LMFDB - Embedded newform 570.2.bf.a.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(-0.00201678 - 1.73205i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23914 + 1.86133i) q^{5} +(0.302753 + 1.70539i) q^{6} +(-4.20953 - 2.43037i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99999 + 0.00698632i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.00201678 - 1.73205i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23914 + 1.86133i) q^{5} +(0.302753 + 1.70539i) q^{6} +(-4.20953 - 2.43037i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99999 + 0.00698632i) q^{9} +(0.897098 - 2.04822i) q^{10} +(0.466984 - 0.269614i) q^{11} +(-0.594291 - 1.62690i) q^{12} +(3.83469 + 3.21768i) q^{13} +(4.56760 + 1.66247i) q^{14} +(3.22641 + 2.14250i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.787939 + 4.46862i) q^{17} +(2.95320 - 0.527823i) q^{18} +(2.88507 + 3.26747i) q^{19} +(-0.527799 + 2.17288i) q^{20} +(-4.20103 + 7.29601i) q^{21} +(-0.413072 + 0.346608i) q^{22} +(3.77516 - 1.37404i) q^{23} +(0.867771 + 1.49899i) q^{24} +(-1.92907 - 4.61288i) q^{25} +(-4.33517 - 2.50291i) q^{26} +(0.0181510 + 5.19612i) q^{27} +(-4.78690 - 0.844059i) q^{28} +(-0.161138 + 0.913858i) q^{29} +(-3.54943 - 1.54969i) q^{30} +(4.96339 + 2.86561i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-0.467926 - 0.808296i) q^{33} +(-1.55194 - 4.26391i) q^{34} +(9.73990 - 4.82373i) q^{35} +(-2.81668 + 1.03262i) q^{36} -8.71474 q^{37} +(-3.40863 - 2.71684i) q^{38} +(5.56546 - 6.64836i) q^{39} +(0.142463 - 2.23153i) q^{40} +(-0.823031 + 0.690605i) q^{41} +(2.87027 - 7.91467i) q^{42} +(-4.14232 + 11.3809i) q^{43} +(0.346608 - 0.413072i) q^{44} +(3.70440 - 5.59262i) q^{45} +(-3.47920 + 2.00872i) q^{46} +(1.74721 - 9.90889i) q^{47} +(-1.11488 - 1.32553i) q^{48} +(8.31341 + 14.3993i) q^{49} +(2.70078 + 4.20783i) q^{50} +(7.73828 - 1.37376i) q^{51} +(4.70394 + 1.71209i) q^{52} +(3.29753 + 9.05989i) q^{53} +(-0.920172 - 5.11403i) q^{54} +(-0.0768201 + 1.20330i) q^{55} +4.86074 q^{56} +(5.65360 - 5.00368i) q^{57} -0.927955i q^{58} +(0.0388901 + 0.220557i) q^{59} +(3.76461 + 0.909792i) q^{60} +(-2.38006 + 0.866272i) q^{61} +(-5.38559 - 1.96019i) q^{62} +(12.6455 + 7.26169i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-10.7409 + 3.15044i) q^{65} +(0.601176 + 0.714762i) q^{66} +(-0.877212 + 4.97491i) q^{67} +(2.26878 + 3.92964i) q^{68} +(-2.38753 - 6.53599i) q^{69} +(-8.75430 + 6.44177i) q^{70} +(-3.58325 - 1.30419i) q^{71} +(2.59458 - 1.50605i) q^{72} +(-0.384508 - 0.458239i) q^{73} +(8.58235 - 1.51330i) q^{74} +(-7.98585 + 3.35054i) q^{75} +(3.82862 + 2.08366i) q^{76} -2.62104 q^{77} +(-4.32643 + 7.51379i) q^{78} +(-3.29052 - 3.92149i) q^{79} +(0.247201 + 2.22236i) q^{80} +(8.99990 - 0.0419178i) q^{81} +(0.690605 - 0.823031i) q^{82} +(-3.89026 + 6.73813i) q^{83} +(-1.45230 + 8.29285i) q^{84} +(-9.29393 - 4.07063i) q^{85} +(2.10311 - 11.9273i) q^{86} +(1.58317 + 0.277256i) q^{87} +(-0.269614 + 0.466984i) q^{88} +(3.04459 + 2.55472i) q^{89} +(-2.67698 + 6.15092i) q^{90} +(-8.32205 - 22.8646i) q^{91} +(3.07754 - 2.58236i) q^{92} +(4.95337 - 8.60261i) q^{93} +10.0618i q^{94} +(-9.65683 + 1.32121i) q^{95} +(1.32812 + 1.11180i) q^{96} +(1.78915 + 10.1468i) q^{97} +(-10.6875 - 12.7369i) q^{98} +(-1.39907 + 0.812101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	−0.00201678	−	1.73205i	−0.00116439	−	0.999999i
$3$	−0.00201678	−	1.73205i	−0.00116439	−	0.999999i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.23914	+	1.86133i	−0.554160	+	0.832410i
$5$	−1.23914	+	1.86133i	−0.554160	+	0.832410i
$6$	0.302753	+	1.70539i	0.123599	+	0.696221i
$7$	−4.20953	−	2.43037i	−1.59105	−	0.918594i	−0.993127	−	0.117042i	$-0.962659\pi$
$7$	−4.20953	−	2.43037i	−1.59105	−	0.918594i	−0.597925	−	0.801552i	$-0.704008\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.99999	+	0.00698632i	−0.999997	+	0.00232877i
$10$	0.897098	−	2.04822i	0.283687	−	0.647705i
$11$	0.466984	−	0.269614i	0.140801	−	0.0812915i	−0.427945	−	0.903805i	$-0.640762\pi$
$11$	0.466984	−	0.269614i	0.140801	−	0.0812915i	0.568746	+	0.822513i	$0.307429\pi$
$12$	−0.594291	−	1.62690i	−0.171557	−	0.469647i
$13$	3.83469	+	3.21768i	1.06355	+	0.892425i	0.994453	−	0.105185i	$-0.0335434\pi$
$13$	3.83469	+	3.21768i	1.06355	+	0.892425i	0.0690982	+	0.997610i	$0.477988\pi$
$14$	4.56760	+	1.66247i	1.22074	+	0.444314i
$15$	3.22641	+	2.14250i	0.833055	+	0.553190i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.787939	+	4.46862i	0.191103	+	1.08380i	0.917860	+	0.396905i	$0.129916\pi$
$17$	0.787939	+	4.46862i	0.191103	+	1.08380i	−0.726757	+	0.686895i	$0.758973\pi$
$18$	2.95320	−	0.527823i	0.696076	−	0.124409i
$19$	2.88507	+	3.26747i	0.661881	+	0.749609i
$19$	2.88507	+	3.26747i	0.661881	+	0.749609i
$20$	−0.527799	+	2.17288i	−0.118019	+	0.485872i
$21$	−4.20103	+	7.29601i	−0.916741	+	1.59212i
$22$	−0.413072	+	0.346608i	−0.0880672	+	0.0738972i
$23$	3.77516	−	1.37404i	0.787175	−	0.286508i	0.0830135	−	0.996548i	$-0.473546\pi$
$23$	3.77516	−	1.37404i	0.787175	−	0.286508i	0.704161	+	0.710040i	$0.251323\pi$
$24$	0.867771	+	1.49899i	0.177133	+	0.305980i
$25$	−1.92907	−	4.61288i	−0.385813	−	0.922577i
$26$	−4.33517	−	2.50291i	−0.850198	−	0.490862i
$27$	0.0181510	+	5.19612i	0.00349316	+	0.999994i
$28$	−4.78690	−	0.844059i	−0.904639	−	0.159512i
$29$	−0.161138	+	0.913858i	−0.0299225	+	0.169699i	−0.996107	−	0.0881529i	$-0.971904\pi$
$29$	−0.161138	+	0.913858i	−0.0299225	+	0.169699i	0.966184	+	0.257852i	$0.0830147\pi$
$30$	−3.54943	−	1.54969i	−0.648035	−	0.282933i
$31$	4.96339	+	2.86561i	0.891450	+	0.514679i	0.874417	−	0.485176i	$-0.161244\pi$
$31$	4.96339	+	2.86561i	0.891450	+	0.514679i	0.0170338	+	0.999855i	$0.494578\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−0.467926	−	0.808296i	−0.0814554	−	0.140706i
$34$	−1.55194	−	4.26391i	−0.266155	−	0.731254i
$35$	9.73990	−	4.82373i	1.64634	−	0.815360i
$36$	−2.81668	+	1.03262i	−0.469447	+	0.172104i
$37$	−8.71474			−1.43269			−0.716347	−	0.697744i	$-0.754187\pi$
$37$	−8.71474			−1.43269			−0.716347	+	0.697744i	$0.754187\pi$
$38$	−3.40863	−	2.71684i	−0.552953	−	0.440730i
$39$	5.56546	−	6.64836i	0.891186	−	1.06459i
$40$	0.142463	−	2.23153i	0.0225254	−	0.352835i
$41$	−0.823031	+	0.690605i	−0.128536	+	0.107854i	−0.704789	−	0.709417i	$-0.748959\pi$
$41$	−0.823031	+	0.690605i	−0.128536	+	0.107854i	0.576254	+	0.817271i	$0.304514\pi$
$42$	2.87027	−	7.91467i	0.442893	−	1.22126i
$43$	−4.14232	+	11.3809i	−0.631697	+	1.73557i	0.0446626	+	0.999002i	$0.485779\pi$
$43$	−4.14232	+	11.3809i	−0.631697	+	1.73557i	−0.676360	+	0.736571i	$0.736443\pi$
$44$	0.346608	−	0.413072i	0.0522532	−	0.0622729i
$45$	3.70440	−	5.59262i	0.552220	−	0.833698i
$46$	−3.47920	+	2.00872i	−0.512981	+	0.296169i
$47$	1.74721	−	9.90889i	0.254856	−	1.44536i	−0.541586	−	0.840645i	$-0.682176\pi$
$47$	1.74721	−	9.90889i	0.254856	−	1.44536i	0.796442	−	0.604715i	$-0.206713\pi$
$48$	−1.11488	−	1.32553i	−0.160920	−	0.191324i
$49$	8.31341	+	14.3993i	1.18763	+	2.05704i
$50$	2.70078	+	4.20783i	0.381948	+	0.595076i
$51$	7.73828	−	1.37376i	1.08358	−	0.192365i
$52$	4.70394	+	1.71209i	0.652319	+	0.237425i
$53$	3.29753	+	9.05989i	0.452950	+	1.24447i	0.930638	+	0.365941i	$0.119253\pi$
$53$	3.29753	+	9.05989i	0.452950	+	1.24447i	−0.477687	+	0.878530i	$0.658525\pi$
$54$	−0.920172	−	5.11403i	−0.125220	−	0.695931i
$55$	−0.0768201	+	1.20330i	−0.0103584	+	0.162253i
$56$	4.86074			0.649544
$57$	5.65360	−	5.00368i	0.748838	−	0.662753i
$58$		−	0.927955i		−	0.121847i
$59$	0.0388901	+	0.220557i	0.00506306	+	0.0287141i	0.987235	−	0.159273i	$-0.0509149\pi$
$59$	0.0388901	+	0.220557i	0.00506306	+	0.0287141i	−0.982172	+	0.187987i	$0.939804\pi$
$60$	3.76461	+	0.909792i	0.486009	+	0.117454i
$61$	−2.38006	+	0.866272i	−0.304736	+	0.110915i	−0.489862	−	0.871800i	$-0.662953\pi$
$61$	−2.38006	+	0.866272i	−0.304736	+	0.110915i	0.185126	+	0.982715i	$0.440731\pi$
$62$	−5.38559	−	1.96019i	−0.683971	−	0.248945i
$63$	12.6455	+	7.26169i	1.59319	+	0.914886i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−10.7409	+	3.15044i	−1.33224	+	0.390764i
$66$	0.601176	+	0.714762i	0.0739997	+	0.0879811i
$67$	−0.877212	+	4.97491i	−0.107168	+	0.607783i	0.883164	+	0.469065i	$0.155409\pi$
$67$	−0.877212	+	4.97491i	−0.107168	+	0.607783i	−0.990332	+	0.138717i	$0.955702\pi$
$68$	2.26878	+	3.92964i	0.275130	+	0.476539i
$69$	−2.38753	−	6.53599i	−0.287424	−	0.786840i
$70$	−8.75430	+	6.44177i	−1.04634	+	0.769938i
$71$	−3.58325	−	1.30419i	−0.425253	−	0.154779i	0.120523	−	0.992711i	$-0.461543\pi$
$71$	−3.58325	−	1.30419i	−0.425253	−	0.154779i	−0.545776	+	0.837931i	$0.683765\pi$
$72$	2.59458	−	1.50605i	0.305774	−	0.177489i
$73$	−0.384508	−	0.458239i	−0.0450033	−	0.0536328i	0.743073	−	0.669210i	$-0.233367\pi$
$73$	−0.384508	−	0.458239i	−0.0450033	−	0.0536328i	−0.788077	+	0.615577i	$0.788923\pi$
$74$	8.58235	−	1.51330i	0.997678	−	0.175917i
$75$	−7.98585	+	3.35054i	−0.922127	+	0.386887i
$76$	3.82862	+	2.08366i	0.439173	+	0.239013i
$77$	−2.62104			−0.298696
$78$	−4.32643	+	7.51379i	−0.489872	+	0.850769i
$79$	−3.29052	−	3.92149i	−0.370213	−	0.441202i	0.548487	−	0.836159i	$-0.315204\pi$
$79$	−3.29052	−	3.92149i	−0.370213	−	0.441202i	−0.918700	+	0.394957i	$0.870760\pi$
$80$	0.247201	+	2.22236i	0.0276379	+	0.248468i
