LMFDB - Embedded newform 80.3.k.a.59.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(19,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("80.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.k (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:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.8
Character	$\chi$	$=$	80.59
Dual form			80.3.k.a.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.860120 + 1.80560i) q^{2} +(1.09715 - 1.09715i) q^{3} +(-2.52039 - 3.10607i) q^{4} +(-2.32699 + 4.42551i) q^{5} +(1.03734 + 2.92470i) q^{6} +12.9438i q^{7} +(7.77615 - 1.87923i) q^{8} +6.59251i q^{9} +O(q^{10})$	\(q+(-0.860120 + 1.80560i) q^{2} +(1.09715 - 1.09715i) q^{3} +(-2.52039 - 3.10607i) q^{4} +(-2.32699 + 4.42551i) q^{5} +(1.03734 + 2.92470i) q^{6} +12.9438i q^{7} +(7.77615 - 1.87923i) q^{8} +6.59251i q^{9} +(-5.98921 - 8.00808i) q^{10} +(4.18265 - 4.18265i) q^{11} +(-6.17308 - 0.642577i) q^{12} +(-3.42187 - 3.42187i) q^{13} +(-23.3714 - 11.1332i) q^{14} +(2.30239 + 7.40853i) q^{15} +(-3.29528 + 15.6570i) q^{16} -22.5343i q^{17} +(-11.9034 - 5.67035i) q^{18} +(8.96024 + 8.96024i) q^{19} +(19.6108 - 3.92621i) q^{20} +(14.2014 + 14.2014i) q^{21} +(3.95462 + 11.1498i) q^{22} -4.85642i q^{23} +(6.46983 - 10.5934i) q^{24} +(-14.1702 - 20.5962i) q^{25} +(9.12175 - 3.23532i) q^{26} +(17.1074 + 17.1074i) q^{27} +(40.2044 - 32.6235i) q^{28} +(29.3539 - 29.3539i) q^{29} +(-15.3572 - 2.21501i) q^{30} +43.7564i q^{31} +(-25.4359 - 19.4168i) q^{32} -9.17802i q^{33} +(40.6879 + 19.3822i) q^{34} +(-57.2830 - 30.1202i) q^{35} +(20.4768 - 16.6157i) q^{36} +(20.1886 - 20.1886i) q^{37} +(-23.8855 + 8.47174i) q^{38} -7.50864 q^{39} +(-9.77849 + 38.7864i) q^{40} +18.6704i q^{41} +(-37.8569 + 13.4271i) q^{42} +(14.4584 + 14.4584i) q^{43} +(-23.5335 - 2.44968i) q^{44} +(-29.1752 - 15.3407i) q^{45} +(8.76876 + 4.17711i) q^{46} +34.6892 q^{47} +(13.5627 + 20.7935i) q^{48} -118.543 q^{49} +(49.3767 - 7.87055i) q^{50} +(-24.7236 - 24.7236i) q^{51} +(-2.00411 + 19.2530i) q^{52} +(-36.7840 + 36.7840i) q^{53} +(-45.6035 + 16.1747i) q^{54} +(8.77736 + 28.2433i) q^{55} +(24.3244 + 100.653i) q^{56} +19.6615 q^{57} +(27.7535 + 78.2492i) q^{58} +(44.2454 - 44.2454i) q^{59} +(17.2084 - 25.8238i) q^{60} +(38.7445 - 38.7445i) q^{61} +(-79.0066 - 37.6357i) q^{62} -85.3324 q^{63} +(56.9370 - 29.2263i) q^{64} +(23.1062 - 7.18085i) q^{65} +(16.5718 + 7.89419i) q^{66} +(64.1047 - 64.1047i) q^{67} +(-69.9930 + 56.7952i) q^{68} +(-5.32824 - 5.32824i) q^{69} +(103.655 - 77.5233i) q^{70} -29.8745 q^{71} +(12.3888 + 51.2643i) q^{72} +12.9519 q^{73} +(19.0879 + 53.8171i) q^{74} +(-38.1441 - 7.05031i) q^{75} +(5.24781 - 50.4144i) q^{76} +(54.1395 + 54.1395i) q^{77} +(6.45833 - 13.5576i) q^{78} +59.1371i q^{79} +(-61.6220 - 51.0170i) q^{80} -21.7938 q^{81} +(-33.7113 - 16.0588i) q^{82} +(-15.4791 + 15.4791i) q^{83} +(8.31741 - 79.9034i) q^{84} +(99.7257 + 52.4371i) q^{85} +(-38.5421 + 13.6702i) q^{86} -64.4114i q^{87} +(24.6648 - 40.3851i) q^{88} -43.3557i q^{89} +(52.7934 - 39.4839i) q^{90} +(44.2922 - 44.2922i) q^{91} +(-15.0844 + 12.2401i) q^{92} +(48.0075 + 48.0075i) q^{93} +(-29.8369 + 62.6349i) q^{94} +(-60.5040 + 18.8032i) q^{95} +(-49.2104 + 6.60385i) q^{96} +101.265i q^{97} +(101.961 - 214.041i) q^{98} +(27.5742 + 27.5742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.860120	+	1.80560i	−0.430060	+	0.902800i
$2$	−0.860120	+	1.80560i	−0.430060	+	0.902800i
$3$	1.09715	−	1.09715i	0.365718	−	0.365718i	−0.500195	−	0.865913i	$-0.666738\pi$
$3$	1.09715	−	1.09715i	0.365718	−	0.365718i	0.865913	+	0.500195i	$0.166738\pi$
$4$	−2.52039	−	3.10607i	−0.630097	−	0.776516i
$5$	−2.32699	+	4.42551i	−0.465398	+	0.885101i
$5$	−2.32699	+	4.42551i	−0.465398	+	0.885101i
$6$	1.03734	+	2.92470i	0.172890	+	0.487451i
$7$			12.9438i			1.84912i	0.381037	+	0.924560i	$0.375567\pi$
$7$			12.9438i			1.84912i	−0.381037	+	0.924560i	$0.624433\pi$
$8$	7.77615	−	1.87923i	0.972019	−	0.234903i
$9$			6.59251i			0.732501i
$10$	−5.98921	−	8.00808i	−0.598921	−	0.800808i
$11$	4.18265	−	4.18265i	0.380241	−	0.380241i	−0.490948	−	0.871189i	$-0.663350\pi$
$11$	4.18265	−	4.18265i	0.380241	−	0.380241i	0.871189	+	0.490948i	$0.163350\pi$
$12$	−6.17308	−	0.642577i	−0.514424	−	0.0535481i
$13$	−3.42187	−	3.42187i	−0.263221	−	0.263221i	0.563140	−	0.826361i	$-0.309593\pi$
$13$	−3.42187	−	3.42187i	−0.263221	−	0.263221i	−0.826361	+	0.563140i	$0.809593\pi$
$14$	−23.3714	−	11.1332i	−1.66939	−	0.795232i
$15$	2.30239	+	7.40853i	0.153493	+	0.493902i
$16$	−3.29528	+	15.6570i	−0.205955	+	0.978561i
$17$		−	22.5343i		−	1.32555i	−0.748820	−	0.662773i	$-0.769379\pi$
$17$		−	22.5343i		−	1.32555i	0.748820	−	0.662773i	$-0.230621\pi$
$18$	−11.9034	−	5.67035i	−0.661302	−	0.315019i
$19$	8.96024	+	8.96024i	0.471592	+	0.471592i	0.902429	−	0.430838i	$-0.141782\pi$
$19$	8.96024	+	8.96024i	0.471592	+	0.471592i	−0.430838	+	0.902429i	$0.641782\pi$
$20$	19.6108	−	3.92621i	0.980542	−	0.196311i
$21$	14.2014	+	14.2014i	0.676256	+	0.676256i
$22$	3.95462	+	11.1498i	0.179755	+	0.506808i
$23$		−	4.85642i		−	0.211149i	−0.994411	−	0.105574i	$-0.966332\pi$
$23$		−	4.85642i		−	0.211149i	0.994411	−	0.105574i	$-0.0336681\pi$
$24$	6.46983	−	10.5934i	0.269576	−	0.441393i
$25$	−14.1702	−	20.5962i	−0.566809	−	0.823849i
$26$	9.12175	−	3.23532i	0.350837	−	0.124435i
$27$	17.1074	+	17.1074i	0.633606	+	0.633606i
$28$	40.2044	−	32.6235i	1.43587	−	1.16512i
$29$	29.3539	−	29.3539i	1.01220	−	1.01220i	0.0122781	−	0.999925i	$-0.496092\pi$
$29$	29.3539	−	29.3539i	1.01220	−	1.01220i	0.999925	−	0.0122781i	$-0.00390833\pi$
$30$	−15.3572	−	2.21501i	−0.511906	−	0.0738338i
$31$			43.7564i			1.41150i	0.708463	+	0.705748i	$0.249389\pi$
$31$			43.7564i			1.41150i	−0.708463	+	0.705748i	$0.750611\pi$
$32$	−25.4359	−	19.4168i	−0.794873	−	0.606776i
$33$		−	9.17802i		−	0.278122i
$34$	40.6879	+	19.3822i	1.19670	+	0.570064i
$35$	−57.2830	−	30.1202i	−1.63666	−	0.860577i
$36$	20.4768	−	16.6157i	0.568799	−	0.461547i
$37$	20.1886	−	20.1886i	0.545637	−	0.545637i	−0.379539	−	0.925176i	$-0.623917\pi$
$37$	20.1886	−	20.1886i	0.545637	−	0.545637i	0.925176	+	0.379539i	$0.123917\pi$
$38$	−23.8855	+	8.47174i	−0.628566	+	0.222941i
$39$	−7.50864			−0.192529
$40$	−9.77849	+	38.7864i	−0.244462	+	0.969659i
$41$			18.6704i			0.455376i	0.973734	+	0.227688i	$0.0731167\pi$
$41$			18.6704i			0.455376i	−0.973734	+	0.227688i	$0.926883\pi$
$42$	−37.8569	+	13.4271i	−0.901355	+	0.319694i
$43$	14.4584	+	14.4584i	0.336242	+	0.336242i	0.854951	−	0.518709i	$-0.173587\pi$
$43$	14.4584	+	14.4584i	0.336242	+	0.336242i	−0.518709	+	0.854951i	$0.673587\pi$
$44$	−23.5335	−	2.44968i	−0.534852	−	0.0556746i
$45$	−29.1752	−	15.3407i	−0.648338	−	0.340905i
$46$	8.76876	+	4.17711i	0.190625	+	0.0908067i
$47$	34.6892			0.738069			0.369034	−	0.929416i	$-0.379688\pi$
$47$	34.6892			0.738069			0.369034	+	0.929416i	$0.379688\pi$
$48$	13.5627	+	20.7935i	0.282556	+	0.433199i
$49$	−118.543			−2.41924
$50$	49.3767	−	7.87055i	0.987533	−	0.157411i
$51$	−24.7236	−	24.7236i	−0.484776	−	0.484776i
$52$	−2.00411	+	19.2530i	−0.0385406	+	0.370250i
$53$	−36.7840	+	36.7840i	−0.694039	+	0.694039i	−0.963118	−	0.269079i	$-0.913281\pi$
$53$	−36.7840	+	36.7840i	−0.694039	+	0.694039i	0.269079	+	0.963118i	$0.413281\pi$
$54$	−45.6035	+	16.1747i	−0.844509	+	0.299531i
$55$	8.77736	+	28.2433i	0.159588	+	0.513515i
$56$	24.3244	+	100.653i	0.434365	+	1.79738i
$57$	19.6615			0.344939
$58$	27.7535	+	78.2492i	0.478509	+	1.34912i
$59$	44.2454	−	44.2454i	0.749923	−	0.749923i	−0.224542	−	0.974464i	$-0.572089\pi$
$59$	44.2454	−	44.2454i	0.749923	−	0.749923i	0.974464	+	0.224542i	$0.0720885\pi$
$60$	17.2084	−	25.8238i	0.286807	−	0.430396i
$61$	38.7445	−	38.7445i	0.635156	−	0.635156i	−0.314200	−	0.949357i	$-0.601736\pi$
$61$	38.7445	−	38.7445i	0.635156	−	0.635156i	0.949357	+	0.314200i	$0.101736\pi$
$62$	−79.0066	−	37.6357i	−1.27430	−	0.607028i
$63$	−85.3324			−1.35448
$64$	56.9370	−	29.2263i	0.889641	−	0.456661i
$65$	23.1062	−	7.18085i	0.355480	−	0.110475i
$66$	16.5718	+	7.89419i	0.251088	+	0.119609i
$67$	64.1047	−	64.1047i	0.956787	−	0.956787i	−0.0423173	−	0.999104i	$-0.513474\pi$
$67$	64.1047	−	64.1047i	0.956787	−	0.956787i	0.999104	+	0.0423173i	$0.0134740\pi$
$68$	−69.9930	+	56.7952i	−1.02931	+	0.835223i
$69$	−5.32824	−	5.32824i	−0.0772209	−	0.0772209i
$70$	103.655	−	77.5233i	1.48079	−	1.10748i
$71$	−29.8745			−0.420768			−0.210384	−	0.977619i	$-0.567471\pi$
$71$	−29.8745			−0.420768			−0.210384	+	0.977619i	$0.567471\pi$
$72$	12.3888	+	51.2643i	0.172067	+	0.712005i
$73$	12.9519			0.177423			0.0887113	−	0.996057i	$-0.471725\pi$
$73$	12.9519			0.177423			0.0887113	+	0.996057i	$0.471725\pi$
$74$	19.0879	+	53.8171i	0.257945	+	0.727258i
$75$	−38.1441	−	7.05031i	−0.508588	−	0.0940042i
$76$	5.24781	−	50.4144i	0.0690501	−	0.663347i
