$-0.129864\pi$
$373$	2.22803	+	3.85906i	0.115363	+	0.199815i	−0.802562	+	0.596569i	$0.796530\pi$
$374$	−3.24810	−	5.62588i	−0.167955	−	0.290907i
$375$	18.0654	−	31.2902i	0.932892	−	1.61582i
$376$	−4.74219	−	8.21371i	−0.244560	−	0.423590i
$377$	17.6362	+	30.5468i	0.908310	+	1.57324i
$378$	18.6067			0.957024
$379$	7.53981	−	13.0593i	0.387294	−	0.670813i	−0.604790	−	0.796385i	$-0.706743\pi$
$379$	7.53981	−	13.0593i	0.387294	−	0.670813i	0.992085	+	0.125571i	$0.0400764\pi$
$380$	−1.39775			−0.0717029
$381$	−0.643759	−	1.11502i	−0.0329808	−	0.0571243i
$382$	22.6991			1.16139
$383$	−3.88889	−	6.73576i	−0.198713	−	0.344181i	0.749398	−	0.662119i	$-0.230343\pi$
$383$	−3.88889	−	6.73576i	−0.198713	−	0.344181i	−0.948111	+	0.317938i	$0.897010\pi$
$384$	1.48752	−	2.57645i	0.0759095	−	0.131479i
$385$	−6.28419	+	10.8845i	−0.320272	+	0.554728i
$386$	−14.7243			−0.749448
$387$	46.9970			2.38899
$388$	−4.71440	−	8.16558i	−0.239337	−	0.414545i
$389$	8.37102	+	14.4990i	0.424428	+	0.735130i	0.996367	−	0.0851657i	$-0.0271420\pi$
$389$	8.37102	+	14.4990i	0.424428	+	0.735130i	−0.571939	+	0.820296i	$0.693809\pi$
$390$	17.5861			0.890505
$391$	−2.91491	+	5.04877i	−0.147413	+	0.255327i
$392$	−2.18697			−0.110459
$393$	−21.8852	−	37.9063i	−1.10396	−	1.91212i
$394$	22.1406			1.11543
$395$	5.84014	−	10.1154i	0.293849	−	0.508962i
$396$	−9.54866	+	16.5388i	−0.479838	+	0.831104i
$397$	−15.9997			−0.803002			−0.401501	−	0.915859i	$-0.631511\pi$
$397$	−15.9997			−0.803002			−0.401501	+	0.915859i	$0.631511\pi$
$398$	13.8449	−	23.9800i	0.693980	−	1.20201i
$399$	−2.59887	−	4.50138i	−0.130106	−	0.225351i
$400$	0.959725	−	1.66229i	0.0479862	−	0.0831146i
$401$	−9.74634	+	16.8812i	−0.486709	+	0.843005i	−0.999883	−	0.0152799i	$-0.995136\pi$
$401$	−9.74634	+	16.8812i	−0.486709	+	0.843005i	0.513174	+	0.858284i	$0.328469\pi$
$402$	−3.64008	−	6.30480i	−0.181551	−	0.314455i
$403$	−16.0276	+	27.7606i	−0.798392	+	1.38286i
$404$	−3.11261	+	5.39120i	−0.154858	+	0.268222i
$405$	−13.4787			−0.669763
$406$	−11.4882	−	19.8981i	−0.570148	−	0.987526i
$407$	−0.755768	+	1.30903i	−0.0374620	+	0.0648861i
$408$	2.96050	−	5.12773i	0.146566	−	0.253861i
$409$	3.84046	+	6.65188i	0.189899	+	0.328914i	0.945216	−	0.326445i	$-0.105851\pi$
$409$	3.84046	+	6.65188i	0.189899	+	0.328914i	−0.755318	+	0.655359i	$0.772517\pi$
$410$	−1.52588	−	2.64290i	−0.0753579	−	0.130524i
$411$	−22.8992	−	39.6626i	−1.12953	−	1.95641i
$412$	−3.47073			−0.170990
$413$	12.7658			0.628163
$414$	17.1383			0.842302
$415$	−1.27829	+	2.21406i	−0.0627488	+	0.108684i
$416$	3.36793			0.165126
$417$	8.66194	+	15.0029i	0.424177	+	0.734696i
$418$	2.59938			0.127140
$419$	23.1354			1.13024			0.565118	−	0.825010i	$-0.308831\pi$
$419$	23.1354			1.13024			0.565118	+	0.825010i	$0.308831\pi$
$420$	−11.4555			−0.558972
$421$	14.6675	−	25.4048i	0.714849	−	1.23816i	−0.248168	−	0.968717i	$-0.579829\pi$
$421$	14.6675	−	25.4048i	0.714849	−	1.23816i	0.963018	−	0.269438i	$-0.0868380\pi$
$422$	−2.42987	+	4.20866i	−0.118284	+	0.204874i
$423$	−27.7456	+	48.0569i	−1.34904	+	2.33660i
$424$	4.33812	+	7.51385i	0.210678	+	0.364905i
$425$	1.91007	−	3.30834i	0.0926521	−	0.160478i
$426$	12.8058	+	22.1803i	0.620442	+	1.07464i
$427$	−11.2076	+	19.4120i	−0.542371	+	0.939415i
$428$	−0.779898	−	1.35082i	−0.0376978	−	0.0652945i
$429$	−32.7048			−1.57900
$430$	−14.0983			−0.679883
$431$	−11.3220			−0.545360			−0.272680	−	0.962105i	$-0.587910\pi$
$431$	−11.3220			−0.545360			−0.272680	+	0.962105i	$0.587910\pi$
$432$	−8.48124			−0.408054
$433$	3.94418			0.189545			0.0947725	−	0.995499i	$-0.469788\pi$
$433$	3.94418			0.189545			0.0947725	+	0.995499i	$0.469788\pi$
$434$	10.4403	−	18.0832i	0.501152	−	0.868021i
$435$	27.3431	+	47.3596i	1.31100	+	2.27072i
$436$	−5.98146	−	10.3602i	−0.286460	−	0.496163i
$437$	−1.16637	−	2.02021i	−0.0557950	−	0.0966398i
$438$	31.8896			1.52374
$439$	19.1853			0.915667			0.457833	−	0.889038i	$-0.348626\pi$
$439$	19.1853			0.915667			0.457833	+	0.889038i	$0.348626\pi$
$440$	2.86445	−	4.96136i	0.136557	−	0.236524i
$441$	6.39779	+	11.0813i	0.304656	+	0.527680i
$442$	6.70296			0.318827
$443$	6.20393	−	10.7455i	0.294758	−	0.510535i	−0.680171	−	0.733054i	$-0.738094\pi$
$443$	6.20393	−	10.7455i	0.294758	−	0.510535i	0.974929	+	0.222518i	$0.0714277\pi$
$444$	−1.37770			−0.0653826
$445$	19.8876			0.942763
$446$	7.27564	+	13.0409i	0.344511	+	0.617505i
$447$	−62.1322			−2.93875
$448$	−2.19386			−0.103650
$449$	−17.5449	+	30.3887i	−0.827995	+	1.43413i	0.0716132	+	0.997432i	$0.477185\pi$
$449$	−17.5449	+	30.3887i	−0.827995	+	1.43413i	−0.899608	+	0.436697i	$0.856148\pi$
$450$	−11.2303			−0.529403
$451$	2.83768	+	4.91500i	0.133621	+	0.231438i
$452$	−0.174842	+	0.302836i	−0.00822388	+	0.0142442i
$453$	−34.9018			−1.63983
$454$	3.37265			0.158286
$455$	−6.48420	−	11.2310i	−0.303984	−	0.526516i
$456$	1.18461	+	2.05181i	0.0554745	+	0.0960846i
$457$	−11.8729	−	20.5645i	−0.555391	−	0.961965i	−0.997873	−	0.0651875i	$-0.979235\pi$
$457$	−11.8729	−	20.5645i	−0.555391	−	0.961965i	0.442482	−	0.896777i	$-0.354098\pi$
$458$	−5.45349	+	9.44573i	−0.254825	+	0.441370i
