LMFDB - Embedded newform 363.3.h.e.251.2

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			251.2
Root			$1.37924 - 1.04771i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.e.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.15430 + 1.02489i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(5.66312 + 4.11450i) q^{4} +(6.30860 - 2.04979i) q^{5} +(-9.46289 + 3.07468i) q^{6} +(6.47214 + 4.70228i) q^{7} +(5.84839 + 8.04962i) q^{8} +(2.78115 - 8.55951i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q - 6 * q^3 + 14 * q^4 + 16 * q^7 - 18 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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	$-0.0888214\pi$
$2$	3.15430	+	1.02489i	1.57715	+	0.512447i	0.615829	+	0.787880i	$0.288821\pi$
$3$	−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	0.399612	−	0.916684i	$-0.369145\pi$
$5$	6.30860	−	2.04979i	1.26172	−	0.409957i	0.862107	+	0.506727i	$0.169145\pi$
$6$	−9.46289	+	3.07468i	−1.57715	+	0.512447i
$7$	6.47214	+	4.70228i	0.924591	+	0.671755i	0.944662	−	0.328044i	$-0.106389\pi$
$7$	6.47214	+	4.70228i	0.924591	+	0.671755i	−0.0200716	+	0.999799i	$0.506389\pi$
$8$	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	$-0.850834\pi$
$13$	1.23607	−	3.80423i	0.0950822	−	0.292633i	0.987275	+	0.159022i	$0.0508340\pi$
$14$	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	$-0.727591\pi$
$17$	−12.6172	+	4.09957i	−0.742188	+	0.241151i	−0.0865714	+	0.996246i	$0.527591\pi$
$18$	17.5452	−	24.1489i	0.974732	−	1.34160i
$19$	4.85410	−	3.52671i	0.255479	−	0.185616i	−0.452673	−	0.891677i	$-0.649529\pi$
$19$	4.85410	−	3.52671i	0.255479	−	0.185616i	0.708152	+	0.706060i	$0.249529\pi$
$20$	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	$0.0460612\pi$
$23$			6.63325i			0.288402i	−0.989548	+	0.144201i	$0.953939\pi$
$24$	−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	0.185154	+	0.982710i	$0.440722\pi$
$29$	−23.3936	+	32.1985i	−0.806674	+	1.11029i	−0.991828	+	0.127582i	$0.959278\pi$
$30$	−53.3951	+	38.7938i	−1.77984	+	1.29313i
$31$	−8.03444	+	24.7275i	−0.259176	+	0.797660i	0.733803	+	0.679363i	$0.237744\pi$
$31$	−8.03444	+	24.7275i	−0.259176	+	0.797660i	−0.992978	+	0.118298i	$0.962256\pi$
$32$		−	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	0.209336	−	0.977844i	$-0.432870\pi$
$37$	−24.2705	−	17.6336i	−0.655960	−	0.476583i	−0.865296	+	0.501261i	$0.832870\pi$
$38$	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	$-0.251726\pi$
$41$	−7.79785	−	10.7328i	−0.190192	−	0.261776i	−0.893455	+	0.449154i	$0.851726\pi$
$42$	−75.7031	−	24.5974i	−1.80246	−	0.585653i
$43$	42.0000			0.976744			0.488372	−	0.872635i	$-0.337591\pi$
$43$	42.0000			0.976744			0.488372	+	0.872635i	$0.337591\pi$
$44$		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	−0.861241	−	0.508196i	$-0.830312\pi$
$47$	−50.6860	−	69.7634i	−1.07843	−	1.48433i	−0.217185	−	0.976130i	$-0.569688\pi$
$48$	−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	−0.280288	−	0.959916i	$-0.590430\pi$
$53$	−56.7774	−	18.4481i	−1.07127	−	0.348077i	−0.790982	+	0.611839i	$0.790430\pi$
$54$			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	−0.338674	−	0.940904i	$-0.609978\pi$
$59$	38.9893	−	53.6641i	0.660835	−	0.909561i	0.999509	+	0.0313426i	$0.00997829\pi$
$60$	−132.480	+	43.0455i	−2.20801	+	0.717425i
$61$	3.70820	+	11.4127i	0.0607902	+	0.187093i	0.976840	−	0.213972i	$-0.0686401\pi$