$77$	54.1395	+	54.1395i	0.703111	+	0.703111i
$78$	6.45833	−	13.5576i	0.0827990	−	0.173815i
$79$			59.1371i			0.748571i	0.927313	+	0.374286i	$0.122112\pi$
$79$			59.1371i			0.748571i	−0.927313	+	0.374286i	$0.877888\pi$
$80$	−61.6220	−	51.0170i	−0.770275	−	0.637712i
$81$	−21.7938			−0.269059
$82$	−33.7113	−	16.0588i	−0.411114	−	0.195839i
$83$	−15.4791	+	15.4791i	−0.186495	+	0.186495i	−0.794179	−	0.607684i	$-0.792099\pi$
$83$	−15.4791	+	15.4791i	−0.186495	+	0.186495i	0.607684	+	0.794179i	$0.292099\pi$
$84$	8.31741	−	79.9034i	0.0990168	−	0.951231i
$85$	99.7257	+	52.4371i	1.17324	+	0.616907i
$86$	−38.5421	+	13.6702i	−0.448164	+	0.158955i
$87$		−	64.4114i		−	0.740361i
$88$	24.6648	−	40.3851i	0.280281	−	0.458921i
$89$		−	43.3557i		−	0.487143i	−0.969883	−	0.243571i	$-0.921681\pi$
$89$		−	43.3557i		−	0.487143i	0.969883	−	0.243571i	$-0.0783190\pi$
$90$	52.7934	−	39.4839i	0.586593	−	0.438710i
$91$	44.2922	−	44.2922i	0.486727	−	0.486727i
$92$	−15.0844	+	12.2401i	−0.163961	+	0.133044i
$93$	48.0075	+	48.0075i	0.516209	+	0.516209i
$94$	−29.8369	+	62.6349i	−0.317414	+	0.666329i
$95$	−60.5040	+	18.8032i	−0.636885	+	0.197929i
$96$	−49.2104	+	6.60385i	−0.512608	+	0.0687901i
$97$			101.265i			1.04397i	0.852955	+	0.521985i	$0.174808\pi$
$97$			101.265i			1.04397i	−0.852955	+	0.521985i	$0.825192\pi$
$98$	101.961	−	214.041i	1.04042	−	2.18409i
$99$	27.5742	+	27.5742i	0.278527	+	0.278527i
$100$	−28.2588	+	95.9241i	−0.282588	+	0.959241i
$101$	4.60089	+	4.60089i	0.0455534	+	0.0455534i	0.729517	−	0.683963i	$-0.239745\pi$
$101$	4.60089	+	4.60089i	0.0455534	+	0.0455534i	−0.683963	+	0.729517i	$0.739745\pi$
$102$	65.9062	−	23.3757i	0.646139	−	0.229173i
$103$		−	88.9427i		−	0.863522i	−0.901988	−	0.431761i	$-0.857892\pi$
$103$		−	88.9427i		−	0.863522i	0.901988	−	0.431761i	$-0.142108\pi$
$104$	−33.0395	−	20.1785i	−0.317687	−	0.194024i
$105$	−95.8947	+	29.8018i	−0.913283	+	0.283827i
$106$	−34.7786	−	98.0560i	−0.328100	−	0.925056i
$107$	−34.8499	−	34.8499i	−0.325700	−	0.325700i	0.525249	−	0.850949i	$-0.323972\pi$
$107$	−34.8499	−	34.8499i	−0.325700	−	0.325700i	−0.850949	+	0.525249i	$0.823972\pi$
$108$	10.0194	−	96.2538i	0.0927721	−	0.891239i
$109$	−101.694	+	101.694i	−0.932977	+	0.932977i	−0.997891	−	0.0649138i	$-0.979323\pi$
$109$	−101.694	+	101.694i	−0.932977	+	0.932977i	0.0649138	+	0.997891i	$0.479323\pi$
$110$	−58.5458	−	8.44424i	−0.532234	−	0.0767658i
$111$		−	44.2999i		−	0.399098i
$112$	−202.661	−	42.6536i	−1.80948	−	0.380836i
$113$		−	76.3759i		−	0.675893i	−0.941165	−	0.337947i	$-0.890268\pi$
$113$		−	76.3759i		−	0.675893i	0.941165	−	0.337947i	$-0.109732\pi$
$114$	−16.9113	+	35.5009i	−0.148344	+	0.311411i
$115$	21.4921	+	11.3009i	0.186888	+	0.0982683i
$116$	−165.158	−	17.1919i	−1.42378	−	0.148206i
$117$	22.5587	−	22.5587i	0.192810	−	0.192810i
$118$	41.8332	+	117.946i	0.354519	+	0.999542i
$119$	291.680			2.45109
$120$	31.8261	+	53.2831i	0.265217	+	0.444026i
$121$			86.0109i			0.710834i
$122$	36.6322	+	103.282i	0.300264	+	0.846575i
$123$	20.4843	+	20.4843i	0.166539	+	0.166539i
$124$	135.910	−	110.283i	1.09605	−	0.889380i
$125$	124.123	−	14.7832i	0.992982	−	0.118265i
$126$	73.3960	−	154.076i	0.582508	−	1.22283i
$127$	59.5041			0.468536			0.234268	−	0.972172i	$-0.424731\pi$
$127$	59.5041			0.468536			0.234268	+	0.972172i	$0.424731\pi$
$128$	3.79843	+	127.944i	0.0296752	+	0.999560i
$129$	31.7262			0.245940
$130$	−6.90833	+	47.8969i	−0.0531410	+	0.368438i
$131$	9.05039	+	9.05039i	0.0690870	+	0.0690870i	0.740806	−	0.671719i	$-0.234444\pi$
$131$	9.05039	+	9.05039i	0.0690870	+	0.0690870i	−0.671719	+	0.740806i	$0.734444\pi$
$132$	−28.5075	+	23.1322i	−0.215966	+	0.175244i
$133$	−115.980	+	115.980i	−0.872030	+	0.872030i
$134$	60.6098	+	170.885i	0.452312	+	1.27526i
$135$	−115.518	+	35.9001i	−0.855685	+	0.265927i
$136$	−42.3471	−	175.230i	−0.311376	−	1.28846i
$137$	113.494			0.828421			0.414211	−	0.910181i	$-0.364058\pi$
$137$	113.494			0.828421			0.414211	+	0.910181i	$0.364058\pi$
$138$	14.2036	−	5.03775i	0.102925	−	0.0365055i
$139$	−24.5515	+	24.5515i	−0.176629	+	0.176629i	−0.789885	−	0.613255i	$-0.789860\pi$
$139$	−24.5515	+	24.5515i	−0.176629	+	0.176629i	0.613255	+	0.789885i	$0.289860\pi$
$140$	50.8202	+	253.839i	0.363002	+	1.81314i
$141$	38.0594	−	38.0594i	0.269925	−	0.269925i
$142$	25.6957	−	53.9414i	0.180955	−	0.379869i
$143$	−28.6250			−0.200175
$144$	−103.219	−	21.7242i	−0.716797	−	0.150862i
$145$	61.5996	+	198.212i	0.424825	+	1.36698i
$146$	−11.1401	+	23.3859i	−0.0763024	+	0.160177i
$147$	−130.060	+	130.060i	−0.884760	+	0.884760i
$148$	−113.590	−	11.8240i	−0.767500	−	0.0798917i
$149$	−142.296	−	142.296i	−0.955009	−	0.955009i	0.0440216	−	0.999031i	$-0.485983\pi$
$149$	−142.296	−	142.296i	−0.955009	−	0.955009i	−0.999031	+	0.0440216i	$0.985983\pi$
$150$	45.5386	−	62.8090i	0.303590	−	0.418726i
$151$	−227.980			−1.50980			−0.754902	−	0.655838i	$-0.772316\pi$
$151$	−227.980			−1.50980			−0.754902	+	0.655838i	$0.772316\pi$
$152$	86.5145	+	52.8379i	0.569175	+	0.347617i
$153$	148.558			0.970964
$154$	−144.321	+	51.1879i	−0.937148	+	0.332389i
$155$	−193.644	−	101.821i	−1.24932	−	0.656908i
$156$	18.9247	+	23.3223i	0.121312	+	0.149502i
$157$	−112.950	−	112.950i	−0.719430	−	0.719430i	0.249059	−	0.968488i	$-0.419879\pi$
$157$	−112.950	−	112.950i	−0.719430	−	0.719430i	−0.968488	+	0.249059i	$0.919879\pi$
$158$	−106.778	−	50.8650i	−0.675811	−	0.321930i
$159$			80.7155i			0.507644i
$160$	145.119	−	67.3840i	0.906991	−	0.421150i
$161$	62.8608			0.390440
$162$	18.7452	−	39.3508i	0.115711	−	0.242906i
$163$	74.5593	−	74.5593i	0.457419	−	0.457419i	−0.440389	−	0.897807i	$-0.645159\pi$
$163$	74.5593	−	74.5593i	0.457419	−	0.457419i	0.897807	+	0.440389i	$0.145159\pi$
$164$	57.9916	−	47.0567i	0.353607	−	0.286931i
$165$	40.6174	+	21.3572i	0.246166	+	0.129437i
$166$	−14.6352	−	41.2629i	−0.0881637	−	0.248572i
$167$			205.674i			1.23158i	0.787911	+	0.615789i	$0.211163\pi$
$167$			205.674i			1.23158i	−0.787911	+	0.615789i	$0.788837\pi$
$168$	137.120	+	83.7444i	0.816188	+	0.498478i
$169$		−	145.582i		−	0.861429i
$170$	−180.457	+	134.963i	−1.06151	+	0.793898i
$171$	−59.0705	+	59.0705i	−0.345441	+	0.345441i
$172$	8.46796	−	81.3497i	0.0492323	−	0.472963i
$173$	−109.655	−	109.655i	−0.633844	−	0.633844i	0.315186	−	0.949030i	$-0.397933\pi$
$173$	−109.655	−	109.655i	−0.633844	−	0.633844i	−0.949030	+	0.315186i	$0.897933\pi$
$174$	116.301	+	55.4015i	0.668398	+	0.318400i
$175$	266.594	−	183.417i	1.52340	−	1.04810i
$176$	51.7047	+	79.2707i	0.293776	+	0.450402i
$177$		−	97.0881i		−	0.548520i
$178$	78.2831	+	37.2911i	0.439793	+	0.209501i
$179$	43.6475	+	43.6475i	0.243841	+	0.243841i	0.818437	−	0.574596i	$-0.194841\pi$
$179$	43.6475	+	43.6475i	0.243841	+	0.243841i	−0.574596	+	0.818437i	$0.694841\pi$
$180$	25.8836	+	129.285i	0.143798	+	0.718248i
$181$	−117.110	−	117.110i	−0.647016	−	0.647016i	0.305254	−	0.952271i	$-0.401258\pi$
$181$	−117.110	−	117.110i	−0.647016	−	0.647016i	−0.952271	+	0.305254i	$0.901258\pi$
$182$	41.8774	+	118.070i	0.230096	+	0.648739i
$183$		−	85.0174i		−	0.464576i
$184$	−9.12633	−	37.7643i	−0.0495996	−	0.205241i
$185$	42.3660	+	136.323i	0.229006	+	0.736882i
$186$	−127.975	+	45.3902i	−0.688035	+	0.244033i
$187$	−94.2531	−	94.2531i	−0.504027	−	0.504027i
$188$	−87.4303	−	107.747i	−0.465055	−	0.573122i
$189$	−221.435	+	221.435i	−1.17161	+	1.17161i
$190$	18.0896	−	125.419i	0.0952084	−	0.660101i
$191$		−	309.015i		−	1.61788i	−0.587892	−	0.808939i	$-0.700042\pi$
$191$		−	309.015i		−	1.61788i	0.587892	−	0.808939i	$-0.299958\pi$
$192$	30.4029	−	94.5344i	0.158348	−	0.492367i
$193$		−	209.788i		−	1.08699i	−0.839413	−	0.543493i	$-0.817101\pi$
$193$		−	209.788i		−	1.08699i	0.839413	−	0.543493i	$-0.182899\pi$
$194$	−182.844	−	87.1001i	−0.942497	−	0.448970i
$195$	17.4725	−	33.2295i	0.0896027	−	0.170408i
$196$	298.774	+	368.202i	1.52436	+	1.87858i
$197$	141.335	−	141.335i	0.717437	−	0.717437i	−0.250643	−	0.968080i	$-0.580642\pi$
$197$	141.335	−	141.335i	0.717437	−	0.717437i	0.968080	+	0.250643i	$0.0806420\pi$
$198$	−73.5050	+	26.0708i	−0.371237	+	0.131671i
$199$	33.2426			0.167048			0.0835240	−	0.996506i	$-0.473382\pi$
$199$	33.2426			0.167048			0.0835240	+	0.996506i	$0.473382\pi$
$200$	−148.895	−	133.530i	−0.744474	−	0.667651i
$201$		−	140.665i		−	0.699828i
$202$	−12.2647	+	4.35006i	−0.0607163	+	0.0215349i
$203$	379.952	+	379.952i	1.87168	+	1.87168i
$204$	−14.4800	+	139.106i	−0.0709805	+	0.681893i
$205$	−82.6261	−	43.4459i	−0.403054	−	0.211931i
$206$	160.595	+	76.5014i	0.779588	+	0.371366i
$207$	32.0160			0.154667
$208$	64.8522	−	42.3002i	0.311790	−	0.203366i
$209$	74.9551			0.358637
$210$	28.6708	−	198.781i	0.136528	−	0.946575i
$211$	41.4510	+	41.4510i	0.196450	+	0.196450i	0.798476	−	0.602026i	$-0.205640\pi$
$211$	41.4510	+	41.4510i	0.196450	+	0.196450i	−0.602026	+	0.798476i	$0.705640\pi$