$81$	8.99990	−	0.0419178i	0.999989	−	0.00465754i
$82$	0.690605	−	0.823031i	0.0762646	−	0.0908886i
$83$	−3.89026	+	6.73813i	−0.427012	+	0.739606i	−0.996606	−	0.0823202i	$-0.973767\pi$
$83$	−3.89026	+	6.73813i	−0.427012	+	0.739606i	0.569594	+	0.821926i	$0.307100\pi$
$84$	−1.45230	+	8.29285i	−0.158459	+	0.904824i
$85$	−9.29393	−	4.07063i	−1.00807	−	0.441522i
$86$	2.10311	−	11.9273i	0.226784	−	1.28616i
$87$	1.58317	+	0.277256i	0.169734	+	0.0297249i
$88$	−0.269614	+	0.466984i	−0.0287409	+	0.0497807i
$89$	3.04459	+	2.55472i	0.322726	+	0.270799i	0.789728	−	0.613457i	$-0.210222\pi$
$89$	3.04459	+	2.55472i	0.322726	+	0.270799i	−0.467002	+	0.884256i	$0.654666\pi$
$90$	−2.67698	+	6.15092i	−0.282178	+	0.648364i
$91$	−8.32205	−	22.8646i	−0.872388	−	2.39687i
$92$	3.07754	−	2.58236i	0.320855	−	0.269230i
$93$	4.95337	−	8.60261i	0.513641	−	0.892049i
$94$			10.0618i			1.03779i
$95$	−9.65683	+	1.32121i	−0.990770	+	0.135553i
$96$	1.32812	+	1.11180i	0.135551	+	0.113472i
$97$	1.78915	+	10.1468i	0.181661	+	1.03025i	0.930171	+	0.367126i	$0.119658\pi$
$97$	1.78915	+	10.1468i	0.181661	+	1.03025i	−0.748510	+	0.663123i	$0.769231\pi$
$98$	−10.6875	−	12.7369i	−1.07960	−	1.28662i
$99$	−1.39907	+	0.812101i	−0.140611	+	0.0816192i
$100$	−3.39043	−	3.67491i	−0.339043	−	0.367491i
$101$	−6.78906	+	8.09089i	−0.675537	+	0.805073i	−0.989526	−	0.144353i	$-0.953890\pi$
$101$	−6.78906	+	8.09089i	−0.675537	+	0.805073i	0.313990	+	0.949426i	$0.398334\pi$
$102$	−7.38217	+	2.69663i	−0.730944	+	0.267006i
$103$	−0.593156	−	1.02738i	−0.0584454	−	0.101230i	0.835322	−	0.549760i	$-0.185281\pi$
$103$	−0.593156	−	1.02738i	−0.0584454	−	0.101230i	−0.893768	+	0.448530i	$0.851948\pi$
$104$	−4.92978	−	0.869253i	−0.483405	−	0.0852373i
$105$	−8.37459	−	16.8603i	−0.817276	−	1.64539i
$106$	−4.82066	−	8.34964i	−0.468224	−	0.810988i
$107$	4.66124	+	2.69117i	0.450619	+	0.260165i	0.708092	−	0.706121i	$-0.249556\pi$
$107$	4.66124	+	2.69117i	0.450619	+	0.260165i	−0.257473	+	0.966286i	$0.582890\pi$
$108$	1.79423	+	4.87655i	0.172650	+	0.469246i
$109$	2.57506	−	7.07493i	0.246646	−	0.677655i	−0.753157	−	0.657840i	$-0.771470\pi$
$109$	2.57506	−	7.07493i	0.246646	−	0.677655i	0.999804	−	0.0198148i	$-0.00630766\pi$
$110$	−0.133298	−	1.19836i	−0.0127094	−	0.114259i
$111$	0.0175757	+	15.0944i	0.00166821	+	1.43269i
$112$	−4.78690	+	0.844059i	−0.452319	+	0.0797561i
$113$		−	8.06127i		−	0.758341i	−0.925327	−	0.379170i	$-0.876209\pi$
$113$		−	8.06127i		−	0.758341i	0.925327	−	0.379170i	$-0.123791\pi$
$114$	−4.69883	+	5.90940i	−0.440086	+	0.553466i
$115$	−2.12040	+	8.72943i	−0.197728	+	0.814023i
$116$	0.161138	+	0.913858i	0.0149613	+	0.0848495i
$117$	−11.5265	−	9.62624i	−1.06563	−	0.889946i
$118$	−0.0765986	−	0.210453i	−0.00705147	−	0.0193738i
$119$	7.54356	−	20.7258i	0.691517	−	1.89993i
$120$	−3.86540	−	0.242253i	−0.352861	−	0.0221146i
$121$	−5.35462	+	9.27447i	−0.486783	+	0.843134i
$122$	2.19348	−	1.26640i	0.198588	−	0.114655i
$123$	1.19782	+	1.42414i	0.108004	+	0.128410i
$124$	5.64415	+	0.995217i	0.506860	+	0.0893731i
$125$	10.9765	+	2.12538i	0.981765	+	0.190100i
$126$	−13.7144	−	4.95549i	−1.22178	−	0.441470i
$127$	−6.35838	−	5.33532i	−0.564215	−	0.473433i	0.315505	−	0.948924i	$-0.397826\pi$
$127$	−6.35838	−	5.33532i	−0.564215	−	0.473433i	−0.879721	+	0.475491i	$0.842270\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	19.7207	+	7.15174i	1.73631	+	0.629676i
$130$	10.0306	−	4.96771i	0.879744	−	0.435697i
$131$	9.56309	−	1.68623i	0.835531	−	0.147327i	0.260516	−	0.965470i	$-0.416107\pi$
$131$	9.56309	−	1.68623i	0.835531	−	0.147327i	0.575015	+	0.818143i	$0.304996\pi$
$132$	−0.716160	−	0.599510i	−0.0623337	−	0.0521807i
$133$	−4.20362	−	20.7663i	−0.364500	−	1.80067i
$134$		−	5.05166i		−	0.436397i
$135$	−9.69416	−	6.40493i	−0.834341	−	0.551249i
$136$	−2.91669	−	3.47597i	−0.250104	−	0.298062i
$137$	−15.6459	+	5.69464i	−1.33672	+	0.486526i	−0.908778	−	0.417281i	$-0.862983\pi$
$137$	−15.6459	+	5.69464i	−1.33672	+	0.486526i	−0.427941	+	0.903807i	$0.640761\pi$
$138$	3.48622	+	6.02210i	0.296767	+	0.512635i
$139$	5.63695	+	4.72996i	0.478120	+	0.401190i	0.849746	−	0.527192i	$-0.176755\pi$
$139$	5.63695	+	4.72996i	0.478120	+	0.401190i	−0.371626	+	0.928383i	$0.621200\pi$
$140$	7.50270	−	7.86407i	0.634094	−	0.664635i
$141$	−17.1662	−	3.00626i	−1.44566	−	0.253173i
$142$	3.75528	+	0.662157i	0.315136	+	0.0555670i
$143$	2.65827	+	0.468725i	0.222296	+	0.0391967i
$144$	−2.29364	+	1.93371i	−0.191136	+	0.161142i
$145$	−1.50131	−	1.43233i	−0.124677	−	0.118948i
$146$	0.458239	+	0.384508i	0.0379241	+	0.0318221i
$147$	24.9235	−	14.4283i	2.05565	−	1.19002i
$148$	−8.18918	+	2.98062i	−0.673146	+	0.245005i
$149$	3.94833	+	4.70544i	0.323460	+	0.385484i	0.903130	−	0.429367i	$-0.141263\pi$
$149$	3.94833	+	4.70544i	0.323460	+	0.385484i	−0.579671	+	0.814851i	$0.696819\pi$
$150$	7.28271	−	4.68637i	0.594631	−	0.382640i
$151$		−	14.0203i		−	1.14095i	−0.821313	−	0.570477i	$-0.806758\pi$
$151$		−	14.0203i		−	1.14095i	0.821313	−	0.570477i	$-0.193242\pi$
$152$	−4.13228	−	1.38718i	−0.335172	−	0.112515i
$153$	−2.39503	−	13.4003i	−0.193627	−	1.08335i
$154$	2.58122	−	0.455140i	0.208001	−	0.0366762i
$155$	−11.4842	+	5.68758i	−0.922430	+	0.456838i
$156$	2.95595	−	8.15091i	0.236665	−	0.652595i
$157$	1.49550	−	4.10885i	0.119354	−	0.327922i	−0.865601	−	0.500735i	$-0.833063\pi$
$157$	1.49550	−	4.10885i	0.119354	−	0.327922i	0.984955	+	0.172813i	$0.0552855\pi$
$158$	3.92149	+	3.29052i	0.311977	+	0.261780i
$159$	15.6855	−	5.72976i	1.24394	−	0.454399i
$160$	−0.629355	−	2.14567i	−0.0497549	−	0.169630i
$161$	−19.2311	−	3.39096i	−1.51562	−	0.267245i
$162$	−8.85589	+	1.60410i	−0.695785	+	0.126030i
$163$	2.67537	−	1.54463i	0.209551	−	0.120985i	−0.391552	−	0.920156i	$-0.628062\pi$
$163$	2.67537	−	1.54463i	0.209551	−	0.120985i	0.601103	+	0.799172i	$0.294728\pi$
$164$	−0.537195	+	0.930450i	−0.0419479	+	0.0726559i
$165$	2.08433	+	0.130629i	0.162265	+	0.0101695i
$166$	2.66109	−	7.31130i	0.206541	−	0.567467i
$167$	5.83488	+	16.0312i	0.451517	+	1.24053i	0.931657	+	0.363340i	$0.118364\pi$
$167$	5.83488	+	16.0312i	0.451517	+	1.24053i	−0.480140	+	0.877192i	$0.659414\pi$
$168$	−0.00980305	−	8.41905i	−0.000756321	−	0.649544i
$169$	2.09391	+	11.8751i	0.161070	+	0.913471i
$170$	9.85959	+	2.39492i	0.756196	+	0.183682i
$171$	−8.67802	−	9.78223i	−0.663625	−	0.748066i
$172$			12.1113i			0.923479i
$173$	−5.14940	+	0.907978i	−0.391502	+	0.0690323i	−0.365934	−	0.930641i	$-0.619250\pi$
$173$	−5.14940	+	0.907978i	−0.391502	+	0.0690323i	−0.0255677	+	0.999673i	$0.508139\pi$
$174$	−1.60726	+	0.00187148i	−0.121846	+	0.000141877i
$175$	−3.09056	+	24.1064i	−0.233625	+	1.82227i
$176$	0.184427	−	0.506708i	0.0139017	−	0.0381945i
$177$	0.381937	−	0.0678045i	0.0287081	−	0.00509650i
$178$	−3.44196	−	1.98722i	−0.257986	−	0.148948i
$179$	−10.6381	−	18.4257i	−0.795127	−	1.37720i	−0.922759	−	0.385378i	$-0.874071\pi$
$179$	−10.6381	−	18.4257i	−0.795127	−	1.37720i	0.127632	−	0.991822i	$-0.459262\pi$
$180$	1.56821	−	6.52232i	0.116888	−	0.486145i
$181$	−2.70329	−	0.476664i	−0.200934	−	0.0354301i	0.0722751	−	0.997385i	$-0.476974\pi$
$181$	−2.70329	−	0.476664i	−0.200934	−	0.0354301i	−0.273209	+	0.961955i	$0.588085\pi$
$182$	12.1660	+	21.0722i	0.901806	+	1.56197i
$183$	1.50523	+	4.12064i	0.111269	+	0.304606i
$184$	−2.58236	+	3.07754i	−0.190374	+	0.226879i
$185$	10.7988	−	16.2210i	0.793942	−	1.19259i
$186$	−3.38429	+	9.33206i	−0.248148	+	0.684260i
$187$	1.57276	+	1.87434i	0.115011	+	0.137065i
$188$	−1.74721	−	9.90889i	−0.127428	−	0.722680i
$189$	12.5521	−	21.9173i	0.913031	−	1.59425i
$190$	9.28070	−	2.97803i	0.673293	−	0.216049i
$191$			3.59987i			0.260477i	0.991483	+	0.130239i	$0.0415743\pi$
$191$			3.59987i			0.260477i	−0.991483	+	0.130239i	$0.958426\pi$
$192$	−1.50101	−	0.864278i	−0.108326	−	0.0623739i
$193$	15.4785	−	12.9880i	1.11417	−	0.934896i	0.115870	−	0.993264i	$-0.463034\pi$
$193$	15.4785	−	12.9880i	1.11417	−	0.934896i	0.998295	+	0.0583686i	$0.0185899\pi$
$194$	−3.52394	−	9.68194i	−0.253004	−	0.695123i
$195$	5.47838	+	18.5974i	0.392315	+	1.33179i
$196$	12.7369	+	10.6875i	0.909778	+	0.763394i
$197$	−0.740333	+	1.28229i	−0.0527465	+	0.0913597i	−0.891193	−	0.453624i	$-0.850131\pi$
$197$	−0.740333	+	1.28229i	−0.0527465	+	0.0913597i	0.838447	+	0.544984i	$0.183464\pi$
$198$	1.23679	−	1.04271i	0.0878949	−	0.0741021i
$199$	−1.87199	+	10.6166i	−0.132702	+	0.752588i	0.843731	+	0.536766i	$0.180354\pi$
$199$	−1.87199	+	10.6166i	−0.132702	+	0.752588i	−0.976433	+	0.215822i	$0.930757\pi$
$200$	3.97706	+	3.03034i	0.281221	+	0.214277i
$201$	8.61857	+	1.50934i	0.607907	+	0.106461i
$202$	5.28095	−	9.14687i	0.371566	−	0.643572i
$203$	2.89933	−	3.45528i	0.203493	−	0.242513i
$204$	6.80176	−	3.93756i	0.476218	−	0.275684i
$205$	−0.265591	−	2.38768i	−0.0185497	−	0.166763i
$206$	0.762546	+	0.908767i	0.0531291	+	0.0633168i
$207$	−11.3158	+	4.14850i	−0.786505	+	0.288340i
$208$	5.00583			0.347092
$209$	2.22824	+	0.748003i	0.154130	+	0.0517404i
$210$	11.1751	+	15.1499i	0.771156	+	1.04544i
$211$	−9.77676	+	1.72391i	−0.673060	+	0.118679i	−0.499725	−	0.866184i	$-0.666566\pi$
$211$	−9.77676	+	1.72391i	−0.673060	+	0.118679i	−0.173335	+	0.984863i	$0.555454\pi$
$212$	6.19733	+	7.38569i	0.425634	+	0.507251i
$213$	−2.25170	+	6.20899i	−0.154284	+	0.425433i
$214$	−5.05774	−	1.84087i	−0.345740	−	0.125839i
