LMFDB - Embedded newform 280.2.w.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.977609 - 1.02190i) q^{2} +(0.532572 + 0.532572i) q^{3} +(-0.0885601 + 1.99804i) q^{4} +(-1.25149 - 1.85304i) q^{5} +(0.0235881 - 1.06488i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.12837 - 1.86280i) q^{8} -2.43273i q^{9} +O(q^{10})$	\(q+(-0.977609 - 1.02190i) q^{2} +(0.532572 + 0.532572i) q^{3} +(-0.0885601 + 1.99804i) q^{4} +(-1.25149 - 1.85304i) q^{5} +(0.0235881 - 1.06488i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.12837 - 1.86280i) q^{8} -2.43273i q^{9} +(-0.670153 + 3.09045i) q^{10} -0.178553 q^{11} +(-1.11126 + 1.01693i) q^{12} +(1.13916 - 1.13916i) q^{13} +(0.0313184 - 1.41387i) q^{14} +(0.320368 - 1.65339i) q^{15} +(-3.98431 - 0.353893i) q^{16} +(4.68019 - 4.68019i) q^{17} +(-2.48601 + 2.37826i) q^{18} -2.34107i q^{19} +(3.81328 - 2.33643i) q^{20} +0.753170i q^{21} +(0.174555 + 0.182463i) q^{22} +(3.97734 - 3.97734i) q^{23} +(2.12559 + 0.141436i) q^{24} +(-1.86753 + 4.63814i) q^{25} +(-2.27777 - 0.0504547i) q^{26} +(2.89332 - 2.89332i) q^{27} +(-1.47545 + 1.35020i) q^{28} -6.54779 q^{29} +(-2.00279 + 1.28898i) q^{30} +2.64081i q^{31} +(3.53346 + 4.41754i) q^{32} +(-0.0950924 - 0.0950924i) q^{33} +(-9.35808 - 0.207290i) q^{34} +(0.425359 - 2.19524i) q^{35} +(4.86070 + 0.215443i) q^{36} +(-3.60824 - 3.60824i) q^{37} +(-2.39234 + 2.28865i) q^{38} +1.21337 q^{39} +(-6.11549 - 1.61268i) q^{40} -2.88156 q^{41} +(0.769665 - 0.736306i) q^{42} +(2.14830 + 2.14830i) q^{43} +(0.0158127 - 0.356756i) q^{44} +(-4.50796 + 3.04455i) q^{45} +(-7.95273 - 0.176160i) q^{46} +(6.59482 + 6.59482i) q^{47} +(-1.93346 - 2.31041i) q^{48} +1.00000i q^{49} +(6.56543 - 2.62586i) q^{50} +4.98507 q^{51} +(2.17521 + 2.37698i) q^{52} +(-0.381073 + 0.381073i) q^{53} +(-5.78522 - 0.128148i) q^{54} +(0.223458 + 0.330866i) q^{55} +(2.82219 + 0.187788i) q^{56} +(1.24679 - 1.24679i) q^{57} +(6.40118 + 6.69119i) q^{58} -9.42525i q^{59} +(3.27516 + 0.786532i) q^{60} +11.7424i q^{61} +(2.69864 - 2.58168i) q^{62} +(1.72020 - 1.72020i) q^{63} +(1.05994 - 7.92947i) q^{64} +(-3.53658 - 0.685264i) q^{65} +(-0.00421173 + 0.190138i) q^{66} +(-7.96968 + 7.96968i) q^{67} +(8.93671 + 9.76567i) q^{68} +4.23644 q^{69} +(-2.65915 + 1.71141i) q^{70} +7.18446i q^{71} +(-4.53170 - 5.17777i) q^{72} +(7.71228 + 7.71228i) q^{73} +(-0.159812 + 7.21471i) q^{74} +(-3.46474 + 1.47555i) q^{75} +(4.67754 + 0.207325i) q^{76} +(-0.126256 - 0.126256i) q^{77} +(-1.18621 - 1.23995i) q^{78} +12.8227 q^{79} +(4.33056 + 7.82600i) q^{80} -4.21640 q^{81} +(2.81704 + 2.94466i) q^{82} +(6.69868 + 6.69868i) q^{83} +(-1.50486 - 0.0667009i) q^{84} +(-14.5298 - 2.81536i) q^{85} +(0.0951504 - 4.29556i) q^{86} +(-3.48717 - 3.48717i) q^{87} +(-0.380028 + 0.332609i) q^{88} +7.74324i q^{89} +(7.51825 + 1.63030i) q^{90} +1.61102 q^{91} +(7.59465 + 8.29912i) q^{92} +(-1.40642 + 1.40642i) q^{93} +(0.292091 - 13.1864i) q^{94} +(-4.33809 + 2.92983i) q^{95} +(-0.470837 + 4.23448i) q^{96} +(7.15533 - 7.15533i) q^{97} +(1.02190 - 0.977609i) q^{98} +0.434372i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.977609	−	1.02190i	−0.691274	−	0.722593i
$2$	−0.977609	−	1.02190i	−0.691274	−	0.722593i
$3$	0.532572	+	0.532572i	0.307481	+	0.307481i	0.843931	−	0.536451i	$-0.180235\pi$
$3$	0.532572	+	0.532572i	0.307481	+	0.307481i	−0.536451	+	0.843931i	$0.680235\pi$
$4$	−0.0885601	+	1.99804i	−0.0442801	+	0.999019i
$5$	−1.25149	−	1.85304i	−0.559685	−	0.828706i
$5$	−1.25149	−	1.85304i	−0.559685	−	0.828706i
$6$	0.0235881	−	1.06488i	0.00962981	−	0.434737i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.12837	−	1.86280i	0.752494	−	0.658600i
$9$		−	2.43273i		−	0.810911i
$10$	−0.670153	+	3.09045i	−0.211921	+	0.977287i
$11$	−0.178553			−0.0538358			−0.0269179	−	0.999638i	$-0.508569\pi$
$11$	−0.178553			−0.0538358			−0.0269179	+	0.999638i	$0.508569\pi$
$12$	−1.11126	+	1.01693i	−0.320794	+	0.293564i
$13$	1.13916	−	1.13916i	0.315948	−	0.315948i	−0.531261	−	0.847208i	$-0.678282\pi$
$13$	1.13916	−	1.13916i	0.315948	−	0.315948i	0.847208	+	0.531261i	$0.178282\pi$
$14$	0.0313184	−	1.41387i	0.00837020	−	0.377872i
$15$	0.320368	−	1.65339i	0.0827187	−	0.426903i
$16$	−3.98431	−	0.353893i	−0.996079	−	0.0884733i
$17$	4.68019	−	4.68019i	1.13511	−	1.13511i	0.145797	−	0.989314i	$-0.453425\pi$
$17$	4.68019	−	4.68019i	1.13511	−	1.13511i	0.989314	−	0.145797i	$-0.0465748\pi$
$18$	−2.48601	+	2.37826i	−0.585959	+	0.560562i
$19$		−	2.34107i		−	0.537077i	−0.963269	−	0.268539i	$-0.913459\pi$
$19$		−	2.34107i		−	0.537077i	0.963269	−	0.268539i	$-0.0865407\pi$
$20$	3.81328	−	2.33643i	0.852676	−	0.522441i
$21$			0.753170i			0.164355i
$22$	0.174555	+	0.182463i	0.0372153	+	0.0389013i
$23$	3.97734	−	3.97734i	0.829333	−	0.829333i	−0.158091	−	0.987424i	$-0.550534\pi$
$23$	3.97734	−	3.97734i	0.829333	−	0.829333i	0.987424	+	0.158091i	$0.0505340\pi$
$24$	2.12559	+	0.141436i	0.433884	+	0.0288705i
$25$	−1.86753	+	4.63814i	−0.373506	+	0.927628i
$26$	−2.27777	−	0.0504547i	−0.446708	−	0.00989498i
$27$	2.89332	−	2.89332i	0.556820	−	0.556820i
$28$	−1.47545	+	1.35020i	−0.278833	+	0.255165i
$29$	−6.54779			−1.21589			−0.607947	−	0.793977i	$-0.708007\pi$
$29$	−6.54779			−1.21589			−0.607947	+	0.793977i	$0.708007\pi$
$30$	−2.00279	+	1.28898i	−0.365658	+	0.235335i
$31$			2.64081i			0.474303i	0.971473	+	0.237152i	$0.0762138\pi$
$31$			2.64081i			0.474303i	−0.971473	+	0.237152i	$0.923786\pi$
$32$	3.53346	+	4.41754i	0.624633	+	0.780918i
$33$	−0.0950924	−	0.0950924i	−0.0165535	−	0.0165535i
$34$	−9.35808	−	0.207290i	−1.60490	−	0.0355499i
$35$	0.425359	−	2.19524i	0.0718989	−	0.371063i
$36$	4.86070	+	0.215443i	0.810116	+	0.0359072i
$37$	−3.60824	−	3.60824i	−0.593191	−	0.593191i	0.345301	−	0.938492i	$-0.387777\pi$
$37$	−3.60824	−	3.60824i	−0.593191	−	0.593191i	−0.938492	+	0.345301i	$0.887777\pi$
$38$	−2.39234	+	2.28865i	−0.388088	+	0.371268i
$39$	1.21337			0.194295
$40$	−6.11549	−	1.61268i	−0.966944	−	0.254987i
$41$	−2.88156			−0.450024			−0.225012	−	0.974356i	$-0.572242\pi$
$41$	−2.88156			−0.450024			−0.225012	+	0.974356i	$0.572242\pi$
$42$	0.769665	−	0.736306i	0.118762	−	0.113615i
$43$	2.14830	+	2.14830i	0.327613	+	0.327613i	0.851678	−	0.524065i	$-0.175585\pi$
$43$	2.14830	+	2.14830i	0.327613	+	0.327613i	−0.524065	+	0.851678i	$0.675585\pi$
$44$	0.0158127	−	0.356756i	0.00238385	−	0.0537830i
$45$	−4.50796	+	3.04455i	−0.672007	+	0.453855i
$46$	−7.95273	−	0.176160i	−1.17257	−	0.0259734i
$47$	6.59482	+	6.59482i	0.961953	+	0.961953i	0.999302	−	0.0373491i	$-0.0118914\pi$
$47$	6.59482	+	6.59482i	0.961953	+	0.961953i	−0.0373491	+	0.999302i	$0.511891\pi$
$48$	−1.93346	−	2.31041i	−0.279071	−	0.333479i
$49$			1.00000i			0.142857i
$50$	6.56543	−	2.62586i	0.928492	−	0.371352i
$51$	4.98507			0.698050
$52$	2.17521	+	2.37698i	0.301647	+	0.329628i
$53$	−0.381073	+	0.381073i	−0.0523444	+	0.0523444i	−0.732794	−	0.680450i	$-0.761784\pi$
$53$	−0.381073	+	0.381073i	−0.0523444	+	0.0523444i	0.680450	+	0.732794i	$0.261784\pi$
$54$	−5.78522	−	0.128148i	−0.787269	−	0.0174387i
$55$	0.223458	+	0.330866i	0.0301311	+	0.0446140i
$56$	2.82219	+	0.187788i	0.377131	+	0.0250942i
$57$	1.24679	−	1.24679i	0.165141	−	0.165141i
$58$	6.40118	+	6.69119i	0.840516	+	0.878596i
$59$		−	9.42525i		−	1.22706i	−0.789670	−	0.613531i	$-0.789748\pi$
$59$		−	9.42525i		−	1.22706i	0.789670	−	0.613531i	$-0.210252\pi$
$60$	3.27516	+	0.786532i	0.422821	+	0.101541i
$61$			11.7424i			1.50346i	0.659471	+	0.751730i	$0.270780\pi$
$61$			11.7424i			1.50346i	−0.659471	+	0.751730i	$0.729220\pi$
$62$	2.69864	−	2.58168i	0.342728	−	0.327874i
$63$	1.72020	−	1.72020i	0.216725	−	0.216725i
$64$	1.05994	−	7.92947i	0.132493	−	0.991184i
$65$	−3.53658	−	0.685264i	−0.438658	−	0.0849965i
$66$	−0.00421173	+	0.190138i	−0.000518428	+	0.0234044i
$67$	−7.96968	+	7.96968i	−0.973652	+	0.973652i	−0.999662	−	0.0260102i	$-0.991720\pi$
$67$	−7.96968	+	7.96968i	−0.973652	+	0.973652i	0.0260102	+	0.999662i	$0.491720\pi$
$68$	8.93671	+	9.76567i	1.08374	+	1.18426i
$69$	4.23644			0.510008
$70$	−2.65915	+	1.71141i	−0.317829	+	0.204553i
$71$			7.18446i			0.852639i	0.904573	+	0.426319i	$0.140190\pi$
$71$			7.18446i			0.852639i	−0.904573	+	0.426319i	$0.859810\pi$
$72$	−4.53170	−	5.17777i	−0.534066	−	0.610206i
$73$	7.71228	+	7.71228i	0.902654	+	0.902654i	0.995665	−	0.0930112i	$-0.0296493\pi$
$73$	7.71228	+	7.71228i	0.902654	+	0.902654i	−0.0930112	+	0.995665i	$0.529649\pi$
$74$	−0.159812	+	7.21471i	−0.0185778	+	0.838693i
$75$	−3.46474	+	1.47555i	−0.400073	+	0.170382i
$76$	4.67754	+	0.207325i	0.536551	+	0.0237818i
$77$	−0.126256	−	0.126256i	−0.0143882	−	0.0143882i
$78$	−1.18621	−	1.23995i	−0.134311	−	0.140396i
$79$	12.8227			1.44266			0.721331	−	0.692591i	$-0.243531\pi$
$79$	12.8227			1.44266			0.721331	+	0.692591i	$0.243531\pi$