$212$	206.964	+	21.5436i	0.976244	+	0.101621i
$213$	−32.7769	+	32.7769i	−0.153882	+	0.153882i
$214$	92.9001	−	32.9499i	0.434113	−	0.153972i
$215$	−97.6305	+	30.3412i	−0.454095	+	0.141122i
$216$	165.178	+	100.881i	0.764714	+	0.467041i
$217$	−566.376			−2.61003
$218$	−96.1502	−	271.089i	−0.441056	−	1.24353i
$219$	14.2102	−	14.2102i	0.0648866	−	0.0648866i
$220$	65.6033	−	98.4472i	0.298197	−	0.447487i
$221$	−77.1095	+	77.1095i	−0.348912	+	0.348912i
$222$	79.9879	+	38.1032i	0.360306	+	0.171636i
$223$	−152.332			−0.683104			−0.341552	−	0.939863i	$-0.610953\pi$
$223$	−152.332			−0.683104			−0.341552	+	0.939863i	$0.610953\pi$
$224$	251.328	−	329.238i	1.12200	−	1.46981i
$225$	135.781	−	93.4173i	0.603470	−	0.415188i
$226$	137.904	+	65.6924i	0.610197	+	0.290675i
$227$	42.8192	−	42.8192i	0.188631	−	0.188631i	−0.606473	−	0.795104i	$-0.707416\pi$
$227$	42.8192	−	42.8192i	0.188631	−	0.188631i	0.795104	+	0.606473i	$0.207416\pi$
$228$	−49.5547	−	61.0700i	−0.217345	−	0.267851i
$229$	−26.1464	−	26.1464i	−0.114176	−	0.114176i	0.647710	−	0.761887i	$-0.275727\pi$
$229$	−26.1464	−	26.1464i	−0.114176	−	0.114176i	−0.761887	+	0.647710i	$0.775727\pi$
$230$	−38.8907	+	29.0861i	−0.169090	+	0.126461i
$231$	118.799			0.514280
$232$	173.098	−	283.423i	0.746110	−	1.22165i
$233$	52.0568			0.223420			0.111710	−	0.993741i	$-0.464367\pi$
$233$	52.0568			0.223420			0.111710	+	0.993741i	$0.464367\pi$
$234$	21.3288	+	60.1352i	0.0911489	+	0.256988i
$235$	−80.7215	+	153.517i	−0.343496	+	0.653266i
$236$	−248.945	−	25.9135i	−1.05485	−	0.109803i
$237$	64.8825	+	64.8825i	0.273766	+	0.273766i
$238$	−250.880	+	526.658i	−1.05412	+	2.21285i
$239$		−	235.621i		−	0.985863i	−0.870068	−	0.492932i	$-0.835925\pi$
$239$		−	235.621i		−	0.985863i	0.870068	−	0.492932i	$-0.164075\pi$
$240$	−123.582	+	11.6353i	−0.514926	+	0.0484806i
$241$	357.273			1.48246			0.741231	−	0.671250i	$-0.234242\pi$
$241$	357.273			1.48246			0.741231	+	0.671250i	$0.234242\pi$
$242$	−155.301	−	73.9797i	−0.641741	−	0.305701i
$243$	−177.877	+	177.877i	−0.732006	+	0.732006i
$244$	−217.994	−	22.6918i	−0.893420	−	0.0929991i
$245$	275.848	−	524.612i	1.12591	−	2.14128i
$246$	−54.6055	+	19.3675i	−0.221974	+	0.0787299i
$247$		−	61.3216i		−	0.248266i
$248$	82.2282	+	340.256i	0.331566	+	1.37200i
$249$			33.9659i			0.136409i
$250$	−80.0679	+	236.831i	−0.320272	+	0.947326i
$251$	−246.315	+	246.315i	−0.981336	+	0.981336i	−0.999829	−	0.0184927i	$-0.994113\pi$
$251$	−246.315	+	246.315i	−0.981336	+	0.981336i	0.0184927	+	0.999829i	$0.494113\pi$
$252$	215.071	+	265.048i	0.853455	+	1.05178i
$253$	−20.3127	−	20.3127i	−0.0802874	−	0.0802874i
$254$	−51.1806	+	107.441i	−0.201498	+	0.422994i
$255$	166.946	−	51.8828i	0.654690	−	0.203462i
$256$	−234.282	−	103.188i	−0.915165	−	0.403080i
$257$			328.148i			1.27684i	0.769687	+	0.638421i	$0.220412\pi$
$257$			328.148i			1.27684i	−0.769687	+	0.638421i	$0.779588\pi$
$258$	−27.2883	+	57.2849i	−0.105769	+	0.222034i
$259$	261.317	+	261.317i	1.00895	+	1.00895i
$260$	−80.5408	−	53.6708i	−0.309772	−	0.206426i
$261$	193.516	+	193.516i	0.741439	+	0.741439i
$262$	−24.1258	+	8.55697i	−0.0920832	+	0.0326602i
$263$			63.7413i			0.242362i	0.992630	+	0.121181i	$0.0386682\pi$
$263$			63.7413i			0.242362i	−0.992630	+	0.121181i	$0.961332\pi$
$264$	−17.2476	−	71.3696i	−0.0653318	−	0.270339i
$265$	−77.1919	−	248.384i	−0.291290	−	0.937299i
$266$	−109.657	−	309.170i	−0.412244	−	1.16229i
$267$	−47.5679	−	47.5679i	−0.178157	−	0.178157i
$268$	−360.682	−	37.5446i	−1.34583	−	0.140092i
$269$	285.461	−	285.461i	1.06119	−	1.06119i	0.0631922	−	0.998001i	$-0.479872\pi$
$269$	285.461	−	285.461i	1.06119	−	1.06119i	0.998001	−	0.0631922i	$-0.0201281\pi$
$270$	34.5376	−	239.457i	0.127917	−	0.886877i
$271$			420.238i			1.55069i	0.631535	+	0.775347i	$0.282425\pi$
$271$			420.238i			1.55069i	−0.631535	+	0.775347i	$0.717575\pi$
$272$	352.819	+	74.2569i	1.29713	+	0.273003i
$273$		−	97.1906i		−	0.356009i
$274$	−97.6181	+	204.924i	−0.356271	+	0.747899i
$275$	−145.416	−	26.8777i	−0.528785	−	0.0977372i
$276$	−3.12063	+	29.9791i	−0.0113066	+	0.108620i
$277$	−289.874	+	289.874i	−1.04648	+	1.04648i	−0.0476123	+	0.998866i	$0.515161\pi$
$277$	−289.874	+	289.874i	−1.04648	+	1.04648i	−0.998866	+	0.0476123i	$0.984839\pi$
$278$	−23.2130	−	65.4474i	−0.0834999	−	0.235422i
$279$	−288.464			−1.03392
$280$	−502.044	−	126.571i	−1.79301	−	0.452040i
$281$			173.850i			0.618683i	0.950951	+	0.309341i	$0.100109\pi$
$281$			173.850i			0.618683i	−0.950951	+	0.309341i	$0.899891\pi$
$282$	35.9844	+	101.456i	0.127604	+	0.359772i
$283$	41.5240	+	41.5240i	0.146728	+	0.146728i	0.776655	−	0.629927i	$-0.216915\pi$
$283$	41.5240	+	41.5240i	0.146728	+	0.146728i	−0.629927	+	0.776655i	$0.716915\pi$
$284$	75.2954	+	92.7922i	0.265125	+	0.326733i
$285$	−45.7522	+	87.0122i	−0.160534	+	0.305306i
$286$	24.6209	−	51.6853i	0.0860871	−	0.180718i
$287$	−241.667			−0.842045
$288$	128.006	−	167.687i	0.444464	−	0.582245i
$289$	−218.795			−0.757075
$290$	−410.875	−	59.2618i	−1.41681	−	0.204351i
$291$	111.103	+	111.103i	0.381798	+	0.381798i
$292$	−32.6437	−	40.2293i	−0.111794	−	0.137772i
$293$	−189.424	+	189.424i	−0.646499	+	0.646499i	−0.952145	−	0.305647i	$-0.901127\pi$
$293$	−189.424	+	189.424i	−0.646499	+	0.646499i	0.305647	+	0.952145i	$0.401127\pi$
$294$	−122.969	−	346.703i	−0.418262	−	1.17926i
$295$	92.8498	+	298.767i	0.314745	+	1.01277i
$296$	119.050	−	194.928i	0.402197	−	0.658541i
$297$	143.108			0.481846
$298$	379.322	−	134.539i	1.27289	−	0.451472i
$299$	−16.6181	+	16.6181i	−0.0555788	+	0.0555788i
$300$	74.2393	+	136.248i	0.247464	+	0.454159i
$301$	−187.147	+	187.147i	−0.621752	+	0.621752i
$302$	196.090	−	411.642i	0.649306	−	1.36305i
$303$	10.0958			0.0333194
$304$	−169.817	+	110.764i	−0.558608	+	0.364355i
$305$	81.3060	+	261.622i	0.266577	+	0.857778i
$306$	−127.777	+	268.236i	−0.417573	+	0.876587i
$307$	−54.3936	+	54.3936i	−0.177178	+	0.177178i	−0.790124	−	0.612947i	$-0.789984\pi$
$307$	−54.3936	+	54.3936i	−0.177178	+	0.177178i	0.612947	+	0.790124i	$0.289984\pi$
$308$	31.7083	−	304.614i	0.102949	−	0.989005i
$309$	−97.5838	−	97.5838i	−0.315805	−	0.315805i
$310$	350.405	−	262.066i	1.13034	−	0.845375i
$311$	489.964			1.57545			0.787724	−	0.616028i	$-0.211259\pi$
$311$	489.964			1.57545			0.787724	+	0.616028i	$0.211259\pi$
$312$	−58.3883	+	14.1104i	−0.187142	+	0.0452258i
$313$	521.568			1.66635			0.833176	−	0.553008i	$-0.186520\pi$
$313$	521.568			1.66635			0.833176	+	0.553008i	$0.186520\pi$
$314$	301.094	−	106.793i	0.958899	−	0.340104i
$315$	198.568	−	377.639i	0.630373	−	1.19885i
$316$	183.684	−	149.049i	0.581278	−	0.471673i
$317$	−240.687	−	240.687i	−0.759266	−	0.759266i	0.216923	−	0.976189i	$-0.430398\pi$
$317$	−240.687	−	240.687i	−0.759266	−	0.759266i	−0.976189	+	0.216923i	$0.930398\pi$
$318$	−145.740	−	69.4250i	−0.458302	−	0.218317i
$319$		−	245.554i		−	0.769762i
$320$	−3.15064	+	319.984i	−0.00984575	+	0.999952i
$321$	−76.4714			−0.238229
$322$	−54.0678	+	113.501i	−0.167912	+	0.352489i
$323$	201.913	−	201.913i	0.625117	−	0.625117i
$324$	54.9287	+	67.6928i	0.169533	+	0.208928i
$325$	−21.9890	+	118.966i	−0.0676584	+	0.366050i
$326$	70.4944	+	198.754i	0.216240	+	0.609675i
$327$			223.149i			0.682413i
$328$	35.0860	+	145.184i	0.106970	+	0.442634i
$329$			449.012i			1.36478i
$330$	−73.4983	+	54.9690i	−0.222722	+	0.166573i
$331$	239.560	−	239.560i	0.723748	−	0.723748i	−0.245619	−	0.969367i	$-0.578991\pi$
$331$	239.560	−	239.560i	0.723748	−	0.723748i	0.969367	+	0.245619i	$0.0789911\pi$
$332$	87.0923	+	9.06574i	0.262326	+	0.0273064i
$333$	133.093	+	133.093i	0.399680	+	0.399680i
$334$	−371.365	−	176.904i	−1.11187	−	0.529653i
$335$	134.525	+	432.867i	0.401567	+	1.29214i
$336$	−269.148	+	175.553i	−0.801036	+	0.522480i
$337$		−	29.4117i		−	0.0872751i	−0.999047	−	0.0436375i	$-0.986105\pi$
$337$		−	29.4117i		−	0.0872751i	0.999047	−	0.0436375i	$-0.0138947\pi$
$338$	262.862	+	125.218i	0.777699	+	0.370466i
$339$	−83.7961	−	83.7961i	−0.247186	−	0.247186i
$340$	−88.4744	−	441.916i	−0.260219	−	1.29975i
$341$	183.018	+	183.018i	0.536709	+	0.536709i
$342$	−55.8500	−	157.465i	−0.163304	−	0.460425i
$343$		−	900.152i		−	2.62435i
$344$	139.602	+	85.2602i	0.405819	+	0.247849i
$345$	35.9790	−	11.1814i	0.104287	−	0.0324099i
$346$	292.310	−	103.677i	0.844826	−	0.299644i
$347$	−404.012	−	404.012i	−1.16430	−	1.16430i	−0.983525	−	0.180775i	$-0.942140\pi$
$347$	−404.012	−	404.012i	−1.16430	−	1.16430i	−0.180775	−	0.983525i	$-0.557860\pi$
$348$	−200.066	+	162.342i	−0.574902	+	0.466499i
$349$	228.642	−	228.642i	0.655135	−	0.655135i	−0.299090	−	0.954225i	$-0.596683\pi$
$349$	228.642	−	228.642i	0.655135	−	0.655135i	0.954225	+	0.299090i	$0.0966830\pi$
$350$	101.875	+	639.123i	0.291072	+	1.82607i
$351$		−	117.078i		−	0.333557i
