LMFDB - Embedded newform 560.2.t.a.547.6

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			547.6
Character	$\chi$	$=$	560.547
Dual form			560.2.t.a.43.6

$q$-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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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	$-0.707075\pi$
$3$		−	2.75657i		−	1.59151i	0.605620	−	0.795754i	$-0.292925\pi$
$4$	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	0.974337	−	0.225092i	$-0.0722684\pi$
$11$	2.48496	+	2.48496i	0.749245	+	0.749245i	−0.225092	+	0.974337i	$0.572268\pi$
$12$	−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	0.480331	−	0.877087i	$-0.340516\pi$
$17$	−1.63587	−	1.63587i	−0.396756	−	0.396756i	−0.877087	+	0.480331i	$0.840516\pi$
$18$	6.39289	−	1.19454i	1.50682	−	0.281556i
$19$	−1.02421	−	1.02421i	−0.234970	−	0.234970i	0.579793	−	0.814764i	$-0.303133\pi$
$19$	−1.02421	−	1.02421i	−0.234970	−	0.234970i	−0.814764	+	0.579793i	$0.803133\pi$
$20$	−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	−0.0192526	+	0.999815i	$0.506129\pi$
$23$	−4.88728	+	4.88728i	−1.01907	+	1.01907i	−0.999815	+	0.0192526i	$0.993871\pi$
$24$	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	−0.486352	−	0.873763i	$-0.661673\pi$
$29$	2.08627	−	2.08627i	0.387411	−	0.387411i	0.873763	+	0.486352i	$0.161673\pi$
$30$	2.72426	−	8.28042i	0.497380	−	1.51179i
$31$		−	5.11030i		−	0.917837i	−0.888478	−	0.458918i	$-0.848237\pi$
$31$		−	5.11030i		−	0.917837i	0.888478	−	0.458918i	$-0.151763\pi$
$32$	−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	$0.182515\pi$
$41$			6.94716i			1.08496i	−0.840067	+	0.542482i	$0.817485\pi$
$42$	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	−0.0533712	+	0.998575i	$0.516997\pi$
$47$	−7.21178	+	7.21178i	−1.05195	+	1.05195i	−0.998575	+	0.0533712i	$0.983003\pi$
$48$	−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	$-0.873978\pi$
$53$		−	5.61513i		−	0.771297i	0.922646	−	0.385649i	$-0.126022\pi$
$54$	−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	−0.0549384	+	0.998490i	$0.517496\pi$
$59$	−8.09154	+	8.09154i	−1.05343	+	1.05343i	−0.998490	+	0.0549384i	$0.982504\pi$
$60$	−1.63625	+	12.2187i	−0.211239	+	1.57743i
$61$	−4.06506	−	4.06506i	−0.520477	−	0.520477i	0.397238	−	0.917716i	$-0.369969\pi$
$61$	−4.06506	−	4.06506i	−0.520477	−	0.520477i	−0.917716	+	0.397238i	$0.869969\pi$
$62$	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	0.311435	−	0.950268i	$-0.399191\pi$
$73$	−5.45819	−	5.45819i	−0.638833	−	0.638833i	−0.950268	+	0.311435i	$0.899191\pi$
$74$	−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	$-0.949829\pi$
$83$		−	2.86002i		−	0.313928i	0.987604	−	0.156964i	$-0.0501706\pi$
$84$	−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	0.285825	−	0.958282i	$-0.407732\pi$
$97$	−6.62293	−	6.62293i	−0.672457	−	0.672457i	−0.958282	+	0.285825i	$0.907732\pi$
$98$	−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	−0.925072	−	0.379791i	$-0.875996\pi$
$101$	−5.48001	+	5.48001i	−0.545282	+	0.545282i	0.379791	+	0.925072i	$0.375996\pi$
$102$	5.09740	−	7.44008i	0.504717	−	0.736678i
$103$	−3.71500	+	3.71500i	−0.366050	+	0.366050i	−0.866034	−	0.499984i	$-0.833339\pi$
$103$	−3.71500	+	3.71500i	−0.366050	+	0.366050i	0.499984	+	0.866034i	$0.333339\pi$