$61$	3.70820	+	11.4127i	0.0607902	+	0.187093i	−0.916050	+	0.401065i	$0.868640\pi$
$62$	−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	0.119460	−	0.992839i	$-0.461884\pi$
$71$	56.7774	−	18.4481i	0.799681	−	0.259832i	0.680221	+	0.733007i	$0.261884\pi$
$72$	85.1660	−	27.6721i	1.18286	−	0.384335i
$73$	59.8673	+	43.4961i	0.820099	+	0.595837i	0.916741	−	0.399482i	$-0.130810\pi$
$73$	59.8673	+	43.4961i	0.820099	+	0.595837i	−0.0966416	+	0.995319i	$0.530810\pi$
$74$	−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	$-0.981471\pi$
$79$	−12.3607	+	38.0423i	−0.156464	+	0.481548i	0.841842	+	0.539724i	$0.181471\pi$
$80$	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	$-0.522933\pi$
$83$	37.8516	−	12.2987i	0.456043	−	0.148177i	0.528025	+	0.849229i	$0.322933\pi$
$84$	−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	$-0.765960\pi$
$89$		−	119.398i		−	1.34156i	0.741658	−	0.670778i	$-0.234040\pi$
$90$	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	−0.802422	−	0.596757i	$-0.796456\pi$
$97$	19.1591	−	58.9655i	0.197516	−	0.607892i	0.999938	−	0.0111348i	$-0.00354438\pi$
$98$			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	$-0.223913\pi$
$101$	100.938	+	32.7966i	0.999381	+	0.324719i	0.236763	+	0.971567i	$0.423913\pi$
$102$	106.790	−	77.5877i	1.04696	−	0.760663i
$103$	−59.8673	−	43.4961i	−0.581236	−	0.422292i	0.257934	−	0.966163i	$-0.416958\pi$
$103$	−59.8673	−	43.4961i	−0.581236	−	0.422292i	−0.839169	+	0.543870i	$0.816958\pi$
$104$	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	$-0.140454\pi$
$107$	23.3936	+	32.1985i	0.218631	+	0.300920i	−0.685587	+	0.727991i	$0.740454\pi$
$108$	−58.4042	+	179.750i	−0.540780	+	1.66435i
$109$	−200.000			−1.83486			−0.917431	−	0.397894i	$-0.869741\pi$
$109$	−200.000			−1.83486			−0.917431	+	0.397894i	$0.869741\pi$
$110$		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	0.899885	−	0.436128i	$-0.143651\pi$
$113$	23.3936	+	32.1985i	0.207023	+	0.284942i	−0.692862	+	0.721070i	$0.743651\pi$
$114$	−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	0.868244	+	0.496138i	$0.165249\pi$
$127$	58.0952	+	178.799i	0.457442	+	1.40786i	−0.410801	+	0.911725i	$0.634751\pi$
$128$	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	−0.653279	−	0.757117i	$-0.726607\pi$
$137$	−100.938	+	32.7966i	−0.736770	+	0.239391i	−0.0834913	+	0.996509i	$0.526607\pi$
$138$	−20.3951	−	62.7697i	−0.147791	−	0.454853i
$139$	59.8673	+	43.4961i	0.430700	+	0.312922i	0.781929	−	0.623368i	$-0.214236\pi$
$139$	59.8673	+	43.4961i	0.430700	+	0.312922i	−0.351229	+	0.936290i	$0.614236\pi$
$140$	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	$-0.499125\pi$
$149$	88.3203	−	28.6970i	0.592754	−	0.192597i	0.590006	+	0.807399i	$0.299125\pi$
$150$	−111.119	+	152.943i	−0.740796	+	1.01962i
$151$	129.443	−	94.0456i	0.857237	−	0.622819i	−0.0698952	−	0.997554i	$-0.522266\pi$
$151$	129.443	−	94.0456i	0.857237	−	0.622819i	0.927132	+	0.374736i	$0.122266\pi$
$152$	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	−0.947900	−	0.318568i	$-0.896798\pi$
$157$	−147.241	+	106.977i	−0.937841	+	0.681382i	0.0100587	+	0.999949i	$0.496798\pi$
$158$	−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	0.159548	+	0.987190i	$0.448996\pi$
$163$	−89.6149	+	275.806i	−0.549785	+	1.69206i	−0.709333	+	0.704874i	$0.751004\pi$
$164$		−	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	$-0.653556\pi$