$352$	−187.603	+	25.1757i	−0.532964	+	0.0715219i
$353$		−	213.553i		−	0.604967i	−0.953155	−	0.302484i	$-0.902184\pi$
$353$		−	213.553i		−	0.604967i	0.953155	−	0.302484i	$-0.0978158\pi$
$354$	175.302	+	83.5073i	0.495204	+	0.235896i
$355$	69.5177	−	132.210i	0.195825	−	0.372422i
$356$	−134.666	+	109.273i	−0.378274	+	0.306947i
$357$	320.018	−	320.018i	0.896409	−	0.896409i
$358$	−116.352	+	41.2679i	−0.325006	+	0.115274i
$359$	−265.765			−0.740292			−0.370146	−	0.928974i	$-0.620692\pi$
$359$	−265.765			−0.740292			−0.370146	+	0.928974i	$0.620692\pi$
$360$	−255.699	−	64.4648i	−0.710276	−	0.179069i
$361$		−	200.428i		−	0.555202i
$362$	312.182	−	110.725i	0.862382	−	0.305871i
$363$	94.3671	+	94.3671i	0.259965	+	0.259965i
$364$	−249.208	−	25.9409i	−0.684637	−	0.0712662i
$365$	−30.1389	+	57.3185i	−0.0825722	+	0.157037i
$366$	153.507	+	73.1251i	0.419419	+	0.199795i
$367$	326.457			0.889530			0.444765	−	0.895647i	$-0.353287\pi$
$367$	326.457			0.889530			0.444765	+	0.895647i	$0.353287\pi$
$368$	76.0370	+	16.0033i	0.206622	+	0.0434872i
$369$	−123.085			−0.333564
$370$	−282.585	−	40.7582i	−0.763744	−	0.110157i
$371$	−476.127	−	476.127i	−1.28336	−	1.28336i
$372$	28.1169	−	270.112i	0.0755830	−	0.726107i
$373$	−321.409	+	321.409i	−0.861686	+	0.861686i	−0.991534	−	0.129848i	$-0.958551\pi$
$373$	−321.409	+	321.409i	−0.861686	+	0.861686i	0.129848	+	0.991534i	$0.458551\pi$
$374$	251.252	−	89.1145i	0.671798	−	0.238274i
$375$	119.962	−	152.401i	0.319899	−	0.406403i
$376$	269.749	−	65.1890i	0.717416	−	0.173375i
$377$	−200.890			−0.532866
$378$	−209.363	−	590.284i	−0.553869	−	1.56160i
$379$	−29.8675	+	29.8675i	−0.0788061	+	0.0788061i	−0.745411	−	0.666605i	$-0.767747\pi$
$379$	−29.8675	+	29.8675i	−0.0788061	+	0.0788061i	0.666605	+	0.745411i	$0.267747\pi$
$380$	210.898	+	140.538i	0.554994	+	0.369837i
$381$	65.2851	−	65.2851i	0.171352	−	0.171352i
$382$	557.957	+	265.790i	1.46062	+	0.695784i
$383$	−574.493			−1.49998			−0.749990	−	0.661449i	$-0.769942\pi$
$383$	−574.493			−1.49998			−0.749990	+	0.661449i	$0.769942\pi$
$384$	144.541	+	136.206i	0.376409	+	0.354704i
$385$	−365.577	+	113.613i	−0.949551	+	0.295098i
$386$	378.794	+	180.443i	0.981332	+	0.467469i
$387$	−95.3173	+	95.3173i	−0.246298	+	0.246298i
$388$	314.536	−	255.227i	0.810660	−	0.657803i
$389$	100.184	+	100.184i	0.257543	+	0.257543i	0.824054	−	0.566511i	$-0.191707\pi$
$389$	100.184	+	100.184i	0.257543	+	0.257543i	−0.566511	+	0.824054i	$0.691707\pi$
$390$	44.9708	+	60.1298i	0.115310	+	0.154179i
$391$	−109.436			−0.279888
$392$	−921.807	+	222.769i	−2.35155	+	0.568289i
$393$	19.8593			0.0505327
$394$	133.630	+	376.760i	0.339161	+	0.956243i
$395$	−261.712	−	137.612i	−0.662562	−	0.348384i
$396$	16.1495	−	155.145i	0.0407817	−	0.391780i
$397$	356.675	+	356.675i	0.898425	+	0.898425i	0.995297	−	0.0968721i	$-0.0308838\pi$
$397$	356.675	+	356.675i	0.898425	+	0.898425i	−0.0968721	+	0.995297i	$0.530884\pi$
$398$	−28.5926	+	60.0228i	−0.0718406	+	0.150811i
$399$			254.496i			0.637833i
$400$	369.170	−	153.993i	0.922924	−	0.384981i
$401$	−749.091			−1.86806			−0.934029	−	0.357197i	$-0.883733\pi$
$401$	−749.091			−1.86806			−0.934029	+	0.357197i	$0.883733\pi$
$402$	253.986	+	120.989i	0.631805	+	0.300968i
$403$	149.729	−	149.729i	0.371535	−	0.371535i
$404$	2.69464	−	25.8867i	0.00666989	−	0.0640760i
$405$	50.7139	−	96.4484i	0.125219	−	0.238144i
$406$	−1012.85	+	359.237i	−2.49469	+	0.884821i
$407$		−	168.883i		−	0.414947i
$408$	−238.716	−	145.793i	−0.585087	−	0.357336i
$409$		−	33.5324i		−	0.0819863i	−0.999159	−	0.0409932i	$-0.986948\pi$
$409$		−	33.5324i		−	0.0819863i	0.999159	−	0.0409932i	$-0.0130522\pi$
$410$	149.514	−	111.821i	0.364669	−	0.272734i
$411$	124.520	−	124.520i	0.302968	−	0.302968i
$412$	−276.262	+	224.170i	−0.670539	+	0.544103i
$413$	572.706	+	572.706i	1.38670	+	1.38670i
$414$	−27.5376	+	57.8082i	−0.0665160	+	0.139633i
$415$	−32.4831	−	104.522i	−0.0782725	−	0.251861i
$416$	20.5965	+	153.480i	0.0495109	+	0.368943i
$417$			53.8735i			0.129193i
$418$	−64.4704	+	135.339i	−0.154235	+	0.323778i
$419$	−297.757	−	297.757i	−0.710637	−	0.710637i	0.256031	−	0.966668i	$-0.417585\pi$
$419$	−297.757	−	297.757i	−0.710637	−	0.710637i	−0.966668	+	0.256031i	$0.917585\pi$
$420$	334.258	+	222.743i	0.795853	+	0.530341i
$421$	−378.162	−	378.162i	−0.898248	−	0.898248i	0.0970332	−	0.995281i	$-0.469065\pi$
$421$	−378.162	−	378.162i	−0.898248	−	0.898248i	−0.995281	+	0.0970332i	$0.969065\pi$
$422$	−110.497	+	39.1912i	−0.261841	+	0.0928700i
$423$			228.689i			0.540636i
$424$	−216.913	+	355.164i	−0.511586	+	0.837650i
$425$	−464.122	+	319.316i	−1.09205	+	0.751332i
$426$	−30.9900	−	87.3741i	−0.0727464	−	0.205104i
$427$	501.503	+	501.503i	1.17448	+	1.17448i
$428$	−20.4108	+	196.081i	−0.0476887	+	0.458134i
$429$	−31.4060	+	31.4060i	−0.0732075	+	0.0732075i
$430$	29.1897	−	202.379i	0.0678831	−	0.470648i
$431$			204.639i			0.474800i	0.971412	+	0.237400i	$0.0762952\pi$
$431$			204.639i			0.474800i	−0.971412	+	0.237400i	$0.923705\pi$
$432$	−324.223	+	211.476i	−0.750517	+	0.489528i
$433$		−	238.284i		−	0.550309i	−0.961400	−	0.275154i	$-0.911271\pi$
$433$		−	238.284i		−	0.550309i	0.961400	−	0.275154i	$-0.0887290\pi$
$434$	487.151	−	1022.65i	1.12247	−	2.35633i
$435$	285.053	+	149.885i	0.655295	+	0.344563i
$436$	572.179	+	59.5601i	1.31234	+	0.136606i
$437$	43.5148	−	43.5148i	0.0995761	−	0.0995761i
$438$	13.4354	+	37.8803i	0.0306745	+	0.0864848i
$439$	−46.2557			−0.105366			−0.0526831	−	0.998611i	$-0.516777\pi$
$439$	−46.2557			−0.105366			−0.0526831	+	0.998611i	$0.516777\pi$
$440$	121.330	+	203.130i	0.275749	+	0.461658i
$441$		−	781.495i		−	1.77210i
$442$	−72.9056	−	205.552i	−0.164945	−	0.465051i
$443$	−137.124	−	137.124i	−0.309535	−	0.309535i	0.535194	−	0.844729i	$-0.320239\pi$
$443$	−137.124	−	137.124i	−0.309535	−	0.309535i	−0.844729	+	0.535194i	$0.820239\pi$
$444$	−137.598	+	111.653i	−0.309906	+	0.251471i
$445$	191.871	+	100.888i	0.431171	+	0.226715i
$446$	131.024	−	275.051i	0.293776	−	0.616707i
$447$	−312.242			−0.698528
$448$	378.301	+	736.983i	0.844421	+	1.64505i
$449$	321.085			0.715112			0.357556	−	0.933892i	$-0.383610\pi$
$449$	321.085			0.715112			0.357556	+	0.933892i	$0.383610\pi$
$450$	51.8867	+	325.516i	0.115304	+	0.723369i
$451$	78.0919	+	78.0919i	0.173153	+	0.173153i
$452$	−237.229	+	192.497i	−0.524842	+	0.425878i
$453$	−250.129	+	250.129i	−0.552162	+	0.552162i
$454$	40.4847	+	114.144i	0.0891734	+	0.251418i
$455$	92.9478	+	299.083i	0.204281	+	0.657325i
$456$	152.891	−	36.9485i	0.335287	−	0.0810274i
$457$	541.547			1.18501			0.592503	−	0.805568i	$-0.298140\pi$
$457$	541.547			1.18501			0.592503	+	0.805568i	$0.298140\pi$
$458$	69.6989	−	24.7209i	0.152181	−	0.0539757i
$459$	385.503	−	385.503i	0.839875	−	0.839875i
$460$	−19.0673	−	95.2385i	−0.0414508	−	0.207040i
$461$	134.676	−	134.676i	0.292138	−	0.292138i	−0.545786	−	0.837924i	$-0.683769\pi$
$461$	134.676	−	134.676i	0.292138	−	0.292138i	0.837924	+	0.545786i	$0.183769\pi$
$462$	−102.181	+	214.503i	−0.221171	+	0.464292i
$463$	−137.495			−0.296965			−0.148482	−	0.988915i	$-0.547439\pi$
$463$	−137.495			−0.296965			−0.148482	+	0.988915i	$0.547439\pi$
$464$	362.864	+	556.323i	0.782034	+	1.19897i
$465$	−324.170	+	100.744i	−0.697141	+	0.216655i
$466$	−44.7750	+	93.9937i	−0.0960838	+	0.201703i
$467$	−31.7765	+	31.7765i	−0.0680438	+	0.0680438i	−0.740310	−	0.672266i	$-0.765321\pi$
$467$	−31.7765	+	31.7765i	−0.0680438	+	0.0680438i	0.672266	+	0.740310i	$0.265321\pi$
$468$	−126.926	−	13.2121i	−0.271209	−	0.0282310i
$469$	829.761	+	829.761i	1.76921	+	1.76921i
$470$	−207.761	−	277.794i	−0.442045	−	0.591051i
$471$	−247.848			−0.526216
$472$	260.912	−	427.206i	0.552779	−	0.905098i
$473$	120.949			0.255706
$474$	−172.959	+	61.3452i	−0.364892	+	0.129420i
$475$	57.5786	−	311.516i	0.121218	−	0.655823i
$476$	−735.148	−	905.978i	−1.54443	−	1.90331i
$477$	−242.499	−	242.499i	−0.508384	−	0.508384i
$478$	425.438	+	202.662i	0.890038	+	0.423980i
$479$			709.389i			1.48098i	0.672067	+	0.740490i	$0.265407\pi$
$479$			709.389i			1.48098i	−0.672067	+	0.740490i	$0.734593\pi$
$480$	85.2867	−	233.148i	0.177681	−	0.485725i
$481$	−138.165			−0.287246
$482$	−307.298	+	645.093i	−0.637547	+	1.33837i
$483$	68.9679	−	68.9679i	0.142791	−	0.142791i
$484$	267.155	−	216.781i	0.551974	−	0.447894i
$485$	−448.149	−	235.643i	−0.924019	−	0.485862i
$486$	−168.180	−	474.172i	−0.346049	−	0.975662i
$487$			209.516i			0.430218i	0.976590	+	0.215109i	$0.0690107\pi$
$487$			209.516i			0.430218i	−0.976590	+	0.215109i	$0.930989\pi$
$488$	228.474	−	374.093i	0.468183	−	0.766584i
$489$		−	163.606i		−	0.334572i
$490$	709.978	+	949.301i	1.44893	+	1.93735i
$491$	−204.872	+	204.872i	−0.417254	+	0.417254i	−0.884256	−	0.467002i	$-0.845334\pi$
$491$	−204.872	+	204.872i	−0.417254	+	0.417254i	0.467002	+	0.884256i	$0.345334\pi$
