LMFDB - Embedded newform 363.3.h.d.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.228765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 $ x^8 - x^7 - 2x^6 + 5x^5 + x^4 + 15x^3 - 18x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Root			$-0.570223 - 1.63550i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.15430 + 1.02489i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(5.66312 - 4.11450i) q^{4} +(6.30860 + 2.04979i) q^{5} +(9.46289 + 3.07468i) q^{6} +(-6.47214 + 4.70228i) q^{7} +(-5.84839 + 8.04962i) q^{8} +(2.78115 + 8.55951i) q^{9} -22.0000 q^{10} -21.0000 q^{12} +(-1.23607 - 3.80423i) q^{13} +(15.5957 - 21.4656i) q^{14} +(-11.6968 - 16.0992i) q^{15} +(1.54508 - 4.75528i) q^{16} +(12.6172 + 4.09957i) q^{17} +(-17.5452 - 24.1489i) q^{18} +(-4.85410 - 3.52671i) q^{19} +(44.1602 - 14.3485i) q^{20} +24.0000 q^{21} -6.63325i q^{23} +(28.3887 - 9.22404i) q^{24} +(15.3713 + 11.1679i) q^{25} +(7.79785 + 10.7328i) q^{26} +(8.34346 - 25.6785i) q^{27} +(-17.3050 + 53.2592i) q^{28} +(23.3936 + 32.1985i) q^{29} +(53.3951 + 38.7938i) q^{30} +(-8.03444 - 24.7275i) q^{31} -23.2164i q^{32} -44.0000 q^{34} +(-50.4688 + 16.3983i) q^{35} +(50.9681 + 37.0305i) q^{36} +(-24.2705 + 17.6336i) q^{37} +(18.9258 + 6.14936i) q^{38} +(-3.70820 + 11.4127i) q^{39} +(-53.3951 + 38.7938i) q^{40} +(7.79785 - 10.7328i) q^{41} +(-75.7031 + 24.5974i) q^{42} -42.0000 q^{43} +59.6992i q^{45} +(6.79837 + 20.9232i) q^{46} +(-50.6860 + 69.7634i) q^{47} +(-12.1353 + 8.81678i) q^{48} +(4.63525 - 14.2658i) q^{49} +(-59.9317 - 19.4730i) q^{50} +(-23.3936 - 32.1985i) q^{51} +(-22.6525 - 16.4580i) q^{52} +(-56.7774 + 18.4481i) q^{53} +89.5489i q^{54} -79.5990i q^{56} +(5.56231 + 17.1190i) q^{57} +(-106.790 - 77.5877i) q^{58} +(38.9893 + 53.6641i) q^{59} +(-132.480 - 43.0455i) q^{60} +(-3.70820 + 11.4127i) q^{61} +(50.6860 + 69.7634i) q^{62} +(-58.2492 - 42.3205i) q^{63} +(29.9746 + 92.2525i) q^{64} -26.5330i q^{65} +2.00000 q^{67} +(88.3203 - 28.6970i) q^{68} +(-11.6968 + 16.0992i) q^{69} +(142.387 - 103.450i) q^{70} +(56.7774 + 18.4481i) q^{71} +(-85.1660 - 27.6721i) q^{72} +(-59.8673 + 43.4961i) q^{73} +(58.4839 - 80.4962i) q^{74} +(-17.6140 - 54.2102i) q^{75} -42.0000 q^{76} -39.7995i q^{78} +(12.3607 + 38.0423i) q^{79} +(19.4946 - 26.8321i) q^{80} +(-65.5304 + 47.6106i) q^{81} +(-13.5967 + 41.8465i) q^{82} +(-37.8516 - 12.2987i) q^{83} +(135.915 - 98.7479i) q^{84} +(71.1935 + 51.7251i) q^{85} +(132.480 - 43.0455i) q^{86} -119.398i q^{87} +119.398i q^{89} +(-61.1854 - 188.309i) q^{90} +(25.8885 + 18.8091i) q^{91} +(-27.2925 - 37.5649i) q^{92} +(-24.1033 + 74.1824i) q^{93} +(88.3789 - 272.002i) q^{94} +(-23.3936 - 32.1985i) q^{95} +(-40.9387 + 56.3473i) q^{96} +(19.1591 + 58.9655i) q^{97} +49.7494i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 14 q^{4} - 16 q^{7} - 18 q^{9} - 176 q^{10} - 168 q^{12} + 8 q^{13} - 10 q^{16} - 12 q^{19} + 192 q^{21} + 38 q^{25} - 54 q^{27} + 112 q^{28} + 132 q^{30} + 52 q^{31} - 352 q^{34} + 126 q^{36}+ \cdots - 124 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 + 14 * q^4 - 16 * q^7 - 18 * q^9 - 176 * q^10 - 168 * q^12 + 8 * q^13 - 10 * q^16 - 12 * q^19 + 192 * q^21 + 38 * q^25 - 54 * q^27 + 112 * q^28 + 132 * q^30 + 52 * q^31 - 352 * q^34 + 126 * q^36 - 60 * q^37 + 24 * q^39 - 132 * q^40 - 336 * q^43 - 44 * q^46 - 30 * q^48 - 30 * q^49 - 56 * q^52 - 36 * q^57 - 264 * q^58 + 24 * q^61 - 144 * q^63 - 194 * q^64 + 16 * q^67 + 352 * q^70 - 148 * q^73 + 114 * q^75 - 336 * q^76 - 80 * q^79 - 162 * q^81 + 88 * q^82 + 336 * q^84 + 176 * q^85 + 396 * q^90 + 64 * q^91 + 156 * q^93 - 572 * q^94 - 124 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−3.15430	+	1.02489i	−1.57715	+	0.512447i	−0.961320	−	0.275433i	$-0.911179\pi$
$2$	−3.15430	+	1.02489i	−1.57715	+	0.512447i	−0.615829	+	0.787880i	$0.711179\pi$
$3$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$3$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$4$	5.66312	−	4.11450i	1.41578	−	1.02862i
$5$	6.30860	+	2.04979i	1.26172	+	0.409957i	0.862107	−	0.506727i	$-0.169145\pi$
$5$	6.30860	+	2.04979i	1.26172	+	0.409957i	0.399612	+	0.916684i	$0.369145\pi$
$6$	9.46289	+	3.07468i	1.57715	+	0.512447i
$7$	−6.47214	+	4.70228i	−0.924591	+	0.671755i	−0.944662	−	0.328044i	$-0.893611\pi$
$7$	−6.47214	+	4.70228i	−0.924591	+	0.671755i	0.0200716	+	0.999799i	$0.493611\pi$
$8$	−5.84839	+	8.04962i	−0.731049	+	1.00620i
$9$	2.78115	+	8.55951i	0.309017	+	0.951057i
$10$	−22.0000			−2.20000
$11$		0			0
$11$		0			0
$12$	−21.0000			−1.75000
$13$	−1.23607	−	3.80423i	−0.0950822	−	0.292633i	0.892193	−	0.451654i	$-0.149166\pi$
$13$	−1.23607	−	3.80423i	−0.0950822	−	0.292633i	−0.987275	+	0.159022i	$0.949166\pi$
$14$	15.5957	−	21.4656i	1.11398	−	1.53326i
$15$	−11.6968	−	16.0992i	−0.779785	−	1.07328i
$16$	1.54508	−	4.75528i	0.0965678	−	0.297205i
$17$	12.6172	+	4.09957i	0.742188	+	0.241151i	0.655616	−	0.755094i	$-0.272409\pi$
$17$	12.6172	+	4.09957i	0.742188	+	0.241151i	0.0865714	+	0.996246i	$0.472409\pi$
$18$	−17.5452	−	24.1489i	−0.974732	−	1.34160i
$19$	−4.85410	−	3.52671i	−0.255479	−	0.185616i	0.452673	−	0.891677i	$-0.350471\pi$
$19$	−4.85410	−	3.52671i	−0.255479	−	0.185616i	−0.708152	+	0.706060i	$0.750471\pi$
$20$	44.1602	−	14.3485i	2.20801	−	0.717425i
$21$	24.0000			1.14286
$22$		0			0
$23$		−	6.63325i		−	0.288402i	−0.989548	−	0.144201i	$-0.953939\pi$
$23$		−	6.63325i		−	0.288402i	0.989548	−	0.144201i	$-0.0460612\pi$
$24$	28.3887	−	9.22404i	1.18286	−	0.384335i
$25$	15.3713	+	11.1679i	0.614853	+	0.446717i
$26$	7.79785	+	10.7328i	0.299917	+	0.412801i
$27$	8.34346	−	25.6785i	0.309017	−	0.951057i
$28$	−17.3050	+	53.2592i	−0.618034	+	1.90211i
$29$	23.3936	+	32.1985i	0.806674	+	1.11029i	0.991828	+	0.127582i	$0.0407217\pi$
$29$	23.3936	+	32.1985i	0.806674	+	1.11029i	−0.185154	+	0.982710i	$0.559278\pi$
$30$	53.3951	+	38.7938i	1.77984	+	1.29313i
$31$	−8.03444	−	24.7275i	−0.259176	−	0.797660i	−0.992978	−	0.118298i	$-0.962256\pi$
$31$	−8.03444	−	24.7275i	−0.259176	−	0.797660i	0.733803	−	0.679363i	$-0.237744\pi$
$32$		−	23.2164i		−	0.725512i
$33$		0			0
$34$	−44.0000			−1.29412
$35$	−50.4688	+	16.3983i	−1.44196	+	0.468523i
$36$	50.9681	+	37.0305i	1.41578	+	1.02862i
$37$	−24.2705	+	17.6336i	−0.655960	+	0.476583i	−0.865296	−	0.501261i	$-0.832870\pi$
$37$	−24.2705	+	17.6336i	−0.655960	+	0.476583i	0.209336	+	0.977844i	$0.432870\pi$
$38$	18.9258	+	6.14936i	0.498047	+	0.161825i
$39$	−3.70820	+	11.4127i	−0.0950822	+	0.292633i
$40$	−53.3951	+	38.7938i	−1.33488	+	0.969846i
$41$	7.79785	−	10.7328i	0.190192	−	0.261776i	−0.703263	−	0.710930i	$-0.748274\pi$
$41$	7.79785	−	10.7328i	0.190192	−	0.261776i	0.893455	+	0.449154i	$0.148274\pi$
$42$	−75.7031	+	24.5974i	−1.80246	+	0.585653i
$43$	−42.0000			−0.976744			−0.488372	−	0.872635i	$-0.662409\pi$
$43$	−42.0000			−0.976744			−0.488372	+	0.872635i	$0.662409\pi$
$44$		0			0
$45$			59.6992i			1.32665i
$46$	6.79837	+	20.9232i	0.147791	+	0.454853i
$47$	−50.6860	+	69.7634i	−1.07843	+	1.48433i	−0.217185	+	0.976130i	$0.569688\pi$
$47$	−50.6860	+	69.7634i	−1.07843	+	1.48433i	−0.861241	+	0.508196i	$0.830312\pi$
$48$	−12.1353	+	8.81678i	−0.252818	+	0.183683i
$49$	4.63525	−	14.2658i	0.0945970	−	0.291140i
$50$	−59.9317	−	19.4730i	−1.19863	−	0.389460i
$51$	−23.3936	−	32.1985i	−0.458697	−	0.631343i
$52$	−22.6525	−	16.4580i	−0.435625	−	0.316500i
$53$	−56.7774	+	18.4481i	−1.07127	+	0.348077i	−0.790982	−	0.611839i	$-0.790430\pi$
$53$	−56.7774	+	18.4481i	−1.07127	+	0.348077i	−0.280288	+	0.959916i	$0.590430\pi$
$54$			89.5489i			1.65831i
$55$		0			0
$56$		−	79.5990i		−	1.42141i
$57$	5.56231	+	17.1190i	0.0975843	+	0.300334i
$58$	−106.790	−	77.5877i	−1.84121	−	1.33772i
$59$	38.9893	+	53.6641i	0.660835	+	0.909561i	0.999509	−	0.0313426i	$-0.00997829\pi$
$59$	38.9893	+	53.6641i	0.660835	+	0.909561i	−0.338674	+	0.940904i	$0.609978\pi$
$60$	−132.480	−	43.0455i	−2.20801	−	0.717425i
$61$	−3.70820	+	11.4127i	−0.0607902	+	0.187093i	−0.976840	−	0.213972i	$-0.931360\pi$
$61$	−3.70820	+	11.4127i	−0.0607902	+	0.187093i	0.916050	+	0.401065i	$0.131360\pi$
$62$	50.6860	+	69.7634i	0.817517	+	1.12522i
$63$	−58.2492	−	42.3205i	−0.924591	−	0.671755i
$64$	29.9746	+	92.2525i	0.468354	+	1.44145i
$65$		−	26.5330i		−	0.408200i
$66$		0			0
$67$	2.00000			0.0298507			0.0149254	−	0.999889i	$-0.495249\pi$
$67$	2.00000			0.0298507			0.0149254	+	0.999889i	$0.495249\pi$
$68$	88.3203	−	28.6970i	1.29883	−	0.422015i
$69$	−11.6968	+	16.0992i	−0.169519	+	0.233322i
$70$	142.387	−	103.450i	2.03410	−	1.47786i
$71$	56.7774	+	18.4481i	0.799681	+	0.259832i	0.680221	−	0.733007i	$-0.261884\pi$
