LMFDB - Embedded newform 560.2.t.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39015 - 0.259757i) q^{2} +2.75657i q^{3} +(1.86505 + 0.722204i) q^{4} +(-1.95957 + 1.07707i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.40511 - 1.48843i) q^{8} -4.59869 q^{9} +O(q^{10})$	\(q+(-1.39015 - 0.259757i) q^{2} +2.75657i q^{3} +(1.86505 + 0.722204i) q^{4} +(-1.95957 + 1.07707i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.40511 - 1.48843i) q^{8} -4.59869 q^{9} +(3.00388 - 0.988279i) q^{10} +(2.48496 - 2.48496i) q^{11} +(-1.99081 + 5.14115i) q^{12} -4.84084 q^{13} +(1.16666 - 0.799311i) q^{14} +(-2.96902 - 5.40170i) q^{15} +(2.95684 + 2.69390i) q^{16} +(-1.63587 + 1.63587i) q^{17} +(6.39289 + 1.19454i) q^{18} +(-1.02421 + 1.02421i) q^{19} +(-4.43257 + 0.593581i) q^{20} +(-1.94919 - 1.94919i) q^{21} +(-4.09997 + 2.80899i) q^{22} +(-4.88728 - 4.88728i) q^{23} +(4.10298 - 6.62987i) q^{24} +(2.67984 - 4.22119i) q^{25} +(6.72951 + 1.25744i) q^{26} -4.40691i q^{27} +(-1.82947 + 0.808116i) q^{28} +(2.08627 + 2.08627i) q^{29} +(2.72426 + 8.28042i) q^{30} +5.11030i q^{31} +(-3.41071 - 4.51299i) q^{32} +(6.84999 + 6.84999i) q^{33} +(2.69903 - 1.84918i) q^{34} +(0.624023 - 2.14723i) q^{35} +(-8.57681 - 3.32120i) q^{36} +8.59247 q^{37} +(1.68986 - 1.15777i) q^{38} -13.3441i q^{39} +(6.31614 + 0.326223i) q^{40} -6.94716i q^{41} +(2.20336 + 3.21599i) q^{42} +2.49682 q^{43} +(6.42924 - 2.83994i) q^{44} +(9.01147 - 4.95311i) q^{45} +(5.52456 + 8.06357i) q^{46} +(-7.21178 - 7.21178i) q^{47} +(-7.42592 + 8.15075i) q^{48} -1.00000i q^{49} +(-4.82188 + 5.17199i) q^{50} +(-4.50939 - 4.50939i) q^{51} +(-9.02842 - 3.49607i) q^{52} +5.61513i q^{53} +(-1.14473 + 6.12629i) q^{54} +(-2.19299 + 7.54595i) q^{55} +(2.75315 - 0.648188i) q^{56} +(-2.82331 - 2.82331i) q^{57} +(-2.35831 - 3.44216i) q^{58} +(-8.09154 - 8.09154i) q^{59} +(-1.63625 - 12.2187i) q^{60} +(-4.06506 + 4.06506i) q^{61} +(1.32744 - 7.10410i) q^{62} +(3.25177 - 3.25177i) q^{63} +(3.56912 + 7.15970i) q^{64} +(9.48597 - 5.21392i) q^{65} +(-7.74320 - 11.3019i) q^{66} +10.8820 q^{67} +(-4.23241 + 1.86955i) q^{68} +(13.4721 - 13.4721i) q^{69} +(-1.42525 + 2.82288i) q^{70} -12.1998 q^{71} +(11.0604 + 6.84486i) q^{72} +(-5.45819 + 5.45819i) q^{73} +(-11.9448 - 2.23195i) q^{74} +(11.6360 + 7.38718i) q^{75} +(-2.64990 + 1.17052i) q^{76} +3.51427i q^{77} +(-3.46623 + 18.5504i) q^{78} -11.5728 q^{79} +(-8.69566 - 2.09416i) q^{80} -1.64810 q^{81} +(-1.80457 + 9.65762i) q^{82} +2.86002i q^{83} +(-2.22763 - 5.04306i) q^{84} +(1.44366 - 4.96754i) q^{85} +(-3.47096 - 0.648566i) q^{86} +(-5.75096 + 5.75096i) q^{87} +(-9.67532 + 2.27791i) q^{88} +6.32940 q^{89} +(-13.8139 + 4.54479i) q^{90} +(3.42299 - 3.42299i) q^{91} +(-5.58542 - 12.6446i) q^{92} -14.0869 q^{93} +(8.15217 + 11.8988i) q^{94} +(0.903869 - 3.11016i) q^{95} +(12.4404 - 9.40186i) q^{96} +(-6.62293 + 6.62293i) q^{97} +(-0.259757 + 1.39015i) q^{98} +(-11.4276 + 11.4276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.39015	−	0.259757i	−0.982987	−	0.183676i
$2$	−1.39015	−	0.259757i	−0.982987	−	0.183676i
$3$			2.75657i			1.59151i	0.605620	+	0.795754i	$0.292925\pi$
$3$			2.75657i			1.59151i	−0.605620	+	0.795754i	$0.707075\pi$
$4$	1.86505	+	0.722204i	0.932526	+	0.361102i
$5$	−1.95957	+	1.07707i	−0.876347	+	0.481680i
$5$	−1.95957	+	1.07707i	−0.876347	+	0.481680i
$6$	0.716039	−	3.83206i	0.292322	−	1.56443i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.40511	−	1.48843i	−0.850335	−	0.526241i
$9$	−4.59869			−1.53290
$10$	3.00388	−	0.988279i	0.949911	−	0.312521i
$11$	2.48496	−	2.48496i	0.749245	−	0.749245i	−0.225092	−	0.974337i	$-0.572268\pi$
$11$	2.48496	−	2.48496i	0.749245	−	0.749245i	0.974337	+	0.225092i	$0.0722684\pi$
$12$	−1.99081	+	5.14115i	−0.574697	+	1.48412i
$13$	−4.84084			−1.34261			−0.671304	−	0.741182i	$-0.734265\pi$
$13$	−4.84084			−1.34261			−0.671304	+	0.741182i	$0.734265\pi$
$14$	1.16666	−	0.799311i	0.311804	−	0.213625i
$15$	−2.96902	−	5.40170i	−0.766598	−	1.39471i
$16$	2.95684	+	2.69390i	0.739211	+	0.673474i
$17$	−1.63587	+	1.63587i	−0.396756	+	0.396756i	−0.877087	−	0.480331i	$-0.840516\pi$
$17$	−1.63587	+	1.63587i	−0.396756	+	0.396756i	0.480331	+	0.877087i	$0.340516\pi$
$18$	6.39289	+	1.19454i	1.50682	+	0.281556i
$19$	−1.02421	+	1.02421i	−0.234970	+	0.234970i	−0.814764	−	0.579793i	$-0.803133\pi$
$19$	−1.02421	+	1.02421i	−0.234970	+	0.234970i	0.579793	+	0.814764i	$0.303133\pi$
$20$	−4.43257	+	0.593581i	−0.991152	+	0.132729i
$21$	−1.94919	−	1.94919i	−0.425348	−	0.425348i
$22$	−4.09997	+	2.80899i	−0.874116	+	0.598880i
$23$	−4.88728	−	4.88728i	−1.01907	−	1.01907i	−0.999815	−	0.0192526i	$-0.993871\pi$
$23$	−4.88728	−	4.88728i	−1.01907	−	1.01907i	−0.0192526	−	0.999815i	$-0.506129\pi$
$24$	4.10298	−	6.62987i	0.837517	−	1.35332i
$25$	2.67984	−	4.22119i	0.535969	−	0.844238i
$26$	6.72951	+	1.25744i	1.31977	+	0.246605i
$27$		−	4.40691i		−	0.848111i
$28$	−1.82947	+	0.808116i	−0.345737	+	0.152720i
$29$	2.08627	+	2.08627i	0.387411	+	0.387411i	0.873763	−	0.486352i	$-0.161673\pi$
$29$	2.08627	+	2.08627i	0.387411	+	0.387411i	−0.486352	+	0.873763i	$0.661673\pi$
$30$	2.72426	+	8.28042i	0.497380	+	1.51179i
$31$			5.11030i			0.917837i	0.888478	+	0.458918i	$0.151763\pi$
$31$			5.11030i			0.917837i	−0.888478	+	0.458918i	$0.848237\pi$
$32$	−3.41071	−	4.51299i	−0.602933	−	0.797792i
$33$	6.84999	+	6.84999i	1.19243	+	1.19243i
$34$	2.69903	−	1.84918i	0.462881	−	0.317131i
$35$	0.624023	−	2.14723i	0.105479	−	0.362948i
$36$	−8.57681	−	3.32120i	−1.42947	−	0.553533i
$37$	8.59247			1.41259			0.706296	−	0.707916i	$-0.250365\pi$
$37$	8.59247			1.41259			0.706296	+	0.707916i	$0.250365\pi$
$38$	1.68986	−	1.15777i	0.274131	−	0.187814i
$39$		−	13.3441i		−	2.13677i
$40$	6.31614	+	0.326223i	0.998669	+	0.0515803i
$41$		−	6.94716i		−	1.08496i	−0.840067	−	0.542482i	$-0.817485\pi$
$41$		−	6.94716i		−	1.08496i	0.840067	−	0.542482i	$-0.182515\pi$
$42$	2.20336	+	3.21599i	0.339986	+	0.496238i
$43$	2.49682			0.380761			0.190380	−	0.981710i	$-0.439028\pi$
$43$	2.49682			0.380761			0.190380	+	0.981710i	$0.439028\pi$
$44$	6.42924	−	2.83994i	0.969245	−	0.428137i
$45$	9.01147	−	4.95311i	1.34335	−	0.738366i
$46$	5.52456	+	8.06357i	0.814552	+	1.18891i
$47$	−7.21178	−	7.21178i	−1.05195	−	1.05195i	−0.998575	−	0.0533712i	$-0.983003\pi$
$47$	−7.21178	−	7.21178i	−1.05195	−	1.05195i	−0.0533712	−	0.998575i	$-0.516997\pi$
$48$	−7.42592	+	8.15075i	−1.07184	+	1.17646i
$49$		−	1.00000i		−	0.142857i
$50$	−4.82188	+	5.17199i	−0.681916	+	0.731430i
$51$	−4.50939	−	4.50939i	−0.631441	−	0.631441i
$52$	−9.02842	−	3.49607i	−1.25202	−	0.484818i
$53$			5.61513i			0.771297i	0.922646	+	0.385649i	$0.126022\pi$
$53$			5.61513i			0.771297i	−0.922646	+	0.385649i	$0.873978\pi$
$54$	−1.14473	+	6.12629i	−0.155778	+	0.833682i
$55$	−2.19299	+	7.54595i	−0.295702	+	1.01750i
$56$	2.75315	−	0.648188i	0.367906	−	0.0866178i
$57$	−2.82331	−	2.82331i	−0.373957	−	0.373957i
$58$	−2.35831	−	3.44216i	−0.309662	−	0.451978i
$59$	−8.09154	−	8.09154i	−1.05343	−	1.05343i	−0.998490	−	0.0549384i	$-0.982504\pi$
$59$	−8.09154	−	8.09154i	−1.05343	−	1.05343i	−0.0549384	−	0.998490i	$-0.517496\pi$
$60$	−1.63625	−	12.2187i	−0.211239	−	1.57743i
$61$	−4.06506	+	4.06506i	−0.520477	+	0.520477i	−0.917716	−	0.397238i	$-0.869969\pi$
$61$	−4.06506	+	4.06506i	−0.520477	+	0.520477i	0.397238	+	0.917716i	$0.369969\pi$
$62$	1.32744	−	7.10410i	0.168585	−	0.902222i
$63$	3.25177	−	3.25177i	0.409684	−	0.409684i
$64$	3.56912	+	7.15970i	0.446140	+	0.894963i
$65$	9.48597	−	5.21392i	1.17659	−	0.646707i
$66$	−7.74320	−	11.3019i	−0.953122	−	1.39116i
$67$	10.8820			1.32945			0.664723	−	0.747090i	$-0.268549\pi$
$67$	10.8820			1.32945			0.664723	+	0.747090i	$0.268549\pi$
$68$	−4.23241	+	1.86955i	−0.513255	+	0.226716i
$69$	13.4721	−	13.4721i	1.62185	−	1.62185i
$70$	−1.42525	+	2.82288i	−0.170349	+	0.337399i
$71$	−12.1998			−1.44785			−0.723927	−	0.689876i	$-0.757665\pi$
$71$	−12.1998			−1.44785			−0.723927	+	0.689876i	$0.757665\pi$
$72$	11.0604	+	6.84486i	1.30348	+	0.806674i
$73$	−5.45819	+	5.45819i	−0.638833	+	0.638833i	−0.950268	−	0.311435i	$-0.899191\pi$
$73$	−5.45819	+	5.45819i	−0.638833	+	0.638833i	0.311435	+	0.950268i	$0.399191\pi$
$74$	−11.9448	−	2.23195i	−1.38856	−	0.259459i
$75$	11.6360	+	7.38718i	1.34361	+	0.852998i
$76$	−2.64990	+	1.17052i	−0.303964	+	0.134268i
$77$			3.51427i			0.400488i
$78$	−3.46623	+	18.5504i	−0.392473	+	2.10042i
$79$	−11.5728			−1.30204			−0.651022	−	0.759059i	$-0.725659\pi$
$79$	−11.5728			−1.30204			−0.651022	+	0.759059i	$0.725659\pi$
$80$	−8.69566	−	2.09416i	−0.972204	−	0.234134i