$215$	−16.0507	−	21.8127i	−1.09465	−	1.48762i
$216$	−2.61378	−	4.49090i	−0.177845	−	0.305567i
$217$	−13.9290	−	24.1257i	−0.945562	−	1.63776i
$218$	−1.30739	+	7.41460i	−0.0885479	+	0.502180i
$219$	−0.792918	+	0.666912i	−0.0535804	+	0.0450657i
$220$	0.339365	+	1.15700i	0.0228800	+	0.0780053i
$221$	−11.3571	+	19.6711i	−0.763962	+	1.32322i
$222$	−2.63842	−	14.8620i	−0.177079	−	0.997472i
$223$	−14.2315	−	5.17985i	−0.953014	−	0.346869i	−0.181722	−	0.983350i	$-0.558167\pi$
$223$	−14.2315	−	5.17985i	−0.953014	−	0.346869i	−0.771292	+	0.636481i	$0.780389\pi$
$224$	4.56760	−	1.66247i	0.305186	−	0.111079i
$225$	5.81941	+	13.8251i	0.387961	+	0.921676i
$226$	1.39983	+	7.93881i	0.0931150	+	0.528082i
$227$			20.9974i			1.39365i	0.717243	+	0.696823i	$0.245404\pi$
$227$			20.9974i			1.39365i	−0.717243	+	0.696823i	$0.754596\pi$
$228$	3.60129	−	6.63556i	0.238501	−	0.439451i
$229$	−24.8343			−1.64110			−0.820549	−	0.571577i	$-0.806332\pi$
$229$	−24.8343			−1.64110			−0.820549	+	0.571577i	$0.806332\pi$
$230$	0.572338	−	8.96501i	0.0377388	−	0.591135i
$231$	0.00528607	+	4.53978i	0.000347798	+	0.298696i
$232$	−0.317379	−	0.871993i	−0.0208370	−	0.0572491i
$233$	27.2033	+	9.90120i	1.78215	+	0.648649i	0.999662	+	0.0259809i	$0.00827090\pi$
$233$	27.2033	+	9.90120i	1.78215	+	0.648649i	0.782486	+	0.622668i	$0.213951\pi$
$234$	13.0230	+	7.47844i	0.851339	+	0.488881i
$235$	16.2786	+	15.5306i	1.06190	+	1.01311i
$236$	0.111980	+	0.193954i	0.00728926	+	0.0126254i
$237$	−6.78558	+	5.70726i	−0.440771	+	0.370726i
$238$	−3.82997	+	21.7208i	−0.248260	+	1.40795i
$239$	−21.5476	+	12.4405i	−1.39380	+	0.804711i	−0.993733	−	0.111776i	$-0.964346\pi$
$239$	−21.5476	+	12.4405i	−1.39380	+	0.804711i	−0.400066	+	0.916486i	$0.631013\pi$
$240$	3.84874	−	0.432647i	0.248435	−	0.0279272i
$241$	1.69599	−	2.02121i	0.109248	−	0.130197i	−0.708649	−	0.705561i	$-0.750695\pi$
$241$	1.69599	−	2.02121i	0.109248	−	0.130197i	0.817898	+	0.575364i	$0.195140\pi$
$242$	3.66277	−	10.0634i	0.235452	−	0.646899i
$243$	−0.0907546	−	15.5882i	−0.00582191	−	0.999983i
$244$	−1.94024	+	1.62806i	−0.124211	+	0.104226i
$245$	−37.1032	−	2.36871i	−2.37044	−	0.151332i
$246$	−1.42692	−	1.19450i	−0.0909773	−	0.0761587i
$247$	0.549661	+	21.8130i	0.0349741	+	1.38793i
$248$	−5.73122			−0.363933
$249$	11.6786	+	6.72454i	0.740102	+	0.426150i
$250$	−11.1788	−	0.187052i	−0.707008	−	0.0118302i
$251$	8.08613	+	22.2164i	0.510392	+	1.40229i	0.880830	+	0.473433i	$0.156985\pi$
$251$	8.08613	+	22.2164i	0.510392	+	1.40229i	−0.370438	+	0.928857i	$0.620793\pi$
$252$	14.3666	+	2.49873i	0.905008	+	0.157405i
$253$	1.39248	−	1.65949i	0.0875443	−	0.104331i
$254$	7.18825	+	4.15014i	0.451031	+	0.260403i
$255$	−7.03180	+	16.1058i	−0.440348	+	1.00858i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−22.7974	−	4.01980i	−1.42206	−	0.250748i	−0.590887	−	0.806755i	$-0.701222\pi$
$257$	−22.7974	−	4.01980i	−1.42206	−	0.250748i	−0.831178	+	0.556006i	$0.812333\pi$
$258$	−20.6630	−	3.61863i	−1.28642	−	0.225286i
$259$	36.6849	+	21.1801i	2.27949	+	1.31607i
$260$	−9.01560	+	6.63404i	−0.559124	+	0.411426i
$261$	0.477027	−	2.74269i	0.0295273	−	0.169768i
$262$	−9.12499	+	3.32123i	−0.563744	+	0.205186i
$263$	17.4891	−	14.6751i	1.07842	−	0.904903i	0.0826329	−	0.996580i	$-0.473667\pi$
$263$	17.4891	−	14.6751i	1.07842	−	0.904903i	0.995789	+	0.0916768i	$0.0292227\pi$
$264$	0.809384	+	0.466042i	0.0498141	+	0.0286829i
$265$	−20.9495	−	5.08869i	−1.28692	−	0.312596i
$266$	7.74579	+	19.7209i	0.474925	+	1.20916i
$267$	4.41875	−	5.27854i	0.270423	−	0.323041i
$268$	0.877212	+	4.97491i	0.0535842	+	0.303891i
$269$	15.2597	−	12.8044i	0.930401	−	0.780699i	−0.0454880	−	0.998965i	$-0.514484\pi$
$269$	15.2597	−	12.8044i	0.930401	−	0.780699i	0.975889	+	0.218265i	$0.0700398\pi$
$270$	10.6591	+	4.62425i	0.648692	+	0.281423i
$271$	−4.43514	−	1.61426i	−0.269415	−	0.0980592i	0.203780	−	0.979017i	$-0.434677\pi$
$271$	−4.43514	−	1.61426i	−0.269415	−	0.0980592i	−0.473195	+	0.880958i	$0.656900\pi$
$272$	3.47597	+	2.91669i	0.210762	+	0.176850i
$273$	−39.5859	+	14.4603i	−2.39585	+	0.875178i
$274$	14.4193	−	8.32501i	0.871104	−	0.502932i
$275$	−2.14454	−	1.63404i	−0.129321	−	0.0985364i
$276$	−4.47898	−	5.32524i	−0.269603	−	0.320542i
$277$	11.5083	−	6.64433i	0.691467	−	0.399219i	−0.112694	−	0.993630i	$-0.535948\pi$
$277$	11.5083	−	6.64433i	0.691467	−	0.399219i	0.804161	+	0.594411i	$0.202615\pi$
$278$	−6.37266	−	3.67926i	−0.382207	−	0.220667i
$279$	−14.9101	−	8.56214i	−0.892647	−	0.512602i
$280$	−6.02314	+	9.04743i	−0.359951	+	0.540687i
$281$	−1.15739	+	0.421254i	−0.0690439	+	0.0251299i	−0.376311	−	0.926493i	$-0.622808\pi$
$281$	−1.15739	+	0.421254i	−0.0690439	+	0.0251299i	0.307267	+	0.951623i	$0.400585\pi$
$282$	17.4275	−	0.0202923i	1.03779	−	0.00120839i
$283$	2.92788	−	0.516264i	0.174044	−	0.0306887i	−0.0859467	−	0.996300i	$-0.527391\pi$
$283$	2.92788	−	0.516264i	0.174044	−	0.0306887i	0.259991	+	0.965611i	$0.416280\pi$
$284$	−3.81321			−0.226272
$285$	2.30787	+	16.7234i	0.136707	+	0.990612i
$286$	−2.69928			−0.159612
$287$	5.14300	−	0.906849i	0.303582	−	0.0535296i
$288$	1.92301	−	2.30262i	0.113314	−	0.135683i
$289$	−3.37296	+	1.22766i	−0.198409	+	0.0722150i
$290$	1.72723	+	1.14987i	0.101426	+	0.0675225i
$291$	17.5711	−	3.11936i	1.03004	−	0.182860i
$292$	−0.518047	−	0.299094i	−0.0303164	−	0.0175032i
$293$	−0.268843	+	0.155217i	−0.0157060	+	0.00906785i	−0.507832	−	0.861456i	$-0.669553\pi$
$293$	−0.268843	+	0.155217i	−0.0157060	+	0.00906785i	0.492126	+	0.870524i	$0.336220\pi$
$294$	−22.0394	+	18.5370i	−1.28536	+	1.08110i
$295$	−0.458719	−	0.200914i	−0.0267076	−	0.0116976i
$296$	7.54719	−	4.35737i	0.438671	−	0.253267i
$297$	1.40942	+	2.42161i	0.0817829	+	0.140516i
$298$	−4.70544	−	3.94833i	−0.272579	−	0.228721i
$299$	18.8978	+	6.87823i	1.09289	+	0.397778i
$300$	−6.35829	+	5.87980i	−0.367096	+	0.339471i
$301$	45.0970	−	37.8409i	2.59935	−	2.18111i
$302$	2.43460	+	13.8073i	0.140095	+	0.794520i
$303$	14.0275	+	11.7427i	0.805859	+	0.674599i
$304$	4.31038	+	0.648539i	0.247217	+	0.0371962i
$305$	1.33681	−	5.50350i	0.0765458	−	0.315130i
$306$	4.68558	+	12.7808i	0.267857	+	0.730633i
$307$	11.1256	−	9.33548i	0.634971	−	0.532804i	−0.267498	−	0.963558i	$-0.586197\pi$
$307$	11.1256	−	9.33548i	0.634971	−	0.532804i	0.902469	+	0.430755i	$0.141753\pi$
$308$	−2.46298	+	0.896450i	−0.140341	+	0.0510800i
$309$	−1.77827	+	1.02945i	−0.101162	+	0.0585632i
$310$	10.3221	−	7.59538i	0.586253	−	0.431389i
$311$	17.3043	+	9.99063i	0.981236	+	0.566517i	0.902643	−	0.430390i	$-0.141624\pi$
$311$	17.3043	+	9.99063i	0.981236	+	0.566517i	0.0785927	+	0.996907i	$0.474957\pi$
$312$	−1.49565	+	8.54037i	−0.0846743	+	0.483504i
$313$	26.9946	+	4.75988i	1.52583	+	0.269044i	0.872720	−	0.488221i	$-0.162354\pi$
$313$	26.9946	+	4.75988i	1.52583	+	0.269044i	0.653107	+	0.757266i	$0.273465\pi$
$314$	−0.759285	+	4.30612i	−0.0428489	+	0.243008i
$315$	−29.1859	+	14.5392i	−1.64444	+	0.819191i
$316$	−4.43331	−	2.55957i	−0.249393	−	0.143987i
$317$	−8.51418	+	10.1468i	−0.478204	+	0.569901i	−0.950177	−	0.311712i	$-0.899098\pi$
$317$	−8.51418	+	10.1468i	−0.478204	+	0.569901i	0.471973	+	0.881613i	$0.343542\pi$
$318$	−14.4523	+	8.36647i	−0.810443	+	0.469168i
$319$	0.171140	+	0.470202i	0.00958198	+	0.0263263i
$320$	0.992386	+	2.00379i	0.0554760	+	0.112015i
$321$	4.65184	−	8.07893i	0.259640	−	0.450922i
$322$	19.5277			1.08824
$323$	−12.3278	+	15.4669i	−0.685939	+	0.860599i
$324$	8.44281	−	3.11754i	0.469045	−	0.173197i
$325$	7.44544	−	23.8961i	0.412999	−	1.32552i
$326$	−2.36651	+	1.98573i	−0.131069	+	0.109980i
$327$	−12.2593	−	4.44587i	−0.677942	−	0.245857i
$328$	0.367463	−	1.00960i	0.0202898	−	0.0557457i
$329$	−31.4372	+	37.4654i	−1.73319	+	2.06553i
$330$	−2.07535	+	0.233295i	−0.114244	+	0.0128425i
$331$	−2.64266	+	1.52574i	−0.145254	+	0.0838622i	−0.570865	−	0.821044i	$-0.693392\pi$
$331$	−2.64266	+	1.52574i	−0.145254	+	0.0838622i	0.425612	+	0.904906i	$0.360059\pi$
$332$	−1.35107	+	7.66232i	−0.0741498	+	0.420524i
$333$	26.1442	−	0.0608840i	1.43269	−	0.00333642i
$334$	−8.53002	−	14.7744i	−0.466742	−	0.808421i
$335$	−8.17295	−	7.79739i	−0.446536	−	0.426017i
$336$	1.47161	+	8.28944i	0.0802827	+	0.452226i
$337$	19.9154	+	7.24861i	1.08486	+	0.394857i	0.821715	−	0.569899i	$-0.193018\pi$
$337$	19.9154	+	7.24861i	1.08486	+	0.394857i	0.263146	+	0.964756i	$0.415240\pi$
$338$	−4.12419	−	11.3311i	−0.224326	−	0.616331i
$339$	−13.9625	+	0.0162578i	−0.758340	+	0.000883003i
$340$	−10.1257	−	0.646435i	−0.549142	−	0.0350579i
$341$	3.09043			0.167356
$342$	10.2448	+	8.12669i	0.553978	+	0.439441i
$343$		−	46.7935i		−	2.52661i
$344$	−2.10311	−	11.9273i	−0.113392	−	0.643078i
$345$	15.1241	+	3.65503i	0.814253	+	0.196780i
$346$	4.91350	−	1.78837i	0.264152	−	0.0961433i
$347$	28.5211	+	10.3808i	1.53109	+	0.557272i	0.963889	−	0.266305i	$-0.0858030\pi$
$347$	28.5211	+	10.3808i	1.53109	+	0.557272i	0.567204	+	0.823578i	$0.308025\pi$
$348$	1.58252	−	0.280942i	0.0848321	−	0.0150601i
$349$	5.84357	−	10.1214i	0.312799	−	0.541784i	−0.666168	−	0.745802i	$-0.732067\pi$
$349$	5.84357	−	10.1214i	0.312799	−	0.541784i	0.978967	+	0.204018i	$0.0654001\pi$
$350$	−1.14242	−	24.2769i	−0.0610652	−	1.29765i
$351$	−16.6499	+	19.9839i	−0.888705	+	1.06666i
$352$	−0.0936358	+	0.531035i	−0.00499080	+	0.0283043i
