LMFDB - Embedded newform 560.2.bl.a.267.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(267,560)]

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, 1, 0]))

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

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

chi := DirichletCharacter("560.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bl (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			267.42
Character	$\chi$	$=$	560.267
Dual form			560.2.bl.a.323.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.259757 - 1.39015i) q^{2} +2.75657 q^{3} +(-1.86505 - 0.722204i) q^{4} +(1.07707 - 1.95957i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.48843 + 2.40511i) q^{8} +4.59869 q^{9} +O(q^{10})$	\(q+(0.259757 - 1.39015i) q^{2} +2.75657 q^{3} +(-1.86505 - 0.722204i) q^{4} +(1.07707 - 1.95957i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.48843 + 2.40511i) q^{8} +4.59869 q^{9} +(-2.44433 - 2.00630i) q^{10} +(2.48496 - 2.48496i) q^{11} +(-5.14115 - 1.99081i) q^{12} +4.84084i 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} +(1.19454 - 6.39289i) q^{18} +(1.02421 - 1.02421i) q^{19} +(-3.42400 + 2.87684i) q^{20} +(-1.94919 - 1.94919i) q^{21} +(-2.80899 - 4.09997i) 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} +4.40691 q^{27} +(0.808116 + 1.82947i) q^{28} +(-2.08627 - 2.08627i) q^{29} +(-6.73797 - 5.53052i) q^{30} +5.11030i q^{31} +(4.51299 - 3.41071i) q^{32} +(6.84999 - 6.84999i) q^{33} +(-2.69903 + 1.84918i) q^{34} +(-2.14723 + 0.624023i) q^{35} +(-8.57681 - 3.32120i) q^{36} +8.59247i q^{37} +(-1.15777 - 1.68986i) q^{38} +13.3441i q^{39} +(3.10984 + 5.50717i) q^{40} -6.94716i q^{41} +(-3.21599 + 2.20336i) q^{42} -2.49682i q^{43} +(-6.42924 + 2.83994i) q^{44} +(4.95311 - 9.01147i) q^{45} +(5.52456 + 8.06357i) q^{46} +(7.21178 - 7.21178i) q^{47} +(8.15075 + 7.42592i) q^{48} +1.00000i q^{49} +(-6.56421 + 2.62891i) q^{50} +(-4.50939 - 4.50939i) q^{51} +(3.49607 - 9.02842i) q^{52} +5.61513 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} +(-3.44216 + 2.35831i) q^{58} +(8.09154 + 8.09154i) q^{59} +(-9.43851 + 7.93022i) q^{60} +(-4.06506 + 4.06506i) q^{61} +(7.10410 + 1.32744i) 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} +10.8820i q^{67} +(1.86955 + 4.23241i) q^{68} +(-13.4721 + 13.4721i) q^{69} +(0.309730 + 3.14707i) q^{70} -12.1998 q^{71} +(-6.84486 + 11.0604i) q^{72} +(5.45819 + 5.45819i) q^{73} +(11.9448 + 2.23195i) q^{74} +(-7.38718 - 11.6360i) q^{75} +(-2.64990 + 1.17052i) q^{76} -3.51427 q^{77} +(18.5504 + 3.46623i) q^{78} +11.5728 q^{79} +(8.46361 - 2.89263i) q^{80} -1.64810 q^{81} +(-9.65762 - 1.80457i) q^{82} +2.86002 q^{83} +(2.22763 + 5.04306i) q^{84} +(-4.96754 + 1.44366i) q^{85} +(-3.47096 - 0.648566i) q^{86} +(-5.75096 - 5.75096i) q^{87} +(2.27791 + 9.67532i) q^{88} -6.32940 q^{89} +(-11.2407 - 9.22638i) q^{90} +(3.42299 - 3.42299i) q^{91} +(12.6446 - 5.58542i) q^{92} +14.0869i 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} +(1.39015 + 0.259757i) 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} - 36 q^{22} + 32 q^{26} - 36 q^{30} - 40 q^{32} - 32 q^{34} - 32 q^{36} - 56 q^{38} - 48 q^{40} + 20 q^{42} + 56 q^{44} - 32 q^{46} - 24 q^{48} + 8 q^{50} - 16 q^{51} - 16 q^{52} - 32 q^{54} - 24 q^{56} - 52 q^{58} - 32 q^{60} - 32 q^{61} + 40 q^{62} - 32 q^{64} + 32 q^{66} + 80 q^{68} + 32 q^{69} + 40 q^{72} + 16 q^{73} + 32 q^{74} - 24 q^{75} - 28 q^{78} + 72 q^{80} + 144 q^{81} + 24 q^{82} - 80 q^{83} + 32 q^{86} - 112 q^{87} + 40 q^{88} + 32 q^{90} - 16 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 - 36 * q^22 + 32 * q^26 - 36 * q^30 - 40 * q^32 - 32 * q^34 - 32 * q^36 - 56 * q^38 - 48 * q^40 + 20 * q^42 + 56 * q^44 - 32 * q^46 - 24 * q^48 + 8 * q^50 - 16 * q^51 - 16 * q^52 - 32 * q^54 - 24 * q^56 - 52 * q^58 - 32 * q^60 - 32 * q^61 + 40 * q^62 - 32 * q^64 + 32 * q^66 + 80 * q^68 + 32 * q^69 + 40 * q^72 + 16 * q^73 + 32 * q^74 - 24 * q^75 - 28 * q^78 + 72 * q^80 + 144 * q^81 + 24 * q^82 - 80 * q^83 + 32 * q^86 - 112 * q^87 + 40 * q^88 + 32 * q^90 - 16 * 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.259757	−	1.39015i	0.183676	−	0.982987i
$2$	0.259757	−	1.39015i	0.183676	−	0.982987i
$3$	2.75657			1.59151			0.795754	−	0.605620i	$-0.207075\pi$
$3$	2.75657			1.59151			0.795754	+	0.605620i	$0.207075\pi$
$4$	−1.86505	−	0.722204i	−0.932526	−	0.361102i
$5$	1.07707	−	1.95957i	0.481680	−	0.876347i
$5$	1.07707	−	1.95957i	0.481680	−	0.876347i
$6$	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
$8$	−1.48843	+	2.40511i	−0.526241	+	0.850335i
$9$	4.59869			1.53290
$10$	−2.44433	−	2.00630i	−0.772965	−	0.634449i
$11$	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	$0.0722684\pi$
$12$	−5.14115	−	1.99081i	−1.48412	−	0.574697i
$13$			4.84084i			1.34261i	0.741182	+	0.671304i	$0.234265\pi$
$13$			4.84084i			1.34261i	−0.741182	+	0.671304i	$0.765735\pi$
$14$	−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	$0.840516\pi$
$18$	1.19454	−	6.39289i	0.281556	−	1.50682i
$19$	1.02421	−	1.02421i	0.234970	−	0.234970i	−0.579793	−	0.814764i	$-0.696867\pi$
$19$	1.02421	−	1.02421i	0.234970	−	0.234970i	0.814764	+	0.579793i	$0.196867\pi$
$20$	−3.42400	+	2.87684i	−0.765630	+	0.643281i
$21$	−1.94919	−	1.94919i	−0.425348	−	0.425348i
$22$	−2.80899	−	4.09997i	−0.598880	−	0.874116i
$23$	−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
$27$	4.40691			0.848111
$28$	0.808116	+	1.82947i	0.152720	+	0.345737i
$29$	−2.08627	−	2.08627i	−0.387411	−	0.387411i	0.486352	−	0.873763i	$-0.338327\pi$
$29$	−2.08627	−	2.08627i	−0.387411	−	0.387411i	−0.873763	+	0.486352i	$0.838327\pi$
$30$	−6.73797	−	5.53052i	−1.23018	−	1.00973i
$31$			5.11030i			0.917837i	0.888478	+	0.458918i	$0.151763\pi$
$31$			5.11030i			0.917837i	−0.888478	+	0.458918i	$0.848237\pi$
$32$	4.51299	−	3.41071i	0.797792	−	0.602933i
$33$	6.84999	−	6.84999i	1.19243	−	1.19243i
$34$	−2.69903	+	1.84918i	−0.462881	+	0.317131i
$35$	−2.14723	+	0.624023i	−0.362948	+	0.105479i
$36$	−8.57681	−	3.32120i	−1.42947	−	0.553533i
$37$			8.59247i			1.41259i	0.707916	+	0.706296i	$0.249635\pi$
$37$			8.59247i			1.41259i	−0.707916	+	0.706296i	$0.750365\pi$
$38$	−1.15777	−	1.68986i	−0.187814	−	0.274131i
$39$			13.3441i			2.13677i
$40$	3.10984	+	5.50717i	0.491709	+	0.870760i
$41$		−	6.94716i		−	1.08496i	−0.840067	−	0.542482i	$-0.817485\pi$
$41$		−	6.94716i		−	1.08496i	0.840067	−	0.542482i	$-0.182515\pi$
$42$	−3.21599	+	2.20336i	−0.496238	+	0.339986i
$43$		−	2.49682i		−	0.380761i	−0.981710	−	0.190380i	$-0.939028\pi$
$43$		−	2.49682i		−	0.380761i	0.981710	−	0.190380i	$-0.0609722\pi$
$44$	−6.42924	+	2.83994i	−0.969245	+	0.428137i
$45$	4.95311	−	9.01147i	0.738366	−	1.34335i
$46$	5.52456	+	8.06357i	0.814552	+	1.18891i
$47$	7.21178	−	7.21178i	1.05195	−	1.05195i	0.0533712	−	0.998575i	$-0.483003\pi$
$47$	7.21178	−	7.21178i	1.05195	−	1.05195i	0.998575	−	0.0533712i	$-0.0169966\pi$
$48$	8.15075	+	7.42592i	1.17646	+	1.07184i
$49$			1.00000i			0.142857i
$50$	−6.56421	+	2.62891i	−0.928319	+	0.371784i
$51$	−4.50939	−	4.50939i	−0.631441	−	0.631441i
$52$	3.49607	−	9.02842i	0.484818	−	1.25202i
$53$	5.61513			0.771297			0.385649	−	0.922646i	$-0.373978\pi$
$53$	5.61513			0.771297			0.385649	+	0.922646i	$0.373978\pi$
$54$	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
$58$	−3.44216	+	2.35831i	−0.451978	+	0.309662i