$167$	−227.109	−	73.7923i	−1.35994	−	0.441870i	−0.896022	+	0.444010i	$0.853556\pi$
$168$	−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	$-0.395051\pi$
$173$	−116.968	−	160.992i	−0.676114	−	0.930592i	−0.999879	+	0.0155460i	$0.995051\pi$
$174$	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	0.345791	−	0.938311i	$-0.387611\pi$
$179$	−116.968	−	160.992i	−0.653451	−	0.899399i	−0.999243	+	0.0389129i	$0.987611\pi$
$180$	245.632	−	338.084i	1.36462	−	1.87824i
$181$	3.09017	+	9.51057i	0.0170728	+	0.0525446i	0.959230	−	0.282627i	$-0.0912058\pi$
$181$	3.09017	+	9.51057i	0.0170728	+	0.0525446i	−0.942157	+	0.335171i	$0.891206\pi$
$182$	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	−0.946477	−	0.322772i	$-0.895385\pi$
$191$	−66.2817	+	91.2290i	−0.347025	+	0.477639i	0.599452	+	0.800411i	$0.295385\pi$
$192$	89.9239	+	276.757i	0.468354	+	1.44145i
$193$	92.0871	+	283.415i	0.477135	+	1.46847i	0.843057	+	0.537825i	$0.180754\pi$
$193$	92.0871	+	283.415i	0.477135	+	1.46847i	−0.365921	+	0.930646i	$0.619246\pi$
$194$	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	−0.592611	−	0.805489i	$-0.701903\pi$
$211$	76.0182	−	233.960i	0.360276	−	1.10881i	0.952887	−	0.303326i	$-0.0980971\pi$
$212$	−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	0.115280	−	0.993333i	$-0.463223\pi$
$223$	244.323	−	177.511i	1.09562	−	0.796014i	0.980339	+	0.197319i	$0.0632234\pi$
$224$	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	$-0.944426\pi$
$227$	−116.968	+	160.992i	−0.515277	+	0.709217i	0.469521	+	0.882921i	$0.344426\pi$
$228$	−101.936	+	74.0609i	−0.447088	+	0.324829i
$229$	46.3525	−	142.658i	0.202413	−	0.622963i	−0.797397	−	0.603455i	$-0.793790\pi$
$229$	46.3525	−	142.658i	0.202413	−	0.622963i	0.999810	−	0.0195075i	$-0.00620982\pi$
$230$			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	$-0.788685\pi$
$233$	−416.367	−	135.286i	−1.78698	−	0.580626i	−0.999368	+	0.0355403i	$0.988685\pi$
$234$	−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	$-0.200000\pi$
$239$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$240$	−94.6289	−	30.7468i	−0.394287	−	0.128112i
$241$	130.000			0.539419			0.269710	−	0.962942i	$-0.413072\pi$
$241$	130.000			0.539419			0.269710	+	0.962942i	$0.413072\pi$
$242$		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	0.804366	−	0.594134i	$-0.202505\pi$
$251$	277.578	+	90.1906i	1.10589	+	0.359325i	0.301523	+	0.953459i	$0.402505\pi$
$252$	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	0.321317	−	0.946972i	$-0.395875\pi$
$257$	288.521	−	397.114i	1.12265	−	1.54519i	0.801331	−	0.598221i	$-0.204125\pi$
$258$	−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	−0.435148	−	0.900359i	$-0.643304\pi$
$269$	−69.3945	+	22.5477i	−0.257972	+	0.0838203i	0.177176	+	0.984179i	$0.443304\pi$
$270$	183.556	+	564.928i	0.679837	+	2.09232i
$271$	362.440	+	263.328i	1.33742	+	0.971689i	0.999535	+	0.0305004i	$0.00971007\pi$
$271$	362.440	+	263.328i	1.33742	+	0.971689i	0.337881	+	0.941189i	$0.390290\pi$
$272$	−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	0.694787	+	0.719216i	$0.255499\pi$
$277$	−80.3444	+	247.275i	−0.290052	+	0.892688i	−0.984839	+	0.173473i	$0.944501\pi$
$278$	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	$-0.484791\pi$
$281$	189.258	−	61.4936i	0.673516	−	0.218838i	0.625754	+	0.780020i	$0.284791\pi$
$282$	694.137	+	504.320i	2.46148	+	1.78837i
$283$	40.4508	−	29.3893i	0.142936	−	0.103849i	−0.514019	−	0.857779i	$-0.671844\pi$