$353$	−12.4926	−	21.6378i	−0.664913	−	1.15166i	−0.979309	−	0.202371i	$-0.935135\pi$
$353$	−12.4926	−	21.6378i	−0.664913	−	1.15166i	0.314396	−	0.949292i	$-0.398198\pi$
$354$	−0.364360	+	0.133097i	−0.0193655	+	0.00707403i
$355$	6.86767	−	5.05351i	0.364498	−	0.268212i
$356$	3.73474	+	1.35934i	0.197941	+	0.0720447i
$357$	−35.9133	−	13.0240i	−1.90073	−	0.689304i
$358$	13.6760	+	16.2985i	0.722801	+	0.861401i
$359$	−5.72944	+	1.01026i	−0.302388	+	0.0533192i	−0.322784	−	0.946473i	$-0.604619\pi$
$359$	−5.72944	+	1.01026i	−0.302388	+	0.0533192i	0.0203953	+	0.999792i	$0.493508\pi$
$360$	−0.411799	+	6.69555i	−0.0217037	+	0.352887i
$361$	−2.35272	+	18.8538i	−0.123827	+	0.992304i
$362$	2.74500			0.144274
$363$	16.0746	+	9.25576i	0.843700	+	0.485801i
$364$	−15.6403	−	18.6394i	−0.819777	−	0.976972i
$365$	1.32939	−	0.147873i	0.0695836	−	0.00774003i
$366$	−2.19790	−	3.79666i	−0.114886	−	0.198454i
$367$	14.1622	−	16.8778i	0.739259	−	0.881014i	−0.257090	−	0.966387i	$-0.582764\pi$
$367$	14.1622	−	16.8778i	0.739259	−	0.881014i	0.996349	+	0.0853731i	$0.0272082\pi$
$368$	2.00872	−	3.47920i	0.104712	−	0.181366i
$369$	2.46426	−	2.07756i	0.128284	−	0.108153i
$370$	−7.81798	+	17.8497i	−0.406437	+	0.927963i
$371$	8.13785	−	46.1521i	0.422496	−	2.39610i
$372$	1.71238	−	9.77796i	0.0887829	−	0.506964i
$373$	−5.96781	+	10.3366i	−0.309002	+	0.535207i	−0.978144	−	0.207927i	$-0.933328\pi$
$373$	−5.96781	+	10.3366i	−0.309002	+	0.535207i	0.669143	+	0.743134i	$0.266662\pi$
$374$	−1.87434	−	1.57276i	−0.0969197	−	0.0813253i
$375$	3.65913	−	19.0161i	0.188957	−	0.981985i
$376$	3.44132	+	9.45496i	0.177473	+	0.487602i
$377$	−3.55842	+	2.98587i	−0.183268	+	0.153780i
$378$	−8.55550	+	23.7640i	−0.440047	+	1.22229i
$379$			5.88480i			0.302282i	0.988512	+	0.151141i	$0.0482947\pi$
$379$			5.88480i			0.302282i	−0.988512	+	0.151141i	$0.951705\pi$
$380$	−8.62257	+	4.54436i	−0.442329	+	0.233121i
$381$	−9.22821	+	11.0238i	−0.472776	+	0.564766i
$382$	−0.625110	−	3.54518i	−0.0319834	−	0.181387i
$383$	−21.5007	−	25.6235i	−1.09863	−	1.30930i	−0.947133	−	0.320841i	$-0.896034\pi$
$383$	−21.5007	−	25.6235i	−1.09863	−	1.30930i	−0.151499	−	0.988457i	$-0.548410\pi$
$384$	1.62828	+	0.590501i	0.0830930	+	0.0301339i
$385$	3.24784	−	4.87862i	0.165525	−	0.248637i
$386$	−12.9880	+	15.4785i	−0.661071	+	0.787834i
$387$	12.3474	−	34.1716i	0.627654	−	1.73704i
$388$	5.15165	+	8.92293i	0.261536	+	0.452993i
$389$	23.6912	+	4.17740i	1.20119	+	0.211803i	0.738214	−	0.674567i	$-0.235670\pi$
$389$	23.6912	+	4.17740i	1.20119	+	0.211803i	0.462978	+	0.886370i	$0.346781\pi$
$390$	−8.62455	−	17.3635i	−0.436721	−	0.879236i
$391$	9.11468	+	15.7871i	0.460949	+	0.798387i
$392$	−14.3993	−	8.31341i	−0.727272	−	0.419891i
$393$	−2.93992	−	16.5603i	−0.148299	−	0.835359i
$394$	0.506418	−	1.39137i	0.0255129	−	0.0700962i
$395$	11.3766	−	1.26546i	0.572418	−	0.0636721i
$396$	−1.03694	+	1.24163i	−0.0521080	+	0.0623945i
$397$	12.6978	−	2.23897i	0.637285	−	0.112370i	0.154335	−	0.988019i	$-0.450677\pi$
$397$	12.6978	−	2.23897i	0.637285	−	0.112370i	0.482950	+	0.875648i	$0.339565\pi$
$398$		−	10.7803i		−	0.540370i
$399$	−35.9598	+	7.32276i	−1.80024	+	0.366597i
$400$	−4.44286	−	2.29369i	−0.222143	−	0.114685i
$401$	−0.169356	−	0.960468i	−0.00845726	−	0.0479635i	0.980287	−	0.197578i	$-0.0633077\pi$
$401$	−0.169356	−	0.960468i	−0.00845726	−	0.0479635i	−0.988744	+	0.149615i	$0.952197\pi$
$402$	−8.74973	+	0.0101881i	−0.436397	+	0.000508135i
$403$	9.81240	+	26.9593i	0.488790	+	1.34294i
$404$	−3.61238	+	9.92494i	−0.179723	+	0.493784i
$405$	−11.0741	+	16.8037i	−0.550277	+	0.834982i
$406$	−2.25528	+	3.90625i	−0.111927	+	0.193864i
$407$	−4.06965	+	2.34961i	−0.201725	+	0.116466i
$408$	−6.01467	+	5.05885i	−0.297771	+	0.250451i
$409$	−25.6614	−	4.52480i	−1.26888	−	0.223737i	−0.501626	−	0.865085i	$-0.667264\pi$
$409$	−25.6614	−	4.52480i	−1.26888	−	0.223737i	−0.767250	+	0.641348i	$0.778376\pi$
$410$	0.676173	+	2.30529i	0.0333938	+	0.113850i
$411$	9.89495	+	27.0880i	0.488082	+	1.33615i
$412$	−0.908767	−	0.762546i	−0.0447717	−	0.0375679i
$413$	0.372326	−	1.02296i	0.0183210	−	0.0503365i
$414$	10.4235	−	6.05045i	0.512289	−	0.297363i
$415$	−7.72128	−	15.5905i	−0.379023	−	0.765309i
$416$	−4.92978	+	0.869253i	−0.241702	+	0.0426186i
$417$	8.18116	−	9.77302i	0.400633	−	0.478587i
$418$	−2.32428	−	0.349710i	−0.113684	−	0.0171049i
$419$		−	9.76360i		−	0.476983i	−0.971145	−	0.238491i	$-0.923347\pi$
$419$		−	9.76360i		−	0.476983i	0.971145	−	0.238491i	$-0.0766529\pi$
$420$	−13.6361	−	12.9792i	−0.665373	−	0.633320i
$421$	7.60520	+	9.06353i	0.370655	+	0.441729i	0.918842	−	0.394627i	$-0.129126\pi$
$421$	7.60520	+	9.06353i	0.370655	+	0.441729i	−0.548187	+	0.836356i	$0.684682\pi$
$422$	9.32888	−	3.39543i	0.454123	−	0.165287i
$423$	−5.17237	+	29.7388i	−0.251489	+	1.44595i
$424$	−7.38569	−	6.19733i	−0.358681	−	0.300969i
$425$	19.0932	−	12.2549i	0.926158	−	0.594452i
$426$	1.13932	−	6.50566i	0.0552000	−	0.315200i
$427$	12.1243	+	2.13784i	0.586736	+	0.103457i
$428$	5.30057	+	0.934633i	0.256213	+	0.0451772i
$429$	0.806493	−	4.60520i	0.0389379	−	0.222341i
$430$	19.5946	+	18.6942i	0.944935	+	0.901514i
$431$	−12.0700	−	10.1280i	−0.581394	−	0.487847i	0.304011	−	0.952669i	$-0.401674\pi$
$431$	−12.0700	−	10.1280i	−0.581394	−	0.487847i	−0.885405	+	0.464821i	$0.846119\pi$
$432$	3.35391	+	3.96879i	0.161365	+	0.190949i
$433$	−4.70348	+	1.71193i	−0.226035	+	0.0822700i	−0.452555	−	0.891737i	$-0.649487\pi$
$433$	−4.70348	+	1.71193i	−0.226035	+	0.0822700i	0.226520	+	0.974007i	$0.427265\pi$
$434$	17.9068	+	21.3405i	0.859553	+	1.02438i
$435$	−2.47783	+	2.60324i	−0.118803	+	0.124816i
$436$		−	7.52898i		−	0.360573i
$437$	15.3812	+	8.37099i	0.735785	+	0.400439i
$438$	0.665063	−	0.794469i	0.0317780	−	0.0379612i
$439$	5.31334	−	0.936885i	0.253592	−	0.0447151i	−0.0454070	−	0.998969i	$-0.514458\pi$
$439$	5.31334	−	0.936885i	0.253592	−	0.0447151i	0.298999	+	0.954254i	$0.403347\pi$
$440$	−0.535121	−	1.08050i	−0.0255109	−	0.0515107i
$441$	−25.0408	−	43.1396i	−1.19242	−	2.05426i
$442$	7.76873	−	21.3444i	0.369521	−	1.01525i
$443$	12.2783	+	10.3027i	0.583361	+	0.489498i	0.886049	−	0.463592i	$-0.153439\pi$
$443$	12.2783	+	10.3027i	0.583361	+	0.489498i	−0.302688	+	0.953090i	$0.597884\pi$
$444$	5.17909	+	14.1781i	0.245789	+	0.672861i
$445$	−8.52783	+	2.50133i	−0.404258	+	0.118574i
$446$	14.9148	+	2.62988i	0.706236	+	0.124528i
$447$	8.14209	−	6.84819i	0.385107	−	0.323908i
$448$	−4.20953	+	2.43037i	−0.198881	+	0.114824i
$449$	−18.7328	+	32.4461i	−0.884055	+	1.53123i	−0.0372619	+	0.999306i	$0.511864\pi$
$449$	−18.7328	+	32.4461i	−0.884055	+	1.53123i	−0.846793	+	0.531923i	$0.821470\pi$
$450$	−8.13171	−	12.6046i	−0.383333	−	0.594185i
$451$	−0.198146	+	0.544402i	−0.00933034	+	0.0256349i
$452$	−2.75712	−	7.57512i	−0.129684	−	0.356304i
$453$	−24.2838	+	0.0282758i	−1.14095	+	0.00132851i
$454$	−3.64616	−	20.6784i	−0.171123	−	0.970485i
$455$	52.8707	+	12.8424i	2.47862	+	0.602063i
$456$	−2.39432	+	7.16011i	−0.112124	+	0.335303i
$457$			35.8059i			1.67493i	0.546490	+	0.837465i	$0.315964\pi$
$457$			35.8059i			1.67493i	−0.546490	+	0.837465i	$0.684036\pi$
$458$	24.4570	−	4.31243i	1.14280	−	0.201507i
$459$	−23.2052	+	4.17533i	−1.08313	+	0.194888i
$460$	0.993116	+	8.92820i	0.0463043	+	0.416279i
$461$	6.07727	−	16.6971i	0.283046	−	0.777664i	−0.713949	−	0.700198i	$-0.753095\pi$
$461$	6.07727	−	16.6971i	0.283046	−	0.777664i	0.996995	−	0.0774656i	$-0.0246828\pi$
$462$	−0.793530	−	4.46989i	−0.0369184	−	0.207958i
$463$	2.84031	+	1.63985i	0.132000	+	0.0762104i	0.564546	−	0.825402i	$-0.309051\pi$
$463$	2.84031	+	1.63985i	0.132000	+	0.0762104i	−0.432546	+	0.901612i	$0.642385\pi$
$464$	0.463978	+	0.803633i	0.0215396	+	0.0373077i
$465$	9.87434	+	19.8797i	0.457912	+	0.921898i
$466$	−28.5094	−	5.02697i	−1.32067	−	0.232870i
$467$	0.909499	+	1.57530i	0.0420866	+	0.0728961i	0.886301	−	0.463109i	$-0.153266\pi$
$467$	0.909499	+	1.57530i	0.0420866	+	0.0728961i	−0.844215	+	0.536005i	$0.819933\pi$
$468$	−14.1237	−	5.10341i	−0.652870	−	0.235905i
$469$	15.7835	−	18.8101i	0.728816	−	0.868569i
$470$	−18.7282	−	12.4679i	−0.863867	−	0.575102i
$471$	−7.11975	−	2.58199i	−0.328061	−	0.118972i
$472$	−0.143958	−	0.171563i	−0.00662622	−	0.00789682i
$473$	1.13405	+	6.43153i	0.0521438	+	0.295722i
$474$	5.69144	−	6.79885i	0.261416	−	0.312282i
$475$	9.50696	−	19.6117i	0.436209	−	0.899845i
$476$		−	22.0559i		−	1.01093i
$477$	−9.95586	−	27.1565i	−0.455847	−	1.24341i
$478$	19.0600	−	15.9932i	0.871784	−	0.731513i
$479$	−9.59031	−	26.3492i	−0.438192	−	1.20392i	−0.940667	−	0.339332i	$-0.889799\pi$
$479$	−9.59031	−	26.3492i	−0.438192	−	1.20392i	0.502474	−	0.864592i	$-0.332423\pi$
$480$	−3.71514	+	1.09440i	−0.169572	+	0.0499523i
$481$	−33.4183	−	28.0413i	−1.52374	−	1.27857i
$482$	−1.31925	+	2.28500i	−0.0600901	+	0.104079i
$483$	−5.83452	+	33.3160i	−0.265480	+	1.51593i
$484$	−1.85964	+	10.5465i	−0.0845290	+	0.479388i
$485$	−21.1035	−	9.24308i	−0.958259	−	0.419707i
$486$	2.79624	+	15.3356i	0.126840	+	0.695638i
$487$	2.70410	−	4.68364i	0.122534	−	0.212236i	−0.798232	−	0.602350i	$-0.794231\pi$
$487$	2.70410	−	4.68364i	0.122534	−	0.212236i	0.920766	+	0.390114i	$0.127564\pi$
$488$	1.62806	−	1.94024i	0.0736987	−	0.0878307i
$489$	−2.68077	−	4.63076i	−0.121228	−	0.209410i
$490$	36.9508	−	4.11017i	1.66927	−	0.185679i