$59$	8.09154	+	8.09154i	1.05343	+	1.05343i	0.998490	+	0.0549384i	$0.0174962\pi$
$59$	8.09154	+	8.09154i	1.05343	+	1.05343i	0.0549384	+	0.998490i	$0.482504\pi$
$60$	−9.43851	+	7.93022i	−1.21851	+	1.02379i
$61$	−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	$0.369969\pi$
$62$	7.10410	+	1.32744i	0.902222	+	0.168585i
$63$	−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
$67$			10.8820i			1.32945i	0.747090	+	0.664723i	$0.231451\pi$
$67$			10.8820i			1.32945i	−0.747090	+	0.664723i	$0.768549\pi$
$68$	1.86955	+	4.23241i	0.226716	+	0.513255i
$69$	−13.4721	+	13.4721i	−1.62185	+	1.62185i
$70$	0.309730	+	3.14707i	0.0370198	+	0.376147i
$71$	−12.1998			−1.44785			−0.723927	−	0.689876i	$-0.757665\pi$
$71$	−12.1998			−1.44785			−0.723927	+	0.689876i	$0.757665\pi$
$72$	−6.84486	+	11.0604i	−0.806674	+	1.30348i
$73$	5.45819	+	5.45819i	0.638833	+	0.638833i	0.950268	−	0.311435i	$-0.100809\pi$
$73$	5.45819	+	5.45819i	0.638833	+	0.638833i	−0.311435	+	0.950268i	$0.600809\pi$
$74$	11.9448	+	2.23195i	1.38856	+	0.259459i
$75$	−7.38718	−	11.6360i	−0.852998	−	1.34361i
$76$	−2.64990	+	1.17052i	−0.303964	+	0.134268i
$77$	−3.51427			−0.400488
$78$	18.5504	+	3.46623i	2.10042	+	0.392473i
$79$	11.5728			1.30204			0.651022	−	0.759059i	$-0.274341\pi$
$79$	11.5728			1.30204			0.651022	+	0.759059i	$0.274341\pi$
$80$	8.46361	−	2.89263i	0.946260	−	0.323406i
$81$	−1.64810			−0.183122
$82$	−9.65762	−	1.80457i	−1.06651	−	0.199282i
$83$	2.86002			0.313928			0.156964	−	0.987604i	$-0.449829\pi$
$83$	2.86002			0.313928			0.156964	+	0.987604i	$0.449829\pi$
$84$	2.22763	+	5.04306i	0.243054	+	0.550243i
$85$	−4.96754	+	1.44366i	−0.538806	+	0.156587i
$86$	−3.47096	−	0.648566i	−0.374283	−	0.0699366i
$87$	−5.75096	−	5.75096i	−0.616568	−	0.616568i
$88$	2.27791	+	9.67532i	0.242826	+	1.03139i
$89$	−6.32940			−0.670915			−0.335458	−	0.942055i	$-0.608891\pi$
$89$	−6.32940			−0.670915			−0.335458	+	0.942055i	$0.608891\pi$
$90$	−11.2407	−	9.22638i	−1.18488	−	0.972546i
$91$	3.42299	−	3.42299i	0.358827	−	0.358827i
$92$	12.6446	−	5.58542i	1.31829	−	0.582320i
$93$			14.0869i			1.46074i
$94$	−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	$0.907732\pi$
$98$	1.39015	+	0.259757i	0.140427	+	0.0262394i
$99$	11.4276	−	11.4276i	1.14852	−	1.14852i
$100$	1.94949	+	9.80813i	0.194949	+	0.980813i
$101$	−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	$0.875996\pi$
$102$	−7.44008	+	5.09740i	−0.736678	+	0.504717i
$103$	−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
$107$	−0.755462			−0.0730333			−0.0365167	−	0.999333i	$-0.511626\pi$
$107$	−0.755462			−0.0730333			−0.0365167	+	0.999333i	$0.511626\pi$
$108$	−8.21913	−	3.18269i	−0.790886	−	0.306255i
$109$	−4.12169	−	4.12169i	−0.394786	−	0.394786i	0.481603	−	0.876389i	$-0.340055\pi$
$109$	−4.12169	−	4.12169i	−0.394786	−	0.394786i	−0.876389	+	0.481603i	$0.840055\pi$
$110$	−11.0597	+	1.08848i	−1.05450	+	0.103782i
$111$			23.6858i			2.24815i
$112$	−0.185930	−	3.99568i	−0.0175688	−	0.377556i
$113$	−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
$115$	4.31303	+	14.8409i	0.402192	+	1.38392i
$116$	2.38429	+	5.39772i	0.221376	+	0.501166i
$117$			22.2615i			2.05808i
$118$	13.3503	−	9.14664i	1.22900	−	0.842017i
$119$			2.31347i			0.212075i
$120$	8.57250	+	15.1809i	0.782559	+	1.38582i
$121$		−	1.35010i		−	0.122736i
$122$	4.59513	+	6.70698i	0.416023	+	0.607221i
$123$		−	19.1504i		−	1.72673i
$124$	3.69068	−	9.53098i	0.331433	−	0.855907i
$125$	−11.1581	+	0.704829i	−0.998011	+	0.0630418i
$126$	−5.36512	+	3.67579i	−0.477963	+	0.327465i
$127$	13.2450	−	13.2450i	1.17531	−	1.17531i	0.194379	−	0.980926i	$-0.437731\pi$
$127$	13.2450	−	13.2450i	1.17531	−	1.17531i	0.980926	−	0.194379i	$-0.0622693\pi$
$128$	−10.8802	+	3.10185i	−0.961682	+	0.274167i
$129$		−	6.88266i		−	0.605984i
$130$	9.71220	−	11.8326i	0.851816	−	1.03779i
$131$	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	$0.520841\pi$
$132$	−17.7227	+	7.82850i	−1.54256	+	0.681383i
$133$	−1.44845			−0.125597
$134$	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	$-0.954921\pi$
$137$	−9.93546	+	9.93546i	−0.848843	+	0.848843i	0.141145	+	0.989989i	$0.454921\pi$
$138$	15.2288	+	22.2278i	1.29637	+	1.89216i
$139$	3.69691	+	3.69691i	0.313568	+	0.313568i	0.846290	−	0.532722i	$-0.178831\pi$
$139$	3.69691	+	3.69691i	0.313568	+	0.313568i	−0.532722	+	0.846290i	$0.678831\pi$
$140$	4.45537	+	0.386902i	0.376547	+	0.0326992i
$141$	19.8798	−	19.8798i	1.67418	−	1.67418i
$142$	−3.16899	+	16.9596i	−0.265936	+	1.42322i
$143$	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
$147$			2.75657i			0.227358i
$148$	6.20551	−	16.0254i	0.510090	−	1.31728i
$149$	13.4801	−	13.4801i	1.10434	−	1.10434i	0.110455	−	0.993881i	$-0.464769\pi$
$149$	13.4801	−	13.4801i	1.10434	−	1.10434i	0.993881	−	0.110455i	$-0.0352307\pi$
$150$	−18.0947	+	7.24678i	−1.47743	+	0.591697i
$151$	1.50233			0.122258			0.0611289	−	0.998130i	$-0.480530\pi$
$151$	1.50233			0.122258			0.0611289	+	0.998130i	$0.480530\pi$
$152$	0.938871	+	3.98782i	0.0761525	+	0.323455i
$153$	−7.52285	−	7.52285i	−0.608187	−	0.608187i
$154$	−0.912856	+	4.88537i	−0.0735601	+	0.393675i
$155$	10.0140	+	5.50415i	0.804344	+	0.442104i
$156$	9.63718	−	24.8875i	0.771592	−	1.99259i
$157$	−19.5243			−1.55821			−0.779104	−	0.626895i	$-0.784326\pi$
$157$	−19.5243			−1.55821			−0.779104	+	0.626895i	$0.784326\pi$
$158$	3.00612	−	16.0880i	0.239154	−	1.27989i
$159$	15.4785			1.22753
$160$	−1.82272	−	12.5171i	−0.144099	−	0.989563i
$161$	6.91165			0.544714
$162$	−0.428105	+	2.29111i	−0.0336351	+	0.180007i
$163$	2.85332			0.223489			0.111745	−	0.993737i	$-0.464356\pi$
$163$	2.85332			0.223489			0.111745	+	0.993737i	$0.464356\pi$
$164$	−5.01727	+	12.9568i	−0.391783	+	1.01176i
$165$	−6.04513	−	20.8009i	−0.470613	−	1.61935i
$166$	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	$0.578856\pi$
$168$	7.58927	−	1.78678i	0.585525	−	0.137853i
$169$	−10.4337			−0.802594
$170$	0.716550	+	7.28065i	0.0549569	+	0.558400i
$171$	4.71004	−	4.71004i	0.360186	−	0.360186i
$172$	−1.80321	+	4.65669i	−0.137494	+	0.355070i
$173$		−	0.635940i		−	0.0483496i	−0.999708	−	0.0241748i	$-0.992304\pi$
$173$		−	0.635940i		−	0.0483496i	0.999708	−	0.0241748i	$-0.00769583\pi$
$174$	−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
$178$	−1.64411	+	8.79884i	−0.123231	+	0.659501i
$179$	17.8546	−	17.8546i	1.33451	−	1.33451i	0.433231	−	0.901283i	$-0.357374\pi$
$179$	17.8546	−	17.8546i	1.33451	−	1.33451i	0.901283	−	0.433231i	$-0.142626\pi$
$180$	−15.7459	+	13.2297i	−1.17363	+	0.986084i
$181$	−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	$-0.549995\pi$
$182$	−3.86934	−	5.64763i	−0.286814	−	0.418630i
$183$	−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
$187$	−8.13014			−0.594535
$188$	−18.6587	+	8.24197i	−1.36083	+	0.601107i
$189$	−3.11616	−	3.11616i	−0.226667	−	0.226667i
$190$	−4.55839	+	0.448630i	−0.330700	+	0.0325470i
$191$			14.8696i			1.07593i	0.842968	+	0.537964i	$0.180806\pi$
$191$			14.8696i			1.07593i	−0.842968	+	0.537964i	$0.819194\pi$
$192$	−9.83855	−	19.7362i	−0.710036	−	1.42434i
$193$	−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
$195$	26.1488	+	14.3726i	1.87255	+	1.02924i
$196$	0.722204	−	1.86505i	0.0515860	−	0.133218i
$197$			7.18026i			0.511572i	0.966733	+	0.255786i	$0.0823342\pi$
$197$			7.18026i			0.511572i	−0.966733	+	0.255786i	$0.917666\pi$
