LMFDB - Embedded newform 280.2.bl.b.221.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(221,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("280.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bl (of order $6$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.18
Character	$\chi$	$=$	280.221
Dual form			280.2.bl.b.261.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.585931 - 1.28712i) q^{2} +(2.20766 + 1.27459i) q^{3} +(-1.31337 - 1.50833i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.93409 - 2.09470i) q^{6} +(-0.879470 - 2.49530i) q^{7} +(-2.71095 + 0.806691i) q^{8} +(1.74917 + 3.02964i) q^{9} +O(q^{10})$	\(q+(0.585931 - 1.28712i) q^{2} +(2.20766 + 1.27459i) q^{3} +(-1.31337 - 1.50833i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.93409 - 2.09470i) q^{6} +(-0.879470 - 2.49530i) q^{7} +(-2.71095 + 0.806691i) q^{8} +(1.74917 + 3.02964i) q^{9} +(-0.136130 - 1.40765i) q^{10} +(1.99839 + 1.15377i) q^{11} +(-0.976966 - 5.00389i) q^{12} -1.62692i q^{13} +(-3.72707 - 0.330088i) q^{14} +2.54918 q^{15} +(-0.550119 + 3.96199i) q^{16} +(-2.15765 + 3.73716i) q^{17} +(4.92441 - 0.476229i) q^{18} +(-1.18985 + 0.686957i) q^{19} +(-1.89158 - 0.649567i) q^{20} +(1.23892 - 6.62974i) q^{21} +(2.65596 - 1.89614i) q^{22} +(4.08835 + 7.08122i) q^{23} +(-7.01305 - 1.67446i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.09404 - 0.953261i) q^{26} +1.27034i q^{27} +(-2.60867 + 4.60379i) q^{28} -4.96693i q^{29} +(1.49365 - 3.28111i) q^{30} +(-3.13946 + 5.43770i) q^{31} +(4.77724 + 3.02952i) q^{32} +(2.94117 + 5.09425i) q^{33} +(3.54595 + 4.96687i) q^{34} +(-2.00929 - 1.72126i) q^{35} +(2.27240 - 6.61736i) q^{36} +(-4.65201 + 2.68584i) q^{37} +(0.187031 + 1.93399i) q^{38} +(2.07365 - 3.59168i) q^{39} +(-1.94441 + 2.05409i) q^{40} -8.00556 q^{41} +(-7.80736 - 5.47921i) q^{42} -3.14465i q^{43} +(-0.884356 - 4.52955i) q^{44} +(3.02964 + 1.74917i) q^{45} +(11.5099 - 1.11310i) q^{46} +(-5.45976 - 9.45659i) q^{47} +(-6.26439 + 8.04554i) q^{48} +(-5.45306 + 4.38909i) q^{49} +(-0.821716 - 1.15099i) q^{50} +(-9.52670 + 5.50024i) q^{51} +(-2.45393 + 2.13674i) q^{52} +(-7.48981 - 4.32425i) q^{53} +(1.63508 + 0.744331i) q^{54} +2.30754 q^{55} +(4.39714 + 6.05518i) q^{56} -3.50236 q^{57} +(-6.39305 - 2.91028i) q^{58} +(12.1528 + 7.01643i) q^{59} +(-3.34802 - 3.84501i) q^{60} +(-0.765526 + 0.441977i) q^{61} +(5.15948 + 7.22699i) q^{62} +(6.02154 - 7.02918i) q^{63} +(6.69850 - 4.37380i) q^{64} +(-0.813459 - 1.40895i) q^{65} +(8.28024 - 0.800764i) q^{66} +(7.98766 + 4.61168i) q^{67} +(8.47066 - 1.65382i) q^{68} +20.8439i q^{69} +(-3.39278 + 1.57767i) q^{70} +9.13738 q^{71} +(-7.18589 - 6.80218i) q^{72} +(-1.10982 + 1.92226i) q^{73} +(0.731249 + 7.56143i) q^{74} +(2.20766 - 1.27459i) q^{75} +(2.59887 + 0.892450i) q^{76} +(1.12148 - 6.00128i) q^{77} +(-3.40791 - 4.77352i) q^{78} +(0.729092 + 1.26282i) q^{79} +(1.50458 + 3.70624i) q^{80} +(3.62833 - 6.28446i) q^{81} +(-4.69070 + 10.3041i) q^{82} -15.5420i q^{83} +(-11.6270 + 6.83859i) q^{84} +4.31530i q^{85} +(-4.04755 - 1.84255i) q^{86} +(6.33081 - 10.9653i) q^{87} +(-6.34826 - 1.51573i) q^{88} +(3.25469 + 5.63729i) q^{89} +(4.02655 - 2.87463i) q^{90} +(-4.05965 + 1.43083i) q^{91} +(5.31131 - 15.4668i) q^{92} +(-13.8617 + 8.00305i) q^{93} +(-15.3708 + 1.48648i) q^{94} +(-0.686957 + 1.18985i) q^{95} +(6.68509 + 12.7772i) q^{96} -1.77157 q^{97} +(2.45418 + 9.59046i) q^{98} +8.07253i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9}+O(q^{10}) $ 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9	$ 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9} + 2 q^{10} - 10 q^{12} + 20 q^{14} - 22 q^{16} - 12 q^{17} + 6 q^{18} - 16 q^{20} - 28 q^{22} - 2 q^{23} - 32 q^{24} + 30 q^{25} - 4 q^{26} - 22 q^{28} - 6 q^{32} - 16 q^{34} + 20 q^{36} - 42 q^{38} + 4 q^{40} - 36 q^{41} - 62 q^{42} + 14 q^{44} + 28 q^{46} - 30 q^{47} + 124 q^{48} + 12 q^{49} + 8 q^{50} + 8 q^{52} - 40 q^{54} - 44 q^{55} + 8 q^{56} - 32 q^{57} - 14 q^{58} + 14 q^{60} - 16 q^{62} - 74 q^{63} + 4 q^{64} + 2 q^{65} + 60 q^{66} + 28 q^{68} + 10 q^{70} - 8 q^{71} - 72 q^{72} - 52 q^{74} - 12 q^{76} - 40 q^{78} + 32 q^{79} - 22 q^{81} - 16 q^{82} - 8 q^{84} - 44 q^{86} + 48 q^{87} - 16 q^{88} + 4 q^{89} - 48 q^{90} + 84 q^{92} - 56 q^{94} + 2 q^{95} - 16 q^{96} - 96 q^{97} - 80 q^{98}+O(q^{100}) $ 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9 + 2 * q^10 - 10 * q^12 + 20 * q^14 - 22 * q^16 - 12 * q^17 + 6 * q^18 - 16 * q^20 - 28 * q^22 - 2 * q^23 - 32 * q^24 + 30 * q^25 - 4 * q^26 - 22 * q^28 - 6 * q^32 - 16 * q^34 + 20 * q^36 - 42 * q^38 + 4 * q^40 - 36 * q^41 - 62 * q^42 + 14 * q^44 + 28 * q^46 - 30 * q^47 + 124 * q^48 + 12 * q^49 + 8 * q^50 + 8 * q^52 - 40 * q^54 - 44 * q^55 + 8 * q^56 - 32 * q^57 - 14 * q^58 + 14 * q^60 - 16 * q^62 - 74 * q^63 + 4 * q^64 + 2 * q^65 + 60 * q^66 + 28 * q^68 + 10 * q^70 - 8 * q^71 - 72 * q^72 - 52 * q^74 - 12 * q^76 - 40 * q^78 + 32 * q^79 - 22 * q^81 - 16 * q^82 - 8 * q^84 - 44 * q^86 + 48 * q^87 - 16 * q^88 + 4 * q^89 - 48 * q^90 + 84 * q^92 - 56 * q^94 + 2 * q^95 - 16 * q^96 - 96 * q^97 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.585931	−	1.28712i	0.414316	−	0.910133i
$2$	0.585931	−	1.28712i	0.414316	−	0.910133i
$3$	2.20766	+	1.27459i	1.27459	+	0.735886i	0.975849	−	0.218448i	$-0.0700994\pi$
$3$	2.20766	+	1.27459i	1.27459	+	0.735886i	0.298743	+	0.954334i	$0.403433\pi$
$4$	−1.31337	−	1.50833i	−0.656685	−	0.754165i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	2.93409	−	2.09470i	1.19784	−	0.855159i
$7$	−0.879470	−	2.49530i	−0.332409	−	0.943135i
$7$	−0.879470	−	2.49530i	−0.332409	−	0.943135i
$8$	−2.71095	+	0.806691i	−0.958466	+	0.285208i
$9$	1.74917	+	3.02964i	0.583055	+	1.00988i
$10$	−0.136130	−	1.40765i	−0.0430482	−	0.445137i
$11$	1.99839	+	1.15377i	0.602536	+	0.347874i	0.770039	−	0.637997i	$-0.220237\pi$
$11$	1.99839	+	1.15377i	0.602536	+	0.347874i	−0.167503	+	0.985872i	$0.553570\pi$
$12$	−0.976966	−	5.00389i	−0.282026	−	1.44450i
$13$		−	1.62692i		−	0.451226i	−0.974217	−	0.225613i	$-0.927562\pi$
$13$		−	1.62692i		−	0.451226i	0.974217	−	0.225613i	$-0.0724384\pi$
$14$	−3.72707	−	0.330088i	−0.996101	−	0.0882198i
$15$	2.54918			0.658196
$16$	−0.550119	+	3.96199i	−0.137530	+	0.990498i
$17$	−2.15765	+	3.73716i	−0.523307	+	0.906394i	0.476325	+	0.879269i	$0.341968\pi$
$17$	−2.15765	+	3.73716i	−0.523307	+	0.906394i	−0.999632	+	0.0271247i	$0.991365\pi$
$18$	4.92441	−	0.476229i	1.16070	−	0.112248i
$19$	−1.18985	+	0.686957i	−0.272969	+	0.157599i	−0.630236	−	0.776403i	$-0.717042\pi$
$19$	−1.18985	+	0.686957i	−0.272969	+	0.157599i	0.357267	+	0.934002i	$0.383709\pi$
$20$	−1.89158	−	0.649567i	−0.422969	−	0.145248i
$21$	1.23892	−	6.62974i	0.270355	−	1.44673i
$22$	2.65596	−	1.89614i	0.566252	−	0.404258i
$23$	4.08835	+	7.08122i	0.852479	+	1.47654i	0.878964	+	0.476888i	$0.158235\pi$
$23$	4.08835	+	7.08122i	0.852479	+	1.47654i	−0.0264853	+	0.999649i	$0.508432\pi$
$24$	−7.01305	−	1.67446i	−1.43153	−	0.341797i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.09404	−	0.953261i	−0.410675	−	0.186950i
$27$			1.27034i			0.244477i
$28$	−2.60867	+	4.60379i	−0.492992	+	0.870034i
$29$		−	4.96693i		−	0.922336i	−0.887313	−	0.461168i	$-0.847431\pi$
$29$		−	4.96693i		−	0.922336i	0.887313	−	0.461168i	$-0.152569\pi$
$30$	1.49365	−	3.28111i	0.272701	−	0.599046i
$31$	−3.13946	+	5.43770i	−0.563863	+	0.976640i	0.433291	+	0.901254i	$0.357352\pi$
$31$	−3.13946	+	5.43770i	−0.563863	+	0.976640i	−0.997154	+	0.0753860i	$0.975981\pi$
$32$	4.77724	+	3.02952i	0.844504	+	0.535549i
$33$	2.94117	+	5.09425i	0.511991	+	0.886795i
$34$	3.54595	+	4.96687i	0.608125	+	0.851812i
$35$	−2.00929	−	1.72126i	−0.339633	−	0.290946i
$36$	2.27240	−	6.61736i	0.378734	−	1.10289i
$37$	−4.65201	+	2.68584i	−0.764786	+	0.441550i	−0.831012	−	0.556255i	$-0.812238\pi$
$37$	−4.65201	+	2.68584i	−0.764786	+	0.441550i	0.0662252	+	0.997805i	$0.478904\pi$
$38$	0.187031	+	1.93399i	0.0303405	+	0.313734i
$39$	2.07365	−	3.59168i	0.332051	−	0.575128i
$40$	−1.94441	+	2.05409i	−0.307438	+	0.324780i
$41$	−8.00556			−1.25026			−0.625129	−	0.780521i	$-0.714954\pi$
$41$	−8.00556			−1.25026			−0.625129	+	0.780521i	$0.714954\pi$
$42$	−7.80736	−	5.47921i	−1.20470	−	0.845461i
$43$		−	3.14465i		−	0.479555i	−0.970828	−	0.239778i	$-0.922925\pi$
$43$		−	3.14465i		−	0.479555i	0.970828	−	0.239778i	$-0.0770745\pi$
$44$	−0.884356	−	4.52955i	−0.133322	−	0.682855i
$45$	3.02964	+	1.74917i	0.451633	+	0.260750i
$46$	11.5099	−	1.11310i	1.69704	−	0.164117i
$47$	−5.45976	−	9.45659i	−0.796388	−	1.37938i	−0.921954	−	0.387300i	$-0.873408\pi$
$47$	−5.45976	−	9.45659i	−0.796388	−	1.37938i	0.125566	−	0.992085i	$-0.459925\pi$
$48$	−6.26439	+	8.04554i	−0.904187	+	1.16127i
$49$	−5.45306	+	4.38909i	−0.779009	+	0.627013i
$50$	−0.821716	−	1.15099i	−0.116208	−	0.162775i
$51$	−9.52670	+	5.50024i	−1.33400	+	0.770188i
$52$	−2.45393	+	2.13674i	−0.340299	+	0.296313i
$53$	−7.48981	−	4.32425i	−1.02881	−	0.593981i	−0.112163	−	0.993690i	$-0.535778\pi$
$53$	−7.48981	−	4.32425i	−1.02881	−	0.593981i	−0.916642	+	0.399709i	$0.869111\pi$
$54$	1.63508	+	0.744331i	0.222507	+	0.101291i
$55$	2.30754			0.311148
$56$	4.39714	+	6.05518i	0.587592	+	0.809157i
$57$	−3.50236			−0.463899
$58$	−6.39305	−	2.91028i	−0.839448	−	0.382138i
$59$	12.1528	+	7.01643i	1.58216	+	0.913461i	0.994544	+	0.104322i	$0.0332671\pi$