$491$	−0.972454	−	1.15893i	−0.0438862	−	0.0523016i	0.743655	−	0.668564i	$-0.233091\pi$
$491$	−0.972454	−	1.15893i	−0.0438862	−	0.0523016i	−0.787541	+	0.616262i	$0.788646\pi$
$492$	1.61267	+	0.928572i	0.0727047	+	0.0418633i
$493$	−4.21065			−0.189638
$494$	−4.32909	−	21.3861i	−0.194775	−	0.962208i
$495$	0.222053	−	3.61042i	0.00998054	−	0.162276i
$496$	5.64415	−	0.995217i	0.253430	−	0.0446865i
$497$	11.9141	+	14.1987i	0.534420	+	0.636897i
$498$	−12.6689	−	4.59440i	−0.567707	−	0.205880i
$499$	−23.4835	−	8.54730i	−1.05127	−	0.382630i	−0.242126	−	0.970245i	$-0.577845\pi$
$499$	−23.4835	−	8.54730i	−1.05127	−	0.382630i	−0.809140	+	0.587615i	$0.800067\pi$
$500$	11.0414	−	1.75696i	0.493788	−	0.0785738i
$501$	27.7551	−	10.1386i	1.24000	−	0.452961i
$502$	−11.8211	−	20.4748i	−0.527603	−	0.913835i
$503$	−1.52911	+	8.67202i	−0.0681797	+	0.386666i	0.931554	+	0.363602i	$0.118453\pi$
$503$	−1.52911	+	8.67202i	−0.0681797	+	0.386666i	−0.999734	+	0.0230641i	$0.992658\pi$
$504$	−14.5822	+	0.0339587i	−0.649542	+	0.00151264i
$505$	−6.64718	−	22.6624i	−0.295796	−	1.00846i
$506$	−1.08316	+	1.87608i	−0.0481521	+	0.0834020i
$507$	20.5641	−	3.65070i	0.913283	−	0.162133i
$508$	−7.79971	−	2.83886i	−0.346056	−	0.125954i
$509$	−1.51623	+	0.551862i	−0.0672056	+	0.0244609i	−0.375404	−	0.926861i	$-0.622496\pi$
$509$	−1.51623	+	0.551862i	−0.0672056	+	0.0244609i	0.308199	+	0.951322i	$0.400274\pi$
$510$	4.12823	−	17.0821i	0.182801	−	0.756409i
$511$	0.504907	+	2.86347i	0.0223358	+	0.126672i
$512$			1.00000i			0.0441942i
$513$	−16.9258	+	15.0505i	−0.747292	+	0.664495i
$514$	23.1491			1.02106
$515$	2.64728	+	0.169006i	0.116653	+	0.00744729i
$516$	20.9774	−	0.0244259i	0.923479	−	0.00107529i
$517$	−1.85565	−	5.09837i	−0.0816116	−	0.224226i
$518$	−39.8055	−	14.4880i	−1.74895	−	0.636567i
$519$	1.58305	+	8.91719i	0.0694881	+	0.391421i
$520$	7.72665	−	8.09880i	0.338836	−	0.355156i
$521$	−6.81796	−	11.8091i	−0.298700	−	0.517364i	0.677139	−	0.735855i	$-0.263220\pi$
$521$	−6.81796	−	11.8091i	−0.298700	−	0.517364i	−0.975839	+	0.218491i	$0.929886\pi$
$522$	0.00648300	+	2.78386i	0.000283753	+	0.121846i
$523$	−0.760544	+	4.31326i	−0.0332563	+	0.188606i	−0.996910	−	0.0785474i	$-0.974972\pi$
$523$	−0.760544	+	4.31326i	−0.0332563	+	0.188606i	0.963654	+	0.267153i	$0.0860829\pi$
$524$	8.40964	−	4.85531i	0.367377	−	0.212105i
$525$	41.7597	+	5.30439i	1.82254	+	0.231503i
$526$	−14.6751	+	17.4891i	−0.639863	+	0.762559i
$527$	−8.89449	+	24.4374i	−0.387450	+	1.06451i
$528$	−0.878015	−	0.318414i	−0.0382107	−	0.0138572i
$529$	−5.25521	+	4.40965i	−0.228488	+	0.191724i
$530$	21.5149	+	1.37354i	0.934546	+	0.0596626i
$531$	−0.118211	−	0.661397i	−0.00512992	−	0.0287022i
$532$	−11.0526	−	18.0762i	−0.479191	−	0.783703i
$533$	−5.37822			−0.232956
$534$	−3.43501	+	5.96565i	−0.148648	+	0.258159i
$535$	−10.7851	+	5.34135i	−0.466279	+	0.230927i
$536$	−1.72777	−	4.74701i	−0.0746283	−	0.205040i
$537$	−31.8927	+	18.4628i	−1.37627	+	0.796730i
$538$	−12.8044	+	15.2597i	−0.552038	+	0.657893i
$539$	7.76447	+	4.48282i	0.334439	+	0.193089i
$540$	−11.3002	−	2.70307i	−0.486281	−	0.116322i
$541$	−3.78990	+	21.4936i	−0.162941	+	0.924082i	0.788222	+	0.615391i	$0.211002\pi$
$541$	−3.78990	+	21.4936i	−0.162941	+	0.924082i	−0.951162	+	0.308691i	$0.900109\pi$
$542$	4.64807	+	0.819580i	0.199652	+	0.0352040i
$543$	−0.820153	+	4.68320i	−0.0351961	+	0.200975i
$544$	−3.92964	−	2.26878i	−0.168482	−	0.0972731i
$545$	9.97788	+	13.5599i	0.427406	+	0.580840i
$546$	36.4735	−	21.1147i	1.56092	−	0.903624i
$547$	−4.51375	+	1.64287i	−0.192994	+	0.0702440i	−0.436709	−	0.899603i	$-0.643856\pi$
$547$	−4.51375	+	1.64287i	−0.192994	+	0.0702440i	0.243715	+	0.969847i	$0.421634\pi$
$548$	−12.7546	+	10.7024i	−0.544852	+	0.457185i
$549$	7.13411	−	2.61544i	0.304477	−	0.111624i
$550$	2.39571	+	1.23682i	0.102153	+	0.0527383i
$551$	−3.45090	+	2.11003i	−0.147013	+	0.0898904i
$552$	5.33565	+	4.46657i	0.227100	+	0.190110i
$553$	4.32086	+	24.5048i	0.183742	+	1.04205i
$554$	−10.1797	+	8.54178i	−0.432494	+	0.362905i
$555$	−28.1173	−	18.6713i	−1.19351	−	0.792553i
$556$	6.91475	+	2.51676i	0.293251	+	0.106734i
$557$	−18.9752	−	15.9220i	−0.804003	−	0.674639i	0.145165	−	0.989407i	$-0.453629\pi$
$557$	−18.9752	−	15.9220i	−0.804003	−	0.674639i	−0.949168	+	0.314769i	$0.898073\pi$
$558$	16.1704	+	5.84294i	0.684548	+	0.247351i
$559$	−52.5047	+	30.3136i	−2.22071	+	1.28213i
$560$	4.36056	−	9.95588i	0.184267	−	0.420713i
$561$	3.24327	−	2.72787i	0.136931	−	0.115171i
$562$	1.06665	−	0.615832i	0.0449940	−	0.0259773i
$563$	25.6777	+	14.8250i	1.08219	+	0.624800i	0.931485	−	0.363779i	$-0.118514\pi$
$563$	25.6777	+	14.8250i	1.08219	+	0.624800i	0.150700	+	0.988579i	$0.451847\pi$
$564$	−17.1592	+	3.04623i	−0.722531	+	0.128269i
$565$	15.0047	+	9.98904i	0.631251	+	0.420242i
$566$	−2.79375	+	1.01684i	−0.117430	+	0.0427410i
$567$	−37.9872	−	21.6967i	−1.59531	−	0.911174i
$568$	3.75528	−	0.662157i	0.157568	−	0.0277835i
$569$	27.0667			1.13469			0.567347	−	0.823479i	$-0.307970\pi$
$569$	27.0667			1.13469			0.567347	+	0.823479i	$0.307970\pi$
$570$	−5.17681	−	16.0686i	−0.216833	−	0.673041i
$571$	−15.1156			−0.632567			−0.316284	−	0.948665i	$-0.602435\pi$
$571$	−15.1156			−0.632567			−0.316284	+	0.948665i	$0.602435\pi$
$572$	2.65827	−	0.468725i	0.111148	−	0.0195984i
$573$	6.23515	−	0.00726014i	0.260477	−	0.000303297i
$574$	−4.90739	+	1.78614i	−0.204831	+	0.0745522i
$575$	−13.6208	−	14.7637i	−0.568028	−	0.615690i
$576$	−1.49395	+	2.60156i	−0.0622477	+	0.108398i
$577$	−17.8586	−	10.3107i	−0.743465	−	0.429240i	0.0798627	−	0.996806i	$-0.474552\pi$
$577$	−17.8586	−	10.3107i	−0.743465	−	0.429240i	−0.823328	+	0.567566i	$0.807885\pi$
$578$	3.10853	−	1.79471i	0.129298	−	0.0746502i
$579$	−22.5271	−	26.7833i	−0.936192	−	1.11308i
$580$	−1.90066	−	0.832467i	−0.0789206	−	0.0345663i
$581$	32.7523	−	18.9096i	1.35880	−	0.784501i
$582$	−16.7625	+	6.12316i	−0.694828	+	0.253813i
$583$	3.98256	+	3.34177i	0.164941	+	0.138402i
$584$	0.562114	+	0.204593i	0.0232604	+	0.00846610i
$585$	32.2005	−	9.52634i	1.33133	−	0.393866i
$586$	0.237806	−	0.199543i	0.00982366	−	0.00824303i
$587$	−2.82242	−	16.0067i	−0.116494	−	0.660668i	−0.986000	−	0.166746i	$-0.946674\pi$
$587$	−2.82242	−	16.0067i	−0.116494	−	0.660668i	0.869506	−	0.493922i	$-0.164437\pi$
$588$	18.4856	−	22.0825i	0.762334	−	0.910666i
$589$	4.95642	+	24.4852i	0.204226	+	1.00890i
$590$	0.486638	+	0.118206i	0.0200346	+	0.00486645i
$591$	2.22249	+	1.27971i	0.0914210	+	0.0526401i
$592$	−6.67588	+	5.60173i	−0.274377	+	0.230230i
$593$	23.4379	−	8.53068i	0.962477	−	0.350313i	0.187474	−	0.982270i	$-0.439970\pi$
$593$	23.4379	−	8.53068i	0.962477	−	0.350313i	0.775004	+	0.631957i	$0.217748\pi$
$594$	−1.80852	−	2.14008i	−0.0742044	−	0.0878086i
$595$	29.2299	+	39.7231i	1.19831	+	1.62849i
$596$	5.31957	+	3.07125i	0.217898	+	0.125804i
$597$	18.3922	+	3.22096i	0.752742	+	0.131825i
$598$	−19.8051	−	3.49217i	−0.809890	−	0.142805i
$599$	1.40992	−	7.99608i	0.0576080	−	0.326711i	−0.942361	−	0.334598i	$-0.891399\pi$
$599$	1.40992	−	7.99608i	0.0576080	−	0.326711i	0.999969	+	0.00788708i	$0.00251056\pi$
$600$	5.24068	−	6.89458i	0.213950	−	0.281470i
$601$	−13.7278	−	7.92576i	−0.559969	−	0.323299i	0.193164	−	0.981167i	$-0.438125\pi$
$601$	−13.7278	−	7.92576i	−0.559969	−	0.323299i	−0.753133	+	0.657868i	$0.771458\pi$
$602$	−37.8409	+	45.0970i	−1.54228	+	1.83802i
$603$	2.59687	−	14.9308i	0.105753	−	0.608030i
$604$	−4.79522	−	13.1748i	−0.195115	−	0.536073i
$605$	−10.6277	−	21.4590i	−0.432077	−	0.872434i
$606$	−15.8535	−	9.12842i	−0.644004	−	0.370817i
$607$	−26.7979			−1.08769			−0.543847	−	0.839184i	$-0.683033\pi$
$607$	−26.7979			−1.08769			−0.543847	+	0.839184i	$0.683033\pi$
$608$	−4.35752	+	0.109804i	−0.176721	+	0.00445315i
$609$	−5.99057	−	5.01481i	−0.242750	−	0.203210i
$610$	−0.360832	+	5.65203i	−0.0146097	+	0.228844i
$611$	38.5837	−	32.3755i	1.56093	−	1.30977i
$612$	−6.83377	−	11.7730i	−0.276239	−	0.475897i
$613$	−4.39087	+	12.0638i	−0.177345	+	0.487252i	−0.996235	−	0.0866993i	$-0.972368\pi$
$613$	−4.39087	+	12.0638i	−0.177345	+	0.487252i	0.818889	+	0.573952i	$0.194590\pi$
$614$	−9.33548	+	11.1256i	−0.376749	+	0.448992i
$615$	−4.13505	+	0.464832i	−0.166741	+	0.0187438i
$616$	2.26989	−	1.31052i	0.0914565	−	0.0528024i
$617$	−3.32232	+	18.8418i	−0.133751	+	0.758542i	0.841970	+	0.539525i	$0.181396\pi$
$617$	−3.32232	+	18.8418i	−0.133751	+	0.758542i	−0.975721	+	0.219017i	$0.929715\pi$
$618$	1.57249	−	1.32260i	0.0632549	−	0.0532028i
$619$	−21.2002	−	36.7199i	−0.852109	−	1.47590i	−0.879301	−	0.476266i	$-0.841990\pi$
$619$	−21.2002	−	36.7199i	−0.852109	−	1.47590i	0.0271922	−	0.999630i	$-0.491343\pi$
$620$	−8.84632	+	9.27240i	−0.355277	+	0.372388i
$621$	7.20822	+	19.5912i	0.289256	+	0.786169i
$622$	−18.7762	−	6.83399i	−0.752859	−	0.274018i
$623$	−6.60738	−	18.1536i	−0.264719	−	0.727310i
$624$	−0.0100957	−	8.67034i	−0.000404149	−	0.347092i
$625$	−17.5574	+	17.7971i	−0.702296	+	0.711885i
$626$	−27.4111			−1.09557
$627$	1.29108	−	3.86093i	0.0515609	−	0.154191i
$628$		−	4.37255i		−	0.174484i
$629$	−6.86668	−	38.9429i	−0.273793	−	1.55275i
$630$	26.2178	−	19.3864i	1.04454	−	0.772373i
$631$	28.9041	−	10.5202i	1.15065	−	0.418803i	0.304903	−	0.952383i	$-0.401376\pi$
$631$	28.9041	−	10.5202i	1.15065	−	0.418803i	0.845749	+	0.533580i	$0.179154\pi$