$492$	11.9972	−	115.254i	0.0243845	−	0.234256i
$493$	−661.469	−	661.469i	−1.34172	−	1.34172i
$494$	110.722	+	52.7439i	0.224134	+	0.106769i
$495$	−186.194	+	57.8648i	−0.376150	+	0.116899i
$496$	−685.093	−	144.190i	−1.38124	−	0.290705i
$497$		−	386.691i		−	0.778050i
$498$	−61.3288	−	29.2147i	−0.123150	−	0.0586640i
$499$	−600.708	−	600.708i	−1.20382	−	1.20382i	−0.972994	−	0.230829i	$-0.925856\pi$
$499$	−600.708	−	600.708i	−1.20382	−	1.20382i	−0.230829	−	0.972994i	$-0.574144\pi$
$500$	−358.755	−	348.274i	−0.717510	−	0.696548i
$501$	225.656	+	225.656i	0.450410	+	0.450410i
$502$	−232.887	−	656.608i	−0.463917	−	1.30798i
$503$			144.881i			0.288033i	0.989575	+	0.144017i	$0.0460019\pi$
$503$			144.881i			0.288033i	−0.989575	+	0.144017i	$0.953998\pi$
$504$	−663.557	+	160.359i	−1.31658	+	0.318173i
$505$	−31.0675	+	9.65504i	−0.0615198	+	0.0191189i
$506$	54.1480	−	19.2053i	0.107012	−	0.0379551i
$507$	−159.725	−	159.725i	−0.315040	−	0.315040i
$508$	−149.973	−	184.823i	−0.295223	−	0.363826i
$509$	202.611	−	202.611i	0.398058	−	0.398058i	−0.479490	−	0.877547i	$-0.659178\pi$
$509$	202.611	−	202.611i	0.398058	−	0.398058i	0.877547	+	0.479490i	$0.159178\pi$
$510$	−49.9138	+	346.063i	−0.0978702	+	0.678555i
$511$			167.647i			0.328076i
$512$	387.828	−	334.266i	0.757476	−	0.652863i
$513$			306.573i			0.597607i
$514$	−592.505	−	282.247i	−1.15273	−	0.549119i
$515$	393.617	+	206.969i	0.764304	+	0.401882i
$516$	−79.9624	−	98.5437i	−0.154966	−	0.190976i
$517$	145.093	−	145.093i	0.280644	−	0.280644i
$518$	−696.599	+	247.071i	−1.34479	+	0.476971i
$519$	−240.617			−0.463616
$520$	166.183	−	99.2612i	0.319582	−	0.190887i
$521$			977.564i			1.87632i	0.346199	+	0.938161i	$0.387472\pi$
$521$			977.564i			1.87632i	−0.346199	+	0.938161i	$0.612528\pi$
$522$	−515.859	+	182.965i	−0.988235	+	0.350509i
$523$	467.380	+	467.380i	0.893652	+	0.893652i	0.994865	−	0.101212i	$-0.0322722\pi$
$523$	467.380	+	467.380i	0.893652	+	0.893652i	−0.101212	+	0.994865i	$0.532272\pi$
$524$	5.30060	−	50.9216i	0.0101157	−	0.0971786i
$525$	91.2581	−	493.731i	0.173825	−	0.940441i
$526$	−115.091	−	54.8251i	−0.218805	−	0.104230i
$527$	986.020			1.87101
$528$	143.700	+	30.2442i	0.272159	+	0.0572806i
$529$	505.415			0.955416
$530$	514.877	+	74.2623i	0.971466	+	0.140118i
$531$	291.688	+	291.688i	0.549319	+	0.549319i
$532$	652.556	+	67.9268i	1.22661	+	0.127682i
$533$	63.8878	−	63.8878i	0.119865	−	0.119865i
$534$	126.803	−	44.9745i	0.237458	−	0.0842220i
$535$	235.324	−	73.1331i	0.439858	−	0.136697i
$536$	378.021	−	618.955i	0.705262	−	1.15477i
$537$	95.7761			0.178354
$538$	269.898	+	760.959i	0.501669	+	1.41442i
$539$	−495.823	+	495.823i	−0.919895	+	0.919895i
$540$	402.657	+	268.323i	0.745661	+	0.496894i
$541$	224.658	−	224.658i	0.415264	−	0.415264i	−0.468304	−	0.883568i	$-0.655135\pi$
$541$	224.658	−	224.658i	0.415264	−	0.415264i	0.883568	+	0.468304i	$0.155135\pi$
$542$	−758.782	−	361.455i	−1.39997	−	0.666891i
$543$	−256.975			−0.473251
$544$	−437.545	+	573.181i	−0.804311	+	1.05364i
$545$	−213.408	−	686.692i	−0.391573	−	1.25999i
$546$	175.487	+	83.5955i	0.321405	+	0.153105i
$547$	646.717	−	646.717i	1.18230	−	1.18230i	0.203151	−	0.979147i	$-0.434882\pi$
$547$	646.717	−	646.717i	1.18230	−	1.18230i	0.979147	−	0.203151i	$-0.0651184\pi$
$548$	−286.048	−	352.519i	−0.521986	−	0.643282i
$549$	255.424	+	255.424i	0.465253	+	0.465253i
$550$	173.606	−	239.445i	0.315646	−	0.435355i
$551$	526.036			0.954693
$552$	−51.4462	−	31.4202i	−0.0931996	−	0.0569207i
$553$	−765.462			−1.38420
$554$	−274.071	−	772.724i	−0.494713	−	1.39481i
$555$	196.050	+	103.085i	0.353242	+	0.185740i
$556$	138.138	+	14.3792i	0.248449	+	0.0258619i
$557$	198.581	+	198.581i	0.356519	+	0.356519i	0.862528	−	0.506009i	$-0.168880\pi$
$557$	198.581	+	198.581i	0.356519	+	0.356519i	−0.506009	+	0.862528i	$0.668880\pi$
$558$	248.114	−	520.852i	0.444649	−	0.933426i
$559$		−	98.9498i		−	0.177012i
$560$	660.355	−	797.625i	1.17921	−	1.42433i
$561$	−206.820			−0.368663
$562$	−313.903	−	149.532i	−0.558547	−	0.266071i
$563$	−723.964	+	723.964i	−1.28590	+	1.28590i	−0.348653	+	0.937252i	$0.613361\pi$
$563$	−723.964	+	723.964i	−1.28590	+	1.28590i	−0.937252	+	0.348653i	$0.886639\pi$
$564$	−214.139	−	22.2905i	−0.379680	−	0.0395222i
$565$	338.002	+	177.726i	0.598234	+	0.314560i
$566$	−110.691	+	39.2602i	−0.195568	+	0.0693643i
$567$		−	282.095i		−	0.497522i
$568$	−232.309	+	56.1410i	−0.408994	+	0.0988398i
$569$		−	37.6363i		−	0.0661446i	−0.999453	−	0.0330723i	$-0.989471\pi$
$569$		−	37.6363i		−	0.0661446i	0.999453	−	0.0330723i	$-0.0105292\pi$
$570$	−117.757	−	157.451i	−0.206591	−	0.276230i
$571$	627.411	−	627.411i	1.09879	−	1.09879i	0.104242	−	0.994552i	$-0.466758\pi$
$571$	627.411	−	627.411i	1.09879	−	1.09879i	0.994552	−	0.104242i	$-0.0332417\pi$
$572$	72.1461	+	88.9111i	0.126130	+	0.155439i
$573$	−339.037	−	339.037i	−0.591687	−	0.591687i
$574$	207.863	−	436.354i	0.362130	−	0.760199i
$575$	−100.024	+	68.8166i	−0.173955	+	0.119681i
$576$	192.675	+	375.358i	0.334505	+	0.651663i
$577$			267.834i			0.464184i	0.972694	+	0.232092i	$0.0745570\pi$
$577$			267.834i			0.464184i	−0.972694	+	0.232092i	$0.925443\pi$
$578$	188.190	−	395.056i	0.325587	−	0.683487i
$579$	−230.170	−	230.170i	−0.397530	−	0.397530i
$580$	460.405	−	690.904i	0.793801	−	1.19121i
$581$	−200.359	−	200.359i	−0.344851	−	0.344851i
$582$	−296.170	+	105.046i	−0.508884	+	0.180492i
$583$			307.709i			0.527804i
$584$	100.716	−	24.3395i	0.172458	−	0.0416772i
$585$	47.3398	+	152.328i	0.0809228	+	0.260389i
$586$	−179.097	−	504.952i	−0.305626	−	0.861692i
$587$	341.415	+	341.415i	0.581627	+	0.581627i	0.935350	−	0.353723i	$-0.115084\pi$
$587$	341.415	+	341.415i	0.581627	+	0.581627i	−0.353723	+	0.935350i	$0.615084\pi$
$588$	731.775	+	76.1730i	1.24452	+	0.129546i
$589$	−392.068	+	392.068i	−0.665650	+	0.665650i
$590$	−619.316	−	89.3260i	−1.04969	−	0.151400i
$591$		−	310.132i		−	0.524759i
$592$	249.565	+	382.619i	0.421562	+	0.646316i
$593$		−	176.800i		−	0.298146i	−0.988826	−	0.149073i	$-0.952371\pi$
$593$		−	176.800i		−	0.298146i	0.988826	−	0.149073i	$-0.0476289\pi$
$594$	−123.090	+	258.396i	−0.207223	+	0.435011i
$595$	−678.737	+	1290.83i	−1.14074	+	2.16947i
$596$	−83.3397	+	800.624i	−0.139832	+	1.34333i
$597$	36.4722	−	36.4722i	0.0610924	−	0.0610924i
$598$	−15.7121	−	44.2991i	−0.0262744	−	0.0740788i
$599$	722.621			1.20638			0.603189	−	0.797598i	$-0.293896\pi$
$599$	722.621			1.20638			0.603189	+	0.797598i	$0.293896\pi$
$600$	−309.864	+	16.8572i	−0.516439	+	0.0280954i
$601$		−	127.389i		−	0.211962i	−0.994368	−	0.105981i	$-0.966202\pi$
$601$		−	127.389i		−	0.211962i	0.994368	−	0.105981i	$-0.0337983\pi$
$602$	−176.944	−	498.883i	−0.293928	−	0.828709i
$603$	422.611	+	422.611i	0.700847	+	0.700847i
$604$	574.599	+	708.122i	0.951323	+	1.17239i
$605$	−380.642	−	200.147i	−0.629160	−	0.330821i
$606$	−8.68357	+	18.2289i	−0.0143293	+	0.0300807i
$607$	−186.334			−0.306975			−0.153487	−	0.988151i	$-0.549050\pi$
$607$	−186.334			−0.306975			−0.153487	+	0.988151i	$0.549050\pi$
$608$	−53.9324	−	401.892i	−0.0887046	−	0.661006i
$609$	833.731			1.36902
$610$	−542.319	−	78.2203i	−0.889047	−	0.128230i
$611$	−118.702	−	118.702i	−0.194275	−	0.194275i
$612$	−374.423	−	461.429i	−0.611802	−	0.753970i
$613$	618.741	−	618.741i	1.00937	−	1.00937i	0.00941004	−	0.999956i	$-0.497005\pi$
$613$	618.741	−	618.741i	1.00937	−	1.00937i	0.999956	−	0.00941004i	$-0.00299535\pi$
$614$	−51.4281	−	144.998i	−0.0837591	−	0.236153i
$615$	−138.320	+	42.9867i	−0.224911	+	0.0698970i
$616$	522.738	+	319.257i	0.848600	+	0.518274i
$617$	−454.374			−0.736425			−0.368212	−	0.929742i	$-0.620030\pi$
$617$	−454.374			−0.736425			−0.368212	+	0.929742i	$0.620030\pi$
$618$	260.131	−	92.2637i	0.420924	−	0.149294i
$619$	−396.836	+	396.836i	−0.641092	+	0.641092i	−0.950824	−	0.309732i	$-0.899761\pi$
$619$	−396.836	+	396.836i	−0.641092	+	0.641092i	0.309732	+	0.950824i	$0.399761\pi$
$620$	171.797	+	858.100i	0.277092	+	1.38403i
$621$	83.0807	−	83.0807i	0.133785	−	0.133785i
$622$	−421.428	+	884.680i	−0.677537	+	1.42232i
$623$	561.189			0.900785
$624$	24.7431	−	117.563i	0.0396524	−	0.188402i
$625$	−223.409	+	583.706i	−0.357455	+	0.933930i
$626$	−448.611	+	941.744i	−0.716631	+	1.50438i
$627$	82.2373	−	82.2373i	0.131160	−	0.131160i
$628$	−66.1525	+	635.511i	−0.105338	+	1.01196i
$629$	−454.935	−	454.935i	−0.723267	−	0.723267i
$630$	511.073	+	683.349i	0.811227	+	1.08468i
$631$	−474.728			−0.752343			−0.376172	−	0.926550i	$-0.622760\pi$
$631$	−474.728			−0.752343			−0.376172	+	0.926550i	$0.622760\pi$
$632$	111.132	+	459.859i	0.175842	+	0.727625i
$633$	90.9563			0.143691
$634$	641.605	−	227.565i	1.01200	−	0.358936i
$635$	−138.465	+	263.336i	−0.218056	+	0.414702i
$636$	250.708	−	203.434i	0.394194	−	0.319865i
$637$	405.639	+	405.639i	0.636795	+	0.636795i