$80$	4.33056	+	7.82600i	0.484172	+	0.874973i
$81$	−4.21640			−0.468489
$82$	2.81704	+	2.94466i	0.311090	+	0.325184i
$83$	6.69868	+	6.69868i	0.735275	+	0.735275i	0.971660	−	0.236384i	$-0.0759624\pi$
$83$	6.69868	+	6.69868i	0.735275	+	0.735275i	−0.236384	+	0.971660i	$0.575962\pi$
$84$	−1.50486	−	0.0667009i	−0.164194	−	0.00727766i
$85$	−14.5298	−	2.81536i	−1.57598	−	0.305369i
$86$	0.0951504	−	4.29556i	0.0102603	−	0.463202i
$87$	−3.48717	−	3.48717i	−0.373864	−	0.373864i
$88$	−0.380028	+	0.332609i	−0.0405111	+	0.0354562i
$89$			7.74324i			0.820782i	0.911910	+	0.410391i	$0.134608\pi$
$89$			7.74324i			0.820782i	−0.911910	+	0.410391i	$0.865392\pi$
$90$	7.51825	+	1.63030i	0.792493	+	0.171849i
$91$	1.61102			0.168881
$92$	7.59465	+	8.29912i	0.791797	+	0.865243i
$93$	−1.40642	+	1.40642i	−0.145839	+	0.145839i
$94$	0.292091	−	13.1864i	0.0301269	−	1.36007i
$95$	−4.33809	+	2.92983i	−0.445079	+	0.300594i
$96$	−0.470837	+	4.23448i	−0.0480546	+	0.432180i
$97$	7.15533	−	7.15533i	0.726514	−	0.726514i	−0.243410	−	0.969924i	$-0.578266\pi$
$97$	7.15533	−	7.15533i	0.726514	−	0.726514i	0.969924	+	0.243410i	$0.0782659\pi$
$98$	1.02190	−	0.977609i	0.103228	−	0.0987535i
$99$			0.434372i			0.0436561i
$100$	−9.10179	−	4.14215i	−0.910179	−	0.414215i
$101$		−	5.93770i		−	0.590823i	−0.955370	−	0.295412i	$-0.904543\pi$
$101$		−	5.93770i		−	0.590823i	0.955370	−	0.295412i	$-0.0954568\pi$
$102$	−4.87345	−	5.09425i	−0.482544	−	0.504405i
$103$	6.18489	−	6.18489i	0.609416	−	0.609416i	−0.333378	−	0.942793i	$-0.608188\pi$
$103$	6.18489	−	6.18489i	0.609416	−	0.609416i	0.942793	+	0.333378i	$0.108188\pi$
$104$	0.302530	−	4.54661i	0.0296655	−	0.445831i
$105$	1.39566	−	0.942588i	0.136202	−	0.0919871i
$106$	0.761959	+	0.0168781i	0.0740080	+	0.00163934i
$107$	−8.72851	+	8.72851i	−0.843816	+	0.843816i	−0.989353	−	0.145536i	$-0.953509\pi$
$107$	−8.72851	+	8.72851i	−0.843816	+	0.843816i	0.145536	+	0.989353i	$0.453509\pi$
$108$	5.52473	+	6.03720i	0.531618	+	0.580930i
$109$	−1.50583			−0.144232			−0.0721161	−	0.997396i	$-0.522975\pi$
$109$	−1.50583			−0.144232			−0.0721161	+	0.997396i	$0.522975\pi$
$110$	0.119658	−	0.551810i	0.0114089	−	0.0526130i
$111$		−	3.84330i		−	0.364789i
$112$	−2.56710	−	3.06758i	−0.242568	−	0.289859i
$113$	−11.7866	−	11.7866i	−1.10879	−	1.10879i	−0.993310	−	0.115481i	$-0.963159\pi$
$113$	−11.7866	−	11.7866i	−1.10879	−	1.10879i	−0.115481	−	0.993310i	$-0.536841\pi$
$114$	−2.49296	−	0.0552213i	−0.233487	−	0.00517195i
$115$	−12.3478	−	2.39257i	−1.15144	−	0.223108i
$116$	0.579873	−	13.0827i	0.0538399	−	1.21470i
$117$	−2.77129	−	2.77129i	−0.256205	−	0.256205i
$118$	−9.63166	+	9.21421i	−0.886666	+	0.848237i
$119$	6.61878			0.606743
$120$	−2.39807	−	4.11581i	−0.218913	−	0.375720i
$121$	−10.9681			−0.997102
$122$	11.9996	−	11.4795i	1.08639	−	1.03930i
$123$	−1.53464	−	1.53464i	−0.138374	−	0.138374i
$124$	−5.27644	−	0.233870i	−0.473838	−	0.0210022i
$125$	10.9319	−	2.34399i	0.977776	−	0.209653i
$126$	−3.43956	−	0.0761894i	−0.306421	−	0.00678749i
$127$	−14.3323	−	14.3323i	−1.27178	−	1.27178i	−0.945152	−	0.326630i	$-0.894087\pi$
$127$	−14.3323	−	14.3323i	−1.27178	−	1.27178i	−0.326630	−	0.945152i	$-0.605913\pi$
$128$	−9.13934	+	6.66877i	−0.807811	+	0.589441i
$129$			2.28825i			0.201469i
$130$	2.75712	+	4.28395i	0.241815	+	0.375727i
$131$	−10.7811			−0.941948			−0.470974	−	0.882147i	$-0.656097\pi$
$131$	−10.7811			−0.941948			−0.470974	+	0.882147i	$0.656097\pi$
$132$	0.198420	−	0.181577i	0.0172702	−	0.0158042i
$133$	1.65538	−	1.65538i	0.143540	−	0.143540i
$134$	15.9355	+	0.352985i	1.37661	+	0.0304932i
$135$	−8.98242	−	1.74047i	−0.773084	−	0.149796i
$136$	1.24293	−	18.6794i	0.106580	−	1.60175i
$137$	−4.70946	+	4.70946i	−0.402356	+	0.402356i	−0.879063	−	0.476706i	$-0.841830\pi$
$137$	−4.70946	+	4.70946i	−0.402356	+	0.402356i	0.476706	+	0.879063i	$0.341830\pi$
$138$	−4.14158	−	4.32922i	−0.352555	−	0.368528i
$139$		−	0.475936i		−	0.0403683i	−0.999796	−	0.0201842i	$-0.993575\pi$
$139$		−	0.475936i		−	0.0403683i	0.999796	−	0.0201842i	$-0.00642526\pi$
$140$	4.34850	+	1.04429i	0.367515	+	0.0882590i
$141$			7.02443i			0.591564i
$142$	7.34181	−	7.02360i	0.616111	−	0.589407i
$143$	−0.203401	+	0.203401i	−0.0170093	+	0.0170093i
$144$	−0.860928	+	9.69278i	−0.0717440	+	0.807731i
$145$	8.19452	+	12.1333i	0.680518	+	1.00762i
$146$	0.341584	−	15.4208i	0.0282697	−	1.27623i
$147$	−0.532572	+	0.532572i	−0.0439258	+	0.0439258i
$148$	7.52895	−	6.88986i	0.618876	−	0.566343i
$149$	12.9237			1.05875			0.529374	−	0.848389i	$-0.322427\pi$
$149$	12.9237			1.05875			0.529374	+	0.848389i	$0.322427\pi$
$150$	4.89502	+	2.09811i	0.399677	+	0.171310i
$151$			0.146569i			0.0119276i	0.999982	+	0.00596379i	$0.00189835\pi$
$151$			0.146569i			0.0119276i	−0.999982	+	0.00596379i	$0.998102\pi$
$152$	−4.36094	−	4.98266i	−0.353719	−	0.404147i
$153$	−11.3856	−	11.3856i	−0.920475	−	0.920475i
$154$	−0.00559200	+	0.252450i	−0.000450616	+	0.0203430i
$155$	4.89353	−	3.30495i	0.393058	−	0.265460i
$156$	−0.107457	+	2.42437i	−0.00860342	+	0.194105i
$157$	−2.74590	−	2.74590i	−0.219147	−	0.219147i	0.588992	−	0.808139i	$-0.299525\pi$
$157$	−2.74590	−	2.74590i	−0.219147	−	0.219147i	−0.808139	+	0.588992i	$0.799525\pi$
$158$	−12.5356	−	13.1035i	−0.997275	−	1.04246i
$159$	−0.405897			−0.0321898
$160$	3.76379	−	12.0762i	0.297554	−	0.954705i
$161$	5.62481			0.443297
$162$	4.12199	+	4.30874i	0.323854	+	0.338527i
$163$	16.8557	+	16.8557i	1.32024	+	1.32024i	0.913580	+	0.406660i	$0.133307\pi$
$163$	16.8557	+	16.8557i	1.32024	+	1.32024i	0.406660	+	0.913580i	$0.366693\pi$
$164$	0.255191	−	5.75746i	0.0199271	−	0.449582i
$165$	−0.0572027	+	0.295218i	−0.00445323	+	0.0229827i
$166$	0.296691	−	13.3941i	0.0230277	−	1.03958i
$167$	6.64299	+	6.64299i	0.514050	+	0.514050i	0.915765	−	0.401715i	$-0.131586\pi$
$167$	6.64299	+	6.64299i	0.514050	+	0.514050i	−0.401715	+	0.915765i	$0.631586\pi$
$168$	1.40301	+	1.60303i	0.108244	+	0.123676i
$169$			10.4046i			0.800354i
$170$	11.3275	+	17.6003i	0.868776	+	1.34988i
$171$	−5.69519			−0.435522
$172$	−4.48265	+	4.10214i	−0.341799	+	0.312785i
$173$	14.5690	−	14.5690i	1.10766	−	1.10766i	0.114200	−	0.993458i	$-0.463570\pi$
$173$	14.5690	−	14.5690i	1.10766	−	1.10766i	0.993458	−	0.114200i	$-0.0364303\pi$
$174$	−0.154450	+	6.97263i	−0.0117088	+	0.528594i
$175$	−4.60020	+	1.95912i	−0.347743	+	0.148095i
$176$	0.711412	+	0.0631887i	0.0536247	+	0.00476303i
$177$	5.01962	−	5.01962i	0.377298	−	0.377298i
$178$	7.91282	−	7.56986i	0.593091	−	0.567385i
$179$		−	6.33863i		−	0.473771i	−0.971538	−	0.236886i	$-0.923873\pi$
$179$		−	6.33863i		−	0.473771i	0.971538	−	0.236886i	$-0.0761266\pi$
$180$	−5.68390	−	9.27670i	−0.423653	−	0.691444i
$181$			2.94658i			0.219017i	0.993986	+	0.109509i	$0.0349277\pi$
$181$			2.94658i			0.219017i	−0.993986	+	0.109509i	$0.965072\pi$
$182$	−1.57495	−	1.64630i	−0.116743	−	0.122032i
$183$	−6.25367	+	6.25367i	−0.462285	+	0.462285i
$184$	1.05627	−	15.8743i	0.0778693	−	1.17027i
$185$	−2.17053	+	11.2019i	−0.159581	+	0.823581i
$186$	2.81215	+	0.0622917i	0.206197	+	0.00456745i
$187$	−0.835662	+	0.835662i	−0.0611096	+	0.0611096i
$188$	−13.7607	+	12.5927i	−1.00361	+	0.918414i
$189$	4.09177			0.297633
$190$	7.23495	+	1.56887i	0.524879	+	0.113818i
$191$			20.0286i			1.44922i	0.689160	+	0.724609i	$0.257980\pi$
$191$			20.0286i			1.44922i	−0.689160	+	0.724609i	$0.742020\pi$
$192$	4.78751	−	3.65852i	0.345509	−	0.264031i
$193$	6.03828	+	6.03828i	0.434645	+	0.434645i	0.890205	−	0.455560i	$-0.150561\pi$
$193$	6.03828	+	6.03828i	0.434645	+	0.434645i	−0.455560	+	0.890205i	$0.650561\pi$
$194$	−14.3072	−	0.316916i	−1.02719	−	0.0227533i
$195$	−1.51853	−	2.24843i	−0.108744	−	0.161014i
$196$	−1.99804	−	0.0885601i	−0.142717	−	0.00632572i
$197$	−2.57011	−	2.57011i	−0.183112	−	0.183112i	0.609598	−	0.792711i	$-0.291331\pi$
$197$	−2.57011	−	2.57011i	−0.183112	−	0.183112i	−0.792711	+	0.609598i	$0.791331\pi$
$198$	0.443885	−	0.424646i	0.0315455	−	0.0301783i
$199$	−15.6097			−1.10654			−0.553271	−	0.833001i	$-0.686621\pi$
$199$	−15.6097			−1.10654			−0.553271	+	0.833001i	$0.686621\pi$
$200$	4.66513	+	13.3505i	0.329874	+	0.944025i
$201$	−8.48886			−0.598758
$202$	−6.06774	+	5.80475i	−0.426925	+	0.408421i
$203$	−4.62999	−	4.62999i	−0.324961	−	0.324961i
$204$	−0.441479	+	9.96036i	−0.0309097	+	0.697365i
$205$	3.60625	+	5.33965i	0.251871	+	0.372937i
$206$	−12.3668	−	0.273935i	−0.861632	−	0.0190859i
$207$	−9.67582	−	9.67582i	−0.672516	−	0.672516i
$208$	−4.94193	+	4.13565i	−0.342661	+	0.286756i
$209$			0.418005i			0.0289140i
$210$	−2.32764	−	0.504739i	−0.160622	−	0.0348303i
$211$	20.6001			1.41817			0.709086	−	0.705122i	$-0.249108\pi$
$211$	20.6001			1.41817			0.709086	+	0.705122i	$0.249108\pi$
$212$	−0.727650	−	0.795146i	−0.0499752	−	0.0546108i
$213$	−3.82624	+	3.82624i	−0.262170	+	0.262170i