$198$	−12.9177	−	18.8545i	−0.918021	−	1.33993i
$199$		−	11.2655i		−	0.798593i	−0.916822	−	0.399297i	$-0.869254\pi$
$199$		−	11.2655i		−	0.798593i	0.916822	−	0.399297i	$-0.130746\pi$
$200$	14.1412	−	0.162354i	0.999934	−	0.0114802i
$201$			29.9970i			2.11582i
$202$	−9.04153	+	6.19459i	−0.636160	+	0.435850i
$203$			2.95043i			0.207080i
$204$	5.15355	+	11.6669i	0.360820	+	0.816849i
$205$	−13.6135	−	7.48257i	−0.950805	−	0.522606i
$206$	4.19942	+	6.12942i	0.292588	+	0.427057i
$207$	−22.4751	+	22.4751i	−1.56213	+	1.56213i
$208$	−13.0407	+	14.3136i	−0.904211	+	0.992469i
$209$		−	5.09026i		−	0.352101i
$210$	0.853794	+	8.67514i	0.0589174	+	0.598641i
$211$	−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	$-0.697179\pi$
$212$	−10.4725	−	4.05527i	−0.719255	−	0.278517i
$213$	−33.6297			−2.30427
$214$	−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
$218$	−6.80042	+	4.65915i	−0.460583	+	0.315557i
$219$	15.0459	+	15.0459i	1.01671	+	1.01671i
$220$	−1.35968	+	15.6574i	−0.0916694	+	1.05562i
$221$	7.91897	−	7.91897i	0.532688	−	0.532688i
$222$	32.9268	+	6.15254i	2.20990	+	0.412932i
$223$	−7.56278	−	7.56278i	−0.506441	−	0.506441i	0.406991	−	0.913432i	$-0.366578\pi$
$223$	−7.56278	−	7.56278i	−0.506441	−	0.506441i	−0.913432	+	0.406991i	$0.866578\pi$
$224$	−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
$227$		−	24.2843i		−	1.61180i	−0.592049	−	0.805902i	$-0.701681\pi$
$227$		−	24.2843i		−	1.61180i	0.592049	−	0.805902i	$-0.298319\pi$
$228$	−7.30464	+	3.22662i	−0.483762	+	0.213688i
$229$	−13.9087	+	13.9087i	−0.919113	+	0.919113i	−0.996965	−	0.0778522i	$-0.975194\pi$
$229$	−13.9087	+	13.9087i	−0.919113	+	0.919113i	0.0778522	+	0.996965i	$0.475194\pi$
$230$	21.7515	−	2.14075i	1.43425	−	0.141157i
$231$	−9.68734			−0.637380
$232$	8.12300	−	1.91244i	0.533301	−	0.125558i
$233$	10.3692	+	10.3692i	0.679310	+	0.679310i	0.959844	−	0.280534i	$-0.0905115\pi$
$233$	10.3692	+	10.3692i	0.679310	+	0.679310i	−0.280534	+	0.959844i	$0.590512\pi$
$234$	30.9469	+	5.78259i	2.02307	+	0.378020i
$235$	−6.36441	−	21.8996i	−0.415168	−	1.42857i
$236$	−9.24740	−	20.9349i	−0.601954	−	1.36274i
$237$	31.9013			2.07221
$238$	3.21607	+	0.600939i	0.208467	+	0.0389531i
$239$	−3.66770			−0.237244			−0.118622	−	0.992940i	$-0.537848\pi$
$239$	−3.66770			−0.237244			−0.118622	+	0.992940i	$0.537848\pi$
$240$	23.3306	−	7.97375i	1.50598	−	0.514703i
$241$	−12.3924			−0.798262			−0.399131	−	0.916894i	$-0.630688\pi$
$241$	−12.3924			−0.798262			−0.399131	+	0.916894i	$0.630688\pi$
$242$	−1.87684	−	0.350697i	−0.120648	−	0.0225437i
$243$	−17.7638			−1.13955
$244$	10.5173	−	4.64574i	0.673304	−	0.297413i
$245$	1.95957	+	1.07707i	0.125192	+	0.0688114i
$246$	−26.6219	−	4.97444i	−1.69735	−	0.317159i
$247$	4.95805	+	4.95805i	0.315473	+	0.315473i
$248$	−12.2908	−	7.60635i	−0.780469	−	0.483004i
$249$	7.88384			0.499618
$250$	−1.91857	+	15.6946i	−0.121341	+	0.992611i
$251$	−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	$0.434817\pi$
$252$	3.71628	+	8.41316i	0.234103	+	0.529979i
$253$			24.2894i			1.52706i
$254$	−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	$0.664939\pi$
$258$	−9.56795	−	1.78782i	−0.595674	−	0.111305i
$259$	6.07579	−	6.07579i	0.377531	−	0.377531i
$260$	−13.9263	−	16.5750i	−0.863674	−	1.02794i
$261$	−9.59413	−	9.59413i	−0.593861	−	0.593861i
$262$	17.6081	−	12.0638i	1.08783	−	0.745302i
$263$	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
$267$	−17.4475			−1.06777
$268$	7.85902	−	20.2955i	0.480066	−	1.23974i
$269$	−17.6264	−	17.6264i	−1.07470	−	1.07470i	−0.996975	−	0.0777265i	$-0.975234\pi$
$269$	−17.6264	−	17.6264i	−1.07470	−	1.07470i	−0.0777265	−	0.996975i	$-0.524766\pi$
$270$	−10.7719	−	8.84161i	−0.655560	−	0.538083i
$271$		−	21.0928i		−	1.28130i	−0.767834	−	0.640649i	$-0.778665\pi$
$271$		−	21.0928i		−	1.28130i	0.767834	−	0.640649i	$-0.221335\pi$
$272$	−0.430144	−	9.24386i	−0.0260813	−	0.560491i
$273$	9.43572	−	9.43572i	0.571076	−	0.571076i
$274$	11.2310	+	16.3926i	0.678490	+	0.990314i
$275$	−17.1488	−	3.83019i	−1.03411	−	0.230969i
$276$	34.8559	−	15.3966i	2.09808	−	0.926767i
$277$		−	32.3123i		−	1.94146i	−0.240181	−	0.970728i	$-0.577207\pi$
$277$		−	32.3123i		−	1.94146i	0.240181	−	0.970728i	$-0.422793\pi$
$278$	6.09957	−	4.17897i	0.365828	−	0.250638i
$279$			23.5007i			1.40695i
$280$	1.69517	−	6.09314i	0.101306	−	0.364135i
$281$			2.13535i			0.127384i	0.997970	+	0.0636920i	$0.0202875\pi$
$281$			2.13535i			0.127384i	−0.997970	+	0.0636920i	$0.979712\pi$
$282$	−22.4720	−	32.7999i	−1.33819	−	1.95320i
$283$			11.2031i			0.665958i	0.942934	+	0.332979i	$0.108054\pi$
$283$			11.2031i			0.665958i	−0.942934	+	0.332979i	$0.891946\pi$
$284$	22.7533	+	8.81077i	1.35016	+	0.522823i
$285$	−2.49158	−	8.57339i	−0.147589	−	0.507844i
$286$	19.8473	−	13.5979i	1.17359	−	0.804060i
$287$	−4.91238	+	4.91238i	−0.289969	+	0.289969i
$288$	20.7539	−	15.6848i	1.22293	−	0.924235i
$289$		−	11.6479i		−	0.685169i
$290$	0.913838	+	9.28523i	0.0536624	+	0.545248i
$291$	−18.2566	−	18.2566i	−1.07022	−	1.07022i
$292$	−6.23789	−	14.1217i	−0.365045	−	0.826412i
$293$	−10.8022			−0.631071			−0.315535	−	0.948914i	$-0.602184\pi$
$293$	−10.8022			−0.631071			−0.315535	+	0.948914i	$0.602184\pi$
$294$	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
$298$	−15.2379	−	22.2410i	−0.882708	−	1.28839i
$299$	−23.6585	−	23.6585i	−1.36821	−	1.36821i
$300$	5.37390	+	27.0368i	0.310262	+	1.56097i
$301$	−1.76552	+	1.76552i	−0.101763	+	0.101763i
$302$	0.390241	−	2.08847i	0.0224558	−	0.120178i
$303$	−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
$307$			12.3400i			0.704279i	0.935948	+	0.352140i	$0.114546\pi$
$307$			12.3400i			0.704279i	−0.935948	+	0.352140i	$0.885454\pi$
$308$	6.55430	+	2.53802i	0.373466	+	0.144617i
$309$	−10.2407	+	10.2407i	−0.582571	+	0.582571i
$310$	10.2528	−	12.4913i	0.582321	−	0.709455i
$311$	8.05926			0.456999			0.228499	−	0.973544i	$-0.426618\pi$
$311$	8.05926			0.456999			0.228499	+	0.973544i	$0.426618\pi$
$312$	−32.0941	−	19.8619i	−1.81697	−	1.12446i
$313$	−5.79372	−	5.79372i	−0.327480	−	0.327480i	0.524147	−	0.851628i	$-0.324384\pi$
$313$	−5.79372	−	5.79372i	−0.327480	−	0.327480i	−0.851628	+	0.524147i	$0.824384\pi$
$314$	−5.07157	+	27.1418i	−0.286205	+	1.53170i
$315$	−9.87445	+	2.86969i	−0.556362	+	0.161689i
$316$	−21.5839	−	8.35794i	−1.21419	−	0.470171i
$317$	−22.9733			−1.29031			−0.645154	−	0.764052i	$-0.723207\pi$
$317$	−22.9733			−1.29031			−0.645154	+	0.764052i	$0.723207\pi$
$318$	4.02065	−	21.5175i	0.225467	−	1.20664i
$319$	−10.3686			−0.580531
$320$	−17.8741	−	0.717546i	−0.999195	−	0.0401120i
$321$	−2.08249			−0.116233
$322$	1.79535	−	9.60825i	0.100051	−	0.535447i
$323$	−3.35095			−0.186452
$324$	3.07379	+	1.19026i	0.170766	+	0.0661258i
$325$	20.4341	−	12.9727i	1.13348	−	0.719595i
$326$	0.741170	−	3.96655i	0.0410496	−	0.219687i
$327$	−11.3617	−	11.3617i	−0.628306	−	0.628306i
$328$	16.7087	+	10.3404i	0.922583	+	0.570953i
$329$	−10.1990			−0.562289
$330$	−30.4868	+	3.00046i	−1.67824	+	0.165170i
$331$	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	$0.150262\pi$
$332$	−5.33408	−	2.06552i	−0.292746	−	0.113360i
$333$			39.5141i			2.16536i
$334$	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	$0.714022\pi$
$338$	−2.71023	+	14.5045i	−0.147417	+	0.788939i
$339$	−10.1532	+	10.1532i	−0.551444	+	0.551444i
$340$	10.3073	+	0.895084i	0.558994	+	0.0485427i