$59$	12.1528	+	7.01643i	1.58216	+	0.913461i	0.587617	+	0.809139i	$0.300066\pi$
$60$	−3.34802	−	3.84501i	−0.432227	−	0.496389i
$61$	−0.765526	+	0.441977i	−0.0980156	+	0.0565893i	−0.548207	−	0.836343i	$-0.684689\pi$
$61$	−0.765526	+	0.441977i	−0.0980156	+	0.0565893i	0.450191	+	0.892932i	$0.351356\pi$
$62$	5.15948	+	7.22699i	0.655255	+	0.917828i
$63$	6.02154	−	7.02918i	0.758642	−	0.885593i
$64$	6.69850	−	4.37380i	0.837312	−	0.546725i
$65$	−0.813459	−	1.40895i	−0.100897	−	0.174759i
$66$	8.28024	−	0.800764i	1.01923	−	0.0985672i
$67$	7.98766	+	4.61168i	0.975848	+	0.563406i	0.901014	−	0.433790i	$-0.142824\pi$
$67$	7.98766	+	4.61168i	0.975848	+	0.563406i	0.0748341	+	0.997196i	$0.476157\pi$
$68$	8.47066	−	1.65382i	1.02722	−	0.200556i
$69$			20.8439i			2.50931i
$70$	−3.39278	+	1.57767i	−0.405515	+	0.188568i
$71$	9.13738			1.08441			0.542204	−	0.840247i	$-0.317590\pi$
$71$	9.13738			1.08441			0.542204	+	0.840247i	$0.317590\pi$
$72$	−7.18589	−	6.80218i	−0.846865	−	0.801644i
$73$	−1.10982	+	1.92226i	−0.129895	+	0.224984i	−0.923636	−	0.383272i	$-0.874797\pi$
$73$	−1.10982	+	1.92226i	−0.129895	+	0.224984i	0.793741	+	0.608256i	$0.208131\pi$
$74$	0.731249	+	7.56143i	0.0850059	+	0.878998i
$75$	2.20766	−	1.27459i	0.254918	−	0.147177i
$76$	2.59887	+	0.892450i	0.298110	+	0.102371i
$77$	1.12148	−	6.00128i	0.127804	−	0.683909i
$78$	−3.40791	−	4.77352i	−0.385870	−	0.540495i
$79$	0.729092	+	1.26282i	0.0820292	+	0.142079i	0.904121	−	0.427276i	$-0.140527\pi$
$79$	0.729092	+	1.26282i	0.0820292	+	0.142079i	−0.822092	+	0.569354i	$0.807193\pi$
$80$	1.50458	+	3.70624i	0.168217	+	0.414371i
$81$	3.62833	−	6.28446i	0.403148	−	0.698273i
$82$	−4.69070	+	10.3041i	−0.518002	+	1.13790i
$83$		−	15.5420i		−	1.70596i	−0.521948	−	0.852978i	$-0.674794\pi$
$83$		−	15.5420i		−	1.70596i	0.521948	−	0.852978i	$-0.325206\pi$
$84$	−11.6270	+	6.83859i	−1.26861	+	0.746152i
$85$			4.31530i			0.468060i
$86$	−4.04755	−	1.84255i	−0.436459	−	0.198687i
$87$	6.33081	−	10.9653i	0.678734	−	1.17560i
$88$	−6.34826	−	1.51573i	−0.676726	−	0.161577i
$89$	3.25469	+	5.63729i	0.344997	+	0.597552i	0.985353	−	0.170526i	$-0.0545467\pi$
$89$	3.25469	+	5.63729i	0.344997	+	0.597552i	−0.640356	+	0.768078i	$0.721213\pi$
$90$	4.02655	−	2.87463i	0.424436	−	0.303013i
$91$	−4.05965	+	1.43083i	−0.425567	+	0.149991i
$92$	5.31131	−	15.4668i	0.553742	−	1.61253i
$93$	−13.8617	+	8.00305i	−1.43739	+	0.829878i
$94$	−15.3708	+	1.48648i	−1.58538	+	0.153318i
$95$	−0.686957	+	1.18985i	−0.0704803	+	0.122076i
$96$	6.68509	+	12.7772i	0.682294	+	1.30406i
$97$	−1.77157			−0.179876			−0.0899379	−	0.995947i	$-0.528667\pi$
$97$	−1.77157			−0.179876			−0.0899379	+	0.995947i	$0.528667\pi$
$98$	2.45418	+	9.59046i	0.247909	+	0.968783i
$99$			8.07253i			0.811320i
$100$	−1.96294	+	0.383247i	−0.196294	+	0.0383247i
$101$	6.01140	+	3.47068i	0.598156	+	0.345346i	0.768316	−	0.640071i	$-0.221095\pi$
$101$	6.01140	+	3.47068i	0.598156	+	0.345346i	−0.170160	+	0.985417i	$0.554428\pi$
$102$	1.49750	+	15.4848i	0.148274	+	1.53322i
$103$	1.81850	+	3.14973i	0.179182	+	0.310352i	0.941601	−	0.336732i	$-0.109322\pi$
$103$	1.81850	+	3.14973i	0.179182	+	0.310352i	−0.762419	+	0.647084i	$0.775988\pi$
$104$	1.31242	+	4.41049i	0.128693	+	0.432484i
$105$	−2.24193	−	6.36098i	−0.218790	−	0.620768i
$106$	−9.95435	+	7.10660i	−0.966852	+	0.690254i
$107$	14.4656	−	8.35170i	1.39844	−	0.807390i	0.404211	−	0.914666i	$-0.367546\pi$
$107$	14.4656	−	8.35170i	1.39844	−	0.807390i	0.994229	+	0.107276i	$0.0342130\pi$
$108$	1.91609	−	1.66843i	0.184376	−	0.160544i
$109$	−0.0973526	−	0.0562065i	−0.00932469	−	0.00538361i	0.495330	−	0.868705i	$-0.335047\pi$
$109$	−0.0973526	−	0.0562065i	−0.00932469	−	0.00538361i	−0.504655	+	0.863321i	$0.668380\pi$
$110$	1.35206	−	2.97008i	0.128914	−	0.283186i
$111$	−13.6934			−1.29972
$112$	10.3702	−	2.11174i	0.979890	−	0.199541i
$113$	−14.6581			−1.37892			−0.689460	−	0.724324i	$-0.742152\pi$
$113$	−14.6581			−1.37892			−0.689460	+	0.724324i	$0.742152\pi$
$114$	−2.05214	+	4.50797i	−0.192201	+	0.422210i
$115$	7.08122	+	4.08835i	0.660327	+	0.381240i
$116$	−7.49177	+	6.52342i	−0.695593	+	0.605684i
$117$	4.92898	−	2.84575i	0.455684	−	0.263090i
$118$	16.1517	−	11.5310i	1.48689	−	1.06152i
$119$	11.2229	+	2.09727i	1.02880	+	0.192256i
$120$	−6.91071	+	2.05640i	−0.630858	+	0.187723i
$121$	−2.83764	−	4.91493i	−0.257967	−	0.446812i
$122$	0.120333	+	1.24429i	0.0108944	+	0.112653i
$123$	−17.6735	−	10.2038i	−1.59357	−	0.920047i
$124$	12.3251	−	2.40637i	1.10683	−	0.216099i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.51921	−	11.8691i	−0.491690	−	1.05738i
$127$	−13.7126			−1.21680			−0.608399	−	0.793631i	$-0.708188\pi$
$127$	−13.7126			−1.21680			−0.608399	+	0.793631i	$0.708188\pi$
$128$	−1.70476	−	11.1845i	−0.150681	−	0.988583i
$129$	4.00815	−	6.94231i	0.352898	−	0.611237i
$130$	−2.29012	+	0.221473i	−0.200857	+	0.0194244i
$131$	−8.05523	+	4.65069i	−0.703788	+	0.406332i	−0.808757	−	0.588143i	$-0.799859\pi$
$131$	−8.05523	+	4.65069i	−0.703788	+	0.406332i	0.104968	+	0.994476i	$0.466526\pi$
$132$	3.82097	−	11.1269i	0.332573	−	0.968471i
$133$	2.76060	+	2.36486i	0.239374	+	0.205060i
$134$	10.6160	−	7.57898i	0.917084	−	0.654724i
$135$	0.635170	+	1.10015i	0.0546667	+	0.0946855i
$136$	2.83455	−	11.8718i	0.243060	−	1.01800i
$137$	9.58812	−	16.6071i	0.819168	−	1.41884i	−0.0871273	−	0.996197i	$-0.527769\pi$
$137$	9.58812	−	16.6071i	0.819168	−	1.41884i	0.906296	−	0.422644i	$-0.138898\pi$
$138$	26.8286	+	12.2131i	2.28380	+	1.03965i
$139$		−	5.94234i		−	0.504023i	−0.967724	−	0.252011i	$-0.918908\pi$
$139$		−	5.94234i		−	0.504023i	0.967724	−	0.252011i	$-0.0810921\pi$
$140$	0.0427191	+	5.29133i	0.00361043	+	0.447199i
$141$		−	27.8359i		−	2.34420i
$142$	5.35387	−	11.7609i	0.449287	−	0.986955i
$143$	1.87709	−	3.25121i	0.156970	−	0.271880i
$144$	−12.9657	+	5.26351i	−1.08047	+	0.438626i
$145$	−2.48346	−	4.30149i	−0.206241	−	0.357219i
$146$	1.82391	+	2.55479i	0.150948	+	0.211436i
$147$	−17.6328	+	2.73917i	−1.45433	+	0.225923i
$148$	10.1610	+	3.48927i	0.835225	+	0.286816i
$149$	11.4628	−	6.61804i	0.939068	−	0.542171i	0.0493998	−	0.998779i	$-0.484269\pi$
$149$	11.4628	−	6.61804i	0.939068	−	0.542171i	0.889668	+	0.456608i	$0.150936\pi$
$150$	−0.347021	−	3.58835i	−0.0283341	−	0.292987i
$151$	−7.36852	+	12.7626i	−0.599641	+	1.03861i	0.393233	+	0.919439i	$0.371357\pi$
$151$	−7.36852	+	12.7626i	−0.599641	+	1.03861i	−0.992874	+	0.119170i	$0.961977\pi$
$152$	2.67145	−	2.82214i	0.216683	−	0.228906i
$153$	−15.0963			−1.22047
$154$	−7.06727	−	4.95982i	−0.569497	−	0.399674i
$155$			6.27892i			0.504335i
$156$	−8.14091	+	1.58944i	−0.651794	+	0.127257i
$157$	−17.1620	−	9.90847i	−1.36967	−	0.790782i	−0.378789	−	0.925483i	$-0.623659\pi$
$157$	−17.1620	−	9.90847i	−1.36967	−	0.790782i	−0.990886	+	0.134701i	$0.956993\pi$
$158$	2.05261	−	0.198503i	0.163297	−	0.0157920i
$159$	−11.0233	−	19.0929i	−0.874204	−	1.51417i
$160$	5.65197	+	0.235027i	0.446827	+	0.0185805i
$161$	14.0742	−	16.4294i	1.10920	−	1.29482i
$162$	−5.96292	−	8.35237i	−0.468491	−	0.656224i
$163$	11.6219	−	6.70989i	0.910295	−	0.525559i	0.0297688	−	0.999557i	$-0.490523\pi$
$163$	11.6219	−	6.70989i	0.910295	−	0.525559i	0.880526	+	0.473998i	$0.157190\pi$
$164$	10.5143	+	12.0750i	0.821026	+	0.942901i
$165$	5.09425	+	2.94117i	0.396587	+	0.228969i
$166$	−20.0045	−	9.10653i	−1.55265	−	0.706804i
$167$	14.0397			1.08643			0.543213	−	0.839595i	$-0.317208\pi$
$167$	14.0397			1.08643			0.543213	+	0.839595i	$0.317208\pi$
$168$	1.98949	+	18.9723i	0.153493	+	1.46375i
$169$	10.3531			0.796395
$170$	5.55432	+	2.52847i	0.425997	+	0.193925i
$171$	−4.16247	−	2.40321i	−0.318312	−	0.183778i
$172$	−4.74317	+	4.13009i	−0.361664	+	0.314917i
$173$	−4.36291	+	2.51893i	−0.331706	+	0.191511i	−0.656598	−	0.754240i	$-0.728005\pi$
$173$	−4.36291	+	2.51893i	−0.331706	+	0.191511i	0.324892	+	0.945751i	$0.394672\pi$
$174$	−10.4042	−	14.5734i	−0.788744	−	1.10481i
$175$	−2.60073	−	0.486007i	−0.196597	−	0.0367387i
$176$	−5.67057	+	7.28287i	−0.427435	+	0.548967i
$177$	17.8861	+	30.9797i	1.34441	+	2.32858i
$178$	9.16291	−	0.886124i	0.686789	−	0.0664178i
$179$	4.92604	+	2.84405i	0.368190	+	0.212574i	0.672667	−	0.739945i	$-0.265149\pi$
$179$	4.92604	+	2.84405i	0.368190	+	0.212574i	−0.304478	+	0.952519i	$0.598482\pi$
$180$	−1.34072	−	6.86701i	−0.0999317	−	0.511836i
$181$			1.66939i			0.124085i	0.998074	+	0.0620423i	$0.0197614\pi$
$181$			1.66939i			0.124085i	−0.998074	+	0.0620423i	$0.980239\pi$
$182$	−0.537027	+	6.06363i	−0.0398071	+	0.449466i
$183$	−2.25336			−0.166573
$184$	−16.7957	−	15.8988i	−1.23819	−	1.17208i
$185$	−2.68584	+	4.65201i	−0.197467	+	0.342023i
$186$	2.17892	+	22.5309i	0.159766	+	1.65205i
$187$	−8.62363	+	4.97885i	−0.630622	+	0.364090i
$188$	−7.09297	+	20.6551i	−0.517308	+	1.50643i
$189$	3.16988	−	1.11723i	0.230575	−	0.0812662i
$190$	1.12897	+	1.58137i	0.0819039	+	0.114724i
$191$	−2.72213	−	4.71487i	−0.196966	−	0.341156i	0.750577	−	0.660783i	$-0.229776\pi$
$191$	−2.72213	−	4.71487i	−0.196966	−	0.341156i	−0.947543	+	0.319627i	$0.896442\pi$
$192$	20.3628	−	1.11799i	1.46956	−	0.0806843i
$193$	3.87271	−	6.70772i	0.278764	−	0.482833i	−0.692314	−	0.721596i	$-0.743409\pi$
$193$	3.87271	−	6.70772i	0.278764	−	0.482833i	0.971078	+	0.238764i	$0.0767421\pi$
$194$	−1.03802	+	2.28023i	−0.0745253	+	0.163711i
$195$		−	4.14731i		−	0.296995i