$459$	−16.8796			−0.787873
$460$	−5.14122			−0.239711
$461$	31.9580			1.48843			0.744217	−	0.667938i	$-0.232823\pi$
$461$	31.9580			1.48843			0.744217	+	0.667938i	$0.232823\pi$
$462$	21.3038			0.991142
$463$	−22.5766			−1.04922			−0.524611	−	0.851342i	$-0.675789\pi$
$463$	−22.5766			−1.04922			−0.524611	+	0.851342i	$0.675789\pi$
$464$	5.23651	+	9.06990i	0.243099	+	0.421059i
$465$	−24.8491	+	43.0399i	−1.15235	+	1.99593i
$466$	1.75202	+	3.03459i	0.0811607	+	0.140574i
$467$	−16.0006	+	27.7138i	−0.740419	+	1.28244i	0.211886	+	0.977294i	$0.432039\pi$
$467$	−16.0006	+	27.7138i	−0.740419	+	1.28244i	−0.952305	+	0.305149i	$0.901294\pi$
$468$	−9.85256	−	17.0651i	−0.455435	−	0.788836i
$469$	−2.68428	+	4.64931i	−0.123949	+	0.214685i
$470$	8.32325	−	14.4163i	0.383923	−	0.664974i
$471$	−27.8483	+	48.2347i	−1.28318	+	2.22254i
$472$	−5.81887			−0.267835
$473$	26.2187			1.20554
$474$	−19.7984			−0.909371
$475$	0.764295	+	1.32380i	0.0350683	+	0.0607400i
$476$	−4.36629			−0.200128
$477$	25.3815	−	43.9621i	1.16214	−	2.01289i
$478$	2.07786			0.0950393
$479$	3.74778			0.171240			0.0856202	−	0.996328i	$-0.472713\pi$
$479$	3.74778			0.171240			0.0856202	+	0.996328i	$0.472713\pi$
$480$	5.22162			0.238333
$481$	−0.779822	−	1.35069i	−0.0355568	−	0.0615862i
$482$	−0.990128	−	1.71495i	−0.0450991	−	0.0781139i
$483$	−9.55922	−	16.5571i	−0.434960	−	0.753372i
$484$	0.173000	−	0.299644i	0.00786362	−	0.0136202i
$485$	8.27448	−	14.3318i	0.375725	−	0.650774i
$486$	−1.29844	−	2.24897i	−0.0588985	−	0.102015i
$487$	−26.5414			−1.20270			−0.601352	−	0.798984i	$-0.705371\pi$
$487$	−26.5414			−1.20270			−0.601352	+	0.798984i	$0.705371\pi$
$488$	5.10860	−	8.84835i	0.231255	−	0.400546i
$489$	−0.881503	+	1.52681i	−0.0398629	+	0.0690446i
$490$	−1.91923	−	3.32421i	−0.0867022	−	0.150173i
$491$	9.47748	−	16.4155i	0.427713	−	0.740820i	−0.568957	−	0.822367i	$-0.692653\pi$
$491$	9.47748	−	16.4155i	0.427713	−	0.740820i	0.996669	+	0.0815474i	$0.0259862\pi$
$492$	−2.58641	+	4.47980i	−0.116605	+	0.201965i
$493$	10.4219	+	18.0512i	0.469377	+	0.812984i
$494$	−1.34106	+	2.32278i	−0.0603370	+	0.104507i
$495$	−33.5186			−1.50655
$496$	−4.75889	+	8.24264i	−0.213680	+	0.370105i
$497$	9.44330	−	16.3563i	0.423590	−	0.733679i
$498$	4.33348			0.194188
$499$	−1.42492	−	2.46803i	−0.0637882	−	0.110484i	0.832368	−	0.554224i	$-0.186985\pi$
$499$	−1.42492	−	2.46803i	−0.0637882	−	0.110484i	−0.896156	+	0.443740i	$0.853652\pi$
$500$	12.1447			0.543126
$501$	25.0963	−	43.4680i	1.12122	−	1.94201i
$502$	26.1184			1.16572
$503$	8.33314	+	14.4334i	0.371557	+	0.643555i	0.989805	−	0.142428i	$-0.0454909\pi$
$503$	8.33314	+	14.4334i	0.371557	+	0.643555i	−0.618249	+	0.785983i	$0.712158\pi$
$504$	6.41793	+	11.1162i	0.285877	+	0.495154i
$505$	−10.9262			−0.486209
$506$	9.56111			0.425043
$507$	−2.46487	+	4.26928i	−0.109469	+	0.189605i
$508$	0.216387	−	0.374794i	0.00960063	−	0.0166288i
$509$	17.7186	+	30.6895i	0.785363	+	1.36029i	0.928782	+	0.370626i	$0.120857\pi$
$509$	17.7186	+	30.6895i	0.785363	+	1.36029i	−0.143420	+	0.989662i	$0.545810\pi$
$510$	10.3922			0.460176
$511$	−11.7581	−	20.3656i	−0.520147	−	0.900920i
$512$	1.00000			0.0441942
$513$	3.37710	−	5.84931i	0.149103	−	0.258253i
$514$	−17.1234			−0.755282
$515$	−3.04582	−	5.27552i	−0.134215	−	0.232467i
$516$	11.9486	+	20.6955i	0.526006	+	0.911069i
$517$	−15.4787	+	26.8099i	−0.680754	+	1.17910i
$518$	0.507974	+	0.879836i	0.0223191	+	0.0386578i
$519$	17.3539	+	30.0578i	0.761752	+	1.31939i
$520$	2.95561	+	5.11927i	0.129612	+	0.224495i
$521$	7.95487	+	13.7782i	0.348509	+	0.603636i	0.985985	−	0.166835i	$-0.0533546\pi$
$521$	7.95487	+	13.7782i	0.348509	+	0.603636i	−0.637476	+	0.770471i	$0.720021\pi$
$522$	30.6378	−	53.0662i	1.34098	−	2.32265i
$523$	−3.04627	−	5.27629i	−0.133204	−	0.230716i	0.791706	−	0.610902i	$-0.209193\pi$
$523$	−3.04627	−	5.27629i	−0.133204	−	0.230716i	−0.924910	+	0.380186i	$0.875860\pi$
$524$	7.35630	−	12.7415i	0.321361	−	0.556614i
$525$	6.26394	+	10.8495i	0.273381	+	0.473509i
$526$	−6.90213	−	11.9548i	−0.300947	−	0.521256i
$527$	−9.47128	+	16.4047i	−0.412575	+	0.714602i
$528$	−9.71064			−0.422601
$529$	7.20983	+	12.4878i	0.313471	+	0.542948i
$530$	−7.61405	+	13.1879i	−0.330733	+	0.572847i
$531$	17.0225	+	29.4839i	0.738715	+	1.27949i
$532$	0.873561	−	1.51305i	0.0378737	−	0.0655991i
$533$	−5.85598			−0.253651
$534$	−16.8550	−	29.1938i	−0.729389	−	1.26334i
$535$	1.36884	−	2.37089i	0.0591800	−	0.102503i
$536$	1.22354	−	2.11924i	0.0528490	−	0.0915372i
$537$	73.4475			3.16949
$538$	−0.908781	+	1.57406i	−0.0391803	+	0.0678623i
$539$	3.56919	+	6.18203i	0.153736	+	0.266279i
$540$	−7.44292	−	12.8915i	−0.320292	−	0.554763i
$541$	−34.3747			−1.47789			−0.738943	−	0.673768i	$-0.764675\pi$
$541$	−34.3747			−1.47789			−0.738943	+	0.673768i	$0.764675\pi$
$542$	−11.4336	+	19.8036i	−0.491116	+	0.850637i
$543$	25.5535	+	44.2599i	1.09660	+	1.89938i
$544$	1.99023			0.0853304
$545$	10.4984	−	18.1837i	0.449700	−	0.778903i
$546$	−10.9909	+	19.0368i	−0.470368	+	0.814701i
$547$	−7.05699	+	12.2231i	−0.301735	+	0.522621i	−0.976529	−	0.215386i	$-0.930899\pi$