$71$	56.7774	+	18.4481i	0.799681	+	0.259832i	0.119460	+	0.992839i	$0.461884\pi$
$72$	−85.1660	−	27.6721i	−1.18286	−	0.384335i
$73$	−59.8673	+	43.4961i	−0.820099	+	0.595837i	−0.916741	−	0.399482i	$-0.869190\pi$
$73$	−59.8673	+	43.4961i	−0.820099	+	0.595837i	0.0966416	+	0.995319i	$0.469190\pi$
$74$	58.4839	−	80.4962i	0.790323	−	1.08779i
$75$	−17.6140	−	54.2102i	−0.234853	−	0.722803i
$76$	−42.0000			−0.552632
$77$		0			0
$78$		−	39.7995i		−	0.510250i
$79$	12.3607	+	38.0423i	0.156464	+	0.481548i	0.998306	−	0.0581764i	$-0.0185286\pi$
$79$	12.3607	+	38.0423i	0.156464	+	0.481548i	−0.841842	+	0.539724i	$0.818529\pi$
$80$	19.4946	−	26.8321i	0.243683	−	0.335401i
$81$	−65.5304	+	47.6106i	−0.809017	+	0.587785i
$82$	−13.5967	+	41.8465i	−0.165814	+	0.510323i
$83$	−37.8516	−	12.2987i	−0.456043	−	0.148177i	0.0719824	−	0.997406i	$-0.477067\pi$
$83$	−37.8516	−	12.2987i	−0.456043	−	0.148177i	−0.528025	+	0.849229i	$0.677067\pi$
$84$	135.915	−	98.7479i	1.61803	−	1.17557i
$85$	71.1935	+	51.7251i	0.837571	+	0.608531i
$86$	132.480	−	43.0455i	1.54047	−	0.500529i
$87$		−	119.398i		−	1.37240i
$88$		0			0
$89$			119.398i			1.34156i	0.741658	+	0.670778i	$0.234040\pi$
$89$			119.398i			1.34156i	−0.741658	+	0.670778i	$0.765960\pi$
$90$	−61.1854	−	188.309i	−0.679837	−	2.09232i
$91$	25.8885	+	18.8091i	0.284489	+	0.206694i
$92$	−27.2925	−	37.5649i	−0.296657	−	0.408314i
$93$	−24.1033	+	74.1824i	−0.259176	+	0.797660i
$94$	88.3789	−	272.002i	0.940201	−	2.89364i
$95$	−23.3936	−	32.1985i	−0.246248	−	0.338931i
$96$	−40.9387	+	56.3473i	−0.426445	+	0.586951i
$97$	19.1591	+	58.9655i	0.197516	+	0.607892i	0.999938	+	0.0111348i	$0.00354438\pi$
$97$	19.1591	+	58.9655i	0.197516	+	0.607892i	−0.802422	+	0.596757i	$0.796456\pi$
$98$			49.7494i			0.507647i
$99$		0			0
$100$	133.000			1.33000
$101$	−100.938	+	32.7966i	−0.999381	+	0.324719i	−0.762618	−	0.646849i	$-0.776087\pi$
$101$	−100.938	+	32.7966i	−0.999381	+	0.324719i	−0.236763	+	0.971567i	$0.576087\pi$
$102$	106.790	+	77.5877i	1.04696	+	0.760663i
$103$	−59.8673	+	43.4961i	−0.581236	+	0.422292i	−0.839169	−	0.543870i	$-0.816958\pi$
$103$	−59.8673	+	43.4961i	−0.581236	+	0.422292i	0.257934	+	0.966163i	$0.416958\pi$
$104$	37.8516	+	12.2987i	0.363957	+	0.118257i
$105$	151.406	+	49.1949i	1.44196	+	0.468523i
$106$	160.185	−	116.381i	1.51118	−	1.09794i
$107$	−23.3936	+	32.1985i	−0.218631	+	0.300920i	−0.904218	−	0.427070i	$-0.859546\pi$
$107$	−23.3936	+	32.1985i	−0.218631	+	0.300920i	0.685587	+	0.727991i	$0.259546\pi$
$108$	−58.4042	−	179.750i	−0.540780	−	1.66435i
$109$	200.000			1.83486			0.917431	−	0.397894i	$-0.130259\pi$
$109$	200.000			1.83486			0.917431	+	0.397894i	$0.130259\pi$
$110$		0			0
$111$	90.0000			0.810811
$112$	12.3607	+	38.0423i	0.110363	+	0.339663i
$113$	23.3936	−	32.1985i	0.207023	−	0.284942i	−0.692862	−	0.721070i	$-0.743651\pi$
$113$	23.3936	−	32.1985i	0.207023	−	0.284942i	0.899885	+	0.436128i	$0.143651\pi$
$114$	−35.0903	−	48.2977i	−0.307810	−	0.423664i
$115$	13.5967	−	41.8465i	0.118233	−	0.363882i
$116$	264.961	+	86.0910i	2.28415	+	0.742164i
$117$	29.1246	−	21.1603i	0.248928	−	0.180857i
$118$	−177.984	−	129.313i	−1.50834	−	1.09587i
$119$	−100.938	+	32.7966i	−0.848214	+	0.275602i
$120$	198.000			1.65000
$121$		0			0
$122$		−	39.7995i		−	0.326225i
$123$	−37.8516	+	12.2987i	−0.307736	+	0.0999896i
$124$	−147.241	−	106.977i	−1.18743	−	0.862717i
$125$	−23.3936	−	32.1985i	−0.187148	−	0.257588i
$126$	227.109	+	73.7923i	1.80246	+	0.585653i
$127$	−58.0952	+	178.799i	−0.457442	+	1.40786i	0.410801	+	0.911725i	$0.365249\pi$
$127$	−58.0952	+	178.799i	−0.457442	+	1.40786i	−0.868244	+	0.496138i	$0.834751\pi$
$128$	−134.513	−	185.141i	−1.05088	−	1.44642i
$129$	101.936	+	74.0609i	0.790203	+	0.574116i
$130$	27.1935	+	83.6930i	0.209181	+	0.643792i
$131$			39.7995i			0.303813i	0.988395	+	0.151906i	$0.0485413\pi$
$131$			39.7995i			0.303813i	−0.988395	+	0.151906i	$0.951459\pi$
$132$		0			0
$133$	48.0000			0.360902
$134$	−6.30860	+	2.04979i	−0.0470791	+	0.0152969i
$135$	105.271	−	144.893i	0.779785	−	1.07328i
$136$	−106.790	+	77.5877i	−0.785222	+	0.570497i
$137$	−100.938	−	32.7966i	−0.736770	−	0.239391i	−0.0834913	−	0.996509i	$-0.526607\pi$
$137$	−100.938	−	32.7966i	−0.736770	−	0.239391i	−0.653279	+	0.757117i	$0.726607\pi$
$138$	20.3951	−	62.7697i	0.147791	−	0.454853i
$139$	−59.8673	+	43.4961i	−0.430700	+	0.312922i	−0.781929	−	0.623368i	$-0.785764\pi$
$139$	−59.8673	+	43.4961i	−0.430700	+	0.312922i	0.351229	+	0.936290i	$0.385764\pi$
$140$	−218.340	+	300.519i	−1.55957	+	2.14656i
$141$	246.035	−	79.9417i	1.74493	−	0.566962i
$142$	−198.000			−1.39437
$143$		0			0
$144$	45.0000			0.312500
$145$	81.5805	+	251.079i	0.562624	+	1.73158i
$146$	144.260	−	198.557i	0.988084	−	1.35998i
$147$	−36.4058	+	26.4503i	−0.247658	+	0.179934i
$148$	−64.8936	+	199.722i	−0.438470	+	1.34947i
$149$	−88.3203	−	28.6970i	−0.592754	−	0.192597i	−0.00274784	−	0.999996i	$-0.500875\pi$
$149$	−88.3203	−	28.6970i	−0.592754	−	0.192597i	−0.590006	+	0.807399i	$0.700875\pi$
$150$	111.119	+	152.943i	0.740796	+	1.01962i
$151$	−129.443	−	94.0456i	−0.857237	−	0.622819i	0.0698952	−	0.997554i	$-0.477734\pi$
$151$	−129.443	−	94.0456i	−0.857237	−	0.622819i	−0.927132	+	0.374736i	$0.877734\pi$
$152$	56.7774	−	18.4481i	0.373535	−	0.121369i
$153$			119.398i			0.780382i
$154$		0			0
$155$		−	172.464i		−	1.11267i
$156$	25.9574	+	79.8887i	0.166394	+	0.512107i
$157$	−147.241	−	106.977i	−0.937841	−	0.681382i	0.0100587	−	0.999949i	$-0.496798\pi$
$157$	−147.241	−	106.977i	−0.937841	−	0.681382i	−0.947900	+	0.318568i	$0.896798\pi$
$158$	−77.9785	−	107.328i	−0.493535	−	0.679293i
$159$	170.332	+	55.3442i	1.07127	+	0.348077i
$160$	47.5886	−	146.463i	0.297429	−	0.915392i
$161$	31.1914	+	42.9313i	0.193735	+	0.266654i
$162$	157.907	−	217.340i	0.974732	−	1.34160i
$163$	−89.6149	−	275.806i	−0.549785	−	1.69206i	−0.709333	−	0.704874i	$-0.751004\pi$
$163$	−89.6149	−	275.806i	−0.549785	−	1.69206i	0.159548	−	0.987190i	$-0.448996\pi$
$164$		−	92.8655i		−	0.566253i
$165$		0			0
$166$	132.000			0.795181
$167$	227.109	−	73.7923i	1.35994	−	0.441870i	0.463915	−	0.885880i	$-0.346444\pi$
$167$	227.109	−	73.7923i	1.35994	−	0.441870i	0.896022	+	0.444010i	$0.146444\pi$
$168$	−140.361	+	193.191i	−0.835484	+	1.14995i
$169$	123.780	−	89.9311i	0.732424	−	0.532137i
$170$	−277.578	−	90.1906i	−1.63281	−	0.530533i
$171$	16.6869	−	51.3571i	0.0975843	−	0.300334i
$172$	−237.851	+	172.809i	−1.38285	+	1.00470i
$173$	116.968	−	160.992i	0.676114	−	0.930592i	−0.323765	−	0.946138i	$-0.604949\pi$
$173$	116.968	−	160.992i	0.676114	−	0.930592i	0.999879	+	0.0155460i	$0.00494864\pi$
$174$	122.371	+	376.618i	0.703280	+	2.16447i
$175$	−152.000			−0.868571
$176$		0			0
$177$		−	198.997i		−	1.12428i
$178$	−122.371	−	376.618i	−0.687476	−	2.11583i
$179$	−116.968	+	160.992i	−0.653451	+	0.899399i	−0.999243	−	0.0389129i	$-0.987611\pi$
$179$	−116.968	+	160.992i	−0.653451	+	0.899399i	0.345791	+	0.938311i	$0.387611\pi$
$180$	245.632	+	338.084i	1.36462	+	1.87824i
$181$	3.09017	−	9.51057i	0.0170728	−	0.0525446i	−0.942157	−	0.335171i	$-0.891206\pi$
$181$	3.09017	−	9.51057i	0.0170728	−	0.0525446i	0.959230	+	0.282627i	$0.0912058\pi$
$182$	−100.938	−	32.7966i	−0.554602	−	0.180201i
$183$	29.1246	−	21.1603i	0.159151	−	0.115630i
$184$	53.3951	+	38.7938i	0.290191	+	0.210836i
$185$	−189.258	+	61.4936i	−1.02302	+	0.332398i
$186$		−	258.697i		−	1.39084i
$187$		0			0
$188$			603.626i			3.21078i
$189$	66.7477	+	205.428i	0.353162	+	1.08692i
$190$	106.790	+	77.5877i	0.562054	+	0.408356i
$191$	−66.2817	−	91.2290i	−0.347025	−	0.477639i	0.599452	−	0.800411i	$-0.295385\pi$
$191$	−66.2817	−	91.2290i	−0.347025	−	0.477639i	−0.946477	+	0.322772i	$0.895385\pi$
$192$	89.9239	−	276.757i	0.468354	−	1.44145i
$193$	−92.0871	+	283.415i	−0.477135	+	1.46847i	0.365921	+	0.930646i	$0.380754\pi$
$193$	−92.0871	+	283.415i	−0.477135	+	1.46847i	−0.843057	+	0.537825i	$0.819246\pi$
$194$	−120.867	−	166.359i	−0.623024	−	0.857519i
$195$	−46.7871	+	64.3969i	−0.239934	+	0.330241i
$196$	−32.4468	−	99.8609i	−0.165545	−	0.509495i
$197$			132.665i			0.673426i	0.941607	+	0.336713i	$0.109315\pi$
$197$			132.665i			0.673426i	−0.941607	+	0.336713i	$0.890685\pi$
$198$		0			0
$199$	−42.0000			−0.211055			−0.105528	−	0.994416i	$-0.533653\pi$
$199$	−42.0000			−0.211055			−0.105528	+	0.994416i	$0.533653\pi$
$200$	−179.795	+	58.4189i	−0.898975	+	0.292095i
$201$	−4.85410	−	3.52671i	−0.0241498	−	0.0175458i
$202$	284.774	−	206.900i	1.40977	−	1.02426i
$203$	−302.813	−	98.3898i	−1.49169	−	0.484679i
$204$	−264.961	−	86.0910i	−1.29883	−	0.422015i
$205$	71.1935	−	51.7251i	0.347285	−	0.252318i