$214$	17.4527	+	0.386594i	1.19304	+	0.0264270i
$215$	1.29231	−	6.66949i	0.0881349	−	0.454855i
$216$	0.768385	−	11.5478i	0.0522820	−	0.785725i
$217$	−1.86733	+	1.86733i	−0.126763	+	0.126763i
$218$	1.47211	+	1.53881i	0.0997039	+	0.104221i
$219$			8.21468i			0.555097i
$220$	−0.680873	+	0.417176i	−0.0459045	+	0.0281260i
$221$		−	10.6630i		−	0.717272i
$222$	−3.92746	+	3.75724i	−0.263594	+	0.252170i
$223$	−3.76122	+	3.76122i	−0.251870	+	0.251870i	−0.821737	−	0.569867i	$-0.806995\pi$
$223$	−3.76122	+	3.76122i	−0.251870	+	0.251870i	0.569867	+	0.821737i	$0.306995\pi$
$224$	−0.625140	+	5.62221i	−0.0417689	+	0.375649i
$225$	11.2834	+	4.54320i	0.752224	+	0.302880i
$226$	−0.522040	+	23.5674i	−0.0347256	+	1.56768i
$227$	−2.42954	+	2.42954i	−0.161254	+	0.161254i	−0.783122	−	0.621868i	$-0.786374\pi$
$227$	−2.42954	+	2.42954i	−0.161254	+	0.161254i	0.621868	+	0.783122i	$0.286374\pi$
$228$	2.38071	+	2.60154i	0.157666	+	0.172291i
$229$	24.5832			1.62451			0.812253	−	0.583306i	$-0.198241\pi$
$229$	24.5832			1.62451			0.812253	+	0.583306i	$0.198241\pi$
$230$	9.62636	+	14.9572i	0.634743	+	0.986249i
$231$		−	0.134481i		−	0.00884819i
$232$	−13.9361	+	12.1972i	−0.914953	+	0.800788i
$233$	−15.0949	−	15.0949i	−0.988898	−	0.988898i	0.0110410	−	0.999939i	$-0.496485\pi$
$233$	−15.0949	−	15.0949i	−0.988898	−	0.988898i	−0.999939	+	0.0110410i	$0.996485\pi$
$234$	−0.122743	+	5.54121i	−0.00802395	+	0.362240i
$235$	3.96711	−	20.4738i	0.258786	−	1.33557i
$236$	18.8320	+	0.834701i	1.22586	+	0.0543344i
$237$	6.82899	+	6.82899i	0.443590	+	0.443590i
$238$	−6.47058	−	6.76374i	−0.419426	−	0.438428i
$239$	−10.3664			−0.670544			−0.335272	−	0.942121i	$-0.608828\pi$
$239$	−10.3664			−0.670544			−0.335272	+	0.942121i	$0.608828\pi$
$240$	−1.86157	+	6.47424i	−0.120164	+	0.417911i
$241$	14.7891			0.952651			0.476325	−	0.879269i	$-0.341968\pi$
$241$	14.7891			0.952651			0.476325	+	0.879269i	$0.341968\pi$
$242$	10.7225	+	11.2083i	0.689271	+	0.720498i
$243$	−10.9255	−	10.9255i	−0.700871	−	0.700871i
$244$	−23.4618	−	1.03991i	−1.50199	−	0.0665733i
$245$	1.85304	−	1.25149i	0.118387	−	0.0799550i
$246$	−0.0679705	+	3.06852i	−0.00433364	+	0.195642i
$247$	−2.66686	−	2.66686i	−0.169688	−	0.169688i
$248$	4.91930	+	5.62062i	0.312376	+	0.356910i
$249$			7.13505i			0.452166i
$250$	−13.0824	−	8.87977i	−0.827405	−	0.561606i
$251$	23.4370			1.47933			0.739665	−	0.672975i	$-0.234984\pi$
$251$	23.4370			1.47933			0.739665	+	0.672975i	$0.234984\pi$
$252$	3.28469	+	3.58937i	0.206916	+	0.226109i
$253$	−0.710167	+	0.710167i	−0.0446478	+	0.0446478i
$254$	−0.634789	+	28.6575i	−0.0398302	+	1.79813i
$255$	−6.23878	−	9.23755i	−0.390688	−	0.578478i
$256$	15.7495	+	2.82004i	0.984345	+	0.176253i
$257$	21.6901	−	21.6901i	1.35299	−	1.35299i	0.470696	−	0.882295i	$-0.344003\pi$
$257$	21.6901	−	21.6901i	1.35299	−	1.35299i	0.882295	−	0.470696i	$-0.155997\pi$
$258$	2.33837	−	2.23702i	0.145580	−	0.139271i
$259$		−	5.10282i		−	0.317074i
$260$	1.68238	−	7.00553i	0.104337	−	0.434465i
$261$			15.9290i			0.985983i
$262$	10.5397	+	11.0172i	0.651144	+	0.680645i
$263$	−4.19065	+	4.19065i	−0.258406	+	0.258406i	−0.824406	−	0.565999i	$-0.808490\pi$
$263$	−4.19065	+	4.19065i	−0.258406	+	0.258406i	0.565999	+	0.824406i	$0.308490\pi$
$264$	−0.379530	−	0.0252539i	−0.0233585	−	0.00155427i
$265$	1.18305	+	0.229234i	0.0726744	+	0.0140817i
$266$	−3.30996	−	0.0733185i	−0.202946	−	0.00449545i
$267$	−4.12383	+	4.12383i	−0.252374	+	0.252374i
$268$	−15.2179	−	16.6295i	−0.929583	−	1.01581i
$269$	3.04921			0.185913			0.0929567	−	0.995670i	$-0.470368\pi$
$269$	3.04921			0.185913			0.0929567	+	0.995670i	$0.470368\pi$
$270$	7.00270	+	10.8806i	0.426171	+	0.662175i
$271$		−	2.18303i		−	0.132610i	−0.997799	−	0.0663049i	$-0.978879\pi$
$271$		−	2.18303i		−	0.132610i	0.997799	−	0.0663049i	$-0.0211210\pi$
$272$	−20.3036	+	16.9910i	−1.23109	+	1.03023i
$273$	0.857985	+	0.857985i	0.0519276	+	0.0519276i
$274$	9.41660	+	0.208586i	0.568878	+	0.0126012i
$275$	0.333453	−	0.828154i	0.0201080	−	0.0499396i
$276$	−0.375180	+	8.46457i	−0.0225832	+	0.509507i
$277$	7.45252	+	7.45252i	0.447779	+	0.447779i	0.894615	−	0.446837i	$-0.147450\pi$
$277$	7.45252	+	7.45252i	0.447779	+	0.447779i	−0.446837	+	0.894615i	$0.647450\pi$
$278$	−0.486359	+	0.465279i	−0.0291699	+	0.0279056i
$279$	6.42438			0.384618
$280$	−3.18397	−	5.46465i	−0.190278	−	0.326575i
$281$	−19.5610			−1.16691			−0.583457	−	0.812144i	$-0.698300\pi$
$281$	−19.5610			−1.16691			−0.583457	+	0.812144i	$0.698300\pi$
$282$	7.17827	−	6.86715i	0.427460	−	0.408933i
$283$	2.10341	+	2.10341i	0.125035	+	0.125035i	0.766855	−	0.641820i	$-0.221820\pi$
$283$	2.10341	+	2.10341i	0.125035	+	0.125035i	−0.641820	+	0.766855i	$0.721820\pi$
$284$	−14.3548	−	0.636257i	−0.851803	−	0.0377549i
$285$	−3.87069	−	0.750003i	−0.229280	−	0.0444263i
$286$	0.406703	+	0.00900884i	0.0240489	+	0.000532704i
$287$	−2.03757	−	2.03757i	−0.120274	−	0.120274i
$288$	10.7467	−	8.59597i	0.633256	−	0.506522i
$289$		−	26.8083i		−	1.57696i
$290$	4.38802	−	20.2356i	0.257674	−	1.18828i
$291$	7.62146			0.446778
$292$	−16.0924	+	14.7264i	−0.941738	+	0.861799i
$293$	−2.32133	+	2.32133i	−0.135613	+	0.135613i	−0.771655	−	0.636042i	$-0.780571\pi$
$293$	−2.32133	+	2.32133i	−0.135613	+	0.135613i	0.636042	+	0.771655i	$0.280571\pi$
$294$	1.06488	+	0.0235881i	0.0621052	+	0.00137569i
$295$	−17.4654	+	11.7956i	−1.01687	+	0.686768i
$296$	−14.4011	−	0.958247i	−0.837048	−	0.0556970i
$297$	−0.516612	+	0.516612i	−0.0299768	+	0.0299768i
$298$	−12.6343	−	13.2067i	−0.731885	−	0.765043i
$299$		−	9.06170i		−	0.524051i
$300$	−2.64136	−	7.05335i	−0.152499	−	0.407225i
$301$			3.03816i			0.175117i
$302$	0.149779	−	0.143287i	0.00861879	−	0.00824523i
$303$	3.16225	−	3.16225i	0.181667	−	0.181667i
$304$	−0.828487	+	9.32754i	−0.0475170	+	0.534971i
$305$	21.7592	−	14.6955i	1.24593	−	0.841464i
$306$	−0.504281	+	22.7657i	−0.0288278	+	1.30143i
$307$	−15.6029	+	15.6029i	−0.890502	+	0.890502i	−0.994570	−	0.104068i	$-0.966814\pi$
$307$	−15.6029	+	15.6029i	−0.890502	+	0.890502i	0.104068	+	0.994570i	$0.466814\pi$
$308$	0.263446	−	0.241083i	0.0150112	−	0.0137370i
$309$	6.58780			0.374767
$310$	−8.16129	−	1.76975i	−0.463530	−	0.100515i
$311$			8.71443i			0.494150i	0.968996	+	0.247075i	$0.0794694\pi$
$311$			8.71443i			0.494150i	−0.968996	+	0.247075i	$0.920531\pi$
$312$	2.58251	−	2.26028i	0.146206	−	0.127963i
$313$	3.17984	+	3.17984i	0.179735	+	0.179735i	0.791240	−	0.611505i	$-0.209436\pi$
$313$	3.17984	+	3.17984i	0.179735	+	0.179735i	−0.611505	+	0.791240i	$0.709436\pi$
$314$	−0.121619	+	5.49046i	−0.00686334	+	0.309845i
$315$	−5.34043	−	1.03479i	−0.300899	−	0.0583036i
$316$	−1.13558	+	25.6202i	−0.0638812	+	1.44125i
$317$	2.30936	+	2.30936i	0.129706	+	0.129706i	0.768980	−	0.639273i	$-0.220765\pi$
$317$	2.30936	+	2.30936i	0.129706	+	0.129706i	−0.639273	+	0.768980i	$0.720765\pi$
$318$	0.396809	+	0.414787i	0.0222519	+	0.0232601i
$319$	1.16913			0.0654586
$320$	−16.0202	+	7.95956i	−0.895554	+	0.444953i
$321$	−9.29711			−0.518914
$322$	−5.49887	−	5.74800i	−0.306440	−	0.320323i
$323$	−10.9566	−	10.9566i	−0.609643	−	0.609643i
$324$	0.373405	−	8.42453i	0.0207447	−	0.468029i
$325$	3.15618	+	7.41103i	0.175073	+	0.411090i
$326$	0.746554	−	33.7031i	0.0413478	−	1.86664i
$327$	−0.801961	−	0.801961i	−0.0443486	−	0.0443486i
$328$	−6.13303	+	5.36777i	−0.338640	+	0.296385i
$329$			9.32648i			0.514186i
$330$	0.357605	−	0.230152i	0.0196855	−	0.0126694i
$331$	28.5796			1.57088			0.785438	−	0.618940i	$-0.212438\pi$
$331$	28.5796			1.57088			0.785438	+	0.618940i	$0.212438\pi$
$332$	−13.9774	+	12.7910i	−0.767112	+	0.701996i
$333$	−8.77789	+	8.77789i	−0.481026	+	0.481026i
$334$	0.294224	−	13.2827i	0.0160992	−	0.726798i
$335$	24.7422	+	4.79415i	1.35181	+	0.261933i
$336$	0.266542	−	3.00087i	0.0145410	−	0.163711i
$337$	10.3891	−	10.3891i	0.565931	−	0.565931i	−0.365055	−	0.930986i	$-0.618950\pi$
$337$	10.3891	−	10.3891i	0.565931	−	0.565931i	0.930986	+	0.365055i	$0.118950\pi$
$338$	10.6325	−	10.1716i	0.578330	−	0.553264i
$339$		−	12.5544i		−	0.681863i
$340$	6.91196	−	28.7818i	0.374854	−	1.56091i
$341$		−	0.471524i		−	0.0255345i
$342$	5.56767	+	5.81992i	0.301065	+	0.314705i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	8.57426	+	0.570529i	0.462293	+	0.0307609i
$345$	−5.30188	−	7.85030i	−0.285443	−	0.422646i
$346$	−29.1308	−	0.645273i	−1.56608	−	0.0346901i
$347$	−10.9000	+	10.9000i	−0.585144	+	0.585144i	−0.936312	−	0.351168i	$-0.885785\pi$
$347$	−10.9000	+	10.9000i	−0.585144	+	0.585144i	0.351168	+	0.936312i	$0.385785\pi$
$348$	7.27632	−	6.65868i	0.390052	−	0.356942i
$349$	−22.9436			−1.22814			−0.614072	−	0.789250i	$-0.710469\pi$
$349$	−22.9436			−1.22814			−0.614072	+	0.789250i	$0.710469\pi$
$350$	6.49922	+	2.78570i	0.347398	+	0.148902i