$632$	4.81042	+	1.75085i	0.191348	+	0.0696451i
$633$	3.00561	+	16.9304i	0.119462	+	0.672922i
$634$	6.62285	−	11.4711i	0.263027	−	0.455576i
$635$	17.8097	−	5.22382i	0.706756	−	0.207301i
$636$	12.7799	−	10.7490i	0.506755	−	0.426225i
$637$	−14.4529	+	81.9666i	−0.572645	+	3.24763i
$638$	−0.250189	−	0.433341i	−0.00990509	−	0.0171561i
$639$	10.7588	+	3.88754i	0.425612	+	0.153789i
$640$	−1.32526	−	1.80102i	−0.0523856	−	0.0711916i
$641$	−20.2952	−	7.38683i	−0.801610	−	0.291762i	−0.0914568	−	0.995809i	$-0.529152\pi$
$641$	−20.2952	−	7.38683i	−0.801610	−	0.291762i	−0.710154	+	0.704047i	$0.751375\pi$
$642$	−3.17827	+	8.76397i	−0.125436	+	0.345886i
$643$	3.40630	+	4.05947i	0.134332	+	0.160090i	0.829017	−	0.559224i	$-0.188901\pi$
$643$	3.40630	+	4.05947i	0.134332	+	0.160090i	−0.694685	+	0.719314i	$0.744456\pi$
$644$	−19.2311	+	3.39096i	−0.757810	+	0.133622i
$645$	−37.7484	+	27.8446i	−1.48634	+	1.09638i
$646$	9.45475	−	17.3726i	0.371992	−	0.683515i
$647$	−38.0110			−1.49437			−0.747184	−	0.664618i	$-0.768594\pi$
$647$	−38.0110			−1.49437			−0.747184	+	0.664618i	$0.768594\pi$
$648$	−7.77319	+	4.53625i	−0.305360	+	0.178201i
$649$	0.0776262	+	0.0925113i	0.00304710	+	0.00363139i
$650$	−3.18281	+	24.8259i	−0.124840	+	0.973754i
$651$	−41.7589	+	24.1744i	−1.63666	+	0.947469i
$652$	1.98573	−	2.36651i	0.0777674	−	0.0926795i
$653$	−0.354102	+	0.613323i	−0.0138571	+	0.0240012i	−0.872871	−	0.487951i	$-0.837744\pi$
$653$	−0.354102	+	0.613323i	−0.0138571	+	0.0240012i	0.859014	+	0.511953i	$0.171078\pi$
$654$	12.8451	+	2.24952i	0.502283	+	0.0879631i
$655$	−8.71137	+	19.8895i	−0.340382	+	0.777147i
$656$	−0.186566	+	1.05807i	−0.00728418	+	0.0413106i
$657$	1.15672	+	1.37203i	0.0451281	+	0.0535279i
$658$	24.4538	−	42.3552i	0.953308	−	1.65118i
$659$	−10.8393	−	9.09528i	−0.422240	−	0.354302i	0.406774	−	0.913529i	$-0.366654\pi$
$659$	−10.8393	−	9.09528i	−0.422240	−	0.354302i	−0.829015	+	0.559227i	$0.811098\pi$
$660$	2.00331	−	0.590131i	0.0779786	−	0.0229708i
$661$	11.7136	+	32.1828i	0.455605	+	1.25177i	0.928726	+	0.370767i	$0.120905\pi$
$661$	11.7136	+	32.1828i	0.455605	+	1.25177i	−0.473121	+	0.880998i	$0.656872\pi$
$662$	2.33757	−	1.96145i	0.0908521	−	0.0762340i
$663$	34.0942	+	19.6314i	1.32411	+	0.762421i
$664$		−	7.78052i		−	0.301943i
$665$	43.8617	+	17.9080i	1.70088	+	0.694444i
$666$	−25.7364	+	4.59984i	−0.997265	+	0.178240i
$667$	0.647361	+	3.67137i	0.0250659	+	0.142156i
$668$	10.9660	+	13.0688i	0.424287	+	0.505645i
$669$	−8.94306	+	24.6602i	−0.345759	+	0.953417i
$670$	9.40279	+	6.25971i	0.363261	+	0.241834i
$671$	−0.877893	+	1.04623i	−0.0338907	+	0.0403893i
$672$	−2.88870	−	7.90797i	−0.111434	−	0.305056i
$673$	0.579758	+	1.00417i	0.0223480	+	0.0387079i	0.876983	−	0.480521i	$-0.159552\pi$
$673$	0.579758	+	1.00417i	0.0223480	+	0.0387079i	−0.854635	+	0.519229i	$0.826219\pi$
$674$	−20.8715	−	3.68022i	−0.803942	−	0.141757i
$675$	23.9341	−	10.1074i	0.921223	−	0.389034i
$676$	6.02916	+	10.4428i	0.231891	+	0.401647i
$677$	19.6923	+	11.3693i	0.756836	+	0.436959i	0.828158	−	0.560494i	$-0.189389\pi$
$677$	19.6923	+	11.3693i	0.756836	+	0.436959i	−0.0713228	+	0.997453i	$0.522722\pi$
$678$	13.7476	−	2.44058i	0.527973	−	0.0937298i
$679$	17.1290	−	47.0614i	0.657349	−	1.80605i
$680$	10.0841	−	1.12169i	0.386707	−	0.0430148i
$681$	36.3685	−	0.0423471i	1.39364	−	0.00162274i
$682$	−3.04348	+	0.536648i	−0.116541	+	0.0205493i
$683$		−	44.0729i		−	1.68640i	−0.537597	−	0.843202i	$-0.680668\pi$
$683$		−	44.0729i		−	1.68640i	0.537597	−	0.843202i	$-0.319332\pi$
$684$	−11.5004	−	6.22423i	−0.439728	−	0.237989i
$685$	8.78786	−	36.1786i	0.335767	−	1.38231i
$686$	8.12561	+	46.0826i	0.310237	+	1.75944i
$687$	0.0500853	+	43.0143i	0.00191087	+	1.64110i
$688$	4.14232	+	11.3809i	0.157924	+	0.433893i
$689$	−16.5069	+	45.3522i	−0.628861	+	1.72778i
$690$	−15.5290	−	0.973237i	−0.591179	−	0.0370505i
$691$	9.58267	−	16.5977i	0.364542	−	0.631405i	−0.624161	−	0.781296i	$-0.714559\pi$
$691$	9.58267	−	16.5977i	0.364542	−	0.631405i	0.988703	+	0.149891i	$0.0478923\pi$
$692$	−4.52831	+	2.61442i	−0.172140	+	0.0993853i
$693$	7.86311	−	0.0183115i	0.298695	−	0.000695595i
$694$	−29.8904	−	5.27048i	−1.13462	−	0.200065i
$695$	−15.7890	+	4.63112i	−0.598910	+	0.175668i
$696$	−1.50969	+	0.551475i	−0.0572248	+	0.0209036i
$697$	−3.73455	−	3.13366i	−0.141456	−	0.118696i
$698$	−3.99724	+	10.9823i	−0.151298	+	0.415687i
$699$	17.0945	−	47.1375i	0.646573	−	1.78290i
$700$	5.34070	+	23.7097i	0.201859	+	0.896141i
$701$	22.7004	−	4.00269i	0.857382	−	0.151180i	0.272358	−	0.962196i	$-0.412196\pi$
$701$	22.7004	−	4.00269i	0.857382	−	0.151180i	0.585023	+	0.811016i	$0.301085\pi$
$702$	12.9268	−	22.5715i	0.487889	−	0.851907i
$703$	−25.1427	−	28.4752i	−0.948273	−	1.07396i
$704$		−	0.539227i		−	0.0203229i
$705$	26.8670	−	28.2267i	1.01187	−	1.06308i
$706$	16.0601	+	19.1397i	0.604431	+	0.720333i
$707$	48.2426	−	17.5589i	1.81435	−	0.660369i
$708$	0.335713	−	0.194346i	0.0126169	−	0.00730395i
$709$	6.81911	+	5.72191i	0.256097	+	0.214891i	0.761792	−	0.647821i	$-0.224320\pi$
$709$	6.81911	+	5.72191i	0.256097	+	0.214891i	−0.505695	+	0.862712i	$0.668764\pi$
$710$	−5.88580	+	6.16929i	−0.220890	+	0.231529i
$711$	9.89894	+	11.7415i	0.371239	+	0.440339i
$712$	−3.91405	−	0.690153i	−0.146685	−	0.0258646i
$713$	22.6750	+	3.99822i	0.849187	+	0.149735i
$714$	37.6293	+	6.58989i	1.40824	+	0.246620i
$715$	−4.16642	+	4.36709i	−0.155815	+	0.163320i
$716$	−16.2985	−	13.6760i	−0.609102	−	0.511097i
$717$	21.5911	+	37.2965i	0.806333	+	1.39286i
$718$	5.46697	−	1.98981i	0.204026	−	0.0742592i
$719$	32.7998	+	39.0893i	1.22323	+	1.45778i	0.847283	+	0.531141i	$0.178237\pi$
$719$	32.7998	+	39.0893i	1.22323	+	1.45778i	0.375943	+	0.926643i	$0.377319\pi$
$720$	−0.757128	−	6.66534i	−0.0282165	−	0.248403i
$721$			5.76635i			0.214750i
$722$	−0.956948	−	18.9759i	−0.0356139	−	0.706209i
$723$	−3.50425	−	2.93347i	−0.130324	−	0.109097i
$724$	−2.70329	+	0.476664i	−0.100467	+	0.0177151i
$725$	4.52636	−	1.01958i	0.168105	−	0.0378664i
$726$	−17.4377	−	6.32381i	−0.647173	−	0.234699i
$727$	2.70548	−	7.43324i	0.100341	−	0.275683i	−0.879357	−	0.476162i	$-0.842028\pi$
$727$	2.70548	−	7.43324i	0.100341	−	0.275683i	0.979698	+	0.200479i	$0.0642497\pi$
$728$	18.6394	+	15.6403i	0.690823	+	0.579670i
$729$	−26.9993	+	0.188629i	−0.999976	+	0.00698627i
$730$	−1.28352	+	0.376473i	−0.0475051	+	0.0139339i
$731$	−54.1209	−	9.54297i	−2.00173	−	0.352960i
$732$	2.82379	+	3.35732i	0.104370	+	0.124090i
$733$	28.2098	−	16.2869i	1.04195	−	0.601571i	0.121566	−	0.992583i	$-0.461208\pi$
$733$	28.2098	−	16.2869i	1.04195	−	0.601571i	0.920386	+	0.391012i	$0.127875\pi$
$734$	−11.0162	+	19.0806i	−0.406616	+	0.704279i
$735$	−4.02790	+	64.2693i	−0.148571	+	2.37061i
$736$	−1.37404	+	3.77516i	−0.0506480	+	0.139154i
$737$	0.931660	+	2.55972i	0.0343181	+	0.0942883i
$738$	−2.06606	+	2.47391i	−0.0760527	+	0.0910659i
$739$	3.49358	+	19.8131i	0.128513	+	0.728835i	0.979159	+	0.203096i	$0.0651002\pi$
$739$	3.49358	+	19.8131i	0.128513	+	0.728835i	−0.850646	+	0.525740i	$0.823789\pi$
$740$	4.59963	−	18.9361i	0.169086	−	0.696106i
$741$	37.7800	−	0.996033i	1.38788	−	0.0365902i
$742$			46.8640i			1.72043i
$743$	−27.6302	+	4.87195i	−1.01365	+	0.178735i	−0.655713	−	0.755010i	$-0.727632\pi$
$743$	−27.6302	+	4.87195i	−1.01365	+	0.178735i	−0.357940	+	0.933744i	$0.616521\pi$
$744$	0.0115586	+	9.92676i	0.000423759	+	0.363933i
$745$	−13.6509	+	1.51844i	−0.500130	+	0.0556312i
$746$	4.08222	−	11.2158i	0.149461	−	0.410640i
$747$	11.6237	−	20.2415i	0.425288	−	0.740598i
$748$	2.11897	+	1.22339i	0.0774771	+	0.0447315i
$749$	−13.0811	−	22.6571i	−0.477972	−	0.827872i
$750$	−0.301438	+	19.3626i	−0.0110070	+	0.707021i
$751$	−0.304362	−	0.0536673i	−0.0111063	−	0.00195835i	0.168092	−	0.985771i	$-0.446239\pi$
$751$	−0.304362	−	0.0536673i	−0.0111063	−	0.00195835i	−0.179199	+	0.983813i	$0.557350\pi$
$752$	−5.03088	−	8.71373i	−0.183457	−	0.317757i
$753$	38.4637	−	14.0504i	1.40169	−	0.512024i
$754$	2.98587	−	3.55842i	0.108739	−	0.129590i
$755$	26.0963	+	17.3731i	0.949742	+	0.632271i
$756$	4.29895	−	24.8886i	0.156351	−	0.905190i
$757$	2.59295	+	3.09015i	0.0942422	+	0.112313i	0.811104	−	0.584901i	$-0.198867\pi$
$757$	2.59295	+	3.09015i	0.0942422	+	0.112313i	−0.716862	+	0.697215i	$0.754422\pi$
$758$	−1.02188	−	5.79539i	−0.0371165	−	0.210498i
$759$	−2.87713	−	2.40849i	−0.104433	−	0.0874228i
$760$	7.70246	−	5.97262i	0.279398	−	0.216650i
$761$			14.3401i			0.519829i	0.965632	+	0.259914i	$0.0836943\pi$
$761$			14.3401i			0.519829i	−0.965632	+	0.259914i	$0.916306\pi$
$762$	7.17375	−	12.4588i	0.259878	−	0.451334i
$763$	−28.0345	+	23.5237i	−1.01492	+	0.851617i
$764$	1.23123	+	3.38277i	0.0445442	+	0.122384i
$765$	27.9101	+	12.1469i	1.00909	+	0.439174i
$766$	25.6235	+	21.5007i	0.925814	+	0.776850i
$767$	−0.560551	+	0.970903i	−0.0202403	+	0.0350573i
$768$	−1.70609	−	0.298781i	−0.0615631	−	0.0107813i
$769$	2.10898	−	11.9606i	0.0760518	−	0.431311i	−0.922879	−	0.385089i	$-0.874171\pi$
$769$	2.10898	−	11.9606i	0.0760518	−	0.431311i	0.998931	−	0.0462222i	$-0.0147182\pi$
$770$	−2.35133	+	5.36848i	−0.0847362	+	0.193467i
$771$	−6.91652	+	39.4944i	−0.249092	+	1.42236i
$772$	10.1029	−	17.4987i	0.363610	−	0.629791i
$773$	21.5467	−	25.6784i	0.774982	−	0.923588i	−0.223713	−	0.974655i	$-0.571818\pi$