$196$	13.7821	+	2.46052i	0.984435	+	0.175752i
$197$		−	4.64670i		−	0.331064i	−0.986204	−	0.165532i	$-0.947066\pi$
$197$		−	4.64670i		−	0.331064i	0.986204	−	0.165532i	$-0.0529341\pi$
$198$	10.3903	+	4.72994i	0.738409	+	0.336143i
$199$	−8.29073	+	14.3600i	−0.587715	+	1.01795i	0.406816	+	0.913510i	$0.366639\pi$
$199$	−8.29073	+	14.3600i	−0.587715	+	1.01795i	−0.994531	+	0.104442i	$0.966694\pi$
$200$	−0.656860	+	2.75110i	−0.0464470	+	0.194532i
$201$	11.7560	+	20.3620i	0.829205	+	1.43623i
$202$	7.98946	−	5.70383i	0.562136	−	0.401320i
$203$	−12.3940	+	4.36827i	−0.869888	+	0.306592i
$204$	20.8083	+	7.14555i	1.45687	+	0.500289i
$205$	−6.93302	+	4.00278i	−0.484223	+	0.279566i
$206$	5.11960	−	0.495105i	0.356700	−	0.0344956i
$207$	−14.3024	+	24.7725i	−0.994085	+	1.72181i
$208$	6.44583	+	0.894999i	0.446938	+	0.0620570i
$209$	−3.17036			−0.219298
$210$	−9.50098	−	0.841456i	−0.655630	−	0.0580660i
$211$		−	6.81650i		−	0.469267i	−0.972084	−	0.234634i	$-0.924611\pi$
$211$		−	6.81650i		−	0.469267i	0.972084	−	0.234634i	$-0.0753890\pi$
$212$	3.31450	+	16.9764i	0.227641	+	1.16595i
$213$	20.1722	+	11.6464i	1.38218	+	0.798000i
$214$	−2.27384	−	23.5125i	−0.155436	−	1.60728i
$215$	−1.57233	−	2.72335i	−0.107232	−	0.185731i
$216$	−1.02477	−	3.44383i	−0.0697268	−	0.234323i
$217$	16.3298	+	3.05160i	1.10854	+	0.207156i
$218$	−0.129387	+	0.0923716i	−0.00876317	+	0.00625619i
$219$	−4.90020	+	2.82913i	−0.331125	+	0.191175i
$220$	−3.03065	−	3.48053i	−0.204326	−	0.234657i
$221$	6.08005	+	3.51032i	0.408988	+	0.236129i
$222$	−8.02339	+	17.6251i	−0.538494	+	1.18292i
$223$	−17.7887			−1.19122			−0.595609	−	0.803275i	$-0.703089\pi$
$223$	−17.7887			−1.19122			−0.595609	+	0.803275i	$0.703089\pi$
$224$	3.35814	−	14.5850i	0.224375	−	0.974503i
$225$	3.49833			0.233222
$226$	−8.58864	+	18.8668i	−0.571308	+	1.25500i
$227$	−2.70639	−	1.56253i	−0.179629	−	0.103709i	0.407489	−	0.913210i	$-0.366404\pi$
$227$	−2.70639	−	1.56253i	−0.179629	−	0.103709i	−0.587118	+	0.809501i	$0.699738\pi$
$228$	4.59989	+	5.28272i	0.304635	+	0.349856i
$229$	7.57925	−	4.37588i	0.500851	−	0.289167i	−0.228214	−	0.973611i	$-0.573289\pi$
$229$	7.57925	−	4.37588i	0.500851	−	0.289167i	0.729065	+	0.684445i	$0.239955\pi$
$230$	9.41131	−	6.71891i	0.620563	−	0.443032i
$231$	10.1250	−	11.8193i	0.666178	−	0.777655i
$232$	4.00678	+	13.4651i	0.263058	+	0.884027i
$233$	−7.02238	−	12.1631i	−0.460051	−	0.796832i	0.538912	−	0.842362i	$-0.318836\pi$
$233$	−7.02238	−	12.1631i	−0.460051	−	0.796832i	−0.998963	+	0.0455301i	$0.985502\pi$
$234$	−0.774785	−	8.01162i	−0.0506493	−	0.523736i
$235$	−9.45659	−	5.45976i	−0.616880	−	0.356156i
$236$	−5.37804	−	27.5456i	−0.350081	−	1.79307i
$237$			3.71718i			0.241456i
$238$	9.27530	−	13.2164i	0.601228	−	0.856694i
$239$	7.75059			0.501344			0.250672	−	0.968072i	$-0.419348\pi$
$239$	7.75059			0.501344			0.250672	+	0.968072i	$0.419348\pi$
$240$	−1.40235	+	10.0998i	−0.0905216	+	0.651942i
$241$	−11.5264	+	19.9642i	−0.742478	+	1.28601i	0.208886	+	0.977940i	$0.433016\pi$
$241$	−11.5264	+	19.9642i	−0.742478	+	1.28601i	−0.951364	+	0.308069i	$0.900317\pi$
$242$	−7.98878	+	0.772577i	−0.513538	+	0.0496631i
$243$	19.3207	−	11.1548i	1.23942	−	0.715581i
$244$	1.67207	+	0.574187i	0.107043	+	0.0367586i
$245$	−2.52795	+	6.52759i	−0.161505	+	0.417033i
$246$	−23.4890	+	16.7693i	−1.49761	+	1.06917i
$247$	1.11762	+	1.93578i	0.0711127	+	0.123171i
$248$	4.12437	−	17.2739i	0.261898	−	1.09689i
$249$	19.8097	−	34.3114i	1.25539	−	2.17440i
$250$	−1.28712	−	0.585931i	−0.0814048	−	0.0370575i
$251$			28.0916i			1.77313i	0.462606	+	0.886564i	$0.346915\pi$
$251$			28.0916i			1.77313i	−0.462606	+	0.886564i	$0.653085\pi$
$252$	−18.5108	+	0.149446i	−1.16607	+	0.00941420i
$253$			18.8680i			1.18622i
$254$	−8.03465	+	17.6498i	−0.504139	+	1.10745i
$255$	−5.50024	+	9.52670i	−0.344438	+	0.596585i
$256$	−15.3947	−	4.35914i	−0.962171	−	0.272446i
$257$	−6.29739	−	10.9074i	−0.392821	−	0.680385i	0.600000	−	0.800000i	$-0.295167\pi$
$257$	−6.29739	−	10.9074i	−0.392821	−	0.680385i	−0.992820	+	0.119615i	$0.961834\pi$
$258$	−6.58711	−	9.22669i	−0.410096	−	0.574429i
$259$	10.7933	+	9.24606i	0.670663	+	0.574522i
$260$	−1.05679	+	3.07744i	−0.0655395	+	0.190855i
$261$	15.0480	−	8.68798i	0.931450	−	0.537773i
$262$	1.26620	+	13.0930i	0.0782260	+	0.808891i
$263$	−3.48885	+	6.04286i	−0.215131	+	0.372619i	−0.953313	−	0.301983i	$-0.902351\pi$
$263$	−3.48885	+	6.04286i	−0.215131	+	0.372619i	0.738182	+	0.674602i	$0.235685\pi$
$264$	−12.0828	−	11.4376i	−0.743647	−	0.703938i
$265$	−8.64849			−0.531273
$266$	4.66139	−	2.16758i	0.285808	−	0.132903i
$267$			16.5936i			1.01551i
$268$	−3.53482	−	18.1049i	−0.215924	−	1.10593i
$269$	−12.6742	−	7.31743i	−0.772758	−	0.446152i	0.0610998	−	0.998132i	$-0.480539\pi$
$269$	−12.6742	−	7.31743i	−0.772758	−	0.446152i	−0.833857	+	0.551980i	$0.813873\pi$
$270$	1.78819	−	0.172932i	0.108826	−	0.0105243i
$271$	−3.01969	−	5.23025i	−0.183433	−	0.317715i	0.759614	−	0.650374i	$-0.225388\pi$
$271$	−3.01969	−	5.23025i	−0.183433	−	0.317715i	−0.943047	+	0.332658i	$0.892054\pi$
$272$	−13.6196	−	10.6045i	−0.825811	−	0.642990i
$273$	−10.7860	−	2.01562i	−0.652800	−	0.121991i
$274$	−15.7574	−	22.0717i	−0.951940	−	1.33340i
$275$	1.99839	−	1.15377i	0.120507	−	0.0695748i
$276$	31.4394	−	27.3757i	1.89243	−	1.64782i
$277$	19.7767	+	11.4181i	1.18827	+	0.686048i	0.957913	−	0.287058i	$-0.0926774\pi$
$277$	19.7767	+	11.4181i	1.18827	+	0.686048i	0.230357	+	0.973106i	$0.426011\pi$
$278$	−7.64852	−	3.48180i	−0.458728	−	0.208825i
$279$	−21.9657			−1.31505
$280$	6.83562	+	3.04537i	0.408507	+	0.181996i
$281$	12.9916			0.775014			0.387507	−	0.921867i	$-0.373336\pi$
$281$	12.9916			0.775014			0.387507	+	0.921867i	$0.373336\pi$
$282$	−35.8282	−	16.3099i	−2.13354	−	0.971240i
$283$	−5.58054	−	3.22193i	−0.331729	−	0.191524i	0.324880	−	0.945755i	$-0.394676\pi$
$283$	−5.58054	−	3.22193i	−0.331729	−	0.191524i	−0.656608	+	0.754232i	$0.728010\pi$
$284$	−12.0008	−	13.7822i	−0.712114	−	0.817822i
$285$	−3.03313	+	1.75118i	−0.179667	+	0.103731i
$286$	−3.08486	−	4.32102i	−0.182412	−	0.255507i
$287$	7.04065	+	19.9763i	0.415596	+	1.17916i
$288$	−0.822202	+	19.7725i	−0.0484487	+	1.16510i
$289$	−0.810896	−	1.40451i	−0.0476998	−	0.0826184i
$290$	−6.99168	+	0.676150i	−0.410566	+	0.0397049i
$291$	−3.91102	−	2.25803i	−0.229268	−	0.132368i
$292$	4.35701	−	0.850669i	0.254975	−	0.0497816i
$293$			20.3472i			1.18870i	0.804207	+	0.594349i	$0.202590\pi$
$293$			20.3472i			1.18870i	−0.804207	+	0.594349i	$0.797410\pi$
$294$	−6.80594	+	24.3005i	−0.396931	+	1.41724i
$295$	14.0329			0.817024
$296$	10.4447	−	11.0339i	0.607088	−	0.641334i
$297$	−1.46568	+	2.53863i	−0.0850472	+	0.147306i
$298$	−1.80183	−	18.6317i	−0.104377	−	1.07931i
$299$	11.5206	−	6.65140i	0.666251	−	0.384660i
$300$	−4.82197	−	1.65587i	−0.278397	−	0.0956014i
$301$	−7.84686	+	2.76563i	−0.452285	+	0.159408i
$302$	12.1096	+	16.9622i	0.696832	+	0.976066i
$303$	8.84740	+	15.3242i	0.508270	+	0.880350i
$304$	−2.06716	−	5.09206i	−0.118560	−	0.292050i
$305$	−0.441977	+	0.765526i	−0.0253075	+	0.0438339i
$306$	−8.84541	+	19.4308i	−0.505659	+	1.11079i
$307$		−	6.27083i		−	0.357895i	−0.983859	−	0.178948i	$-0.942731\pi$
$307$		−	6.27083i		−	0.357895i	0.983859	−	0.178948i	$-0.0572693\pi$
$308$	−10.5248	+	6.19034i	−0.599708	+	0.352727i
$309$			9.27136i			0.527429i
$310$	8.08174	+	3.67901i	0.459012	+	0.208954i
$311$	−5.32745	+	9.22741i	−0.302092	+	0.523238i	−0.976610	−	0.215020i	$-0.931018\pi$
$311$	−5.32745	+	9.22741i	−0.302092	+	0.523238i	0.674518	+	0.738259i	$0.264352\pi$
$312$	−2.72420	+	11.4097i	−0.154228	+	0.645944i
$313$	2.41442	+	4.18191i	0.136471	+	0.236375i	0.926159	−	0.377134i	$-0.123091\pi$
$313$	2.41442	+	4.18191i	0.136471	+	0.236375i	−0.789687	+	0.613510i	$0.789757\pi$
$314$	−22.8092	+	16.2839i	−1.28719	+	0.918953i
$315$	1.70021	−	9.09822i	0.0957963	−	0.512626i
$316$	0.947188	−	2.75827i	0.0532835	−	0.155165i
$317$	17.3580	−	10.0217i	0.974923	−	0.562872i	0.0741894	−	0.997244i	$-0.476363\pi$
$317$	17.3580	−	10.0217i	0.974923	−	0.562872i	0.900733	+	0.434372i	$0.143030\pi$
$318$	−31.0338	+	3.00121i	−1.74029	+	0.168299i
$319$	5.73069	−	9.92584i	0.320857	−	0.555740i
$320$	3.61417	−	7.13707i	0.202038	−	0.398974i
$321$	42.5800			2.37659
$322$	−12.9001	−	27.7417i	−0.718895	−	1.54599i
$323$		−	5.92885i		−	0.329890i
$324$	−14.2444	+	2.78109i	−0.791355	+	0.154505i
$325$	−1.40895	−	0.813459i	−0.0781546	−	0.0451226i
$326$	−1.82684	−	18.8903i	−0.101179	−	1.04624i
$327$	−0.143281	−	0.248170i	−0.00792344	−	0.0137238i
$328$	21.7027	−	6.45801i	1.19833	−	0.356584i
$329$	−18.7953	+	21.9405i	−1.03622	+	1.20962i
$330$	6.77052	−	4.83360i	0.372705	−	0.266081i
$331$	24.2236	−	13.9855i	1.33145	−	0.768713i	0.345928	−	0.938261i	$-0.387564\pi$
$331$	24.2236	−	13.9855i	1.33145	−	0.768713i	0.985522	+	0.169548i	$0.0542307\pi$
$332$	−23.4425	+	20.4124i	−1.28657	+	1.12028i
$333$	−16.2743	−	9.39596i	−0.891826	−	0.514896i
$334$	8.22631	−	18.0708i	0.450124	−	0.988793i
$335$	9.22336			0.503926
$336$	25.5854	+	8.55574i	1.39580	+	0.466754i
$337$	−24.3637			−1.32717			−0.663586	−	0.748100i	$-0.730966\pi$
$337$	−24.3637			−1.32717			−0.663586	+	0.748100i	$0.730966\pi$
$338$	6.06623	−	13.3258i	0.329959	−	0.724826i
$339$	−32.3601	−	18.6831i	−1.75756	−	1.01473i
$340$	6.50889	−	5.66758i	0.352994	−	0.307368i
$341$	−12.5477	+	7.24442i	−0.679496	+	0.392307i