$351$		−	6.59194i		−	0.351852i
$352$	−0.630910	−	0.788766i	−0.0336276	−	0.0420413i
$353$	5.83221	+	5.83221i	0.310417	+	0.310417i	0.845071	−	0.534654i	$-0.179558\pi$
$353$	5.83221	+	5.83221i	0.310417	+	0.310417i	−0.534654	+	0.845071i	$0.679558\pi$
$354$	−10.0368	−	0.222324i	−0.533449	−	0.0118164i
$355$	13.3131	−	8.99131i	0.706587	−	0.477209i
$356$	−15.4713	−	0.685742i	−0.819977	−	0.0363443i
$357$	3.52498	+	3.52498i	0.186562	+	0.186562i
$358$	−6.47744	+	6.19670i	−0.342343	+	0.327506i
$359$	−22.6416			−1.19498			−0.597488	−	0.801878i	$-0.703834\pi$
$359$	−22.6416			−1.19498			−0.597488	+	0.801878i	$0.703834\pi$
$360$	−3.92323	+	14.8774i	−0.206772	+	0.784106i
$361$	13.5194			0.711548
$362$	3.01111	−	2.88060i	0.158260	−	0.151401i
$363$	−5.84131	−	5.84131i	−0.306589	−	0.306589i
$364$	−0.142672	+	3.21888i	−0.00747807	+	0.168715i
$365$	4.63931	−	23.9430i	0.242833	−	1.25324i
$366$	12.5043	+	0.276981i	0.653609	+	0.0144780i
$367$	11.1092	+	11.1092i	0.579894	+	0.579894i	0.934874	−	0.354980i	$-0.115512\pi$
$367$	11.1092	+	11.1092i	0.579894	+	0.579894i	−0.354980	+	0.934874i	$0.615512\pi$
$368$	−17.2545	+	14.4394i	−0.899455	+	0.752707i
$369$			7.01006i			0.364929i
$370$	13.5692	−	8.73302i	0.705428	−	0.454008i
$371$	−0.538918			−0.0279792
$372$	−2.68553	−	2.93463i	−0.139238	−	0.152154i
$373$	18.2443	−	18.2443i	0.944654	−	0.944654i	−0.0538928	−	0.998547i	$-0.517163\pi$
$373$	18.2443	−	18.2443i	0.944654	−	0.944654i	0.998547	+	0.0538928i	$0.0171629\pi$
$374$	1.67091	+	0.0370122i	0.0864009	+	0.00191386i
$375$	7.07035	+	4.57366i	0.365111	+	0.236183i
$376$	26.3211	+	1.75140i	1.35741	+	0.0903215i
$377$	−7.45902	+	7.45902i	−0.384159	+	0.384159i
$378$	−4.00016	−	4.18139i	−0.205746	−	0.215067i
$379$			29.8869i			1.53519i	0.640936	+	0.767595i	$0.278547\pi$
$379$			29.8869i			1.53519i	−0.640936	+	0.767595i	$0.721453\pi$
$380$	−5.46973	−	8.92715i	−0.280591	−	0.457953i
$381$		−	15.2659i		−	0.782096i
$382$	20.4672	−	19.5801i	1.04719	−	1.00181i
$383$	−14.8192	+	14.8192i	−0.757228	+	0.757228i	−0.975817	−	0.218589i	$-0.929855\pi$
$383$	−14.8192	+	14.8192i	−0.757228	+	0.757228i	0.218589	+	0.975817i	$0.429855\pi$
$384$	−8.41895	−	1.31576i	−0.429628	−	0.0671444i
$385$	−0.0759492	+	0.391967i	−0.00387073	+	0.0199765i
$386$	0.267441	−	12.0736i	0.0136124	−	0.614530i
$387$	5.22625	−	5.22625i	0.265665	−	0.265665i
$388$	13.6630	+	14.9303i	0.693631	+	0.757971i
$389$	−29.3982			−1.49055			−0.745275	−	0.666757i	$-0.767682\pi$
$389$	−29.3982			−1.49055			−0.745275	+	0.666757i	$0.767682\pi$
$390$	−0.813146	+	3.74988i	−0.0411753	+	0.189882i
$391$		−	37.2294i		−	1.88277i
$392$	1.86280	+	2.12837i	0.0940857	+	0.107499i
$393$	−5.74171	−	5.74171i	−0.289631	−	0.289631i
$394$	−0.113832	+	5.13895i	−0.00573479	+	0.258897i
$395$	−16.0475	−	23.7609i	−0.807436	−	1.19554i
$396$	−0.867892	−	0.0384681i	−0.0436132	−	0.00193309i
$397$	4.63280	+	4.63280i	0.232513	+	0.232513i	0.813741	−	0.581228i	$-0.197427\pi$
$397$	4.63280	+	4.63280i	0.232513	+	0.232513i	−0.581228	+	0.813741i	$0.697427\pi$
$398$	15.2602	+	15.9515i	0.764924	+	0.799579i
$399$	1.76322			0.0882715
$400$	9.08223	−	17.8189i	0.454112	−	0.890945i
$401$	−7.56821			−0.377938			−0.188969	−	0.981983i	$-0.560515\pi$
$401$	−7.56821			−0.377938			−0.188969	+	0.981983i	$0.560515\pi$
$402$	8.29879	+	8.67476i	0.413906	+	0.432658i
$403$	3.00832	+	3.00832i	0.149855	+	0.149855i
$404$	11.8638	+	0.525844i	0.590244	+	0.0261617i
$405$	5.27679	+	7.81317i	0.262206	+	0.388239i
$406$	−0.205067	+	9.25771i	−0.0101773	+	0.459452i
$407$	0.644263	+	0.644263i	0.0319349	+	0.0319349i
$408$	10.6101	−	9.28620i	0.525278	−	0.459735i
$409$			13.4700i			0.666049i	0.942918	+	0.333025i	$0.108069\pi$
$409$			13.4700i			0.666049i	−0.942918	+	0.333025i	$0.891931\pi$
$410$	1.93108	−	8.90532i	0.0953695	−	0.439802i
$411$	−5.01625			−0.247433
$412$	11.8099	+	12.9054i	0.581833	+	0.635803i
$413$	6.66466	−	6.66466i	0.327946	−	0.327946i
$414$	−0.428551	+	19.3469i	−0.0210621	+	0.950848i
$415$	4.02958	−	20.7963i	0.197804	−	1.02085i
$416$	9.05750	+	1.00711i	0.444080	+	0.0493779i
$417$	0.253470	−	0.253470i	0.0124125	−	0.0124125i
$418$	0.427159	−	0.408645i	0.0208930	−	0.0199875i
$419$			36.7012i			1.79297i	0.443072	+	0.896486i	$0.353889\pi$
$419$			36.7012i			1.79297i	−0.443072	+	0.896486i	$0.646111\pi$
$420$	1.75973	+	2.87205i	0.0858659	+	0.140142i
$421$			19.5465i			0.952637i	0.879273	+	0.476318i	$0.158029\pi$
$421$			19.5465i			0.952637i	−0.879273	+	0.476318i	$0.841971\pi$
$422$	−20.1389	−	21.0513i	−0.980346	−	1.02476i
$423$	16.0434	−	16.0434i	0.780059	−	0.780059i
$424$	−0.101202	+	1.52093i	−0.00491481	+	0.0738628i
$425$	12.9670	+	30.4477i	0.628990	+	1.47693i
$426$	7.65061	+	0.169468i	0.370673	+	0.00821075i
$427$	−8.30313	+	8.30313i	−0.401817	+	0.401817i
$428$	−16.6669	−	18.2129i	−0.805625	−	0.880353i
$429$	−0.216652			−0.0104600
$430$	−8.07893	+	5.19954i	−0.389600	+	0.250744i
$431$		−	13.2799i		−	0.639670i	−0.947473	−	0.319835i	$-0.896372\pi$
$431$		−	13.2799i		−	0.639670i	0.947473	−	0.319835i	$-0.103628\pi$
$432$	−12.5518	+	10.5040i	−0.603900	+	0.505373i
$433$	−14.0414	−	14.0414i	−0.674788	−	0.674788i	0.284028	−	0.958816i	$-0.408329\pi$
$433$	−14.0414	−	14.0414i	−0.674788	−	0.674788i	−0.958816	+	0.284028i	$0.908329\pi$
$434$	3.73375	+	0.0827059i	0.179226	+	0.00397001i
$435$	−2.09770	+	10.8260i	−0.100577	+	0.519069i
$436$	0.133356	−	3.00870i	0.00638661	−	0.144091i
$437$	−9.31122	−	9.31122i	−0.445416	−	0.445416i
$438$	8.39459	−	8.03075i	0.401109	−	0.383724i
$439$	17.9725			0.857779			0.428889	−	0.903357i	$-0.358905\pi$
$439$	17.9725			0.857779			0.428889	+	0.903357i	$0.358905\pi$
$440$	1.09194	+	0.287949i	0.0520562	+	0.0137274i
$441$	2.43273			0.115844
$442$	−10.8965	+	10.4243i	−0.518295	+	0.495831i
$443$	25.1666	+	25.1666i	1.19570	+	1.19570i	0.975441	+	0.220260i	$0.0706905\pi$
$443$	25.1666	+	25.1666i	1.19570	+	1.19570i	0.220260	+	0.975441i	$0.429310\pi$
$444$	7.67905	+	0.340363i	0.364432	+	0.0161529i
$445$	14.3485	−	9.69061i	0.680186	−	0.459379i
$446$	7.52060	+	0.166588i	0.356111	+	0.00788817i
$447$	6.88278	+	6.88278i	0.325544	+	0.325544i
$448$	6.35648	−	4.85749i	0.300315	−	0.229495i
$449$		−	5.75350i		−	0.271524i	−0.990741	−	0.135762i	$-0.956652\pi$
$449$		−	5.75350i		−	0.271524i	0.990741	−	0.135762i	$-0.0433483\pi$
$450$	−6.38801	−	15.9719i	−0.301134	−	0.752925i
$451$	0.514511			0.0242274
$452$	24.5939	−	22.5063i	1.15680	−	1.05861i
$453$	−0.0780583	+	0.0780583i	−0.00366750	+	0.00366750i
$454$	4.85789	+	0.107607i	0.227992	+	0.00505023i
$455$	−2.01618	−	2.98529i	−0.0945201	−	0.139953i
$456$	0.331111	−	4.97614i	0.0155057	−	0.233029i
$457$	−14.0684	+	14.0684i	−0.658093	+	0.658093i	−0.954929	−	0.296836i	$-0.904069\pi$
$457$	−14.0684	+	14.0684i	−0.658093	+	0.658093i	0.296836	+	0.954929i	$0.404069\pi$
$458$	−24.0328	−	25.1216i	−1.12298	−	1.17386i
$459$		−	27.0826i		−	1.26411i
$460$	5.87396	−	24.4595i	0.273875	−	1.14043i
$461$		−	30.2593i		−	1.40932i	−0.709547	−	0.704658i	$-0.751100\pi$
$461$		−	30.2593i		−	1.40932i	0.709547	−	0.704658i	$-0.248900\pi$
$462$	−0.137426	+	0.131470i	−0.00639364	+	0.00611653i
$463$	18.1308	−	18.1308i	0.842611	−	0.842611i	−0.146587	−	0.989198i	$-0.546829\pi$
$463$	18.1308	−	18.1308i	0.842611	−	0.842611i	0.989198	+	0.146587i	$0.0468288\pi$
$464$	26.0885	+	2.31722i	1.21113	+	0.107574i
$465$	4.36628	+	0.846031i	0.202481	+	0.0392337i
$466$	−0.668566	+	30.1823i	−0.0309707	+	1.39817i
$467$	21.0062	−	21.0062i	0.972051	−	0.972051i	−0.0275693	−	0.999620i	$-0.508777\pi$
$467$	21.0062	−	21.0062i	0.972051	−	0.972051i	0.999620	+	0.0275693i	$0.00877670\pi$
$468$	5.78256	−	5.29171i	0.267299	−	0.244609i
$469$	−11.2708			−0.520439
$470$	−24.8005	+	15.9614i	−1.14396	+	0.736246i
$471$		−	2.92478i		−	0.134767i
$472$	−17.5574	−	20.0604i	−0.808143	−	0.923357i
$473$	−0.383586	−	0.383586i	−0.0176373	−	0.0176373i
$474$	0.302462	−	13.6546i	0.0138926	−	0.627178i
$475$	10.8582	+	4.37201i	0.498208	+	0.200602i
$476$	−0.586160	+	13.2246i	−0.0268666	+	0.606148i
$477$	0.927049	+	0.927049i	0.0424467	+	0.0424467i
$478$	10.1343	+	10.5934i	0.463530	+	0.484530i
$479$	−27.8977			−1.27468			−0.637338	−	0.770584i	$-0.719965\pi$
$479$	−27.8977			−1.27468			−0.637338	+	0.770584i	$0.719965\pi$
$480$	8.43592	−	4.42694i	0.385045	−	0.202061i
$481$	−8.22076			−0.374835
$482$	−14.4580	−	15.1130i	−0.658543	−	0.688378i
$483$	2.99562	+	2.99562i	0.136305	+	0.136305i
$484$	0.971338	−	21.9147i	0.0441517	−	0.996124i
$485$	−22.2140	−	4.30428i	−1.00868	−	0.195447i
$486$	−0.483901	+	21.8456i	−0.0219502	+	0.990938i
$487$	17.0811	+	17.0811i	0.774019	+	0.774019i	0.978806	−	0.204788i	$-0.0656505\pi$
$487$	17.0811	+	17.0811i	0.774019	+	0.774019i	−0.204788	+	0.978806i	$0.565650\pi$
$488$	21.8738	+	24.9922i	0.990179	+	1.13134i
$489$			17.9537i			0.811896i