$104$	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	$-0.988374\pi$
$107$		−	0.755462i		−	0.0730333i	0.999333	−	0.0365167i	$-0.0116262\pi$
$108$	3.18269	+	8.21913i	0.306255	+	0.790886i
$109$	4.12169	−	4.12169i	0.394786	−	0.394786i	−0.481603	−	0.876389i	$-0.659945\pi$
$109$	4.12169	−	4.12169i	0.394786	−	0.394786i	0.876389	+	0.481603i	$0.159945\pi$
$110$	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	−0.858801	−	0.512309i	$-0.828790\pi$
$113$	−3.68326	+	3.68326i	−0.346492	+	0.346492i	0.512309	+	0.858801i	$0.328790\pi$
$114$	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	−0.194379	+	0.980926i	$0.562269\pi$
$127$	−13.2450	+	13.2450i	−1.17531	+	1.17531i	−0.980926	+	0.194379i	$0.937731\pi$
$128$	−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	−0.0654271	−	0.997857i	$-0.520841\pi$
$131$	10.6722	−	10.6722i	0.932430	−	0.932430i	0.997857	+	0.0654271i	$0.0208410\pi$
$132$	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	−0.141145	−	0.989989i	$-0.545079\pi$
$137$	9.93546	−	9.93546i	0.848843	−	0.848843i	0.989989	+	0.141145i	$0.0450785\pi$
$138$	−22.2278	−	15.2288i	−1.89216	−	1.29637i
$139$	−3.69691	+	3.69691i	−0.313568	+	0.313568i	−0.846290	−	0.532722i	$-0.821169\pi$
$139$	−3.69691	+	3.69691i	−0.313568	+	0.313568i	0.532722	+	0.846290i	$0.321169\pi$
$140$	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	−0.993881	−	0.110455i	$-0.964769\pi$
$149$	−13.4801	−	13.4801i	−1.10434	−	1.10434i	−0.110455	−	0.993881i	$-0.535231\pi$
$150$	−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	$-0.715674\pi$
$157$		−	19.5243i		−	1.55821i	0.626895	−	0.779104i	$-0.284326\pi$
$158$	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	$-0.964356\pi$
$163$		−	2.85332i		−	0.223489i	0.993737	−	0.111745i	$-0.0356439\pi$
$164$	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	0.969470	−	0.245208i	$-0.0788563\pi$
$167$	9.35953	+	9.35953i	0.724262	+	0.724262i	−0.245208	+	0.969470i	$0.578856\pi$
$168$	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	−0.901283	−	0.433231i	$-0.857374\pi$
$179$	−17.8546	−	17.8546i	−1.33451	−	1.33451i	−0.433231	−	0.901283i	$-0.642626\pi$
$180$	20.3840	+	2.72970i	1.51934	+	0.203459i
$181$	−15.3924	+	15.3924i	−1.14411	+	1.14411i	−0.156420	+	0.987691i	$0.549995\pi$
$181$	−15.3924	+	15.3924i	−1.14411	+	1.14411i	−0.987691	+	0.156420i	$0.950005\pi$
$182$	−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	$-0.819194\pi$
$191$		−	14.8696i		−	1.07593i	0.842968	−	0.537964i	$-0.180806\pi$
$192$	−19.7362	−	9.83855i	−1.42434	−	0.710036i
$193$	−2.14146	+	2.14146i	−0.154146	+	0.154146i	−0.779967	−	0.625821i	$-0.784764\pi$
$193$	−2.14146	+	2.14146i	−0.154146	+	0.154146i	0.625821	+	0.779967i	$0.284764\pi$
$194$	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	$-0.869254\pi$
$199$		−	11.2655i		−	0.798593i	0.916822	−	0.399297i	$-0.130746\pi$
$200$	−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	−0.580592	+	0.814195i	$0.697179\pi$
$211$	−20.2604	+	20.2604i	−1.39479	+	1.39479i	−0.814195	+	0.580592i	$0.802821\pi$
$212$	−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	0.913432	−	0.406991i	$-0.133422\pi$
$223$	7.56278	+	7.56278i	0.506441	+	0.506441i	−0.406991	+	0.913432i	$0.633422\pi$