$81$	−1.64810			−0.183122
$82$	−1.80457	+	9.65762i	−0.199282	+	1.06651i
$83$			2.86002i			0.313928i	0.987604	+	0.156964i	$0.0501706\pi$
$83$			2.86002i			0.313928i	−0.987604	+	0.156964i	$0.949829\pi$
$84$	−2.22763	−	5.04306i	−0.243054	−	0.550243i
$85$	1.44366	−	4.96754i	0.156587	−	0.538806i
$86$	−3.47096	−	0.648566i	−0.374283	−	0.0699366i
$87$	−5.75096	+	5.75096i	−0.616568	+	0.616568i
$88$	−9.67532	+	2.27791i	−1.03139	+	0.242826i
$89$	6.32940			0.670915			0.335458	−	0.942055i	$-0.391109\pi$
$89$	6.32940			0.670915			0.335458	+	0.942055i	$0.391109\pi$
$90$	−13.8139	+	4.54479i	−1.45612	+	0.479063i
$91$	3.42299	−	3.42299i	0.358827	−	0.358827i
$92$	−5.58542	−	12.6446i	−0.582320	−	1.31829i
$93$	−14.0869			−1.46074
$94$	8.15217	+	11.8988i	0.840832	+	1.22727i
$95$	0.903869	−	3.11016i	0.0927350	−	0.319096i
$96$	12.4404	−	9.40186i	1.26969	−	0.959573i
$97$	−6.62293	+	6.62293i	−0.672457	+	0.672457i	−0.958282	−	0.285825i	$-0.907732\pi$
$97$	−6.62293	+	6.62293i	−0.672457	+	0.672457i	0.285825	+	0.958282i	$0.407732\pi$
$98$	−0.259757	+	1.39015i	−0.0262394	+	0.140427i
$99$	−11.4276	+	11.4276i	−1.14852	+	1.14852i
$100$	8.04661	−	5.93735i	0.804661	−	0.593735i
$101$	−5.48001	−	5.48001i	−0.545282	−	0.545282i	0.379791	−	0.925072i	$-0.375996\pi$
$101$	−5.48001	−	5.48001i	−0.545282	−	0.545282i	−0.925072	+	0.379791i	$0.875996\pi$
$102$	5.09740	+	7.44008i	0.504717	+	0.736678i
$103$	−3.71500	−	3.71500i	−0.366050	−	0.366050i	0.499984	−	0.866034i	$-0.333339\pi$
$103$	−3.71500	−	3.71500i	−0.366050	−	0.366050i	−0.866034	+	0.499984i	$0.833339\pi$
$104$	11.6428	+	7.20527i	1.14167	+	0.706535i
$105$	5.91899	+	1.72017i	0.577635	+	0.167871i
$106$	1.45857	−	7.80589i	0.141669	−	0.758175i
$107$			0.755462i			0.0730333i	0.999333	+	0.0365167i	$0.0116262\pi$
$107$			0.755462i			0.0730333i	−0.999333	+	0.0365167i	$0.988374\pi$
$108$	3.18269	−	8.21913i	0.306255	−	0.790886i
$109$	4.12169	+	4.12169i	0.394786	+	0.394786i	0.876389	−	0.481603i	$-0.159945\pi$
$109$	4.12169	+	4.12169i	0.394786	+	0.394786i	−0.481603	+	0.876389i	$0.659945\pi$
$110$	5.00870	−	9.92038i	0.477561	−	0.945871i
$111$			23.6858i			2.24815i
$112$	−3.99568	+	0.185930i	−0.377556	+	0.0175688i
$113$	−3.68326	−	3.68326i	−0.346492	−	0.346492i	0.512309	−	0.858801i	$-0.328790\pi$
$113$	−3.68326	−	3.68326i	−0.346492	−	0.346492i	−0.858801	+	0.512309i	$0.828790\pi$
$114$	3.19146	+	4.65822i	0.298908	+	0.436282i
$115$	14.8409	+	4.31303i	1.38392	+	0.402192i
$116$	2.38429	+	5.39772i	0.221376	+	0.501166i
$117$	22.2615			2.05808
$118$	9.14664	+	13.3503i	0.842017	+	1.22900i
$119$		−	2.31347i		−	0.212075i
$120$	−0.899256	+	17.4109i	−0.0820905	+	1.58939i
$121$		−	1.35010i		−	0.122736i
$122$	6.70698	−	4.59513i	0.607221	−	0.416023i
$123$	19.1504			1.72673
$124$	−3.69068	+	9.53098i	−0.331433	+	0.855907i
$125$	−0.704829	+	11.1581i	−0.0630418	+	0.998011i
$126$	−5.36512	+	3.67579i	−0.477963	+	0.327465i
$127$	−13.2450	−	13.2450i	−1.17531	−	1.17531i	−0.980926	−	0.194379i	$-0.937731\pi$
$127$	−13.2450	−	13.2450i	−1.17531	−	1.17531i	−0.194379	−	0.980926i	$-0.562269\pi$
$128$	−3.10185	−	10.8802i	−0.274167	−	0.961682i
$129$			6.88266i			0.605984i
$130$	−14.5413	+	4.78410i	−1.27536	+	0.419593i
$131$	10.6722	+	10.6722i	0.932430	+	0.932430i	0.997857	−	0.0654271i	$-0.0208410\pi$
$131$	10.6722	+	10.6722i	0.932430	+	0.932430i	−0.0654271	+	0.997857i	$0.520841\pi$
$132$	7.82850	+	17.7227i	0.681383	+	1.54256i
$133$		−	1.44845i		−	0.125597i
$134$	−15.1276	−	2.82667i	−1.30683	−	0.244187i
$135$	4.74655	+	8.63567i	0.408518	+	0.743240i
$136$	6.36933	−	1.49956i	0.546165	−	0.128586i
$137$	9.93546	+	9.93546i	0.848843	+	0.848843i	0.989989	−	0.141145i	$-0.0450785\pi$
$137$	9.93546	+	9.93546i	0.848843	+	0.848843i	−0.141145	+	0.989989i	$0.545079\pi$
$138$	−22.2278	+	15.2288i	−1.89216	+	1.29637i
$139$	−3.69691	−	3.69691i	−0.313568	−	0.313568i	0.532722	−	0.846290i	$-0.321169\pi$
$139$	−3.69691	−	3.69691i	−0.313568	−	0.313568i	−0.846290	+	0.532722i	$0.821169\pi$
$140$	2.71457	−	3.55402i	0.229423	−	0.300370i
$141$	19.8798	−	19.8798i	1.67418	−	1.67418i
$142$	16.9596	+	3.16899i	1.42322	+	0.265936i
$143$	−12.0293	+	12.0293i	−1.00594	+	1.00594i
$144$	−13.5976	−	12.3884i	−1.13313	−	1.03237i
$145$	−6.33526	−	1.84114i	−0.526115	−	0.152898i
$146$	9.00553	−	6.16992i	0.745303	−	0.510626i
$147$	2.75657			0.227358
$148$	16.0254	+	6.20551i	1.31728	+	0.510090i
$149$	−13.4801	+	13.4801i	−1.10434	+	1.10434i	−0.110455	+	0.993881i	$0.535231\pi$
$149$	−13.4801	+	13.4801i	−1.10434	+	1.10434i	−0.993881	+	0.110455i	$0.964769\pi$
$150$	−14.2570	−	13.2919i	−1.16408	−	1.08528i
$151$	1.50233			0.122258			0.0611289	−	0.998130i	$-0.480530\pi$
$151$	1.50233			0.122258			0.0611289	+	0.998130i	$0.480530\pi$
$152$	3.98782	−	0.938871i	0.323455	−	0.0761525i
$153$	7.52285	−	7.52285i	0.608187	−	0.608187i
$154$	0.912856	−	4.88537i	0.0735601	−	0.393675i
$155$	−5.50415	−	10.0140i	−0.442104	−	0.804344i
$156$	9.63718	−	24.8875i	0.771592	−	1.99259i
$157$			19.5243i			1.55821i	0.626895	+	0.779104i	$0.284326\pi$
$157$			19.5243i			1.55821i	−0.626895	+	0.779104i	$0.715674\pi$
$158$	16.0880	+	3.00612i	1.27989	+	0.239154i
$159$	−15.4785			−1.22753
$160$	11.5443	+	5.16996i	0.912659	+	0.408721i
$161$	6.91165			0.544714
$162$	2.29111	+	0.428105i	0.180007	+	0.0336351i
$163$			2.85332i			0.223489i	0.993737	+	0.111745i	$0.0356439\pi$
$163$			2.85332i			0.223489i	−0.993737	+	0.111745i	$0.964356\pi$
$164$	5.01727	−	12.9568i	0.391783	−	1.01176i
$165$	−20.8009	−	6.04513i	−1.61935	−	0.470613i
$166$	0.742909	−	3.97586i	0.0576609	−	0.308587i
$167$	9.35953	−	9.35953i	0.724262	−	0.724262i	−0.245208	−	0.969470i	$-0.578856\pi$
$167$	9.35953	−	9.35953i	0.724262	−	0.724262i	0.969470	+	0.245208i	$0.0788563\pi$
$168$	1.78678	+	7.58927i	0.137853	+	0.585525i
$169$	10.4337			0.802594
$170$	−3.29726	+	6.53065i	−0.252888	+	0.500878i
$171$	4.71004	−	4.71004i	0.360186	−	0.360186i
$172$	4.65669	+	1.80321i	0.355070	+	0.137494i
$173$	0.635940			0.0483496			0.0241748	−	0.999708i	$-0.492304\pi$
$173$	0.635940			0.0483496			0.0241748	+	0.999708i	$0.492304\pi$
$174$	9.48857	−	6.50086i	0.719327	−	0.492829i
$175$	1.08990	+	4.87977i	0.0823885	+	0.368876i
$176$	14.0419	−	0.653410i	1.05845	−	0.0492526i
$177$	22.3049	−	22.3049i	1.67654	−	1.67654i
$178$	−8.79884	−	1.64411i	−0.659501	−	0.123231i
$179$	−17.8546	+	17.8546i	−1.33451	+	1.33451i	−0.433231	+	0.901283i	$0.642626\pi$
$179$	−17.8546	+	17.8546i	−1.33451	+	1.33451i	−0.901283	+	0.433231i	$0.857374\pi$
$180$	20.3840	−	2.72970i	1.51934	−	0.203459i
$181$	−15.3924	−	15.3924i	−1.14411	−	1.14411i	−0.987691	−	0.156420i	$-0.950005\pi$
$181$	−15.3924	−	15.3924i	−1.14411	−	1.14411i	−0.156420	−	0.987691i	$-0.549995\pi$
$182$	−5.64763	+	3.86934i	−0.418630	+	0.286814i
$183$	−11.2056	−	11.2056i	−0.828344	−	0.828344i
$184$	4.48005	+	19.0288i	0.330274	+	1.40282i
$185$	−16.8376	+	9.25468i	−1.23792	+	0.680418i
$186$	19.5830	+	3.65917i	1.43589	+	0.268304i
$187$			8.13014i			0.594535i
$188$	−8.24197	−	18.6587i	−0.601107	−	1.36083i
$189$	3.11616	+	3.11616i	0.226667	+	0.226667i
$190$	−2.06440	+	4.08882i	−0.149768	+	0.296634i
$191$			14.8696i			1.07593i	0.842968	+	0.537964i	$0.180806\pi$
$191$			14.8696i			1.07593i	−0.842968	+	0.537964i	$0.819194\pi$
$192$	−19.7362	+	9.83855i	−1.42434	+	0.710036i
$193$	−2.14146	−	2.14146i	−0.154146	−	0.154146i	0.625821	−	0.779967i	$-0.284764\pi$
$193$	−2.14146	−	2.14146i	−0.154146	−	0.154146i	−0.779967	+	0.625821i	$0.784764\pi$
$194$	10.9272	−	7.48653i	0.784530	−	0.537502i
$195$	14.3726	+	26.1488i	1.02924	+	1.87255i
$196$	0.722204	−	1.86505i	0.0515860	−	0.133218i
$197$	7.18026			0.511572			0.255786	−	0.966733i	$-0.417666\pi$
$197$	7.18026			0.511572			0.255786	+	0.966733i	$0.417666\pi$
$198$	18.8545	−	12.9177i	1.33993	−	0.918021i
$199$			11.2655i			0.798593i	0.916822	+	0.399297i	$0.130746\pi$
$199$			11.2655i			0.798593i	−0.916822	+	0.399297i	$0.869254\pi$
$200$	−12.7283	+	6.16366i	−0.900026	+	0.435837i
$201$			29.9970i			2.11582i
$202$	6.19459	+	9.04153i	0.435850	+	0.636160i
$203$	−2.95043			−0.207080
$204$	−5.15355	−	11.6669i	−0.360820	−	0.816849i
$205$	7.48257	+	13.6135i	0.522606	+	0.950805i
$206$	4.19942	+	6.12942i	0.292588	+	0.427057i
$207$	22.4751	+	22.4751i	1.56213	+	1.56213i
$208$	−14.3136	−	13.0407i	−0.992469	−	0.904211i
$209$			5.09026i			0.352101i
$210$	−7.78149	−	3.92879i	−0.536973	−	0.271113i
$211$	−20.2604	−	20.2604i	−1.39479	−	1.39479i	−0.814195	−	0.580592i	$-0.802821\pi$
$211$	−20.2604	−	20.2604i	−1.39479	−	1.39479i	−0.580592	−	0.814195i	$-0.697179\pi$
$212$	−4.05527	+	10.4725i	−0.278517	+	0.719255i