$490$	−3.09045	−	0.670153i	−0.139612	−	0.0302744i
$491$	−40.0440			−1.80716			−0.903581	−	0.428417i	$-0.859072\pi$
$491$	−40.0440			−1.80716			−0.903581	+	0.428417i	$0.859072\pi$
$492$	3.20217	−	2.93036i	0.144365	−	0.132111i
$493$	−30.6449	+	30.6449i	−1.38018	+	1.38018i
$494$	−0.118118	+	5.33241i	−0.00531437	+	0.239917i
$495$	0.804910	−	0.543614i	0.0361780	−	0.0244336i
$496$	0.934564	−	10.5218i	0.0419632	−	0.472443i
$497$	−5.08018	+	5.08018i	−0.227877	+	0.227877i
$498$	7.29131	−	6.97530i	0.326732	−	0.312570i
$499$		−	5.52663i		−	0.247406i	−0.992319	−	0.123703i	$-0.960523\pi$
$499$		−	5.52663i		−	0.247406i	0.992319	−	0.123703i	$-0.0394770\pi$
$500$	3.71525	+	22.0499i	0.166151	+	0.986100i
$501$			7.07574i			0.316121i
$502$	−22.9122	−	23.9503i	−1.02262	−	1.06895i
$503$	−20.5759	+	20.5759i	−0.917435	+	0.917435i	−0.996842	−	0.0794072i	$-0.974697\pi$
$503$	−20.5759	+	20.5759i	−0.917435	+	0.917435i	0.0794072	+	0.996842i	$0.474697\pi$
$504$	0.456837	−	6.86563i	0.0203492	−	0.305819i
$505$	−11.0028	+	7.43099i	−0.489619	+	0.330675i
$506$	1.41999	+	0.0314539i	0.0631260	+	0.00139830i
$507$	−5.54120	+	5.54120i	−0.246093	+	0.246093i
$508$	29.9057	−	27.3671i	1.32685	−	1.21422i
$509$	−23.3913			−1.03680			−0.518400	−	0.855138i	$-0.673472\pi$
$509$	−23.3913			−1.03680			−0.518400	+	0.855138i	$0.673472\pi$
$510$	−3.34076	+	15.4061i	−0.147931	+	0.682195i
$511$			10.9068i			0.482489i
$512$	−12.5151	−	18.8513i	−0.553093	−	0.833119i
$513$	−6.77346	−	6.77346i	−0.299055	−	0.299055i
$514$	−43.3696	−	0.960675i	−1.91295	−	0.0423736i
$515$	−19.2012	−	3.72052i	−0.846107	−	0.163946i
$516$	−4.57202	−	0.202648i	−0.201272	−	0.00892108i
$517$	−1.17753	−	1.17753i	−0.0517875	−	0.0517875i
$518$	−5.21458	+	4.98857i	−0.229115	+	0.219185i
$519$	15.5180			0.681166
$520$	−8.80367	+	5.12944i	−0.386066	+	0.224941i
$521$	−21.1630			−0.927169			−0.463585	−	0.886053i	$-0.653437\pi$
$521$	−21.1630			−0.927169			−0.463585	+	0.886053i	$0.653437\pi$
$522$	16.2779	−	15.5724i	0.712464	−	0.681584i
$523$	−15.4844	−	15.4844i	−0.677085	−	0.677085i	0.282254	−	0.959340i	$-0.408918\pi$
$523$	−15.4844	−	15.4844i	−0.677085	−	0.677085i	−0.959340	+	0.282254i	$0.908918\pi$
$524$	0.954775	−	21.5410i	0.0417095	−	0.941024i
$525$	−3.49331	−	1.40657i	−0.152461	−	0.0613877i
$526$	8.37924	+	0.185608i	0.365352	+	0.00809288i
$527$	12.3595	+	12.3595i	0.538387	+	0.538387i
$528$	0.345225	+	0.412530i	0.0150240	+	0.0179531i
$529$		−	8.63850i		−	0.375587i
$530$	−0.922310	−	1.43306i	−0.0400626	−	0.0622483i
$531$	−22.9291			−0.995039
$532$	3.16092	+	3.45412i	0.137043	+	0.149755i
$533$	−3.28257	+	3.28257i	−0.142184	+	0.142184i
$534$	8.24564	+	0.182648i	0.356824	+	0.00790397i
$535$	27.0980	+	5.25062i	1.17155	+	0.227004i
$536$	−2.11652	+	31.8084i	−0.0914199	+	1.37391i
$537$	3.37577	−	3.37577i	0.145675	−	0.145675i
$538$	−2.98093	−	3.11598i	−0.128517	−	0.134340i
$539$		−	0.178553i		−	0.00769083i
$540$	4.27302	−	17.7931i	0.183882	−	0.765692i
$541$		−	28.4007i		−	1.22104i	−0.792000	−	0.610522i	$-0.790960\pi$
$541$		−	28.4007i		−	1.22104i	0.792000	−	0.610522i	$-0.209040\pi$
$542$	−2.23084	+	2.13415i	−0.0958229	+	0.0916697i
$543$	−1.56926	+	1.56926i	−0.0673435	+	0.0673435i
$544$	37.2122	+	4.13767i	1.59546	+	0.177401i
$545$	1.88453	+	2.79036i	0.0807245	+	0.119526i
$546$	0.0380010	−	1.71555i	0.00162629	−	0.0734188i
$547$	−0.171388	+	0.171388i	−0.00732803	+	0.00732803i	−0.710761	−	0.703433i	$-0.751649\pi$
$547$	−0.171388	+	0.171388i	−0.00732803	+	0.00732803i	0.703433	+	0.710761i	$0.251649\pi$
$548$	−8.99261	−	9.82675i	−0.384145	−	0.419778i
$549$	28.5661			1.21917
$550$	−1.17228	+	0.468855i	−0.0499861	+	0.0199920i
$551$			15.3288i			0.653030i
$552$	9.01673	−	7.89165i	0.383777	−	0.335891i
$553$	9.06699	+	9.06699i	0.385568	+	0.385568i
$554$	0.330079	−	14.9014i	0.0140237	−	0.633099i
$555$	−7.12179	+	4.80986i	−0.302303	+	0.204167i
$556$	0.950938	+	0.0421489i	0.0403288	+	0.00178751i
$557$	8.81151	+	8.81151i	0.373356	+	0.373356i	0.868698	−	0.495342i	$-0.164957\pi$
$557$	8.81151	+	8.81151i	0.373356	+	0.373356i	−0.495342	+	0.868698i	$0.664957\pi$
$558$	−6.28054	−	6.56508i	−0.265876	−	0.277922i
$559$	4.89455			0.207017
$560$	−2.47165	+	8.59599i	−0.104446	+	0.363247i
$561$	−0.890100			−0.0375800
$562$	19.1230	+	19.9894i	0.806657	+	0.843203i
$563$	−3.37490	−	3.37490i	−0.142235	−	0.142235i	0.632404	−	0.774639i	$-0.282068\pi$
$563$	−3.37490	−	3.37490i	−0.142235	−	0.142235i	−0.774639	+	0.632404i	$0.782068\pi$
$564$	−14.0351	−	0.622085i	−0.590984	−	0.0261945i
$565$	−7.09022	+	36.5919i	−0.298288	+	1.53943i
$566$	0.0931621	−	4.20579i	0.00391590	−	0.176783i
$567$	−2.98144	−	2.98144i	−0.125209	−	0.125209i
$568$	13.3832	+	15.2912i	0.561548	+	0.641605i
$569$		−	9.24221i		−	0.387454i	−0.981056	−	0.193727i	$-0.937942\pi$
$569$		−	9.24221i		−	0.387454i	0.981056	−	0.193727i	$-0.0620575\pi$
$570$	3.01760	+	4.68867i	0.126393	+	0.196387i
$571$	13.2840			0.555917			0.277958	−	0.960593i	$-0.410342\pi$
$571$	13.2840			0.555917			0.277958	+	0.960593i	$0.410342\pi$
$572$	−0.388391	−	0.424417i	−0.0162394	−	0.0177458i
$573$	−10.6667	+	10.6667i	−0.445606	+	0.445606i
$574$	−0.0902458	+	4.07414i	−0.00376679	+	0.170051i
$575$	11.0197	+	25.8753i	0.459552	+	1.07907i
$576$	−19.2903	−	2.57856i	−0.803762	−	0.107440i
$577$	−8.92884	+	8.92884i	−0.371713	+	0.371713i	−0.868101	−	0.496388i	$-0.834659\pi$
$577$	−8.92884	+	8.92884i	−0.371713	+	0.371713i	0.496388	+	0.868101i	$0.334659\pi$
$578$	−27.3954	+	26.2080i	−1.13950	+	1.09011i
$579$			6.43164i			0.267290i
$580$	−24.9686	+	15.2984i	−1.03676	+	0.635233i
$581$			9.47336i			0.393021i
$582$	−7.45081	−	7.78837i	−0.308846	−	0.322838i
$583$	0.0680417	−	0.0680417i	0.00281800	−	0.00281800i
$584$	30.7810	+	2.04816i	1.27373	+	0.0847536i
$585$	−1.66706	+	8.60355i	−0.0689246	+	0.355713i
$586$	4.64151	+	0.102814i	0.191739	+	0.00424719i
$587$	16.6495	−	16.6495i	0.687197	−	0.687197i	−0.274414	−	0.961612i	$-0.588484\pi$
$587$	16.6495	−	16.6495i	0.687197	−	0.687197i	0.961612	+	0.274414i	$0.0884839\pi$
$588$	−1.01693	−	1.11126i	−0.0419377	−	0.0458277i
$589$	6.18231			0.254738
$590$	29.1283	+	6.31636i	1.19919	+	0.260040i
$591$		−	2.73753i		−	0.112607i
$592$	13.0994	+	15.6533i	0.538383	+	0.643347i
$593$	−3.83499	−	3.83499i	−0.157484	−	0.157484i	0.623967	−	0.781451i	$-0.285520\pi$
$593$	−3.83499	−	3.83499i	−0.157484	−	0.157484i	−0.781451	+	0.623967i	$0.785520\pi$
$594$	1.03297	+	0.0228812i	0.0423833	+	0.000938827i
$595$	−8.28336	−	12.2649i	−0.339585	−	0.502811i
$596$	−1.14452	+	25.8220i	−0.0468814	+	1.05771i
$597$	−8.31328	−	8.31328i	−0.340240	−	0.340240i
$598$	−9.26015	+	8.85880i	−0.378676	+	0.362263i
$599$	2.24631			0.0917816			0.0458908	−	0.998946i	$-0.485387\pi$
$599$	2.24631			0.0917816			0.0458908	+	0.998946i	$0.485387\pi$
$600$	−4.62560	+	9.59463i	−0.188839	+	0.391699i
$601$	−24.7245			−1.00853			−0.504266	−	0.863548i	$-0.668237\pi$
$601$	−24.7245			−1.00853			−0.504266	+	0.863548i	$0.668237\pi$
$602$	3.10470	−	2.97014i	0.126538	−	0.121054i
$603$	19.3881	+	19.3881i	0.789545	+	0.789545i
$604$	−0.292850	−	0.0129801i	−0.0119159	−	0.000528154i
$605$	13.7265	+	20.3244i	0.558063	+	0.826304i
$606$	−6.32295	−	0.140059i	−0.256852	−	0.00568951i
$607$	−18.9262	−	18.9262i	−0.768190	−	0.768190i	0.209598	−	0.977788i	$-0.432784\pi$
$607$	−18.9262	−	18.9262i	−0.768190	−	0.768190i	−0.977788	+	0.209598i	$0.932784\pi$
$608$	10.3418	−	8.27206i	0.419414	−	0.335476i
$609$		−	4.93160i		−	0.199839i
$610$	−36.2893	−	7.86921i	−1.46931	−	0.318615i
$611$	15.0252			0.607853
$612$	23.7573	−	21.7406i	0.960331	−	0.878814i
$613$	1.60732	−	1.60732i	0.0649190	−	0.0649190i	−0.673902	−	0.738821i	$-0.735383\pi$
$613$	1.60732	−	1.60732i	0.0649190	−	0.0649190i	0.738821	+	0.673902i	$0.235383\pi$
$614$	31.1981	+	0.691065i	1.25905	+	0.0278891i
$615$	−0.923159	+	4.76433i	−0.0372254	+	0.192116i
$616$	−0.503910	−	0.0335301i	−0.0203031	−	0.00135096i
$617$	7.67931	−	7.67931i	0.309157	−	0.309157i	−0.535425	−	0.844583i	$-0.679849\pi$
$617$	7.67931	−	7.67931i	0.309157	−	0.309157i	0.844583	+	0.535425i	$0.179849\pi$
$618$	−6.44029	−	6.73207i	−0.259067	−	0.270804i
$619$			11.7834i			0.473616i	0.971556	+	0.236808i	$0.0761013\pi$
$619$			11.7834i			0.473616i	−0.971556	+	0.236808i	$0.923899\pi$
$620$	6.17005	+	10.0701i	0.247795	+	0.404427i
$621$		−	23.0155i		−	0.923579i
$622$	8.90528	−	8.51931i	0.357069	−	0.341593i
$623$	−5.47530	+	5.47530i	−0.219363	+	0.219363i
$624$	−4.83447	−	0.429405i	−0.193533	−	0.0171900i
$625$	−18.0247	−	17.3237i	−0.720986	−	0.692949i
$626$	0.140838	−	6.35813i	0.00562903	−	0.254122i
$627$	−0.222618	+	0.222618i	−0.00889049	+	0.00889049i
$628$	5.72960	−	5.24324i	0.228636	−	0.209228i
$629$	−33.7745			−1.34668
$630$	4.16341	+	6.46900i	0.165874	+	0.257731i
$631$		−	16.8155i		−	0.669416i	−0.942322	−	0.334708i	$-0.891362\pi$