$341$	12.6989	+	12.6989i	0.687685	+	0.687685i
$342$	−5.32421	−	7.77114i	−0.287900	−	0.420215i
$343$	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
$347$	21.4335			1.15061			0.575305	−	0.817939i	$-0.304883\pi$
$347$	21.4335			1.15061			0.575305	+	0.817939i	$0.304883\pi$
$348$	6.57248	+	14.8792i	0.352322	+	0.797609i
$349$	−21.0849	−	21.0849i	−1.12865	−	1.12865i	−0.990397	−	0.138252i	$-0.955852\pi$
$349$	−21.0849	−	21.0849i	−1.12865	−	1.12865i	−0.138252	−	0.990397i	$-0.544148\pi$
$350$	6.50052	+	2.78268i	0.347467	+	0.148740i
$351$			21.3332i			1.13868i
$352$	2.73914	−	19.6901i	0.145997	−	1.04949i
$353$	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
$355$	−13.1401	+	23.9065i	−0.697403	+	1.26882i
$356$	11.8047	+	4.57112i	0.625646	+	0.242269i
$357$			6.37724i			0.337519i
$358$	−20.1827	−	29.4585i	−1.06669	−	1.55693i
$359$			27.1270i			1.43171i	0.698251	+	0.715853i	$0.253962\pi$
$359$			27.1270i			1.43171i	−0.698251	+	0.715853i	$0.746038\pi$
$360$	14.3012	+	25.3258i	0.753740	+	1.33479i
$361$			16.9020i			0.889578i
$362$	−25.3961	+	17.3995i	−1.33479	+	0.914500i
$363$		−	3.72164i		−	0.195335i
$364$	−8.85615	+	3.91196i	−0.464189	+	0.205042i
$365$	16.5746	−	4.81687i	0.867553	−	0.252126i
$366$	12.6668	+	18.4883i	0.662104	+	0.966398i
$367$	−14.2201	+	14.2201i	−0.742284	+	0.742284i	−0.973017	−	0.230733i	$-0.925887\pi$
$367$	−14.2201	+	14.2201i	−0.742284	+	0.742284i	0.230733	+	0.973017i	$0.425887\pi$
$368$	−27.6167	+	1.28509i	−1.43962	+	0.0669897i
$369$		−	31.9479i		−	1.66314i
$370$	17.2391	−	21.0028i	0.896218	−	1.09188i
$371$	−3.97050	−	3.97050i	−0.206138	−	0.206138i
$372$	10.1736	−	26.2728i	0.527478	−	1.36218i
$373$	17.4713			0.904631			0.452315	−	0.891858i	$-0.350598\pi$
$373$	17.4713			0.904631			0.452315	+	0.891858i	$0.350598\pi$
$374$	−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
$378$	−5.14138	+	3.52250i	−0.264444	+	0.181178i
$379$	−20.2052	−	20.2052i	−1.03787	−	1.03787i	−0.999254	−	0.0386164i	$-0.987705\pi$
$379$	−20.2052	−	20.2052i	−1.03787	−	1.03787i	−0.0386164	−	0.999254i	$-0.512295\pi$
$380$	−0.560410	+	6.45340i	−0.0287484	+	0.331052i
$381$	36.5109	−	36.5109i	1.87051	−	1.87051i
$382$	20.6711	+	3.86249i	1.05762	+	0.197622i
$383$	−17.2009	−	17.2009i	−0.878923	−	0.878923i	0.114501	−	0.993423i	$-0.463473\pi$
$383$	−17.2009	−	17.2009i	−0.878923	−	0.878923i	−0.993423	+	0.114501i	$0.963473\pi$
$384$	−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
$387$		−	11.4821i		−	0.583668i
$388$	7.56900	+	17.1352i	0.384258	+	0.869909i
$389$	10.1366	−	10.1366i	0.513945	−	0.513945i	−0.401788	−	0.915733i	$-0.631611\pi$
$389$	10.1366	−	10.1366i	0.513945	−	0.513945i	0.915733	+	0.401788i	$0.131611\pi$
$390$	26.7724	−	32.6174i	1.35567	−	1.65165i
$391$	15.9899			0.808642
$392$	−2.40511	−	1.48843i	−0.121476	−	0.0751773i
$393$	29.4186	+	29.4186i	1.48397	+	1.48397i
$394$	9.98166	+	1.86512i	0.502869	+	0.0939635i
$395$	12.4647	−	22.6778i	0.627169	−	1.14104i
$396$	−29.5661	+	13.0600i	−1.48575	+	0.656290i
$397$	26.9825			1.35421			0.677107	−	0.735884i	$-0.263233\pi$
$397$	26.9825			1.35421			0.677107	+	0.735884i	$0.263233\pi$
$398$	−15.6608	−	2.92630i	−0.785007	−	0.146682i
$399$	−3.99277			−0.199889
$400$	3.44758	−	19.7006i	0.172379	−	0.985031i
$401$	−12.6110			−0.629766			−0.314883	−	0.949131i	$-0.601965\pi$
$401$	−12.6110			−0.629766			−0.314883	+	0.949131i	$0.601965\pi$
$402$	41.7004	+	7.79193i	2.07983	+	0.388626i
$403$	−24.7381			−1.23229
$404$	6.26283	+	14.1782i	0.311587	+	0.705392i
$405$	−1.77512	+	3.22957i	−0.0882063	+	0.160479i
$406$	4.10156	+	0.766396i	0.203557	+	0.0380356i
$407$	21.3520	+	21.3520i	1.05838	+	1.05838i
$408$	17.5575	−	4.13365i	0.869226	−	0.204646i
$409$	−30.9798			−1.53185			−0.765925	−	0.642930i	$-0.777719\pi$
$409$	−30.9798			−1.53185			−0.765925	+	0.642930i	$0.777719\pi$
$410$	−13.9381	+	16.9811i	−0.688354	+	0.838639i
$411$	−27.3878	+	27.3878i	−1.35094	+	1.35094i
$412$	9.61166	−	4.24568i	0.473533	−	0.209170i
$413$		−	11.4432i		−	0.563081i
$414$	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
$418$	−7.07624	−	1.32223i	−0.346110	−	0.0646724i
$419$	−4.37756	+	4.37756i	−0.213858	+	0.213858i	−0.805904	−	0.592046i	$-0.798320\pi$
$419$	−4.37756	+	4.37756i	−0.213858	+	0.213858i	0.592046	+	0.805904i	$0.298320\pi$
$420$	12.2815	+	1.06652i	0.599278	+	0.0520410i
$421$	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	$0.608232\pi$
$422$	−33.4279	+	22.9023i	−1.62725	+	1.11487i
$423$	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
$427$	5.74886			0.278207
$428$	1.40898	+	0.545598i	0.0681055	+	0.0263725i
$429$	33.1597	+	33.1597i	1.60096	+	1.60096i
$430$	−5.00937	+	6.10304i	−0.241573	+	0.294315i
$431$			3.76636i			0.181419i	0.995877	+	0.0907096i	$0.0289135\pi$
$431$			3.76636i			0.181419i	−0.995877	+	0.0907096i	$0.971086\pi$
$432$	13.0306	+	11.8718i	0.626933	+	0.571181i
$433$	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
$435$	−17.4636	+	5.07524i	−0.837316	+	0.243339i
$436$	4.71047	+	10.6639i	0.225591	+	0.510707i
$437$			10.0112i			0.478901i
$438$	24.8244	−	17.0078i	1.18616	−	0.812666i
$439$			22.7533i			1.08595i	0.839748	+	0.542977i	$0.182703\pi$
$439$			22.7533i			1.08595i	−0.839748	+	0.542977i	$0.817297\pi$
$440$	21.4130	+	5.95727i	1.02082	+	0.284002i
$441$			4.59869i			0.218985i
$442$	−8.95158	−	13.0656i	−0.425783	−	0.621467i
$443$		−	8.76302i		−	0.416344i	−0.978092	−	0.208172i	$-0.933249\pi$
$443$		−	8.76302i		−	0.416344i	0.978092	−	0.208172i	$-0.0667513\pi$
$444$	17.1060	−	44.1752i	0.811813	−	2.09646i
$445$	−6.81721	+	12.4029i	−0.323167	+	0.587955i
$446$	−12.4779	+	8.54894i	−0.590846	+	0.404804i
$447$	37.1590	−	37.1590i	1.75756	−	1.75756i
$448$	−2.53892	+	7.58643i	−0.119953	+	0.358425i
$449$		−	27.0012i		−	1.27427i	−0.770753	−	0.637134i	$-0.780120\pi$
$449$		−	27.0012i		−	1.27427i	0.770753	−	0.637134i	$-0.219880\pi$
$450$	−30.1868	+	12.0895i	−1.42302	+	0.569907i
$451$	−17.2634	−	17.2634i	−0.812904	−	0.812904i
$452$	9.52953	−	4.20941i	0.448232	−	0.197994i
$453$	4.14128			0.194574
$454$	−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	$-0.756117\pi$
$457$	−0.580944	+	0.580944i	−0.0271754	+	0.0271754i	0.693389	+	0.720564i	$0.256117\pi$
$458$	15.7223	+	22.9481i	0.734657	+	1.07229i
$459$	−7.20913	−	7.20913i	−0.336493	−	0.336493i
$460$	2.67413	−	30.7939i	0.124682	−	1.43578i
$461$	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	$0.161392\pi$
$462$	−2.51635	+	13.4669i	−0.117071	+	0.626536i
$463$	29.3567	+	29.3567i	1.36432	+	1.36432i	0.868321	+	0.496002i	$0.165199\pi$
$463$	29.3567	+	29.3567i	1.36432	+	1.36432i	0.496002	+	0.868321i	$0.334801\pi$
$464$	−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
$467$			9.81342i			0.454111i	0.973882	+	0.227056i	$0.0729099\pi$
$467$			9.81342i			0.454111i	−0.973882	+	0.227056i	$0.927090\pi$
$468$	16.0774	−	41.5189i	0.743177	−	1.91921i
$469$	7.69473	−	7.69473i	0.355309	−	0.355309i
$470$	−32.0970	+	3.15894i	−1.48052	+	0.145711i
$471$	−53.8201			−2.47990
$472$	−31.5048	+	7.41732i	−1.45012	+	0.341410i
$473$	−6.20450	−	6.20450i	−0.285283	−	0.285283i
$474$	8.28659	−	44.3477i	0.380616	−	2.03696i
$475$	−7.06812	−	1.57867i	−0.324308	−	0.0724342i
$476$	1.67079	−	4.31474i	0.0765807	−	0.197766i
$477$	25.8223			1.18232
$478$	−0.952710	+	5.09866i	−0.0435759	+	0.233207i
$479$	−6.71897			−0.306997			−0.153499	−	0.988149i	$-0.549054\pi$