$224$	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	0.996965	−	0.0778522i	$-0.0248062\pi$
$229$	13.9087	+	13.9087i	0.919113	+	0.919113i	−0.0778522	+	0.996965i	$0.524806\pi$
$230$	−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	0.280534	−	0.959844i	$-0.409488\pi$
$233$	−10.3692	−	10.3692i	−0.679310	−	0.679310i	−0.959844	+	0.280534i	$0.909488\pi$
$234$	−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	0.203351	−	0.979106i	$-0.434817\pi$
$251$	−12.2903	−	12.2903i	−0.775755	−	0.775755i	−0.979106	+	0.203351i	$0.934817\pi$
$252$	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	0.868726	−	0.495293i	$-0.164939\pi$
$257$	5.98659	+	5.98659i	0.373433	+	0.373433i	−0.495293	+	0.868726i	$0.664939\pi$
$258$	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	−0.509108	−	0.860703i	$-0.670024\pi$
$263$	5.70192	−	5.70192i	0.351595	−	0.351595i	0.860703	+	0.509108i	$0.170024\pi$
$264$	−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	0.0777265	−	0.996975i	$-0.475234\pi$
$269$	17.6264	−	17.6264i	1.07470	−	1.07470i	0.996975	−	0.0777265i	$-0.0247661\pi$
$270$	−4.35526	+	13.2378i	−0.265053	+	0.805630i
$271$			21.0928i			1.28130i	0.767834	+	0.640649i	$0.221335\pi$
$271$			21.0928i			1.28130i	−0.767834	+	0.640649i	$0.778665\pi$
$272$	−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	$-0.979712\pi$
$281$		−	2.13535i		−	0.127384i	0.997970	−	0.0636920i	$-0.0202875\pi$
$282$	−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	$0.102184\pi$
$293$			10.8022i			0.631071i	−0.948914	+	0.315535i	$0.897816\pi$
$294$	−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	0.851628	−	0.524147i	$-0.175616\pi$
$313$	5.79372	+	5.79372i	0.327480	+	0.327480i	−0.524147	+	0.851628i	$0.675616\pi$
$314$	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	$-0.776793\pi$
$317$		−	22.9733i		−	1.29031i	0.764052	−	0.645154i	$-0.223207\pi$
$318$	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	0.890633	−	0.454723i	$-0.150262\pi$
$331$	7.93068	+	7.93068i	0.435909	+	0.435909i	−0.454723	+	0.890633i	$0.650262\pi$
$332$	−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	0.782348	−	0.622842i	$-0.214022\pi$
$337$	2.92814	+	2.92814i	0.159506	+	0.159506i	−0.622842	+	0.782348i	$0.714022\pi$
$338$	−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	$0.195117\pi$
$347$			21.4335i			1.15061i	−0.817939	+	0.575305i	$0.804883\pi$
$348$	−14.8792	−	6.57248i	−0.797609	−	0.352322i
$349$	21.0849	−	21.0849i	1.12865	−	1.12865i	0.138252	−	0.990397i	$-0.455852\pi$
$349$	21.0849	−	21.0849i	1.12865	−	1.12865i	0.990397	−	0.138252i	$-0.0441483\pi$
$350$	−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	−0.651904	−	0.758302i	$-0.726029\pi$
$353$	1.99903	−	1.99903i	0.106398	−	0.106398i	0.758302	+	0.651904i	$0.226029\pi$
$354$	−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	$0.253962\pi$
$359$			27.1270i			1.43171i	−0.698251	+	0.715853i	$0.746038\pi$
$360$	−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	−0.230733	−	0.973017i	$-0.574113\pi$
$367$	14.2201	−	14.2201i	0.742284	−	0.742284i	0.973017	+	0.230733i	$0.0741125\pi$
$368$	−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	$-0.850598\pi$
$373$		−	17.4713i		−	0.904631i	0.891858	−	0.452315i	$-0.149402\pi$