$631$		−	16.8155i		−	0.669416i	0.942322	−	0.334708i	$-0.108638\pi$
$632$	27.2914	−	23.8861i	1.08559	−	0.950137i
$633$	10.9711	+	10.9711i	0.436061	+	0.436061i
$634$	0.102284	−	4.61758i	0.00406220	−	0.183387i
$635$	−8.62155	+	44.4950i	−0.342136	+	1.76573i
$636$	0.0359463	−	0.810999i	0.00142536	−	0.0321582i
$637$	1.13916	+	1.13916i	0.0451354	+	0.0451354i
$638$	−1.14295	−	1.19473i	−0.0452499	−	0.0472999i
$639$	17.4779			0.691415
$640$	23.7953	+	8.58966i	0.940593	+	0.339536i
$641$	36.7583			1.45187			0.725933	−	0.687765i	$-0.241408\pi$
$641$	36.7583			1.45187			0.725933	+	0.687765i	$0.241408\pi$
$642$	9.08894	+	9.50072i	0.358712	+	0.374964i
$643$	2.46543	+	2.46543i	0.0972269	+	0.0972269i	0.754047	−	0.656820i	$-0.228099\pi$
$643$	2.46543	+	2.46543i	0.0972269	+	0.0972269i	−0.656820	+	0.754047i	$0.728099\pi$
$644$	−0.498134	+	11.2386i	−0.0196292	+	0.442862i
$645$	4.24023	−	2.86373i	0.166959	−	0.112759i
$646$	−0.485279	+	21.9079i	−0.0190931	+	0.861954i
$647$	30.1115	+	30.1115i	1.18380	+	1.18380i	0.978751	+	0.205053i	$0.0657366\pi$
$647$	30.1115	+	30.1115i	1.18380	+	1.18380i	0.205053	+	0.978751i	$0.434263\pi$
$648$	−8.97407	+	7.85431i	−0.352535	+	0.308547i
$649$			1.68291i			0.0660599i
$650$	4.48782	−	10.4704i	0.176027	−	0.410683i
$651$	−1.98898			−0.0779542
$652$	−35.1711	+	32.1856i	−1.37740	+	1.26048i
$653$	−15.4764	+	15.4764i	−0.605640	+	0.605640i	−0.941804	−	0.336164i	$-0.890870\pi$
$653$	−15.4764	+	15.4764i	−0.605640	+	0.605640i	0.336164	+	0.941804i	$0.390870\pi$
$654$	−0.0355196	+	1.60353i	−0.00138893	+	0.0627030i
$655$	13.4925	+	19.9778i	0.527194	+	0.780598i
$656$	11.4810	+	1.01976i	0.448259	+	0.0398151i
$657$	18.7619	−	18.7619i	0.731972	−	0.731972i
$658$	9.53073	−	9.11766i	0.371547	−	0.355443i
$659$		−	30.2565i		−	1.17863i	−0.807905	−	0.589313i	$-0.799399\pi$
$659$		−	30.2565i		−	1.17863i	0.807905	−	0.589313i	$-0.200601\pi$
$660$	−0.584790	−	0.140438i	−0.0227629	−	0.00546653i
$661$		−	17.1872i		−	0.668505i	−0.942484	−	0.334253i	$-0.891516\pi$
$661$		−	17.1872i		−	0.668505i	0.942484	−	0.334253i	$-0.108484\pi$
$662$	−27.9397	−	29.2055i	−1.08591	−	1.13510i
$663$	5.67882	−	5.67882i	0.220547	−	0.220547i
$664$	26.7356	+	1.77898i	1.03754	+	0.0690378i
$665$	−5.13920	−	0.995795i	−0.199290	−	0.0386153i
$666$	17.5515	+	0.388781i	0.680106	+	0.0150650i
$667$	−26.0428	+	26.0428i	−1.00838	+	1.00838i
$668$	−13.8613	+	12.6846i	−0.536308	+	0.490784i
$669$	−4.00624			−0.154890
$670$	−19.2890	−	29.9708i	−0.745200	−	1.15787i
$671$		−	2.09664i		−	0.0809400i
$672$	−3.32716	+	2.66130i	−0.128348	+	0.102662i
$673$	15.2384	+	15.2384i	0.587396	+	0.587396i	0.936925	−	0.349530i	$-0.113659\pi$
$673$	15.2384	+	15.2384i	0.587396	+	0.587396i	−0.349530	+	0.936925i	$0.613659\pi$
$674$	−20.7731	−	0.460144i	−0.800151	−	0.0177241i
$675$	8.01626	+	18.8230i	0.308546	+	0.724497i
$676$	−20.7888	−	0.921433i	−0.799569	−	0.0354397i
$677$	−29.7024	−	29.7024i	−1.14156	−	1.14156i	−0.988166	−	0.153391i	$-0.950981\pi$
$677$	−29.7024	−	29.7024i	−1.14156	−	1.14156i	−0.153391	−	0.988166i	$-0.549019\pi$
$678$	−12.8294	+	12.2733i	−0.492709	+	0.471354i
$679$	10.1192			0.388338
$680$	−36.1693	+	21.0740i	−1.38703	+	0.808151i
$681$	−2.58781			−0.0991651
$682$	−0.481851	+	0.460967i	−0.0184510	+	0.0176513i
$683$	0.851445	+	0.851445i	0.0325796	+	0.0325796i	0.723209	−	0.690629i	$-0.242666\pi$
$683$	0.851445	+	0.851445i	0.0325796	+	0.0325796i	−0.690629	+	0.723209i	$0.742666\pi$
$684$	0.504367	−	11.3792i	0.0192850	−	0.435095i
$685$	14.6207	+	2.83297i	0.558627	+	0.108242i
$686$	1.41387	+	0.0313184i	0.0539817	+	0.00119574i
$687$	13.0923	+	13.0923i	0.499504	+	0.499504i
$688$	−7.79925	−	9.31979i	−0.297344	−	0.355314i
$689$			0.868210i			0.0330762i
$690$	−2.83906	+	13.0925i	−0.108081	+	0.498424i
$691$	−24.5586			−0.934255			−0.467127	−	0.884190i	$-0.654711\pi$
$691$	−24.5586			−0.934255			−0.467127	+	0.884190i	$0.654711\pi$
$692$	27.8191	+	30.3996i	1.05752	+	1.15562i
$693$	−0.307148	+	0.307148i	−0.0116676	+	0.0116676i
$694$	21.7947	+	0.482772i	0.827316	+	0.0183258i
$695$	−0.881929	+	0.595630i	−0.0334535	+	0.0225935i
$696$	−13.9179	−	0.926094i	−0.527557	−	0.0351035i
$697$	−13.4862	+	13.4862i	−0.510827	+	0.510827i
$698$	22.4299	+	23.4461i	0.848984	+	0.887447i
$699$		−	16.0782i		−	0.608134i
$700$	−3.50699	−	9.36488i	−0.132552	−	0.353959i
$701$		−	8.37172i		−	0.316196i	−0.987423	−	0.158098i	$-0.949464\pi$
$701$		−	8.37172i		−	0.316196i	0.987423	−	0.158098i	$-0.0505361\pi$
$702$	−6.73631	+	6.44434i	−0.254245	+	0.243226i
$703$	−8.44713	+	8.44713i	−0.318590	+	0.318590i
$704$	−0.189256	+	1.41583i	−0.00713286	+	0.0533612i
$705$	13.0166	−	8.79103i	0.490232	−	0.331089i
$706$	0.258314	−	11.6616i	0.00972178	−	0.438889i
$707$	4.19859	−	4.19859i	0.157904	−	0.157904i
$708$	9.58486	+	10.4739i	0.360221	+	0.393635i
$709$	−6.05507			−0.227403			−0.113701	−	0.993515i	$-0.536271\pi$
$709$	−6.05507			−0.227403			−0.113701	+	0.993515i	$0.536271\pi$
$710$	−22.2032	−	4.81469i	−0.833273	−	0.180692i
$711$		−	31.1941i		−	1.16987i
$712$	14.4241	+	16.4805i	0.540567	+	0.617633i
$713$	10.5034	+	10.5034i	0.393355	+	0.393355i
$714$	0.156125	−	7.04823i	0.00584281	−	0.263773i
$715$	0.631467	+	0.122356i	0.0236155	+	0.00457585i
$716$	12.6648	+	0.561350i	0.473306	+	0.0209786i
$717$	−5.52083	−	5.52083i	−0.206179	−	0.206179i
$718$	22.1346	+	23.1374i	0.826056	+	0.863481i
$719$	−14.2215			−0.530372			−0.265186	−	0.964197i	$-0.585433\pi$
$719$	−14.2215			−0.530372			−0.265186	+	0.964197i	$0.585433\pi$
$720$	19.0386	−	10.5351i	0.709526	−	0.392620i
$721$	8.74676			0.325746
$722$	−13.2167	−	13.8155i	−0.491875	−	0.514159i
$723$	7.87627	+	7.87627i	0.292922	+	0.292922i
$724$	−5.88737	−	0.260949i	−0.218802	−	0.00969810i
$725$	12.2282	−	30.3696i	0.454144	−	1.12790i
$726$	−0.258717	+	11.6798i	−0.00960190	+	0.433477i
$727$	−25.7952	−	25.7952i	−0.956692	−	0.956692i	0.0424080	−	0.999100i	$-0.486497\pi$
$727$	−25.7952	−	25.7952i	−0.956692	−	0.956692i	−0.999100	+	0.0424080i	$0.986497\pi$
$728$	3.42886	−	3.00101i	0.127082	−	0.111225i
$729$			1.01197i			0.0374803i
$730$	−29.0028	+	18.6660i	−1.07344	+	0.690860i
$731$	20.1089			0.743756
$732$	−11.9413	−	13.0489i	−0.441361	−	0.482301i
$733$	−36.5642	+	36.5642i	−1.35053	+	1.35053i	−0.465462	+	0.885068i	$0.654112\pi$
$733$	−36.5642	+	36.5642i	−1.35053	+	1.35053i	−0.885068	+	0.465462i	$0.845888\pi$
$734$	0.492036	−	22.2129i	0.0181614	−	0.819893i
$735$	1.65339	+	0.320368i	0.0609861	+	0.0118170i
$736$	31.6238	+	3.51630i	1.16567	+	0.129612i
$737$	1.42301	−	1.42301i	0.0524173	−	0.0524173i
$738$	7.16359	−	6.85310i	0.263695	−	0.252266i
$739$		−	11.7762i		−	0.433193i	−0.976261	−	0.216597i	$-0.930504\pi$
$739$		−	11.7762i		−	0.433193i	0.976261	−	0.216597i	$-0.0694957\pi$
$740$	−22.1896	−	5.32885i	−0.815707	−	0.195893i
$741$		−	2.84059i		−	0.104352i
$742$	0.526852	+	0.550721i	0.0193413	+	0.0202176i
$743$	11.0276	−	11.0276i	0.404565	−	0.404565i	−0.475273	−	0.879838i	$-0.657651\pi$
$743$	11.0276	−	11.0276i	0.404565	−	0.404565i	0.879838	+	0.475273i	$0.157651\pi$
$744$	−0.373506	+	5.61327i	−0.0136934	+	0.205792i
$745$	−16.1739	−	23.9481i	−0.592565	−	0.877390i
$746$	−36.4796	−	0.808057i	−1.33561	−	0.0295851i
$747$	16.2961	−	16.2961i	0.596243	−	0.596243i
$748$	−1.59568	−	1.74369i	−0.0583438	−	0.0637556i
$749$	−12.3440			−0.451039
$750$	−2.23821	−	11.6964i	−0.0817278	−	0.427094i
$751$		−	13.6810i		−	0.499227i	−0.968346	−	0.249613i	$-0.919696\pi$
$751$		−	13.6810i		−	0.499227i	0.968346	−	0.249613i	$-0.0803035\pi$
$752$	−23.9420	−	28.6097i	−0.873074	−	1.04329i
$753$	12.4819	+	12.4819i	0.454865	+	0.454865i
$754$	14.9144	+	0.330367i	0.543149	+	0.0120312i
$755$	0.271598	−	0.183430i	0.00988446	−	0.00667569i
$756$	−0.362368	+	8.17552i	−0.0131792	+	0.297341i
$757$	14.7686	+	14.7686i	0.536774	+	0.536774i	0.922580	−	0.385806i	$-0.126076\pi$
$757$	14.7686	+	14.7686i	0.536774	+	0.536774i	−0.385806	+	0.922580i	$0.626076\pi$
$758$	30.5415	−	29.2178i	1.10932	−	1.06124i
$759$	−0.756430			−0.0274567
$760$	−3.77540	+	14.3168i	−0.136948	+	0.519324i
$761$	−7.56168			−0.274111			−0.137055	−	0.990563i	$-0.543764\pi$
$761$	−7.56168			−0.274111			−0.137055	+	0.990563i	$0.543764\pi$
$762$	−15.6002	+	14.9241i	−0.565137	+	0.540643i
$763$	−1.06478	−	1.06478i	−0.0385477	−	0.0385477i
$764$	−40.0179	−	1.77373i	−1.44780	−	0.0641715i
$765$	−6.84903	+	35.3471i	−0.247627	+	1.27798i
$766$	29.6312	+	0.656358i	1.07062	+	0.0237152i
$767$	−10.7369	−	10.7369i	−0.387687	−	0.387687i
$768$	6.88588	+	9.88963i	0.248473	+	0.356861i
$769$		−	29.2872i		−	1.05612i	−0.849206	−	0.528062i	$-0.822919\pi$
$769$		−	29.2872i		−	1.05612i	0.849206	−	0.528062i	$-0.177081\pi$
$770$	0.474799	−	0.305578i	0.0171106	−	0.0110123i
$771$	23.1031			0.832037
$772$	−12.5995	+	11.5300i	−0.453465	+	0.414973i
$773$	20.4965	−	20.4965i	0.737206	−	0.737206i	−0.234830	−	0.972036i	$-0.575453\pi$