$638$	443.372	+	211.206i	0.694941	+	0.331044i
$639$		−	196.948i		−	0.308213i
$640$	−575.054	−	280.914i	−0.898522	−	0.438928i
$641$	59.4277			0.0927110			0.0463555	−	0.998925i	$-0.485239\pi$
$641$	59.4277			0.0927110			0.0463555	+	0.998925i	$0.485239\pi$
$642$	65.7745	−	138.077i	0.102453	−	0.215073i
$643$	169.865	−	169.865i	0.264176	−	0.264176i	−0.562572	−	0.826748i	$-0.690188\pi$
$643$	169.865	−	169.865i	0.264176	−	0.264176i	0.826748	+	0.562572i	$0.190188\pi$
$644$	−158.434	−	195.250i	−0.246015	−	0.303183i
$645$	−73.8266	+	140.405i	−0.114460	+	0.217682i
$646$	190.905	+	538.243i	0.295518	+	0.833194i
$647$		−	110.915i		−	0.171430i	−0.996320	−	0.0857149i	$-0.972683\pi$
$647$		−	110.915i		−	0.171430i	0.996320	−	0.0857149i	$-0.0273174\pi$
$648$	−169.471	+	40.9554i	−0.261530	+	0.0632028i
$649$		−	370.126i		−	0.570302i
$650$	−195.893	−	142.029i	−0.301373	−	0.218506i
$651$	−621.401	+	621.401i	−0.954533	+	0.954533i
$652$	−419.504	−	43.6676i	−0.643411	−	0.0669749i
$653$	122.174	+	122.174i	0.187096	+	0.187096i	0.794439	−	0.607343i	$-0.207765\pi$
$653$	122.174	+	122.174i	0.187096	+	0.187096i	−0.607343	+	0.794439i	$0.707765\pi$
$654$	−402.918	−	191.935i	−0.616082	−	0.293478i
$655$	−61.1127	+	18.9924i	−0.0933019	+	0.0289960i
$656$	−292.323	−	61.5244i	−0.445614	−	0.0937871i
$657$			85.3852i			0.129962i
$658$	−810.736	−	386.204i	−1.23212	−	0.586936i
$659$	−230.851	−	230.851i	−0.350304	−	0.350304i	0.509918	−	0.860223i	$-0.329676\pi$
$659$	−230.851	−	230.851i	−0.350304	−	0.350304i	−0.860223	+	0.509918i	$0.829676\pi$
$660$	−36.0348	−	179.989i	−0.0545982	−	0.272710i
$661$	−200.446	−	200.446i	−0.303247	−	0.303247i	0.539036	−	0.842283i	$-0.318789\pi$
$661$	−200.446	−	200.446i	−0.303247	−	0.303247i	−0.842283	+	0.539036i	$0.818789\pi$
$662$	226.500	+	638.601i	0.342145	+	0.964655i
$663$			169.202i			0.255206i
$664$	−91.2789	+	149.456i	−0.137468	+	0.225085i
$665$	−243.386	−	783.154i	−0.365994	−	1.17768i
$666$	−354.789	+	125.837i	−0.532717	+	0.188945i
$667$	−142.555	−	142.555i	−0.213725	−	0.213725i
$668$	638.836	−	518.378i	0.956341	−	0.776014i
$669$	−167.132	+	167.132i	−0.249823	+	0.249823i
$670$	−897.292	−	129.419i	−1.33924	−	0.193163i
$671$		−	324.110i		−	0.483025i
$672$	−85.4792	−	636.971i	−0.127201	−	0.947873i
$673$		−	674.203i		−	1.00179i	−0.865509	−	0.500894i	$-0.833005\pi$
$673$		−	674.203i		−	1.00179i	0.865509	−	0.500894i	$-0.166995\pi$
$674$	53.1058	+	25.2976i	0.0787920	+	0.0375335i
$675$	109.932	−	594.763i	0.162862	−	0.881130i
$676$	−452.186	+	366.922i	−0.668914	+	0.542784i
$677$	−197.936	+	197.936i	−0.292372	+	0.292372i	−0.838017	−	0.545644i	$-0.816285\pi$
$677$	−197.936	+	197.936i	−0.292372	+	0.292372i	0.545644	+	0.838017i	$0.316285\pi$
$678$	223.377	−	79.2277i	0.329465	−	0.116855i
$679$	−1310.76			−1.93043
$680$	874.023	+	220.352i	1.28533	+	0.324046i
$681$		−	93.9584i		−	0.137971i
$682$	−487.874	+	173.040i	−0.715358	+	0.253724i
$683$	−746.480	−	746.480i	−1.09294	−	1.09294i	−0.995213	−	0.0977292i	$-0.968842\pi$
$683$	−746.480	−	746.480i	−1.09294	−	1.09294i	−0.0977292	−	0.995213i	$-0.531158\pi$
$684$	332.357	+	34.5962i	0.485903	+	0.0505793i
$685$	−264.099	+	502.267i	−0.385546	+	0.733237i
$686$	1625.31	+	774.238i	2.36926	+	1.12863i
$687$	−57.3731			−0.0835126
$688$	−274.020	+	178.731i	−0.398285	+	0.259783i
$689$	251.741			0.365371
$690$	−10.7571	+	74.5810i	−0.0155899	+	0.108088i
$691$	761.568	+	761.568i	1.10212	+	1.10212i	0.994154	+	0.107970i	$0.0344350\pi$
$691$	761.568	+	761.568i	1.10212	+	1.10212i	0.107970	+	0.994154i	$0.465565\pi$
$692$	−64.2224	+	616.969i	−0.0928070	+	0.891574i
$693$	−356.915	+	356.915i	−0.515029	+	0.515029i
$694$	1076.98	−	381.986i	1.55185	−	0.550411i
$695$	−51.5217	−	165.784i	−0.0741319	−	0.238538i
$696$	−121.044	−	500.873i	−0.173913	−	0.719645i
$697$	420.725			0.603623
$698$	216.177	+	609.496i	0.309709	+	0.873204i
$699$	57.1142	−	57.1142i	0.0817085	−	0.0817085i
$700$	−1241.63	−	365.777i	−1.77375	−	0.522538i
$701$	−581.914	+	581.914i	−0.830119	+	0.830119i	−0.987533	−	0.157413i	$-0.949684\pi$
$701$	−581.914	+	581.914i	−0.830119	+	0.830119i	0.157413	+	0.987533i	$0.449684\pi$
$702$	211.397	+	100.702i	0.301135	+	0.143449i
$703$	361.789			0.514636
$704$	115.904	−	360.391i	0.164637	−	0.511919i
$705$	79.8683	+	256.996i	0.113288	+	0.364533i
$706$	385.592	+	183.682i	0.546165	+	0.260172i
$707$	−59.5532	+	59.5532i	−0.0842336	+	0.0842336i
$708$	−301.562	+	244.700i	−0.425935	+	0.345621i
$709$	−442.305	−	442.305i	−0.623843	−	0.623843i	0.322669	−	0.946512i	$-0.395420\pi$
$709$	−442.305	−	442.305i	−0.623843	−	0.623843i	−0.946512	+	0.322669i	$0.895420\pi$
$710$	178.925	+	239.238i	0.252007	+	0.336954i
$711$	−389.862			−0.548329
$712$	−81.4753	−	337.140i	−0.114432	−	0.473512i
$713$	212.500			0.298036
$714$	302.571	+	853.078i	0.423769	+	1.19479i
$715$	66.6101	−	126.680i	0.0931610	−	0.177175i
$716$	25.5634	−	245.581i	0.0357030	−	0.342990i
$717$	−258.513	−	258.513i	−0.360548	−	0.360548i
$718$	228.589	−	479.865i	0.318370	−	0.668336i
$719$		−	1325.15i		−	1.84304i	−0.388327	−	0.921522i	$-0.626947\pi$
$719$		−	1325.15i		−	1.84304i	0.388327	−	0.921522i	$-0.373053\pi$
$720$	336.330	−	406.244i	0.467125	−	0.564227i
$721$	1151.26			1.59675
$722$	361.893	+	172.392i	0.501237	+	0.238770i
$723$	391.984	−	391.984i	0.542163	−	0.542163i
$724$	−68.5886	+	658.914i	−0.0947356	+	0.910102i
$725$	−1020.53	−	188.628i	−1.40763	−	0.260177i
$726$	−251.556	+	89.2224i	−0.346496	+	0.122896i
$727$			763.348i			1.05000i	0.851103	+	0.524999i	$0.175934\pi$
$727$			763.348i			1.05000i	−0.851103	+	0.524999i	$0.824066\pi$
$728$	261.187	−	427.657i	0.358774	−	0.587442i
$729$			194.174i			0.266357i
$730$	−77.5714	−	103.720i	−0.106262	−	0.142082i
$731$	325.810	−	325.810i	0.445705	−	0.445705i
$732$	−264.070	+	214.277i	−0.360751	+	0.292728i
$733$	−51.4053	−	51.4053i	−0.0701301	−	0.0701301i	0.671172	−	0.741302i	$-0.265791\pi$
$733$	−51.4053	−	51.4053i	−0.0701301	−	0.0701301i	−0.741302	+	0.671172i	$0.765791\pi$
$734$	−280.792	+	589.452i	−0.382551	+	0.803068i
$735$	−272.932	−	878.228i	−0.371337	−	1.19487i
$736$	−94.2964	+	123.528i	−0.128120	+	0.167836i
$737$		−	536.255i		−	0.727619i
$738$	105.868	−	222.242i	0.143452	−	0.301141i
$739$	777.183	+	777.183i	1.05167	+	1.05167i	0.998590	+	0.0530776i	$0.0169031\pi$
$739$	777.183	+	777.183i	1.05167	+	1.05167i	0.0530776	+	0.998590i	$0.483097\pi$
$740$	316.650	−	475.179i	0.427905	−	0.642134i
$741$	−67.2792	−	67.2792i	−0.0907952	−	0.0907952i
$742$	1269.22	−	450.169i	1.71054	−	0.606696i
$743$			278.857i			0.375312i	0.982235	+	0.187656i	$0.0600890\pi$
$743$			278.857i			0.375312i	−0.982235	+	0.187656i	$0.939911\pi$
$744$	463.530	+	283.096i	0.623025	+	0.380506i
$745$	960.856	−	298.611i	1.28974	−	0.400820i
$746$	−303.886	−	856.786i	−0.407354	−	1.14851i
$747$	−102.046	−	102.046i	−0.136608	−	0.136608i
$748$	−55.2018	+	530.311i	−0.0737992	+	0.708971i
$749$	451.091	−	451.091i	0.602258	−	0.602258i
$750$	171.994	+	347.687i	0.229325	+	0.463583i
$751$			302.489i			0.402782i	0.979511	+	0.201391i	$0.0645462\pi$
$751$			302.489i			0.402782i	−0.979511	+	0.201391i	$0.935454\pi$
$752$	−114.311	+	543.129i	−0.152009	+	0.722245i
$753$			540.492i			0.717784i
$754$	172.790	−	362.728i	0.229164	−	0.481072i
$755$	530.508	−	1008.93i	0.702660	−	1.33633i
$756$	1245.89	+	129.689i	1.64801	+	0.171547i
$757$	409.757	−	409.757i	0.541290	−	0.541290i	−0.382617	−	0.923907i	$-0.624977\pi$
$757$	409.757	−	409.757i	0.541290	−	0.541290i	0.923907	+	0.382617i	$0.124977\pi$
$758$	−28.2392	−	79.6184i	−0.0372548	−	0.105037i
$759$	−44.5723			−0.0587251
$760$	−435.153	+	259.917i	−0.572570	+	0.341997i
$761$			1093.02i			1.43629i	0.695892	+	0.718146i	$0.255009\pi$
$761$			1093.02i			1.43629i	−0.695892	+	0.718146i	$0.744991\pi$
$762$	61.7258	+	174.032i	0.0810050	+	0.228388i
$763$	−1316.32	−	1316.32i	−1.72519	−	1.72519i
$764$	−959.820	+	778.837i	−1.25631	+	1.01942i
$765$	−345.692	+	657.443i	−0.451885	+	0.859402i
$766$	494.132	−	1037.30i	0.645081	−	1.35418i
$767$	−302.804			−0.394791
$768$	−370.257	+	143.830i	−0.482105	+	0.187279i
$769$	−1170.30			−1.52185			−0.760925	−	0.648840i	$-0.775254\pi$
$769$	−1170.30			−1.52185			−0.760925	+	0.648840i	$0.775254\pi$
$770$	109.301	−	757.807i	0.141949	−	0.984165i
$771$	360.029	+	360.029i	0.466964	+	0.466964i
$772$	−651.617	+	528.748i	−0.844063	+	0.684907i
$773$	382.873	−	382.873i	0.495308	−	0.495308i	−0.414666	−	0.909974i	$-0.636102\pi$
$773$	382.873	−	382.873i	0.495308	−	0.495308i	0.909974	+	0.414666i	$0.136102\pi$
$774$	−90.1207	−	254.089i	−0.116435	−	0.328281i
$775$	901.217	−	620.038i	1.16286	−	0.800049i
$776$	190.300	+	787.452i	0.245232	+	1.01476i
$777$	573.411			0.737980
$778$	−267.064	+	94.7225i	−0.343269	+	0.121751i
$779$	−167.292	+	167.292i	−0.214752	+	0.214752i
$780$	−147.251	+	29.4805i	−0.188783	+	0.0377955i