$213$		−	33.6297i		−	2.30427i
$214$	0.196237	−	1.05021i	0.0134145	−	0.0717908i
$215$	−4.89269	+	2.68924i	−0.333679	+	0.183405i
$216$	−6.55941	+	10.5991i	−0.446311	+	0.721179i
$217$	−3.61353	−	3.61353i	−0.245302	−	0.245302i
$218$	−4.65915	−	6.80042i	−0.315557	−	0.460583i
$219$	−15.0459	−	15.0459i	−1.01671	−	1.01671i
$220$	−9.53975	+	12.4898i	−0.643170	+	0.842062i
$221$	7.91897	−	7.91897i	0.532688	−	0.532688i
$222$	6.15254	−	32.9268i	0.412932	−	2.20990i
$223$	7.56278	−	7.56278i	0.506441	−	0.506441i	−0.406991	−	0.913432i	$-0.633422\pi$
$223$	7.56278	−	7.56278i	0.506441	−	0.506441i	0.913432	+	0.406991i	$0.133422\pi$
$224$	5.60290	+	0.779433i	0.374359	+	0.0520781i
$225$	−12.3238	+	19.4120i	−0.821585	+	1.29413i
$226$	4.16354	+	6.07705i	0.276955	+	0.404239i
$227$	−24.2843			−1.61180			−0.805902	−	0.592049i	$-0.798319\pi$
$227$	−24.2843			−1.61180			−0.805902	+	0.592049i	$0.798319\pi$
$228$	−3.22662	−	7.30464i	−0.213688	−	0.483762i
$229$	13.9087	−	13.9087i	0.919113	−	0.919113i	−0.0778522	−	0.996965i	$-0.524806\pi$
$229$	13.9087	−	13.9087i	0.919113	−	0.919113i	0.996965	+	0.0778522i	$0.0248062\pi$
$230$	−19.5108	−	9.85080i	−1.28650	−	0.649543i
$231$	−9.68734			−0.637380
$232$	−1.91244	−	8.12300i	−0.125558	−	0.533301i
$233$	−10.3692	+	10.3692i	−0.679310	+	0.679310i	−0.959844	−	0.280534i	$-0.909488\pi$
$233$	−10.3692	+	10.3692i	−0.679310	+	0.679310i	0.280534	+	0.959844i	$0.409488\pi$
$234$	−30.9469	−	5.78259i	−2.02307	−	0.378020i
$235$	21.8996	+	6.36441i	1.42857	+	0.415168i
$236$	−9.24740	−	20.9349i	−0.601954	−	1.36274i
$237$		−	31.9013i		−	2.07221i
$238$	−0.600939	+	3.21607i	−0.0389531	+	0.208467i
$239$	3.66770			0.237244			0.118622	−	0.992940i	$-0.462152\pi$
$239$	3.66770			0.237244			0.118622	+	0.992940i	$0.462152\pi$
$240$	5.77270	−	23.9702i	0.372626	−	1.54727i
$241$	−12.3924			−0.798262			−0.399131	−	0.916894i	$-0.630688\pi$
$241$	−12.3924			−0.798262			−0.399131	+	0.916894i	$0.630688\pi$
$242$	−0.350697	+	1.87684i	−0.0225437	+	0.120648i
$243$		−	17.7638i		−	1.13955i
$244$	−10.5173	+	4.64574i	−0.673304	+	0.297413i
$245$	1.07707	+	1.95957i	0.0688114	+	0.125192i
$246$	−26.6219	−	4.97444i	−1.69735	−	0.317159i
$247$	4.95805	−	4.95805i	0.315473	−	0.315473i
$248$	7.60635	−	12.2908i	0.483004	−	0.780469i
$249$	−7.88384			−0.499618
$250$	3.87821	−	15.3284i	0.245280	−	0.969452i
$251$	−12.2903	+	12.2903i	−0.775755	+	0.775755i	−0.979106	−	0.203351i	$-0.934817\pi$
$251$	−12.2903	+	12.2903i	−0.775755	+	0.775755i	0.203351	+	0.979106i	$0.434817\pi$
$252$	8.41316	−	3.71628i	0.529979	−	0.234103i
$253$	−24.2894			−1.52706
$254$	14.9721	+	21.8531i	0.939435	+	1.37119i
$255$	13.6934	+	3.97954i	0.857513	+	0.249209i
$256$	1.48584	+	15.9309i	0.0928647	+	0.995679i
$257$	5.98659	−	5.98659i	0.373433	−	0.373433i	−0.495293	−	0.868726i	$-0.664939\pi$
$257$	5.98659	−	5.98659i	0.373433	−	0.373433i	0.868726	+	0.495293i	$0.164939\pi$
$258$	1.78782	−	9.56795i	0.111305	−	0.595674i
$259$	−6.07579	+	6.07579i	−0.377531	+	0.377531i
$260$	21.4573	−	2.87343i	1.33073	−	0.178202i
$261$	−9.59413	−	9.59413i	−0.593861	−	0.593861i
$262$	−12.0638	−	17.6081i	−0.745302	−	1.08783i
$263$	5.70192	+	5.70192i	0.351595	+	0.351595i	0.860703	−	0.509108i	$-0.170024\pi$
$263$	5.70192	+	5.70192i	0.351595	+	0.351595i	−0.509108	+	0.860703i	$0.670024\pi$
$264$	−6.27922	−	26.6707i	−0.386459	−	1.64147i
$265$	−6.04788	−	11.0032i	−0.371519	−	0.675924i
$266$	−0.376246	+	2.01357i	−0.0230691	+	0.123460i
$267$			17.4475i			1.06777i
$268$	20.2955	+	7.85902i	1.23974	+	0.480066i
$269$	17.6264	+	17.6264i	1.07470	+	1.07470i	0.996975	+	0.0777265i	$0.0247661\pi$
$269$	17.6264	+	17.6264i	1.07470	+	1.07470i	0.0777265	+	0.996975i	$0.475234\pi$
$270$	−4.35526	−	13.2378i	−0.265053	−	0.805630i
$271$		−	21.0928i		−	1.28130i	−0.767834	−	0.640649i	$-0.778665\pi$
$271$		−	21.0928i		−	1.28130i	0.767834	−	0.640649i	$-0.221335\pi$
$272$	−9.24386	+	0.430144i	−0.560491	+	0.0260813i
$273$	9.43572	+	9.43572i	0.571076	+	0.571076i
$274$	−11.2310	−	16.3926i	−0.678490	−	0.990314i
$275$	−3.83019	−	17.1488i	−0.230969	−	1.03411i
$276$	34.8559	−	15.3966i	2.09808	−	0.926767i
$277$	−32.3123			−1.94146			−0.970728	−	0.240181i	$-0.922793\pi$
$277$	−32.3123			−1.94146			−0.970728	+	0.240181i	$0.922793\pi$
$278$	4.17897	+	6.09957i	0.250638	+	0.365828i
$279$		−	23.5007i		−	1.40695i
$280$	−4.69686	+	4.23551i	−0.280691	+	0.253120i
$281$			2.13535i			0.127384i	0.997970	+	0.0636920i	$0.0202875\pi$
$281$			2.13535i			0.127384i	−0.997970	+	0.0636920i	$0.979712\pi$
$282$	−32.7999	+	22.4720i	−1.95320	+	1.33819i
$283$	−11.2031			−0.665958			−0.332979	−	0.942934i	$-0.608054\pi$
$283$	−11.2031			−0.665958			−0.332979	+	0.942934i	$0.608054\pi$
$284$	−22.7533	−	8.81077i	−1.35016	−	0.522823i
$285$	8.57339	+	2.49158i	0.507844	+	0.147589i
$286$	19.8473	−	13.5979i	1.17359	−	0.804060i
$287$	4.91238	+	4.91238i	0.289969	+	0.289969i
$288$	15.6848	+	20.7539i	0.924235	+	1.22293i
$289$			11.6479i			0.685169i
$290$	8.32873	+	4.20509i	0.489080	+	0.246932i
$291$	−18.2566	−	18.2566i	−1.07022	−	1.07022i
$292$	−14.1217	+	6.23789i	−0.826412	+	0.365045i
$293$		−	10.8022i		−	0.631071i	−0.948914	−	0.315535i	$-0.897816\pi$
$293$		−	10.8022i		−	0.631071i	0.948914	−	0.315535i	$-0.102184\pi$
$294$	−3.83206	−	0.716039i	−0.223490	−	0.0417602i
$295$	24.5711	+	7.14080i	1.43058	+	0.415753i
$296$	−20.6658	−	12.7893i	−1.20118	−	0.743365i
$297$	−10.9510	−	10.9510i	−0.635443	−	0.635443i
$298$	22.2410	−	15.2379i	1.28839	−	0.882708i
$299$	23.6585	+	23.6585i	1.36821	+	1.36821i
$300$	16.3667	+	22.1811i	0.944934	+	1.28062i
$301$	−1.76552	+	1.76552i	−0.101763	+	0.101763i
$302$	−2.08847	−	0.390241i	−0.120178	−	0.0224558i
$303$	15.1061	−	15.1061i	0.867820	−	0.867820i
$304$	−5.78756	+	0.269312i	−0.331939	+	0.0154461i
$305$	3.58742	−	12.3441i	0.205415	−	0.706822i
$306$	−12.4120	+	8.50380i	−0.709549	+	0.486130i
$307$	12.3400			0.704279			0.352140	−	0.935948i	$-0.385454\pi$
$307$	12.3400			0.704279			0.352140	+	0.935948i	$0.385454\pi$
$308$	−2.53802	+	6.55430i	−0.144617	+	0.373466i
$309$	10.2407	−	10.2407i	0.582571	−	0.582571i
$310$	5.05040	+	15.3507i	0.286844	+	0.871863i
$311$	8.05926			0.456999			0.228499	−	0.973544i	$-0.426618\pi$
$311$	8.05926			0.456999			0.228499	+	0.973544i	$0.426618\pi$
$312$	−19.8619	+	32.0941i	−1.12446	+	1.81697i
$313$	5.79372	−	5.79372i	0.327480	−	0.327480i	−0.524147	−	0.851628i	$-0.675616\pi$
$313$	5.79372	−	5.79372i	0.327480	−	0.327480i	0.851628	+	0.524147i	$0.175616\pi$
$314$	5.07157	−	27.1418i	0.286205	−	1.53170i
$315$	−2.86969	+	9.87445i	−0.161689	+	0.556362i
$316$	−21.5839	−	8.35794i	−1.21419	−	0.470171i
$317$			22.9733i			1.29031i	0.764052	+	0.645154i	$0.223207\pi$
$317$			22.9733i			1.29031i	−0.764052	+	0.645154i	$0.776793\pi$
$318$	21.5175	+	4.02065i	1.20664	+	0.225467i
$319$	10.3686			0.580531
$320$	−14.7055	−	10.1858i	−0.822060	−	0.569401i
$321$	−2.08249			−0.116233
$322$	−9.60825	−	1.79535i	−0.535447	−	0.100051i
$323$		−	3.35095i		−	0.186452i
$324$	−3.07379	−	1.19026i	−0.170766	−	0.0661258i
$325$	−12.9727	+	20.4341i	−0.719595	+	1.13348i
$326$	0.741170	−	3.96655i	0.0410496	−	0.219687i
$327$	−11.3617	+	11.3617i	−0.628306	+	0.628306i
$328$	−10.3404	+	16.7087i	−0.570953	+	0.922583i
$329$	10.1990			0.562289
$330$	27.3462	+	13.8068i	1.50536	+	0.760042i
$331$	7.93068	−	7.93068i	0.435909	−	0.435909i	−0.454723	−	0.890633i	$-0.650262\pi$
$331$	7.93068	−	7.93068i	0.435909	−	0.435909i	0.890633	+	0.454723i	$0.150262\pi$
$332$	−2.06552	+	5.33408i	−0.113360	+	0.292746i
$333$	−39.5141			−2.16536
$334$	−15.4424	+	10.5800i	−0.844970	+	0.578911i
$335$	−21.3240	+	11.7207i	−1.16506	+	0.640368i
$336$	−0.512531	−	11.0144i	−0.0279608	−	0.600883i
$337$	2.92814	−	2.92814i	0.159506	−	0.159506i	−0.622842	−	0.782348i	$-0.714022\pi$
$337$	2.92814	−	2.92814i	0.159506	−	0.159506i	0.782348	+	0.622842i	$0.214022\pi$
$338$	−14.5045	−	2.71023i	−0.788939	−	0.147417i
$339$	10.1532	−	10.1532i	0.551444	−	0.551444i
$340$	6.28007	−	8.22211i	0.340585	−	0.445907i
$341$	12.6989	+	12.6989i	0.687685	+	0.687685i
$342$	−7.77114	+	5.32421i	−0.420215	+	0.287900i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−6.00512	−	3.71635i	−0.323774	−	0.200372i
$345$	−11.8892	+	40.9100i	−0.640092	+	2.20252i
$346$	−0.884054	−	0.165190i	−0.0475270	−	0.00888066i
$347$		−	21.4335i		−	1.15061i	−0.817939	−	0.575305i	$-0.804883\pi$
$347$		−	21.4335i		−	1.15061i	0.817939	−	0.575305i	$-0.195117\pi$
$348$	−14.8792	+	6.57248i	−0.797609	+	0.352322i
$349$	21.0849	+	21.0849i	1.12865	+	1.12865i	0.990397	+	0.138252i	$0.0441483\pi$
$349$	21.0849	+	21.0849i	1.12865	+	1.12865i	0.138252	+	0.990397i	$0.455852\pi$