$773$	20.4965	−	20.4965i	0.737206	−	0.737206i	0.972036	+	0.234830i	$0.0754534\pi$
$774$	−10.4499	−	0.231476i	−0.375616	−	0.00832022i
$775$	−12.2484	−	4.93179i	−0.439977	−	0.177155i
$776$	1.90025	−	28.5582i	0.0682152	−	1.02518i
$777$	2.71762	−	2.71762i	0.0974941	−	0.0974941i
$778$	28.7400	+	30.0421i	1.03038	+	1.07706i
$779$			6.74592i			0.241698i
$780$	4.62694	−	2.83496i	0.165671	−	0.101508i
$781$		−	1.28281i		−	0.0459025i
$782$	−38.0447	+	36.3958i	−1.36048	+	1.30151i
$783$	−18.9449	+	18.9449i	−0.677034	+	0.677034i
$784$	0.353893	−	3.98431i	0.0126390	−	0.142297i
$785$	−1.65180	+	8.52475i	−0.0589551	+	0.304262i
$786$	−0.254306	+	11.4806i	−0.00907078	+	0.409499i
$787$	−6.18074	+	6.18074i	−0.220320	+	0.220320i	−0.808633	−	0.588313i	$-0.799792\pi$
$787$	−6.18074	+	6.18074i	−0.220320	+	0.220320i	0.588313	+	0.808633i	$0.299792\pi$
$788$	5.36278	−	4.90756i	0.191041	−	0.174825i
$789$	−4.46364			−0.158910
$790$	−8.59314	+	39.6278i	−0.305730	+	1.40989i
$791$		−	16.6688i		−	0.592673i
$792$	0.809149	+	0.924506i	0.0287519	+	0.0328509i
$793$	13.3765	+	13.3765i	0.475015	+	0.475015i
$794$	0.205191	−	9.26332i	0.00728195	−	0.328743i
$795$	0.507978	+	0.752145i	0.0180161	+	0.0266758i
$796$	1.38240	−	31.1888i	0.0489977	−	1.10546i
$797$	25.4950	+	25.4950i	0.903080	+	0.903080i	0.995701	−	0.0926214i	$-0.0295246\pi$
$797$	25.4950	+	25.4950i	0.903080	+	0.903080i	−0.0926214	+	0.995701i	$0.529525\pi$
$798$	−1.72374	−	1.80184i	−0.0610198	−	0.0637843i
$799$	61.7300			2.18385
$800$	−27.0880	+	8.13878i	−0.957706	+	0.287749i
$801$	18.8372			0.665581
$802$	7.39875	+	7.73396i	0.261259	+	0.273095i
$803$	−1.37705	−	1.37705i	−0.0485951	−	0.0485951i
$804$	0.751774	−	16.9611i	0.0265130	−	0.598171i
$805$	−7.03941	−	10.4230i	−0.248107	−	0.367363i
$806$	0.133241	−	6.01516i	0.00469322	−	0.211875i
$807$	1.62392	+	1.62392i	0.0571647	+	0.0571647i
$808$	−11.0608	−	12.6376i	−0.389116	−	0.444591i
$809$		−	22.6197i		−	0.795268i	−0.917544	−	0.397634i	$-0.869831\pi$
$809$		−	22.6197i		−	0.795268i	0.917544	−	0.397634i	$-0.130169\pi$
$810$	2.82563	−	13.0306i	0.0992826	−	0.457848i
$811$	−10.0669			−0.353497			−0.176749	−	0.984256i	$-0.556558\pi$
$811$	−10.0669			−0.353497			−0.176749	+	0.984256i	$0.556558\pi$
$812$	9.66093	−	8.84086i	0.339032	−	0.310253i
$813$	1.16262	−	1.16262i	0.0407749	−	0.0407749i
$814$	0.0285350	−	1.28821i	0.00100015	−	0.0451517i
$815$	10.1395	−	52.3291i	0.355172	−	1.83301i
$816$	−19.8621	−	1.76418i	−0.695312	−	0.0617587i
$817$	5.02932	−	5.02932i	0.175954	−	0.175954i
$818$	13.7650	−	13.1684i	0.481282	−	0.460423i
$819$		−	3.91919i		−	0.136948i
$820$	−10.9882	+	6.73255i	−0.383724	+	0.235111i
$821$			18.7143i			0.653134i	0.945174	+	0.326567i	$0.105892\pi$
$821$			18.7143i			0.653134i	−0.945174	+	0.326567i	$0.894108\pi$
$822$	4.90393	+	5.12611i	0.171044	+	0.178793i
$823$	−3.60679	+	3.60679i	−0.125725	+	0.125725i	−0.767169	−	0.641445i	$-0.778335\pi$
$823$	−3.60679	+	3.60679i	−0.125725	+	0.125725i	0.641445	+	0.767169i	$0.278335\pi$
$824$	1.64253	−	24.6850i	0.0572204	−	0.859942i
$825$	0.618639	−	0.263464i	0.0215383	−	0.00917263i
$826$	−13.3260	−	0.295184i	−0.463672	−	0.0102708i
$827$	40.0085	−	40.0085i	1.39123	−	1.39123i	0.568654	−	0.822577i	$-0.307464\pi$
$827$	40.0085	−	40.0085i	1.39123	−	1.39123i	0.822577	−	0.568654i	$-0.192536\pi$
$828$	20.1895	−	18.4758i	0.701635	−	0.642077i
$829$	30.9727			1.07572			0.537862	−	0.843033i	$-0.319232\pi$
$829$	30.9727			1.07572			0.537862	+	0.843033i	$0.319232\pi$
$830$	−25.1911	+	16.2128i	−0.874395	+	0.562755i
$831$			7.93801i			0.275366i
$832$	−7.82553	−	10.2404i	−0.271301	−	0.355023i
$833$	4.68019	+	4.68019i	0.162159	+	0.162159i
$834$	−0.506816	−	0.0112264i	−0.0175496	−	0.000388739i
$835$	3.99608	−	20.6234i	0.138290	−	0.713702i
$836$	−0.835189	−	0.0370186i	−0.0288856	−	0.00128031i
$837$	7.64071	+	7.64071i	0.264101	+	0.264101i
$838$	37.5050	−	35.8795i	1.29559	−	1.23944i
$839$	−37.9907			−1.31158			−0.655792	−	0.754942i	$-0.727665\pi$
$839$	−37.9907			−1.31158			−0.655792	+	0.754942i	$0.727665\pi$
$840$	1.21462	−	4.60601i	0.0419085	−	0.158922i
$841$	13.8736			0.478399
$842$	19.9745	−	19.1088i	0.688368	−	0.658533i
$843$	−10.4177	−	10.4177i	−0.358803	−	0.358803i
$844$	−1.82435	+	41.1599i	−0.0627968	+	1.41678i
$845$	19.2802	−	13.0213i	0.663258	−	0.447946i
$846$	−32.0790	−	0.710579i	−1.10290	−	0.0244302i
$847$	−7.75563	−	7.75563i	−0.266487	−	0.266487i
$848$	1.65317	−	1.38345i	0.0567702	−	0.0475080i
$849$			2.24044i			0.0768916i
$850$	18.4379	−	43.0169i	0.632416	−	1.47547i
$851$	−28.7024			−0.983906
$852$	−7.30613	−	7.98383i	−0.250304	−	0.273522i
$853$	12.3815	−	12.3815i	0.423935	−	0.423935i	−0.462621	−	0.886556i	$-0.653091\pi$
$853$	12.3815	−	12.3815i	0.423935	−	0.423935i	0.886556	+	0.462621i	$0.153091\pi$
$854$	16.6022	+	0.367754i	0.568115	+	0.0125843i
$855$	7.12749	+	10.5534i	0.243755	+	0.360920i
$856$	−2.31805	+	34.8370i	−0.0792292	+	1.19070i
$857$	−12.9421	+	12.9421i	−0.442093	+	0.442093i	−0.892715	−	0.450622i	$-0.851202\pi$
$857$	−12.9421	+	12.9421i	−0.442093	+	0.442093i	0.450622	+	0.892715i	$0.351202\pi$
$858$	0.211801	+	0.221396i	0.00723076	+	0.00755835i
$859$		−	2.98370i		−	0.101803i	−0.998704	−	0.0509013i	$-0.983791\pi$
$859$		−	2.98370i		−	0.101803i	0.998704	−	0.0509013i	$-0.0162094\pi$
$860$	13.2114	+	3.17274i	0.450507	+	0.108189i
$861$		−	2.17030i		−	0.0739638i
$862$	−13.5707	+	12.9826i	−0.462221	+	0.442187i
$863$	13.1401	−	13.1401i	0.447296	−	0.447296i	−0.447159	−	0.894455i	$-0.647564\pi$
$863$	13.1401	−	13.1401i	0.447296	−	0.447296i	0.894455	+	0.447159i	$0.147564\pi$
$864$	23.0048	+	2.55793i	0.782639	+	0.0870226i
$865$	−45.2298	−	8.76394i	−1.53786	−	0.297983i
$866$	−0.621908	+	28.0760i	−0.0211333	+	0.954060i
$867$	14.2773	−	14.2773i	0.484884	−	0.484884i
$868$	−3.56563	−	3.89637i	−0.121025	−	0.132252i
$869$	−2.28953			−0.0776668
$870$	13.1139	−	8.44000i	0.444602	−	0.286143i
$871$			18.1576i			0.615246i
$872$	−3.20496	+	2.80506i	−0.108534	+	0.0949912i
$873$	−17.4070	−	17.4070i	−0.589138	−	0.589138i
$874$	−0.412403	+	18.6179i	−0.0139497	+	0.629759i
$875$	9.38745	+	6.07255i	0.317354	+	0.205290i
$876$	−16.4133	−	0.727494i	−0.554553	−	0.0245797i
$877$	−23.1556	−	23.1556i	−0.781908	−	0.781908i	0.198245	−	0.980153i	$-0.436476\pi$
$877$	−23.1556	−	23.1556i	−0.781908	−	0.781908i	−0.980153	+	0.198245i	$0.936476\pi$
$878$	−17.5700	−	18.3661i	−0.592960	−	0.619825i
$879$	−2.47255			−0.0833969
$880$	−0.773235	−	1.39736i	−0.0260658	−	0.0471049i
$881$	27.6809			0.932593			0.466297	−	0.884628i	$-0.345588\pi$
$881$	27.6809			0.932593			0.466297	+	0.884628i	$0.345588\pi$
$882$	−2.37826	−	2.48601i	−0.0800803	−	0.0837084i
$883$	−17.4938	−	17.4938i	−0.588712	−	0.588712i	0.348570	−	0.937283i	$-0.386667\pi$
$883$	−17.4938	−	17.4938i	−0.588712	−	0.588712i	−0.937283	+	0.348570i	$0.886667\pi$
$884$	21.3051	+	0.944318i	0.716568	+	0.0317608i
$885$	−15.5836	−	3.01955i	−0.523837	−	0.101501i
$886$	1.11465	−	50.3208i	0.0374475	−	1.69056i
$887$	20.6115	+	20.6115i	0.692065	+	0.692065i	0.962686	−	0.270621i	$-0.0872291\pi$
$887$	20.6115	+	20.6115i	0.692065	+	0.692065i	−0.270621	+	0.962686i	$0.587229\pi$
$888$	−7.15930	−	8.17997i	−0.240250	−	0.274502i
$889$		−	20.2689i		−	0.679796i
$890$	−23.9301	−	5.18915i	−0.802139	−	0.173941i
$891$	0.752851			0.0252215
$892$	−7.18197	−	7.84816i	−0.240470	−	0.262776i
$893$	15.4389	−	15.4389i	0.516643	−	0.516643i
$894$	0.304845	−	13.7622i	0.0101955	−	0.460276i
$895$	−11.7457	+	7.93275i	−0.392617	+	0.265162i
$896$	−11.1780	−	1.74696i	−0.373431	−	0.0583618i
$897$	4.82601	−	4.82601i	0.161136	−	0.161136i
$898$	−5.87950	+	5.62467i	−0.196201	+	0.187698i
$899$		−	17.2915i		−	0.576703i
$900$	−10.0768	+	22.1422i	−0.335892	+	0.738075i
$901$			3.56698i			0.118833i
$902$	−0.502991	−	0.525779i	−0.0167478	−	0.0175065i
$903$	−1.61804	+	1.61804i	−0.0538450	+	0.0538450i
$904$	−47.0424	−	3.13019i	−1.56461	−	0.104109i
$905$	5.46013	−	3.68762i	0.181501	−	0.122581i
$906$	0.156078	+	0.00345728i	0.00518536	+	0.000114860i
$907$	4.21936	−	4.21936i	0.140102	−	0.140102i	−0.633578	−	0.773679i	$-0.718414\pi$
$907$	4.21936	−	4.21936i	0.140102	−	0.140102i	0.773679	+	0.633578i	$0.218414\pi$
$908$	−4.63916	−	5.06948i	−0.153956	−	0.168237i
$909$	−14.4448			−0.479105
$910$	−1.07963	+	4.97879i	−0.0357894	+	0.165045i
$911$			24.8921i			0.824712i	0.911023	+	0.412356i	$0.135294\pi$
$911$			24.8921i			0.824712i	−0.911023	+	0.412356i	$0.864706\pi$
$912$	−5.40882	+	4.52636i	−0.179104	+	0.149883i
$913$	−1.19607	−	1.19607i	−0.0395841	−	0.0395841i
$914$	28.1299	+	0.623103i	0.930456	+	0.0206104i
$915$	19.4148	+	3.76189i	0.641832	+	0.124364i
$916$	−2.17709	+	49.1182i	−0.0719332	+	1.62291i
$917$	−7.62338	−	7.62338i	−0.251746	−	0.251746i
$918$	−27.6757	+	26.4762i	−0.913434	+	0.873844i