$283$	40.4508	−	29.3893i	0.142936	−	0.103849i	0.656955	+	0.753930i	$0.271844\pi$
$284$	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	0.0102629	−	0.999947i	$-0.496733\pi$
$293$	280.723	−	386.382i	0.958098	−	1.31871i	0.947835	−	0.318761i	$-0.103267\pi$
$294$	−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	$-0.455269\pi$
$307$	86.0000			0.280130			0.140065	+	0.990142i	$0.455269\pi$
$308$		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	0.789798	−	0.613367i	$-0.210185\pi$
$311$	−11.6968	−	16.0992i	−0.0376102	−	0.0517660i	−0.827408	+	0.561601i	$0.810185\pi$
$312$	−70.1807	+	96.5954i	−0.224938	+	0.309601i
$313$	30.2837	+	93.2035i	0.0967529	+	0.297775i	0.987707	−	0.156319i	$-0.0499629\pi$
$313$	30.2837	+	93.2035i	0.0967529	+	0.297775i	−0.890954	+	0.454094i	$0.849963\pi$
$314$	−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	0.736746	−	0.676169i	$-0.236361\pi$
$317$	296.504	+	96.3400i	0.935344	+	0.303912i	0.198598	+	0.980081i	$0.436361\pi$
$318$	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	$-0.435331\pi$
$337$	−224.907	−	163.404i	−0.667379	−	0.484879i	−0.869147	+	0.494554i	$0.835331\pi$
$338$	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	$-0.758602\pi$
$347$	−315.430	+	102.489i	−0.909019	+	0.295358i	−0.183065	+	0.983101i	$0.558602\pi$
$348$	491.265	−	676.168i	1.41168	−	1.94301i
$349$	−262.122	+	190.442i	−0.751064	+	0.545680i	−0.896157	−	0.443738i	$-0.853652\pi$
$349$	−262.122	+	190.442i	−0.751064	+	0.545680i	0.145092	+	0.989418i	$0.453652\pi$
$350$	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	$0.190635\pi$
$353$			397.995i			1.12746i	−0.825958	+	0.563732i	$0.809365\pi$
$354$	−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	$-0.939716\pi$
$359$	−179.351	+	246.855i	−0.499584	+	0.687618i	0.482536	+	0.875876i	$0.339716\pi$
$360$	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	0.850408	−	0.526124i	$-0.176355\pi$
$367$	224.907	+	163.404i	0.612825	+	0.445243i	−0.237583	+	0.971367i	$0.576355\pi$
$368$	−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	$-0.529055\pi$
$373$	−68.0000			−0.182306			−0.0911528	+	0.995837i	$0.529055\pi$
$374$		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	0.717919	+	0.696127i	$0.245095\pi$
$379$	207.041	+	637.208i	0.546283	+	1.68129i	−0.171636	+	0.985161i	$0.554905\pi$
$380$	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	0.267548	−	0.963544i	$-0.413786\pi$
$383$	−31.5430	−	10.2489i	−0.0823576	−	0.0267596i	−0.349906	+	0.936785i	$0.613786\pi$
$384$			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	−0.998123	−	0.0612377i	$-0.980495\pi$
$389$	−245.632	+	338.084i	−0.631446	+	0.869110i	0.366678	+	0.930348i	$0.380495\pi$
$390$	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	0.00555318	−	0.999985i	$-0.498232\pi$
$401$	239.727	−	77.8919i	0.597822	−	0.194244i	0.592269	+	0.805740i	$0.298232\pi$
$402$	−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	−0.550916	−	0.834561i	$-0.685722\pi$
$409$	157.599	−	485.039i	0.385327	−	1.18591i	0.936243	−	0.351353i	$-0.114278\pi$
$410$	−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	$-0.781722\pi$
$419$		−	530.660i		−	1.26649i	0.773951	−	0.633246i	$-0.218278\pi$
$420$	−1059.84	−	344.364i	−2.52344	−	0.819915i
$421$	137.533	−	99.9235i	0.326681	−	0.237348i	−0.412340	−	0.911030i	$-0.635288\pi$
$421$	137.533	−	99.9235i	0.326681	−	0.237348i	0.739021	+	0.673682i	$0.235288\pi$