$547$	−7.05699	+	12.2231i	−0.301735	+	0.522621i	0.674794	+	0.738006i	$0.264233\pi$
$548$	7.69713	−	13.3318i	0.328805	−	0.569507i
$549$	−59.7788			−2.55130
$550$	−6.26517			−0.267148
$551$	−8.34038			−0.355312
$552$	4.35726	+	7.54700i	0.185457	+	0.321221i
$553$	7.29992	+	12.6438i	0.310424	+	0.537670i
$554$	−6.56234			−0.278807
$555$	−1.20903	−	2.09410i	−0.0513206	−	0.0888898i
$556$	−2.91155	+	5.04294i	−0.123477	+	0.213869i
$557$	7.97227			0.337796			0.168898	−	0.985634i	$-0.445979\pi$
$557$	7.97227			0.337796			0.168898	+	0.985634i	$0.445979\pi$
$558$	55.6867			2.35741
$559$	−13.5266	+	23.4287i	−0.572112	+	0.990928i
$560$	−1.92528	−	3.33468i	−0.0813578	−	0.140916i
$561$	−19.3264			−0.815961
$562$	−9.91792	−	17.1783i	−0.418362	−	0.724624i
$563$	5.86544	+	10.1592i	0.247199	+	0.428161i	0.962748	−	0.270402i	$-0.0871565\pi$
$563$	5.86544	+	10.1592i	0.247199	+	0.428161i	−0.715549	+	0.698563i	$0.753823\pi$
$564$	−28.2163			−1.18812
$565$	−0.613748			−0.0258206
$566$	−18.8395			−0.791881
$567$	8.42391	−	14.5906i	0.353771	−	0.612749i
$568$	−4.30442	+	7.45548i	−0.180610	+	0.312825i
$569$	11.2615	−	19.5055i	0.472106	−	0.817712i	−0.527384	−	0.849627i	$-0.676827\pi$
$569$	11.2615	−	19.5055i	0.472106	−	0.817712i	0.999491	+	0.0319150i	$0.0101606\pi$
$570$	−2.07917	+	3.60123i	−0.0870868	+	0.150839i
$571$	44.4680			1.86093			0.930465	−	0.366381i	$-0.119403\pi$
$571$	44.4680			1.86093			0.930465	+	0.366381i	$0.119403\pi$
$572$	−5.49654	−	9.52029i	−0.229822	−	0.398063i
$573$	33.7652	−	58.4831i	1.41056	−	2.44317i
$574$	3.81457			0.159217
$575$	2.81125	+	4.86922i	0.117237	+	0.203061i
$576$	−2.92540	−	5.06695i	−0.121892	−	0.211123i
$577$	3.30737	−	5.72853i	0.137687	−	0.238482i	−0.788933	−	0.614479i	$-0.789366\pi$
$577$	3.30737	−	5.72853i	0.137687	−	0.238482i	0.926621	+	0.375997i	$0.122700\pi$
$578$	−13.0390			−0.542350
$579$	−21.9026	+	37.9365i	−0.910243	+	1.57659i
$580$	−9.19085	+	15.9190i	−0.381629	+	0.661002i
$581$	−1.59781	−	2.76748i	−0.0662882	−	0.114815i
$582$	−28.0510			−1.16275
$583$	14.1598	−	24.5256i	0.586440	−	1.01574i
$584$	5.35953	+	9.28299i	0.221779	+	0.384133i
$585$	17.2927	−	29.9519i	0.714966	−	1.23836i
$586$	−12.9709	−	22.4663i	−0.535824	−	0.928074i
$587$	−30.8495			−1.27329			−0.636647	−	0.771155i	$-0.719679\pi$
$587$	−30.8495			−1.27329			−0.636647	+	0.771155i	$0.719679\pi$
$588$	−3.25316	+	5.63464i	−0.134158	+	0.232368i
$589$	−3.78983	−	6.56418i	−0.156157	−	0.270472i
$590$	−5.10649	−	8.84470i	−0.210231	−	0.364131i
$591$	32.9345	−	57.0442i	1.35474	−	2.34648i
$592$	−0.231543	−	0.401045i	−0.00951637	−	0.0164828i
$593$	20.8961	−	36.1931i	0.858099	−	1.48627i	−0.0156406	−	0.999878i	$-0.504979\pi$
$593$	20.8961	−	36.1931i	0.858099	−	1.48627i	0.873740	−	0.486394i	$-0.161688\pi$
$594$	13.8416	+	23.9743i	0.567927	+	0.983679i
$595$	−3.83174	−	6.63677i	−0.157086	−	0.272081i
$596$	−10.4423	−	18.0866i	−0.427733	−	0.740855i
$597$	−41.1889	−	71.3412i	−1.68575	−	2.91980i
$598$	−4.93271	+	8.54370i	−0.201713	+	0.349378i
$599$	3.32819	+	5.76459i	0.135986	+	0.235535i	0.925974	−	0.377588i	$-0.123246\pi$
$599$	3.32819	+	5.76459i	0.135986	+	0.235535i	−0.789988	+	0.613123i	$0.789913\pi$
$600$	−2.85521	−	4.94537i	−0.116564	−	0.201894i
$601$	28.6129			1.16714			0.583572	−	0.812062i	$-0.301655\pi$
$601$	28.6129			1.16714			0.583572	+	0.812062i	$0.301655\pi$
$602$	8.81116	−	15.2614i	0.359116	−	0.622007i
$603$	−14.3174			−0.583051
$604$	−5.86579	−	10.1598i	−0.238675	−	0.413398i
$605$	0.607280			0.0246894
$606$	9.26011	+	16.0390i	0.376166	+	0.651539i
$607$	−1.67512	+	2.90139i	−0.0679909	+	0.117764i	−0.898017	−	0.439961i	$-0.854992\pi$
$607$	−1.67512	+	2.90139i	−0.0679909	+	0.117764i	0.830026	+	0.557725i	$0.188326\pi$
$608$	−0.398184	+	0.689676i	−0.0161485	+	0.0279700i
$609$	−68.3553			−2.76990
$610$	17.9327			0.726074
$611$	−15.9714	−	27.6632i	−0.646133	−	1.11913i
$612$	−5.82223	−	10.0844i	−0.235350	−	0.407637i
$613$	−16.5054			−0.666647			−0.333324	−	0.942813i	$-0.608170\pi$
$613$	−16.5054			−0.666647			−0.333324	+	0.942813i	$0.608170\pi$
$614$	−2.18053	+	3.77678i	−0.0879989	+	0.152419i
$615$	−9.07909			−0.366104
$616$	3.58043	+	6.20149i	0.144260	+	0.249865i
$617$	−17.3632			−0.699015			−0.349507	−	0.936934i	$-0.613651\pi$
$617$	−17.3632			−0.699015			−0.349507	+	0.936934i	$0.613651\pi$
$618$	−5.16276	+	8.94216i	−0.207677	+	0.359706i
$619$	13.3767	−	23.1692i	0.537657	−	0.931249i	−0.461373	−	0.887206i	$-0.652643\pi$
$619$	13.3767	−	23.1692i	0.537657	−	0.931249i	0.999030	−	0.0440425i	$-0.0140237\pi$
$620$	−16.7051			−0.670894
$621$	12.4217	−	21.5150i	0.498466	−	0.863369i
$622$	1.39938	+	2.42380i	0.0561102	+	0.0971857i
$623$	−12.4293	+	21.5282i	−0.497970	+	0.862509i
$624$	5.00985	−	8.67731i	0.200555	−	0.347371i
$625$	5.85923	+	10.1485i	0.234369	+	0.405939i
$626$	−14.6562	+	25.3852i	−0.585778	+	1.01460i
$627$	3.86662	−	6.69719i	0.154418	−	0.267460i
$628$	−18.7214			−0.747064
$629$	−0.460824	−	0.798171i	−0.0183743	−	0.0318252i
$630$	−11.2644	+	19.5106i	−0.448785	+	0.777319i
$631$	−14.7704	+	25.5831i	−0.588000	+	1.01845i	0.406494	+	0.913653i	$0.366751\pi$