$350$	−0.247571	−	7.06673i	−0.0132332	−	0.377733i
$351$			21.3332i			1.13868i
$352$	−19.6901	−	2.73914i	−1.04949	−	0.145997i
$353$	1.99903	+	1.99903i	0.106398	+	0.106398i	0.758302	−	0.651904i	$-0.226029\pi$
$353$	1.99903	+	1.99903i	0.106398	+	0.106398i	−0.651904	+	0.758302i	$0.726029\pi$
$354$	−36.8011	+	25.2134i	−1.95596	+	1.34008i
$355$	23.9065	−	13.1401i	1.26882	−	0.697403i
$356$	11.8047	+	4.57112i	0.625646	+	0.242269i
$357$	6.37724			0.337519
$358$	29.4585	−	20.1827i	1.55693	−	1.06669i
$359$		−	27.1270i		−	1.43171i	−0.698251	−	0.715853i	$-0.746038\pi$
$359$		−	27.1270i		−	1.43171i	0.698251	−	0.715853i	$-0.253962\pi$
$360$	−29.0460	−	1.50020i	−1.53086	−	0.0790674i
$361$			16.9020i			0.889578i
$362$	17.3995	+	25.3961i	0.914500	+	1.33479i
$363$	3.72164			0.195335
$364$	8.85615	−	3.91196i	0.464189	−	0.205042i
$365$	4.81687	−	16.5746i	0.252126	−	0.867553i
$366$	12.6668	+	18.4883i	0.662104	+	0.966398i
$367$	14.2201	+	14.2201i	0.742284	+	0.742284i	0.973017	−	0.230733i	$-0.0741125\pi$
$367$	14.2201	+	14.2201i	0.742284	+	0.742284i	−0.230733	+	0.973017i	$0.574113\pi$
$368$	−1.28509	−	27.6167i	−0.0669897	−	1.43962i
$369$			31.9479i			1.66314i
$370$	25.8108	−	8.49176i	1.34184	−	0.441465i
$371$	−3.97050	−	3.97050i	−0.206138	−	0.206138i
$372$	−26.2728	−	10.1736i	−1.36218	−	0.527478i
$373$			17.4713i			0.904631i	0.891858	+	0.452315i	$0.149402\pi$
$373$			17.4713i			0.904631i	−0.891858	+	0.452315i	$0.850598\pi$
$374$	2.11186	−	11.3021i	0.109202	−	0.584420i
$375$	−30.7581	−	1.94291i	−1.58834	−	0.100332i
$376$	6.61087	+	28.0794i	0.340930	+	1.44808i
$377$	−10.0993	−	10.0993i	−0.520141	−	0.520141i
$378$	−3.52250	−	5.14138i	−0.181178	−	0.264444i
$379$	20.2052	+	20.2052i	1.03787	+	1.03787i	0.999254	+	0.0386164i	$0.0122950\pi$
$379$	20.2052	+	20.2052i	1.03787	+	1.03787i	0.0386164	+	0.999254i	$0.487705\pi$
$380$	3.93194	−	5.14784i	0.201704	−	0.264079i
$381$	36.5109	−	36.5109i	1.87051	−	1.87051i
$382$	3.86249	−	20.6711i	0.197622	−	1.05762i
$383$	17.2009	−	17.2009i	0.878923	−	0.878923i	−0.114501	−	0.993423i	$-0.536527\pi$
$383$	17.2009	−	17.2009i	0.878923	−	0.878923i	0.993423	+	0.114501i	$0.0365268\pi$
$384$	29.9920	−	8.55046i	1.53052	−	0.436339i
$385$	−3.78511	−	6.88646i	−0.192907	−	0.350967i
$386$	2.42070	+	3.53321i	0.123210	+	0.179836i
$387$	−11.4821			−0.583668
$388$	−17.1352	+	7.56900i	−0.869909	+	0.384258i
$389$	−10.1366	+	10.1366i	−0.513945	+	0.513945i	−0.915733	−	0.401788i	$-0.868389\pi$
$389$	−10.1366	+	10.1366i	−0.513945	+	0.513945i	0.401788	+	0.915733i	$0.368389\pi$
$390$	−13.1877	−	40.0842i	−0.667786	−	2.02974i
$391$	15.9899			0.808642
$392$	−1.48843	+	2.40511i	−0.0751773	+	0.121476i
$393$	−29.4186	+	29.4186i	−1.48397	+	1.48397i
$394$	−9.98166	−	1.86512i	−0.502869	−	0.0939635i
$395$	22.6778	−	12.4647i	1.14104	−	0.627169i
$396$	−29.5661	+	13.0600i	−1.48575	+	0.656290i
$397$		−	26.9825i		−	1.35421i	−0.735884	−	0.677107i	$-0.763233\pi$
$397$		−	26.9825i		−	1.35421i	0.735884	−	0.677107i	$-0.236767\pi$
$398$	2.92630	−	15.6608i	0.146682	−	0.785007i
$399$	3.99277			0.199889
$400$	19.2953	−	5.26217i	0.964766	−	0.263109i
$401$	−12.6110			−0.629766			−0.314883	−	0.949131i	$-0.601965\pi$
$401$	−12.6110			−0.629766			−0.314883	+	0.949131i	$0.601965\pi$
$402$	7.79193	−	41.7004i	0.388626	−	2.07983i
$403$		−	24.7381i		−	1.23229i
$404$	−6.26283	−	14.1782i	−0.311587	−	0.705392i
$405$	3.22957	−	1.77512i	0.160479	−	0.0882063i
$406$	4.10156	+	0.766396i	0.203557	+	0.0380356i
$407$	21.3520	−	21.3520i	1.05838	−	1.05838i
$408$	4.13365	+	17.5575i	0.204646	+	0.869226i
$409$	30.9798			1.53185			0.765925	−	0.642930i	$-0.222281\pi$
$409$	30.9798			1.53185			0.765925	+	0.642930i	$0.222281\pi$
$410$	−6.86573	−	20.8684i	−0.339074	−	1.03062i
$411$	−27.3878	+	27.3878i	−1.35094	+	1.35094i
$412$	−4.24568	−	9.61166i	−0.209170	−	0.473533i
$413$	11.4432			0.563081
$414$	−25.4057	−	37.0819i	−1.24862	−	1.82247i
$415$	−3.08044	−	5.60441i	−0.151213	−	0.275110i
$416$	16.5107	+	21.8467i	0.809503	+	1.07112i
$417$	10.1908	−	10.1908i	0.499046	−	0.499046i
$418$	1.32223	−	7.07624i	0.0646724	−	0.346110i
$419$	4.37756	−	4.37756i	0.213858	−	0.213858i	−0.592046	−	0.805904i	$-0.701680\pi$
$419$	4.37756	−	4.37756i	0.213858	−	0.213858i	0.805904	+	0.592046i	$0.201680\pi$
$420$	9.79693	+	7.48292i	0.478041	+	0.365129i
$421$	12.5006	+	12.5006i	0.609242	+	0.609242i	0.942748	−	0.333506i	$-0.108232\pi$
$421$	12.5006	+	12.5006i	0.609242	+	0.609242i	−0.333506	+	0.942748i	$0.608232\pi$
$422$	22.9023	+	33.4279i	1.11487	+	1.62725i
$423$	33.1648	+	33.1648i	1.61253	+	1.61253i
$424$	8.35775	−	13.5050i	0.405888	−	0.655861i
$425$	2.52144	+	11.2892i	0.122308	+	0.547605i
$426$	−8.73556	+	46.7505i	−0.423239	+	2.26507i
$427$		−	5.74886i		−	0.278207i
$428$	−0.545598	+	1.40898i	−0.0263725	+	0.0681055i
$429$	−33.1597	−	33.1597i	−1.60096	−	1.60096i
$430$	7.50014	−	2.46755i	0.361689	−	0.118996i
$431$			3.76636i			0.181419i	0.995877	+	0.0907096i	$0.0289135\pi$
$431$			3.76636i			0.181419i	−0.995877	+	0.0907096i	$0.971086\pi$
$432$	11.8718	−	13.0306i	0.571181	−	0.626933i
$433$	0.265304	+	0.265304i	0.0127497	+	0.0127497i	0.713453	−	0.700703i	$-0.247130\pi$
$433$	0.265304	+	0.265304i	0.0127497	+	0.0127497i	−0.700703	+	0.713453i	$0.747130\pi$
$434$	4.08472	+	5.96200i	0.196073	+	0.286185i
$435$	5.07524	−	17.4636i	0.243339	−	0.837316i
$436$	4.71047	+	10.6639i	0.225591	+	0.510707i
$437$	10.0112			0.478901
$438$	17.0078	+	24.8244i	0.812666	+	1.18616i
$439$		−	22.7533i		−	1.08595i	−0.839748	−	0.542977i	$-0.817297\pi$
$439$		−	22.7533i		−	1.08595i	0.839748	−	0.542977i	$-0.182703\pi$
$440$	16.5060	−	14.8847i	0.786894	−	0.709601i
$441$			4.59869i			0.218985i
$442$	−13.0656	+	8.95158i	−0.621467	+	0.425783i
$443$	8.76302			0.416344			0.208172	−	0.978092i	$-0.433249\pi$
$443$	8.76302			0.416344			0.208172	+	0.978092i	$0.433249\pi$
$444$	−17.1060	+	44.1752i	−0.811813	+	2.09646i
$445$	−12.4029	+	6.81721i	−0.587955	+	0.323167i
$446$	−12.4779	+	8.54894i	−0.590846	+	0.404804i
$447$	−37.1590	−	37.1590i	−1.75756	−	1.75756i
$448$	−7.58643	−	2.53892i	−0.358425	−	0.119953i
$449$			27.0012i			1.27427i	0.770753	+	0.637134i	$0.219880\pi$
$449$			27.0012i			1.27427i	−0.770753	+	0.637134i	$0.780120\pi$
$450$	22.1743	−	23.7844i	1.04531	−	1.12121i
$451$	−17.2634	−	17.2634i	−0.812904	−	0.812904i
$452$	−4.20941	−	9.52953i	−0.197994	−	0.448232i
$453$			4.14128i			0.194574i
$454$	33.7589	+	6.30801i	1.58438	+	0.296050i
$455$	−3.02080	+	10.3944i	−0.141617	+	0.487297i
$456$	2.58807	+	10.9927i	0.121197	+	0.514781i
$457$	0.580944	+	0.580944i	0.0271754	+	0.0271754i	0.720564	−	0.693389i	$-0.243883\pi$
$457$	0.580944	+	0.580944i	0.0271754	+	0.0271754i	−0.693389	+	0.720564i	$0.743883\pi$
$458$	−22.9481	+	15.7223i	−1.07229	+	0.734657i
$459$	7.20913	+	7.20913i	0.336493	+	0.336493i
$460$	24.5642	+	18.7622i	1.14531	+	0.874792i
$461$	8.34383	−	8.34383i	0.388611	−	0.388611i	−0.485581	−	0.874192i	$-0.661392\pi$
$461$	8.34383	−	8.34383i	0.388611	−	0.388611i	0.874192	+	0.485581i	$0.161392\pi$
$462$	13.4669	+	2.51635i	0.626536	+	0.117071i
$463$	−29.3567	+	29.3567i	−1.36432	+	1.36432i	−0.496002	+	0.868321i	$0.665199\pi$
$463$	−29.3567	+	29.3567i	−1.36432	+	1.36432i	−0.868321	+	0.496002i	$0.834801\pi$
$464$	0.548575	+	11.7890i	0.0254670	+	0.547290i
$465$	27.6043	−	15.1726i	1.28012	−	0.703612i
$466$	17.1083	−	11.7213i	0.792526	−	0.542980i
$467$	9.81342			0.454111			0.227056	−	0.973882i	$-0.427090\pi$
$467$	9.81342			0.454111			0.227056	+	0.973882i	$0.427090\pi$
$468$	41.5189	+	16.0774i	1.91921	+	0.743177i
$469$	−7.69473	+	7.69473i	−0.355309	+	0.355309i
$470$	−28.7906	−	14.5361i	−1.32801	−	0.670499i
$471$	−53.8201			−2.47990
$472$	7.41732	+	31.5048i	0.341410	+	1.45012i
$473$	6.20450	−	6.20450i	0.285283	−	0.285283i
$474$	−8.28659	+	44.3477i	−0.380616	+	2.03696i
$475$	1.57867	+	7.06812i	0.0724342	+	0.324308i
$476$	1.67079	−	4.31474i	0.0765807	−	0.197766i
$477$		−	25.8223i		−	1.18232i
$478$	−5.09866	−	0.952710i	−0.233207	−	0.0435759i
$479$	6.71897			0.306997			0.153499	−	0.988149i	$-0.450946\pi$
$479$	6.71897			0.306997			0.153499	+	0.988149i	$0.450946\pi$
$480$	−14.2514	+	31.8228i	−0.650483	+	1.45250i
$481$	−41.5947			−1.89656
$482$	17.2273	+	3.21900i	0.784681	+	0.146621i
$483$			19.0525i			0.866917i
$484$	0.975045	−	2.51800i	0.0443202	−	0.114455i
$485$	5.84475	−	20.1115i	0.265396	−	0.913214i
$486$	−4.61428	+	24.6945i	−0.209308	+	1.12016i
$487$	5.98522	−	5.98522i	0.271216	−	0.271216i	−0.558373	−	0.829590i	$-0.688574\pi$
$487$	5.98522	−	5.98522i	0.271216	−	0.271216i	0.829590	+	0.558373i	$0.188574\pi$