$919$	−51.1818			−1.68833			−0.844166	−	0.536083i	$-0.819904\pi$
$919$	−51.1818			−1.68833			−0.844166	+	0.536083i	$0.819904\pi$
$920$	−30.7376	+	17.9092i	−1.01339	+	0.590450i
$921$	−16.6193			−0.547624
$922$	−30.9220	+	29.5818i	−1.01836	+	0.974224i
$923$	8.18429	+	8.18429i	0.269389	+	0.269389i
$924$	0.268698	+	0.0119096i	0.00883952	+	0.000391799i
$925$	23.4740	−	9.99702i	0.771821	−	0.328700i
$926$	−36.2528	−	0.803031i	−1.19134	−	0.0263892i
$927$	−15.0462	−	15.0462i	−0.494182	−	0.494182i
$928$	−23.1364	−	28.9251i	−0.759488	−	0.949514i
$929$			42.8085i			1.40450i	0.711929	+	0.702251i	$0.247822\pi$
$929$			42.8085i			1.40450i	−0.711929	+	0.702251i	$0.752178\pi$
$930$	−3.40396	−	5.28899i	−0.111620	−	0.173433i
$931$	2.34107			0.0767254
$932$	31.4969	−	28.8233i	1.03172	−	0.944140i
$933$	−4.64106	+	4.64106i	−0.151941	+	0.151941i
$934$	−42.0021	−	0.930384i	−1.37435	−	0.0304431i
$935$	2.59434	+	0.502691i	0.0848440	+	0.0164398i
$936$	−11.0607	−	0.735975i	−0.361530	−	0.0240561i
$937$	15.9494	−	15.9494i	0.521043	−	0.521043i	−0.396843	−	0.917886i	$-0.629894\pi$
$937$	15.9494	−	15.9494i	0.521043	−	0.521043i	0.917886	+	0.396843i	$0.129894\pi$
$938$	11.0185	+	11.5177i	0.359766	+	0.376065i
$939$			3.38699i			0.110530i
$940$	40.5562	+	9.73960i	1.32280	+	0.317671i
$941$		−	18.0925i		−	0.589797i	−0.955529	−	0.294899i	$-0.904714\pi$
$941$		−	18.0925i		−	0.589797i	0.955529	−	0.294899i	$-0.0952859\pi$
$942$	−2.98884	+	2.85929i	−0.0973815	+	0.0931608i
$943$	−11.4609	+	11.4609i	−0.373220	+	0.373220i
$944$	−3.33553	+	37.5531i	−0.108562	+	1.22225i
$945$	−5.12083	−	7.58223i	−0.166581	−	0.246650i
$946$	−0.0169894	+	0.766985i	−0.000552373	+	0.0249368i
$947$	10.1407	−	10.1407i	0.329530	−	0.329530i	−0.522878	−	0.852408i	$-0.675142\pi$
$947$	10.1407	−	10.1407i	0.329530	−	0.329530i	0.852408	+	0.522878i	$0.175142\pi$
$948$	−14.2494	+	13.0398i	−0.462798	+	0.423513i
$949$	17.5711			0.570382
$950$	−6.14731	−	15.3701i	−0.199445	−	0.498672i
$951$			2.45980i			0.0797643i
$952$	14.0872	−	12.3295i	0.456570	−	0.399601i
$953$	−22.7189	−	22.7189i	−0.735936	−	0.735936i	0.235853	−	0.971789i	$-0.424212\pi$
$953$	−22.7189	−	22.7189i	−0.735936	−	0.735936i	−0.971789	+	0.235853i	$0.924212\pi$
$954$	0.0410599	−	1.85364i	0.00132936	−	0.0600139i
$955$	37.1138	−	25.0656i	1.20097	−	0.811105i
$956$	0.918047	−	20.7124i	0.0296918	−	0.669887i
$957$	0.622645	+	0.622645i	0.0201273	+	0.0201273i
$958$	27.2730	+	28.5086i	0.881151	+	0.921072i
$959$	−6.66018			−0.215068
$960$	−12.7709	−	4.29285i	−0.412180	−	0.138551i
$961$	24.0261			0.775037
$962$	8.03669	+	8.40080i	0.259113	+	0.270853i
$963$	21.2341	+	21.2341i	0.684260	+	0.684260i
$964$	−1.30973	+	29.5492i	−0.0421834	+	0.951716i
$965$	3.63232	−	18.7461i	0.116929	−	0.603457i
$966$	0.132679	−	5.98976i	0.00426887	−	0.192717i
$967$	−32.1119	−	32.1119i	−1.03265	−	1.03265i	−0.999449	−	0.0331991i	$-0.989430\pi$
$967$	−32.1119	−	32.1119i	−1.03265	−	1.03265i	−0.0331991	−	0.999449i	$-0.510570\pi$
$968$	−23.3442	+	20.4314i	−0.750313	+	0.656691i
$969$		−	11.6704i		−	0.374907i
$970$	17.3180	+	26.9084i	0.556049	+	0.863976i
$971$	−36.8297			−1.18192			−0.590961	−	0.806700i	$-0.701251\pi$
$971$	−36.8297			−1.18192			−0.590961	+	0.806700i	$0.701251\pi$
$972$	22.7971	−	20.8620i	0.731218	−	0.669149i
$973$	0.336537	−	0.336537i	0.0107889	−	0.0107889i
$974$	0.756538	−	34.1538i	0.0242410	−	1.09436i
$975$	−2.26601	+	5.62780i	−0.0725705	+	0.180234i
$976$	4.15556	−	46.7854i	0.133016	−	1.49756i
$977$	−14.7802	+	14.7802i	−0.472860	+	0.472860i	−0.902839	−	0.429979i	$-0.858521\pi$
$977$	−14.7802	+	14.7802i	−0.472860	+	0.472860i	0.429979	+	0.902839i	$0.358521\pi$
$978$	18.3469	−	17.5517i	0.586670	−	0.561243i
$979$		−	1.38258i		−	0.0441874i
$980$	2.33643	+	3.81328i	0.0746344	+	0.121811i
$981$			3.66328i			0.116959i
$982$	39.1474	+	40.9210i	1.24924	+	1.30584i
$983$	25.7794	−	25.7794i	0.822234	−	0.822234i	−0.164194	−	0.986428i	$-0.552502\pi$
$983$	25.7794	−	25.7794i	0.822234	−	0.822234i	0.986428	+	0.164194i	$0.0525023\pi$
$984$	−6.12500	−	0.407556i	−0.195258	−	0.0129924i
$985$	−1.54605	+	7.97899i	−0.0492611	+	0.254232i
$986$	61.2747	+	1.35729i	1.95139	+	0.0432249i
$987$	−4.96702	+	4.96702i	−0.158102	+	0.158102i
$988$	5.56467	−	5.09231i	0.177036	−	0.162008i
$989$	17.0891			0.543401
$990$	−1.34241	−	0.291096i	−0.0426645	−	0.00925163i
$991$			3.06202i			0.0972683i	0.998817	+	0.0486341i	$0.0154868\pi$
$991$			3.06202i			0.0972683i	−0.998817	+	0.0486341i	$0.984513\pi$
$992$	−11.6659	+	9.33119i	−0.370392	+	0.296266i
$993$	15.2207	+	15.2207i	0.483014	+	0.483014i
$994$	10.1579	+	0.225006i	0.322188	+	0.00713676i
$995$	19.5354	+	28.9254i	0.619314	+	0.916997i
$996$	−14.2561	−	0.631881i	−0.451722	−	0.0200219i
$997$	6.74672	+	6.74672i	0.213671	+	0.213671i	0.805825	−	0.592154i	$-0.201722\pi$
$997$	6.74672	+	6.74672i	0.213671	+	0.213671i	−0.592154	+	0.805825i	$0.701722\pi$
$998$	−5.64766	+	5.40288i	−0.178774	+	0.171025i
$999$	−20.8796			−0.660601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.10	✓	72
4.3	odd	2		1120.2.bi.a.463.16		72
5.2	odd	4	inner	280.2.w.a.267.28	yes	72
8.3	odd	2	inner	280.2.w.a.43.28	yes	72
8.5	even	2		1120.2.bi.a.463.15		72
20.7	even	4		1120.2.bi.a.687.15		72
40.27	even	4	inner	280.2.w.a.267.10	yes	72
40.37	odd	4		1120.2.bi.a.687.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.10	✓	72	1.1	even	1	trivial
280.2.w.a.43.28	yes	72	8.3	odd	2	inner
280.2.w.a.267.10	yes	72	40.27	even	4	inner
280.2.w.a.267.28	yes	72	5.2	odd	4	inner
1120.2.bi.a.463.15		72	8.5	even	2
1120.2.bi.a.463.16		72	4.3	odd	2
1120.2.bi.a.687.15		72	20.7	even	4
1120.2.bi.a.687.16		72	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.977609 - 1.02190i) q^{2} +(0.532572 + 0.532572i) q^{3} +(-0.0885601 + 1.99804i) q^{4} +(-1.25149 - 1.85304i) q^{5} +(0.0235881 - 1.06488i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.12837 - 1.86280i) q^{8} -2.43273i q^{9} +O(q^{10})\)	\(q+(-0.977609 - 1.02190i) q^{2} +(0.532572 + 0.532572i) q^{3} +(-0.0885601 + 1.99804i) q^{4} +(-1.25149 - 1.85304i) q^{5} +(0.0235881 - 1.06488i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.12837 - 1.86280i) q^{8} -2.43273i q^{9} +(-0.670153 + 3.09045i) q^{10} -0.178553 q^{11} +(-1.11126 + 1.01693i) q^{12} +(1.13916 - 1.13916i) q^{13} +(0.0313184 - 1.41387i) q^{14} +(0.320368 - 1.65339i) q^{15} +(-3.98431 - 0.353893i) q^{16} +(4.68019 - 4.68019i) q^{17} +(-2.48601 + 2.37826i) q^{18} -2.34107i q^{19} +(3.81328 - 2.33643i) q^{20} +0.753170i q^{21} +(0.174555 + 0.182463i) q^{22} +(3.97734 - 3.97734i) q^{23} +(2.12559 + 0.141436i) q^{24} +(-1.86753 + 4.63814i) q^{25} +(-2.27777 - 0.0504547i) q^{26} +(2.89332 - 2.89332i) q^{27} +(-1.47545 + 1.35020i) q^{28} -6.54779 q^{29} +(-2.00279 + 1.28898i) q^{30} +2.64081i q^{31} +(3.53346 + 4.41754i) q^{32} +(-0.0950924 - 0.0950924i) q^{33} +(-9.35808 - 0.207290i) q^{34} +(0.425359 - 2.19524i) q^{35} +(4.86070 + 0.215443i) q^{36} +(-3.60824 - 3.60824i) q^{37} +(-2.39234 + 2.28865i) q^{38} +1.21337 q^{39} +(-6.11549 - 1.61268i) q^{40} -2.88156 q^{41} +(0.769665 - 0.736306i) q^{42} +(2.14830 + 2.14830i) q^{43} +(0.0158127 - 0.356756i) q^{44} +(-4.50796 + 3.04455i) q^{45} +(-7.95273 - 0.176160i) q^{46} +(6.59482 + 6.59482i) q^{47} +(-1.93346 - 2.31041i) q^{48} +1.00000i q^{49} +(6.56543 - 2.62586i) q^{50} +4.98507 q^{51} +(2.17521 + 2.37698i) q^{52} +(-0.381073 + 0.381073i) q^{53} +(-5.78522 - 0.128148i) q^{54} +(0.223458 + 0.330866i) q^{55} +(2.82219 + 0.187788i) q^{56} +(1.24679 - 1.24679i) q^{57} +(6.40118 + 6.69119i) q^{58} -9.42525i q^{59} +(3.27516 + 0.786532i) q^{60} +11.7424i q^{61} +(2.69864 - 2.58168i) q^{62} +(1.72020 - 1.72020i) q^{63} +(1.05994 - 7.92947i) q^{64} +(-3.53658 - 0.685264i) q^{65} +(-0.00421173 + 0.190138i) q^{66} +(-7.96968 + 7.96968i) q^{67} +(8.93671 + 9.76567i) q^{68} +4.23644 q^{69} +(-2.65915 + 1.71141i) q^{70} +7.18446i q^{71} +(-4.53170 - 5.17777i) q^{72} +(7.71228 + 7.71228i) q^{73} +(-0.159812 + 7.21471i) q^{74} +(-3.46474 + 1.47555i) q^{75} +(4.67754 + 0.207325i) q^{76} +(-0.126256 - 0.126256i) q^{77} +(-1.18621 - 1.23995i) q^{78} +12.8227 q^{79} +(4.33056 + 7.82600i) q^{80} -4.21640 q^{81} +(2.81704 + 2.94466i) q^{82} +(6.69868 + 6.69868i) q^{83} +(-1.50486 - 0.0667009i) q^{84} +(-14.5298 - 2.81536i) q^{85} +(0.0951504 - 4.29556i) q^{86} +(-3.48717 - 3.48717i) q^{87} +(-0.380028 + 0.332609i) q^{88} +7.74324i q^{89} +(7.51825 + 1.63030i) q^{90} +1.61102 q^{91} +(7.59465 + 8.29912i) q^{92} +(-1.40642 + 1.40642i) q^{93} +(0.292091 - 13.1864i) q^{94} +(-4.33809 + 2.92983i) q^{95} +(-0.470837 + 4.23448i) q^{96} +(7.15533 - 7.15533i) q^{97} +(1.02190 - 0.977609i) q^{98} +0.434372i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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