$773$	21.5467	−	25.6784i	0.774982	−	0.923588i	0.998695	+	0.0510670i	$0.0162622\pi$
$774$	−6.22598	+	35.7966i	−0.223788	+	1.28668i
$775$	3.64403	−	28.4235i	0.130898	−	1.02100i
$776$	−6.62284	−	7.89279i	−0.237746	−	0.283335i
$777$	36.6109	−	63.5829i	1.31341	−	2.28102i
$778$	−24.0567			−0.862474
$779$	−4.63103	−	0.696784i	−0.165924	−	0.0249649i
$780$	11.5087	+	15.6021i	0.412077	+	0.558645i
$781$	−2.02495	+	0.357053i	−0.0724583	+	0.0127764i
$782$	−11.7176	−	13.9645i	−0.419021	−	0.499369i
$783$	−4.75144	−	0.820704i	−0.169803	−	0.0293296i
$784$	15.6241	+	5.68671i	0.558004	+	0.203097i
$785$	5.79478	+	7.87505i	0.206825	+	0.281073i
$786$	5.77093	+	15.7982i	0.205842	+	0.563505i
$787$	−13.7716	−	23.8531i	−0.490903	−	0.850270i	0.509042	−	0.860742i	$-0.330000\pi$
$787$	−13.7716	−	23.8531i	−0.490903	−	0.850270i	−0.999945	+	0.0104722i	$0.996667\pi$
$788$	−0.257115	+	1.45817i	−0.00915934	+	0.0519452i
$789$	−25.4532	−	30.2623i	−0.906158	−	1.07737i
$790$	−10.9840	+	3.22176i	−0.390793	+	0.114625i
$791$	−19.5919	+	33.9342i	−0.696608	+	1.20656i
$792$	0.805576	−	1.40283i	0.0286249	−	0.0498475i
$793$	−11.9142	−	4.33641i	−0.423085	−	0.153990i
$794$	−12.1161	+	4.40990i	−0.429984	+	0.156502i
$795$	−8.77161	+	36.2958i	−0.311097	+	1.28728i
$796$	1.87199	+	10.6166i	0.0663508	+	0.376294i
$797$		−	27.0148i		−	0.956912i	−0.878112	−	0.478456i	$-0.841197\pi$
$797$		−	27.0148i		−	0.956912i	0.878112	−	0.478456i	$-0.158803\pi$
$798$	34.1419	−	13.4559i	1.20861	−	0.476333i
$799$	45.6558			1.61519
$800$	4.77365	+	1.48735i	0.168774	+	0.0525859i
$801$	−9.15160	−	7.64286i	−0.323356	−	0.270047i
$802$	0.333567	+	0.916468i	0.0117787	+	0.0323616i
$803$	−0.303107	−	0.110322i	−0.0106964	−	0.00389317i
$804$	8.61503	−	1.52941i	0.303829	−	0.0539380i
$805$	30.1416	−	31.5934i	1.06235	−	1.11352i
$806$	−14.3448	−	24.8459i	−0.505273	−	0.875158i
$807$	−22.2087	−	26.4048i	−0.781782	−	0.929492i
$808$	1.83405	−	10.4014i	0.0645218	−	0.365921i
$809$	−44.4456	+	25.6607i	−1.56262	+	0.902181i	−0.565632	+	0.824658i	$0.691368\pi$
$809$	−44.4456	+	25.6607i	−1.56262	+	0.902181i	−0.996991	+	0.0775227i	$0.975299\pi$
$810$	7.98794	−	18.4714i	0.280668	−	0.649019i
$811$	26.1321	−	31.1430i	0.917621	−	1.09358i	−0.0777018	−	0.996977i	$-0.524758\pi$
$811$	26.1321	−	31.1430i	0.917621	−	1.09358i	0.995323	−	0.0966018i	$-0.0307973\pi$
$812$	1.54270	−	4.23853i	0.0541382	−	0.148743i
$813$	−2.78703	+	7.68513i	−0.0977454	+	0.269529i
$814$	3.59982	−	3.02060i	0.126173	−	0.105872i
$815$	−0.440105	+	6.89375i	−0.0154162	+	0.241477i
$816$	5.04483	−	6.02644i	0.176605	−	0.210967i
$817$	−49.1377	+	19.2999i	−1.71911	+	0.675217i
$818$	26.0573			0.911072
$819$	25.1258	+	68.5356i	0.877967	+	2.39483i
$820$	−1.06621	−	2.15285i	−0.0372337	−	0.0751809i
$821$	1.08607	+	2.98396i	0.0379042	+	0.104141i	0.957201	−	0.289424i	$-0.0934638\pi$
$821$	1.08607	+	2.98396i	0.0379042	+	0.104141i	−0.919297	+	0.393565i	$0.871242\pi$
$822$	−14.4484	−	24.9582i	−0.503946	−	0.870518i
$823$	5.30044	−	6.31682i	0.184762	−	0.220190i	−0.665711	−	0.746210i	$-0.731872\pi$
$823$	5.30044	−	6.31682i	0.184762	−	0.220190i	0.850473	+	0.526019i	$0.176316\pi$
$824$	1.02738	+	0.593156i	0.0357903	+	0.0206636i
$825$	−2.82592	+	3.71775i	−0.0983858	+	0.129435i
$826$	−0.189035	+	1.07207i	−0.00657737	+	0.0373021i
$827$	−16.7668	−	2.95643i	−0.583038	−	0.102805i	−0.125653	−	0.992074i	$-0.540103\pi$
$827$	−16.7668	−	2.95643i	−0.583038	−	0.102805i	−0.457385	+	0.889269i	$0.651214\pi$
$828$	−9.21454	+	7.76856i	−0.320227	+	0.269976i
$829$	−11.3528	−	6.55456i	−0.394300	−	0.227649i	0.289721	−	0.957111i	$-0.406437\pi$
$829$	−11.3528	−	6.55456i	−0.394300	−	0.227649i	−0.684022	+	0.729462i	$0.739771\pi$
$830$	10.3112	+	14.0129i	0.357908	+	0.486394i
$831$	−11.5315	−	19.9196i	−0.400024	−	0.691002i
$832$	4.70394	−	1.71209i	0.163080	−	0.0593562i
$833$	−57.7944	+	48.4952i	−2.00246	+	1.68026i
$834$	−6.35981	+	11.0452i	−0.220222	+	0.382464i
$835$	−37.0695	−	9.00428i	−1.28284	−	0.311606i
$836$	2.34969	−	0.0592094i	0.0812657	−	0.00204780i
$837$	−14.8000	+	25.8424i	−0.511562	+	0.893243i
$838$	1.69543	+	9.61526i	0.0585677	+	0.332154i
$839$	11.5360	−	9.67985i	0.398267	−	0.334185i	−0.421557	−	0.906802i	$-0.638516\pi$
$839$	11.5360	−	9.67985i	0.398267	−	0.334185i	0.819823	+	0.572617i	$0.194072\pi$
$840$	15.6827	+	10.4141i	0.541106	+	0.359322i
$841$	26.4419	+	9.62407i	0.911790	+	0.331864i
$842$	−9.06353	−	7.60520i	−0.312350	−	0.262093i
$843$	0.731967	+	2.00380i	0.0252103	+	0.0690145i
$844$	−8.59754	+	4.96379i	−0.295940	+	0.170861i
$845$	−24.6981	−	10.8175i	−0.849641	−	0.372133i
$846$	−0.0702947	−	30.1852i	−0.00241678	−	1.03779i
$847$	45.0808	−	26.0274i	1.54900	−	0.894313i
$848$	8.34964	+	4.82066i	0.286728	+	0.165542i
$849$	−0.900100	−	5.07019i	−0.0308914	−	0.174009i
$850$	−16.6751	+	15.3843i	−0.571952	+	0.527676i
$851$	−32.8995	+	11.9744i	−1.12778	+	0.410479i
$852$	0.00769040	+	6.60467i	0.000263469	+	0.226272i
$853$	−28.2863	+	4.98764i	−0.968504	+	0.170773i	−0.635457	−	0.772136i	$-0.719188\pi$
$853$	−28.2863	+	4.98764i	−0.968504	+	0.170773i	−0.333048	+	0.942910i	$0.608077\pi$
$854$	−12.3113			−0.421285
$855$	28.9612	−	4.03108i	0.990452	−	0.137860i
$856$	−5.38234			−0.183964
$857$	−5.43157	+	0.957732i	−0.185539	+	0.0327155i	−0.265645	−	0.964071i	$-0.585585\pi$
$857$	−5.43157	+	0.957732i	−0.185539	+	0.0327155i	0.0801066	+	0.996786i	$0.474474\pi$
$858$	0.00544385	+	4.67528i	0.000185850	+	0.159612i
$859$	5.61825	−	2.04487i	0.191692	−	0.0697702i	−0.244390	−	0.969677i	$-0.578588\pi$
$859$	5.61825	−	2.04487i	0.191692	−	0.0697702i	0.436082	+	0.899907i	$0.356366\pi$
$860$	−22.5431	−	15.0076i	−0.768714	−	0.511755i
$861$	−1.58108	−	8.90610i	−0.0538831	−	0.303519i
$862$	13.6454	+	7.87817i	0.464764	+	0.268331i
$863$	−38.2495	+	22.0833i	−1.30203	+	0.751726i	−0.980751	−	0.195260i	$-0.937445\pi$
$863$	−38.2495	+	22.0833i	−1.30203	+	0.751726i	−0.321275	+	0.946986i	$0.604112\pi$
$864$	−3.99213	−	3.32610i	−0.135815	−	0.113156i
$865$	4.69078	−	10.7098i	0.159491	−	0.364145i
$866$	4.33475	−	2.50267i	0.147301	−	0.0850442i
$867$	2.13316	+	5.83965i	0.0724460	+	0.198325i
$868$	−21.3405	−	17.9068i	−0.724343	−	0.607796i
$869$	−2.59391	−	0.944106i	−0.0879924	−	0.0320266i
$870$	1.98814	−	2.99396i	0.0674043	−	0.101505i
$871$	−19.3715	+	16.2547i	−0.656380	+	0.550768i
$872$	1.30739	+	7.41460i	0.0442739	+	0.251090i
$873$	−5.43833	−	30.4277i	−0.184059	−	1.02982i
$874$	−16.6012	−	5.57289i	−0.561543	−	0.188506i
$875$	−41.0402	−	35.6237i	−1.38741	−	1.20430i
$876$	−0.517002	+	0.897886i	−0.0174679	+	0.0303367i
$877$	12.9028	−	10.8268i	0.435698	−	0.365594i	−0.398399	−	0.917212i	$-0.630434\pi$
$877$	12.9028	−	10.8268i	0.435698	−	0.365594i	0.834097	+	0.551618i	$0.185989\pi$
$878$	−5.06993	+	1.84530i	−0.171102	+	0.0622759i
$879$	0.269385	+	0.465336i	0.00908613	+	0.0156954i
$880$	0.714618	+	0.971159i	0.0240898	+	0.0327378i
$881$	20.7022	+	11.9524i	0.697476	+	0.402688i	0.806407	−	0.591361i	$-0.201409\pi$
$881$	20.7022	+	11.9524i	0.697476	+	0.402688i	−0.108931	+	0.994049i	$0.534743\pi$
$882$	32.1514	+	38.1359i	1.08260	+	1.28410i
$883$	2.19282	+	0.386653i	0.0737942	+	0.0130119i	0.210423	−	0.977610i	$-0.432516\pi$
$883$	2.19282	+	0.386653i	0.0737942	+	0.0130119i	−0.136629	+	0.990622i	$0.543627\pi$
$884$	−3.94429	+	22.3692i	−0.132661	+	0.752356i
$885$	−0.347067	+	0.794929i	−0.0116665	+	0.0267212i
$886$	−13.8809	−	8.01411i	−0.466336	−	0.269239i
$887$	21.8578	−	26.0492i	0.733915	−	0.874645i	−0.261989	−	0.965071i	$-0.584378\pi$
$887$	21.8578	−	26.0492i	0.733915	−	0.874645i	0.995903	+	0.0904256i	$0.0288227\pi$
$888$	−7.56240	−	13.0633i	−0.253778	−	0.438376i
$889$	13.7990	+	37.9124i	0.462803	+	1.27154i
$890$	7.96392	−	3.94417i	0.266951	−	0.132209i
$891$	4.19151	−	2.44607i	0.140421	−	0.0819464i
$892$	−15.1449			−0.507088
$893$	37.4178	−	22.8789i	1.25214	−	0.765614i
$894$	−6.82921	+	8.15801i	−0.228403	+	0.272845i
$895$	47.4782	+	3.03107i	1.58702	+	0.101317i
$896$	3.72355	−	3.12443i	0.124395	−	0.104380i
$897$	11.8753	−	32.7458i	0.396506	−	1.09335i
$898$	12.8140	−	35.2061i	0.427608	−	1.17484i
$899$	−3.41855	+	4.07407i	−0.114015	+	0.135878i
$900$	10.1969	+	11.0010i	0.339898	+	0.366701i
$901$	−37.8870	+	21.8740i	−1.26220	+	0.728730i
$902$	0.100601	−	0.570539i	0.00334966	−	0.0189969i
$903$	−65.6333	−	78.0340i	−2.18414	−	2.59681i
$904$	4.03064	+	6.98127i	0.134057	+	0.232194i
$905$	4.23698	−	4.44106i	0.140842	−	0.147626i
$906$	23.9100	−	4.24469i	0.794356	−	0.141020i
$907$	1.04456	+	0.380189i	0.0346840	+	0.0126240i	0.359304	−	0.933221i	$-0.383014\pi$
$907$	1.04456	+	0.380189i	0.0346840	+	0.0126240i	−0.324620	+	0.945845i	$0.605236\pi$
$908$	7.18153	+	19.7311i	0.238327	+	0.654799i
$909$	20.3106	−	24.3200i	0.673660	−	0.806644i
$910$	−54.2976	−	3.46642i	−1.79995	−	0.114911i
$911$	29.2478			0.969023			0.484512	−	0.874785i	$-0.338997\pi$
$911$	29.2478			0.969023			0.484512	+	0.874785i	$0.338997\pi$
$912$	1.11461	−	7.46710i	0.0369084	−	0.247261i
$913$			4.19547i			0.138850i
$914$	−6.21763	−	35.2620i	−0.205661	−	1.16636i
$915$	−9.53503	−	2.30433i	−0.315219	−	0.0761788i
$916$	−23.3366	+	8.49383i	−0.771064	+	0.280644i
$917$	−44.3542	−	16.1436i	−1.46471	−	0.533109i
$918$	22.1276	−	8.14144i	0.730320	−	0.268708i
$919$	4.26983	−	7.39556i	0.140849	−	0.243957i	−0.786968	−	0.616994i	$-0.788350\pi$