$342$	−5.53214	+	3.94950i	−0.299144	+	0.213565i
$343$	15.7479	+	9.74697i	0.850307	+	0.526287i
$344$	2.53676	+	8.52500i	0.136773	+	0.459637i
$345$	10.4219	+	18.0513i	0.561098	+	0.971851i
$346$	0.685805	+	7.09153i	0.0368691	+	0.381243i
$347$	−21.7352	−	12.5488i	−1.16681	−	0.673657i	−0.213882	−	0.976859i	$-0.568611\pi$
$347$	−21.7352	−	12.5488i	−1.16681	−	0.673657i	−0.952926	+	0.303202i	$0.901944\pi$
$348$	−24.8539	+	4.85252i	−1.33231	+	0.260122i
$349$			8.53683i			0.456966i	0.973548	+	0.228483i	$0.0733766\pi$
$349$			8.53683i			0.456966i	−0.973548	+	0.228483i	$0.926623\pi$
$350$	−2.14940	+	3.06269i	−0.114890	+	0.163708i
$351$	2.06674			0.110314
$352$	6.05139	+	11.5660i	0.322540	+	0.616469i
$353$	7.12245	−	12.3365i	0.379090	−	0.656603i	−0.611840	−	0.790981i	$-0.709570\pi$
$353$	7.12245	−	12.3365i	0.379090	−	0.656603i	0.990930	+	0.134378i	$0.0429038\pi$
$354$	50.3548	−	4.86969i	2.67632	−	0.258821i
$355$	7.91320	−	4.56869i	0.419989	−	0.242481i
$356$	4.22828	−	12.3130i	0.224099	−	0.652588i
$357$	22.1032	+	18.9347i	1.16983	+	1.00213i
$358$	6.54696	−	4.67400i	0.346018	−	0.247029i
$359$	17.7356	+	30.7190i	0.936050	+	1.62129i	0.772751	+	0.634710i	$0.218880\pi$
$359$	17.7356	+	30.7190i	0.936050	+	1.62129i	0.163299	+	0.986577i	$0.447786\pi$
$360$	−9.62425	−	2.29792i	−0.507243	−	0.121111i
$361$	−8.55618	+	14.8197i	−0.450325	+	0.779986i
$362$	2.14871	+	0.978146i	0.112934	+	0.0514102i
$363$		−	14.4673i		−	0.759337i
$364$	7.48998	+	4.24409i	0.392582	+	0.222451i
$365$			2.21964i			0.116181i
$366$	−1.32031	+	2.90035i	−0.0690138	+	0.151604i
$367$	−2.01754	+	3.49448i	−0.105315	+	0.182411i	−0.913867	−	0.406014i	$-0.866918\pi$
$367$	−2.01754	+	3.49448i	−0.105315	+	0.182411i	0.808552	+	0.588425i	$0.200252\pi$
$368$	−30.3048	+	12.3025i	−1.57975	+	0.641311i
$369$	−14.0030	−	24.2540i	−0.728970	−	1.26261i
$370$	4.41400	+	6.18277i	0.229473	+	0.321427i
$371$	−4.20323	+	22.4924i	−0.218221	+	1.16775i
$372$	30.2768	+	10.3970i	1.56978	+	0.539062i
$373$	1.26954	−	0.732968i	0.0657342	−	0.0379516i	−0.466773	−	0.884377i	$-0.654583\pi$
$373$	1.26954	−	0.732968i	0.0657342	−	0.0379516i	0.532507	+	0.846426i	$0.321250\pi$
$374$	1.35555	+	14.0169i	0.0700936	+	0.724798i
$375$	1.27459	−	2.20766i	0.0658196	−	0.114003i
$376$	22.4297	+	21.2320i	1.15672	+	1.09496i
$377$	−8.08078			−0.416182
$378$	0.419324	−	4.73464i	0.0215677	−	0.243524i
$379$			10.4297i			0.535740i	0.963455	+	0.267870i	$0.0863197\pi$
$379$			10.4297i			0.535740i	−0.963455	+	0.267870i	$0.913680\pi$
$380$	2.69691	−	0.526548i	0.138348	−	0.0270114i
$381$	−30.2728	−	17.4780i	−1.55092	−	0.895424i
$382$	−7.66359	+	0.741129i	−0.392104	+	0.0379194i
$383$	5.07768	+	8.79480i	0.259457	+	0.449394i	0.966097	−	0.258180i	$-0.0831229\pi$
$383$	5.07768	+	8.79480i	0.259457	+	0.449394i	−0.706639	+	0.707574i	$0.749790\pi$
$384$	10.4922	−	26.8645i	0.535428	−	1.37092i
$385$	−2.02941	−	5.75800i	−0.103428	−	0.293455i
$386$	−6.36453	−	8.91491i	−0.323946	−	0.453757i
$387$	9.52718	−	5.50052i	0.484294	−	0.279607i
$388$	2.32673	+	2.67211i	0.118122	+	0.135656i
$389$	6.30729	+	3.64151i	0.319792	+	0.184632i	0.651300	−	0.758820i	$-0.274224\pi$
$389$	6.30729	+	3.64151i	0.319792	+	0.184632i	−0.331508	+	0.943452i	$0.607557\pi$
$390$	−5.33810	−	2.43004i	−0.270305	−	0.123050i
$391$	−35.2849			−1.78443
$392$	11.2423	−	16.2975i	0.567824	−	0.823150i
$393$	−23.7109			−1.19606
$394$	−5.98087	−	2.72265i	−0.301312	−	0.137165i
$395$	1.26282	+	0.729092i	0.0635396	+	0.0366846i
$396$	12.1760	−	10.6022i	0.611869	−	0.532781i
$397$	−15.7019	+	9.06549i	−0.788056	+	0.454984i	−0.839278	−	0.543703i	$-0.817022\pi$
$397$	−15.7019	+	9.06549i	−0.788056	+	0.454984i	0.0512219	+	0.998687i	$0.483688\pi$
$398$	13.6252	+	19.0851i	0.682972	+	0.956652i
$399$	3.08022	+	8.73945i	0.154204	+	0.437520i
$400$	3.15612	+	2.45741i	0.157806	+	0.122871i
$401$	0.944887	+	1.63659i	0.0471854	+	0.0817275i	0.888653	−	0.458579i	$-0.151642\pi$
$401$	0.944887	+	1.63659i	0.0471854	+	0.0817275i	−0.841468	+	0.540307i	$0.818308\pi$
$402$	33.0966	−	3.20070i	1.65071	−	0.159636i
$403$	8.84669	+	5.10764i	0.440685	+	0.254430i
$404$	−2.66025	−	13.6255i	−0.132353	−	0.677892i
$405$		−	7.25667i		−	0.360587i
$406$	−1.63953	+	18.5121i	−0.0813683	+	0.918740i
$407$	−12.3954			−0.614415
$408$	21.3894	−	22.5960i	1.05893	−	1.11867i
$409$	−4.32472	+	7.49063i	−0.213843	+	0.370388i	−0.952914	−	0.303240i	$-0.901932\pi$
$409$	−4.32472	+	7.49063i	−0.213843	+	0.370388i	0.739071	+	0.673628i	$0.235265\pi$
$410$	1.08980	+	11.2690i	0.0538213	+	0.556536i
$411$	42.3346	−	24.4419i	2.08821	−	1.20563i
$412$	2.36247	−	6.87965i	0.116391	−	0.338936i
$413$	6.82007	−	36.4957i	0.335594	−	1.79583i
$414$	23.5050	+	32.9239i	1.15521	+	1.61812i
$415$	−7.77100	−	13.4598i	−0.381463	−	0.660714i
$416$	4.92879	−	7.77217i	0.241654	−	0.381062i
$417$	7.57406	−	13.1187i	0.370903	−	0.642423i
$418$	−1.85761	+	4.08064i	−0.0908588	+	0.199591i
$419$		−	8.04003i		−	0.392781i	−0.980526	−	0.196391i	$-0.937078\pi$
$419$		−	8.04003i		−	0.392781i	0.980526	−	0.196391i	$-0.0629221\pi$
$420$	−6.64997	+	11.7359i	−0.324486	+	0.572653i
$421$			6.68681i			0.325895i	0.986635	+	0.162948i	$0.0521002\pi$
$421$			6.68681i			0.325895i	−0.986635	+	0.162948i	$0.947900\pi$
$422$	−8.77367	−	3.99400i	−0.427096	−	0.194425i
$423$	19.1001	−	33.0823i	0.928677	−	1.60852i
$424$	23.7928	+	5.68085i	1.15548	+	0.275886i
$425$	2.15765	+	3.73716i	0.104661	+	0.181279i
$426$	26.8099	−	19.1401i	1.29894	−	0.927341i
$427$	1.77612	+	1.52151i	0.0859526	+	0.0736312i
$428$	−31.5958	−	10.8500i	−1.52724	−	0.524454i
$429$	8.28792	−	4.78503i	0.400145	−	0.231024i
$430$	−4.42656	+	0.428082i	−0.213468	+	0.0206440i
$431$	15.2902	−	26.4834i	0.736502	−	1.27566i	−0.217560	−	0.976047i	$-0.569810\pi$
$431$	15.2902	−	26.4834i	0.736502	−	1.27566i	0.954061	−	0.299611i	$-0.0968570\pi$
$432$	−5.03307	−	0.698838i	−0.242154	−	0.0336229i
$433$	32.9704			1.58446			0.792228	−	0.610226i	$-0.208921\pi$
$433$	32.9704			1.58446			0.792228	+	0.610226i	$0.208921\pi$
$434$	13.4959	−	19.2304i	0.647824	−	0.923088i
$435$		−	12.6616i		−	0.607078i
$436$	0.0430819	+	0.220660i	0.00206325	+	0.0105677i
$437$	−9.72900	−	5.61704i	−0.465401	−	0.268699i
$438$	0.770261	+	7.96484i	0.0368045	+	0.380575i
$439$	−16.5228	−	28.6183i	−0.788589	−	1.36588i	−0.926832	−	0.375477i	$-0.877479\pi$
$439$	−16.5228	−	28.6183i	−0.788589	−	1.36588i	0.138243	−	0.990398i	$-0.455855\pi$
$440$	−6.25562	+	1.86147i	−0.298225	+	0.0887420i
$441$	−22.8357	−	8.84360i	−1.08741	−	0.421124i
$442$	8.08069	−	5.76896i	0.384359	−	0.274402i
$443$	−17.9130	+	10.3421i	−0.851072	+	0.491366i	−0.861012	−	0.508584i	$-0.830169\pi$
$443$	−17.9130	+	10.3421i	−0.851072	+	0.491366i	0.00994068	+	0.999951i	$0.496836\pi$
$444$	17.9845	+	20.6542i	0.853507	+	0.980203i
$445$	5.63729	+	3.25469i	0.267233	+	0.154287i
$446$	−10.4229	+	22.8962i	−0.493540	+	1.08417i
$447$	33.7412			1.59590
$448$	−16.8051	−	12.8682i	−0.793965	−	0.607963i
$449$	−12.5881			−0.594071			−0.297035	−	0.954866i	$-0.595998\pi$
$449$	−12.5881			−0.594071			−0.297035	+	0.954866i	$0.595998\pi$
$450$	2.04978	−	4.50278i	0.0966276	−	0.212263i
$451$	−15.9982	−	9.23656i	−0.753325	−	0.434933i
$452$	19.2515	+	22.1093i	0.905515	+	1.03993i
$453$	−32.5343	+	18.7837i	−1.52860	+	0.882535i
$454$	−3.59693	+	2.56792i	−0.168812	+	0.120518i
$455$	−2.80035	+	3.26896i	−0.131282	+	0.153251i
$456$	9.49472	−	2.82532i	0.444631	−	0.132308i
$457$	−0.392078	−	0.679099i	−0.0183406	−	0.0317669i	0.856709	−	0.515799i	$-0.172505\pi$
$457$	−0.392078	−	0.679099i	−0.0183406	−	0.0317669i	−0.875050	+	0.484032i	$0.839172\pi$
$458$	−1.19138	−	12.3194i	−0.0556695	−	0.575647i
$459$	−4.74746	−	2.74095i	−0.221592	−	0.127936i
$460$	−3.13369	−	16.0503i	−0.146109	−	0.748351i
$461$		−	20.5467i		−	0.956957i	−0.878099	−	0.478478i	$-0.841188\pi$
$461$		−	20.5467i		−	0.956957i	0.878099	−	0.478478i	$-0.158812\pi$
$462$	−9.28038	−	19.9575i	−0.431762	−	0.928505i
$463$	26.1354			1.21461			0.607307	−	0.794467i	$-0.292250\pi$
$463$	26.1354			1.21461			0.607307	+	0.794467i	$0.292250\pi$
$464$	19.6789	+	2.73240i	0.913571	+	0.126849i
$465$	−8.00305	+	13.8617i	−0.371133	+	0.642821i
$466$	−19.7700	+	1.91192i	−0.915830	+	0.0885678i
$467$	−36.6192	+	21.1421i	−1.69453	+	0.978339i	−0.743762	+	0.668445i	$0.766960\pi$
$467$	−36.6192	+	21.1421i	−1.69453	+	0.978339i	−0.950771	+	0.309894i	$0.899706\pi$
$468$	−10.7659	−	3.69701i	−0.497654	−	0.170894i
$469$	4.48262	−	23.9875i	0.206988	−	1.10764i
$470$	−12.5683	+	8.97274i	−0.579732	+	0.413882i
$471$	−25.2585	−	43.7490i	−1.16385	−	2.01585i
$472$	−38.6057	−	9.21762i	−1.77697	−	0.424275i
$473$	3.62820	−	6.28423i	0.166825	−	0.288949i
$474$	4.78446	+	2.17801i	0.219758	+	0.100039i
$475$			1.37391i			0.0630395i
$476$	−11.5765	−	19.6824i	−0.530607	−	0.902139i
$477$		−	30.2553i		−	1.38529i
$478$	4.54131	−	9.97596i	0.207715	−	0.456290i
$479$	4.97696	−	8.62034i	0.227403	−	0.393873i	−0.729635	−	0.683837i	$-0.760310\pi$
$479$	4.97696	−	8.62034i	0.227403	−	0.393873i	0.957038	+	0.289964i	$0.0936432\pi$
$480$	12.1780	+	7.72281i	0.555849	+	0.352496i
$481$	4.36964	+	7.56844i	0.199239	+	0.345091i
$482$	18.9428	+	26.5335i	0.862820	+	1.20857i
$483$	52.0118	−	18.3316i	2.36662	−	0.834115i
$484$	−3.68647	+	10.7352i	−0.167567	+	0.487964i
$485$	−1.53422	+	0.885785i	−0.0696656	+	0.0402214i
$486$	−3.03701	−	31.4040i	−0.137762	−	1.42452i