$374$	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	0.0386164	−	0.999254i	$-0.487705\pi$
$379$	20.2052	−	20.2052i	1.03787	−	1.03787i	0.999254	−	0.0386164i	$-0.0122950\pi$
$380$	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	0.993423	−	0.114501i	$-0.0365268\pi$
$383$	17.2009	+	17.2009i	0.878923	+	0.878923i	−0.114501	+	0.993423i	$0.536527\pi$
$384$	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	0.401788	−	0.915733i	$-0.368389\pi$
$389$	−10.1366	−	10.1366i	−0.513945	−	0.513945i	−0.915733	+	0.401788i	$0.868389\pi$
$390$	−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	$0.236767\pi$
$397$			26.9825i			1.35421i	−0.735884	+	0.677107i	$0.763233\pi$
$398$	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	0.805904	−	0.592046i	$-0.201680\pi$
$419$	4.37756	+	4.37756i	0.213858	+	0.213858i	−0.592046	+	0.805904i	$0.701680\pi$
$420$	9.79693	−	7.48292i	0.478041	−	0.365129i
$421$	12.5006	−	12.5006i	0.609242	−	0.609242i	−0.333506	−	0.942748i	$-0.608232\pi$
$421$	12.5006	−	12.5006i	0.609242	−	0.609242i	0.942748	+	0.333506i	$0.108232\pi$
$422$	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	$-0.971086\pi$
$431$		−	3.76636i		−	0.181419i	0.995877	−	0.0907096i	$-0.0289135\pi$
$432$	11.8718	+	13.0306i	0.571181	+	0.626933i
$433$	0.265304	−	0.265304i	0.0127497	−	0.0127497i	−0.700703	−	0.713453i	$-0.747130\pi$
$433$	0.265304	−	0.265304i	0.0127497	−	0.0127497i	0.713453	+	0.700703i	$0.247130\pi$
$434$	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	$0.182703\pi$
$439$			22.7533i			1.08595i	−0.839748	+	0.542977i	$0.817297\pi$
$440$	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	$-0.780120\pi$
$449$		−	27.0012i		−	1.27427i	0.770753	−	0.637134i	$-0.219880\pi$
$450$	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	−0.693389	−	0.720564i	$-0.743883\pi$
$457$	0.580944	−	0.580944i	0.0271754	−	0.0271754i	0.720564	+	0.693389i	$0.243883\pi$
$458$	−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	0.874192	−	0.485581i	$-0.161392\pi$
$461$	8.34383	+	8.34383i	0.388611	+	0.388611i	−0.485581	+	0.874192i	$0.661392\pi$
$462$	13.4669	−	2.51635i	0.626536	−	0.117071i
$463$	−29.3567	−	29.3567i	−1.36432	−	1.36432i	−0.868321	−	0.496002i	$-0.834801\pi$
$463$	−29.3567	−	29.3567i	−1.36432	−	1.36432i	−0.496002	−	0.868321i	$-0.665199\pi$
$464$	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	0.829590	−	0.558373i	$-0.188574\pi$
$487$	5.98522	+	5.98522i	0.271216	+	0.271216i	−0.558373	+	0.829590i	$0.688574\pi$
$488$	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	0.963425	−	0.267977i	$-0.0863552\pi$
$491$	15.4101	+	15.4101i	0.695448	+	0.695448i	−0.267977	+	0.963425i	$0.586355\pi$
$492$	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	0.586556	−	0.809909i	$-0.300483\pi$
$499$	−4.98932	−	4.98932i	−0.223353	−	0.223353i	−0.809909	+	0.586556i	$0.800483\pi$
$500$	−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	−0.893415	−	0.449233i	$-0.851697\pi$
$503$	−9.96195	+	9.96195i	−0.444181	+	0.444181i	0.449233	+	0.893415i	$0.351697\pi$
$504$	−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	−0.770424	−	0.637532i	$-0.779955\pi$
$509$	−2.99819	+	2.99819i	−0.132892	+	0.132892i	0.637532	+	0.770424i	$0.279955\pi$
$510$	−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	$-0.838683\pi$