$919$	4.26983	−	7.39556i	0.140849	−	0.243957i	0.927816	+	0.373037i	$0.121684\pi$
$920$	−2.52839	−	8.62011i	−0.0833587	−	0.284197i
$921$	−16.1919	−	19.2512i	−0.533543	−	0.634350i
$922$	−3.08551	+	17.4988i	−0.101616	+	0.576292i
$923$	−9.54414	−	16.5309i	−0.314149	−	0.544122i
$924$	1.55766	+	4.26419i	0.0512434	+	0.140282i
$925$	16.8113	+	40.2001i	0.552753	+	1.32177i
$926$	−3.08191	−	1.12172i	−0.101278	−	0.0368622i
$927$	1.78664	+	3.07797i	0.0586809	+	0.101094i
$928$	−0.596478	−	0.710855i	−0.0195804	−	0.0233350i
$929$	10.8179	−	1.90750i	0.354925	−	0.0625829i	0.00665716	−	0.999978i	$-0.497881\pi$
$929$	10.8179	−	1.90750i	0.354925	−	0.0625829i	0.348268	+	0.937395i	$0.386770\pi$
$930$	−13.1764	−	17.8630i	−0.432071	−	0.585751i
$931$	−23.0643	+	68.7067i	−0.755903	+	2.25177i
$932$	28.9492			0.948261
$933$	17.2694	−	29.9920i	0.565374	−	0.981895i
$934$	−1.16923	−	1.39343i	−0.0382583	−	0.0455945i
$935$	−5.43762	+	0.604846i	−0.177829	+	0.0197806i
$936$	14.7954	+	2.57331i	0.483602	+	0.0841113i
$937$	10.1941	−	12.1489i	0.333028	−	0.396887i	−0.573381	−	0.819289i	$-0.694368\pi$
$937$	10.1941	−	12.1489i	0.333028	−	0.396887i	0.906409	+	0.422402i	$0.138813\pi$
$938$	−12.2774	+	21.2651i	−0.400872	+	0.694330i
$939$	8.18991	−	46.7656i	0.267268	−	1.52614i
$940$	20.6087	+	9.02638i	0.672182	+	0.294408i
$941$	−6.61918	+	37.5393i	−0.215779	+	1.22374i	0.663770	+	0.747937i	$0.268955\pi$
$941$	−6.61918	+	37.5393i	−0.215779	+	1.22374i	−0.879549	+	0.475808i	$0.842156\pi$
$942$	7.45995	+	1.30644i	0.243058	+	0.0425660i
$943$	−2.15815	+	3.73802i	−0.0702790	+	0.121727i
$944$	0.171563	+	0.143958i	0.00558389	+	0.00468544i
$945$	25.2415	+	50.5222i	0.821106	+	1.64349i
$946$	−2.23365	−	6.13690i	−0.0726222	−	0.199528i
$947$	−0.356205	+	0.298891i	−0.0115751	+	0.00971266i	−0.648557	−	0.761166i	$-0.724627\pi$
$947$	−0.356205	+	0.298891i	−0.0115751	+	0.00971266i	0.636982	+	0.770879i	$0.280183\pi$
$948$	−4.42436	+	7.68387i	−0.143697	+	0.249561i
$949$		−	2.99443i		−	0.0972033i
$950$	−5.95700	+	20.9646i	−0.193271	+	0.680181i
$951$	17.5919	+	14.7265i	0.570458	+	0.477540i
$952$	3.82997	+	21.7208i	0.124130	+	0.703976i
$953$	37.7058	+	44.9360i	1.22141	+	1.45562i	0.849696	+	0.527272i	$0.176785\pi$
$953$	37.7058	+	44.9360i	1.22141	+	1.45562i	0.371713	+	0.928348i	$0.378770\pi$
$954$	14.5203	+	25.0152i	0.470112	+	0.809896i
$955$	−6.70052	−	4.46074i	−0.216824	−	0.144346i
$956$	−15.9932	+	19.0600i	−0.517258	+	0.616444i
$957$	0.814068	−	0.297371i	0.0263151	−	0.00961262i
$958$	14.0201	+	24.2835i	0.452969	+	0.784565i
$959$	79.7019	+	14.0536i	2.57371	+	0.453814i
$960$	3.46866	−	1.72290i	0.111951	−	0.0556064i
$961$	0.923466	+	1.59949i	0.0297892	+	0.0515964i
$962$	37.7799	+	21.8123i	1.21807	+	0.703255i
$963$	−14.0025	−	8.04092i	−0.451224	−	0.259115i
$964$	0.902419	−	2.47938i	0.0290650	−	0.0798553i
$965$	4.99488	+	44.9044i	0.160791	+	1.44552i
$966$	−0.0393831	−	33.8230i	−0.00126713	−	1.08824i
$967$	20.6785	−	3.64617i	0.664975	−	0.117253i	0.169035	−	0.985610i	$-0.445935\pi$
$967$	20.6785	−	3.64617i	0.664975	−	0.117253i	0.495940	+	0.868357i	$0.334824\pi$
$968$		−	10.7092i		−	0.344208i
$969$	26.8142	+	21.3212i	0.861397	+	0.684936i
$970$	22.3879	+	5.43808i	0.718832	+	0.174606i
$971$	3.79379	+	21.5157i	0.121749	+	0.690470i	0.983186	+	0.182607i	$0.0584535\pi$
$971$	3.79379	+	21.5157i	0.121749	+	0.690470i	−0.861437	+	0.507864i	$0.830435\pi$
$972$	−5.41676	−	14.6171i	−0.173743	−	0.468843i
$973$	−12.2333	−	33.6108i	−0.392183	−	1.07751i
$974$	−1.84971	+	5.08204i	−0.0592686	+	0.162839i
$975$	−41.4042	−	12.8477i	−1.32600	−	0.411455i
$976$	−1.26640	+	2.19348i	−0.0405366	+	0.0702115i
$977$	−12.2796	+	7.08961i	−0.392858	+	0.226817i	−0.683398	−	0.730046i	$-0.739499\pi$
$977$	−12.2796	+	7.08961i	−0.392858	+	0.226817i	0.290540	+	0.956863i	$0.406165\pi$
$978$	3.44416	+	4.09490i	0.110132	+	0.130941i
$979$	2.11056	+	0.372149i	0.0674539	+	0.0118939i
$980$	−35.6757	+	10.4642i	−1.13962	+	0.334266i
$981$	−7.67574	+	21.2427i	−0.245068	+	0.678228i
$982$	1.15893	+	0.972454i	0.0369828	+	0.0310322i
$983$	−11.2172	+	30.8191i	−0.357774	+	0.982977i	0.622026	+	0.782997i	$0.286310\pi$
$983$	−11.2172	+	30.8191i	−0.357774	+	0.982977i	−0.979800	+	0.199980i	$0.935912\pi$
$984$	−1.74941	−	0.634428i	−0.0557693	−	0.0202248i
$985$	−1.46939	−	2.96694i	−0.0468187	−	0.0945346i
$986$	4.14668	−	0.731172i	0.132057	−	0.0232853i
$987$	64.9553	+	54.3752i	2.06755	+	1.73078i
$988$	7.97699	+	20.3095i	0.253782	+	0.646131i
$989$			48.6565i			1.54719i
$990$	0.408264	+	3.59413i	0.0129755	+	0.114229i
$991$	−3.14141	−	3.74379i	−0.0997902	−	0.118925i	0.713838	−	0.700311i	$-0.246955\pi$
$991$	−3.14141	−	3.74379i	−0.0997902	−	0.118925i	−0.813628	+	0.581386i	$0.802511\pi$
$992$	−5.38559	+	1.96019i	−0.170993	+	0.0622362i
$993$	2.64798	+	4.57414i	0.0840312	+	0.145156i
$994$	−14.1987	−	11.9141i	−0.450354	−	0.377892i
$995$	−17.4412	−	16.6398i	−0.552924	−	0.527516i
$996$	13.2742	+	2.32467i	0.420610	+	0.0736601i
$997$	−18.7501	−	3.30614i	−0.593821	−	0.104707i	−0.131342	−	0.991337i	$-0.541929\pi$
$997$	−18.7501	−	3.30614i	−0.593821	−	0.104707i	−0.462479	+	0.886630i	$0.653040\pi$
$998$	24.6110	+	4.33958i	0.779046	+	0.137367i
$999$	−0.158181	−	45.2829i	−0.00500463	−	1.43269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.29.10	yes	240
3.2	odd	2	inner	570.2.bf.a.29.40	yes	240
5.4	even	2	inner	570.2.bf.a.29.31	yes	240
15.14	odd	2	inner	570.2.bf.a.29.1	✓	240
19.2	odd	18	inner	570.2.bf.a.59.1	yes	240
57.2	even	18	inner	570.2.bf.a.59.31	yes	240
95.59	odd	18	inner	570.2.bf.a.59.40	yes	240
285.59	even	18	inner	570.2.bf.a.59.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.1	✓	240	15.14	odd	2	inner
570.2.bf.a.29.10	yes	240	1.1	even	1	trivial
570.2.bf.a.29.31	yes	240	5.4	even	2	inner
570.2.bf.a.29.40	yes	240	3.2	odd	2	inner
570.2.bf.a.59.1	yes	240	19.2	odd	18	inner
570.2.bf.a.59.10	yes	240	285.59	even	18	inner
570.2.bf.a.59.31	yes	240	57.2	even	18	inner
570.2.bf.a.59.40	yes	240	95.59	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.00201678 - 1.73205i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23914 + 1.86133i) q^{5} +(0.302753 + 1.70539i) q^{6} +(-4.20953 - 2.43037i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99999 + 0.00698632i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.00201678 - 1.73205i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.23914 + 1.86133i) q^{5} +(0.302753 + 1.70539i) q^{6} +(-4.20953 - 2.43037i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99999 + 0.00698632i) q^{9} +(0.897098 - 2.04822i) q^{10} +(0.466984 - 0.269614i) q^{11} +(-0.594291 - 1.62690i) q^{12} +(3.83469 + 3.21768i) q^{13} +(4.56760 + 1.66247i) q^{14} +(3.22641 + 2.14250i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.787939 + 4.46862i) q^{17} +(2.95320 - 0.527823i) q^{18} +(2.88507 + 3.26747i) q^{19} +(-0.527799 + 2.17288i) q^{20} +(-4.20103 + 7.29601i) q^{21} +(-0.413072 + 0.346608i) q^{22} +(3.77516 - 1.37404i) q^{23} +(0.867771 + 1.49899i) q^{24} +(-1.92907 - 4.61288i) q^{25} +(-4.33517 - 2.50291i) q^{26} +(0.0181510 + 5.19612i) q^{27} +(-4.78690 - 0.844059i) q^{28} +(-0.161138 + 0.913858i) q^{29} +(-3.54943 - 1.54969i) q^{30} +(4.96339 + 2.86561i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-0.467926 - 0.808296i) q^{33} +(-1.55194 - 4.26391i) q^{34} +(9.73990 - 4.82373i) q^{35} +(-2.81668 + 1.03262i) q^{36} -8.71474 q^{37} +(-3.40863 - 2.71684i) q^{38} +(5.56546 - 6.64836i) q^{39} +(0.142463 - 2.23153i) q^{40} +(-0.823031 + 0.690605i) q^{41} +(2.87027 - 7.91467i) q^{42} +(-4.14232 + 11.3809i) q^{43} +(0.346608 - 0.413072i) q^{44} +(3.70440 - 5.59262i) q^{45} +(-3.47920 + 2.00872i) q^{46} +(1.74721 - 9.90889i) q^{47} +(-1.11488 - 1.32553i) q^{48} +(8.31341 + 14.3993i) q^{49} +(2.70078 + 4.20783i) q^{50} +(7.73828 - 1.37376i) q^{51} +(4.70394 + 1.71209i) q^{52} +(3.29753 + 9.05989i) q^{53} +(-0.920172 - 5.11403i) q^{54} +(-0.0768201 + 1.20330i) q^{55} +4.86074 q^{56} +(5.65360 - 5.00368i) q^{57} -0.927955i q^{58} +(0.0388901 + 0.220557i) q^{59} +(3.76461 + 0.909792i) q^{60} +(-2.38006 + 0.866272i) q^{61} +(-5.38559 - 1.96019i) q^{62} +(12.6455 + 7.26169i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-10.7409 + 3.15044i) q^{65} +(0.601176 + 0.714762i) q^{66} +(-0.877212 + 4.97491i) q^{67} +(2.26878 + 3.92964i) q^{68} +(-2.38753 - 6.53599i) q^{69} +(-8.75430 + 6.44177i) q^{70} +(-3.58325 - 1.30419i) q^{71} +(2.59458 - 1.50605i) q^{72} +(-0.384508 - 0.458239i) q^{73} +(8.58235 - 1.51330i) q^{74} +(-7.98585 + 3.35054i) q^{75} +(3.82862 + 2.08366i) q^{76} -2.62104 q^{77} +(-4.32643 + 7.51379i) q^{78} +(-3.29052 - 3.92149i) q^{79} +(0.247201 + 2.22236i) q^{80} +(8.99990 - 0.0419178i) q^{81} +(0.690605 - 0.823031i) q^{82} +(-3.89026 + 6.73813i) q^{83} +(-1.45230 + 8.29285i) q^{84} +(-9.29393 - 4.07063i) q^{85} +(2.10311 - 11.9273i) q^{86} +(1.58317 + 0.277256i) q^{87} +(-0.269614 + 0.466984i) q^{88} +(3.04459 + 2.55472i) q^{89} +(-2.67698 + 6.15092i) q^{90} +(-8.32205 - 22.8646i) q^{91} +(3.07754 - 2.58236i) q^{92} +(4.95337 - 8.60261i) q^{93} +10.0618i q^{94} +(-9.65683 + 1.32121i) q^{95} +(1.32812 + 1.11180i) q^{96} +(1.78915 + 10.1468i) q^{97} +(-10.6875 - 12.7369i) q^{98} +(-1.39907 + 0.812101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more