$631$	−14.7704	+	25.5831i	−0.588000	+	1.01845i	−0.994494	+	0.104793i	$0.966582\pi$
$632$	−3.32743	−	5.76328i	−0.132358	−	0.229251i
$633$	7.22894	+	12.5209i	0.287325	+	0.497661i
$634$	−16.1589	−	27.9881i	−0.641753	−	1.11155i
$635$	0.759584			0.0301432
$636$	25.8121			1.02352
$637$	−7.36558			−0.291835
$638$	17.0922	−	29.6046i	0.676687	−	1.17206i
$639$	50.3687			1.99255
$640$	0.877575	+	1.52000i	0.0346892	+	0.0600834i
$641$	−30.2564			−1.19506			−0.597528	−	0.801848i	$-0.703850\pi$
$641$	−30.2564			−1.19506			−0.597528	+	0.801848i	$0.703850\pi$
$642$	−4.64044			−0.183143
$643$	26.1644			1.03182			0.515912	−	0.856642i	$-0.327453\pi$
$643$	26.1644			1.03182			0.515912	+	0.856642i	$0.327453\pi$
$644$	3.21315	−	5.56534i	0.126616	−	0.219305i
$645$	−20.9715	+	36.3237i	−0.825752	+	1.43025i
$646$	−0.792478	+	1.37261i	−0.0311796	+	0.0540047i
$647$	−2.02059	−	3.49976i	−0.0794375	−	0.137590i	0.823570	−	0.567215i	$-0.191979\pi$
$647$	−2.02059	−	3.49976i	−0.0794375	−	0.137590i	−0.903007	+	0.429625i	$0.858646\pi$
$648$	−3.83977	+	6.65067i	−0.150840	+	0.261263i
$649$	9.49653	+	16.4485i	0.372771	+	0.645659i
$650$	3.23229	−	5.59849i	0.126781	−	0.219591i
$651$	−31.0603	−	53.7981i	−1.21735	−	2.10851i
$652$	−0.592601			−0.0232080
$653$	−4.00404			−0.156690			−0.0783452	−	0.996926i	$-0.524964\pi$
$653$	−4.00404			−0.156690			−0.0783452	+	0.996926i	$0.524964\pi$
$654$	−35.5900			−1.39168
$655$	25.8228			1.00898
$656$	−1.73875			−0.0678867
$657$	31.3576	−	54.3130i	1.22338	−	2.11895i
$658$	10.4037	+	18.0197i	0.405579	+	0.702483i
$659$	1.08974	+	1.88749i	0.0424503	+	0.0735260i	0.886470	−	0.462786i	$-0.153150\pi$
$659$	1.08974	+	1.88749i	0.0424503	+	0.0735260i	−0.844020	+	0.536312i	$0.819817\pi$
$660$	−8.52181	−	14.7602i	−0.331711	−	0.574540i
$661$	45.9046			1.78548			0.892742	−	0.450569i	$-0.148779\pi$
$661$	45.9046			1.78548			0.892742	+	0.450569i	$0.148779\pi$
$662$	−12.5600			−0.488157
$663$	9.97075	−	17.2698i	0.387232	−	0.670705i
$664$	0.728309	+	1.26147i	0.0282639	+	0.0489544i
$665$	3.06646			0.118912
$666$	−1.35472	+	2.34644i	−0.0524942	+	0.0909225i
$667$	−30.6778			−1.18785
$668$	16.8713			0.652768
$669$	44.4219	+	0.653207i	1.71745	+	0.0252545i
$670$	4.29500			0.165930
$671$	−33.3494			−1.28744
$672$	−3.26340	+	5.65238i	−0.125888	+	0.218045i
$673$	21.0795			0.812555			0.406277	−	0.913750i	$-0.366827\pi$
$673$	21.0795			0.812555			0.406277	+	0.913750i	$0.366827\pi$
$674$	−5.95873	−	10.3208i	−0.229522	−	0.397543i
$675$	−8.13966	+	14.0983i	−0.313296	+	0.542644i
$676$	−1.65704			−0.0637322
$677$	−25.2847			−0.971772			−0.485886	−	0.874022i	$-0.661503\pi$
$677$	−25.2847			−0.971772			−0.485886	+	0.874022i	$0.661503\pi$
$678$	0.520161	+	0.900945i	0.0199767	+	0.0346006i
$679$	10.3427	+	17.9141i	0.396918	+	0.687482i
$680$	1.74658	+	3.02516i	0.0669781	+	0.116009i
$681$	5.01687	−	8.68948i	0.192247	−	0.332982i
$682$	31.0665			1.18960
$683$	35.4149			1.35511			0.677557	−	0.735470i	$-0.263039\pi$
$683$	35.4149			1.35511			0.677557	+	0.735470i	$0.263039\pi$
$684$	4.65940			0.178157
$685$	27.0192			1.03235
$686$	20.1549			0.769519
$687$	16.2243	+	28.1013i	0.618996	+	1.07213i
$688$	−4.01628	+	6.95640i	−0.153119	+	0.265210i
$689$	14.6105	+	25.3061i	0.556616	+	0.964087i
$690$	−7.64764	+	13.2461i	−0.291141	+	0.504271i
$691$	3.33261	+	5.77224i	0.126778	+	0.219586i	0.922427	−	0.386172i	$-0.126203\pi$
$691$	3.33261	+	5.77224i	0.126778	+	0.219586i	−0.795648	+	0.605759i	$0.792870\pi$
$692$	−5.83318	+	10.1034i	−0.221744	+	0.384073i
$693$	20.9484	−	36.2837i	0.795765	−	1.37830i
$694$	6.96499	−	12.0637i	0.264387	−	0.457932i
$695$	−10.2204			−0.387682
$696$	31.1575			1.18102
$697$	−3.46051			−0.131076
$698$	−11.1497	−	19.3119i	−0.422024	−	0.730967i
$699$	10.4246			0.394295
$700$	−2.10550	+	3.64684i	−0.0795805	+	0.137838i
$701$	32.9004			1.24263			0.621315	−	0.783561i	$-0.286599\pi$
$701$	32.9004			1.24263			0.621315	+	0.783561i	$0.286599\pi$
$702$	−28.5642			−1.07809
$703$	0.368788			0.0139091
$704$	−1.63202	−	2.82675i	−0.0615092	−	0.106537i
$705$	−24.7619	−	42.8889i	−0.932588	−	1.61529i
$706$	16.3468	+	28.3136i	0.615221	+	1.06559i
$707$	6.82863	−	11.8275i	0.256817	−	0.444820i
$708$	−8.65565	+	14.9920i	−0.325299	+	0.563435i
$709$	4.25381	+	7.36782i	0.159755	+	0.276704i	0.934780	−	0.355226i	$-0.115596\pi$
$709$	4.25381	+	7.36782i	0.159755	+	0.276704i	−0.775025	+	0.631930i	$0.782263\pi$
$710$	−15.1098			−0.567061
$711$	−19.4682	+	33.7198i	−0.730113	+	1.26459i
$712$	5.66550	−	9.81293i	0.212324	−	0.367755i
$713$	−13.9398	−	24.1445i	−0.522051	−	0.904218i
$714$	−6.49492	+	11.2495i	−0.243066	+	0.421003i
$715$	9.64725	−	16.7095i	0.360787	−	0.624901i
$716$	12.3440	+	21.3804i	0.461317	+	0.799024i
$717$	3.09086	−	5.35352i	0.115430	−	0.199931i
$718$	−2.13668			−0.0797402
$719$	−17.1285	+	29.6674i	−0.638784	+	1.10641i	0.346916	+	0.937896i	$0.387229\pi$
$719$	−17.1285	+	29.6674i	−0.638784	+	1.10641i	−0.985700	+	0.168510i	$0.946104\pi$
$720$	5.13452	−	8.89325i	0.191352	−	0.331432i
$721$	7.61429			0.283571
$722$	9.18290	+	15.9052i	0.341752	+	0.591932i
$723$	−5.89132			−0.219101