$521$		−	22.1577i		−	0.970748i	0.874307	−	0.485374i	$-0.161317\pi$
$522$	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	0.999992	−	0.00396338i	$-0.00126159\pi$
$541$	23.1670	+	23.1670i	0.996029	+	0.996029i	−0.00396338	+	0.999992i	$0.501262\pi$
$542$	−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	$-0.914626\pi$
$557$		−	12.5088i		−	0.530015i	0.964246	−	0.265007i	$-0.0853744\pi$
$558$	−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	$0.0753961\pi$
$563$			11.1356i			0.469310i	−0.972079	+	0.234655i	$0.924604\pi$
$564$	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	0.725902	−	0.687798i	$-0.241423\pi$
$571$	0.910506	+	0.910506i	0.0381035	+	0.0381035i	−0.687798	+	0.725902i	$0.741423\pi$
$572$	−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	0.863875	−	0.503705i	$-0.168030\pi$
$577$	8.65158	+	8.65158i	0.360170	+	0.360170i	−0.503705	+	0.863875i	$0.668030\pi$
$578$	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	$-0.801104\pi$
$587$		−	28.3456i		−	1.16995i	0.811051	−	0.584975i	$-0.198896\pi$
$588$	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	−0.265292	−	0.964168i	$-0.585468\pi$
$593$	17.0187	−	17.0187i	0.698876	−	0.698876i	0.964168	+	0.265292i	$0.0854683\pi$
$594$	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	$-0.807761\pi$
$599$		−	27.7975i		−	1.13578i	0.823106	−	0.567888i	$-0.192239\pi$
$600$	−16.9906	+	35.0864i	−0.693638	+	1.43240i
$601$		−	11.6173i		−	0.473880i	−0.971524	−	0.236940i	$-0.923856\pi$
$601$		−	11.6173i		−	0.473880i	0.971524	−	0.236940i	$-0.0761445\pi$
$602$	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	−0.736225	−	0.676737i	$-0.763394\pi$
$607$	−1.46563	+	1.46563i	−0.0594882	+	0.0594882i	0.676737	+	0.736225i	$0.263394\pi$
$608$	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	$-0.927576\pi$
$613$		−	11.1696i		−	0.451137i	0.974227	−	0.225568i	$-0.0724239\pi$
$614$	−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	−0.957824	−	0.287356i	$-0.907224\pi$
$617$	−16.6541	+	16.6541i	−0.670468	+	0.670468i	0.287356	+	0.957824i	$0.407224\pi$
$618$	−16.8962	−	11.5760i	−0.679664	−	0.465656i
$619$	−0.0485986	+	0.0485986i	−0.00195334	+	0.00195334i	−0.708083	−	0.706129i	$-0.750440\pi$
$619$	−0.0485986	+	0.0485986i	−0.00195334	+	0.00195334i	0.706129	+	0.708083i	$0.250440\pi$
$620$	−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	$-0.808890\pi$
$643$		−	28.6521i		−	1.12993i	0.825115	−	0.564965i	$-0.191110\pi$
$644$	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	0.661065	−	0.750329i	$-0.270105\pi$
$647$	−2.27054	−	2.27054i	−0.0892640	−	0.0892640i	−0.750329	+	0.661065i	$0.770105\pi$
$648$	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	0.436261	−	0.899820i	$-0.356302\pi$
$659$	−11.9000	−	11.9000i	−0.463559	−	0.463559i	−0.899820	+	0.436261i	$0.856302\pi$
$660$	−34.4290	+	26.2970i	−1.34015	+	1.02361i
$661$	−30.9844	+	30.9844i	−1.20515	+	1.20515i	−0.232576	+	0.972578i	$0.574715\pi$
$661$	−30.9844	+	30.9844i	−1.20515	+	1.20515i	−0.972578	+	0.232576i	$0.925285\pi$
$662$	−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	−0.917436	−	0.397884i	$-0.869745\pi$
$673$	−13.4783	+	13.4783i	−0.519551	+	0.519551i	0.397884	+	0.917436i	$0.369745\pi$