$488$	15.8275	−	3.72634i	0.716477	−	0.168684i
$489$	−7.86539			−0.355685
$490$	−0.988279	−	3.00388i	−0.0446459	−	0.135702i
$491$	15.4101	−	15.4101i	0.695448	−	0.695448i	−0.267977	−	0.963425i	$-0.586355\pi$
$491$	15.4101	−	15.4101i	0.695448	−	0.695448i	0.963425	+	0.267977i	$0.0863552\pi$
$492$	35.7164	+	13.8305i	1.61022	+	0.623525i
$493$	−6.82573			−0.307415
$494$	−8.18033	+	5.60456i	−0.368050	+	0.252161i
$495$	10.0849	−	34.7015i	0.453281	−	1.55972i
$496$	−13.7666	+	15.1104i	−0.618140	+	0.678475i
$497$	8.62659	−	8.62659i	0.386955	−	0.386955i
$498$	10.9598	+	2.04788i	0.491118	+	0.0917678i
$499$	−4.98932	+	4.98932i	−0.223353	+	0.223353i	−0.809909	−	0.586556i	$-0.800483\pi$
$499$	−4.98932	+	4.98932i	−0.223353	+	0.223353i	0.586556	+	0.809909i	$0.300483\pi$
$500$	−9.37297	+	20.3014i	−0.419172	+	0.907907i
$501$	25.8002	+	25.8002i	1.15267	+	1.15267i
$502$	20.2778	−	13.8929i	0.905044	−	0.620069i
$503$	−9.96195	−	9.96195i	−0.444181	−	0.444181i	0.449233	−	0.893415i	$-0.351697\pi$
$503$	−9.96195	−	9.96195i	−0.444181	−	0.444181i	−0.893415	+	0.449233i	$0.851697\pi$
$504$	−12.6609	+	2.98082i	−0.563962	+	0.132776i
$505$	16.6408	+	4.83612i	0.740507	+	0.215205i
$506$	33.7660	+	6.30934i	1.50108	+	0.280485i
$507$			28.7613i			1.27733i
$508$	−15.1371	−	34.2683i	−0.671598	−	1.52041i
$509$	−2.99819	−	2.99819i	−0.132892	−	0.132892i	0.637532	−	0.770424i	$-0.279955\pi$
$509$	−2.99819	−	2.99819i	−0.132892	−	0.132892i	−0.770424	+	0.637532i	$0.779955\pi$
$510$	−18.0022	−	9.08913i	−0.797151	−	0.402473i
$511$		−	7.71905i		−	0.341471i
$512$	2.07261	−	22.5323i	0.0915974	−	0.995796i
$513$	4.51361	+	4.51361i	0.199281	+	0.199281i
$514$	−9.87733	+	6.76722i	−0.435670	+	0.298489i
$515$	11.2811	+	3.27850i	0.497106	+	0.144468i
$516$	−4.97068	+	12.8365i	−0.218822	+	0.565096i
$517$	−35.8420			−1.57633
$518$	10.0245	−	6.86805i	0.440452	−	0.301765i
$519$			1.75302i			0.0769488i
$520$	−30.5754	−	1.57919i	−1.34082	−	0.0692521i
$521$			22.1577i			0.970748i	0.874307	+	0.485374i	$0.161317\pi$
$521$			22.1577i			0.970748i	−0.874307	+	0.485374i	$0.838683\pi$
$522$	10.8452	+	15.8294i	0.474680	+	0.692836i
$523$	−1.20225			−0.0525706			−0.0262853	−	0.999654i	$-0.508368\pi$
$523$	−1.20225			−0.0525706			−0.0262853	+	0.999654i	$0.508368\pi$
$524$	12.1967	+	27.6116i	0.532813	+	1.20622i
$525$	−13.4514	+	3.00438i	−0.587069	+	0.131122i
$526$	−6.44543	−	9.40765i	−0.281034	−	0.410193i
$527$	−8.35977	−	8.35977i	−0.364157	−	0.364157i
$528$	1.80117	+	38.7075i	0.0783859	+	1.68453i
$529$			24.7709i			1.07700i
$530$	5.54932	+	16.8672i	0.241047	+	0.732664i
$531$	37.2105	+	37.2105i	1.61480	+	1.61480i
$532$	1.04608	−	2.70144i	0.0453533	−	0.117122i
$533$			33.6301i			1.45668i
$534$	4.53210	−	24.2546i	0.196123	−	1.04960i
$535$	−0.813686	−	1.48038i	−0.0351787	−	0.0640025i
$536$	−26.1724	−	16.1971i	−1.13048	−	0.699609i
$537$	−49.2174	−	49.2174i	−2.12389	−	2.12389i
$538$	−19.9248	−	29.0820i	−0.859020	−	1.25381i
$539$	−2.48496	−	2.48496i	−0.107035	−	0.107035i
$540$	2.61586	+	19.5340i	0.112569	+	0.840607i
$541$	23.1670	−	23.1670i	0.996029	−	0.996029i	−0.00396338	−	0.999992i	$-0.501262\pi$
$541$	23.1670	−	23.1670i	0.996029	−	0.996029i	0.999992	+	0.00396338i	$0.00126159\pi$
$542$	−5.47901	+	29.3223i	−0.235344	+	1.25950i
$543$	42.4304	−	42.4304i	1.82086	−	1.82086i
$544$	12.9621	+	1.80319i	0.555746	+	0.0773112i
$545$	−12.5161	−	3.63740i	−0.536131	−	0.155809i
$546$	−10.6661	−	15.5681i	−0.456467	−	0.666253i
$547$	7.51457			0.321300			0.160650	−	0.987011i	$-0.448641\pi$
$547$	7.51457			0.321300			0.160650	+	0.987011i	$0.448641\pi$
$548$	11.3547	+	25.7056i	0.485050	+	1.09809i
$549$	18.6940	−	18.6940i	0.797838	−	0.797838i
$550$	0.870030	+	24.8344i	0.0370982	+	1.05894i
$551$	−4.27357			−0.182060
$552$	−52.4544	+	12.3496i	−2.23261	+	0.525633i
$553$	8.18322	−	8.18322i	0.347986	−	0.347986i
$554$	44.9190	+	8.39334i	1.90843	+	0.356599i
$555$	−25.5112	−	46.4139i	−1.08289	−	1.97016i
$556$	−4.22501	−	9.56486i	−0.179180	−	0.405640i
$557$			12.5088i			0.530015i	0.964246	+	0.265007i	$0.0853744\pi$
$557$			12.5088i			0.530015i	−0.964246	+	0.265007i	$0.914626\pi$
$558$	−6.10447	+	32.6696i	−0.258423	+	1.38301i
$559$	−12.0867			−0.511212
$560$	7.62955	−	4.66797i	0.322408	−	0.197258i
$561$	−22.4113			−0.946207
$562$	0.554671	−	2.96846i	0.0233974	−	0.125217i
$563$		−	11.1356i		−	0.469310i	−0.972079	−	0.234655i	$-0.924604\pi$
$563$		−	11.1356i		−	0.469310i	0.972079	−	0.234655i	$-0.0753961\pi$
$564$	51.4341	−	22.7196i	2.16577	−	0.956667i
$565$	11.1847	+	3.25048i	0.470545	+	0.136749i
$566$	15.5741	+	2.91009i	0.654628	+	0.122320i
$567$	1.16538	−	1.16538i	0.0489414	−	0.0489414i
$568$	29.3420	+	18.1587i	1.23116	+	0.761921i
$569$	−38.9443			−1.63263			−0.816316	−	0.577606i	$-0.803987\pi$
$569$	−38.9443			−1.63263			−0.816316	+	0.577606i	$0.803987\pi$
$570$	−11.2711	−	5.69068i	−0.472096	−	0.238356i
$571$	0.910506	−	0.910506i	0.0381035	−	0.0381035i	−0.687798	−	0.725902i	$-0.741423\pi$
$571$	0.910506	−	0.910506i	0.0381035	−	0.0381035i	0.725902	+	0.687798i	$0.241423\pi$
$572$	−31.1229	+	13.7477i	−1.30131	+	0.574819i
$573$	−40.9892			−1.71235
$574$	−5.55294	−	8.10499i	−0.231775	−	0.338296i
$575$	−33.7272	+	7.53299i	−1.40652	+	0.314147i
$576$	−16.4133	−	32.9253i	−0.683888	−	1.37189i
$577$	8.65158	−	8.65158i	0.360170	−	0.360170i	−0.503705	−	0.863875i	$-0.668030\pi$
$577$	8.65158	−	8.65158i	0.360170	−	0.360170i	0.863875	+	0.503705i	$0.168030\pi$
$578$	3.02562	−	16.1923i	0.125849	−	0.673512i
$579$	5.90308	−	5.90308i	0.245324	−	0.245324i
$580$	−10.4859	−	8.00917i	−0.435404	−	0.332563i
$581$	−2.02234	−	2.02234i	−0.0839007	−	0.0839007i
$582$	20.6372	+	30.1217i	0.855439	+	1.24859i
$583$	13.9534	+	13.9534i	0.577891	+	0.577891i
$584$	21.2517	−	5.00340i	0.879402	−	0.207042i
$585$	−43.6231	+	23.9772i	−1.80359	+	0.991336i
$586$	−2.80595	+	15.0167i	−0.115913	+	0.620334i
$587$			28.3456i			1.16995i	0.811051	+	0.584975i	$0.198896\pi$
$587$			28.3456i			1.16995i	−0.811051	+	0.584975i	$0.801104\pi$
$588$	5.14115	+	1.99081i	0.212018	+	0.0820995i
$589$	−5.23403	−	5.23403i	−0.215664	−	0.215664i
$590$	−32.3027	−	16.3093i	−1.32988	−	0.671444i
$591$			19.7929i			0.814171i
$592$	25.4066	+	23.1472i	1.04420	+	0.951345i
$593$	17.0187	+	17.0187i	0.698876	+	0.698876i	0.964168	−	0.265292i	$-0.0854683\pi$
$593$	17.0187	+	17.0187i	0.698876	+	0.698876i	−0.265292	+	0.964168i	$0.585468\pi$
$594$	12.3790	+	18.0682i	0.507917	+	0.741348i
$595$	2.49176	+	4.53340i	0.102152	+	0.185851i
$596$	−34.8766	+	15.4058i	−1.42860	+	0.631044i
$597$	−31.0543			−1.27097
$598$	−26.7435	−	39.0344i	−1.09362	−	1.59624i
$599$			27.7975i			1.13578i	0.823106	+	0.567888i	$0.192239\pi$
$599$			27.7975i			1.13578i	−0.823106	+	0.567888i	$0.807761\pi$
$600$	−16.9906	−	35.0864i	−0.693638	−	1.43240i
$601$			11.6173i			0.473880i	0.971524	+	0.236940i	$0.0761445\pi$
$601$			11.6173i			0.473880i	−0.971524	+	0.236940i	$0.923856\pi$
$602$	2.91294	−	1.99573i	0.118723	−	0.0813400i
$603$	−50.0429			−2.03791
$604$	2.80192	+	1.08499i	0.114009	+	0.0441476i
$605$	1.45415	+	2.64561i	0.0591195	+	0.107559i
$606$	−24.9236	+	17.0758i	−1.01245	+	0.693658i
$607$	−1.46563	−	1.46563i	−0.0594882	−	0.0594882i	0.676737	−	0.736225i	$-0.263394\pi$
$607$	−1.46563	−	1.46563i	−0.0594882	−	0.0594882i	−0.736225	+	0.676737i	$0.763394\pi$
$608$	8.11555	+	1.12897i	0.329129	+	0.0457859i
$609$		−	8.13309i		−	0.329569i
$610$	−8.19354	+	16.2284i	−0.331747	+	0.657067i
$611$	34.9111	+	34.9111i	1.41235	+	1.41235i
$612$	19.4636	−	8.59748i	0.786767	−	0.347533i
$613$			11.1696i			0.451137i	0.974227	+	0.225568i	$0.0724239\pi$
$613$			11.1696i			0.451137i	−0.974227	+	0.225568i	$0.927576\pi$
$614$	−17.1544	−	3.20539i	−0.692297	−	0.129359i
$615$	−37.5265	+	20.6263i	−1.51321	+	0.831731i
$616$	5.23076	−	8.45221i	0.210753	−	0.340549i
$617$	−16.6541	−	16.6541i	−0.670468	−	0.670468i	0.287356	−	0.957824i	$-0.407224\pi$
$617$	−16.6541	−	16.6541i	−0.670468	−	0.670468i	−0.957824	+	0.287356i	$0.907224\pi$
$618$	−16.8962	+	11.5760i	−0.679664	+	0.465656i
$619$	−0.0485986	−	0.0485986i	−0.00195334	−	0.00195334i	0.706129	−	0.708083i	$-0.250440\pi$
$619$	−0.0485986	−	0.0485986i	−0.00195334	−	0.00195334i	−0.708083	+	0.706129i	$0.750440\pi$
$620$	−3.03337	−	22.6518i	−0.121823	−	0.909716i
$621$	−21.5378	+	21.5378i	−0.864282	+	0.864282i
$622$	−11.2036	−	2.09345i	−0.449224	−	0.0839396i
$623$	−4.47556	+	4.47556i	−0.179310	+	0.179310i
$624$	35.9477	−	39.4565i	1.43906	−	1.57952i
$625$	−10.6369	−	22.6242i	−0.425476	−	0.904970i
$626$	−9.55911	+	6.54920i	−0.382059	+	0.261759i
$627$	−14.0317			−0.560371
$628$	−14.1005	+	36.4138i	−0.562672	+	1.45307i