$724$	−8.58932	+	14.8771i	−0.319219	+	0.552904i
$725$	20.1024			0.746585
$726$	−0.514679	−	0.891450i	−0.0191015	−	0.0330848i
$727$	−8.67751	−	15.0299i	−0.321831	−	0.557428i	0.659035	−	0.752113i	$-0.270965\pi$
$727$	−8.67751	−	15.0299i	−0.321831	−	0.557428i	−0.980866	+	0.194685i	$0.937632\pi$
$728$	−7.38877			−0.273846
$729$	−30.7644			−1.13942
$730$	−9.40679	+	16.2930i	−0.348161	+	0.603032i
$731$	−7.99332	+	13.8448i	−0.295644	+	0.512070i
$732$	−15.1982	−	26.3241i	−0.561743	−	0.972967i
$733$	40.0916			1.48082			0.740408	−	0.672158i	$-0.234632\pi$
$733$	40.0916			1.48082			0.740408	+	0.672158i	$0.234632\pi$
$734$	13.2396	+	22.9317i	0.488683	+	0.846424i
$735$	−11.4196			−0.421217
$736$	−1.46461	+	2.53678i	−0.0539862	+	0.0935069i
$737$	−7.98740			−0.294220
$738$	5.08654	+	8.81014i	0.187238	+	0.324306i
$739$	−24.7321	−	42.8372i	−0.909784	−	1.57579i	−0.814363	−	0.580355i	$-0.802914\pi$
$739$	−24.7321	−	42.8372i	−0.909784	−	1.57579i	−0.0954207	−	0.995437i	$-0.530420\pi$
$740$	0.406393	−	0.703894i	0.0149393	−	0.0258756i
$741$	3.98969	+	6.91034i	0.146565	+	0.253858i
$742$	−9.51724	−	16.4843i	−0.349389	−	0.605159i
$743$	14.9909	+	25.9650i	0.549964	+	0.952565i	0.998276	+	0.0586880i	$0.0186917\pi$
$743$	14.9909	+	25.9650i	0.549964	+	0.952565i	−0.448313	+	0.893877i	$0.647975\pi$
$744$	14.1578	+	24.5221i	0.519051	+	0.899024i
$745$	18.3278	−	31.7446i	0.671477	−	1.16303i
$746$	2.22803	+	3.85906i	0.0815739	+	0.141290i
$747$	4.26119	−	7.38061i	0.155909	−	0.270042i
$748$	−3.24810	−	5.62588i	−0.118762	−	0.205702i
$749$	1.71099	+	2.96352i	0.0625181	+	0.108285i
$750$	18.0654	−	31.2902i	0.659655	−	1.14256i
$751$	51.2216			1.86910			0.934552	−	0.355827i	$-0.115801\pi$
$751$	51.2216			1.86910			0.934552	+	0.355827i	$0.115801\pi$
$752$	−4.74219	−	8.21371i	−0.172930	−	0.299523i
$753$	38.8515	−	67.2927i	1.41583	−	2.45228i
$754$	17.6362	+	30.5468i	0.642273	+	1.11245i
$755$	10.2953	−	17.8320i	0.374686	−	0.648974i
$756$	18.6067			0.676718
$757$	−0.305177	−	0.528583i	−0.0110919	−	0.0192117i	0.860426	−	0.509575i	$-0.170197\pi$
$757$	−0.305177	−	0.528583i	−0.0110919	−	0.0192117i	−0.871518	+	0.490363i	$0.836864\pi$
$758$	7.53981	−	13.0593i	0.273858	−	0.474337i
$759$	14.2223	−	24.6337i	0.516237	−	0.894148i
$760$	−1.39775			−0.0507016
$761$	−2.63964	+	4.57198i	−0.0956867	+	0.165734i	−0.909895	−	0.414839i	$-0.863838\pi$
$761$	−2.63964	+	4.57198i	−0.0956867	+	0.165734i	0.814208	+	0.580573i	$0.197171\pi$
$762$	−0.643759	−	1.11502i	−0.0233209	−	0.0403930i
$763$	13.1225	+	22.7288i	0.475066	+	0.822838i
$764$	22.6991			0.821224
$765$	10.2189	−	17.6996i	0.369464	−	0.639931i
$766$	−3.88889	−	6.73576i	−0.140511	−	0.243373i
$767$	−19.5975			−0.707626
$768$	1.48752	−	2.57645i	0.0536761	−	0.0929697i
$769$	10.9993	−	19.0514i	0.396647	−	0.687012i	−0.596663	−	0.802492i	$-0.703507\pi$
$769$	10.9993	−	19.0514i	0.396647	−	0.687012i	0.993310	+	0.115480i	$0.0368405\pi$
$770$	−6.28419	+	10.8845i	−0.226467	+	0.392252i
$771$	−25.4714	+	44.1177i	−0.917329	+	1.58886i
$772$	−14.7243			−0.529940
$773$	−8.91084			−0.320501			−0.160250	−	0.987076i	$-0.551230\pi$
$773$	−8.91084			−0.320501			−0.160250	+	0.987076i	$0.551230\pi$
$774$	46.9970			1.68927
$775$	9.13445	+	15.8213i	0.328119	+	0.568319i
$776$	−4.71440	−	8.16558i	−0.169237	−	0.293127i
$777$	3.02248			0.108431
$778$	8.37102	+	14.4990i	0.300116	+	0.519816i
$779$	0.692342	−	1.19917i	0.0248057	−	0.0429648i
$780$	17.5861			0.629682
$781$	28.0997			1.00549
$782$	−2.91491	+	5.04877i	−0.104237	+	0.180544i
$783$	−44.4121	−	76.9240i	−1.58716	−	2.74904i
$784$	−2.18697			−0.0781062
$785$	−16.4294	−	28.4566i	−0.586391	−	1.01566i
$786$	−21.8852	−	37.9063i	−0.780620	−	1.35207i
$787$	14.6146			0.520955			0.260478	−	0.965480i	$-0.416120\pi$
$787$	14.6146			0.520955			0.260478	+	0.965480i	$0.416120\pi$
$788$	22.1406			0.788726
$789$	−41.0681			−1.46206
$790$	5.84014	−	10.1154i	0.207783	−	0.359890i
$791$	0.383579	−	0.664379i	0.0136385	−	0.0236226i
$792$	−9.54866	+	16.5388i	−0.339297	+	0.587679i
$793$	17.2054	−	29.8006i	0.610982	−	1.05825i
$794$	−15.9997			−0.567808
$795$	22.6520	+	39.2345i	0.803385	+	1.39150i
$796$	13.8449	−	23.9800i	0.490718	−	0.849948i
$797$	−8.39365			−0.297318			−0.148659	−	0.988888i	$-0.547496\pi$
$797$	−8.39365			−0.297318			−0.148659	+	0.988888i	$0.547496\pi$
$798$	−2.59887	−	4.50138i	−0.0919990	−	0.159347i
$799$	−9.43805	−	16.3472i	−0.333894	−	0.578322i
$800$	0.959725	−	1.66229i	0.0339314	−	0.0587709i
$801$	−66.2955			−2.34244
$802$	−9.74634	+	16.8812i	−0.344155	+	0.596094i
$803$	17.4938	−	30.3001i	0.617342	−	1.06927i
$804$	−3.64008	−	6.30480i	−0.128376	−	0.222353i
$805$	11.2791			0.397537
$806$	−16.0276	+	27.7606i	−0.564548	+	0.977826i
$807$	2.70365	+	4.68286i	0.0951731	+	0.164845i
$808$	−3.11261	+	5.39120i	−0.109501	+	0.189662i
$809$	9.72117	+	16.8376i	0.341778	+	0.591977i	0.984763	−	0.173902i	$-0.0556375\pi$
$809$	9.72117	+	16.8376i	0.341778	+	0.591977i	−0.642985	+	0.765879i	$0.722304\pi$
$810$	−13.4787			−0.473594
$811$	17.6312	−	30.5382i	0.619116	−	1.07234i	−0.370532	−	0.928820i	$-0.620825\pi$