$781$	−124.955	+	124.955i	−0.159993	+	0.159993i
$782$	94.1282	−	197.598i	0.120368	−	0.252683i
$783$	1004.34			1.28268
$784$	390.632	−	1856.02i	0.498256	−	2.36738i
$785$	762.698	−	237.028i	0.971589	−	0.301947i
$786$	−17.0814	+	35.8580i	−0.0217321	+	0.0456209i
$787$	−817.689	+	817.689i	−1.03900	+	1.03900i	−0.0397870	+	0.999208i	$0.512668\pi$
$787$	−817.689	+	817.689i	−1.03900	+	1.03900i	−0.999208	+	0.0397870i	$0.987332\pi$
$788$	−795.215	−	82.7766i	−1.00916	−	0.105047i
$789$	69.9339	+	69.9339i	0.0886362	+	0.0886362i
$790$	473.575	−	354.185i	0.599462	−	0.448335i
$791$	988.598			1.24981
$792$	266.239	+	162.603i	0.336160	+	0.205306i
$793$	−265.158			−0.334373
$794$	−950.795	+	337.229i	−1.19747	+	0.424722i
$795$	−357.207	−	187.824i	−0.449317	−	0.236257i
$796$	−83.7842	−	103.254i	−0.105256	−	0.129716i
$797$	−308.695	−	308.695i	−0.387321	−	0.387321i	0.486410	−	0.873731i	$-0.338306\pi$
$797$	−308.695	−	308.695i	−0.387321	−	0.387321i	−0.873731	+	0.486410i	$0.838306\pi$
$798$	−459.517	−	218.897i	−0.575836	−	0.274307i
$799$		−	781.697i		−	0.978345i
$800$	−39.4811	+	799.025i	−0.0493513	+	0.998781i
$801$	285.823			0.356833
$802$	644.308	−	1352.56i	0.803377	−	1.68648i
$803$	54.1731	−	54.1731i	0.0674633	−	0.0674633i
$804$	−436.916	+	354.532i	−0.543428	+	0.440960i
$805$	−146.276	+	278.191i	−0.181710	+	0.345579i
$806$	141.566	+	399.135i	0.175640	+	0.495205i
$807$		−	626.389i		−	0.776195i
$808$	44.4233	+	27.1311i	0.0549794	+	0.0335781i
$809$			370.069i			0.457440i	0.973492	+	0.228720i	$0.0734540\pi$
$809$			370.069i			0.457440i	−0.973492	+	0.228720i	$0.926546\pi$
$810$	130.527	+	174.526i	0.161145	+	0.215464i
$811$	−433.814	+	433.814i	−0.534912	+	0.534912i	−0.922030	−	0.387118i	$-0.873471\pi$
$811$	−433.814	+	433.814i	−0.534912	+	0.534912i	0.387118	+	0.922030i	$0.373471\pi$
$812$	222.529	−	2137.78i	0.274050	−	2.63274i
$813$	461.066	+	461.066i	0.567117	+	0.567117i
$814$	304.936	+	145.260i	0.374614	+	0.178452i
$815$	156.464	+	503.461i	0.191980	+	0.617744i
$816$	468.568	−	305.625i	0.574225	−	0.374541i
$817$			259.102i			0.317138i
$818$	60.5461	+	28.8419i	0.0740173	+	0.0352590i
$819$	291.996	+	291.996i	0.356528	+	0.356528i
$820$	73.3040	+	366.143i	0.0893952	+	0.446516i
$821$	−505.005	−	505.005i	−0.615109	−	0.615109i	0.329164	−	0.944273i	$-0.393233\pi$
$821$	−505.005	−	505.005i	−0.615109	−	0.615109i	−0.944273	+	0.329164i	$0.893233\pi$
$822$	117.731	+	331.935i	0.143225	+	0.403814i
$823$		−	601.074i		−	0.730345i	−0.930940	−	0.365172i	$-0.881010\pi$
$823$		−	601.074i		−	0.730345i	0.930940	−	0.365172i	$-0.118990\pi$
$824$	−167.144	−	691.632i	−0.202844	−	0.839359i
$825$	−189.033	+	130.055i	−0.229130	+	0.157642i
$826$	−1526.67	+	541.482i	−1.84827	+	0.655548i
$827$	277.149	+	277.149i	0.335126	+	0.335126i	0.854529	−	0.519403i	$-0.173846\pi$
$827$	277.149	+	277.149i	0.335126	+	0.335126i	−0.519403	+	0.854529i	$0.673846\pi$
$828$	−80.6928	−	99.4439i	−0.0974551	−	0.120101i
$829$	−121.301	+	121.301i	−0.146322	+	0.146322i	−0.776473	−	0.630151i	$-0.782993\pi$
$829$	−121.301	+	121.301i	−0.146322	+	0.146322i	0.630151	+	0.776473i	$0.282993\pi$
$830$	216.665	+	31.2503i	0.261042	+	0.0376510i
$831$			636.073i			0.765431i
$832$	−294.840	−	94.8224i	−0.354375	−	0.113969i
$833$			2671.28i			3.20682i
$834$	−97.2740	−	46.3377i	−0.116636	−	0.0555607i
$835$	−910.210	−	478.601i	−1.09007	−	0.573175i
$836$	−188.916	−	232.816i	−0.225976	−	0.278487i
$837$	−748.557	+	748.557i	−0.894333	+	0.894333i
$838$	793.737	−	281.524i	0.947180	−	0.335947i
$839$	−68.1620			−0.0812420			−0.0406210	−	0.999175i	$-0.512934\pi$
$839$	−68.1620			−0.0812420			−0.0406210	+	0.999175i	$0.512934\pi$
$840$	−689.688	+	411.951i	−0.821057	+	0.490418i
$841$		−	882.300i		−	1.04911i
$842$	1008.08	−	357.545i	1.19724	−	0.424638i
$843$	190.740	+	190.740i	0.226263	+	0.226263i
$844$	24.2769	−	233.222i	0.0287641	−	0.276330i
$845$	644.272	+	338.767i	0.762452	+	0.400908i
$846$	−412.921	−	196.700i	−0.488086	−	0.232506i
$847$	−1113.31			−1.31442
$848$	−454.713	−	697.141i	−0.536218	−	0.822100i
$849$	91.1164			0.107322
$850$	−177.357	−	1112.67i	−0.208656	−	1.30902i
$851$	−98.0442	−	98.0442i	−0.115211	−	0.115211i
$852$	184.418	+	19.1967i	0.216453	+	0.0225313i
$853$	618.619	−	618.619i	0.725227	−	0.725227i	−0.244438	−	0.969665i	$-0.578603\pi$
$853$	618.619	−	618.619i	0.725227	−	0.725227i	0.969665	+	0.244438i	$0.0786034\pi$
$854$	−1336.87	+	474.162i	−1.56542	+	0.555224i
$855$	−123.960	−	398.873i	−0.144983	−	0.466519i
$856$	−336.489	−	205.507i	−0.393095	−	0.240078i
$857$	−151.362			−0.176619			−0.0883094	−	0.996093i	$-0.528146\pi$
$857$	−151.362			−0.176619			−0.0883094	+	0.996093i	$0.528146\pi$
$858$	−29.6938	−	83.7196i	−0.0346081	−	0.0975753i
$859$	364.086	−	364.086i	0.423849	−	0.423849i	−0.462678	−	0.886527i	$-0.653111\pi$
$859$	364.086	−	364.086i	0.423849	−	0.423849i	0.886527	+	0.462678i	$0.153111\pi$
$860$	340.309	+	226.775i	0.395708	+	0.263692i
$861$	−265.146	+	265.146i	−0.307951	+	0.307951i
$862$	−369.496	−	176.014i	−0.428650	−	0.204192i
$863$	−125.057			−0.144910			−0.0724550	−	0.997372i	$-0.523083\pi$
$863$	−125.057			−0.144910			−0.0724550	+	0.997372i	$0.523083\pi$
$864$	−102.971	−	767.313i	−0.119179	−	0.888094i
$865$	740.446	−	230.113i	0.856006	−	0.266026i
$866$	430.245	+	204.952i	0.496819	+	0.236666i
$867$	−240.051	+	240.051i	−0.276876	+	0.276876i
$868$	1427.49	+	1759.20i	1.64457	+	2.02673i
$869$	247.350	+	247.350i	0.284637	+	0.284637i
$870$	−515.812	+	385.773i	−0.592887	+	0.443418i
$871$	−438.716			−0.503693
$872$	−599.684	+	981.899i	−0.687712	+	1.12603i
$873$	−667.591			−0.764709
$874$	41.1424	+	115.998i	0.0470737	+	0.132721i
$875$	191.351	+	1606.62i	0.218687	+	1.83614i
$876$	−79.9529	−	8.32257i	−0.0912704	−	0.00950065i
$877$	12.6291	+	12.6291i	0.0144003	+	0.0144003i	0.714270	−	0.699870i	$-0.246759\pi$
$877$	12.6291	+	12.6291i	0.0144003	+	0.0144003i	−0.699870	+	0.714270i	$0.746759\pi$
$878$	39.7855	−	83.5194i	0.0453137	−	0.0951246i
$879$			415.654i			0.472872i
$880$	−471.129	+	44.3571i	−0.535374	+	0.0504058i
$881$	517.834			0.587780			0.293890	−	0.955839i	$-0.405050\pi$
$881$	517.834			0.587780			0.293890	+	0.955839i	$0.405050\pi$
$882$	1411.07	+	672.179i	1.59985	+	0.762108i
$883$	−834.272	+	834.272i	−0.944815	+	0.944815i	−0.998555	−	0.0537397i	$-0.982886\pi$
$883$	−834.272	+	834.272i	−0.944815	+	0.944815i	0.0537397	+	0.998555i	$0.482886\pi$
$884$	433.853	+	45.1612i	0.490784	+	0.0510874i
$885$	429.664	+	225.923i	0.485496	+	0.255280i
$886$	365.535	−	129.648i	0.412567	−	0.146330i
$887$		−	1239.46i		−	1.39737i	−0.715431	−	0.698683i	$-0.753770\pi$
$887$		−	1239.46i		−	1.39737i	0.715431	−	0.698683i	$-0.246230\pi$
$888$	−83.2496	−	344.483i	−0.0937496	−	0.387931i
$889$			770.211i			0.866379i
$890$	−347.196	+	259.666i	−0.390108	+	0.291760i
$891$	−91.1556	+	91.1556i	−0.102307	+	0.102307i
$892$	383.936	+	473.154i	0.430422	+	0.530442i
$893$	310.824	+	310.824i	0.348067	+	0.348067i
$894$	268.565	−	563.784i	0.300409	−	0.630631i
$895$	−294.730	+	91.5951i	−0.329307	+	0.102341i
$896$	−1656.08	+	49.1662i	−1.84831	+	0.0548730i
$897$			36.4651i			0.0406523i
$898$	−276.172	+	579.752i	−0.307541	+	0.645604i
$899$	1284.42	+	1284.42i	1.42872	+	1.42872i
$900$	−632.381	−	186.296i	−0.702645	−	0.206996i
$901$	828.903	+	828.903i	0.919981	+	0.919981i
$902$	−208.171	+	73.8344i	−0.230788	+	0.0818563i
$903$			410.659i			0.454772i
$904$	−143.528	−	593.911i	−0.158770	−	0.656981i
$905$	790.785	−	245.757i	0.873795	−	0.271555i
$906$	−236.493	−	666.775i	−0.261029	−	0.735955i
$907$	−673.806	−	673.806i	−0.742895	−	0.742895i	0.230239	−	0.973134i	$-0.426049\pi$
$907$	−673.806	−	673.806i	−0.742895	−	0.742895i	−0.973134	+	0.230239i	$0.926049\pi$
$908$	−240.920	−	25.0782i	−0.265330	−	0.0276191i
$909$	−30.3314	+	30.3314i	−0.0333679	+	0.0333679i
$910$	−619.970	−	89.4203i	−0.681286	−	0.0982640i
$911$		−	1705.70i		−	1.87234i	−0.351550	−	0.936169i	$-0.614345\pi$
$911$		−	1705.70i		−	1.87234i	0.351550	−	0.936169i	$-0.385655\pi$
$912$	−64.7903	+	307.840i	−0.0710420	+	0.337544i
$913$			129.487i			0.141826i
$914$	−465.796	+	977.819i	−0.509623	+	1.06982i
$915$	376.245	+	197.835i	0.411197	+	0.216213i
$916$	−15.3133	+	147.111i	−0.0167176	+	0.160602i
$917$	−117.147	+	117.147i	−0.127750	+	0.127750i
$918$	364.486	+	1027.64i	0.397043	+	1.11944i
$919$	1368.08			1.48867			0.744333	−	0.667808i	$-0.232767\pi$
$919$	1368.08			1.48867			0.744333	+	0.667808i	$0.232767\pi$
$920$	188.363	+	47.4885i	0.204742	+	0.0516180i
$921$			119.356i			0.129594i
$922$	127.333	+	359.008i	0.138106	+	0.389379i
$923$	102.227	+	102.227i	0.110755	+	0.110755i
$924$	−299.419	−	368.997i	−0.324046	−	0.399347i
$925$	−701.885	−	129.732i	−0.758794	−	0.140251i
$926$	118.262	−	248.260i	0.127713	−	0.268100i
$927$	586.356			0.632531
$928$	−1316.60	+	176.683i	−1.41875	+	0.190392i