$487$	−15.5045	+	26.8545i	−0.702574	+	1.21689i	0.264985	+	0.964252i	$0.414633\pi$
$487$	−15.5045	+	26.8545i	−0.702574	+	1.21689i	−0.967560	+	0.252642i	$0.918700\pi$
$488$	1.71876	−	1.81572i	0.0778048	−	0.0821938i
$489$	34.2095			1.54701
$490$	6.92061	+	7.07850i	0.312641	+	0.319774i
$491$			6.66913i			0.300974i	0.988612	+	0.150487i	$0.0480841\pi$
$491$			6.66913i			0.300974i	−0.988612	+	0.150487i	$0.951916\pi$
$492$	7.82115	+	40.0589i	0.352605	+	1.80599i
$493$	18.5622	+	10.7169i	0.835999	+	0.482664i
$494$	3.14644	−	0.304285i	0.141565	−	0.0136904i
$495$	4.03626	+	6.99102i	0.181417	+	0.314223i
$496$	−19.8170	−	15.4299i	−0.889812	−	0.692822i
$497$	−8.03605	−	22.8005i	−0.360466	−	1.02274i
$498$	−32.5559	−	45.6016i	−1.45886	−	2.04346i
$499$	−27.0342	+	15.6082i	−1.21022	+	0.698719i	−0.962807	−	0.270192i	$-0.912913\pi$
$499$	−27.0342	+	15.6082i	−1.21022	+	0.698719i	−0.247411	+	0.968911i	$0.579580\pi$
$500$	−1.50833	+	1.31337i	−0.0674546	+	0.0587357i
$501$	30.9949	+	17.8949i	1.38475	+	0.799486i
$502$	36.1574	+	16.4598i	1.61378	+	0.734635i
$503$	−2.69120			−0.119994			−0.0599972	−	0.998199i	$-0.519109\pi$
$503$	−2.69120			−0.119994			−0.0599972	+	0.998199i	$0.519109\pi$
$504$	−10.6537	+	23.9133i	−0.474554	+	1.06518i
$505$	6.94136			0.308887
$506$	24.2855	+	11.0554i	1.07962	+	0.491470i
$507$	22.8562	+	13.1960i	1.01508	+	0.586056i
$508$	18.0097	+	20.6832i	0.799053	+	0.917667i
$509$	−9.12824	+	5.27019i	−0.404602	+	0.233597i	−0.688468	−	0.725267i	$-0.741716\pi$
$509$	−9.12824	+	5.27019i	−0.404602	+	0.233597i	0.283866	+	0.958864i	$0.408383\pi$
$510$	9.03927	+	12.6615i	0.400265	+	0.560659i
$511$	5.77268	+	1.07876i	0.255368	+	0.0477216i
$512$	−14.6310	+	17.2608i	−0.646605	+	0.762825i
$513$	−0.872669	−	1.51151i	−0.0385293	−	0.0667347i
$514$	−17.7290	+	1.71453i	−0.781993	+	0.0756247i
$515$	3.14973	+	1.81850i	0.138794	+	0.0801326i
$516$	−15.7355	+	3.07222i	−0.692716	+	0.135247i
$517$		−	25.1972i		−	1.10817i
$518$	18.2249	−	8.47474i	0.800758	−	0.372359i
$519$	−12.8424			−0.563720
$520$	3.34183	+	3.16339i	0.146549	+	0.138724i
$521$	−1.62124	+	2.80807i	−0.0710278	+	0.123024i	−0.899352	−	0.437225i	$-0.855961\pi$
$521$	−1.62124	+	2.80807i	−0.0710278	+	0.123024i	0.828324	+	0.560249i	$0.189295\pi$
$522$	−2.36540	−	24.4592i	−0.103531	−	1.07055i
$523$	−17.1302	+	9.89014i	−0.749052	+	0.432466i	−0.825351	−	0.564619i	$-0.809023\pi$
$523$	−17.1302	+	9.89014i	−0.749052	+	0.432466i	0.0762990	+	0.997085i	$0.475690\pi$
$524$	17.5943	+	6.04187i	0.768609	+	0.263940i
$525$	−5.12206	−	4.38781i	−0.223545	−	0.191500i
$526$	5.73368	+	8.03127i	0.250000	+	0.350180i
$527$	−13.5477	−	23.4653i	−0.590147	−	1.02216i
$528$	−21.8014	+	8.85043i	−0.948782	+	0.385165i
$529$	−21.9291	+	37.9824i	−0.953441	+	1.65141i
$530$	−5.06742	+	11.1317i	−0.220115	+	0.483529i
$531$			49.0916i			2.13039i
$532$	−0.0586925	−	7.26984i	−0.00254464	−	0.315187i
$533$			13.0244i			0.564148i
$534$	21.3580	+	9.72271i	0.924252	+	0.420743i
$535$	8.35170	−	14.4656i	0.361076	−	0.625401i
$536$	−25.3744	−	6.05846i	−1.09601	−	0.261685i
$537$	7.25001	+	12.5574i	0.312861	+	0.541891i
$538$	−16.8446	+	12.0257i	−0.726223	+	0.518465i
$539$	−15.9613	+	2.47952i	−0.687502	+	0.106800i
$540$	0.825171	−	2.40294i	0.0355097	−	0.103406i
$541$	14.9024	−	8.60391i	0.640705	−	0.369911i	−0.144181	−	0.989551i	$-0.546055\pi$
$541$	14.9024	−	8.60391i	0.640705	−	0.369911i	0.784886	+	0.619640i	$0.212721\pi$
$542$	−8.50131	+	0.822142i	−0.365162	+	0.0353140i
$543$	−2.12779	+	3.68543i	−0.0913121	+	0.158157i
$544$	−21.6294	+	11.3166i	−0.927353	+	0.485197i
$545$	−0.112413			−0.00481525
$546$	−8.91422	+	12.7019i	−0.381494	+	0.543592i
$547$			28.8056i			1.23164i	0.787887	+	0.615820i	$0.211175\pi$
$547$			28.8056i			1.23164i	−0.787887	+	0.615820i	$0.788825\pi$
$548$	−37.6418	+	7.34923i	−1.60798	+	0.313943i
$549$	−2.67806	−	1.54618i	−0.114297	−	0.0659894i
$550$	−0.314126	−	3.24820i	−0.0133944	−	0.138504i
$551$	3.41207	+	5.90988i	0.145359	+	0.251769i
$552$	−16.8146	−	56.5067i	−0.715675	−	2.40509i
$553$	2.50991	−	2.92992i	0.106732	−	0.124593i
$554$	26.2843	−	18.7649i	1.11671	−	0.797243i
$555$	−11.8588	+	6.84670i	−0.503379	+	0.290626i
$556$	−8.96301	+	7.80449i	−0.380116	+	0.330984i
$557$	−8.33499	−	4.81221i	−0.353165	−	0.203900i	0.312913	−	0.949782i	$-0.398695\pi$
$557$	−8.33499	−	4.81221i	−0.353165	−	0.203900i	−0.666078	+	0.745882i	$0.732028\pi$
$558$	−12.8704	+	28.2726i	−0.544848	+	1.19687i
$559$	−5.11609			−0.216388
$560$	7.92497	−	7.01391i	0.334891	−	0.296392i
$561$	−25.3840			−1.07171
$562$	7.61218	−	16.7218i	0.321100	−	0.705366i
$563$	37.9605	+	21.9165i	1.59985	+	0.923672i	0.991516	+	0.129988i	$0.0414937\pi$
$563$	37.9605	+	21.9165i	1.59985	+	0.923672i	0.608330	+	0.793684i	$0.291840\pi$
$564$	−41.9857	+	36.5588i	−1.76792	+	1.53940i
$565$	−12.6943	+	7.32906i	−0.534053	+	0.308336i
$566$	−7.41683	+	5.29501i	−0.311752	+	0.222566i
$567$	−18.8726	−	3.52679i	−0.792576	−	0.148111i
$568$	−24.7710	+	7.37104i	−1.03937	+	0.309282i
$569$	−12.3572	−	21.4033i	−0.518041	−	0.897274i	−0.999780	−	0.0209590i	$-0.993328\pi$
$569$	−12.3572	−	21.4033i	−0.518041	−	0.897274i	0.481739	−	0.876315i	$-0.340005\pi$
$570$	0.476777	+	4.93008i	0.0199700	+	0.206499i
$571$	−13.4697	−	7.77672i	−0.563688	−	0.325446i	0.190936	−	0.981602i	$-0.438848\pi$
$571$	−13.4697	−	7.77672i	−0.563688	−	0.325446i	−0.754625	+	0.656157i	$0.772181\pi$
$572$	−7.36920	+	1.43877i	−0.308122	+	0.0601581i
$573$		−	13.8784i		−	0.579779i
$574$	29.8373	+	2.64254i	1.24538	+	0.110298i
$575$	8.17669			0.340992
$576$	24.9678	+	12.6436i	1.04033	+	0.526816i
$577$	12.3169	−	21.3335i	0.512759	−	0.888124i	−0.487132	−	0.873328i	$-0.661957\pi$
$577$	12.3169	−	21.3335i	0.512759	−	0.888124i	0.999891	−	0.0147956i	$-0.00470976\pi$
$578$	−2.28291	+	0.220775i	−0.0949565	+	0.00918303i
$579$	17.0992	−	9.87224i	0.710619	−	0.410276i
$580$	−3.22636	+	9.39533i	−0.133967	+	0.390120i
$581$	−38.7820	+	13.6687i	−1.60895	+	0.567074i
$582$	−5.19795	+	3.71091i	−0.215462	+	0.153822i
$583$	−9.97836	−	17.2830i	−0.413261	−	0.715790i
$584$	1.45799	−	6.10644i	0.0603322	−	0.252686i
$585$	2.84575	−	4.92898i	0.117657	−	0.203788i
$586$	26.1894	+	11.9221i	1.08187	+	0.492496i
$587$			18.4581i			0.761846i	0.924607	+	0.380923i	$0.124394\pi$
$587$			18.4581i			0.761846i	−0.924607	+	0.380923i	$0.875606\pi$
$588$	27.2899	+	22.9985i	1.12542	+	0.948443i
$589$		−	8.62670i		−	0.355457i
$590$	8.22228	−	18.0620i	0.338506	−	0.743601i
$591$	5.92264	−	10.2583i	0.243625	−	0.421971i
$592$	−8.08212	−	19.9088i	−0.332173	−	0.818245i
$593$	20.2979	+	35.1569i	0.833533	+	1.44372i	0.895219	+	0.445627i	$0.147019\pi$
$593$	20.2979	+	35.1569i	0.833533	+	1.44372i	−0.0616855	+	0.998096i	$0.519648\pi$
$594$	2.40874	+	3.37397i	0.0988318	+	0.138436i
$595$	10.7680	−	3.79518i	0.441444	−	0.155587i
$596$	−25.0371	−	8.59772i	−1.02556	−	0.352177i
$597$	−36.6062	+	21.1346i	−1.49819	+	0.864981i
$598$	−1.81091	−	18.7256i	−0.0740538	−	0.765748i
$599$	11.2792	−	19.5362i	0.460858	−	0.798229i	−0.538146	−	0.842851i	$-0.680875\pi$
$599$	11.2792	−	19.5362i	0.460858	−	0.798229i	0.999004	+	0.0446227i	$0.0142086\pi$
$600$	−4.95665	+	5.23625i	−0.202354	+	0.213769i
$601$	−8.01383			−0.326891			−0.163446	−	0.986552i	$-0.552261\pi$
$601$	−8.01383			−0.326891			−0.163446	+	0.986552i	$0.552261\pi$
$602$	−1.03801	+	11.7203i	−0.0423063	+	0.477685i
$603$			32.2664i			1.31399i
$604$	28.9279	−	5.64792i	1.17706	−	0.229810i
$605$	−4.91493	−	2.83764i	−0.199820	−	0.115366i
$606$	24.9080	−	2.40880i	1.01182	−	0.0978508i
$607$	−2.10338	−	3.64317i	−0.0853737	−	0.147872i	0.820177	−	0.572110i	$-0.193875\pi$
$607$	−2.10338	−	3.64317i	−0.0853737	−	0.147872i	−0.905550	+	0.424239i	$0.860542\pi$
$608$	−7.76533	−	0.322907i	−0.314926	−	0.0130956i
$609$	−32.9294	−	6.15364i	−1.33437	−	0.249358i
$610$	0.726358	+	1.01742i	0.0294094	+	0.0411943i
$611$	−15.3851	+	8.88258i	−0.622414	+	0.359351i
$612$	19.8271	+	22.7703i	0.801462	+	0.920434i
$613$	42.5890	+	24.5888i	1.72015	+	0.993131i	0.918580	+	0.395236i	$0.129337\pi$
$613$	42.5890	+	24.5888i	1.72015	+	0.993131i	0.801574	+	0.597895i	$0.203996\pi$
$614$	−8.07133	−	3.67428i	−0.325732	−	0.148282i
$615$	−20.4076			−0.822915
$616$	1.80090	+	17.1739i	0.0725604	+	0.691954i
$617$	−28.2756			−1.13833			−0.569167	−	0.822222i	$-0.692734\pi$
$617$	−28.2756			−1.13833			−0.569167	+	0.822222i	$0.692734\pi$
$618$	11.9334	+	5.43238i	0.480031	+	0.218522i
$619$	−9.48756	−	5.47765i	−0.381337	−	0.220165i	0.297063	−	0.954858i	$-0.403993\pi$
$619$	−9.48756	−	5.47765i	−0.381337	−	0.220165i	−0.678400	+	0.734693i	$0.737326\pi$
$620$	9.47068	−	8.24654i	0.380352	−	0.331189i
$621$	−8.99555	+	5.19359i	−0.360979	+	0.208411i
$622$	8.75529	+	12.2637i	0.351055	+	0.491730i
$623$	11.2043	−	13.0793i	0.448892	−	0.524010i
$624$	13.0894	+	10.1917i	0.523996	+	0.407993i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.79731	−	0.657353i	0.271675	−	0.0262731i
$627$	−6.99907	−	4.04091i	−0.279516	−	0.161378i
$628$	7.59478	+	38.8994i	0.303065	+	1.55226i
$629$		−	23.1804i		−	0.924263i
$630$	−10.7143	−	7.51931i	−0.426868	−	0.299577i
$631$	9.73761			0.387648			0.193824	−	0.981036i	$-0.437911\pi$
$631$	9.73761			0.387648			0.193824	+	0.981036i	$0.437911\pi$
$632$	−2.99524	−	2.83530i	−0.119144	−	0.112782i
$633$	8.68825	−	15.0485i	0.345327	−	0.598124i
$634$	−2.72850	−	28.2139i	−0.108363	−	1.12052i
$635$	−11.8755	+	6.85631i	−0.471264	+	0.272084i