$811$	17.6312	−	30.5382i	0.619116	−	1.07234i	0.989647	−	0.143520i	$-0.0458422\pi$
$812$	−11.4882	−	19.8981i	−0.403156	−	0.698286i
$813$	34.0154	+	58.9163i	1.19297	+	2.06629i
$814$	−0.755768	+	1.30903i	−0.0264897	+	0.0458814i
$815$	−0.520051	−	0.900755i	−0.0182166	−	0.0315521i
$816$	2.96050	−	5.12773i	0.103638	−	0.179507i
$817$	−3.19844	−	5.53986i	−0.111899	−	0.193815i
$818$	3.84046	+	6.65188i	0.134279	+	0.232577i
$819$	21.6151	+	37.4385i	0.755294	+	1.30821i
$820$	−1.52588	−	2.64290i	−0.0532861	−	0.0922942i
$821$	−12.3686	+	21.4231i	−0.431667	+	0.747670i	−0.997017	−	0.0771815i	$-0.975408\pi$
$821$	−12.3686	+	21.4231i	−0.431667	+	0.747670i	0.565350	+	0.824851i	$0.308741\pi$
$822$	−22.8992	−	39.6626i	−0.798701	−	1.38339i
$823$	−14.6185	−	25.3201i	−0.509570	−	0.882602i	−0.999939	−	0.0110864i	$-0.996471\pi$
$823$	−14.6185	−	25.3201i	−0.509570	−	0.882602i	0.490368	−	0.871515i	$-0.336862\pi$
$824$	−3.47073			−0.120908
$825$	−9.31954	+	16.1419i	−0.324465	+	0.561990i
$826$	12.7658			0.444178
$827$	8.44789	+	14.6322i	0.293762	+	0.508811i	0.974696	−	0.223534i	$-0.0717594\pi$
$827$	8.44789	+	14.6322i	0.293762	+	0.508811i	−0.680934	+	0.732345i	$0.738426\pi$
$828$	17.1383			0.595597
$829$	−9.47815	−	16.4166i	−0.329190	−	0.570174i	0.653161	−	0.757219i	$-0.273442\pi$
$829$	−9.47815	−	16.4166i	−0.329190	−	0.570174i	−0.982351	+	0.187045i	$0.940109\pi$
$830$	−1.27829	+	2.21406i	−0.0443701	+	0.0768513i
$831$	−9.76158	+	16.9075i	−0.338625	+	0.586516i
$832$	3.36793			0.116762
$833$	−4.35258			−0.150808
$834$	8.66194	+	15.0029i	0.299938	+	0.519509i
$835$	14.8058	+	25.6444i	0.512375	+	0.887460i
$836$	2.59938			0.0899016
$837$	40.3613	−	69.9078i	1.39509	−	2.41637i
$838$	23.1354			0.799198
$839$	9.72940	+	16.8518i	0.335896	+	0.581789i	0.983657	−	0.180055i	$-0.0576276\pi$
$839$	9.72940	+	16.8518i	0.335896	+	0.581789i	−0.647760	+	0.761844i	$0.724294\pi$
$840$	−11.4555			−0.395253
$841$	−40.3420	+	69.8744i	−1.39110	+	2.40946i
$842$	14.6675	−	25.4048i	0.505475	−	0.875508i
$843$	−59.0122			−2.03249
$844$	−2.42987	+	4.20866i	−0.0836396	+	0.144868i
$845$	−1.45417	−	2.51870i	−0.0500251	−	0.0866461i
$846$	−27.7456	+	48.0569i	−0.953915	+	1.65223i
$847$	−0.379537	+	0.657377i	−0.0130410	+	0.0225877i
$848$	4.33812	+	7.51385i	0.148972	+	0.258027i
$849$	−28.0240	+	48.5389i	−0.961780	+	1.66585i
$850$	1.91007	−	3.30834i	0.0655150	−	0.113475i
$851$	1.35648			0.0464996
$852$	12.8058	+	22.1803i	0.438719	+	0.759884i
$853$	−23.0706	+	39.9595i	−0.789923	+	1.36819i	0.136090	+	0.990696i	$0.456546\pi$
$853$	−23.0706	+	39.9595i	−0.789923	+	1.36819i	−0.926013	+	0.377491i	$0.876787\pi$
$854$	−11.2076	+	19.4120i	−0.383515	+	0.664267i
$855$	4.08897	+	7.08231i	0.139840	+	0.242210i
$856$	−0.779898	−	1.35082i	−0.0266563	−	0.0461701i
$857$	0.930876	+	1.61232i	0.0317981	+	0.0550759i	0.881487	−	0.472209i	$-0.156543\pi$
$857$	0.930876	+	1.61232i	0.0317981	+	0.0550759i	−0.849688	+	0.527285i	$0.823210\pi$
$858$	−32.7048			−1.11652
$859$	54.8820			1.87255			0.936274	−	0.351270i	$-0.114250\pi$
$859$	54.8820			1.87255			0.936274	+	0.351270i	$0.114250\pi$
$860$	−14.0983			−0.480750
$861$	5.67423	−	9.82806i	0.193377	−	0.334939i
$862$	−11.3220			−0.385628
$863$	2.09450	+	3.62778i	0.0712977	+	0.123491i	0.899470	−	0.436982i	$-0.143953\pi$
$863$	2.09450	+	3.62778i	0.0712977	+	0.123491i	−0.828173	+	0.560473i	$0.810619\pi$
$864$	−8.48124			−0.288538
$865$	−20.4762			−0.696212
$866$	3.94418			0.134029
$867$	−19.3957	+	33.5943i	−0.658712	+	1.14092i
$868$	10.4403	−	18.0832i	0.354368	−	0.613784i
$869$	−10.8609	+	18.8116i	−0.368430	+	0.638140i
$870$	27.3431	+	47.3596i	0.927017	+	1.60564i
$871$	4.12081	−	7.13745i	0.139628	−	0.241843i
$872$	−5.98146	−	10.3602i	−0.202558	−	0.350840i
$873$	−27.5830	+	47.7752i	−0.933545	+	1.61695i
$874$	−1.16637	−	2.02021i	−0.0394530	−	0.0683347i
$875$	−26.6437			−0.900722
$876$	31.8896			1.07745
$877$	4.79523			0.161923			0.0809617	−	0.996717i	$-0.474201\pi$
$877$	4.79523			0.161923			0.0809617	+	0.996717i	$0.474201\pi$
$878$	19.1853			0.647474
$879$	−77.1778			−2.60314
$880$	2.86445	−	4.96136i	0.0965604	−	0.167248i
$881$	17.3918	+	30.1234i	0.585944	+	1.01488i	0.994757	+	0.102266i	$0.0326094\pi$
$881$	17.3918	+	30.1234i	0.585944	+	1.01488i	−0.408813	+	0.912618i	$0.634057\pi$
$882$	6.39779	+	11.0813i	0.215425	+	0.373126i
$883$	−24.1165	−	41.7711i	−0.811586	−	1.40571i	−0.911754	−	0.410737i	$-0.865271\pi$
$883$	−24.1165	−	41.7711i	−0.811586	−	1.40571i	0.100168	−	0.994971i	$-0.468062\pi$
$884$	6.70296			0.225445
$885$	−30.3839			−1.02134
$886$	6.20393	−	10.7455i	0.208425	−	0.361003i
$887$	−3.63392	−	6.29414i	−0.122015	−	0.211337i	0.798547	−	0.601932i	$-0.205602\pi$
$887$	−3.63392	−	6.29414i	−0.122015	−	0.211337i	−0.920562	+	0.390596i	$0.872269\pi$
$888$	−1.37770			−0.0462325
$889$	−0.474723	+	0.822245i	−0.0159217	+	0.0275772i
$890$	19.8876			0.666634
$891$	25.0664			0.839754
$892$	7.27564	+	13.0409i	0.243606	+	0.436642i
$893$	7.55306			0.252754
$894$	−62.1322			−2.07801
$895$	−21.6655	+	37.5258i	−0.724199	+	1.25435i
$896$	−2.19386			−0.0732917
$897$	14.6750	+	25.4178i	0.489982	+	0.848674i