$629$	−14.0561	+	14.0561i	−0.560455	+	0.560455i
$630$	6.55427	−	12.9816i	0.261128	−	0.517198i
$631$	13.0513			0.519565			0.259782	−	0.965667i	$-0.416349\pi$
$631$	13.0513			0.519565			0.259782	+	0.965667i	$0.416349\pi$
$632$	27.8339	+	17.2254i	1.10717	+	0.685189i
$633$	55.8494	−	55.8494i	2.21981	−	2.21981i
$634$	5.96747	−	31.9364i	0.236999	−	1.26836i
$635$	40.2204	+	11.6888i	1.59610	+	0.463854i
$636$	−28.8682	−	11.1786i	−1.14470	−	0.443262i
$637$			4.84084i			0.191801i
$638$	−14.4140	−	2.69332i	−0.570655	−	0.106630i
$639$	56.1033			2.21941
$640$	17.7970	+	17.9796i	0.703489	+	0.710707i
$641$	34.2117			1.35128			0.675641	−	0.737231i	$-0.263867\pi$
$641$	34.2117			1.35128			0.675641	+	0.737231i	$0.263867\pi$
$642$	2.89498	+	0.540941i	0.114256	+	0.0213492i
$643$			28.6521i			1.12993i	0.825115	+	0.564965i	$0.191110\pi$
$643$			28.6521i			1.12993i	−0.825115	+	0.564965i	$0.808890\pi$
$644$	12.8906	+	4.99162i	0.507960	+	0.196697i
$645$	−7.41310	−	13.4871i	−0.291890	−	0.531052i
$646$	−0.870433	+	4.65833i	−0.0342467	+	0.183280i
$647$	−2.27054	+	2.27054i	−0.0892640	+	0.0892640i	−0.750329	−	0.661065i	$-0.770105\pi$
$647$	−2.27054	+	2.27054i	−0.0892640	+	0.0892640i	0.661065	+	0.750329i	$0.270105\pi$
$648$	3.96386	+	2.45309i	0.155715	+	0.0963664i
$649$	−40.2144			−1.57855
$650$	23.3419	−	25.0368i	0.915546	−	0.982024i
$651$	9.96095	−	9.96095i	0.390400	−	0.390400i
$652$	−2.06068	+	5.32159i	−0.0807025	+	0.208410i
$653$	−4.22100			−0.165181			−0.0825903	−	0.996584i	$-0.526319\pi$
$653$	−4.22100			−0.165181			−0.0825903	+	0.996584i	$0.526319\pi$
$654$	18.7459	−	12.8433i	0.733021	−	0.502212i
$655$	−32.4075	−	9.41820i	−1.26627	−	0.367999i
$656$	18.7149	−	20.5417i	0.730695	−	0.802017i
$657$	25.1005	−	25.1005i	0.979266	−	0.979266i
$658$	−14.1782	−	2.64926i	−0.552722	−	0.103279i
$659$	−11.9000	+	11.9000i	−0.463559	+	0.463559i	−0.899820	−	0.436261i	$-0.856302\pi$
$659$	−11.9000	+	11.9000i	−0.463559	+	0.463559i	0.436261	+	0.899820i	$0.356302\pi$
$660$	−34.4290	−	26.2970i	−1.34015	−	1.02361i
$661$	−30.9844	−	30.9844i	−1.20515	−	1.20515i	−0.972578	−	0.232576i	$-0.925285\pi$
$661$	−30.9844	−	30.9844i	−1.20515	−	1.20515i	−0.232576	−	0.972578i	$-0.574715\pi$
$662$	−13.0849	+	8.96481i	−0.508559	+	0.348427i
$663$	21.8292	+	21.8292i	0.847777	+	0.847777i
$664$	4.25695	−	6.87866i	0.165202	−	0.266944i
$665$	1.56009	+	2.83835i	0.0604975	+	0.110067i
$666$	54.9307	+	10.2641i	2.12852	+	0.397725i
$667$		−	20.3924i		−	0.789596i
$668$	24.2155	−	10.6965i	0.936926	−	0.413861i
$669$	20.8474	+	20.8474i	0.806005	+	0.806005i
$670$	32.6882	−	10.7544i	1.26286	−	0.415480i
$671$			20.2030i			0.779930i
$672$	−2.14856	+	15.4448i	−0.0828827	+	0.595796i
$673$	−13.4783	−	13.4783i	−0.519551	−	0.519551i	0.397884	−	0.917436i	$-0.369745\pi$
$673$	−13.4783	−	13.4783i	−0.519551	−	0.519551i	−0.917436	+	0.397884i	$0.869745\pi$
$674$	−4.83118	+	3.30996i	−0.186090	+	0.127495i
$675$	−18.6024	−	11.8098i	−0.716008	−	0.454561i
$676$	19.4594	+	7.53528i	0.748440	+	0.289818i
$677$	6.46862			0.248609			0.124305	−	0.992244i	$-0.460330\pi$
$677$	6.46862			0.248609			0.124305	+	0.992244i	$0.460330\pi$
$678$	−16.7518	+	11.4771i	−0.643350	+	0.440776i
$679$		−	9.36624i		−	0.359443i
$680$	−10.8660	+	9.79870i	−0.416693	+	0.375763i
$681$		−	66.9414i		−	2.56520i
$682$	−14.3548	−	20.9521i	−0.549674	−	0.802296i
$683$	−42.9729			−1.64431			−0.822155	−	0.569263i	$-0.807229\pi$
$683$	−42.9729			−1.64431			−0.822155	+	0.569263i	$0.807229\pi$
$684$	12.1861	−	5.38286i	0.465946	−	0.205819i
$685$	−30.1704	−	8.76806i	−1.15275	−	0.335010i
$686$	−0.799311	−	1.16666i	−0.0305178	−	0.0445434i
$687$	38.3403	+	38.3403i	1.46278	+	1.46278i
$688$	7.38269	+	6.72617i	0.281463	+	0.256433i
$689$		−	27.1819i		−	1.03555i
$690$	27.1545	−	53.7829i	1.03375	−	2.04748i
$691$	2.17093	+	2.17093i	0.0825860	+	0.0825860i	0.747193	−	0.664607i	$-0.231401\pi$
$691$	2.17093	+	2.17093i	0.0825860	+	0.0825860i	−0.664607	+	0.747193i	$0.731401\pi$
$692$	1.18606	+	0.459279i	0.0450873	+	0.0174591i
$693$		−	16.1611i		−	0.613908i
$694$	−5.56750	+	29.7959i	−0.211340	+	1.13104i
$695$	11.2262	+	3.26253i	0.425834	+	0.123755i
$696$	22.3916	−	5.27177i	0.848753	−	0.199826i
$697$	11.3646	+	11.3646i	0.430466	+	0.430466i
$698$	−23.8343	−	34.7882i	−0.902141	−	1.31675i
$699$	−28.5835	−	28.5835i	−1.08113	−	1.08113i
$700$	−1.49147	+	9.88815i	−0.0563723	+	0.373737i
$701$	1.86030	−	1.86030i	0.0702627	−	0.0702627i	−0.671102	−	0.741365i	$-0.734179\pi$
$701$	1.86030	−	1.86030i	0.0702627	−	0.0702627i	0.741365	+	0.671102i	$0.234179\pi$
$702$	5.54144	−	29.6564i	0.209148	−	1.11931i
$703$	−8.80051	+	8.80051i	−0.331917	+	0.331917i
$704$	26.6608	+	8.92247i	1.00481	+	0.336278i
$705$	−17.5440	+	60.3678i	−0.660744	+	2.27358i
$706$	−2.25970	−	3.29822i	−0.0850449	−	0.124130i
$707$	7.74991			0.291465
$708$	57.7085	−	25.4911i	2.16882	−	0.958015i
$709$	19.6414	−	19.6414i	0.737649	−	0.737649i	−0.234473	−	0.972123i	$-0.575337\pi$
$709$	19.6414	−	19.6414i	0.737649	−	0.737649i	0.972123	+	0.234473i	$0.0753366\pi$
$710$	−36.6469	+	12.0568i	−1.37533	+	0.452485i
$711$	53.2199			1.99590
$712$	−15.2229	−	9.42090i	−0.570503	−	0.353063i
$713$	24.9754	−	24.9754i	0.935337	−	0.935337i
$714$	−8.86534	−	1.65653i	−0.331777	−	0.0619941i
$715$	10.6159	−	36.5287i	0.397012	−	1.36610i
$716$	−46.1944	+	20.4051i	−1.72636	+	0.762574i
$717$			10.1103i			0.377575i
$718$	−7.04642	+	37.7106i	−0.262970	+	1.40735i
$719$	−13.6872			−0.510445			−0.255222	−	0.966882i	$-0.582149\pi$
$719$	−13.6872			−0.510445			−0.255222	+	0.966882i	$0.582149\pi$
$720$	39.9887	+	9.63040i	1.49029	+	0.358904i
$721$	5.25380			0.195662
$722$	4.39041	−	23.4963i	0.163394	−	0.874443i
$723$		−	34.1604i		−	1.27044i
$724$	−17.5912	−	39.8242i	−0.653772	−	1.48005i
$725$	14.3974	−	3.21567i	0.534707	−	0.119427i
$726$	−5.17365	−	0.966722i	−0.192012	−	0.0358784i
$727$	25.6782	−	25.6782i	0.952350	−	0.952350i	−0.0465653	−	0.998915i	$-0.514828\pi$
$727$	25.6782	−	25.6782i	0.952350	−	0.952350i	0.998915	+	0.0465653i	$0.0148275\pi$
$728$	−13.3276	+	3.13778i	−0.493953	+	0.116294i
$729$	44.0230			1.63048
$730$	−11.0015	+	21.7900i	−0.407185	+	0.806483i
$731$	−4.08446	+	4.08446i	−0.151069	+	0.151069i
$732$	−12.8063	−	28.9918i	−0.473336	−	1.07157i
$733$	−10.9558			−0.404663			−0.202332	−	0.979317i	$-0.564852\pi$
$733$	−10.9558			−0.404663			−0.202332	+	0.979317i	$0.564852\pi$
$734$	−16.0744	−	23.4619i	−0.593315	−	0.865995i
$735$	−5.40170	+	2.96902i	−0.199245	+	0.109514i
$736$	−5.38717	+	38.7253i	−0.198574	+	1.42743i
$737$	27.0414	−	27.0414i	0.996081	−	0.996081i
$738$	8.29868	−	44.4124i	0.305479	−	1.63484i
$739$	11.1809	−	11.1809i	0.411294	−	0.411294i	−0.470895	−	0.882189i	$-0.656069\pi$
$739$	11.1809	−	11.1809i	0.411294	−	0.411294i	0.882189	+	0.470895i	$0.156069\pi$
$740$	−38.0867	+	5.10032i	−1.40009	+	0.187492i
$741$	13.6672	+	13.6672i	0.502078	+	0.502078i
$742$	4.48823	+	6.55096i	0.164768	+	0.240493i
$743$	−3.74955	−	3.74955i	−0.137558	−	0.137558i	0.634975	−	0.772533i	$-0.281010\pi$
$743$	−3.74955	−	3.74955i	−0.137558	−	0.137558i	−0.772533	+	0.634975i	$0.781010\pi$
$744$	33.8806	+	20.9675i	1.24212	+	0.768704i
$745$	11.8962	−	40.9343i	0.435845	−	1.49972i
$746$	4.53830	−	24.2878i	0.166159	−	0.889240i
$747$		−	13.1523i		−	0.481219i
$748$	−5.87162	+	15.1631i	−0.214688	+	0.554420i
$749$	−0.534193	−	0.534193i	−0.0195190	−	0.0195190i
$750$	42.2538	+	10.6906i	1.54289	+	0.390365i
$751$			6.56902i			0.239707i	0.992792	+	0.119854i	$0.0382425\pi$
$751$			6.56902i			0.239707i	−0.992792	+	0.119854i	$0.961758\pi$
$752$	−1.89630	−	40.7519i	−0.0691510	−	1.48607i
$753$	−33.8790	−	33.8790i	−1.23462	−	1.23462i
$754$	11.4162	+	16.6630i	0.415754	+	0.606829i
$755$	−2.94392	+	1.61811i	−0.107140	+	0.0588892i
$756$	3.56130	+	8.06230i	0.129523	+	0.293223i
$757$	35.7256			1.29847			0.649234	−	0.760589i	$-0.275090\pi$
$757$	35.7256			1.29847			0.649234	+	0.760589i	$0.275090\pi$
$758$	−22.8399	−	33.3367i	−0.829581	−	1.21084i
$759$		−	66.9555i		−	2.43033i
$760$	−6.80318	+	6.13494i	−0.246777	+	0.222538i
$761$		−	23.5949i		−	0.855315i	−0.903941	−	0.427658i	$-0.859339\pi$
$761$		−	23.5949i		−	0.855315i	0.903941	−	0.427658i	$-0.140661\pi$
$762$	−60.2397	+	41.2718i	−2.18225	+	1.49512i
$763$	−5.82895			−0.211022
$764$	−10.7389	+	27.7326i	−0.388520	+	1.00333i
$765$	−6.63893	+	22.8442i	−0.240031	+	0.825934i
$766$	−28.3799	+	19.4438i	−1.02541	+	0.702532i
$767$	39.1698	+	39.1698i	1.41434	+	1.41434i
$768$	−43.9146	+	4.09581i	−1.58463	+	0.147795i
$769$		−	20.1520i		−	0.726700i	−0.931653	−	0.363350i	$-0.881633\pi$