$479$	−6.71897			−0.306997			−0.153499	+	0.988149i	$0.549054\pi$
$480$	−5.02445	−	34.5043i	−0.229334	−	1.57490i
$481$	−41.5947			−1.89656
$482$	−3.21900	+	17.2273i	−0.146621	+	0.784681i
$483$	19.0525			0.866917
$484$	−0.975045	+	2.51800i	−0.0443202	+	0.114455i
$485$	−20.1115	+	5.84475i	−0.913214	+	0.265396i
$486$	−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	$0.688574\pi$
$488$	−3.72634	−	15.8275i	−0.168684	−	0.716477i
$489$	7.86539			0.355685
$490$	2.00630	−	2.44433i	0.0906356	−	0.110424i
$491$	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	$0.0863552\pi$
$492$	−13.8305	+	35.7164i	−0.623525	+	1.61022i
$493$			6.82573i			0.307415i
$494$	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
$498$	2.04788	−	10.9598i	0.0917678	−	0.491118i
$499$	4.98932	−	4.98932i	0.223353	−	0.223353i	−0.586556	−	0.809909i	$-0.699517\pi$
$499$	4.98932	−	4.98932i	0.223353	−	0.223353i	0.809909	+	0.586556i	$0.199517\pi$
$500$	21.3195	+	6.74388i	0.953436	+	0.301596i
$501$	25.8002	+	25.8002i	1.15267	+	1.15267i
$502$	13.8929	+	20.2778i	0.620069	+	0.905044i
$503$	−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
$507$	−28.7613			−1.27733
$508$	−34.2683	+	15.1371i	−1.52041	+	0.671598i
$509$	2.99819	+	2.99819i	0.132892	+	0.132892i	0.770424	−	0.637532i	$-0.220045\pi$
$509$	2.99819	+	2.99819i	0.132892	+	0.132892i	−0.637532	+	0.770424i	$0.720045\pi$
$510$	1.97522	+	20.0696i	0.0874643	+	0.888698i
$511$		−	7.71905i		−	0.341471i
$512$	22.5323	+	2.07261i	0.995796	+	0.0915974i
$513$	4.51361	−	4.51361i	0.199281	−	0.199281i
$514$	9.87733	−	6.76722i	0.435670	−	0.298489i
$515$	3.27850	+	11.2811i	0.144468	+	0.497106i
$516$	−4.97068	+	12.8365i	−0.218822	+	0.565096i
$517$		−	35.8420i		−	1.57633i
$518$	−6.86805	−	10.0245i	−0.301765	−	0.440452i
$519$		−	1.75302i		−	0.0769488i
$520$	−26.6593	+	15.0542i	−1.16909	+	0.660172i
$521$			22.1577i			0.970748i	0.874307	+	0.485374i	$0.161317\pi$
$521$			22.1577i			0.970748i	−0.874307	+	0.485374i	$0.838683\pi$
$522$	−15.8294	+	10.8452i	−0.692836	+	0.474680i
$523$			1.20225i			0.0525706i	0.999654	+	0.0262853i	$0.00836784\pi$
$523$			1.20225i			0.0525706i	−0.999654	+	0.0262853i	$0.991632\pi$
$524$	−12.1967	−	27.6116i	−0.532813	−	1.20622i
$525$	−3.00438	+	13.4514i	−0.131122	+	0.587069i
$526$	−6.44543	−	9.40765i	−0.281034	−	0.410193i
$527$	8.35977	−	8.35977i	0.364157	−	0.364157i
$528$	38.7075	−	1.80117i	1.68453	−	0.0783859i
$529$		−	24.7709i		−	1.07700i
$530$	−13.7252	−	11.2657i	−0.596186	−	0.489349i
$531$	37.2105	+	37.2105i	1.61480	+	1.61480i
$532$	2.70144	+	1.04608i	0.117122	+	0.0453533i
$533$	33.6301			1.45668
$534$	−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
$538$	−29.0820	+	19.9248i	−1.25381	+	0.859020i
$539$	2.48496	+	2.48496i	0.107035	+	0.107035i
$540$	−15.0893	+	12.6780i	−0.649339	+	0.545574i
$541$	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	$0.00126159\pi$
$542$	−29.3223	−	5.47901i	−1.25950	−	0.235344i
$543$	−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
$547$			7.51457i			0.321300i	0.987011	+	0.160650i	$0.0513590\pi$
$547$			7.51457i			0.321300i	−0.987011	+	0.160650i	$0.948641\pi$
$548$	25.7056	−	11.3547i	1.09809	−	0.485050i
$549$	−18.6940	+	18.6940i	−0.797838	+	0.797838i
$550$	−9.77908	+	22.8446i	−0.416981	+	0.974096i
$551$	−4.27357			−0.182060
$552$	−12.3496	−	52.4544i	−0.525633	−	2.23261i
$553$	−8.18322	−	8.18322i	−0.347986	−	0.347986i
$554$	−44.9190	−	8.39334i	−1.90843	−	0.356599i
$555$	46.4139	+	25.5112i	1.97016	+	1.08289i
$556$	−4.22501	−	9.56486i	−0.179180	−	0.405640i
$557$	−12.5088			−0.530015			−0.265007	−	0.964246i	$-0.585374\pi$
$557$	−12.5088			−0.530015			−0.265007	+	0.964246i	$0.585374\pi$
$558$	32.6696	+	6.10447i	1.38301	+	0.258423i
$559$	12.0867			0.511212
$560$	−8.03007	−	3.93928i	−0.339333	−	0.166465i
$561$	−22.4113			−0.946207
$562$	2.96846	+	0.554671i	0.125217	+	0.0233974i
$563$	−11.1356			−0.469310			−0.234655	−	0.972079i	$-0.575396\pi$
$563$	−11.1356			−0.469310			−0.234655	+	0.972079i	$0.575396\pi$
$564$	−51.4341	+	22.7196i	−2.16577	+	0.956667i
$565$	3.25048	+	11.1847i	0.136749	+	0.470545i
$566$	15.5741	+	2.91009i	0.654628	+	0.122320i
$567$	1.16538	+	1.16538i	0.0489414	+	0.0489414i
$568$	18.1587	−	29.3420i	0.761921	−	1.23116i
$569$	38.9443			1.63263			0.816316	−	0.577606i	$-0.196013\pi$
$569$	38.9443			1.63263			0.816316	+	0.577606i	$0.196013\pi$
$570$	−12.5655	+	1.23668i	−0.526312	+	0.0517989i
$571$	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	$0.241423\pi$
$572$	−13.7477	−	31.1229i	−0.574819	−	1.30131i
$573$			40.9892i			1.71235i
$574$	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	$0.668030\pi$
$578$	−16.1923	−	3.02562i	−0.673512	−	0.125849i
$579$	−5.90308	+	5.90308i	−0.245324	+	0.245324i
$580$	13.1453	+	1.14153i	0.545828	+	0.0473994i
$581$	−2.02234	−	2.02234i	−0.0839007	−	0.0839007i
$582$	−30.1217	+	20.6372i	−1.24859	+	0.855439i
$583$	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
$587$	−28.3456			−1.16995			−0.584975	−	0.811051i	$-0.698896\pi$
$587$	−28.3456			−1.16995			−0.584975	+	0.811051i	$0.698896\pi$
$588$	1.99081	−	5.14115i	0.0820995	−	0.212018i
$589$	5.23403	+	5.23403i	0.215664	+	0.215664i
$590$	−3.54429	−	36.0125i	−0.145916	−	1.48261i
$591$			19.7929i			0.814171i
$592$	−23.1472	+	25.4066i	−0.951345	+	1.04420i
$593$	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
$595$	4.53340	+	2.49176i	0.185851	+	0.102152i
$596$	−34.8766	+	15.4058i	−1.42860	+	0.631044i
$597$		−	31.0543i		−	1.27097i
$598$	−39.0344	+	26.7435i	−1.59624	+	1.09362i
$599$		−	27.7975i		−	1.13578i	−0.823106	−	0.567888i	$-0.807761\pi$
$599$		−	27.7975i		−	1.13578i	0.823106	−	0.567888i	$-0.192239\pi$
$600$	38.9813	−	0.447541i	1.59140	−	0.0182708i
$601$			11.6173i			0.473880i	0.971524	+	0.236940i	$0.0761445\pi$
$601$			11.6173i			0.473880i	−0.971524	+	0.236940i	$0.923856\pi$
$602$	1.99573	+	2.91294i	0.0813400	+	0.118723i
$603$			50.0429i			2.03791i
$604$	−2.80192	−	1.08499i	−0.114009	−	0.0441476i
$605$	−2.64561	−	1.45415i	−0.107559	−	0.0591195i
$606$	−24.9236	+	17.0758i	−1.01245	+	0.693658i
$607$	1.46563	−	1.46563i	0.0594882	−	0.0594882i	−0.676737	−	0.736225i	$-0.736606\pi$
$607$	1.46563	−	1.46563i	0.0594882	−	0.0594882i	0.736225	+	0.676737i	$0.236606\pi$
$608$	1.12897	−	8.11555i	0.0457859	−	0.329129i
$609$			8.13309i			0.329569i
$610$	18.0921	−	1.78059i	0.732527	−	0.0720942i
$611$	34.9111	+	34.9111i	1.41235	+	1.41235i
$612$	8.59748	+	19.4636i	0.347533	+	0.786767i
$613$	11.1696			0.451137			0.225568	−	0.974227i	$-0.427576\pi$
$613$	11.1696			0.451137			0.225568	+	0.974227i	$0.427576\pi$
$614$	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	$-0.592776\pi$
$617$	16.6541	−	16.6541i	0.670468	−	0.670468i	0.957824	+	0.287356i	$0.0927763\pi$
$618$	11.5760	+	16.8962i	0.465656	+	0.679664i
$619$	0.0485986	+	0.0485986i	0.00195334	+	0.00195334i	0.708083	−	0.706129i	$-0.249560\pi$
$619$	0.0485986	+	0.0485986i	0.00195334	+	0.00195334i	−0.706129	+	0.708083i	$0.749560\pi$
$620$	−14.7015	−	17.4977i	−0.590427	−	0.702724i
$621$	−21.5378	+	21.5378i	−0.864282	+	0.864282i
$622$	2.09345	−	11.2036i	0.0839396	−	0.449224i
$623$	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
$627$		−	14.0317i		−	0.560371i
$628$	36.4138	+	14.1005i	1.45307	+	0.562672i
$629$	14.0561	−	14.0561i	0.560455	−	0.560455i
$630$	1.42435	+	14.4724i	0.0567476	+	0.576595i