$206$	144.260	−	198.557i	0.700293	−	0.963870i
$207$	56.7774	−	18.4481i	0.274287	−	0.0891212i
$208$	−20.0000			−0.0961538
$209$		0			0
$210$	−528.000			−2.51429
$211$	−76.0182	−	233.960i	−0.360276	−	1.10881i	−0.952887	−	0.303326i	$-0.901903\pi$
$211$	−76.0182	−	233.960i	−0.360276	−	1.10881i	0.592611	−	0.805489i	$-0.298097\pi$
$212$	−245.632	+	338.084i	−1.15864	+	1.59474i
$213$	−105.271	−	144.893i	−0.494230	−	0.680249i
$214$	40.7902	−	125.539i	0.190609	−	0.586633i
$215$	−264.961	−	86.0910i	−1.23238	−	0.400423i
$216$	157.907	+	217.340i	0.731049	+	1.00620i
$217$	168.276	+	122.259i	0.775463	+	0.563407i
$218$	−630.860	+	204.979i	−2.89385	+	0.940269i
$219$	222.000			1.01370
$220$		0			0
$221$		−	53.0660i		−	0.240118i
$222$	−283.887	+	92.2404i	−1.27877	+	0.415497i
$223$	244.323	+	177.511i	1.09562	+	0.796014i	0.980339	−	0.197319i	$-0.0632234\pi$
$223$	244.323	+	177.511i	1.09562	+	0.796014i	0.115280	+	0.993333i	$0.463223\pi$
$224$	109.170	+	150.260i	0.487366	+	0.670801i
$225$	−52.8419	+	162.631i	−0.234853	+	0.722803i
$226$	−40.7902	+	125.539i	−0.180488	+	0.555484i
$227$	116.968	+	160.992i	0.515277	+	0.709217i	0.984798	−	0.173704i	$-0.0555735\pi$
$227$	116.968	+	160.992i	0.515277	+	0.709217i	−0.469521	+	0.882921i	$0.655574\pi$
$228$	101.936	+	74.0609i	0.447088	+	0.324829i
$229$	46.3525	+	142.658i	0.202413	+	0.622963i	0.999810	+	0.0195075i	$0.00620982\pi$
$229$	46.3525	+	142.658i	0.202413	+	0.622963i	−0.797397	+	0.603455i	$0.793790\pi$
$230$			145.931i			0.634485i
$231$		0			0
$232$	−396.000			−1.70690
$233$	416.367	−	135.286i	1.78698	−	0.580626i	0.787616	−	0.616167i	$-0.211315\pi$
$233$	416.367	−	135.286i	1.78698	−	0.580626i	0.999368	+	0.0355403i	$0.0113152\pi$
$234$	−70.1807	+	96.5954i	−0.299917	+	0.412801i
$235$	−462.758	+	336.213i	−1.96918	+	1.43069i
$236$	441.602	+	143.485i	1.87119	+	0.607988i
$237$	37.0820	−	114.127i	0.156464	−	0.481548i
$238$	284.774	−	206.900i	1.19653	−	0.869329i
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$	−94.6289	+	30.7468i	−0.394287	+	0.128112i
$241$	−130.000			−0.539419			−0.269710	−	0.962942i	$-0.586928\pi$
$241$	−130.000			−0.539419			−0.269710	+	0.962942i	$0.586928\pi$
$242$		0			0
$243$	243.000			1.00000
$244$	25.9574	+	79.8887i	0.106383	+	0.327413i
$245$	58.4839	−	80.4962i	0.238710	−	0.328556i
$246$	106.790	−	77.5877i	0.434107	−	0.315397i
$247$	−7.41641	+	22.8254i	−0.0300259	+	0.0924103i
$248$	246.035	+	79.9417i	0.992077	+	0.322346i
$249$	70.1807	+	96.5954i	0.281850	+	0.387933i
$250$	106.790	+	77.5877i	0.427161	+	0.310351i
$251$	277.578	−	90.1906i	1.10589	−	0.359325i	0.301523	−	0.953459i	$-0.402505\pi$
$251$	277.578	−	90.1906i	1.10589	−	0.359325i	0.804366	+	0.594134i	$0.202505\pi$
$252$	−504.000			−2.00000
$253$		0			0
$254$		−	623.525i		−	2.45482i
$255$	−81.5805	−	251.079i	−0.319923	−	0.984623i
$256$	300.145	+	218.068i	1.17244	+	0.851829i
$257$	288.521	+	397.114i	1.12265	+	1.54519i	0.801331	+	0.598221i	$0.204125\pi$
$257$	288.521	+	397.114i	1.12265	+	1.54519i	0.321317	+	0.946972i	$0.395875\pi$
$258$	−397.441	−	129.137i	−1.54047	−	0.500529i
$259$	74.1641	−	228.254i	0.286348	−	0.881288i
$260$	−109.170	−	150.260i	−0.419884	−	0.577921i
$261$	−210.542	+	289.786i	−0.806674	+	1.11029i
$262$	−40.7902	−	125.539i	−0.155688	−	0.479158i
$263$			225.530i			0.857530i	0.903416	+	0.428765i	$0.141051\pi$
$263$			225.530i			0.857530i	−0.903416	+	0.428765i	$0.858949\pi$
$264$		0			0
$265$	−396.000			−1.49434
$266$	−151.406	+	49.1949i	−0.569197	+	0.184943i
$267$	210.542	−	289.786i	0.788547	−	1.08534i
$268$	11.3262	−	8.22899i	0.0422621	−	0.0307052i
$269$	−69.3945	−	22.5477i	−0.257972	−	0.0838203i	0.177176	−	0.984179i	$-0.443304\pi$
$269$	−69.3945	−	22.5477i	−0.257972	−	0.0838203i	−0.435148	+	0.900359i	$0.643304\pi$
$270$	−183.556	+	564.928i	−0.679837	+	2.09232i
$271$	−362.440	+	263.328i	−1.33742	+	0.971689i	−0.337881	+	0.941189i	$0.609710\pi$
$271$	−362.440	+	263.328i	−1.33742	+	0.971689i	−0.999535	+	0.0305004i	$0.990290\pi$
$272$	38.9893	−	53.6641i	0.143343	−	0.197295i
$273$	−29.6656	−	91.3014i	−0.108665	−	0.334437i
$274$	352.000			1.28467
$275$		0			0
$276$			139.298i			0.504704i
$277$	80.3444	+	247.275i	0.290052	+	0.892688i	0.984839	+	0.173473i	$0.0554988\pi$
$277$	80.3444	+	247.275i	0.290052	+	0.892688i	−0.694787	+	0.719216i	$0.744501\pi$
$278$	144.260	−	198.557i	0.518922	−	0.714235i
$279$	189.310	−	137.542i	0.678530	−	0.492981i
$280$	163.161	−	502.158i	0.582718	−	1.79342i
$281$	−189.258	−	61.4936i	−0.673516	−	0.218838i	−0.0477613	−	0.998859i	$-0.515209\pi$
$281$	−189.258	−	61.4936i	−0.673516	−	0.218838i	−0.625754	+	0.780020i	$0.715209\pi$
$282$	−694.137	+	504.320i	−2.46148	+	1.78837i
$283$	−40.4508	−	29.3893i	−0.142936	−	0.103849i	0.514019	−	0.857779i	$-0.328156\pi$
$283$	−40.4508	−	29.3893i	−0.142936	−	0.103849i	−0.656955	+	0.753930i	$0.728156\pi$
$284$	397.441	−	129.137i	1.39944	−	0.454706i
$285$			119.398i			0.418942i
$286$		0			0
$287$			106.132i			0.369798i
$288$	198.721	−	64.5683i	0.690003	−	0.224195i
$289$	−91.4189	−	66.4197i	−0.316328	−	0.229826i
$290$	−514.658	−	708.366i	−1.77468	−	2.44264i
$291$	57.4772	−	176.897i	0.197516	−	0.607892i
$292$	−160.071	+	492.647i	−0.548188	+	1.68715i
$293$	−280.723	−	386.382i	−0.958098	−	1.31871i	−0.947835	−	0.318761i	$-0.896733\pi$
$293$	−280.723	−	386.382i	−0.958098	−	1.31871i	−0.0102629	−	0.999947i	$-0.503267\pi$
$294$	87.7258	−	120.744i	0.298387	−	0.410695i
$295$	135.967	+	418.465i	0.460907	+	1.41852i
$296$		−	298.496i		−	1.00843i
$297$		0			0
$298$	308.000			1.03356
$299$	−25.2344	+	8.19915i	−0.0843959	+	0.0274219i
$300$	−322.798	−	234.526i	−1.07599	−	0.781754i
$301$	271.830	−	197.496i	0.903089	−	0.656132i
$302$	504.688	+	163.983i	1.67115	+	0.542990i
$303$	302.813	+	98.3898i	0.999381	+	0.324719i
$304$	−24.2705	+	17.6336i	−0.0798372	+	0.0580051i
$305$	−46.7871	+	64.3969i	−0.153400	+	0.211138i
$306$	−122.371	−	376.618i	−0.399904	−	1.23078i
$307$	−86.0000			−0.280130			−0.140065	−	0.990142i	$-0.544731\pi$
$307$	−86.0000			−0.280130			−0.140065	+	0.990142i	$0.544731\pi$
$308$		0			0
$309$	222.000			0.718447
$310$	176.758	+	544.004i	0.570186	+	1.75485i
$311$	−11.6968	+	16.0992i	−0.0376102	+	0.0517660i	−0.827408	−	0.561601i	$-0.810185\pi$
$311$	−11.6968	+	16.0992i	−0.0376102	+	0.0517660i	0.789798	+	0.613367i	$0.210185\pi$
$312$	−70.1807	−	96.5954i	−0.224938	−	0.309601i
$313$	30.2837	−	93.2035i	0.0967529	−	0.297775i	−0.890954	−	0.454094i	$-0.849963\pi$
$313$	30.2837	−	93.2035i	0.0967529	−	0.297775i	0.987707	+	0.156319i	$0.0499629\pi$
$314$	574.082	+	186.531i	1.82829	+	0.594047i
$315$	−280.723	−	386.382i	−0.891183	−	1.22661i
$316$	226.525	+	164.580i	0.716851	+	0.520822i
$317$	296.504	−	96.3400i	0.935344	−	0.303912i	0.198598	−	0.980081i	$-0.436361\pi$
$317$	296.504	−	96.3400i	0.935344	−	0.303912i	0.736746	+	0.676169i	$0.236361\pi$
$318$	−594.000			−1.86792
$319$		0			0
$320$			643.425i			2.01070i
$321$	113.555	−	36.8962i	0.353753	−	0.114941i
$322$	−142.387	−	103.450i	−0.442196	−	0.321274i
$323$	−46.7871	−	64.3969i	−0.144852	−	0.199371i
$324$	−175.213	+	539.249i	−0.540780	+	1.66435i
$325$	23.4853	−	72.2803i	0.0722624	−	0.222401i
$326$	565.344	+	778.130i	1.73419	+	2.38690i
$327$	−485.410	−	352.671i	−1.48443	−	1.07851i
$328$	40.7902	+	125.539i	0.124360	+	0.382742i
$329$		−	689.858i		−	2.09683i
$330$		0			0
$331$	−218.000			−0.658610			−0.329305	−	0.944224i	$-0.606814\pi$
$331$	−218.000			−0.658610			−0.329305	+	0.944224i	$0.606814\pi$
$332$	−264.961	+	86.0910i	−0.798075	+	0.259310i
$333$	−218.435	−	158.702i	−0.655960	−	0.476583i
$334$	−640.741	+	465.526i	−1.91839	+	1.39379i
$335$	12.6172	+	4.09957i	0.0376633	+	0.0122375i
$336$	37.0820	−	114.127i	0.110363	−	0.339663i
$337$	224.907	−	163.404i	0.667379	−	0.484879i	−0.201768	−	0.979433i	$-0.564669\pi$
$337$	224.907	−	163.404i	0.667379	−	0.484879i	0.869147	+	0.494554i	$0.164669\pi$
$338$	−298.268	+	410.530i	−0.882449	+	1.21459i
$339$	−113.555	+	36.8962i	−0.334970	+	0.108838i
$340$	616.000			1.81176
$341$		0			0
$342$			179.098i			0.523678i
$343$	−84.0526	−	258.687i	−0.245051	−	0.754191i
$344$	245.632	−	338.084i	0.714048	−	0.982802i
$345$	−106.790	+	77.5877i	−0.309537	+	0.224892i
$346$	−203.951	+	627.697i	−0.589454	+	1.81415i
$347$	315.430	+	102.489i	0.909019	+	0.295358i	0.725955	−	0.687743i	$-0.241398\pi$
$347$	315.430	+	102.489i	0.909019	+	0.295358i	0.183065	+	0.983101i	$0.441398\pi$
$348$	−491.265	−	676.168i	−1.41168	−	1.94301i
$349$	262.122	+	190.442i	0.751064	+	0.545680i	0.896157	−	0.443738i	$-0.146348\pi$
$349$	262.122	+	190.442i	0.751064	+	0.545680i	−0.145092	+	0.989418i	$0.546348\pi$