$636$	−14.3207	+	41.7028i	−0.567854	+	1.65362i
$637$	7.14068	+	8.87168i	0.282924	+	0.351509i
$638$	−9.41799	−	13.1920i	−0.372862	−	0.522274i
$639$	15.9828	+	27.6830i	0.632270	+	1.09512i
$640$	−7.06863	−	8.83371i	−0.279412	−	0.349183i
$641$	−4.95181	+	8.57678i	−0.195585	+	0.338762i	−0.947092	−	0.320962i	$-0.895994\pi$
$641$	−4.95181	+	8.57678i	−0.195585	+	0.338762i	0.751507	+	0.659725i	$0.229327\pi$
$642$	24.9490	−	54.8057i	0.984657	−	2.16301i
$643$		−	13.0770i		−	0.515705i	−0.966184	−	0.257853i	$-0.916985\pi$
$643$		−	13.0770i		−	0.515705i	0.966184	−	0.257853i	$-0.0830149\pi$
$644$	−43.2656	+	0.349301i	−1.70490	+	0.0137644i
$645$		−	8.01629i		−	0.315641i
$646$	−7.63116	−	3.47390i	−0.300244	−	0.136679i
$647$	18.9146	−	32.7611i	0.743610	−	1.28797i	−0.207231	−	0.978292i	$-0.566445\pi$
$647$	18.9146	−	32.7611i	0.743610	−	1.28797i	0.950841	−	0.309679i	$-0.100222\pi$
$648$	−4.76662	+	19.9638i	−0.187250	+	0.784252i
$649$	16.1907	+	28.0430i	0.635539	+	1.10079i
$650$	−1.87257	+	1.33686i	−0.0734482	+	0.0524361i
$651$	32.1610	+	27.5507i	1.26049	+	1.07980i
$652$	−25.3845	−	8.71705i	−0.994135	−	0.341386i
$653$	−0.0189368	+	0.0109332i	−0.000741055	+	0.000427848i	−0.500370	−	0.865811i	$-0.666803\pi$
$653$	−0.0189368	+	0.0109332i	−0.000741055	+	0.000427848i	0.499629	+	0.866239i	$0.333470\pi$
$654$	−0.403377	+	0.0390097i	−0.0157733	+	0.00152540i
$655$	−4.65069	+	8.05523i	−0.181717	+	0.314744i
$656$	4.40401	−	31.7179i	0.171948	−	1.23838i
$657$	−7.76503			−0.302943
$658$	17.2274	+	37.0476i	0.671594	+	1.44426i
$659$		−	14.1048i		−	0.549444i	−0.961524	−	0.274722i	$-0.911414\pi$
$659$		−	14.1048i		−	0.549444i	0.961524	−	0.274722i	$-0.0885859\pi$
$660$	−2.25438	−	11.5466i	−0.0877518	−	0.449453i
$661$	0.136298	+	0.0786918i	0.00530139	+	0.00306076i	0.502648	−	0.864491i	$-0.332359\pi$
$661$	0.136298	+	0.0786918i	0.00530139	+	0.00306076i	−0.497347	+	0.867552i	$0.665692\pi$
$662$	−3.80770	−	39.3733i	−0.147991	−	1.53029i
$663$	8.94844	+	15.4991i	0.347528	+	0.601937i
$664$	12.5376	+	42.1336i	0.486553	+	1.63510i
$665$	3.57318	+	0.667733i	0.138562	+	0.0258936i
$666$	−21.6294	+	15.4416i	−0.838121	+	0.598351i
$667$	35.1719	−	20.3065i	1.36186	−	0.786272i
$668$	−18.4393	−	21.1765i	−0.713440	−	0.819345i
$669$	−39.2713	−	22.6733i	−1.51832	−	0.876600i
$670$	5.40425	−	11.8716i	0.208784	−	0.458640i
$671$	−2.03975			−0.0787439
$672$	26.0036	−	27.9185i	1.00311	−	1.07698i
$673$	21.3973			0.824805			0.412403	−	0.911002i	$-0.364690\pi$
$673$	21.3973			0.824805			0.412403	+	0.911002i	$0.364690\pi$
$674$	−14.2754	+	31.3590i	−0.549869	+	1.20790i
$675$	1.10015	+	0.635170i	0.0423446	+	0.0244477i
$676$	−13.5975	−	15.6160i	−0.522981	−	0.600614i
$677$	37.8020	−	21.8250i	1.45285	−	0.838803i	0.454207	−	0.890896i	$-0.349923\pi$
$677$	37.8020	−	21.8250i	1.45285	−	0.838803i	0.998642	+	0.0520932i	$0.0165893\pi$
$678$	−43.0082	+	30.7044i	−1.65172	+	1.17920i
$679$	1.55804	+	4.42060i	0.0597922	+	0.169647i
$680$	−3.48111	−	11.6986i	−0.133495	−	0.448619i
$681$	−3.98318	−	6.89907i	−0.152636	−	0.264373i
$682$	1.97237	+	20.3952i	0.0755259	+	0.780971i
$683$	−7.73241	−	4.46431i	−0.295873	−	0.170822i	0.344715	−	0.938708i	$-0.387976\pi$
$683$	−7.73241	−	4.46431i	−0.295873	−	0.170822i	−0.640587	+	0.767885i	$0.721309\pi$
$684$	1.84204	+	9.43468i	0.0704322	+	0.360744i
$685$		−	19.1762i		−	0.732686i
$686$	21.7727	−	14.5584i	0.831287	−	0.555844i
$687$	22.3099			0.851174
$688$	12.4591	+	1.72993i	0.474998	+	0.0659531i
$689$	−7.03519	+	12.1853i	−0.268019	+	0.464223i
$690$	29.3408	−	2.83748i	1.11699	−	0.108021i
$691$	−1.14481	+	0.660959i	−0.0435508	+	0.0251441i	−0.521617	−	0.853180i	$-0.674671\pi$
$691$	−1.14481	+	0.660959i	−0.0435508	+	0.0251441i	0.478067	+	0.878324i	$0.341338\pi$
$692$	9.52950	+	3.27243i	0.362257	+	0.124399i
$693$	20.1434	−	7.09955i	0.765184	−	0.269690i
$694$	−28.8873	+	20.6232i	−1.09655	+	0.782844i
$695$	−2.97117	−	5.14622i	−0.112703	−	0.195207i
$696$	−8.31691	+	34.8333i	−0.315252	+	1.32035i
$697$	17.2732	−	29.9180i	0.654268	−	1.13323i
$698$	10.9880	+	5.00200i	0.415900	+	0.189328i
$699$		−	35.8026i		−	1.35418i
$700$	2.68266	+	4.56107i	0.101395	+	0.172392i
$701$			23.9285i			0.903767i	0.892077	+	0.451884i	$0.149248\pi$
$701$			23.9285i			0.903767i	−0.892077	+	0.451884i	$0.850752\pi$
$702$	1.21097	−	2.66014i	0.0457049	−	0.100401i
$703$	3.69012	−	6.39147i	0.139175	−	0.241059i
$704$	18.4325	−	1.01202i	0.694702	−	0.0381418i
$705$	−13.9179	−	24.1066i	−0.524180	−	0.907906i
$706$	−11.7053	−	16.3958i	−0.440533	−	0.617063i
$707$	3.37355	−	18.0526i	0.126876	−	0.678939i
$708$	23.2365	−	67.6660i	0.873282	−	2.54305i
$709$	−22.5163	+	12.9998i	−0.845618	+	0.488218i	−0.859170	−	0.511690i	$-0.829020\pi$
$709$	−22.5163	+	12.9998i	−0.845618	+	0.488218i	0.0135518	+	0.999908i	$0.495686\pi$
$710$	−1.24387	−	12.8622i	−0.0466818	−	0.482710i
$711$	−2.55060	+	4.41778i	−0.0956551	+	0.165680i
$712$	−13.3709	−	12.6569i	−0.501094	−	0.474337i
$713$	−51.3408			−1.92273
$714$	37.3222	−	17.3551i	1.39675	−	0.649499i
$715$		−	3.75417i		−	0.140398i
$716$	−2.17995	−	11.1654i	−0.0814684	−	0.417270i
$717$	17.1106	+	9.87883i	0.639009	+	0.368932i
$718$	49.9310	−	4.82871i	1.86341	−	0.180206i
$719$	2.73186	+	4.73173i	0.101881	+	0.176464i	0.912460	−	0.409166i	$-0.134180\pi$
$719$	2.73186	+	4.73173i	0.101881	+	0.176464i	−0.810578	+	0.585630i	$0.800847\pi$
$720$	−8.59685	+	11.0412i	−0.320386	+	0.411480i
$721$	6.26021	−	7.30779i	0.233142	−	0.272156i
$722$	14.0615	+	19.6962i	0.523314	+	0.733016i
$723$	−50.8925	+	29.3828i	−1.89271	+	1.09276i
$724$	2.51799	−	2.19252i	0.0935803	−	0.0814845i
$725$	−4.30149	−	2.48346i	−0.159753	−	0.0922336i
$726$	−18.6212	−	8.47685i	−0.691098	−	0.314605i
$727$	10.4930			0.389164			0.194582	−	0.980886i	$-0.437665\pi$
$727$	10.4930			0.389164			0.194582	+	0.980886i	$0.437665\pi$
$728$	9.85127	−	7.15378i	0.365113	−	0.265137i
$729$	35.1012			1.30005
$730$	2.85695	+	1.30056i	0.105740	+	0.0481357i
$731$	11.7521	+	6.78506i	0.434666	+	0.250954i
$732$	2.95949	+	3.39881i	0.109386	+	0.125624i
$733$	−13.6344	+	7.87180i	−0.503596	+	0.290751i	−0.730197	−	0.683236i	$-0.760572\pi$
$733$	−13.6344	+	7.87180i	−0.503596	+	0.290751i	0.226601	+	0.973988i	$0.427239\pi$
$734$	3.31569	+	4.64435i	0.122384	+	0.171426i
$735$	−13.9009	+	11.1886i	−0.512741	+	0.412697i
$736$	−1.92174	+	46.2144i	−0.0708363	+	1.70349i
$737$	10.6416	+	18.4318i	0.391989	+	0.678945i
$738$	−39.4227	+	3.81248i	−1.45117	+	0.140339i
$739$	3.82144	+	2.20631i	0.140574	+	0.0811604i	0.568637	−	0.822588i	$-0.307471\pi$
$739$	3.82144	+	2.20631i	0.140574	+	0.0811604i	−0.428064	+	0.903749i	$0.640804\pi$
$740$	10.5443	−	2.05868i	0.387615	−	0.0756786i
$741$			5.69805i			0.209323i
$742$	26.4877	+	18.5891i	0.972393	+	0.682426i
$743$	−31.3074			−1.14856			−0.574278	−	0.818660i	$-0.694717\pi$
$743$	−31.3074			−1.14856			−0.574278	+	0.818660i	$0.694717\pi$
$744$	31.1224	−	32.8780i	1.14100	−	1.20537i
$745$	6.61804	−	11.4628i	0.242466	−	0.419964i
$746$	−0.199558	−	2.06352i	−0.00730635	−	0.0755508i
$747$	47.0867	−	27.1855i	1.72281	−	0.994666i
$748$	18.8358	+	6.46820i	0.688704	+	0.236501i
$749$	−33.5621	−	28.7509i	−1.22633	−	1.05053i
$750$	−2.09470	−	2.93409i	−0.0764877	−	0.107138i
$751$	5.13091	+	8.88700i	0.187230	+	0.324291i	0.944326	−	0.329013i	$-0.106716\pi$
$751$	5.13091	+	8.88700i	0.187230	+	0.324291i	−0.757096	+	0.653304i	$0.773383\pi$
$752$	40.4704	−	16.4293i	1.47580	−	0.599114i
$753$	−35.8054	+	62.0167i	−1.30482	+	2.26001i
$754$	−4.73478	+	10.4010i	−0.172431	+	0.378781i
$755$			14.7370i			0.536336i
$756$	−5.84837	−	3.31389i	−0.212703	−	0.120525i
$757$			21.4848i			0.780879i	0.920629	+	0.390440i	$0.127677\pi$
$757$			21.4848i			0.780879i	−0.920629	+	0.390440i	$0.872323\pi$
$758$	13.4244	+	6.11111i	0.487594	+	0.221965i
$759$	−24.0490	+	41.6541i	−0.872924	+	1.51195i
$760$	0.902470	−	3.77977i	0.0327360	−	0.137107i
$761$	−9.52950	−	16.5056i	−0.345444	−	0.598327i	0.639990	−	0.768383i	$-0.278938\pi$
$761$	−9.52950	−	16.5056i	−0.345444	−	0.598327i	−0.985434	+	0.170056i	$0.945605\pi$
$762$	−40.2341	+	28.7239i	−1.45753	+	1.04056i
$763$	−0.0546336	+	0.292356i	−0.00197787	+	0.0105840i
$764$	−3.53641	+	10.2982i	−0.127943	+	0.372577i
$765$	−13.0738	+	7.54817i	−0.472685	+	0.272905i
$766$	14.2952	−	1.38245i	0.516505	−	0.0499500i
$767$	11.4151	−	19.7716i	0.412177	−	0.713911i
$768$	−28.4302	−	29.2455i	−1.02589	−	1.05531i
$769$	28.0251			1.01061			0.505305	−	0.862941i	$-0.331380\pi$
$769$	28.0251			1.01061			0.505305	+	0.862941i	$0.331380\pi$
$770$	−8.60035	−	0.761691i	−0.309935	−	0.0274494i
$771$		−	32.1064i		−	1.15628i
$772$	−15.2038	+	2.96840i	−0.547195	+	0.106835i
$773$	11.2133	+	6.47400i	0.403314	+	0.232853i	0.687913	−	0.725793i	$-0.258527\pi$
$773$	11.2133	+	6.47400i	0.403314	+	0.232853i	−0.284599	+	0.958647i	$0.591860\pi$
$774$	−1.49757	−	15.4856i	−0.0538292	−	0.556618i
$775$	3.13946	+	5.43770i	0.112773	+	0.195328i
$776$	4.80264	−	1.42911i	0.172405	−	0.0513020i
$777$	12.0429	+	34.1692i	0.432038	+	1.22581i
$778$	8.38271	−	5.98458i	0.300535	−	0.214557i
$779$	9.52537	−	5.49948i	0.341282	−	0.197039i
$780$	−6.25551	+	5.44695i	−0.223983	+	0.195032i
$781$	18.2600	+	10.5424i	0.653394	+	0.377237i
$782$	−20.6745	+	45.4159i	−0.739318	+	1.62407i
$783$	6.30969			0.225490
$784$	−14.3897	−	24.0195i	−0.513917	−	0.857840i
$785$	−19.8169			−0.707297
$786$	−13.8930	+	30.5188i	−0.495545	+	1.08857i