$674$	−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	−0.664607	−	0.747193i	$-0.731401\pi$
$691$	2.17093	−	2.17093i	0.0825860	−	0.0825860i	0.747193	+	0.664607i	$0.231401\pi$
$692$	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	0.741365	−	0.671102i	$-0.234179\pi$
$701$	1.86030	+	1.86030i	0.0702627	+	0.0702627i	−0.671102	+	0.741365i	$0.734179\pi$
$702$	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	0.972123	−	0.234473i	$-0.0753366\pi$
$709$	19.6414	+	19.6414i	0.737649	+	0.737649i	−0.234473	+	0.972123i	$0.575337\pi$
$710$	−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	0.998915	−	0.0465653i	$-0.0148275\pi$
$727$	25.6782	+	25.6782i	0.952350	+	0.952350i	−0.0465653	+	0.998915i	$0.514828\pi$
$728$	−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	0.882189	−	0.470895i	$-0.156069\pi$
$739$	11.1809	+	11.1809i	0.411294	+	0.411294i	−0.470895	+	0.882189i	$0.656069\pi$
$740$	−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	−0.772533	−	0.634975i	$-0.781010\pi$
$743$	−3.74955	+	3.74955i	−0.137558	+	0.137558i	0.634975	+	0.772533i	$0.281010\pi$
$744$	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	$-0.961758\pi$
$751$		−	6.56902i		−	0.239707i	0.992792	−	0.119854i	$-0.0382425\pi$
$752$	−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	$0.140661\pi$
$761$			23.5949i			0.855315i	−0.903941	+	0.427658i	$0.859339\pi$
$762$	−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	$0.118367\pi$
$769$			20.1520i			0.726700i	−0.931653	+	0.363350i	$0.881633\pi$
$770$	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	$-0.970986\pi$
$773$		−	5.06146i		−	0.182048i	0.995849	−	0.0910240i	$-0.0290140\pi$
$774$	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	$-0.855273\pi$
$797$		−	24.7966i		−	0.878340i	0.898404	−	0.439170i	$-0.144727\pi$
$798$	−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	0.437638	−	0.899151i	$-0.355815\pi$
$811$	−13.1430	−	13.1430i	−0.461514	−	0.461514i	−0.899151	+	0.437638i	$0.855815\pi$
$812$	−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	−0.580082	−	0.814558i	$-0.696979\pi$
$821$	6.71849	−	6.71849i	0.234477	−	0.234477i	0.814558	+	0.580082i	$0.196979\pi$
$822$	45.1874	+	30.9591i	1.57609	+	1.07982i
$823$	20.1460	−	20.1460i	0.702246	−	0.702246i	−0.262646	−	0.964892i	$-0.584595\pi$
$823$	20.1460	−	20.1460i	0.702246	−	0.702246i	0.964892	+	0.262646i	$0.0845952\pi$
$824$	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	$-0.845254\pi$
$827$		−	26.8726i		−	0.934451i	0.884138	−	0.467225i	$-0.154746\pi$
$828$	25.6856	−	58.1488i	0.892637	−	2.02081i
$829$	15.5232	−	15.5232i	0.539144	−	0.539144i	−0.384134	−	0.923277i	$-0.625500\pi$
$829$	15.5232	−	15.5232i	0.539144	−	0.539144i	0.923277	+	0.384134i	$0.125500\pi$
$830$	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	$-0.657822\pi$
$839$		−	50.9551i		−	1.75917i	0.475746	−	0.879583i	$-0.342178\pi$
$840$	−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	$-0.698666\pi$
$853$		−	47.4000i		−	1.62294i	0.584391	−	0.811472i	$-0.301334\pi$
$854$	−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	−0.337535	−	0.941313i	$-0.609593\pi$
$857$	17.6753	−	17.6753i	0.603778	−	0.603778i	0.941313	+	0.337535i	$0.109593\pi$
$858$	37.4836	−	54.7105i	1.27967	−	1.86779i
$859$	−10.3000	+	10.3000i	−0.351431	+	0.351431i	−0.860642	−	0.509211i	$-0.829937\pi$