$350$	479.453	−	155.784i	1.36987	−	0.445097i
$351$	−108.000			−0.307692
$352$		0			0
$353$		−	397.995i		−	1.12746i	−0.825958	−	0.563732i	$-0.809365\pi$
$353$		−	397.995i		−	1.12746i	0.825958	−	0.563732i	$-0.190635\pi$
$354$	203.951	+	627.697i	0.576133	+	1.77316i
$355$	320.371	+	232.763i	0.902453	+	0.655670i
$356$	491.265	+	676.168i	1.37996	+	1.89935i
$357$	302.813	+	98.3898i	0.848214	+	0.275602i
$358$	203.951	−	627.697i	0.569696	−	1.75334i
$359$	179.351	+	246.855i	0.499584	+	0.687618i	0.982120	−	0.188258i	$-0.0602841\pi$
$359$	179.351	+	246.855i	0.499584	+	0.687618i	−0.482536	+	0.875876i	$0.660284\pi$
$360$	−480.556	−	349.144i	−1.33488	−	0.969846i
$361$	−100.431	−	309.093i	−0.278201	−	0.856214i
$362$			33.1662i			0.0916195i
$363$		0			0
$364$	224.000			0.615385
$365$	−466.836	+	151.684i	−1.27900	+	0.415573i
$366$	−70.1807	+	96.5954i	−0.191750	+	0.263922i
$367$	224.907	−	163.404i	0.612825	−	0.445243i	−0.237583	−	0.971367i	$-0.576355\pi$
$367$	224.907	−	163.404i	0.612825	−	0.445243i	0.850408	+	0.526124i	$0.176355\pi$
$368$	−31.5430	−	10.2489i	−0.0857146	−	0.0278504i
$369$	113.555	+	36.8962i	0.307736	+	0.0999896i
$370$	533.951	−	387.938i	1.44311	−	1.04848i
$371$	280.723	−	386.382i	0.756665	−	1.04146i
$372$	168.723	+	519.277i	0.453557	+	1.39591i
$373$	68.0000			0.182306			0.0911528	−	0.995837i	$-0.470945\pi$
$373$	68.0000			0.182306			0.0911528	+	0.995837i	$0.470945\pi$
$374$		0			0
$375$			119.398i			0.318396i
$376$	−265.137	−	816.006i	−0.705150	−	2.17023i
$377$	93.5742	−	128.794i	0.248208	−	0.341628i
$378$	−421.084	−	579.572i	−1.11398	−	1.53326i
$379$	207.041	−	637.208i	0.546283	−	1.68129i	−0.171636	−	0.985161i	$-0.554905\pi$
$379$	207.041	−	637.208i	0.546283	−	1.68129i	0.717919	−	0.696127i	$-0.245095\pi$
$380$	−264.961	−	86.0910i	−0.697266	−	0.226555i
$381$	456.286	−	331.511i	1.19760	−	0.870107i
$382$	302.572	+	219.832i	0.792074	+	0.575476i
$383$	−31.5430	+	10.2489i	−0.0823576	+	0.0267596i	−0.349906	−	0.936785i	$-0.613786\pi$
$383$	−31.5430	+	10.2489i	−0.0823576	+	0.0267596i	0.267548	+	0.963544i	$0.413786\pi$
$384$			686.541i			1.78787i
$385$		0			0
$386$		−	988.354i		−	2.56050i
$387$	−116.808	−	359.499i	−0.301831	−	0.928939i
$388$	351.113	+	255.099i	0.904931	+	0.657471i
$389$	−245.632	−	338.084i	−0.631446	−	0.869110i	0.366678	−	0.930348i	$-0.380495\pi$
$389$	−245.632	−	338.084i	−0.631446	−	0.869110i	−0.998123	+	0.0612377i	$0.980495\pi$
$390$	81.5805	−	251.079i	0.209181	−	0.643792i
$391$	27.1935	−	83.6930i	0.0695486	−	0.214049i
$392$	87.7258	+	120.744i	0.223790	+	0.308021i
$393$	70.1807	−	96.5954i	0.178577	−	0.245790i
$394$	−135.967	−	418.465i	−0.345095	−	1.06209i
$395$			265.330i			0.671721i
$396$		0			0
$397$	−86.0000			−0.216625			−0.108312	−	0.994117i	$-0.534545\pi$
$397$	−86.0000			−0.216625			−0.108312	+	0.994117i	$0.534545\pi$
$398$	132.480	−	43.0455i	0.332866	−	0.108155i
$399$	−116.498	−	84.6411i	−0.291976	−	0.212133i
$400$	76.8566	−	55.8396i	0.192142	−	0.139599i
$401$	239.727	+	77.8919i	0.597822	+	0.194244i	0.592269	−	0.805740i	$-0.298232\pi$
$401$	239.727	+	77.8919i	0.597822	+	0.194244i	0.00555318	+	0.999985i	$0.498232\pi$
$402$	18.9258	+	6.14936i	0.0470791	+	0.0152969i
$403$	−84.1378	+	61.1297i	−0.208779	+	0.151687i
$404$	−436.680	+	601.038i	−1.08089	+	1.48772i
$405$	−510.996	+	166.033i	−1.26172	+	0.409957i
$406$	1056.00			2.60099
$407$		0			0
$408$	396.000			0.970588
$409$	−157.599	−	485.039i	−0.385327	−	1.18591i	−0.936243	−	0.351353i	$-0.885722\pi$
$409$	−157.599	−	485.039i	−0.385327	−	1.18591i	0.550916	−	0.834561i	$-0.314278\pi$
$410$	−171.553	+	236.122i	−0.418421	+	0.575908i
$411$	187.148	+	257.588i	0.455349	+	0.626734i
$412$	−160.071	+	492.647i	−0.388521	+	1.19575i
$413$	−504.688	−	163.983i	−1.22200	−	0.397053i
$414$	−160.185	+	116.381i	−0.386921	+	0.281115i
$415$	−213.580	−	155.175i	−0.514652	−	0.373916i
$416$	−88.3203	+	28.6970i	−0.212308	+	0.0689832i
$417$	222.000			0.532374
$418$		0			0
$419$			530.660i			1.26649i	0.773951	+	0.633246i	$0.218278\pi$
$419$			530.660i			1.26649i	−0.773951	+	0.633246i	$0.781722\pi$
$420$	1059.84	−	344.364i	2.52344	−	0.819915i
$421$	137.533	+	99.9235i	0.326681	+	0.237348i	0.739021	−	0.673682i	$-0.235288\pi$
$421$	137.533	+	99.9235i	0.326681	+	0.237348i	−0.412340	+	0.911030i	$0.635288\pi$
$422$	479.568	+	660.069i	1.13642	+	1.56414i
$423$	−738.106	−	239.825i	−1.74493	−	0.566962i
$424$	183.556	−	564.928i	0.432915	−	1.33238i
$425$	148.159	+	203.924i	0.348610	+	0.479820i
$426$	480.556	+	349.144i	1.12807	+	0.819588i
$427$	−29.6656	−	91.3014i	−0.0694745	−	0.213821i
$428$			278.596i			0.650926i
$429$		0			0
$430$	924.000			2.14884
$431$	−264.961	+	86.0910i	−0.614759	+	0.199747i	−0.599812	−	0.800141i	$-0.704758\pi$
$431$	−264.961	+	86.0910i	−0.614759	+	0.199747i	−0.0149469	+	0.999888i	$0.504758\pi$
$432$	−109.217	−	79.3510i	−0.252818	−	0.183683i
$433$	438.487	−	318.580i	1.01267	−	0.735750i	0.0479046	−	0.998852i	$-0.484746\pi$
$433$	438.487	−	318.580i	1.01267	−	0.735750i	0.964768	+	0.263102i	$0.0847457\pi$
$434$	−656.094	−	213.178i	−1.51174	−	0.491193i
$435$	244.741	−	753.237i	0.562624	−	1.73158i
$436$	1132.62	−	822.899i	2.59776	−	1.88738i
$437$	−23.3936	+	32.1985i	−0.0535322	+	0.0736807i
$438$	−700.254	+	227.526i	−1.59875	+	0.519467i
$439$	−328.000			−0.747153			−0.373576	−	0.927599i	$-0.621869\pi$
$439$	−328.000			−0.747153			−0.373576	+	0.927599i	$0.621869\pi$
$440$		0			0
$441$	135.000			0.306122
$442$	54.3870	+	167.386i	0.123047	+	0.378701i
$443$	−77.9785	+	107.328i	−0.176024	+	0.242276i	−0.887908	−	0.460021i	$-0.847842\pi$
$443$	−77.9785	+	107.328i	−0.176024	+	0.242276i	0.711884	+	0.702297i	$0.247842\pi$
$444$	509.681	−	370.305i	1.14793	−	0.834020i
$445$	−244.741	+	753.237i	−0.549981	+	1.69267i
$446$	−952.598	−	309.518i	−2.13587	−	0.693986i
$447$	163.755	+	225.389i	0.366342	+	0.504227i
$448$	−627.797	−	456.121i	−1.40133	−	1.01813i
$449$	−428.984	+	139.386i	−0.955422	+	0.310435i	−0.744917	−	0.667157i	$-0.767511\pi$
$449$	−428.984	+	139.386i	−0.955422	+	0.310435i	−0.210505	+	0.977593i	$0.567511\pi$
$450$		−	567.143i		−	1.26032i
$451$		0			0
$452$		−	278.596i		−	0.616364i
$453$	148.328	+	456.507i	0.327435	+	1.00774i
$454$	−533.951	−	387.938i	−1.17610	−	0.854490i
$455$	124.766	+	171.725i	0.274210	+	0.377418i
$456$	−170.332	−	55.3442i	−0.373535	−	0.121369i
$457$	−105.684	+	325.261i	−0.231256	+	0.711732i	0.766340	+	0.642435i	$0.222076\pi$
$457$	−105.684	+	325.261i	−0.231256	+	0.711732i	−0.997596	+	0.0692969i	$0.977924\pi$
$458$	−292.419	−	402.481i	−0.638470	−	0.878779i
$459$	210.542	−	289.786i	0.458697	−	0.631343i
$460$	−95.1772	−	292.925i	−0.206907	−	0.636794i
$461$		−	79.5990i		−	0.172666i	−0.996266	−	0.0863330i	$-0.972485\pi$
$461$		−	79.5990i		−	0.172666i	0.996266	−	0.0863330i	$-0.0275149\pi$
$462$		0			0
$463$	−86.0000			−0.185745			−0.0928726	−	0.995678i	$-0.529605\pi$
$463$	−86.0000			−0.185745			−0.0928726	+	0.995678i	$0.529605\pi$
$464$	189.258	−	61.4936i	0.407883	−	0.132529i
$465$	−304.116	+	418.580i	−0.654013	+	0.900172i
$466$	−1174.69	+	853.464i	−2.52080	+	1.83147i
$467$	567.774	+	184.481i	1.21579	+	0.395034i	0.845547	−	0.533901i	$-0.179275\pi$
$467$	567.774	+	184.481i	1.21579	+	0.395034i	0.370242	+	0.928935i	$0.379275\pi$
$468$	77.8723	−	239.666i	0.166394	−	0.512107i
$469$	−12.9443	+	9.40456i	−0.0275997	+	0.0200524i
$470$	1115.09	−	1534.79i	2.37254	−	3.26552i
$471$	168.723	+	519.277i	0.358224	+	1.10250i
$472$	−660.000			−1.39831
$473$		0			0
$474$			397.995i			0.839652i
$475$	−35.2279	−	108.420i	−0.0741641	−	0.228254i
$476$	−436.680	+	601.038i	−0.917394	+	1.26269i
$477$	−315.813	−	434.679i	−0.662082	−	0.911277i
$478$		0			0
$479$	214.492	+	69.6928i	0.447792	+	0.145496i	0.524228	−	0.851578i	$-0.324354\pi$
$479$	214.492	+	69.6928i	0.447792	+	0.145496i	−0.0764360	+	0.997074i	$0.524354\pi$
$480$	−373.766	+	271.557i	−0.778679	+	0.565743i
$481$	97.0820	+	70.5342i	0.201834	+	0.146641i
$482$	410.059	−	133.236i	0.850744	−	0.276424i
$483$		−	159.198i		−	0.329602i
$484$		0			0
$485$			411.261i			0.847962i
$486$	−766.494	+	249.049i	−1.57715	+	0.512447i
$487$	−360.822	−	262.152i	−0.740907	−	0.538300i	0.152088	−	0.988367i	$-0.451400\pi$
$487$	−360.822	−	262.152i	−0.740907	−	0.538300i	−0.892995	+	0.450067i	$0.851400\pi$
$488$	−70.1807	−	96.5954i	−0.143813	−	0.197941i
$489$	−268.845	+	827.419i	−0.549785	+	1.69206i
$490$	−101.976	+	313.849i	−0.208113	+	0.640507i
$491$	413.286	+	568.840i	0.841723	+	1.15853i	0.985626	+	0.168941i	$0.0540347\pi$
$491$	413.286	+	568.840i	0.841723	+	1.15853i	−0.143903	+	0.989592i	$0.545965\pi$
$492$	−163.755	+	225.389i	−0.332835	+	0.458108i