$631$	13.0513			0.519565			0.259782	−	0.965667i	$-0.416349\pi$
$631$	13.0513			0.519565			0.259782	+	0.965667i	$0.416349\pi$
$632$	−17.2254	+	27.8339i	−0.685189	+	1.10717i
$633$	−55.8494	−	55.8494i	−2.21981	−	2.21981i
$634$	−5.96747	+	31.9364i	−0.236999	+	1.26836i
$635$	−11.6888	−	40.2204i	−0.463854	−	1.59610i
$636$	−28.8682	−	11.1786i	−1.14470	−	0.443262i
$637$	−4.84084			−0.191801
$638$	−2.69332	+	14.4140i	−0.106630	+	0.570655i
$639$	−56.1033			−2.21941
$640$	−5.64043	+	24.6614i	−0.222958	+	0.974828i
$641$	34.2117			1.35128			0.675641	−	0.737231i	$-0.263867\pi$
$641$	34.2117			1.35128			0.675641	+	0.737231i	$0.263867\pi$
$642$	−0.540941	+	2.89498i	−0.0213492	+	0.114256i
$643$	28.6521			1.12993			0.564965	−	0.825115i	$-0.308890\pi$
$643$	28.6521			1.12993			0.564965	+	0.825115i	$0.308890\pi$
$644$	−12.8906	−	4.99162i	−0.507960	−	0.196697i
$645$	−13.4871	−	7.41310i	−0.531052	−	0.291890i
$646$	−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	$0.770105\pi$
$648$	2.45309	−	3.96386i	0.0963664	−	0.155715i
$649$	40.2144			1.57855
$650$	−12.7261	−	31.7763i	−0.499160	−	1.24637i
$651$	9.96095	−	9.96095i	0.390400	−	0.390400i
$652$	−5.32159	−	2.06068i	−0.208410	−	0.0807025i
$653$			4.22100i			0.165181i	0.996584	+	0.0825903i	$0.0263193\pi$
$653$			4.22100i			0.165181i	−0.996584	+	0.0825903i	$0.973681\pi$
$654$	−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
$658$	−2.64926	+	14.1782i	−0.103279	+	0.552722i
$659$	11.9000	−	11.9000i	0.463559	−	0.463559i	−0.436261	−	0.899820i	$-0.643698\pi$
$659$	11.9000	−	11.9000i	0.463559	−	0.463559i	0.899820	+	0.436261i	$0.143698\pi$
$660$	−3.74805	+	43.1607i	−0.145893	+	1.68003i
$661$	−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	$-0.574715\pi$
$662$	−8.96481	−	13.0849i	−0.348427	−	0.508559i
$663$	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
$667$	20.3924			0.789596
$668$	−10.6965	−	24.2155i	−0.413861	−	0.936926i
$669$	−20.8474	−	20.8474i	−0.806005	−	0.806005i
$670$	21.8326	−	26.5992i	0.843466	−	1.02762i
$671$			20.2030i			0.779930i
$672$	−15.4448	−	2.14856i	−0.595796	−	0.0828827i
$673$	−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
$675$	−11.8098	−	18.6024i	−0.454561	−	0.716008i
$676$	19.4594	+	7.53528i	0.748440	+	0.289818i
$677$			6.46862i			0.248609i	0.992244	+	0.124305i	$0.0396700\pi$
$677$			6.46862i			0.248609i	−0.992244	+	0.124305i	$0.960330\pi$
$678$	11.4771	+	16.7518i	0.440776	+	0.643350i
$679$			9.36624i			0.359443i
$680$	3.92171	−	14.0963i	0.150391	−	0.540568i
$681$		−	66.9414i		−	2.56520i
$682$	20.9521	−	14.3548i	0.802296	−	0.549674i
$683$			42.9729i			1.64431i	0.569263	+	0.822155i	$0.307229\pi$
$683$			42.9729i			1.64431i	−0.569263	+	0.822155i	$0.692771\pi$
$684$	−12.1861	+	5.38286i	−0.465946	+	0.205819i
$685$	8.76806	+	30.1704i	0.335010	+	1.15275i
$686$	−0.799311	−	1.16666i	−0.0305178	−	0.0445434i
$687$	−38.3403	+	38.3403i	−1.46278	+	1.46278i
$688$	6.72617	−	7.38269i	0.256433	−	0.281463i
$689$			27.1819i			1.03555i
$690$	59.9595	−	5.90112i	2.28262	−	0.224652i
$691$	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	$0.731401\pi$
$692$	−0.459279	+	1.18606i	−0.0174591	+	0.0450873i
$693$	−16.1611			−0.613908
$694$	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
$698$	−34.7882	+	23.8343i	−1.31675	+	0.902141i
$699$	28.5835	+	28.5835i	1.08113	+	1.08113i
$700$	5.55690	−	8.31389i	0.210031	−	0.314236i
$701$	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	$0.234179\pi$
$702$	29.6564	+	5.54144i	1.11931	+	0.209148i
$703$	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
$707$			7.74991i			0.291465i
$708$	−25.4911	−	57.7085i	−0.958015	−	2.16882i
$709$	−19.6414	+	19.6414i	−0.737649	+	0.737649i	−0.972123	−	0.234473i	$-0.924663\pi$
$709$	−19.6414	+	19.6414i	−0.737649	+	0.737649i	0.234473	+	0.972123i	$0.424663\pi$
$710$	29.8204	+	24.4766i	1.11914	+	0.918590i
$711$	53.2199			1.99590
$712$	9.42090	−	15.2229i	0.353063	−	0.570503i
$713$	−24.9754	−	24.9754i	−0.935337	−	0.935337i
$714$	8.86534	+	1.65653i	0.331777	+	0.0619941i
$715$	36.5287	−	10.6159i	1.36610	−	0.397012i
$716$	−46.1944	+	20.4051i	−1.72636	+	0.762574i
$717$	−10.1103			−0.377575
$718$	37.7106	+	7.04642i	1.40735	+	0.262970i
$719$	13.6872			0.510445			0.255222	−	0.966882i	$-0.417851\pi$
$719$	13.6872			0.510445			0.255222	+	0.966882i	$0.417851\pi$
$720$	38.9215	−	13.3023i	1.45052	−	0.495748i
$721$	5.25380			0.195662
$722$	23.4963	+	4.39041i	0.874443	+	0.163394i
$723$	−34.1604			−1.27044
$724$	17.5912	+	39.8242i	0.653772	+	1.48005i
$725$	−3.21567	+	14.3974i	−0.119427	+	0.534707i
$726$	−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	$0.514828\pi$
$728$	3.13778	+	13.3276i	0.116294	+	0.493953i
$729$	−44.0230			−1.63048
$730$	−2.39082	−	24.2924i	−0.0884883	−	0.899102i
$731$	−4.08446	+	4.08446i	−0.151069	+	0.151069i
$732$	28.9918	−	12.8063i	1.07157	−	0.473336i
$733$			10.9558i			0.404663i	0.979317	+	0.202332i	$0.0648519\pi$
$733$			10.9558i			0.404663i	−0.979317	+	0.202332i	$0.935148\pi$
$734$	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
$738$	−44.4124	−	8.29868i	−1.63484	−	0.305479i
$739$	−11.1809	+	11.1809i	−0.411294	+	0.411294i	−0.882189	−	0.470895i	$-0.843931\pi$
$739$	−11.1809	+	11.1809i	−0.411294	+	0.411294i	0.470895	+	0.882189i	$0.343931\pi$
$740$	−24.7192	−	29.4206i	−0.908694	−	1.08152i
$741$	13.6672	+	13.6672i	0.502078	+	0.502078i
$742$	−6.55096	+	4.48823i	−0.240493	+	0.164768i
$743$	−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
$747$	13.1523			0.481219
$748$	15.1631	+	5.87162i	0.554420	+	0.214688i
$749$	0.534193	+	0.534193i	0.0195190	+	0.0195190i
$750$	−5.28869	+	43.2632i	−0.193116	+	1.57975i
$751$			6.56902i			0.239707i	0.992792	+	0.119854i	$0.0382425\pi$
$751$			6.56902i			0.239707i	−0.992792	+	0.119854i	$0.961758\pi$
$752$	40.7519	−	1.89630i	1.48607	−	0.0691510i
$753$	−33.8790	+	33.8790i	−1.23462	+	1.23462i
$754$	−11.4162	−	16.6630i	−0.415754	−	0.606829i
$755$	1.61811	−	2.94392i	0.0588892	−	0.107140i
$756$	3.56130	+	8.06230i	0.129523	+	0.293223i
$757$			35.7256i			1.29847i	0.760589	+	0.649234i	$0.224910\pi$
$757$			35.7256i			1.29847i	−0.760589	+	0.649234i	$0.775090\pi$
$758$	−33.3367	+	22.8399i	−1.21084	+	0.829581i
$759$			66.9555i			2.43033i
$760$	8.82564	+	2.45537i	0.320140	+	0.0890656i
$761$		−	23.5949i		−	0.855315i	−0.903941	−	0.427658i	$-0.859339\pi$
$761$		−	23.5949i		−	0.855315i	0.903941	−	0.427658i	$-0.140661\pi$
$762$	−41.2718	−	60.2397i	−1.49512	−	2.18225i
$763$			5.82895i			0.211022i
$764$	10.7389	−	27.7326i	0.388520	−	1.00333i
$765$	−22.8442	+	6.63893i	−0.825934	+	0.240031i
$766$	−28.3799	+	19.4438i	−1.02541	+	0.702532i
$767$	−39.1698	+	39.1698i	−1.41434	+	1.41434i
$768$	4.09581	+	43.9146i	0.147795	+	1.58463i
$769$			20.1520i			0.726700i	0.931653	+	0.363350i	$0.118367\pi$
$769$			20.1520i			0.726700i	−0.931653	+	0.363350i	$0.881633\pi$
$770$	8.59003	+	7.05070i	0.309563	+	0.254089i
$771$	16.5025	+	16.5025i	0.594322	+	0.594322i
$772$	5.54050	−	2.44736i	0.199407	−	0.0880825i
$773$	5.06146			0.182048			0.0910240	−	0.995849i	$-0.470986\pi$
$773$	5.06146			0.182048			0.0910240	+	0.995849i	$0.470986\pi$
$774$	−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
$778$	−11.4584	−	16.7245i	−0.410802	−	0.599601i
$779$	−7.11536	−	7.11536i	−0.254934	−	0.254934i
$780$	−38.3889	−	45.6903i	−1.37454	−	1.63598i