$422$	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	$-0.295242\pi$
$431$	264.961	+	86.0910i	0.614759	+	0.199747i	0.0149469	+	0.999888i	$0.495242\pi$
$432$	−109.217	+	79.3510i	−0.252818	+	0.183683i
$433$	438.487	+	318.580i	1.01267	+	0.735750i	0.964768	−	0.263102i	$-0.0847457\pi$
$433$	438.487	+	318.580i	1.01267	+	0.735750i	0.0479046	+	0.998852i	$0.484746\pi$
$434$	−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	$-0.378131\pi$
$439$	328.000			0.747153			0.373576	+	0.927599i	$0.378131\pi$
$440$		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	0.711884	−	0.702297i	$-0.247842\pi$
$443$	−77.9785	−	107.328i	−0.176024	−	0.242276i	−0.887908	+	0.460021i	$0.847842\pi$
$444$	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	−0.210505	−	0.977593i	$-0.567511\pi$
$449$	−428.984	−	139.386i	−0.955422	−	0.310435i	−0.744917	+	0.667157i	$0.767511\pi$
$450$		−	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	0.997596	+	0.0692969i	$0.0220756\pi$
$457$	105.684	+	325.261i	0.231256	+	0.711732i	−0.766340	+	0.642435i	$0.777924\pi$
$458$	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	0.370242	−	0.928935i	$-0.379275\pi$
$467$	567.774	−	184.481i	1.21579	−	0.395034i	0.845547	+	0.533901i	$0.179275\pi$
$468$	−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	$-0.675646\pi$
$479$	−214.492	+	69.6928i	−0.447792	+	0.145496i	0.0764360	+	0.997074i	$0.475646\pi$
$480$	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	−0.892995	−	0.450067i	$-0.851400\pi$
$487$	−360.822	+	262.152i	−0.740907	+	0.538300i	0.152088	+	0.988367i	$0.451400\pi$
$488$	−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	0.143903	+	0.989592i	$0.454035\pi$
$491$	−413.286	+	568.840i	−0.841723	+	1.15853i	−0.985626	+	0.168941i	$0.945965\pi$
$492$	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	0.633809	−	0.773490i	$-0.281491\pi$
$499$	46.9230	+	34.0915i	0.0940340	+	0.0683197i	−0.539775	+	0.841809i	$0.681491\pi$
$500$	−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	$-0.0329214\pi$
$503$	296.318	+	407.847i	0.589102	+	0.810830i	−0.405554	+	0.914071i	$0.632921\pi$
$504$	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	−0.983806	−	0.179236i	$-0.942637\pi$
$509$	−432.781	−	595.672i	−0.850257	−	1.17028i	0.133549	−	0.991042i	$-0.457363\pi$
$510$	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	−0.622410	−	0.782691i	$-0.713846\pi$
$521$	163.755	−	225.389i	0.314309	−	0.432609i	0.936719	+	0.350082i	$0.113846\pi$
$522$	367.112	+	1129.86i	0.703280	+	2.16447i
$523$	−43.8804	−	135.050i	−0.0839014	−	0.258222i	0.900301	−	0.435267i	$-0.143346\pi$
$523$	−43.8804	−	135.050i	−0.0839014	−	0.258222i	−0.984203	+	0.177045i	$0.943346\pi$
$524$	−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	−0.769441	−	0.638717i	$-0.779465\pi$
$541$	123.607	−	380.423i	0.228478	−	0.703184i	0.997920	−	0.0644668i	$-0.0205347\pi$
$542$	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	$-0.749664\pi$
$547$	−137.533	+	99.9235i	−0.251431	+	0.182675i	0.454930	+	0.890527i	$0.349664\pi$
$548$	−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	−0.0757486	−	0.997127i	$-0.524135\pi$
$557$	499.063	−	686.901i	0.895983	−	1.23321i	0.971732	−	0.236088i	$-0.0758653\pi$
$558$	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	$-0.614675\pi$
$563$	−668.711	−	217.277i	−1.18776	−	0.385928i	−0.835246	+	0.549877i	$0.814675\pi$