$493$	163.161	+	502.158i	0.330955	+	1.01858i
$494$		−	79.5990i		−	0.161132i
$495$		0			0
$496$	−130.000			−0.262097
$497$	−454.219	+	147.585i	−0.913921	+	0.296951i
$498$	−320.371	−	232.763i	−0.643315	−	0.467396i
$499$	46.9230	−	34.0915i	0.0940340	−	0.0683197i	−0.539775	−	0.841809i	$-0.681491\pi$
$499$	46.9230	−	34.0915i	0.0940340	−	0.0683197i	0.633809	+	0.773490i	$0.281491\pi$
$500$	−264.961	−	86.0910i	−0.529922	−	0.172182i
$501$	−681.328	−	221.377i	−1.35994	−	0.441870i
$502$	−783.128	+	568.976i	−1.56002	+	1.13342i
$503$	−296.318	+	407.847i	−0.589102	+	0.810830i	−0.994656	−	0.103241i	$-0.967079\pi$
$503$	−296.318	+	407.847i	−0.589102	+	0.810830i	0.405554	+	0.914071i	$0.367079\pi$
$504$	681.328	−	221.377i	1.35184	−	0.439240i
$505$	−704.000			−1.39406
$506$		0			0
$507$	−459.000			−0.905325
$508$	406.666	+	1251.59i	0.800524	+	2.46376i
$509$	−432.781	+	595.672i	−0.850257	+	1.17028i	0.133549	+	0.991042i	$0.457363\pi$
$509$	−432.781	+	595.672i	−0.850257	+	1.17028i	−0.983806	+	0.179236i	$0.942637\pi$
$510$	514.658	+	708.366i	1.00913	+	1.38895i
$511$	182.938	−	563.025i	0.358000	−	1.10181i
$512$	−299.658	−	97.3649i	−0.585270	−	0.190166i
$513$	−131.061	+	95.2212i	−0.255479	+	0.185616i
$514$	−1317.08	−	956.914i	−2.56241	−	1.86170i
$515$	−466.836	+	151.684i	−0.906478	+	0.294532i
$516$	882.000			1.70930
$517$		0			0
$518$			795.990i			1.53666i
$519$	−567.774	+	184.481i	−1.09398	+	0.355454i
$520$	213.580	+	155.175i	0.410732	+	0.298414i
$521$	163.755	+	225.389i	0.314309	+	0.432609i	0.936719	−	0.350082i	$-0.113846\pi$
$521$	163.755	+	225.389i	0.314309	+	0.432609i	−0.622410	+	0.782691i	$0.713846\pi$
$522$	367.112	−	1129.86i	0.703280	−	2.16447i
$523$	43.8804	−	135.050i	0.0839014	−	0.258222i	−0.900301	−	0.435267i	$-0.856654\pi$
$523$	43.8804	−	135.050i	0.0839014	−	0.258222i	0.984203	+	0.177045i	$0.0566539\pi$
$524$	163.755	+	225.389i	0.312509	+	0.430132i
$525$	368.912	+	268.030i	0.702689	+	0.510533i
$526$	−231.145	−	711.390i	−0.439439	−	1.35245i
$527$		−	344.929i		−	0.654514i
$528$		0			0
$529$	485.000			0.916824
$530$	1249.10	−	405.858i	2.35680	−	0.765769i
$531$	−350.903	+	482.977i	−0.660835	+	0.909561i
$532$	271.830	−	197.496i	0.510958	−	0.371233i
$533$	−50.4688	−	16.3983i	−0.0946881	−	0.0307660i
$534$	−367.112	+	1129.86i	−0.687476	+	2.11583i
$535$	−213.580	+	155.175i	−0.399216	+	0.290047i
$536$	−11.6968	+	16.0992i	−0.0218223	+	0.0300359i
$537$	567.774	−	184.481i	1.05731	−	0.343540i
$538$	242.000			0.449814
$539$		0			0
$540$		−	1253.68i		−	2.32164i
$541$	−123.607	−	380.423i	−0.228478	−	0.703184i	−0.997920	−	0.0644668i	$-0.979465\pi$
$541$	−123.607	−	380.423i	−0.228478	−	0.703184i	0.769441	−	0.638717i	$-0.220535\pi$
$542$	873.359	−	1202.08i	1.61136	−	2.21785i
$543$	−24.2705	+	17.6336i	−0.0446971	+	0.0324743i
$544$	95.1772	−	292.925i	0.174958	−	0.538466i
$545$	1261.72	+	409.957i	2.31508	+	0.752215i
$546$	187.148	+	257.588i	0.342763	+	0.471772i
$547$	137.533	+	99.9235i	0.251431	+	0.182675i	0.706361	−	0.707852i	$-0.250336\pi$
$547$	137.533	+	99.9235i	0.251431	+	0.182675i	−0.454930	+	0.890527i	$0.650336\pi$
$548$	−706.563	+	229.576i	−1.28935	+	0.418935i
$549$	−108.000			−0.196721
$550$		0			0
$551$		−	238.797i		−	0.433388i
$552$	−61.1854	−	188.309i	−0.110843	−	0.341140i
$553$	−258.885	−	188.091i	−0.468147	−	0.340129i
$554$	−506.860	−	697.634i	−0.914910	−	1.25927i
$555$	567.774	+	184.481i	1.02302	+	0.332398i
$556$	−160.071	+	492.647i	−0.287897	+	0.886056i
$557$	−499.063	−	686.901i	−0.895983	−	1.23321i	−0.971732	−	0.236088i	$-0.924135\pi$
$557$	−499.063	−	686.901i	−0.895983	−	1.23321i	0.0757486	−	0.997127i	$-0.475865\pi$
$558$	−456.174	+	627.870i	−0.817517	+	1.12522i
$559$	51.9149	+	159.777i	0.0928709	+	0.285827i
$560$			265.330i			0.473804i
$561$		0			0
$562$	660.000			1.17438
$563$	668.711	−	217.277i	1.18776	−	0.385928i	0.352518	−	0.935805i	$-0.385325\pi$
$563$	668.711	−	217.277i	1.18776	−	0.385928i	0.835246	+	0.549877i	$0.185325\pi$
$564$	1064.41	−	1465.03i	1.88725	−	2.59757i
$565$	213.580	−	155.175i	0.378019	−	0.274647i
$566$	157.715	+	51.2447i	0.278648	+	0.0905383i
$567$	200.243	−	616.285i	0.353162	−	1.08692i
$568$	−480.556	+	349.144i	−0.846049	+	0.614691i
$569$	−70.1807	+	96.5954i	−0.123340	+	0.169763i	−0.866222	−	0.499659i	$-0.833459\pi$
$569$	−70.1807	+	96.5954i	−0.123340	+	0.169763i	0.742882	+	0.669423i	$0.233459\pi$
$570$	−122.371	−	376.618i	−0.214685	−	0.660734i
$571$	706.000			1.23643			0.618214	−	0.786010i	$-0.287857\pi$
$571$	706.000			1.23643			0.618214	+	0.786010i	$0.287857\pi$
$572$		0			0
$573$			338.296i			0.590394i
$574$	−108.774	−	334.772i	−0.189502	−	0.583226i
$575$	74.0796	−	101.962i	0.128834	−	0.177325i
$576$	−706.272	+	513.137i	−1.22617	+	0.890862i
$577$	−228.055	+	701.880i	−0.395242	+	1.21643i	0.533531	+	0.845780i	$0.320865\pi$
$577$	−228.055	+	701.880i	−0.395242	+	1.21643i	−0.928773	+	0.370649i	$0.879135\pi$
$578$	356.436	+	115.813i	0.616671	+	0.200368i
$579$	723.261	−	525.480i	1.24916	−	0.907565i
$580$	1495.06	+	1086.23i	2.57770	+	1.87281i
$581$	302.813	−	98.3898i	0.521192	−	0.169346i
$582$			616.892i			1.05995i
$583$		0			0
$584$		−	736.291i		−	1.26077i
$585$	227.109	−	73.7923i	0.388221	−	0.126141i
$586$	1281.48	+	931.052i	2.18683	+	1.58883i
$587$	−553.648	−	762.030i	−0.943181	−	1.29818i	−0.954490	−	0.298242i	$-0.903600\pi$
$587$	−553.648	−	762.030i	−0.943181	−	1.29818i	0.0113088	−	0.999936i	$-0.496400\pi$
$588$	−97.3404	+	299.583i	−0.165545	+	0.509495i
$589$	−48.2067	+	148.365i	−0.0818449	+	0.251893i
$590$	−857.764	−	1180.61i	−1.45384	−	2.00103i
$591$	233.936	−	321.985i	0.395830	−	0.544813i
$592$	46.3525	+	142.658i	0.0782982	+	0.240977i
$593$			543.926i			0.917245i	0.888631	+	0.458623i	$0.151657\pi$
$593$			543.926i			0.917245i	−0.888631	+	0.458623i	$0.848343\pi$
$594$		0			0
$595$	−704.000			−1.18319
$596$	−618.242	+	200.879i	−1.03732	+	0.337045i
$597$	101.936	+	74.0609i	0.170747	+	0.124055i
$598$	71.1935	−	51.7251i	0.119053	−	0.0864968i
$599$	44.1602	+	14.3485i	0.0737231	+	0.0239541i	0.345646	−	0.938365i	$-0.387660\pi$
$599$	44.1602	+	14.3485i	0.0737231	+	0.0239541i	−0.271923	+	0.962319i	$0.587660\pi$
$600$	539.385	+	175.257i	0.898975	+	0.292095i
$601$	438.487	−	318.580i	0.729596	−	0.530083i	−0.159840	−	0.987143i	$-0.551098\pi$
$601$	438.487	−	318.580i	0.729596	−	0.530083i	0.889436	+	0.457060i	$0.151098\pi$
$602$	−655.020	+	901.557i	−1.08807	+	1.49760i
$603$	5.56231	+	17.1190i	0.00922439	+	0.0283897i
$604$	−1120.00			−1.85430
$605$		0			0
$606$	−1056.00			−1.74257
$607$	216.312	+	665.740i	0.356362	+	1.09677i	0.955215	+	0.295911i	$0.0956233\pi$
$607$	216.312	+	665.740i	0.356362	+	1.09677i	−0.598853	+	0.800859i	$0.704377\pi$
$608$	−81.8775	+	112.695i	−0.134667	+	0.185353i
$609$	561.445	+	772.763i	0.921914	+	1.26891i
$610$	81.5805	−	251.079i	0.133739	−	0.411605i
$611$	328.047	+	106.589i	0.536902	+	0.174450i
$612$	491.265	+	676.168i	0.802720	+	1.10485i
$613$	618.089	+	449.068i	1.00830	+	0.732574i	0.963852	−	0.266438i	$-0.0858466\pi$
$613$	618.089	+	449.068i	1.00830	+	0.732574i	0.0444496	+	0.999012i	$0.485847\pi$
$614$	271.270	−	88.1408i	0.441807	−	0.143552i
$615$	−264.000			−0.429268
$616$		0			0
$617$		−	39.7995i		−	0.0645049i	−0.999480	−	0.0322524i	$-0.989732\pi$
$617$		−	39.7995i		−	0.0645049i	0.999480	−	0.0322524i	$-0.0102680\pi$
$618$	−700.254	+	227.526i	−1.13310	+	0.368166i
$619$	600.291	+	436.137i	0.969775	+	0.704583i	0.955400	−	0.295314i	$-0.0954243\pi$
$619$	600.291	+	436.137i	0.969775	+	0.704583i	0.0143746	+	0.999897i	$0.495424\pi$
$620$	−709.605	−	976.687i	−1.14452	−	1.57530i
$621$	−170.332	−	55.3442i	−0.274287	−	0.0891212i
$622$	20.3951	−	62.7697i	0.0327896	−	0.100916i
$623$	−561.445	−	772.763i	−0.901196	−	1.24039i
$624$	48.5410	+	35.2671i	0.0777901	+	0.0565178i
$625$	−228.364	−	702.831i	−0.365382	−	1.12453i
$626$			325.029i			0.519216i
$627$		0			0
$628$	−1274.00			−2.02866
$629$	−378.516	+	122.987i	−0.601774	+	0.195528i
$630$	1281.48	+	931.052i	2.03410	+	1.47786i
$631$	331.697	−	240.992i	0.525669	−	0.381921i	−0.293066	−	0.956092i	$-0.594676\pi$
$631$	331.697	−	240.992i	0.525669	−	0.381921i	0.818735	+	0.574171i	$0.194676\pi$
$632$	−378.516	−	122.987i	−0.598917	−	0.194600i
$633$	−228.055	+	701.880i	−0.360276	+	1.10881i
$634$	−836.524	+	607.770i	−1.31944	+	0.958628i
$635$	−732.998	+	1008.89i	−1.15433	+	1.58880i
$636$	1192.32	−	387.410i	1.87472	−	0.609135i
$637$	−60.0000			−0.0941915
$638$		0			0
$639$			537.293i			0.840834i
$640$	−469.088	−	1443.70i	−0.732950	−	2.25579i
$641$	444.478	−	611.771i	0.693413	−	0.954401i	−0.306584	−	0.951844i	$-0.599186\pi$
$641$	444.478	−	611.771i	0.693413	−	0.954401i	0.999997	−	0.00255720i	$-0.000813982\pi$