$929$	−705.228			−0.759126			−0.379563	−	0.925166i	$-0.623926\pi$
$929$	−705.228			−0.759126			−0.379563	+	0.925166i	$0.623926\pi$
$930$	96.9211	−	671.975i	0.104216	−	0.722553i
$931$	−1062.17	−	1062.17i	−1.14090	−	1.14090i
$932$	−131.203	−	161.692i	−0.140776	−	0.173489i
$933$	537.566	−	537.566i	0.576169	−	0.576169i
$934$	−30.0440	−	84.7072i	−0.0321671	−	0.0906929i
$935$	636.444	−	197.792i	0.680688	−	0.211542i
$936$	133.027	−	217.813i	0.142123	−	0.232706i
$937$	−1213.49			−1.29508			−0.647542	−	0.762030i	$-0.724203\pi$
$937$	−1213.49			−1.29508			−0.647542	+	0.762030i	$0.724203\pi$
$938$	−2211.91	+	784.523i	−2.35811	+	0.836379i
$939$	572.240	−	572.240i	0.609415	−	0.609415i
$940$	680.285	−	136.197i	0.723707	−	0.144891i
$941$	371.697	−	371.697i	0.395002	−	0.395002i	−0.481464	−	0.876466i	$-0.659895\pi$
$941$	371.697	−	371.697i	0.395002	−	0.395002i	0.876466	+	0.481464i	$0.159895\pi$
$942$	213.179	−	447.514i	0.226305	−	0.475068i
$943$	90.6715			0.0961522
$944$	546.949	+	838.551i	0.579395	+	0.888296i
$945$	−464.685	−	1495.24i	−0.491730	−	1.58226i
$946$	−104.031	+	218.386i	−0.109969	+	0.230852i
$947$	262.936	−	262.936i	0.277652	−	0.277652i	−0.554519	−	0.832171i	$-0.687098\pi$
$947$	262.936	−	262.936i	0.277652	−	0.277652i	0.832171	+	0.554519i	$0.187098\pi$
$948$	38.0002	−	365.058i	0.0400846	−	0.385083i
$949$	−44.3196	−	44.3196i	−0.0467014	−	0.0467014i
$950$	512.949	+	371.905i	0.539946	+	0.391479i
$951$	−528.142			−0.555354
$952$	2268.15	−	548.134i	2.38251	−	0.575771i
$953$	−567.839			−0.595843			−0.297922	−	0.954590i	$-0.596293\pi$
$953$	−567.839			−0.595843			−0.297922	+	0.954590i	$0.596293\pi$
$954$	646.435	−	229.278i	0.677605	−	0.240334i
$955$	1367.55	+	719.075i	1.43199	+	0.752958i
$956$	−731.855	+	593.857i	−0.765539	+	0.621190i
$957$	−269.410	−	269.410i	−0.281516	−	0.281516i
$958$	−1280.87	−	610.160i	−1.33703	−	0.636910i
$959$			1469.04i			1.53185i
$960$	347.615	+	354.529i	0.362099	+	0.369301i
$961$	−953.622			−0.992323
$962$	118.839	−	249.471i	0.123533	−	0.259326i
$963$	229.748	−	229.748i	0.238576	−	0.238576i
$964$	−900.468	−	1109.71i	−0.934095	−	1.15116i
$965$	928.420	+	488.176i	0.962094	+	0.505882i
$966$	65.2079	+	183.849i	0.0675030	+	0.190320i
$967$			769.368i			0.795623i	0.917467	+	0.397812i	$0.130230\pi$
$967$			769.368i			0.795623i	−0.917467	+	0.397812i	$0.869770\pi$
$968$	161.634	+	668.834i	0.166977	+	0.690944i
$969$		−	443.059i		−	0.457233i
$970$	810.939	−	606.498i	0.836020	−	0.625255i
$971$	1185.07	−	1185.07i	1.22046	−	1.22046i	0.252991	−	0.967469i	$-0.418586\pi$
$971$	1185.07	−	1185.07i	1.22046	−	1.22046i	0.967469	−	0.252991i	$-0.0814143\pi$
$972$	1000.82	+	104.179i	1.02965	+	0.107180i
$973$	−317.790	−	317.790i	−0.326609	−	0.326609i
$974$	−378.302	−	180.209i	−0.388401	−	0.185019i
$975$	106.399	+	154.650i	0.109127	+	0.158615i
$976$	478.948	+	734.297i	0.490726	+	0.752353i
$977$			1517.04i			1.55275i	0.630268	+	0.776377i	$0.282945\pi$
$977$			1517.04i			1.55275i	−0.630268	+	0.776377i	$0.717055\pi$
$978$	295.407	+	140.721i	0.302052	+	0.143886i
$979$	−181.342	−	181.342i	−0.185232	−	0.185232i
$980$	−2324.73	+	465.424i	−2.37217	+	0.474923i
$981$	−670.422	−	670.422i	−0.683407	−	0.683407i
$982$	−193.702	−	546.130i	−0.197253	−	0.556141i
$983$			1476.56i			1.50209i	0.660250	+	0.751046i	$0.270450\pi$
$983$			1476.56i			1.50209i	−0.660250	+	0.751046i	$0.729550\pi$
$984$	197.784	+	120.794i	0.201000	+	0.122759i
$985$	296.594	+	954.365i	0.301110	+	0.968898i
$986$	1763.29	−	625.407i	1.78833	−	0.634287i
$987$	492.635	+	492.635i	0.499123	+	0.499123i
$988$	−190.469	+	154.554i	−0.192782	+	0.156431i
$989$	70.2163	−	70.2163i	0.0709972	−	0.0709972i
$990$	55.6687	−	385.963i	0.0562311	−	0.389862i
$991$		−	287.344i		−	0.289953i	−0.989435	−	0.144977i	$-0.953689\pi$
$991$		−	287.344i		−	0.289953i	0.989435	−	0.144977i	$-0.0463107\pi$
$992$	849.611	−	1112.98i	0.856463	−	1.12196i
$993$		−	525.669i		−	0.529375i
$994$	698.209	+	332.600i	0.702424	+	0.334608i
$995$	−77.3551	+	147.115i	−0.0777439	+	0.147854i
$996$	105.500	−	85.6071i	0.105924	−	0.0859510i
$997$	−1060.39	+	1060.39i	−1.06358	+	1.06358i	−0.0657466	+	0.997836i	$0.520943\pi$
$997$	−1060.39	+	1060.39i	−1.06358	+	1.06358i	−0.997836	+	0.0657466i	$0.979057\pi$
$998$	1601.32	−	567.958i	1.60453	−	0.569096i
$999$	690.747			0.691438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.k.a.59.8	yes	44
4.3	odd	2		320.3.k.a.79.9		44
5.2	odd	4		400.3.r.g.251.4		44
5.3	odd	4		400.3.r.g.251.19		44
5.4	even	2	inner	80.3.k.a.59.15	yes	44
8.3	odd	2		640.3.k.a.159.14		44
8.5	even	2		640.3.k.b.159.9		44
16.3	odd	4	inner	80.3.k.a.19.15	yes	44
16.5	even	4		640.3.k.a.479.9		44
16.11	odd	4		640.3.k.b.479.14		44
16.13	even	4		320.3.k.a.239.14		44
20.19	odd	2		320.3.k.a.79.14		44
40.19	odd	2		640.3.k.a.159.9		44
40.29	even	2		640.3.k.b.159.14		44
80.3	even	4		400.3.r.g.51.19		44
80.19	odd	4	inner	80.3.k.a.19.8	✓	44
80.29	even	4		320.3.k.a.239.9		44
80.59	odd	4		640.3.k.b.479.9		44
80.67	even	4		400.3.r.g.51.4		44
80.69	even	4		640.3.k.a.479.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.8	✓	44	80.19	odd	4	inner
80.3.k.a.19.15	yes	44	16.3	odd	4	inner
80.3.k.a.59.8	yes	44	1.1	even	1	trivial
80.3.k.a.59.15	yes	44	5.4	even	2	inner
320.3.k.a.79.9		44	4.3	odd	2
320.3.k.a.79.14		44	20.19	odd	2
320.3.k.a.239.9		44	80.29	even	4
320.3.k.a.239.14		44	16.13	even	4
400.3.r.g.51.4		44	80.67	even	4
400.3.r.g.51.19		44	80.3	even	4
400.3.r.g.251.4		44	5.2	odd	4
400.3.r.g.251.19		44	5.3	odd	4
640.3.k.a.159.9		44	40.19	odd	2
640.3.k.a.159.14		44	8.3	odd	2
640.3.k.a.479.9		44	16.5	even	4
640.3.k.a.479.14		44	80.69	even	4
640.3.k.b.159.9		44	8.5	even	2
640.3.k.b.159.14		44	40.29	even	2
640.3.k.b.479.9		44	80.59	odd	4
640.3.k.b.479.14		44	16.11	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.860120 + 1.80560i) q^{2} +(1.09715 - 1.09715i) q^{3} +(-2.52039 - 3.10607i) q^{4} +(-2.32699 + 4.42551i) q^{5} +(1.03734 + 2.92470i) q^{6} +12.9438i q^{7} +(7.77615 - 1.87923i) q^{8} +6.59251i q^{9} +O(q^{10})\)	\(q+(-0.860120 + 1.80560i) q^{2} +(1.09715 - 1.09715i) q^{3} +(-2.52039 - 3.10607i) q^{4} +(-2.32699 + 4.42551i) q^{5} +(1.03734 + 2.92470i) q^{6} +12.9438i q^{7} +(7.77615 - 1.87923i) q^{8} +6.59251i q^{9} +(-5.98921 - 8.00808i) q^{10} +(4.18265 - 4.18265i) q^{11} +(-6.17308 - 0.642577i) q^{12} +(-3.42187 - 3.42187i) q^{13} +(-23.3714 - 11.1332i) q^{14} +(2.30239 + 7.40853i) q^{15} +(-3.29528 + 15.6570i) q^{16} -22.5343i q^{17} +(-11.9034 - 5.67035i) q^{18} +(8.96024 + 8.96024i) q^{19} +(19.6108 - 3.92621i) q^{20} +(14.2014 + 14.2014i) q^{21} +(3.95462 + 11.1498i) q^{22} -4.85642i q^{23} +(6.46983 - 10.5934i) q^{24} +(-14.1702 - 20.5962i) q^{25} +(9.12175 - 3.23532i) q^{26} +(17.1074 + 17.1074i) q^{27} +(40.2044 - 32.6235i) q^{28} +(29.3539 - 29.3539i) q^{29} +(-15.3572 - 2.21501i) q^{30} +43.7564i q^{31} +(-25.4359 - 19.4168i) q^{32} -9.17802i q^{33} +(40.6879 + 19.3822i) q^{34} +(-57.2830 - 30.1202i) q^{35} +(20.4768 - 16.6157i) q^{36} +(20.1886 - 20.1886i) q^{37} +(-23.8855 + 8.47174i) q^{38} -7.50864 q^{39} +(-9.77849 + 38.7864i) q^{40} +18.6704i q^{41} +(-37.8569 + 13.4271i) q^{42} +(14.4584 + 14.4584i) q^{43} +(-23.5335 - 2.44968i) q^{44} +(-29.1752 - 15.3407i) q^{45} +(8.76876 + 4.17711i) q^{46} +34.6892 q^{47} +(13.5627 + 20.7935i) q^{48} -118.543 q^{49} +(49.3767 - 7.87055i) q^{50} +(-24.7236 - 24.7236i) q^{51} +(-2.00411 + 19.2530i) q^{52} +(-36.7840 + 36.7840i) q^{53} +(-45.6035 + 16.1747i) q^{54} +(8.77736 + 28.2433i) q^{55} +(24.3244 + 100.653i) q^{56} +19.6615 q^{57} +(27.7535 + 78.2492i) q^{58} +(44.2454 - 44.2454i) q^{59} +(17.2084 - 25.8238i) q^{60} +(38.7445 - 38.7445i) q^{61} +(-79.0066 - 37.6357i) q^{62} -85.3324 q^{63} +(56.9370 - 29.2263i) q^{64} +(23.1062 - 7.18085i) q^{65} +(16.5718 + 7.89419i) q^{66} +(64.1047 - 64.1047i) q^{67} +(-69.9930 + 56.7952i) q^{68} +(-5.32824 - 5.32824i) q^{69} +(103.655 - 77.5233i) q^{70} -29.8745 q^{71} +(12.3888 + 51.2643i) q^{72} +12.9519 q^{73} +(19.0879 + 53.8171i) q^{74} +(-38.1441 - 7.05031i) q^{75} +(5.24781 - 50.4144i) q^{76} +(54.1395 + 54.1395i) q^{77} +(6.45833 - 13.5576i) q^{78} +59.1371i q^{79} +(-61.6220 - 51.0170i) q^{80} -21.7938 q^{81} +(-33.7113 - 16.0588i) q^{82} +(-15.4791 + 15.4791i) q^{83} +(8.31741 - 79.9034i) q^{84} +(99.7257 + 52.4371i) q^{85} +(-38.5421 + 13.6702i) q^{86} -64.4114i q^{87} +(24.6648 - 40.3851i) q^{88} -43.3557i q^{89} +(52.7934 - 39.4839i) q^{90} +(44.2922 - 44.2922i) q^{91} +(-15.0844 + 12.2401i) q^{92} +(48.0075 + 48.0075i) q^{93} +(-29.8369 + 62.6349i) q^{94} +(-60.5040 + 18.8032i) q^{95} +(-49.2104 + 6.60385i) q^{96} +101.265i q^{97} +(101.961 - 214.041i) q^{98} +(27.5742 + 27.5742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

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