$769$		−	20.1520i		−	0.726700i	0.931653	−	0.363350i	$-0.118367\pi$
$770$	3.47308	+	10.5565i	0.125161	+	0.380428i
$771$	16.5025	+	16.5025i	0.594322	+	0.594322i
$772$	−2.44736	−	5.54050i	−0.0880825	−	0.199407i
$773$			5.06146i			0.182048i	0.995849	+	0.0910240i	$0.0290140\pi$
$773$			5.06146i			0.182048i	−0.995849	+	0.0910240i	$0.970986\pi$
$774$	15.9619	+	2.98255i	0.573738	+	0.107206i
$775$	21.5715	+	13.6948i	0.774873	+	0.491932i
$776$	25.7867	−	6.07108i	0.925688	−	0.217939i
$777$	−16.7484	−	16.7484i	−0.600844	−	0.600844i
$778$	16.7245	−	11.4584i	0.599601	−	0.410802i
$779$	7.11536	+	7.11536i	0.254934	+	0.254934i
$780$	7.92081	+	59.1487i	0.283611	+	2.11786i
$781$	−30.3162	+	30.3162i	−1.08480	+	1.08480i
$782$	−22.2284	−	4.15348i	−0.794885	−	0.148528i
$783$	9.19402	−	9.19402i	0.328568	−	0.328568i
$784$	2.69390	−	2.95684i	0.0962106	−	0.105602i
$785$	−21.0290	−	38.2592i	−0.750558	−	1.36553i
$786$	48.5380	−	33.2546i	1.73129	−	1.18615i
$787$	11.1184			0.396328			0.198164	−	0.980169i	$-0.436502\pi$
$787$	11.1184			0.396328			0.198164	+	0.980169i	$0.436502\pi$
$788$	13.3916	+	5.18561i	0.477054	+	0.184730i
$789$	−15.7178	+	15.7178i	−0.559567	+	0.559567i
$790$	−34.7634	+	11.4372i	−1.23683	+	0.406917i
$791$	5.20891			0.185208
$792$	44.4939	−	10.4754i	1.58102	−	0.372227i
$793$	19.6783	−	19.6783i	0.698796	−	0.698796i
$794$	−7.00890	+	37.5099i	−0.248737	+	1.33118i
$795$	30.3313	−	16.6714i	1.07574	−	0.591275i
$796$	−8.13602	+	21.0108i	−0.288374	+	0.744709i
$797$			24.7966i			0.878340i	0.898404	+	0.439170i	$0.144727\pi$
$797$			24.7966i			0.878340i	−0.898404	+	0.439170i	$0.855273\pi$
$798$	−5.55056	−	1.03715i	−0.196488	−	0.0367147i
$799$	23.5950			0.834732
$800$	−28.1903	+	2.30313i	−0.996679	+	0.0814280i
$801$	−29.1070			−1.02844
$802$	17.5313	+	3.27581i	0.619051	+	0.115673i
$803$			27.1268i			0.957285i
$804$	−21.6639	+	55.9460i	−0.764029	+	1.97306i
$805$	−13.5439	+	7.44433i	−0.477359	+	0.262378i
$806$	−6.42590	+	34.3898i	−0.226343	+	1.21133i
$807$	−48.5885	+	48.5885i	−1.71040	+	1.71040i
$808$	5.02340	+	21.3367i	0.176723	+	0.750622i
$809$	−42.9948			−1.51162			−0.755808	−	0.654793i	$-0.772756\pi$
$809$	−42.9948			−1.51162			−0.755808	+	0.654793i	$0.772756\pi$
$810$	−4.95069	+	1.62878i	−0.173950	+	0.0572296i
$811$	−13.1430	+	13.1430i	−0.461514	+	0.461514i	−0.899151	−	0.437638i	$-0.855815\pi$
$811$	−13.1430	+	13.1430i	−0.461514	+	0.461514i	0.437638	+	0.899151i	$0.355815\pi$
$812$	−5.50272	−	2.13082i	−0.193107	−	0.0747770i
$813$	58.1439			2.03920
$814$	−35.2288	+	24.1362i	−1.23477	+	0.845973i
$815$	−3.07323	−	5.59129i	−0.107650	−	0.195854i
$816$	−1.18572	−	25.4814i	−0.0415086	−	0.892027i
$817$	−2.55727	+	2.55727i	−0.0894675	+	0.0894675i
$818$	−43.0666	−	8.04721i	−1.50579	−	0.281364i
$819$	−15.7413	+	15.7413i	−0.550045	+	0.550045i
$820$	4.12370	+	30.7938i	0.144006	+	1.07536i
$821$	6.71849	+	6.71849i	0.234477	+	0.234477i	0.814558	−	0.580082i	$-0.196979\pi$
$821$	6.71849	+	6.71849i	0.234477	+	0.234477i	−0.580082	+	0.814558i	$0.696979\pi$
$822$	45.1874	−	30.9591i	1.57609	−	1.07982i
$823$	20.1460	+	20.1460i	0.702246	+	0.702246i	0.964892	−	0.262646i	$-0.0845952\pi$
$823$	20.1460	+	20.1460i	0.702246	+	0.702246i	−0.262646	+	0.964892i	$0.584595\pi$
$824$	3.40545	+	14.4645i	0.118635	+	0.503896i
$825$	47.2720	−	10.5582i	1.64580	−	0.367590i
$826$	−15.9077	−	2.97244i	−0.553501	−	0.103424i
$827$			26.8726i			0.934451i	0.884138	+	0.467225i	$0.154746\pi$
$827$			26.8726i			0.934451i	−0.884138	+	0.467225i	$0.845254\pi$
$828$	25.6856	+	58.1488i	0.892637	+	2.02081i
$829$	15.5232	+	15.5232i	0.539144	+	0.539144i	0.923277	−	0.384134i	$-0.125500\pi$
$829$	15.5232	+	15.5232i	0.539144	+	0.539144i	−0.384134	+	0.923277i	$0.625500\pi$
$830$	2.82649	+	8.59115i	0.0981091	+	0.298203i
$831$		−	89.0711i		−	3.08984i
$832$	−17.2776	−	34.6590i	−0.598991	−	1.20158i
$833$	1.63587	+	1.63587i	0.0566794	+	0.0566794i
$834$	−16.8139	+	11.5196i	−0.582218	+	0.398893i
$835$	−8.25981	+	28.4215i	−0.285842	+	0.983568i
$836$	−3.67621	+	9.49360i	−0.127144	+	0.328343i
$837$	22.5207			0.778428
$838$	−7.22259	+	4.94838i	−0.249500	+	0.170939i
$839$			50.9551i			1.75917i	0.475746	+	0.879583i	$0.342178\pi$
$839$			50.9551i			1.75917i	−0.475746	+	0.879583i	$0.657822\pi$
$840$	−11.6755	−	12.9472i	−0.402843	−	0.446722i
$841$		−	20.2949i		−	0.699825i
$842$	−14.1306	−	20.6249i	−0.486973	−	0.710780i
$843$	−5.88624			−0.202733
$844$	−23.1546	−	52.4190i	−0.797015	−	1.80434i
$845$	−20.4456	+	11.2378i	−0.703351	+	0.386594i
$846$	−37.4893	−	54.7189i	−1.28891	−	1.88127i
$847$	0.954662	+	0.954662i	0.0328026	+	0.0328026i
$848$	−15.1266	+	16.6031i	−0.519449	+	0.570151i
$849$		−	30.8823i		−	1.05988i
$850$	−0.572746	−	16.3486i	−0.0196450	−	0.560754i
$851$	−41.9937	−	41.9937i	−1.43953	−	1.43953i
$852$	24.2875	−	62.7212i	0.832077	−	2.14879i
$853$			47.4000i			1.62294i	0.584391	+	0.811472i	$0.301334\pi$
$853$			47.4000i			1.62294i	−0.584391	+	0.811472i	$0.698666\pi$
$854$	−1.49331	+	7.99180i	−0.0510999	+	0.273474i
$855$	−4.15662	+	14.3027i	−0.142153	+	0.489142i
$856$	1.12446	−	1.81697i	0.0384331	−	0.0621028i
$857$	17.6753	+	17.6753i	0.603778	+	0.603778i	0.941313	−	0.337535i	$-0.109593\pi$
$857$	17.6753	+	17.6753i	0.603778	+	0.603778i	−0.337535	+	0.941313i	$0.609593\pi$
$858$	37.4836	+	54.7105i	1.27967	+	1.86779i
$859$	−10.3000	−	10.3000i	−0.351431	−	0.351431i	0.509211	−	0.860642i	$-0.329937\pi$
$859$	−10.3000	−	10.3000i	−0.351431	−	0.351431i	−0.860642	+	0.509211i	$0.829937\pi$
$860$	−11.0673	+	1.48206i	−0.377392	+	0.0505379i
$861$	−13.5413	+	13.5413i	−0.461488	+	0.461488i
$862$	0.978338	−	5.23582i	0.0333223	−	0.178333i
$863$	3.80338	−	3.80338i	0.129469	−	0.129469i	−0.639403	−	0.768872i	$-0.720818\pi$
$863$	3.80338	−	3.80338i	0.129469	−	0.129469i	0.768872	+	0.639403i	$0.220818\pi$
$864$	−19.8884	+	15.0307i	−0.676616	+	0.511354i
$865$	−1.24617	+	0.684952i	−0.0423711	+	0.0232891i
$866$	−0.299899	−	0.437728i	−0.0101910	−	0.0148746i
$867$	−32.1082			−1.09045
$868$	−4.12971	−	9.34912i	−0.140172	−	0.317330i
$869$	−28.7580	+	28.7580i	−0.975550	+	0.975550i
$870$	−11.5916	+	22.9588i	−0.392994	+	0.778375i
$871$	−52.6780			−1.78492
$872$	−3.77826	−	16.0480i	−0.127948	−	0.543454i
$873$	30.4568	−	30.4568i	1.03081	−	1.03081i
$874$	−13.9171	−	2.60048i	−0.470754	−	0.0879626i
$875$	−7.39158	−	8.38836i	−0.249881	−	0.283578i
$876$	−17.1952	−	38.9276i	−0.580971	−	1.31524i
$877$			20.5582i			0.694203i	0.937828	+	0.347101i	$0.112834\pi$
$877$			20.5582i			0.694203i	−0.937828	+	0.347101i	$0.887166\pi$
$878$	−5.91032	+	31.6305i	−0.199464	+	1.06748i
$879$	29.7770			1.00435
$880$	−26.8123	+	16.4045i	−0.903843	+	0.552995i
$881$	50.4861			1.70092			0.850461	−	0.526039i	$-0.176323\pi$
$881$	50.4861			1.70092			0.850461	+	0.526039i	$0.176323\pi$
$882$	1.19454	−	6.39289i	0.0402223	−	0.215260i
$883$		−	0.350512i		−	0.0117957i	−0.999983	−	0.00589784i	$-0.998123\pi$
$883$		−	0.350512i		−	0.0117957i	0.999983	−	0.00589784i	$-0.00187735\pi$
$884$	20.4884	−	9.05018i	0.689100	−	0.304391i
$885$	−19.6841	+	67.7320i	−0.661675	+	2.27679i
$886$	−12.1819	−	2.27626i	−0.409260	−	0.0764723i
$887$	−7.80320	+	7.80320i	−0.262006	+	0.262006i	−0.825869	−	0.563863i	$-0.809315\pi$
$887$	−7.80320	+	7.80320i	−0.262006	+	0.262006i	0.563863	+	0.825869i	$0.309315\pi$
$888$	35.2547	−	56.9669i	1.18307	−	1.91168i
$889$	18.7313			0.628227
$890$	19.0128	−	6.25522i	0.637310	−	0.209675i
$891$	−4.09547	+	4.09547i	−0.137203	+	0.137203i
$892$	19.5669	−	8.64311i	0.655147	−	0.289393i
$893$	14.7728			0.494352
$894$	42.0044	+	61.3090i	1.40484	+	2.05048i
$895$	15.7567	−	54.2179i	0.526689	−	1.81231i
$896$	9.88679	+	5.50012i	0.330295	+	0.183746i
$897$	−65.2164	+	65.2164i	−2.17751	+	2.17751i
$898$	7.01376	−	37.5359i	0.234052	−	1.25259i
$899$	−10.6615	+	10.6615i	−0.355580	+	0.355580i
$900$	−37.0039	+	27.3040i	−1.23346	+	0.910135i
$901$	−9.18561	−	9.18561i	−0.306017	−	0.306017i
$902$	19.5145	+	28.4831i	0.649763	+	0.948385i
$903$	−4.86677	−	4.86677i	−0.161956	−	0.161956i
$904$	3.37636	+	14.3409i	0.112296	+	0.476972i
$905$	46.7413	+	13.5839i	1.55373	+	0.451543i
$906$	1.07573	−	5.75702i	0.0357386	−	0.191264i
$907$		−	11.3958i		−	0.378391i	−0.981939	−	0.189195i	$-0.939412\pi$
$907$		−	11.3958i		−	0.378391i	0.981939	−	0.189195i	$-0.0605879\pi$
$908$	−45.2915	−	17.5382i	−1.50305	−	0.582026i
$909$	25.2009	+	25.2009i	0.835861	+	0.835861i
$910$	6.89939	−	13.6651i	0.228712	−	0.452995i
$911$			5.90154i			0.195527i	0.995210	+	0.0977634i	$0.0311688\pi$
$911$			5.90154i			0.195527i	−0.995210	+	0.0977634i	$0.968831\pi$
$912$	−0.742377	−	15.9538i	−0.0245826	−	0.528284i