$642$	−320.371	+	232.763i	−0.499020	+	0.362559i
$643$	275.025	−	846.440i	0.427722	−	1.31639i	−0.472642	−	0.881255i	$-0.656700\pi$
$643$	275.025	−	846.440i	0.427722	−	1.31639i	0.900364	−	0.435138i	$-0.143300\pi$
$644$	353.281	+	114.788i	0.548573	+	0.178242i
$645$	491.265	+	676.168i	0.761651	+	1.04832i
$646$	213.580	+	155.175i	0.330620	+	0.240209i
$647$	460.527	−	149.634i	0.711789	−	0.231274i	0.0693294	−	0.997594i	$-0.477914\pi$
$647$	460.527	−	149.634i	0.711789	−	0.231274i	0.642460	+	0.766320i	$0.277914\pi$
$648$		−	805.940i		−	1.24373i
$649$		0			0
$650$			252.063i			0.387790i
$651$	−192.827	−	593.459i	−0.296201	−	0.911612i
$652$	−1642.30	−	1193.20i	−2.51887	−	1.83007i
$653$	230.037	+	316.618i	0.352277	+	0.484867i	0.947977	−	0.318340i	$-0.103125\pi$
$653$	230.037	+	316.618i	0.352277	+	0.484867i	−0.595700	+	0.803207i	$0.703125\pi$
$654$	1892.58	+	614.936i	2.89385	+	0.940269i
$655$	−81.5805	+	251.079i	−0.124550	+	0.383327i
$656$	−38.9893	−	53.6641i	−0.0594349	−	0.0818051i
$657$	−538.805	−	391.465i	−0.820099	−	0.595837i
$658$	707.031	+	2176.02i	1.07452	+	3.30702i
$659$		−	384.728i		−	0.583806i	−0.956448	−	0.291903i	$-0.905711\pi$
$659$		−	384.728i		−	0.583806i	0.956448	−	0.291903i	$-0.0942885\pi$
$660$		0			0
$661$	−746.000			−1.12859			−0.564297	−	0.825572i	$-0.690853\pi$
$661$	−746.000			−1.12859			−0.564297	+	0.825572i	$0.690853\pi$
$662$	687.637	−	223.427i	1.03873	−	0.337503i
$663$	−93.5742	+	128.794i	−0.141138	+	0.194259i
$664$	320.371	−	232.763i	0.482486	−	0.350547i
$665$	302.813	+	98.3898i	0.455357	+	0.147955i
$666$	851.660	+	276.721i	1.27877	+	0.415497i
$667$	213.580	−	155.175i	0.320211	−	0.232647i
$668$	982.529	−	1352.34i	1.47085	−	2.02445i
$669$	−279.969	−	861.657i	−0.418489	−	1.28798i
$670$	−44.0000			−0.0656716
$671$		0			0
$672$		−	557.193i		−	0.829156i
$673$	195.917	+	602.970i	0.291110	+	0.895943i	0.984501	+	0.175382i	$0.0561159\pi$
$673$	195.917	+	602.970i	0.291110	+	0.895943i	−0.693391	+	0.720562i	$0.743884\pi$
$674$	−541.951	+	745.931i	−0.804081	+	1.10672i
$675$	415.026	−	301.534i	0.614853	−	0.446717i
$676$	330.957	−	1018.58i	0.489582	−	1.50678i
$677$	757.031	+	245.974i	1.11821	+	0.363330i	0.809086	−	0.587690i	$-0.199963\pi$
$677$	757.031	+	245.974i	1.11821	+	0.363330i	0.309129	+	0.951020i	$0.399963\pi$
$678$	320.371	−	232.763i	0.472523	−	0.343308i
$679$	−401.272	−	291.541i	−0.590976	−	0.429369i
$680$	−832.735	+	270.572i	−1.22461	+	0.397900i
$681$		−	596.992i		−	0.876641i
$682$		0			0
$683$			451.061i			0.660411i	0.943909	+	0.330206i	$0.107118\pi$
$683$			451.061i			0.660411i	−0.943909	+	0.330206i	$0.892882\pi$
$684$	−116.808	−	359.499i	−0.170773	−	0.525584i
$685$	−569.548	−	413.801i	−0.831457	−	0.604089i
$686$	530.254	+	729.832i	0.772965	+	1.06390i
$687$	139.058	−	427.975i	0.202413	−	0.622963i
$688$	−64.8936	+	199.722i	−0.0943220	+	0.290293i
$689$	140.361	+	193.191i	0.203717	+	0.280393i
$690$	257.329	−	354.183i	0.372941	−	0.513309i
$691$	141.530	+	435.584i	0.204819	+	0.630367i	0.999721	+	0.0236296i	$0.00752222\pi$
$691$	141.530	+	435.584i	0.204819	+	0.630367i	−0.794902	+	0.606738i	$0.792478\pi$
$692$		−	1392.98i		−	2.01298i
$693$		0			0
$694$	−1100.00			−1.58501
$695$	−466.836	+	151.684i	−0.671707	+	0.218251i
$696$	961.112	+	698.289i	1.38091	+	1.00329i
$697$	142.387	−	103.450i	0.204285	−	0.148422i
$698$	−1021.99	−	332.065i	−1.46417	−	0.475738i
$699$	−1249.10	−	405.858i	−1.78698	−	0.580626i
$700$	−860.794	+	625.404i	−1.22971	+	0.893434i
$701$	296.318	−	407.847i	0.422708	−	0.581808i	−0.543552	−	0.839375i	$-0.682921\pi$
$701$	296.318	−	407.847i	0.422708	−	0.581808i	0.966260	+	0.257568i	$0.0829210\pi$
$702$	340.664	−	110.688i	0.485277	−	0.157676i
$703$	180.000			0.256046
$704$		0			0
$705$	1716.00			2.43404
$706$	407.902	+	1255.39i	0.577765	+	1.77818i
$707$	499.063	−	686.901i	0.705888	−	0.971571i
$708$	−818.775	−	1126.95i	−1.15646	−	1.59173i
$709$	−173.668	+	534.494i	−0.244947	+	0.753870i	0.750698	+	0.660646i	$0.229717\pi$
$709$	−173.668	+	534.494i	−0.244947	+	0.753870i	−0.995645	+	0.0932243i	$0.970283\pi$
$710$	−1249.10	−	405.858i	−1.75930	−	0.571631i
$711$	−291.246	+	211.603i	−0.409629	+	0.297613i
$712$	−961.112	−	698.289i	−1.34988	−	0.980743i
$713$	−164.023	+	53.2945i	−0.230047	+	0.0747468i
$714$	−1056.00			−1.47899
$715$		0			0
$716$			1392.98i			1.94551i
$717$		0			0
$718$	−818.725	−	594.839i	−1.14029	−	0.828466i
$719$	198.845	+	273.687i	0.276558	+	0.380650i	0.924590	−	0.380964i	$-0.124408\pi$
$719$	198.845	+	273.687i	0.276558	+	0.380650i	−0.648032	+	0.761613i	$0.724408\pi$
$720$	283.887	+	92.2404i	0.394287	+	0.128112i
$721$	182.938	−	563.025i	0.253728	−	0.780895i
$722$	633.576	+	872.042i	0.877528	+	1.20781i
$723$	315.517	+	229.236i	0.436399	+	0.317063i
$724$	−21.6312	−	66.5740i	−0.0298773	−	0.0919530i
$725$			756.190i			1.04302i
$726$		0			0
$727$	−42.0000			−0.0577717			−0.0288858	−	0.999583i	$-0.509196\pi$
$727$	−42.0000			−0.0577717			−0.0288858	+	0.999583i	$0.509196\pi$
$728$	−302.813	+	98.3898i	−0.415951	+	0.135151i
$729$	−589.773	−	428.495i	−0.809017	−	0.587785i
$730$	1317.08	−	956.914i	1.80422	−	1.31084i
$731$	−529.922	−	172.182i	−0.724927	−	0.235543i
$732$	77.8723	−	239.666i	0.106383	−	0.327413i
$733$	−504.827	+	366.778i	−0.688713	+	0.500379i	−0.876237	−	0.481881i	$-0.839954\pi$
$733$	−504.827	+	366.778i	−0.688713	+	0.500379i	0.187524	+	0.982260i	$0.439954\pi$
$734$	−541.951	+	745.931i	−0.738353	+	1.01626i
$735$	−283.887	+	92.2404i	−0.386241	+	0.125497i
$736$	−154.000			−0.209239
$737$		0			0
$738$	−396.000			−0.536585
$739$	−211.986	−	652.425i	−0.286855	−	0.882848i	−0.985837	−	0.167709i	$-0.946363\pi$
$739$	−211.986	−	652.425i	−0.286855	−	0.882848i	0.698982	−	0.715139i	$-0.253637\pi$
$740$	−818.775	+	1126.95i	−1.10645	+	1.52290i
$741$	58.2492	−	42.3205i	0.0786089	−	0.0571127i
$742$	−489.483	+	1506.47i	−0.659680	+	2.03029i
$743$	−820.117	−	266.472i	−1.10379	−	0.358644i	−0.300231	−	0.953866i	$-0.597064\pi$
$743$	−820.117	−	266.472i	−1.10379	−	0.358644i	−0.803561	+	0.595223i	$0.797064\pi$
$744$	−456.174	−	627.870i	−0.613138	−	0.843912i
$745$	−498.354	−	362.076i	−0.668932	−	0.486008i
$746$	−214.492	+	69.6928i	−0.287523	+	0.0934219i
$747$		−	358.195i		−	0.479512i
$748$		0			0
$749$		−	318.396i		−	0.425095i
$750$	−122.371	−	376.618i	−0.163161	−	0.502158i
$751$	−76.0476	−	55.2518i	−0.101262	−	0.0735710i	0.536002	−	0.844217i	$-0.319934\pi$
$751$	−76.0476	−	55.2518i	−0.101262	−	0.0735710i	−0.637264	+	0.770646i	$0.719934\pi$
$752$	253.430	+	348.817i	0.337008	+	0.463852i
$753$	−832.735	−	270.572i	−1.10589	−	0.359325i
$754$	−163.161	+	502.158i	−0.216394	+	0.665992i
$755$	−623.828	−	858.626i	−0.826263	−	1.13725i
$756$	1223.23	+	888.731i	1.61803	+	1.17557i
$757$	345.481	+	1063.28i	0.456382	+	1.40460i	0.869505	+	0.493924i	$0.164438\pi$
$757$	345.481	+	1063.28i	0.456382	+	1.40460i	−0.413124	+	0.910675i	$0.635562\pi$
$758$			2222.14i			2.93158i
$759$		0			0
$760$	396.000			0.521053
$761$	1097.70	−	356.663i	1.44244	−	0.468677i	0.519782	−	0.854299i	$-0.326013\pi$
$761$	1097.70	−	356.663i	1.44244	−	0.468677i	0.922657	+	0.385623i	$0.126013\pi$
$762$	−1099.50	+	1513.33i	−1.44291	+	1.98599i
$763$	−1294.43	+	940.456i	−1.69650	+	1.23258i
$764$	−750.723	−	243.925i	−0.982622	−	0.319273i
$765$	−244.741	+	753.237i	−0.319923	+	0.984623i
$766$	88.9919	−	64.6564i	0.116177	−	0.0844078i
$767$	155.957	−	214.656i	0.203334	−	0.279865i
$768$	−343.936	−	1058.53i	−0.447833	−	1.37829i
$769$	−1274.00			−1.65670			−0.828349	−	0.560213i	$-0.810719\pi$
$769$	−1274.00			−1.65670			−0.828349	+	0.560213i	$0.810719\pi$
$770$		0			0
$771$		−	1472.58i		−	1.90996i
$772$	644.609	+	1983.90i	0.834986	+	2.56982i
$773$	549.749	−	756.664i	0.711188	−	0.978867i	−0.288582	−	0.957455i	$-0.593184\pi$
$773$	549.749	−	756.664i	0.711188	−	0.978867i	0.999771	−	0.0214117i	$-0.00681609\pi$
$774$	736.897	+	1014.25i	0.952063	+	1.31040i
$775$	152.654	−	469.822i	0.196973	−	0.606222i
$776$	−586.699	−	190.630i	−0.756056	−	0.245657i
$777$	−582.492	+	423.205i	−0.749668	+	0.544666i
$778$	1121.30	+	814.670i	1.44126	+	1.04713i
$779$	−75.7031	+	24.5974i	−0.0971799	+	0.0315757i
$780$			557.193i			0.714350i
$781$		0			0
$782$			291.863i			0.373226i
$783$	1021.99	−	332.065i	1.30523	−	0.424094i
$784$	−60.6763	−	44.0839i	−0.0773932	−	0.0562295i
$785$	−709.605	−	976.687i	−0.903955	−	1.24419i
$786$	−122.371	+	376.618i	−0.155688	+	0.479158i
$787$	−92.0871	+	283.415i	−0.117010	+	0.360121i	−0.992361	−	0.123368i	$-0.960630\pi$
$787$	−92.0871	+	283.415i	−0.117010	+	0.360121i	0.875351	+	0.483488i	$0.160630\pi$
$788$	545.850	+	751.298i	0.692703	+	0.953423i