$898$	−17.5449	+	30.3887i	−0.585481	+	1.01408i
$899$	−99.6798			−3.32451
$900$	−11.2303			−0.374344
$901$	8.63386	+	14.9543i	0.287636	+	0.498199i
$902$	2.83768	+	4.91500i	0.0944843	+	0.163652i
$903$	−26.2135	−	45.4031i	−0.872330	−	1.51092i
$904$	−0.174842	+	0.302836i	−0.00581516	+	0.0100722i
$905$	−30.1511			−1.00226
$906$	−34.9018			−1.15953
$907$	−26.8157			−0.890401			−0.445201	−	0.895431i	$-0.646868\pi$
$907$	−26.8157			−0.890401			−0.445201	+	0.895431i	$0.646868\pi$
$908$	3.37265			0.111925
$909$	36.4226			1.20806
$910$	−6.48420	−	11.2310i	−0.214949	−	0.372303i
$911$	16.0896	−	27.8681i	0.533073	−	0.923310i	−0.466181	−	0.884690i	$-0.654370\pi$
$911$	16.0896	−	27.8681i	0.533073	−	0.923310i	0.999254	−	0.0386204i	$-0.0122963\pi$
$912$	1.18461	+	2.05181i	0.0392264	+	0.0679421i
$913$	2.37723	−	4.11749i	0.0786750	−	0.136269i
$914$	−11.8729	−	20.5645i	−0.392720	−	0.680212i
$915$	26.6752	−	46.2028i	0.881854	−	1.52742i
$916$	−5.45349	+	9.44573i	−0.180188	+	0.312096i
$917$	−16.1387	+	27.9530i	−0.532947	+	0.923091i
$918$	−16.8796			−0.557110
$919$	14.8936			0.491296			0.245648	−	0.969359i	$-0.420999\pi$
$919$	14.8936			0.491296			0.245648	+	0.969359i	$0.420999\pi$
$920$	−5.14122			−0.169501
$921$	6.48713	+	11.2360i	0.213758	+	0.370240i
$922$	31.9580			1.05248
$923$	−14.4970	+	25.1095i	−0.477174	+	0.826490i
$924$	21.3038			0.700843
$925$	−0.888871			−0.0292259
$926$	−22.5766			−0.741912
$927$	10.1533	+	17.5860i	0.333477	+	0.577600i
$928$	5.23651	+	9.06990i	0.171897	+	0.297734i
$929$	26.1913	+	45.3646i	0.859307	+	1.48836i	0.872591	+	0.488452i	$0.162438\pi$
$929$	26.1913	+	45.3646i	0.859307	+	1.48836i	−0.0132838	+	0.999912i	$0.504228\pi$
$930$	−24.8491	+	43.0399i	−0.814835	+	1.41134i
$931$	0.870819	−	1.50830i	0.0285399	−	0.0494326i
$932$	1.75202	+	3.03459i	0.0573893	+	0.0994012i
$933$	8.32642			0.272595
$934$	−16.0006	+	27.7138i	−0.523555	+	0.906824i
$935$	5.70090	−	9.87425i	0.186439	−	0.322923i
$936$	−9.85256	−	17.0651i	−0.322041	−	0.557791i
$937$	3.69018	−	6.39158i	0.120553	−	0.208804i	−0.799433	−	0.600755i	$-0.794867\pi$
$937$	3.69018	−	6.39158i	0.120553	−	0.208804i	0.919986	+	0.391952i	$0.128200\pi$
$938$	−2.68428	+	4.64931i	−0.0876449	+	0.151805i
$939$	43.6025	+	75.5218i	1.42291	+	2.46456i
$940$	8.32325	−	14.4163i	0.271475	−	0.470208i
$941$	9.63459			0.314079			0.157039	−	0.987592i	$-0.449805\pi$
$941$	9.63459			0.314079			0.157039	+	0.987592i	$0.449805\pi$
$942$	−27.8483	+	48.2347i	−0.907348	+	1.57157i
$943$	2.54659	−	4.41082i	0.0829283	−	0.143636i
$944$	−5.81887			−0.189388
$945$	16.3287	+	28.2822i	0.531174	+	0.920020i
$946$	26.2187			0.852442
$947$	17.8331	−	30.8879i	0.579499	−	1.00372i	−0.416038	−	0.909347i	$-0.636582\pi$
$947$	17.8331	−	30.8879i	0.579499	−	1.00372i	0.995537	−	0.0943740i	$-0.0300849\pi$
$948$	−19.7984			−0.643023
$949$	18.0505	+	31.2645i	0.585946	+	1.01489i
$950$	0.764295	+	1.32380i	0.0247970	+	0.0429497i
$951$	−96.1466			−3.11777
$952$	−4.36629			−0.141512
$953$	21.8386	−	37.8255i	0.707420	−	1.22529i	−0.258391	−	0.966041i	$-0.583192\pi$
$953$	21.8386	−	37.8255i	0.707420	−	1.22529i	0.965811	−	0.259247i	$-0.0834745\pi$
$954$	25.3815	−	43.9621i	0.821757	−	1.42333i
$955$	19.9201	+	34.5027i	0.644601	+	1.11648i
$956$	2.07786			0.0672029
$957$	−50.8498	−	88.0745i	−1.64374	−	2.84704i
$958$	3.74778			0.121085
$959$	−16.8864	+	29.2482i	−0.545291	+	0.944473i
$960$	5.22162			0.168527
$961$	−29.7940	−	51.6048i	−0.961097	−	1.66467i
$962$	−0.779822	−	1.35069i	−0.0251425	−	0.0435480i
$963$	−4.56303	+	7.90340i	−0.147042	+	0.254684i
$964$	−0.990128	−	1.71495i	−0.0318899	−	0.0552349i
$965$	−12.9217	−	22.3810i	−0.415964	−	0.720471i
$966$	−9.55922	−	16.5571i	−0.307563	−	0.532715i
$967$	−0.634568	−	1.09910i	−0.0204063	−	0.0353448i	0.855642	−	0.517568i	$-0.173163\pi$
$967$	−0.634568	−	1.09910i	−0.0204063	−	0.0353448i	−0.876048	+	0.482223i	$0.839829\pi$
$968$	0.173000	−	0.299644i	0.00556042	−	0.00963092i
$969$	2.35765	+	4.08356i	0.0757385	+	0.131183i
$970$	8.27448	−	14.3318i	0.265677	−	0.460167i
$971$	−14.2723	−	24.7203i	−0.458019	−	0.793312i	0.540838	−	0.841127i	$-0.318107\pi$
$971$	−14.2723	−	24.7203i	−0.458019	−	0.793312i	−0.998856	+	0.0478155i	$0.984774\pi$
$972$	−1.29844	−	2.24897i	−0.0416475	−	0.0721356i
$973$	6.38753	−	11.0635i	0.204775	−	0.354680i
$974$	−26.5414			−0.850440
$975$	−9.61616	−	16.6557i	−0.307963	−	0.533408i
$976$	5.10860	−	8.84835i	0.163522	−	0.283229i
$977$	−23.2954	−	40.3489i	−0.745287	−	1.29088i	−0.950060	−	0.312066i	$-0.898979\pi$
$977$	−23.2954	−	40.3489i	−0.745287	−	1.29088i	0.204773	−	0.978809i	$-0.434354\pi$
$978$	−0.881503	+	1.52681i	−0.0281873	+	0.0488219i
$979$	−36.9849			−1.18204
$980$	−1.91923	−	3.32421i	−0.0613077	−	0.106188i
$981$	−34.9964	+	60.6155i	−1.11735	+	1.93530i
$982$	9.47748	−	16.4155i	0.302439	−	0.523839i
$983$	−40.5059			−1.29194			−0.645969	−	0.763364i	$-0.723546\pi$
$983$	−40.5059			−1.29194			−0.645969	+	0.763364i	$0.723546\pi$
$984$	−2.58641	+	4.47980i	−0.0824519	+	0.142811i
$985$	19.4300	+	33.6538i	0.619092	+	1.07230i
$986$	10.4219	+	18.0512i	0.331899	+	0.574867i