$787$	−16.3117	−	9.41757i	−0.581449	−	0.335700i	0.180260	−	0.983619i	$-0.442306\pi$
$787$	−16.3117	−	9.41757i	−0.581449	−	0.335700i	−0.761709	+	0.647919i	$0.775640\pi$
$788$	−7.00876	+	6.10284i	−0.249677	+	0.217405i
$789$	−15.4043	+	8.89370i	−0.548409	+	0.316624i
$790$	1.67836	−	1.19821i	0.0597133	−	0.0426305i
$791$	12.8914	+	36.5764i	0.458365	+	1.30051i
$792$	−6.51204	−	21.8842i	−0.231395	−	0.777622i
$793$	0.719060	+	1.24545i	0.0255346	+	0.0442271i
$794$	2.46818	+	25.5220i	0.0875923	+	0.905743i
$795$	−19.0929	−	11.0233i	−0.677155	−	0.390956i
$796$	32.5484	−	6.35479i	1.15365	−	0.225240i
$797$			1.37390i			0.0486659i	0.999704	+	0.0243330i	$0.00774618\pi$
$797$			1.37390i			0.0486659i	−0.999704	+	0.0243330i	$0.992254\pi$
$798$	13.0535	+	1.15609i	0.462090	+	0.0409251i
$799$	47.1210			1.66702
$800$	5.01226	−	2.62245i	0.177210	−	0.0927175i
$801$	−11.3860	+	19.7211i	−0.402304	+	0.696811i
$802$	2.66013	−	0.257255i	0.0939326	−	0.00908401i
$803$	−4.43569	+	2.56095i	−0.156532	+	0.0903739i
$804$	15.2726	−	44.4748i	0.538625	−	1.56851i
$805$	3.97393	−	21.2654i	0.140063	−	0.749506i
$806$	11.7577	−	8.39405i	0.414148	−	0.295668i
$807$	−18.6535	−	32.3088i	−0.656633	−	1.13732i
$808$	−19.0964	−	4.55951i	−0.671808	−	0.160403i
$809$	−10.4621	+	18.1210i	−0.367830	+	0.637099i	−0.989226	−	0.146397i	$-0.953232\pi$
$809$	−10.4621	+	18.1210i	−0.367830	+	0.637099i	0.621396	+	0.783496i	$0.286566\pi$
$810$	−9.34022	−	4.25191i	−0.328182	−	0.149397i
$811$		−	31.6489i		−	1.11134i	−0.831402	−	0.555671i	$-0.812461\pi$
$811$		−	31.6489i		−	1.11134i	0.831402	−	0.555671i	$-0.187539\pi$
$812$	22.8667	+	12.9571i	0.802463	+	0.454704i
$813$		−	15.3955i		−	0.539943i
$814$	−7.26282	+	15.9543i	−0.254562	+	0.559199i
$815$	6.70989	−	11.6219i	0.235037	−	0.407096i
$816$	−16.5511	−	40.7705i	−0.579404	−	1.42725i
$817$	2.16024	+	3.74165i	0.0755773	+	0.130904i
$818$	7.10737	+	9.95543i	0.248503	+	0.348083i
$819$	−11.4359	−	9.79654i	−0.399602	−	0.342319i
$820$	15.1431	+	5.20015i	0.528821	+	0.181597i
$821$	38.7234	−	22.3570i	1.35146	−	0.780264i	0.363004	−	0.931788i	$-0.381751\pi$
$821$	38.7234	−	22.3570i	1.35146	−	0.780264i	0.988454	+	0.151523i	$0.0484179\pi$
$822$	−6.65456	−	68.8110i	−0.232104	−	2.40006i
$823$	−8.49182	+	14.7083i	−0.296006	+	0.512698i	−0.975218	−	0.221244i	$-0.928988\pi$
$823$	−8.49182	+	14.7083i	−0.296006	+	0.512698i	0.679212	+	0.733942i	$0.262322\pi$
$824$	−7.47071	−	7.07179i	−0.260255	−	0.246358i
$825$	5.88233			0.204797
$826$	−42.9783	−	30.1622i	−1.49541	−	1.04948i
$827$		−	33.3828i		−	1.16083i	−0.814320	−	0.580417i	$-0.802890\pi$
$827$		−	33.3828i		−	1.16083i	0.814320	−	0.580417i	$-0.197110\pi$
$828$	56.1494	−	10.9627i	1.95133	−	0.380980i
$829$	10.9134	+	6.30088i	0.379039	+	0.218839i	0.677400	−	0.735615i	$-0.263107\pi$
$829$	10.9134	+	6.30088i	0.379039	+	0.218839i	−0.298361	+	0.954453i	$0.596440\pi$
$830$	−21.8776	+	2.11574i	−0.759384	+	0.0734383i
$831$	29.1069	+	50.4145i	1.00971	+	1.74886i
$832$	−7.11581	−	10.8979i	−0.246696	−	0.377817i
$833$	−4.63692	−	29.8491i	−0.160660	−	1.03421i
$834$	−12.4474	−	17.4354i	−0.431020	−	0.603737i
$835$	12.1588	−	7.01986i	0.420771	−	0.242932i
$836$	4.16385	+	4.78195i	0.144010	+	0.165387i
$837$	−6.90773	−	3.98818i	−0.238766	−	0.137852i
$838$	−10.3485	−	4.71090i	−0.357483	−	0.162735i
$839$	19.7349			0.681324			0.340662	−	0.940186i	$-0.389349\pi$
$839$	19.7349			0.681324			0.340662	+	0.940186i	$0.389349\pi$
$840$	11.2091	+	15.4358i	0.386751	+	0.532584i
$841$	4.32961			0.149297
$842$	8.60675	+	3.91801i	0.296608	+	0.135024i
$843$	28.6810	+	16.5590i	0.987826	+	0.570321i
$844$	−10.2815	+	8.95259i	−0.353905	+	0.308161i
$845$	8.96608	−	5.17657i	0.308443	−	0.178079i
$846$	−31.3896	−	43.9681i	−1.07920	−	1.51165i
$847$	−9.76862	+	11.4033i	−0.335654	+	0.391822i
$848$	21.2529	−	27.2957i	0.729828	−	0.937339i
$849$	−8.21328	−	14.2258i	−0.281879	−	0.488229i
$850$	6.07441	−	0.587443i	0.208351	−	0.0201491i
$851$	−38.0381	−	21.9613i	−1.30393	−	0.752824i
$852$	−8.92690	−	45.7224i	−0.305831	−	1.56642i
$853$		−	27.7972i		−	0.951757i	−0.879511	−	0.475878i	$-0.842130\pi$
$853$		−	27.7972i		−	0.951757i	0.879511	−	0.475878i	$-0.157870\pi$
$854$	2.99906	−	1.39459i	0.102626	−	0.0477218i
$855$	−4.80641			−0.164376
$856$	−32.4782	+	34.3103i	−1.11008	+	1.17270i
$857$	−18.8484	+	32.6463i	−0.643848	+	1.11518i	0.340719	+	0.940165i	$0.389330\pi$
$857$	−18.8484	+	32.6463i	−0.643848	+	1.11518i	−0.984566	+	0.175011i	$0.944004\pi$
$858$	−1.30278	−	13.4713i	−0.0444760	−	0.459902i
$859$	−7.79385	+	4.49978i	−0.265923	+	0.153531i	−0.627033	−	0.778992i	$-0.715731\pi$
$859$	−7.79385	+	4.49978i	−0.265923	+	0.153531i	0.361111	+	0.932523i	$0.382398\pi$
$860$	−2.04266	+	5.94835i	−0.0696543	+	0.202837i
$861$	−9.91826	+	53.0747i	−0.338013	+	1.80878i
$862$	−25.1283	−	35.1977i	−0.855875	−	1.19884i
$863$	11.4725	+	19.8709i	0.390528	+	0.676414i	0.992519	−	0.122088i	$-0.0389592\pi$
$863$	11.4725	+	19.8709i	0.390528	+	0.676414i	−0.601991	+	0.798503i	$0.705626\pi$
$864$	−3.84852	+	6.06871i	−0.130929	+	0.206462i
$865$	−2.51893	+	4.36291i	−0.0856462	+	0.148344i
$866$	19.3184	−	42.4369i	0.656465	−	1.44207i
$867$		−	4.13424i		−	0.140406i
$868$	−16.8442	−	28.6386i	−0.571730	−	0.972056i
$869$			3.36481i			0.114143i
$870$	−16.2970	−	7.41883i	−0.552522	−	0.251522i
$871$	7.50282	−	12.9953i	0.254223	−	0.440328i
$872$	0.309259	+	0.0738397i	0.0104728	+	0.00250053i
$873$	−3.09877	−	5.36723i	−0.104878	−	0.181653i
$874$	−12.9303	+	9.23122i	−0.437375	+	0.312251i
$875$	−2.49530	+	0.879470i	−0.0843566	+	0.0297315i
$876$	10.7030	+	3.67542i	0.361622	+	0.124181i
$877$	−44.6289	+	25.7665i	−1.50701	+	0.870073i	−0.507044	+	0.861920i	$0.669262\pi$
$877$	−44.6289	+	25.7665i	−1.50701	+	0.870073i	−0.999967	+	0.00815270i	$0.997405\pi$
$878$	−46.5164	+	4.49850i	−1.56985	+	0.151817i
$879$	−25.9344	+	44.9197i	−0.874745	+	1.51510i
$880$	−1.26942	+	9.14244i	−0.0427922	+	0.308192i
$881$	49.9506			1.68288			0.841439	−	0.540352i	$-0.181709\pi$
$881$	49.9506			1.68288			0.841439	+	0.540352i	$0.181709\pi$
$882$	−24.7629	+	24.2106i	−0.833811	+	0.815213i
$883$		−	10.1937i		−	0.343044i	−0.985180	−	0.171522i	$-0.945131\pi$
$883$		−	10.1937i		−	0.343044i	0.985180	−	0.171522i	$-0.0548685\pi$
$884$	−2.69063	−	13.7811i	−0.0904958	−	0.463507i
$885$	30.9797	+	17.8861i	1.04137	+	0.601236i
$886$	2.81574	+	29.1159i	0.0945965	+	0.978169i
$887$	1.22862	+	2.12803i	0.0412530	+	0.0714524i	0.885915	−	0.463848i	$-0.153532\pi$
$887$	1.22862	+	2.12803i	0.0412530	+	0.0714524i	−0.844662	+	0.535301i	$0.820198\pi$
$888$	37.1221	−	11.0463i	1.24574	−	0.370691i
$889$	12.0598	+	34.2171i	0.404474	+	1.14761i
$890$	7.49225	−	5.34886i	0.251141	−	0.179294i
$891$	14.5016	−	8.37252i	0.485823	−	0.280490i
$892$	23.3631	+	26.8312i	0.782255	+	0.898375i
$893$	12.9925	+	7.50125i	0.434779	+	0.251020i
$894$	19.7700	−	43.4290i	0.661208	−	1.45248i
$895$	5.68810			0.190132
$896$	−26.4095	+	14.0903i	−0.882280	+	0.470725i
$897$	33.9113			1.13226
$898$	−7.37578	+	16.2025i	−0.246133	+	0.540684i
$899$	27.0087	+	15.5935i	0.900790	+	0.520071i
$900$	−4.59460	−	5.27664i	−0.153153	−	0.175888i
$901$	32.3208	−	18.6604i	1.07676	−	0.621668i
$902$	−21.2624	+	15.1796i	−0.707961	+	0.505427i
$903$	−20.8482	−	3.89598i	−0.693785	−	0.129650i
$904$	39.7374	−	11.8246i	1.32165	−	0.393279i
$905$	0.834694	+	1.44573i	0.0277462	+	0.0480578i
$906$	5.11406	+	52.8816i	0.169903	+	1.75687i
$907$	23.8668	+	13.7795i	0.792486	+	0.457542i	0.840837	−	0.541289i	$-0.182063\pi$
$907$	23.8668	+	13.7795i	0.792486	+	0.457542i	−0.0483512	+	0.998830i	$0.515397\pi$
$908$	1.19767	+	6.13431i	0.0397461	+	0.203574i
$909$			24.2832i			0.805423i
$910$	2.56674	+	5.51977i	0.0850865	+	0.182979i
$911$	2.26502			0.0750434			0.0375217	−	0.999296i	$-0.488054\pi$
$911$	2.26502			0.0750434			0.0375217	+	0.999296i	$0.488054\pi$
$912$	1.92672	−	13.8763i	0.0637999	−	0.459491i
$913$	17.9319	−	31.0589i	0.593458	−	1.02790i
$914$	−1.10381	+	0.106747i	−0.0365109	+	0.00353089i
$915$	−1.95147	+	1.12668i	−0.0645135	+	0.0372469i
$916$	−16.5546	−	5.68486i	−0.546981	−	0.187833i
$917$	18.6892	+	16.0101i	0.617172	+	0.528699i
$918$	−6.30962	+	4.50456i	−0.208248	+	0.148672i
$919$	−18.1681	−	31.4680i	−0.599309	−	1.03803i	−0.992923	−	0.118759i	$-0.962109\pi$
$919$	−18.1681	−	31.4680i	−0.599309	−	1.03803i	0.393614	−	0.919276i	$-0.371225\pi$
$920$	−22.4949	−	5.37094i	−0.741634	−	0.177075i
$921$	7.99275	−	13.8439i	0.263370	−	0.456170i
$922$	−26.4462	−	12.0390i	−0.870958	−	0.396482i
$923$		−	14.8658i		−	0.489312i
$924$	−31.1254	+	0.251288i	−1.02395	+	0.00826678i
$925$			5.37168i			0.176620i
$926$	15.3135	−	33.6394i	0.503234	−	1.10546i
$927$	−6.36171	+	11.0188i	−0.208946	+	0.361905i
$928$	15.0474	−	23.7282i	0.493956	−	0.778916i
$929$	0.850727	+	1.47350i	0.0279114	+	0.0483440i	0.879644	−	0.475633i	$-0.157781\pi$
$929$	0.850727	+	1.47350i	0.0279114	+	0.0483440i	−0.851732	+	0.523977i	$0.824448\pi$
$930$	13.1525	+	18.4229i	0.431286	+	0.604111i
$931$	3.47319	−	8.96836i	0.113829	−	0.293926i
$932$	−9.12301	+	26.5667i	−0.298834	+	0.870222i
$933$	−23.5223	+	13.5806i	−0.770087	+	0.444610i
$934$	5.75616	+	59.5212i	0.188347	+	1.94759i
$935$	−4.97885	+	8.62363i	−0.162826	+	0.282023i
$936$	−11.0666	+	11.6908i	−0.361723	+	0.382127i
$937$	−53.2124			−1.73837			−0.869186	−	0.494484i	$-0.835357\pi$
$937$	−53.2124			−1.73837			−0.869186	+	0.494484i	$0.835357\pi$