$789$	397.690	−	547.374i	0.504044	−	0.693757i
$790$	−271.935	−	836.930i	−0.344221	−	1.05940i
$791$			318.396i			0.402523i
$792$		0			0
$793$	48.0000			0.0605296
$794$	271.270	−	88.1408i	0.341649	−	0.111009i
$795$	961.112	+	698.289i	1.20895	+	0.878351i
$796$	−237.851	+	172.809i	−0.298808	+	0.217097i
$797$	−498.379	−	161.933i	−0.625319	−	0.203178i	−0.0208184	−	0.999783i	$-0.506627\pi$
$797$	−498.379	−	161.933i	−0.625319	−	0.203178i	−0.604500	+	0.796605i	$0.706627\pi$
$798$	454.219	+	147.585i	0.569197	+	0.184943i
$799$	−925.515	+	672.426i	−1.15834	+	0.841585i
$800$	259.279	−	356.866i	0.324098	−	0.446083i
$801$	−1021.99	+	332.065i	−1.27590	+	0.414564i
$802$	−836.000			−1.04239
$803$		0			0
$804$	−42.0000			−0.0522388
$805$	108.774	+	334.772i	0.135123	+	0.415866i
$806$	202.744	−	279.053i	0.251544	−	0.346220i
$807$	128.665	+	177.092i	0.159436	+	0.219444i
$808$	326.322	−	1004.32i	0.403864	−	1.24296i
$809$	−870.586	−	282.871i	−1.07613	−	0.349655i	−0.283256	−	0.959044i	$-0.591414\pi$
$809$	−870.586	−	282.871i	−1.07613	−	0.349655i	−0.792871	+	0.609390i	$0.791414\pi$
$810$	1441.67	−	1047.43i	1.77984	−	1.29313i
$811$	−147.241	−	106.977i	−0.181555	−	0.131907i	0.493296	−	0.869862i	$-0.335792\pi$
$811$	−147.241	−	106.977i	−0.181555	−	0.131907i	−0.674851	+	0.737954i	$0.735792\pi$
$812$	−2119.69	+	688.728i	−2.61045	+	0.848188i
$813$	1344.00			1.65314
$814$		0			0
$815$		−	1923.64i		−	2.36030i
$816$	−189.258	+	61.4936i	−0.231934	+	0.0753598i
$817$	203.872	+	148.122i	0.249538	+	0.181300i
$818$	994.226	+	1368.43i	1.21544	+	1.67290i
$819$	−88.9969	+	273.904i	−0.108665	+	0.334437i
$820$	190.354	−	585.851i	0.232140	−	0.714452i
$821$	483.467	+	665.435i	0.588876	+	0.810518i	0.994633	−	0.103463i	$-0.0329923\pi$
$821$	483.467	+	665.435i	0.588876	+	0.810518i	−0.405758	+	0.913981i	$0.632992\pi$
$822$	−854.322	−	620.701i	−1.03932	−	0.755111i
$823$	−76.0182	−	233.960i	−0.0923672	−	0.284277i	0.894191	−	0.447685i	$-0.147751\pi$
$823$	−76.0182	−	233.960i	−0.0923672	−	0.284277i	−0.986559	+	0.163408i	$0.947751\pi$
$824$		−	736.291i		−	0.893557i
$825$		0			0
$826$	1760.00			2.13075
$827$	−517.305	+	168.083i	−0.625520	+	0.203244i	−0.604589	−	0.796537i	$-0.706663\pi$
$827$	−517.305	+	168.083i	−0.625520	+	0.203244i	−0.0209303	+	0.999781i	$0.506663\pi$
$828$	245.632	−	338.084i	0.296657	−	0.408314i
$829$	−202.254	+	146.946i	−0.243974	+	0.177257i	−0.703052	−	0.711139i	$-0.748180\pi$
$829$	−202.254	+	146.946i	−0.243974	+	0.177257i	0.459078	+	0.888396i	$0.348180\pi$
$830$	832.735	+	270.572i	1.00329	+	0.325990i
$831$	241.033	−	741.824i	0.290052	−	0.892688i
$832$	313.899	−	228.061i	0.377282	−	0.274111i
$833$	116.968	−	160.992i	0.140418	−	0.193268i
$834$	−700.254	+	227.526i	−0.839633	+	0.272813i
$835$	1584.00			1.89701
$836$		0			0
$837$	−702.000			−0.838710
$838$	−543.870	−	1673.86i	−0.649009	−	1.99745i
$839$	−276.824	+	381.015i	−0.329945	+	0.454130i	−0.941471	−	0.337094i	$-0.890556\pi$
$839$	−276.824	+	381.015i	−0.329945	+	0.454130i	0.611526	+	0.791224i	$0.290556\pi$
$840$	−1281.48	+	931.052i	−1.52557	+	1.10840i
$841$	−229.600	+	706.635i	−0.273008	+	0.840232i
$842$	−536.231	−	174.232i	−0.636853	−	0.206926i
$843$	350.903	+	482.977i	0.416255	+	0.572927i
$844$	−1393.13	−	1012.17i	−1.65062	−	1.19925i
$845$	965.215	−	313.617i	1.14227	−	0.371145i
$846$	2574.00			3.04255
$847$		0			0
$848$			298.496i			0.352000i
$849$	46.3525	+	142.658i	0.0545966	+	0.168031i
$850$	−676.338	−	491.388i	−0.795692	−	0.578104i
$851$	116.968	+	160.992i	0.137447	+	0.189180i
$852$	−1192.32	−	387.410i	−1.39944	−	0.454706i
$853$	−17.3050	+	53.2592i	−0.0202872	+	0.0624375i	−0.960688	−	0.277632i	$-0.910451\pi$
$853$	−17.3050	+	53.2592i	−0.0202872	+	0.0624375i	0.940400	+	0.340069i	$0.110451\pi$
$854$	187.148	+	257.588i	0.219143	+	0.301625i
$855$	210.542	−	289.786i	0.246248	−	0.338931i
$856$	−122.371	−	376.618i	−0.142956	−	0.439975i
$857$		−	252.063i		−	0.294123i	−0.989127	−	0.147062i	$-0.953018\pi$
$857$		−	252.063i		−	0.294123i	0.989127	−	0.147062i	$-0.0469815\pi$
$858$		0			0
$859$	1278.00			1.48778			0.743888	−	0.668304i	$-0.232979\pi$
$859$	1278.00			1.48778			0.743888	+	0.668304i	$0.232979\pi$
$860$	−1854.73	+	602.637i	−2.15666	+	0.700741i
$861$	187.148	−	257.588i	0.217362	−	0.299173i
$862$	747.532	−	543.114i	0.867206	−	0.630062i
$863$	1078.77	+	350.514i	1.25002	+	0.406157i	0.857929	−	0.513768i	$-0.171751\pi$
$863$	1078.77	+	350.514i	1.25002	+	0.406157i	0.392094	+	0.919925i	$0.371751\pi$
$864$	−596.162	−	193.705i	−0.690003	−	0.224195i
$865$	1067.90	−	775.877i	1.23457	−	0.896967i
$866$	−1056.61	+	1454.30i	−1.22010	+	1.67933i
$867$	104.757	+	322.408i	0.120827	+	0.371866i
$868$	1456.00			1.67742
$869$		0			0
$870$			2626.77i			3.01927i
$871$	−2.47214	−	7.60845i	−0.00283827	−	0.00873531i
$872$	−1169.68	+	1609.92i	−1.34137	+	1.84624i
$873$	−451.431	+	327.984i	−0.517104	+	0.375698i
$874$	40.7902	−	125.539i	0.0466708	−	0.143638i
$875$	302.813	+	98.3898i	0.346072	+	0.112445i
$876$	1257.21	−	913.418i	1.43517	−	1.04271i
$877$	368.912	+	268.030i	0.420652	+	0.305622i	0.777900	−	0.628388i	$-0.216285\pi$
$877$	368.912	+	268.030i	0.420652	+	0.305622i	−0.357248	+	0.934010i	$0.616285\pi$
$878$	1034.61	−	336.165i	1.17837	−	0.382876i
$879$			1432.78i			1.63001i
$880$		0			0
$881$			610.259i			0.692689i	0.938107	+	0.346344i	$0.112577\pi$
$881$			610.259i			0.692689i	−0.938107	+	0.346344i	$0.887423\pi$
$882$	−425.830	+	138.361i	−0.482801	+	0.156871i
$883$	885.065	+	643.037i	1.00234	+	0.728241i	0.962588	−	0.270968i	$-0.0873439\pi$
$883$	885.065	+	643.037i	1.00234	+	0.728241i	0.0397499	+	0.999210i	$0.487344\pi$
$884$	−218.340	−	300.519i	−0.246991	−	0.339954i
$885$	407.902	−	1255.39i	0.460907	−	1.41852i
$886$	135.967	−	418.465i	0.153462	−	0.472308i
$887$	−85.7764	−	118.061i	−0.0967039	−	0.133102i	0.757923	−	0.652344i	$-0.226214\pi$
$887$	−85.7764	−	118.061i	−0.0967039	−	0.133102i	−0.854627	+	0.519242i	$0.826214\pi$
$888$	−526.355	+	724.466i	−0.592742	+	0.815840i
$889$	−464.762	−	1430.39i	−0.522791	−	1.60899i
$890$		−	2626.77i		−	2.95142i
$891$		0			0
$892$	2114.00			2.36996
$893$	492.070	−	159.883i	0.551031	−	0.179041i
$894$	−747.532	−	543.114i	−0.836165	−	0.607510i
$895$	−1067.90	+	775.877i	−1.19319	+	0.866901i
$896$	1741.17	+	565.741i	1.94327	+	0.631408i
$897$	75.7031	+	24.5974i	0.0843959	+	0.0274219i
$898$	1210.29	−	879.327i	1.34776	−	0.979206i
$899$	608.232	−	837.160i	0.676566	−	0.931213i
$900$	369.893	+	1138.41i	0.410993	+	1.26491i
$901$	−792.000			−0.879023
$902$		0			0
$903$	−1008.00			−1.11628
$904$	122.371	+	376.618i	0.135366	+	0.416613i
$905$	38.9893	−	53.6641i	0.0430821	−	0.0592974i
$906$	−935.742	−	1287.94i	−1.03283	−	1.42157i
$907$	57.4772	−	176.897i	0.0633706	−	0.195035i	−0.914358	−	0.404906i	$-0.867304\pi$
$907$	57.4772	−	176.897i	0.0633706	−	0.195035i	0.977729	+	0.209871i	$0.0673044\pi$
$908$	1324.80	+	430.455i	1.45904	+	0.474070i
$909$	−561.445	−	772.763i	−0.617652	−	0.850125i
$910$	−569.548	−	413.801i	−0.625877	−	0.454726i
$911$	813.809	−	264.423i	0.893314	−	0.290255i	0.173839	−	0.984774i	$-0.444383\pi$
$911$	813.809	−	264.423i	0.893314	−	0.290255i	0.719475	+	0.694519i	$0.244383\pi$
$912$	90.0000			0.0986842
$913$		0			0
$914$		−	1134.29i		−	1.24101i
$915$	227.109	−	73.7923i	0.248207	−	0.0806474i
$916$	849.468	+	617.175i	0.927367	+	0.673771i
$917$	−187.148	−	257.588i	−0.204088	−	0.280903i
$918$	−367.112	+	1129.86i	−0.399904	+	1.23078i
$919$	132.259	−	407.052i	0.143917	−	0.442929i	−0.852954	−	0.521987i	$-0.825191\pi$
$919$	132.259	−	407.052i	0.143917	−	0.442929i	0.996870	+	0.0790573i	$0.0251910\pi$
$920$	257.329	+	354.183i	0.279706	+	0.384982i
$921$	208.726	+	151.649i	0.226630	+	0.164656i
$922$	81.5805	+	251.079i	0.0884821	+	0.272320i
$923$		−	238.797i		−	0.258718i
$924$		0			0
$925$	−570.000			−0.616216
$926$	271.270	−	88.1408i	0.292948	−	0.0951845i
$927$	−538.805	−	391.465i	−0.581236	−	0.422292i
$928$	747.532	−	543.114i	0.805530	−	0.585252i
$929$	−605.625	−	196.780i	−0.651911	−	0.211819i	−0.0356543	−	0.999364i	$-0.511352\pi$
$929$	−605.625	−	196.780i	−0.651911	−	0.211819i	−0.616256	+	0.787546i	$0.711352\pi$
$930$	530.273	−	1632.01i	0.570186	−	1.75485i
$931$	−72.8115	+	52.9007i	−0.0782079	+	0.0568213i
$932$	1801.30	−	2479.28i	1.93273	−	2.66017i
$933$	56.7774	−	18.4481i	0.0608546	−	0.0197729i
$934$	−1980.00			−2.11991
$935$		0			0
$936$			358.195i			0.382687i
$937$	−89.6149	−	275.806i	−0.0956403	−	0.294350i	0.891780	−	0.452470i	$-0.149457\pi$
$937$	−89.6149	−	275.806i	−0.0956403	−	0.294350i	−0.987420	+	0.158119i	$0.949457\pi$
$938$	31.1914	−	42.9313i	0.0332531	−	0.0457690i