$987$	61.9027			1.97038
$988$	−1.34106	+	2.32278i	−0.0426647	+	0.0738975i
$989$	−11.7646	−	20.3768i	−0.374092	−	0.647946i
$990$	−33.5186			−1.06529
$991$	21.5622	−	37.3469i	0.684946	−	1.18636i	−0.288507	−	0.957478i	$-0.593159\pi$
$991$	21.5622	−	37.3469i	0.684946	−	1.18636i	0.973454	−	0.228884i	$-0.0735078\pi$
$992$	−4.75889	+	8.24264i	−0.151095	+	0.261704i
$993$	−18.6831	+	32.3601i	−0.592891	+	1.02692i
$994$	9.44330	−	16.3563i	0.299523	−	0.518790i
$995$	48.5996			1.54071
$996$	4.33348			0.137312
$997$	8.43187			0.267040			0.133520	−	0.991046i	$-0.457372\pi$
$997$	8.43187			0.267040			0.133520	+	0.991046i	$0.457372\pi$
$998$	−1.42492	−	2.46803i	−0.0451050	−	0.0781242i
$999$	1.96377	+	3.40136i	0.0621311	+	0.107614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	446.2.c.d.39.7	✓	14
223.183	even	3	inner	446.2.c.d.183.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
446.2.c.d.39.7	✓	14	1.1	even	1	trivial
446.2.c.d.183.7	yes	14	223.183	even	3	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:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.48752 - 2.57645i) q^{3} +1.00000 q^{4} +(0.877575 + 1.52000i) q^{5} +(1.48752 - 2.57645i) q^{6} -2.19386 q^{7} +1.00000 q^{8} +(-2.92540 - 5.06695i) q^{9} +(0.877575 + 1.52000i) q^{10} +(-1.63202 - 2.82675i) q^{11} +(1.48752 - 2.57645i) q^{12} +3.36793 q^{13} -2.19386 q^{14} +5.22162 q^{15} +1.00000 q^{16} +1.99023 q^{17} +(-2.92540 - 5.06695i) q^{18} +(-0.398184 + 0.689676i) q^{19} +(0.877575 + 1.52000i) q^{20} +(-3.26340 + 5.65238i) q^{21} +(-1.63202 - 2.82675i) q^{22} +(-1.46461 + 2.53678i) q^{23} +(1.48752 - 2.57645i) q^{24} +(0.959725 - 1.66229i) q^{25} +3.36793 q^{26} -8.48124 q^{27} -2.19386 q^{28} +(5.23651 + 9.06990i) q^{29} +5.22162 q^{30} +(-4.75889 + 8.24264i) q^{31} +1.00000 q^{32} -9.71064 q^{33} +1.99023 q^{34} +(-1.92528 - 3.33468i) q^{35} +(-2.92540 - 5.06695i) q^{36} +(-0.231543 - 0.401045i) q^{37} +(-0.398184 + 0.689676i) q^{38} +(5.00985 - 8.67731i) q^{39} +(0.877575 + 1.52000i) q^{40} -1.73875 q^{41} +(-3.26340 + 5.65238i) q^{42} +(-4.01628 + 6.95640i) q^{43} +(-1.63202 - 2.82675i) q^{44} +(5.13452 - 8.89325i) q^{45} +(-1.46461 + 2.53678i) q^{46} +(-4.74219 - 8.21371i) q^{47} +(1.48752 - 2.57645i) q^{48} -2.18697 q^{49} +(0.959725 - 1.66229i) q^{50} +(2.96050 - 5.12773i) q^{51} +3.36793 q^{52} +(4.33812 + 7.51385i) q^{53} -8.48124 q^{54} +(2.86445 - 4.96136i) q^{55} -2.19386 q^{56} +(1.18461 + 2.05181i) q^{57} +(5.23651 + 9.06990i) q^{58} -5.81887 q^{59} +5.22162 q^{60} +(5.10860 - 8.84835i) q^{61} +(-4.75889 + 8.24264i) q^{62} +(6.41793 + 11.1162i) q^{63} +1.00000 q^{64} +(2.95561 + 5.11927i) q^{65} -9.71064 q^{66} +(1.22354 - 2.11924i) q^{67} +1.99023 q^{68} +(4.35726 + 7.54700i) q^{69} +(-1.92528 - 3.33468i) q^{70} +(-4.30442 + 7.45548i) q^{71} +(-2.92540 - 5.06695i) q^{72} +(5.35953 + 9.28299i) q^{73} +(-0.231543 - 0.401045i) q^{74} +(-2.85521 - 4.94537i) q^{75} +(-0.398184 + 0.689676i) q^{76} +(3.58043 + 6.20149i) q^{77} +(5.00985 - 8.67731i) q^{78} +(-3.32743 - 5.76328i) q^{79} +(0.877575 + 1.52000i) q^{80} +(-3.83977 + 6.65067i) q^{81} -1.73875 q^{82} +(0.728309 + 1.26147i) q^{83} +(-3.26340 + 5.65238i) q^{84} +(1.74658 + 3.02516i) q^{85} +(-4.01628 + 6.95640i) q^{86} +31.1575 q^{87} +(-1.63202 - 2.82675i) q^{88} +(5.66550 - 9.81293i) q^{89} +(5.13452 - 8.89325i) q^{90} -7.38877 q^{91} +(-1.46461 + 2.53678i) q^{92} +(14.1578 + 24.5221i) q^{93} +(-4.74219 - 8.21371i) q^{94} -1.39775 q^{95} +(1.48752 - 2.57645i) q^{96} +(-4.71440 - 8.16558i) q^{97} -2.18697 q^{98} +(-9.54866 + 16.5388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 3 q^{3} + 14 q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{7} + 14 q^{8} - 18 q^{9} - 6 q^{10} - 5 q^{11} - 3 q^{12} + 14 q^{13} - 6 q^{14} - 8 q^{15} + 14 q^{16} - 18 q^{18} - 4 q^{19} - 6 q^{20}+ \cdots - 43 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 - 3 * q^3 + 14 * q^4 - 6 * q^5 - 3 * q^6 - 6 * q^7 + 14 * q^8 - 18 * q^9 - 6 * q^10 - 5 * q^11 - 3 * q^12 + 14 * q^13 - 6 * q^14 - 8 * q^15 + 14 * q^16 - 18 * q^18 - 4 * q^19 - 6 * q^20 - 15 * q^21 - 5 * q^22 + 2 * q^23 - 3 * q^24 - 23 * q^25 + 14 * q^26 + 12 * q^27 - 6 * q^28 + 2 * q^29 - 8 * q^30 - 11 * q^31 + 14 * q^32 + 4 * q^33 + 9 * q^35 - 18 * q^36 - 5 * q^37 - 4 * q^38 + 11 * q^39 - 6 * q^40 + 44 * q^41 - 15 * q^42 - 14 * q^43 - 5 * q^44 - 3 * q^45 + 2 * q^46 - 13 * q^47 - 3 * q^48 + 24 * q^49 - 23 * q^50 + 13 * q^51 + 14 * q^52 + 17 * q^53 + 12 * q^54 + 3 * q^55 - 6 * q^56 - 5 * q^57 + 2 * q^58 + 20 * q^59 - 8 * q^60 + 24 * q^61 - 11 * q^62 + 21 * q^63 + 14 * q^64 - q^65 + 4 * q^66 - 10 * q^67 - 8 * q^69 + 9 * q^70 - 18 * q^71 - 18 * q^72 + 28 * q^73 - 5 * q^74 - 14 * q^75 - 4 * q^76 - 35 * q^77 + 11 * q^78 - 7 * q^79 - 6 * q^80 + 17 * q^81 + 44 * q^82 - 15 * q^83 - 15 * q^84 + 9 * q^85 - 14 * q^86 + 38 * q^87 - 5 * q^88 + 8 * q^89 - 3 * q^90 - 20 * q^91 + 2 * q^92 - 4 * q^93 - 13 * q^94 - 24 * q^95 - 3 * q^96 + 24 * q^98 - 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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