$564$	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	$-0.166541\pi$
$569$	70.1807	+	96.5954i	0.123340	+	0.169763i	−0.742882	+	0.669423i	$0.766541\pi$
$570$	−122.371	+	376.618i	−0.214685	+	0.660734i
$571$	−706.000			−1.23643			−0.618214	−	0.786010i	$-0.712143\pi$
$571$	−706.000			−1.23643			−0.618214	+	0.786010i	$0.712143\pi$
$572$		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	−0.928773	−	0.370649i	$-0.879135\pi$
$577$	−228.055	−	701.880i	−0.395242	−	1.21643i	0.533531	−	0.845780i	$-0.320865\pi$
$578$	−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	0.0113088	+	0.999936i	$0.496400\pi$
$587$	−553.648	+	762.030i	−0.943181	+	1.29818i	−0.954490	+	0.298242i	$0.903600\pi$
$588$	−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	−0.271923	−	0.962319i	$-0.587660\pi$
$599$	44.1602	−	14.3485i	0.0737231	−	0.0239541i	0.345646	+	0.938365i	$0.387660\pi$
$600$	−539.385	+	175.257i	−0.898975	+	0.292095i
$601$	−438.487	−	318.580i	−0.729596	−	0.530083i	0.159840	−	0.987143i	$-0.448902\pi$
$601$	−438.487	−	318.580i	−0.729596	−	0.530083i	−0.889436	+	0.457060i	$0.848902\pi$
$602$	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	0.598853	+	0.800859i	$0.295623\pi$
$607$	−216.312	+	665.740i	−0.356362	+	1.09677i	−0.955215	+	0.295911i	$0.904377\pi$
$608$	−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	$-0.914153\pi$
$613$	−618.089	+	449.068i	−1.00830	+	0.732574i	−0.0444496	+	0.999012i	$0.514153\pi$
$614$	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	$0.0102680\pi$
$617$			39.7995i			0.0645049i	−0.999480	+	0.0322524i	$0.989732\pi$
$618$	700.254	+	227.526i	1.13310	+	0.368166i
$619$	600.291	−	436.137i	0.969775	−	0.704583i	0.0143746	−	0.999897i	$-0.495424\pi$
$619$	600.291	−	436.137i	0.969775	−	0.704583i	0.955400	+	0.295314i	$0.0954243\pi$
$620$	−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	0.818735	−	0.574171i	$-0.194676\pi$
$631$	331.697	+	240.992i	0.525669	+	0.381921i	−0.293066	+	0.956092i	$0.594676\pi$
$632$	−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	0.999997	+	0.00255720i	$0.000813982\pi$
$641$	444.478	+	611.771i	0.693413	+	0.954401i	−0.306584	+	0.951844i	$0.599186\pi$
$642$	−320.371	−	232.763i	−0.499020	−	0.362559i
$643$	275.025	+	846.440i	0.427722	+	1.31639i	0.900364	+	0.435138i	$0.143300\pi$
$643$	275.025	+	846.440i	0.427722	+	1.31639i	−0.472642	+	0.881255i	$0.656700\pi$
$644$	−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	0.642460	−	0.766320i	$-0.277914\pi$
$647$	460.527	+	149.634i	0.711789	+	0.231274i	0.0693294	+	0.997594i	$0.477914\pi$
$648$		−	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	−0.595700	−	0.803207i	$-0.703125\pi$
$653$	230.037	−	316.618i	0.352277	−	0.484867i	0.947977	+	0.318340i	$0.103125\pi$
$654$	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	0.693391	+	0.720562i	$0.256116\pi$
$673$	−195.917	+	602.970i	−0.291110	+	0.895943i	−0.984501	+	0.175382i	$0.943884\pi$
$674$	−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	$-0.800037\pi$
$677$	−757.031	+	245.974i	−1.11821	+	0.363330i	−0.309129	+	0.951020i	$0.600037\pi$
$678$	−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	$-0.892882\pi$
$683$		−	451.061i		−	0.660411i	0.943909	−	0.330206i	$-0.107118\pi$
$684$	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	−0.794902	−	0.606738i	$-0.792478\pi$
$691$	141.530	−	435.584i	0.204819	−	0.630367i	0.999721	−	0.0236296i	$-0.00752222\pi$