$938$	−28.2483	−	19.8247i	−0.922340	−	0.647299i
$939$			12.3096i			0.401709i
$940$	4.18487	+	21.4343i	0.136495	+	0.699111i
$941$	12.3762	+	7.14541i	0.403453	+	0.232934i	0.687973	−	0.725737i	$-0.258501\pi$
$941$	12.3762	+	7.14541i	0.403453	+	0.232934i	−0.284520	+	0.958670i	$0.591834\pi$
$942$	−71.1101	+	6.87689i	−2.31689	+	0.224061i
$943$	−32.7295	−	56.6891i	−1.06582	−	1.84605i
$944$	−34.4845	+	44.2894i	−1.12238	+	1.44150i
$945$	2.18658	−	2.55249i	0.0711296	−	0.0830324i
$946$	−5.96270	−	8.35206i	−0.193864	−	0.271549i
$947$	17.9779	−	10.3796i	0.584204	−	0.337290i	−0.178598	−	0.983922i	$-0.557156\pi$
$947$	17.9779	−	10.3796i	0.584204	−	0.337290i	0.762802	+	0.646632i	$0.223823\pi$
$948$	5.60673	−	4.88203i	0.182098	−	0.158561i
$949$	3.12736	+	1.80558i	0.101519	+	0.0586118i
$950$	1.76840	+	0.805019i	0.0573744	+	0.0261183i
$951$	51.0940			1.65684
$952$	−32.1166	+	3.36785i	−1.04091	+	0.109153i
$953$	18.6139			0.602965			0.301482	−	0.953472i	$-0.402519\pi$
$953$	18.6139			0.602965			0.301482	+	0.953472i	$0.402519\pi$
$954$	−38.9423	−	17.7275i	−1.26080	−	0.573949i
$955$	−4.71487	−	2.72213i	−0.152570	−	0.0880861i
$956$	−10.1794	−	11.6904i	−0.329225	−	0.378096i
$957$	25.3028	−	14.6086i	0.817923	−	0.472228i
$958$	−8.17928	−	11.4569i	−0.264261	−	0.370155i
$959$	−49.8722	−	9.31979i	−1.61046	−	0.300952i
$960$	17.0757	−	11.1496i	0.551116	−	0.359852i
$961$	−4.21240	−	7.29609i	−0.135884	−	0.235358i
$962$	12.3018	−	1.18968i	0.396627	−	0.0383569i
$963$	50.6054	+	29.2170i	1.63074	+	0.941506i
$964$	45.2510	−	8.83487i	1.45744	−	0.284552i
$965$		−	7.74541i		−	0.249334i
$966$	6.88032	−	77.6866i	0.221371	−	2.49952i
$967$	44.7357			1.43860			0.719301	−	0.694698i	$-0.244462\pi$
$967$	44.7357			1.43860			0.719301	+	0.694698i	$0.244462\pi$
$968$	11.6575	+	11.0350i	0.374687	+	0.354680i
$969$	7.55686	−	13.0889i	0.242761	−	0.420475i
$970$	0.241164	+	2.49374i	0.00774332	+	0.0800693i
$971$	18.0644	−	10.4295i	0.579714	−	0.334698i	−0.181306	−	0.983427i	$-0.558032\pi$
$971$	18.0644	−	10.4295i	0.579714	−	0.334698i	0.761020	+	0.648729i	$0.224699\pi$
$972$	−42.2003	−	14.4916i	−1.35358	−	0.464818i
$973$	−14.8279	+	5.22611i	−0.475362	+	0.167542i
$974$	25.4805	+	35.6911i	0.816449	+	1.14362i
$975$	−2.07365	−	3.59168i	−0.0664101	−	0.115026i
$976$	−1.32998	−	3.27615i	−0.0425715	−	0.104867i
$977$	1.09425	−	1.89530i	0.0350081	−	0.0606359i	−0.847990	−	0.530011i	$-0.822188\pi$
$977$	1.09425	−	1.89530i	0.0350081	−	0.0606359i	0.882999	+	0.469376i	$0.155521\pi$
$978$	20.0444	−	44.0318i	0.640949	−	1.40798i
$979$			15.0206i			0.480062i
$980$	13.1659	−	4.76017i	0.420569	−	0.152058i
$981$		−	0.393258i		−	0.0125558i
$982$	8.58399	+	3.90765i	0.273926	+	0.124698i
$983$	−24.5926	+	42.5957i	−0.784383	+	1.35859i	0.144984	+	0.989434i	$0.453687\pi$
$983$	−24.5926	+	42.5957i	−0.784383	+	1.35859i	−0.929367	+	0.369158i	$0.879646\pi$
$984$	56.1434	+	13.4050i	1.78978	+	0.427334i
$985$	−2.32335	−	4.02416i	−0.0740281	−	0.128220i
$986$	24.6701	−	17.6125i	0.785657	−	0.560895i
$987$	−69.4589	+	24.4808i	−2.21090	+	0.779233i
$988$	1.45194	−	4.22814i	0.0461925	−	0.134515i
$989$	22.2680	−	12.8564i	0.708081	−	0.408811i
$990$	11.3633	−	1.09892i	0.361148	−	0.0349258i
$991$	−5.04153	+	8.73218i	−0.160149	+	0.277387i	−0.934922	−	0.354853i	$-0.884531\pi$
$991$	−5.04153	+	8.73218i	−0.160149	+	0.277387i	0.774773	+	0.632240i	$0.217864\pi$
$992$	−31.4716	+	16.4661i	−0.999224	+	0.522800i
$993$	71.3032			2.26274
$994$	−34.0556	−	3.01614i	−1.08018	−	0.0956662i
$995$			16.5815i			0.525668i
$996$	−77.7703	+	15.1840i	−2.46425	+	0.481123i
$997$	−34.2899	−	19.7973i	−1.08597	−	0.626987i	−0.153472	−	0.988153i	$-0.549045\pi$
$997$	−34.2899	−	19.7973i	−1.08597	−	0.626987i	−0.932501	+	0.361166i	$0.882379\pi$
$998$	4.24950	+	43.9417i	0.134516	+	1.39095i
$999$	−3.41193	−	5.90964i	−0.107949	−	0.186973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bl.b.221.18	yes	60
4.3	odd	2		1120.2.cb.b.81.4		60
7.2	even	3	inner	280.2.bl.b.261.2	yes	60
8.3	odd	2		1120.2.cb.b.81.27		60
8.5	even	2	inner	280.2.bl.b.221.2	✓	60
28.23	odd	6		1120.2.cb.b.401.27		60
56.37	even	6	inner	280.2.bl.b.261.18	yes	60
56.51	odd	6		1120.2.cb.b.401.4		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bl.b.221.2	✓	60	8.5	even	2	inner
280.2.bl.b.221.18	yes	60	1.1	even	1	trivial
280.2.bl.b.261.2	yes	60	7.2	even	3	inner
280.2.bl.b.261.18	yes	60	56.37	even	6	inner
1120.2.cb.b.81.4		60	4.3	odd	2
1120.2.cb.b.81.27		60	8.3	odd	2
1120.2.cb.b.401.4		60	56.51	odd	6
1120.2.cb.b.401.27		60	28.23	odd	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.585931 - 1.28712i) q^{2} +(2.20766 + 1.27459i) q^{3} +(-1.31337 - 1.50833i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.93409 - 2.09470i) q^{6} +(-0.879470 - 2.49530i) q^{7} +(-2.71095 + 0.806691i) q^{8} +(1.74917 + 3.02964i) q^{9} +O(q^{10})\)	\(q+(0.585931 - 1.28712i) q^{2} +(2.20766 + 1.27459i) q^{3} +(-1.31337 - 1.50833i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.93409 - 2.09470i) q^{6} +(-0.879470 - 2.49530i) q^{7} +(-2.71095 + 0.806691i) q^{8} +(1.74917 + 3.02964i) q^{9} +(-0.136130 - 1.40765i) q^{10} +(1.99839 + 1.15377i) q^{11} +(-0.976966 - 5.00389i) q^{12} -1.62692i q^{13} +(-3.72707 - 0.330088i) q^{14} +2.54918 q^{15} +(-0.550119 + 3.96199i) q^{16} +(-2.15765 + 3.73716i) q^{17} +(4.92441 - 0.476229i) q^{18} +(-1.18985 + 0.686957i) q^{19} +(-1.89158 - 0.649567i) q^{20} +(1.23892 - 6.62974i) q^{21} +(2.65596 - 1.89614i) q^{22} +(4.08835 + 7.08122i) q^{23} +(-7.01305 - 1.67446i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.09404 - 0.953261i) q^{26} +1.27034i q^{27} +(-2.60867 + 4.60379i) q^{28} -4.96693i q^{29} +(1.49365 - 3.28111i) q^{30} +(-3.13946 + 5.43770i) q^{31} +(4.77724 + 3.02952i) q^{32} +(2.94117 + 5.09425i) q^{33} +(3.54595 + 4.96687i) q^{34} +(-2.00929 - 1.72126i) q^{35} +(2.27240 - 6.61736i) q^{36} +(-4.65201 + 2.68584i) q^{37} +(0.187031 + 1.93399i) q^{38} +(2.07365 - 3.59168i) q^{39} +(-1.94441 + 2.05409i) q^{40} -8.00556 q^{41} +(-7.80736 - 5.47921i) q^{42} -3.14465i q^{43} +(-0.884356 - 4.52955i) q^{44} +(3.02964 + 1.74917i) q^{45} +(11.5099 - 1.11310i) q^{46} +(-5.45976 - 9.45659i) q^{47} +(-6.26439 + 8.04554i) q^{48} +(-5.45306 + 4.38909i) q^{49} +(-0.821716 - 1.15099i) q^{50} +(-9.52670 + 5.50024i) q^{51} +(-2.45393 + 2.13674i) q^{52} +(-7.48981 - 4.32425i) q^{53} +(1.63508 + 0.744331i) q^{54} +2.30754 q^{55} +(4.39714 + 6.05518i) q^{56} -3.50236 q^{57} +(-6.39305 - 2.91028i) q^{58} +(12.1528 + 7.01643i) q^{59} +(-3.34802 - 3.84501i) q^{60} +(-0.765526 + 0.441977i) q^{61} +(5.15948 + 7.22699i) q^{62} +(6.02154 - 7.02918i) q^{63} +(6.69850 - 4.37380i) q^{64} +(-0.813459 - 1.40895i) q^{65} +(8.28024 - 0.800764i) q^{66} +(7.98766 + 4.61168i) q^{67} +(8.47066 - 1.65382i) q^{68} +20.8439i q^{69} +(-3.39278 + 1.57767i) q^{70} +9.13738 q^{71} +(-7.18589 - 6.80218i) q^{72} +(-1.10982 + 1.92226i) q^{73} +(0.731249 + 7.56143i) q^{74} +(2.20766 - 1.27459i) q^{75} +(2.59887 + 0.892450i) q^{76} +(1.12148 - 6.00128i) q^{77} +(-3.40791 - 4.77352i) q^{78} +(0.729092 + 1.26282i) q^{79} +(1.50458 + 3.70624i) q^{80} +(3.62833 - 6.28446i) q^{81} +(-4.69070 + 10.3041i) q^{82} -15.5420i q^{83} +(-11.6270 + 6.83859i) q^{84} +4.31530i q^{85} +(-4.04755 - 1.84255i) q^{86} +(6.33081 - 10.9653i) q^{87} +(-6.34826 - 1.51573i) q^{88} +(3.25469 + 5.63729i) q^{89} +(4.02655 - 2.87463i) q^{90} +(-4.05965 + 1.43083i) q^{91} +(5.31131 - 15.4668i) q^{92} +(-13.8617 + 8.00305i) q^{93} +(-15.3708 + 1.48648i) q^{94} +(-0.686957 + 1.18985i) q^{95} +(6.68509 + 12.7772i) q^{96} -1.77157 q^{97} +(2.45418 + 9.59046i) q^{98} +8.07253i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9}+O(q^{10}) \) 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9	\( 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9} + 2 q^{10} - 10 q^{12} + 20 q^{14} - 22 q^{16} - 12 q^{17} + 6 q^{18} - 16 q^{20} - 28 q^{22} - 2 q^{23} - 32 q^{24} + 30 q^{25} - 4 q^{26} - 22 q^{28} - 6 q^{32} - 16 q^{34} + 20 q^{36} - 42 q^{38} + 4 q^{40} - 36 q^{41} - 62 q^{42} + 14 q^{44} + 28 q^{46} - 30 q^{47} + 124 q^{48} + 12 q^{49} + 8 q^{50} + 8 q^{52} - 40 q^{54} - 44 q^{55} + 8 q^{56} - 32 q^{57} - 14 q^{58} + 14 q^{60} - 16 q^{62} - 74 q^{63} + 4 q^{64} + 2 q^{65} + 60 q^{66} + 28 q^{68} + 10 q^{70} - 8 q^{71} - 72 q^{72} - 52 q^{74} - 12 q^{76} - 40 q^{78} + 32 q^{79} - 22 q^{81} - 16 q^{82} - 8 q^{84} - 44 q^{86} + 48 q^{87} - 16 q^{88} + 4 q^{89} - 48 q^{90} + 84 q^{92} - 56 q^{94} + 2 q^{95} - 16 q^{96} - 96 q^{97} - 80 q^{98}+O(q^{100}) \) 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9 + 2 * q^10 - 10 * q^12 + 20 * q^14 - 22 * q^16 - 12 * q^17 + 6 * q^18 - 16 * q^20 - 28 * q^22 - 2 * q^23 - 32 * q^24 + 30 * q^25 - 4 * q^26 - 22 * q^28 - 6 * q^32 - 16 * q^34 + 20 * q^36 - 42 * q^38 + 4 * q^40 - 36 * q^41 - 62 * q^42 + 14 * q^44 + 28 * q^46 - 30 * q^47 + 124 * q^48 + 12 * q^49 + 8 * q^50 + 8 * q^52 - 40 * q^54 - 44 * q^55 + 8 * q^56 - 32 * q^57 - 14 * q^58 + 14 * q^60 - 16 * q^62 - 74 * q^63 + 4 * q^64 + 2 * q^65 + 60 * q^66 + 28 * q^68 + 10 * q^70 - 8 * q^71 - 72 * q^72 - 52 * q^74 - 12 * q^76 - 40 * q^78 + 32 * q^79 - 22 * q^81 - 16 * q^82 - 8 * q^84 - 44 * q^86 + 48 * q^87 - 16 * q^88 + 4 * q^89 - 48 * q^90 + 84 * q^92 - 56 * q^94 + 2 * q^95 - 16 * q^96 - 96 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more