$859$	−10.3000	+	10.3000i	−0.351431	+	0.351431i	0.509211	+	0.860642i	$0.329937\pi$
$860$	−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	0.768872	−	0.639403i	$-0.220818\pi$
$863$	3.80338	+	3.80338i	0.129469	+	0.129469i	−0.639403	+	0.768872i	$0.720818\pi$
$864$	−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	$-0.887166\pi$
$877$		−	20.5582i		−	0.694203i	0.937828	−	0.347101i	$-0.112834\pi$
$878$	−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	$0.00187735\pi$
$883$			0.350512i			0.0117957i	−0.999983	+	0.00589784i	$0.998123\pi$
$884$	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	0.563863	−	0.825869i	$-0.309315\pi$
$887$	−7.80320	−	7.80320i	−0.262006	−	0.262006i	−0.825869	+	0.563863i	$0.809315\pi$
$888$	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	$0.0605879\pi$
$907$			11.3958i			0.378391i	−0.981939	+	0.189195i	$0.939412\pi$
$908$	−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	$-0.968831\pi$
$911$		−	5.90154i		−	0.195527i	0.995210	−	0.0977634i	$-0.0311688\pi$
$912$	−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	$0.0441794\pi$
$919$			8.38806i			0.276697i	−0.990384	+	0.138348i	$0.955821\pi$
$920$	−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	$0.0841275\pi$
$929$			15.9242i			0.522456i	−0.965277	+	0.261228i	$0.915873\pi$
$930$	−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	−0.620337	−	0.784335i	$-0.713004\pi$
$937$	5.02005	−	5.02005i	0.163998	−	0.163998i	0.784335	+	0.620337i	$0.213004\pi$
$938$	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	0.543723	−	0.839265i	$-0.317014\pi$
$941$	−9.06596	−	9.06596i	−0.295542	−	0.295542i	−0.839265	+	0.543723i	$0.817014\pi$
$942$	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	0.942564	−	0.334025i	$-0.108407\pi$
$953$	18.7860	+	18.7860i	0.608539	+	0.608539i	−0.334025	+	0.942564i	$0.608407\pi$
$954$	−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	0.761711	−	0.647917i	$-0.224360\pi$
$967$	3.53862	+	3.53862i	0.113794	+	0.113794i	−0.647917	+	0.761711i	$0.724360\pi$
$968$	−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	0.374390	−	0.927271i	$-0.377852\pi$
$971$	−17.2283	−	17.2283i	−0.552881	−	0.552881i	−0.927271	+	0.374390i	$0.877852\pi$
$972$	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	0.856156	−	0.516718i	$-0.172846\pi$
$977$	10.6098	+	10.6098i	0.339438	+	0.339438i	−0.516718	+	0.856156i	$0.672846\pi$
$978$	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	−0.710634	−	0.703562i	$-0.751592\pi$
$983$	−0.221714	+	0.221714i	−0.00707158	+	0.00707158i	0.703562	+	0.710634i	$0.251592\pi$
$984$	−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	$0.0894338\pi$
$991$			17.4578i			0.554565i	−0.960788	+	0.277283i	$0.910566\pi$
$992$	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.547.6	yes	144
5.3	odd	4		560.2.bl.a.323.42	yes	144
16.11	odd	4		560.2.bl.a.267.42	yes	144
80.43	even	4	inner	560.2.t.a.43.6	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.6	✓	144	80.43	even	4	inner
560.2.t.a.547.6	yes	144	1.1	even	1	trivial
560.2.bl.a.267.42	yes	144	16.11	odd	4
560.2.bl.a.323.42	yes	144	5.3	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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