$939$	−237.851	+	172.809i	−0.253302	+	0.184035i
$940$	−1237.30	+	3808.03i	−1.31628	+	4.05110i
$941$	832.735	+	270.572i	0.884946	+	0.287537i	0.716010	−	0.698090i	$-0.245967\pi$
$941$	832.735	+	270.572i	0.884946	+	0.287537i	0.168937	+	0.985627i	$0.445967\pi$
$942$	−1064.41	−	1465.03i	−1.12994	−	1.55523i
$943$	−71.1935	−	51.7251i	−0.0754968	−	0.0548516i
$944$	315.430	−	102.489i	0.334142	−	0.108569i
$945$			1432.78i			1.51617i
$946$		0			0
$947$			79.5990i			0.0840538i	0.999116	+	0.0420269i	$0.0133815\pi$
$947$			79.5990i			0.0840538i	−0.999116	+	0.0420269i	$0.986618\pi$
$948$	−259.574	−	798.887i	−0.273813	−	0.842708i
$949$	239.469	+	173.984i	0.252338	+	0.183334i
$950$	222.239	+	305.885i	0.233936	+	0.321985i
$951$	−889.512	−	289.020i	−0.935344	−	0.303912i
$952$	326.322	−	1004.32i	0.342775	−	1.05495i
$953$	460.073	+	633.237i	0.482763	+	0.664466i	0.979033	−	0.203702i	$-0.0652973\pi$
$953$	460.073	+	633.237i	0.482763	+	0.664466i	−0.496270	+	0.868168i	$0.665297\pi$
$954$	1441.67	+	1047.43i	1.51118	+	1.09794i
$955$	−231.145	−	711.390i	−0.242036	−	0.744911i
$956$		0			0
$957$		0			0
$958$	−748.000			−0.780793
$959$	807.500	−	262.373i	0.842023	−	0.273590i
$960$	1134.59	−	1561.63i	1.18186	−	1.62669i
$961$	230.570	−	167.519i	0.239927	−	0.174317i
$962$	−378.516	−	122.987i	−0.393467	−	0.127845i
$963$	−340.664	−	110.688i	−0.353753	−	0.114941i
$964$	−736.205	+	534.885i	−0.763699	+	0.554860i
$965$	−1161.88	+	1599.19i	−1.20402	+	1.65719i
$966$	163.161	+	502.158i	0.168904	+	0.519832i
$967$	−460.000			−0.475698			−0.237849	−	0.971302i	$-0.576442\pi$
$967$	−460.000			−0.475698			−0.237849	+	0.971302i	$0.576442\pi$
$968$		0			0
$969$			238.797i			0.246437i
$970$	−421.499	−	1297.24i	−0.434535	−	1.33736i
$971$	686.211	−	944.488i	0.706705	−	0.972697i	−0.293156	−	0.956065i	$-0.594706\pi$
$971$	686.211	−	944.488i	0.706705	−	0.972697i	0.999862	−	0.0166321i	$-0.00529440\pi$
$972$	1376.14	−	999.823i	1.41578	−	1.02862i
$973$	182.938	−	563.025i	0.188014	−	0.578649i
$974$	1406.82	+	457.102i	1.44437	+	0.469304i
$975$	−184.456	+	134.015i	−0.189186	+	0.137451i
$976$	48.5410	+	35.2671i	0.0497347	+	0.0361343i
$977$	1249.10	−	405.858i	1.27851	−	0.415412i	0.410453	−	0.911882i	$-0.365370\pi$
$977$	1249.10	−	405.858i	1.27851	−	0.415412i	0.868054	+	0.496469i	$0.165370\pi$
$978$		−	2885.46i		−	2.95037i
$979$		0			0
$980$		−	696.491i		−	0.710705i
$981$	556.231	+	1711.90i	0.567004	+	1.74506i
$982$	−1886.63	−	1370.72i	−1.92121	−	1.39584i
$983$	245.632	+	338.084i	0.249880	+	0.343931i	0.915469	−	0.402388i	$-0.131820\pi$
$983$	245.632	+	338.084i	0.249880	+	0.343931i	−0.665589	+	0.746318i	$0.731820\pi$
$984$	122.371	−	376.618i	0.124360	−	0.382742i
$985$	−271.935	+	836.930i	−0.276076	+	0.849675i
$986$	−1029.32	−	1416.73i	−1.04393	−	1.43685i
$987$	−1216.46	+	1674.32i	−1.23249	+	1.69637i
$988$	51.9149	+	159.777i	0.0525454	+	0.161718i
$989$			278.596i			0.281695i
$990$		0			0
$991$	838.000			0.845610			0.422805	−	0.906221i	$-0.361045\pi$
$991$	838.000			0.845610			0.422805	+	0.906221i	$0.361045\pi$
$992$	−574.082	+	186.531i	−0.578712	+	0.188035i
$993$	529.097	+	384.412i	0.532827	+	0.387121i
$994$	1281.48	−	931.052i	1.28922	−	0.936672i
$995$	−264.961	−	86.0910i	−0.266292	−	0.0865237i
$996$	794.883	+	258.273i	0.798075	+	0.259310i
$997$	−42.0689	+	30.5648i	−0.0421955	+	0.0306568i	−0.608683	−	0.793413i	$-0.708302\pi$
$997$	−42.0689	+	30.5648i	−0.0421955	+	0.0306568i	0.566488	+	0.824070i	$0.308302\pi$
$998$	−113.069	+	155.626i	−0.113295	+	0.155938i
$999$	250.304	+	770.356i	0.250554	+	0.771127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.d.269.1		8
3.2	odd	2	inner	363.3.h.d.269.2		8
11.2	odd	10		363.3.h.e.251.1		8
11.3	even	5		363.3.b.d.122.2		2
11.4	even	5	inner	363.3.h.d.245.1		8
11.5	even	5	inner	363.3.h.d.323.2		8
11.6	odd	10		363.3.h.e.323.1		8
11.7	odd	10		363.3.h.e.245.2		8
11.8	odd	10		33.3.b.a.23.1	✓	2
11.9	even	5	inner	363.3.h.d.251.2		8
11.10	odd	2		363.3.h.e.269.2		8
33.2	even	10		363.3.h.e.251.2		8
33.5	odd	10	inner	363.3.h.d.323.1		8
33.8	even	10		33.3.b.a.23.2	yes	2
33.14	odd	10		363.3.b.d.122.1		2
33.17	even	10		363.3.h.e.323.2		8
33.20	odd	10	inner	363.3.h.d.251.1		8
33.26	odd	10	inner	363.3.h.d.245.2		8
33.29	even	10		363.3.h.e.245.1		8
33.32	even	2		363.3.h.e.269.1		8
44.19	even	10		528.3.i.a.353.2		2
132.107	odd	10		528.3.i.a.353.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.a.23.1	✓	2	11.8	odd	10
33.3.b.a.23.2	yes	2	33.8	even	10
363.3.b.d.122.1		2	33.14	odd	10
363.3.b.d.122.2		2	11.3	even	5
363.3.h.d.245.1		8	11.4	even	5	inner
363.3.h.d.245.2		8	33.26	odd	10	inner
363.3.h.d.251.1		8	33.20	odd	10	inner
363.3.h.d.251.2		8	11.9	even	5	inner
363.3.h.d.269.1		8	1.1	even	1	trivial
363.3.h.d.269.2		8	3.2	odd	2	inner
363.3.h.d.323.1		8	33.5	odd	10	inner
363.3.h.d.323.2		8	11.5	even	5	inner
363.3.h.e.245.1		8	33.29	even	10
363.3.h.e.245.2		8	11.7	odd	10
363.3.h.e.251.1		8	11.2	odd	10
363.3.h.e.251.2		8	33.2	even	10
363.3.h.e.269.1		8	33.32	even	2
363.3.h.e.269.2		8	11.10	odd	2
363.3.h.e.323.1		8	11.6	odd	10
363.3.h.e.323.2		8	33.17	even	10
528.3.i.a.353.1		2	132.107	odd	10
528.3.i.a.353.2		2	44.19	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.15430 + 1.02489i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(5.66312 - 4.11450i) q^{4} +(6.30860 + 2.04979i) q^{5} +(9.46289 + 3.07468i) q^{6} +(-6.47214 + 4.70228i) q^{7} +(-5.84839 + 8.04962i) q^{8} +(2.78115 + 8.55951i) q^{9} -22.0000 q^{10} -21.0000 q^{12} +(-1.23607 - 3.80423i) q^{13} +(15.5957 - 21.4656i) q^{14} +(-11.6968 - 16.0992i) q^{15} +(1.54508 - 4.75528i) q^{16} +(12.6172 + 4.09957i) q^{17} +(-17.5452 - 24.1489i) q^{18} +(-4.85410 - 3.52671i) q^{19} +(44.1602 - 14.3485i) q^{20} +24.0000 q^{21} -6.63325i q^{23} +(28.3887 - 9.22404i) q^{24} +(15.3713 + 11.1679i) q^{25} +(7.79785 + 10.7328i) q^{26} +(8.34346 - 25.6785i) q^{27} +(-17.3050 + 53.2592i) q^{28} +(23.3936 + 32.1985i) q^{29} +(53.3951 + 38.7938i) q^{30} +(-8.03444 - 24.7275i) q^{31} -23.2164i q^{32} -44.0000 q^{34} +(-50.4688 + 16.3983i) q^{35} +(50.9681 + 37.0305i) q^{36} +(-24.2705 + 17.6336i) q^{37} +(18.9258 + 6.14936i) q^{38} +(-3.70820 + 11.4127i) q^{39} +(-53.3951 + 38.7938i) q^{40} +(7.79785 - 10.7328i) q^{41} +(-75.7031 + 24.5974i) q^{42} -42.0000 q^{43} +59.6992i q^{45} +(6.79837 + 20.9232i) q^{46} +(-50.6860 + 69.7634i) q^{47} +(-12.1353 + 8.81678i) q^{48} +(4.63525 - 14.2658i) q^{49} +(-59.9317 - 19.4730i) q^{50} +(-23.3936 - 32.1985i) q^{51} +(-22.6525 - 16.4580i) q^{52} +(-56.7774 + 18.4481i) q^{53} +89.5489i q^{54} -79.5990i q^{56} +(5.56231 + 17.1190i) q^{57} +(-106.790 - 77.5877i) q^{58} +(38.9893 + 53.6641i) q^{59} +(-132.480 - 43.0455i) q^{60} +(-3.70820 + 11.4127i) q^{61} +(50.6860 + 69.7634i) q^{62} +(-58.2492 - 42.3205i) q^{63} +(29.9746 + 92.2525i) q^{64} -26.5330i q^{65} +2.00000 q^{67} +(88.3203 - 28.6970i) q^{68} +(-11.6968 + 16.0992i) q^{69} +(142.387 - 103.450i) q^{70} +(56.7774 + 18.4481i) q^{71} +(-85.1660 - 27.6721i) q^{72} +(-59.8673 + 43.4961i) q^{73} +(58.4839 - 80.4962i) q^{74} +(-17.6140 - 54.2102i) q^{75} -42.0000 q^{76} -39.7995i q^{78} +(12.3607 + 38.0423i) q^{79} +(19.4946 - 26.8321i) q^{80} +(-65.5304 + 47.6106i) q^{81} +(-13.5967 + 41.8465i) q^{82} +(-37.8516 - 12.2987i) q^{83} +(135.915 - 98.7479i) q^{84} +(71.1935 + 51.7251i) q^{85} +(132.480 - 43.0455i) q^{86} -119.398i q^{87} +119.398i q^{89} +(-61.1854 - 188.309i) q^{90} +(25.8885 + 18.8091i) q^{91} +(-27.2925 - 37.5649i) q^{92} +(-24.1033 + 74.1824i) q^{93} +(88.3789 - 272.002i) q^{94} +(-23.3936 - 32.1985i) q^{95} +(-40.9387 + 56.3473i) q^{96} +(19.1591 + 58.9655i) q^{97} +49.7494i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 14 q^{4} - 16 q^{7} - 18 q^{9} - 176 q^{10} - 168 q^{12} + 8 q^{13} - 10 q^{16} - 12 q^{19} + 192 q^{21} + 38 q^{25} - 54 q^{27} + 112 q^{28} + 132 q^{30} + 52 q^{31} - 352 q^{34} + 126 q^{36}+ \cdots - 124 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 + 14 * q^4 - 16 * q^7 - 18 * q^9 - 176 * q^10 - 168 * q^12 + 8 * q^13 - 10 * q^16 - 12 * q^19 + 192 * q^21 + 38 * q^25 - 54 * q^27 + 112 * q^28 + 132 * q^30 + 52 * q^31 - 352 * q^34 + 126 * q^36 - 60 * q^37 + 24 * q^39 - 132 * q^40 - 336 * q^43 - 44 * q^46 - 30 * q^48 - 30 * q^49 - 56 * q^52 - 36 * q^57 - 264 * q^58 + 24 * q^61 - 144 * q^63 - 194 * q^64 + 16 * q^67 + 352 * q^70 - 148 * q^73 + 114 * q^75 - 336 * q^76 - 80 * q^79 - 162 * q^81 + 88 * q^82 + 336 * q^84 + 176 * q^85 + 396 * q^90 + 64 * q^91 + 156 * q^93 - 572 * q^94 - 124 * q^97

Introduction

L-functions

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