$781$	−30.3162	+	30.3162i	−1.08480	+	1.08480i
$782$	4.15348	−	22.2284i	0.148528	−	0.794885i
$783$	−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
$787$			11.1184i			0.396328i	0.980169	+	0.198164i	$0.0634979\pi$
$787$			11.1184i			0.396328i	−0.980169	+	0.198164i	$0.936502\pi$
$788$	5.18561	−	13.3916i	0.184730	−	0.477054i
$789$	15.7178	−	15.7178i	0.559567	−	0.559567i
$790$	−28.2878	−	23.2186i	−1.00643	−	0.826081i
$791$	5.20891			0.185208
$792$	10.4754	+	44.4939i	0.372227	+	1.58102i
$793$	−19.6783	−	19.6783i	−0.698796	−	0.698796i
$794$	7.00890	−	37.5099i	0.248737	−	1.33118i
$795$	16.6714	−	30.3313i	0.591275	−	1.07574i
$796$	−8.13602	+	21.0108i	−0.288374	+	0.744709i
$797$	−24.7966			−0.878340			−0.439170	−	0.898404i	$-0.644727\pi$
$797$	−24.7966			−0.878340			−0.439170	+	0.898404i	$0.644727\pi$
$798$	−1.03715	+	5.55056i	−0.0367147	+	0.196488i
$799$	−23.5950			−0.834732
$800$	−26.4913	−	9.91004i	−0.936610	−	0.350373i
$801$	−29.1070			−1.02844
$802$	−3.27581	+	17.5313i	−0.115673	+	0.619051i
$803$	27.1268			0.957285
$804$	21.6639	−	55.9460i	0.764029	−	1.97306i
$805$	7.44433	−	13.5439i	0.262378	−	0.477359i
$806$	−6.42590	+	34.3898i	−0.226343	+	1.21133i
$807$	−48.5885	−	48.5885i	−1.71040	−	1.71040i
$808$	21.3367	−	5.02340i	0.750622	−	0.176723i
$809$	42.9948			1.51162			0.755808	−	0.654793i	$-0.227244\pi$
$809$	42.9948			1.51162			0.755808	+	0.654793i	$0.227244\pi$
$810$	4.02850	+	3.30659i	0.141547	+	0.116182i
$811$	−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	$0.355815\pi$
$812$	2.13082	−	5.50272i	0.0747770	−	0.193107i
$813$		−	58.1439i		−	2.03920i
$814$	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
$818$	−8.04721	+	43.0666i	−0.281364	+	1.50579i
$819$	15.7413	−	15.7413i	0.550045	−	0.550045i
$820$	19.9859	+	23.7871i	0.697937	+	0.830681i
$821$	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	$0.696979\pi$
$822$	30.9591	+	45.1874i	1.07982	+	1.57609i
$823$	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
$827$	−26.8726			−0.934451			−0.467225	−	0.884138i	$-0.654746\pi$
$827$	−26.8726			−0.934451			−0.467225	+	0.884138i	$0.654746\pi$
$828$	58.1488	−	25.6856i	2.02081	−	0.892637i
$829$	−15.5232	−	15.5232i	−0.539144	−	0.539144i	0.384134	−	0.923277i	$-0.374500\pi$
$829$	−15.5232	−	15.5232i	−0.539144	−	0.539144i	−0.923277	+	0.384134i	$0.874500\pi$
$830$	−6.99082	−	5.73806i	−0.242655	−	0.199171i
$831$		−	89.0711i		−	3.08984i
$832$	34.6590	−	17.2776i	1.20158	−	0.598991i
$833$	1.63587	−	1.63587i	0.0566794	−	0.0566794i
$834$	16.8139	−	11.5196i	0.582218	−	0.398893i
$835$	28.4215	−	8.25981i	0.983568	−	0.285842i
$836$	−3.67621	+	9.49360i	−0.127144	+	0.328343i
$837$			22.5207i			0.778428i
$838$	4.94838	+	7.22259i	0.170939	+	0.249500i
$839$		−	50.9551i		−	1.75917i	−0.475746	−	0.879583i	$-0.657822\pi$
$839$		−	50.9551i		−	1.75917i	0.475746	−	0.879583i	$-0.342178\pi$
$840$	4.67285	−	16.7962i	0.161229	−	0.579524i
$841$		−	20.2949i		−	0.699825i
$842$	20.6249	−	14.1306i	0.710780	−	0.486973i
$843$			5.88624i			0.202733i
$844$	23.1546	+	52.4190i	0.797015	+	1.80434i
$845$	−11.2378	+	20.4456i	−0.386594	+	0.703351i
$846$	−37.4893	−	54.7189i	−1.28891	−	1.88127i
$847$	−0.954662	+	0.954662i	−0.0328026	+	0.0328026i
$848$	16.6031	+	15.1266i	0.570151	+	0.519449i
$849$			30.8823i			1.05988i
$850$	15.0387	+	6.43763i	0.515824	+	0.220809i
$851$	−41.9937	−	41.9937i	−1.43953	−	1.43953i
$852$	62.7212	+	24.2875i	2.14879	+	0.832077i
$853$	47.4000			1.62294			0.811472	−	0.584391i	$-0.198666\pi$
$853$	47.4000			1.62294			0.811472	+	0.584391i	$0.198666\pi$
$854$	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	$-0.890407\pi$
$857$	−17.6753	+	17.6753i	−0.603778	+	0.603778i	0.337535	+	0.941313i	$0.390407\pi$
$858$	54.7105	−	37.4836i	1.86779	−	1.27967i
$859$	10.3000	+	10.3000i	0.351431	+	0.351431i	0.860642	−	0.509211i	$-0.170063\pi$
$859$	10.3000	+	10.3000i	0.351431	+	0.351431i	−0.509211	+	0.860642i	$0.670063\pi$
$860$	7.18294	+	8.54910i	0.244936	+	0.291522i
$861$	−13.5413	+	13.5413i	−0.461488	+	0.461488i
$862$	5.23582	+	0.978338i	0.178333	+	0.0333223i
$863$	−3.80338	−	3.80338i	−0.129469	−	0.129469i	0.639403	−	0.768872i	$-0.279182\pi$
$863$	−3.80338	−	3.80338i	−0.129469	−	0.129469i	−0.768872	+	0.639403i	$0.779182\pi$
$864$	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
$867$		−	32.1082i		−	1.09045i
$868$	−9.34912	+	4.12971i	−0.317330	+	0.140172i
$869$	28.7580	−	28.7580i	0.975550	−	0.975550i
$870$	2.51906	+	25.5954i	0.0854042	+	0.867766i
$871$	−52.6780			−1.78492
$872$	16.0480	−	3.77826i	0.543454	−	0.127948i
$873$	−30.4568	−	30.4568i	−1.03081	−	1.03081i
$874$	13.9171	+	2.60048i	0.470754	+	0.0879626i
$875$	8.38836	+	7.39158i	0.283578	+	0.249881i
$876$	−17.1952	−	38.9276i	−0.580971	−	1.31524i
$877$	−20.5582			−0.694203			−0.347101	−	0.937828i	$-0.612834\pi$
$877$	−20.5582			−0.694203			−0.347101	+	0.937828i	$0.612834\pi$
$878$	31.6305	+	5.91032i	1.06748	+	0.199464i
$879$	−29.7770			−1.00435
$880$	13.8437	−	28.2199i	0.466671	−	0.951291i
$881$	50.4861			1.70092			0.850461	−	0.526039i	$-0.176323\pi$
$881$	50.4861			1.70092			0.850461	+	0.526039i	$0.176323\pi$
$882$	6.39289	+	1.19454i	0.215260	+	0.0402223i
$883$	−0.350512			−0.0117957			−0.00589784	−	0.999983i	$-0.501877\pi$
$883$	−0.350512			−0.0117957			−0.00589784	+	0.999983i	$0.501877\pi$
$884$	−20.4884	+	9.05018i	−0.689100	+	0.304391i
$885$	67.7320	−	19.6841i	2.27679	−	0.661675i
$886$	−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	$0.809315\pi$
$888$	−56.9669	−	35.2547i	−1.91168	−	1.18307i
$889$	−18.7313			−0.628227
$890$	15.4711	+	12.6987i	0.518594	+	0.425662i
$891$	−4.09547	+	4.09547i	−0.137203	+	0.137203i
$892$	8.64311	+	19.5669i	0.289393	+	0.655147i
$893$		−	14.7728i		−	0.494352i
$894$	−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
$898$	−37.5359	−	7.01376i	−1.25259	−	0.234052i
$899$	10.6615	−	10.6615i	0.355580	−	0.355580i
$900$	8.96509	+	45.1046i	0.298836	+	1.50349i
$901$	−9.18561	−	9.18561i	−0.306017	−	0.306017i
$902$	−28.4831	+	19.5145i	−0.948385	+	0.649763i
$903$	−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
$907$	11.3958			0.378391			0.189195	−	0.981939i	$-0.439412\pi$
$907$	11.3958			0.378391			0.189195	+	0.981939i	$0.439412\pi$
$908$	−17.5382	+	45.2915i	−0.582026	+	1.50305i
$909$	−25.2009	−	25.2009i	−0.835861	−	0.835861i
$910$	−15.2345	+	1.49935i	−0.505018	+	0.0497031i
$911$			5.90154i			0.195527i	0.995210	+	0.0977634i	$0.0311688\pi$
$911$			5.90154i			0.195527i	−0.995210	+	0.0977634i	$0.968831\pi$
$912$	15.9538	−	0.742377i	0.528284	−	0.0245826i
$913$	7.10704	−	7.10704i	0.235209	−	0.235209i
$914$	0.656697	+	0.958505i	0.0217216	+	0.0317045i
$915$	9.88899	+	34.0275i	0.326920	+	1.12491i
$916$	35.9854	−	15.8955i	1.18899	−	0.525203i
$917$		−	15.0927i		−	0.498405i
$918$	−11.8944	+	8.14917i	−0.392574	+	0.268963i
$919$			8.38806i			0.276697i	0.990384	+	0.138348i	$0.0441794\pi$
$919$			8.38806i			0.276697i	−0.990384	+	0.138348i	$0.955821\pi$
$920$	−42.1137	−	11.7164i	−1.38845	−	0.386278i
$921$			34.0160i			1.12087i
$922$	−9.43184	−	13.7666i	−0.310621	−	0.453378i
$923$		−	59.0575i		−	1.94390i
$924$	18.0674	+	6.99624i	0.594374	+	0.230159i
$925$	36.2704	−	23.0265i	1.19256	−	0.757105i
$926$	48.4360	−	33.1848i	1.59171	−	1.09052i
$927$	−17.0841	+	17.0841i	−0.561117	+	0.561117i
$928$	−16.5310	−	2.29967i	−0.542656	−	0.0754902i