$913$	7.10704	+	7.10704i	0.235209	+	0.235209i
$914$	−0.656697	−	0.958505i	−0.0217216	−	0.0317045i
$915$	34.0275	+	9.88899i	1.12491	+	0.326920i
$916$	35.9854	−	15.8955i	1.18899	−	0.525203i
$917$	−15.0927			−0.498405
$918$	−8.14917	−	11.8944i	−0.268963	−	0.392574i
$919$		−	8.38806i		−	0.276697i	−0.990384	−	0.138348i	$-0.955821\pi$
$919$		−	8.38806i		−	0.276697i	0.990384	−	0.138348i	$-0.0441794\pi$
$920$	−29.2744	−	32.4630i	−0.965147	−	1.07027i
$921$			34.0160i			1.12087i
$922$	−13.7666	+	9.43184i	−0.453378	+	0.310621i
$923$	59.0575			1.94390
$924$	−18.0674	−	6.99624i	−0.594374	−	0.230159i
$925$	23.0265	−	36.2704i	0.757105	−	1.19256i
$926$	48.4360	−	33.1848i	1.59171	−	1.09052i
$927$	17.0841	+	17.0841i	0.561117	+	0.561117i
$928$	2.29967	−	16.5310i	0.0754902	−	0.542656i
$929$		−	15.9242i		−	0.522456i	−0.965277	−	0.261228i	$-0.915873\pi$
$929$		−	15.9242i		−	0.522456i	0.965277	−	0.261228i	$-0.0841275\pi$
$930$	−42.3154	+	13.9218i	−1.38758	+	0.456514i
$931$	1.02421	+	1.02421i	0.0335672	+	0.0335672i
$932$	−26.8278	+	11.8504i	−0.878775	+	0.388174i
$933$			22.2159i			0.727317i
$934$	−13.6422	−	2.54911i	−0.446385	−	0.0834093i
$935$	−8.75673	−	15.9316i	−0.286376	−	0.521019i
$936$	−53.5415	−	33.1348i	−1.75006	−	1.08305i
$937$	5.02005	+	5.02005i	0.163998	+	0.163998i	0.784335	−	0.620337i	$-0.213004\pi$
$937$	5.02005	+	5.02005i	0.163998	+	0.163998i	−0.620337	+	0.784335i	$0.713004\pi$
$938$	12.6956	−	8.69809i	0.414526	−	0.284003i
$939$	15.9708	+	15.9708i	0.521187	+	0.521187i
$940$	36.2475	+	27.6859i	1.18226	+	0.903015i
$941$	−9.06596	+	9.06596i	−0.295542	+	0.295542i	−0.839265	−	0.543723i	$-0.817014\pi$
$941$	−9.06596	+	9.06596i	−0.295542	+	0.295542i	0.543723	+	0.839265i	$0.317014\pi$
$942$	74.8182	+	13.9802i	2.43771	+	0.455498i
$943$	−33.9527	+	33.9527i	−1.10565	+	1.10565i
$944$	−2.12763	−	45.7232i	−0.0692485	−	1.48816i
$945$	−9.46266	−	2.75002i	−0.307820	−	0.0894581i
$946$	−10.2369	+	7.01354i	−0.332829	+	0.228030i
$947$	−22.0953			−0.718000			−0.359000	−	0.933337i	$-0.616882\pi$
$947$	−22.0953			−0.718000			−0.359000	+	0.933337i	$0.616882\pi$
$948$	23.0393	−	59.4976i	0.748281	−	1.93239i
$949$	26.4222	−	26.4222i	0.857702	−	0.857702i
$950$	−0.358595	−	10.2358i	−0.0116344	−	0.332095i
$951$	−63.3275			−2.05354
$952$	−3.44344	+	5.56414i	−0.111603	+	0.180335i
$953$	18.7860	−	18.7860i	0.608539	−	0.608539i	−0.334025	−	0.942564i	$-0.608407\pi$
$953$	18.7860	−	18.7860i	0.608539	−	0.608539i	0.942564	+	0.334025i	$0.108407\pi$
$954$	−6.70751	+	35.8969i	−0.217164	+	1.16220i
$955$	−16.0156	−	29.1381i	−0.518253	−	0.942887i
$956$	6.84045	+	2.64883i	0.221236	+	0.0856691i
$957$			28.5819i			0.923920i
$958$	−9.34039	−	1.74530i	−0.301774	−	0.0563880i
$959$	−14.0509			−0.453726
$960$	28.0778	−	40.5366i	0.906207	−	1.30831i
$961$	4.88484			0.157576
$962$	57.8231	+	10.8045i	1.86429	+	0.348352i
$963$		−	3.47414i		−	0.111953i
$964$	−23.1124	−	8.94981i	−0.744400	−	0.288254i
$965$	6.50284	+	1.88984i	0.209334	+	0.0608361i
$966$	4.94901	−	26.4859i	0.159232	−	0.852168i
$967$	3.53862	−	3.53862i	0.113794	−	0.113794i	−0.647917	−	0.761711i	$-0.724360\pi$
$967$	3.53862	−	3.53862i	0.113794	−	0.113794i	0.761711	+	0.647917i	$0.224360\pi$
$968$	−2.00953	+	3.24713i	−0.0645888	+	0.104367i
$969$	9.23714			0.296740
$970$	−13.3492	+	26.4398i	−0.428617	+	0.848931i
$971$	−17.2283	+	17.2283i	−0.552881	+	0.552881i	−0.927271	−	0.374390i	$-0.877852\pi$
$971$	−17.2283	+	17.2283i	−0.552881	+	0.552881i	0.374390	+	0.927271i	$0.377852\pi$
$972$	12.8291	−	33.1305i	0.411494	−	1.06266i
$973$	5.22822			0.167609
$974$	−9.87508	+	6.76567i	−0.316418	+	0.216786i
$975$	−56.3281	−	35.7602i	−1.80394	−	1.14524i
$976$	−22.9706	+	1.06889i	−0.735270	+	0.0342143i
$977$	10.6098	−	10.6098i	0.339438	−	0.339438i	−0.516718	−	0.856156i	$-0.672846\pi$
$977$	10.6098	−	10.6098i	0.339438	−	0.339438i	0.856156	+	0.516718i	$0.172846\pi$
$978$	10.9341	+	2.04309i	0.349634	+	0.0653308i
$979$	15.7283	−	15.7283i	0.502680	−	0.502680i
$980$	0.593581	+	4.43257i	0.0189612	+	0.141593i
$981$	−18.9544	−	18.9544i	−0.605167	−	0.605167i
$982$	−25.4253	+	17.4195i	−0.811354	+	0.555879i
$983$	−0.221714	−	0.221714i	−0.00707158	−	0.00707158i	0.703562	−	0.710634i	$-0.251592\pi$
$983$	−0.221714	−	0.221714i	−0.00707158	−	0.00707158i	−0.710634	+	0.703562i	$0.751592\pi$
$984$	−46.0587	−	28.5040i	−1.46830	−	0.908676i
$985$	−14.0702	+	7.73363i	−0.448315	+	0.246414i
$986$	9.48881	+	1.77303i	0.302185	+	0.0564648i
$987$			28.1143i			0.894887i
$988$	12.8277	−	5.66629i	0.408105	−	0.180269i
$989$	−12.2026	−	12.2026i	−0.388021	−	0.388021i
$990$	−23.0335	+	45.6208i	−0.732052	+	1.44992i
$991$		−	17.4578i		−	0.554565i	−0.960788	−	0.277283i	$-0.910566\pi$
$991$		−	17.4578i		−	0.554565i	0.960788	−	0.277283i	$-0.0894338\pi$
$992$	23.0627	−	17.4297i	0.732243	−	0.553394i
$993$	21.8615	+	21.8615i	0.693753	+	0.693753i
$994$	−14.2331	+	9.75146i	−0.451446	+	0.309298i
$995$	−12.1338	−	22.0756i	−0.384667	−	0.699845i
$996$	−14.7038	−	5.69374i	−0.465907	−	0.180413i
$997$	17.6800			0.559932			0.279966	−	0.960010i	$-0.409677\pi$
$997$	17.6800			0.559932			0.279966	+	0.960010i	$0.409677\pi$
$998$	8.23194	−	5.63991i	0.260577	−	0.178528i
$999$		−	37.8663i		−	1.19804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.6	✓	144
5.2	odd	4		560.2.bl.a.267.42	yes	144
16.3	odd	4		560.2.bl.a.323.42	yes	144
80.67	even	4	inner	560.2.t.a.547.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.6	✓	144	1.1	even	1	trivial
560.2.t.a.547.6	yes	144	80.67	even	4	inner
560.2.bl.a.267.42	yes	144	5.2	odd	4
560.2.bl.a.323.42	yes	144	16.3	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39015 - 0.259757i) q^{2} +2.75657i q^{3} +(1.86505 + 0.722204i) q^{4} +(-1.95957 + 1.07707i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.40511 - 1.48843i) q^{8} -4.59869 q^{9} +O(q^{10})\)	\(q+(-1.39015 - 0.259757i) q^{2} +2.75657i q^{3} +(1.86505 + 0.722204i) q^{4} +(-1.95957 + 1.07707i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.40511 - 1.48843i) q^{8} -4.59869 q^{9} +(3.00388 - 0.988279i) q^{10} +(2.48496 - 2.48496i) q^{11} +(-1.99081 + 5.14115i) q^{12} -4.84084 q^{13} +(1.16666 - 0.799311i) q^{14} +(-2.96902 - 5.40170i) q^{15} +(2.95684 + 2.69390i) q^{16} +(-1.63587 + 1.63587i) q^{17} +(6.39289 + 1.19454i) q^{18} +(-1.02421 + 1.02421i) q^{19} +(-4.43257 + 0.593581i) q^{20} +(-1.94919 - 1.94919i) q^{21} +(-4.09997 + 2.80899i) q^{22} +(-4.88728 - 4.88728i) q^{23} +(4.10298 - 6.62987i) q^{24} +(2.67984 - 4.22119i) q^{25} +(6.72951 + 1.25744i) q^{26} -4.40691i q^{27} +(-1.82947 + 0.808116i) q^{28} +(2.08627 + 2.08627i) q^{29} +(2.72426 + 8.28042i) q^{30} +5.11030i q^{31} +(-3.41071 - 4.51299i) q^{32} +(6.84999 + 6.84999i) q^{33} +(2.69903 - 1.84918i) q^{34} +(0.624023 - 2.14723i) q^{35} +(-8.57681 - 3.32120i) q^{36} +8.59247 q^{37} +(1.68986 - 1.15777i) q^{38} -13.3441i q^{39} +(6.31614 + 0.326223i) q^{40} -6.94716i q^{41} +(2.20336 + 3.21599i) q^{42} +2.49682 q^{43} +(6.42924 - 2.83994i) q^{44} +(9.01147 - 4.95311i) q^{45} +(5.52456 + 8.06357i) q^{46} +(-7.21178 - 7.21178i) q^{47} +(-7.42592 + 8.15075i) q^{48} -1.00000i q^{49} +(-4.82188 + 5.17199i) q^{50} +(-4.50939 - 4.50939i) q^{51} +(-9.02842 - 3.49607i) q^{52} +5.61513i q^{53} +(-1.14473 + 6.12629i) q^{54} +(-2.19299 + 7.54595i) q^{55} +(2.75315 - 0.648188i) q^{56} +(-2.82331 - 2.82331i) q^{57} +(-2.35831 - 3.44216i) q^{58} +(-8.09154 - 8.09154i) q^{59} +(-1.63625 - 12.2187i) q^{60} +(-4.06506 + 4.06506i) q^{61} +(1.32744 - 7.10410i) q^{62} +(3.25177 - 3.25177i) q^{63} +(3.56912 + 7.15970i) q^{64} +(9.48597 - 5.21392i) q^{65} +(-7.74320 - 11.3019i) q^{66} +10.8820 q^{67} +(-4.23241 + 1.86955i) q^{68} +(13.4721 - 13.4721i) q^{69} +(-1.42525 + 2.82288i) q^{70} -12.1998 q^{71} +(11.0604 + 6.84486i) q^{72} +(-5.45819 + 5.45819i) q^{73} +(-11.9448 - 2.23195i) q^{74} +(11.6360 + 7.38718i) q^{75} +(-2.64990 + 1.17052i) q^{76} +3.51427i q^{77} +(-3.46623 + 18.5504i) q^{78} -11.5728 q^{79} +(-8.69566 - 2.09416i) q^{80} -1.64810 q^{81} +(-1.80457 + 9.65762i) q^{82} +2.86002i q^{83} +(-2.22763 - 5.04306i) q^{84} +(1.44366 - 4.96754i) q^{85} +(-3.47096 - 0.648566i) q^{86} +(-5.75096 + 5.75096i) q^{87} +(-9.67532 + 2.27791i) q^{88} +6.32940 q^{89} +(-13.8139 + 4.54479i) q^{90} +(3.42299 - 3.42299i) q^{91} +(-5.58542 - 12.6446i) q^{92} -14.0869 q^{93} +(8.15217 + 11.8988i) q^{94} +(0.903869 - 3.11016i) q^{95} +(12.4404 - 9.40186i) q^{96} +(-6.62293 + 6.62293i) q^{97} +(-0.259757 + 1.39015i) q^{98} +(-11.4276 + 11.4276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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