$929$			15.9242i			0.522456i	0.965277	+	0.261228i	$0.0841275\pi$
$929$			15.9242i			0.522456i	−0.965277	+	0.261228i	$0.915873\pi$
$930$	28.2626	−	34.4330i	0.926768	−	1.12910i
$931$	1.02421	+	1.02421i	0.0335672	+	0.0335672i
$932$	−11.8504	−	26.8278i	−0.388174	−	0.878775i
$933$	22.2159			0.727317
$934$	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	$-0.786996\pi$
$937$	−5.02005	+	5.02005i	−0.163998	+	0.163998i	0.620337	+	0.784335i	$0.286996\pi$
$938$	−8.69809	−	12.6956i	−0.284003	−	0.414526i
$939$	−15.9708	−	15.9708i	−0.521187	−	0.521187i
$940$	−3.94601	+	45.4403i	−0.128705	+	1.48210i
$941$	−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	$0.317014\pi$
$942$	−13.9802	+	74.8182i	−0.455498	+	2.43771i
$943$	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
$947$		−	22.0953i		−	0.718000i	−0.933337	−	0.359000i	$-0.883118\pi$
$947$		−	22.0953i		−	0.718000i	0.933337	−	0.359000i	$-0.116882\pi$
$948$	−59.4976	−	23.0393i	−1.93239	−	0.748281i
$949$	−26.4222	+	26.4222i	−0.857702	+	0.857702i
$950$	−4.03058	+	9.41570i	−0.130769	+	0.305486i
$951$	−63.3275			−2.05354
$952$	−5.56414	−	3.44344i	−0.180335	−	0.111603i
$953$	−18.7860	−	18.7860i	−0.608539	−	0.608539i	0.334025	−	0.942564i	$-0.391593\pi$
$953$	−18.7860	−	18.7860i	−0.608539	−	0.608539i	−0.942564	+	0.334025i	$0.891593\pi$
$954$	6.70751	−	35.8969i	0.217164	−	1.16220i
$955$	29.1381	+	16.0156i	0.942887	+	0.518253i
$956$	6.84045	+	2.64883i	0.221236	+	0.0856691i
$957$	−28.5819			−0.923920
$958$	−1.74530	+	9.34039i	−0.0563880	+	0.301774i
$959$	14.0509			0.453726
$960$	−49.2714	−	1.97797i	−1.59023	−	0.0638386i
$961$	4.88484			0.157576
$962$	−10.8045	+	57.8231i	−0.348352	+	1.86429i
$963$	−3.47414			−0.111953
$964$	23.1124	+	8.94981i	0.744400	+	0.288254i
$965$	1.88984	+	6.50284i	0.0608361	+	0.209334i
$966$	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	$0.724360\pi$
$968$	3.24713	+	2.00953i	0.104367	+	0.0645888i
$969$	−9.23714			−0.296740
$970$	2.90101	+	29.4762i	0.0931457	+	0.946425i
$971$	−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	$0.377852\pi$
$972$	33.1305	+	12.8291i	1.06266	+	0.411494i
$973$		−	5.22822i		−	0.167609i
$974$	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	$0.672846\pi$
$978$	2.04309	−	10.9341i	0.0653308	−	0.349634i
$979$	−15.7283	+	15.7283i	−0.502680	+	0.502680i
$980$	−2.87684	−	3.42400i	−0.0918973	−	0.109376i
$981$	−18.9544	−	18.9544i	−0.605167	−	0.605167i
$982$	−17.4195	−	25.4253i	−0.555879	−	0.811354i
$983$	−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
$987$	−28.1143			−0.894887
$988$	−5.66629	−	12.8277i	−0.180269	−	0.408105i
$989$	12.2026	+	12.2026i	0.388021	+	0.388021i
$990$	−50.8600	+	5.00557i	−1.61644	+	0.159087i
$991$		−	17.4578i		−	0.554565i	−0.960788	−	0.277283i	$-0.910566\pi$
$991$		−	17.4578i		−	0.554565i	0.960788	−	0.277283i	$-0.0894338\pi$
$992$	17.4297	+	23.0627i	0.553394	+	0.732243i
$993$	21.8615	−	21.8615i	0.693753	−	0.693753i
$994$	14.2331	−	9.75146i	0.451446	−	0.309298i
$995$	−22.0756	−	12.1338i	−0.699845	−	0.384667i
$996$	−14.7038	−	5.69374i	−0.465907	−	0.180413i
$997$			17.6800i			0.559932i	0.960010	+	0.279966i	$0.0903231\pi$
$997$			17.6800i			0.559932i	−0.960010	+	0.279966i	$0.909677\pi$
$998$	−5.63991	−	8.23194i	−0.178528	−	0.260577i
$999$			37.8663i			1.19804i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.6	✓	144	5.3	odd	4
560.2.t.a.547.6	yes	144	16.3	odd	4
560.2.bl.a.267.42	yes	144	1.1	even	1	trivial
560.2.bl.a.323.42	yes	144	80.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.259757 - 1.39015i) q^{2} +2.75657 q^{3} +(-1.86505 - 0.722204i) q^{4} +(1.07707 - 1.95957i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.48843 + 2.40511i) q^{8} +4.59869 q^{9} +O(q^{10})\)	\(q+(0.259757 - 1.39015i) q^{2} +2.75657 q^{3} +(-1.86505 - 0.722204i) q^{4} +(1.07707 - 1.95957i) q^{5} +(0.716039 - 3.83206i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.48843 + 2.40511i) q^{8} +4.59869 q^{9} +(-2.44433 - 2.00630i) q^{10} +(2.48496 - 2.48496i) q^{11} +(-5.14115 - 1.99081i) q^{12} +4.84084i 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} +(1.19454 - 6.39289i) q^{18} +(1.02421 - 1.02421i) q^{19} +(-3.42400 + 2.87684i) q^{20} +(-1.94919 - 1.94919i) q^{21} +(-2.80899 - 4.09997i) 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} +4.40691 q^{27} +(0.808116 + 1.82947i) q^{28} +(-2.08627 - 2.08627i) q^{29} +(-6.73797 - 5.53052i) q^{30} +5.11030i q^{31} +(4.51299 - 3.41071i) q^{32} +(6.84999 - 6.84999i) q^{33} +(-2.69903 + 1.84918i) q^{34} +(-2.14723 + 0.624023i) q^{35} +(-8.57681 - 3.32120i) q^{36} +8.59247i q^{37} +(-1.15777 - 1.68986i) q^{38} +13.3441i q^{39} +(3.10984 + 5.50717i) q^{40} -6.94716i q^{41} +(-3.21599 + 2.20336i) q^{42} -2.49682i q^{43} +(-6.42924 + 2.83994i) q^{44} +(4.95311 - 9.01147i) q^{45} +(5.52456 + 8.06357i) q^{46} +(7.21178 - 7.21178i) q^{47} +(8.15075 + 7.42592i) q^{48} +1.00000i q^{49} +(-6.56421 + 2.62891i) q^{50} +(-4.50939 - 4.50939i) q^{51} +(3.49607 - 9.02842i) q^{52} +5.61513 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} +(-3.44216 + 2.35831i) q^{58} +(8.09154 + 8.09154i) q^{59} +(-9.43851 + 7.93022i) q^{60} +(-4.06506 + 4.06506i) q^{61} +(7.10410 + 1.32744i) 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} +10.8820i q^{67} +(1.86955 + 4.23241i) q^{68} +(-13.4721 + 13.4721i) q^{69} +(0.309730 + 3.14707i) q^{70} -12.1998 q^{71} +(-6.84486 + 11.0604i) q^{72} +(5.45819 + 5.45819i) q^{73} +(11.9448 + 2.23195i) q^{74} +(-7.38718 - 11.6360i) q^{75} +(-2.64990 + 1.17052i) q^{76} -3.51427 q^{77} +(18.5504 + 3.46623i) q^{78} +11.5728 q^{79} +(8.46361 - 2.89263i) q^{80} -1.64810 q^{81} +(-9.65762 - 1.80457i) q^{82} +2.86002 q^{83} +(2.22763 + 5.04306i) q^{84} +(-4.96754 + 1.44366i) q^{85} +(-3.47096 - 0.648566i) q^{86} +(-5.75096 - 5.75096i) q^{87} +(2.27791 + 9.67532i) q^{88} -6.32940 q^{89} +(-11.2407 - 9.22638i) q^{90} +(3.42299 - 3.42299i) q^{91} +(12.6446 - 5.58542i) q^{92} +14.0869i 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} +(1.39015 + 0.259757i) 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	\( 144 q - 8 q^{4} + 144 q^{9} - 16 q^{12} + 8 q^{16} + 28 q^{18} + 16 q^{19} - 36 q^{22} + 32 q^{26} - 36 q^{30} - 40 q^{32} - 32 q^{34} - 32 q^{36} - 56 q^{38} - 48 q^{40} + 20 q^{42} + 56 q^{44} - 32 q^{46} - 24 q^{48} + 8 q^{50} - 16 q^{51} - 16 q^{52} - 32 q^{54} - 24 q^{56} - 52 q^{58} - 32 q^{60} - 32 q^{61} + 40 q^{62} - 32 q^{64} + 32 q^{66} + 80 q^{68} + 32 q^{69} + 40 q^{72} + 16 q^{73} + 32 q^{74} - 24 q^{75} - 28 q^{78} + 72 q^{80} + 144 q^{81} + 24 q^{82} - 80 q^{83} + 32 q^{86} - 112 q^{87} + 40 q^{88} + 32 q^{90} - 16 q^{92} + 8 q^{94} - 80 q^{95} + 32 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q - 8 * q^4 + 144 * q^9 - 16 * q^12 + 8 * q^16 + 28 * q^18 + 16 * q^19 - 36 * q^22 + 32 * q^26 - 36 * q^30 - 40 * q^32 - 32 * q^34 - 32 * q^36 - 56 * q^38 - 48 * q^40 + 20 * q^42 + 56 * q^44 - 32 * q^46 - 24 * q^48 + 8 * q^50 - 16 * q^51 - 16 * q^52 - 32 * q^54 - 24 * q^56 - 52 * q^58 - 32 * q^60 - 32 * q^61 + 40 * q^62 - 32 * q^64 + 32 * q^66 + 80 * q^68 + 32 * q^69 + 40 * q^72 + 16 * q^73 + 32 * q^74 - 24 * q^75 - 28 * q^78 + 72 * q^80 + 144 * q^81 + 24 * q^82 - 80 * q^83 + 32 * q^86 - 112 * q^87 + 40 * q^88 + 32 * q^90 - 16 * q^92 + 8 * q^94 - 80 * q^95 + 32 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more