$692$		−	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	$-0.317079\pi$
$701$	−296.318	−	407.847i	−0.422708	−	0.581808i	−0.966260	+	0.257568i	$0.917079\pi$
$702$	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	−0.995645	−	0.0932243i	$-0.970283\pi$
$709$	−173.668	−	534.494i	−0.244947	−	0.753870i	0.750698	−	0.660646i	$-0.229717\pi$
$710$	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	−0.648032	−	0.761613i	$-0.724408\pi$
$719$	198.845	−	273.687i	0.276558	−	0.380650i	0.924590	+	0.380964i	$0.124408\pi$
$720$	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	$-0.160046\pi$
$733$	504.827	+	366.778i	0.688713	+	0.500379i	−0.187524	+	0.982260i	$0.560046\pi$
$734$	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	−0.698982	−	0.715139i	$-0.746363\pi$
$739$	211.986	−	652.425i	0.286855	−	0.882848i	0.985837	−	0.167709i	$-0.0536368\pi$
$740$	−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	$-0.402936\pi$
$743$	820.117	−	266.472i	1.10379	−	0.358644i	0.803561	+	0.595223i	$0.202936\pi$
$744$	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	−0.637264	−	0.770646i	$-0.719934\pi$
$751$	−76.0476	+	55.2518i	−0.101262	+	0.0735710i	0.536002	+	0.844217i	$0.319934\pi$
$752$	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	−0.413124	−	0.910675i	$-0.635562\pi$
$757$	345.481	−	1063.28i	0.456382	−	1.40460i	0.869505	−	0.493924i	$-0.164438\pi$
$758$			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	$-0.673987\pi$
$761$	−1097.70	−	356.663i	−1.44244	−	0.468677i	−0.922657	+	0.385623i	$0.873987\pi$
$762$	−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	$-0.189281\pi$
$769$	1274.00			1.65670			0.828349	+	0.560213i	$0.189281\pi$
$770$		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	0.999771	+	0.0214117i	$0.00681609\pi$
$773$	549.749	+	756.664i	0.711188	+	0.978867i	−0.288582	+	0.957455i	$0.593184\pi$
$774$	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	$-0.0393695\pi$
$787$	92.0871	+	283.415i	0.117010	+	0.360121i	−0.875351	+	0.483488i	$0.839370\pi$
$788$	−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	−0.604500	−	0.796605i	$-0.706627\pi$
$797$	−498.379	+	161.933i	−0.625319	+	0.203178i	−0.0208184	+	0.999783i	$0.506627\pi$
$798$	−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	$-0.408586\pi$
$809$	870.586	−	282.871i	1.07613	−	0.349655i	0.792871	+	0.609390i	$0.208586\pi$
$810$	−1441.67	−	1047.43i	−1.77984	−	1.29313i
$811$	147.241	−	106.977i	0.181555	−	0.131907i	−0.493296	−	0.869862i	$-0.664208\pi$
$811$	147.241	−	106.977i	0.181555	−	0.131907i	0.674851	+	0.737954i	$0.264208\pi$
$812$	−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	$-0.967008\pi$
$821$	−483.467	+	665.435i	−0.588876	+	0.810518i	0.405758	+	0.913981i	$0.367008\pi$
$822$	854.322	−	620.701i	1.03932	−	0.755111i
$823$	−76.0182	+	233.960i	−0.0923672	+	0.284277i	−0.986559	−	0.163408i	$-0.947751\pi$
$823$	−76.0182	+	233.960i	−0.0923672	+	0.284277i	0.894191	+	0.447685i	$0.147751\pi$
$824$		−	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	$-0.293337\pi$
$827$	517.305	+	168.083i	0.625520	+	0.203244i	0.0209303	+	0.999781i	$0.493337\pi$
$828$	245.632	+	338.084i	0.296657	+	0.408314i
$829$	−202.254	−	146.946i	−0.243974	−	0.177257i	0.459078	−	0.888396i	$-0.348180\pi$
$829$	−202.254	−	146.946i	−0.243974	−	0.177257i	−0.703052	+	0.711139i	$0.748180\pi$
$830$	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	0.611526	−	0.791224i	$-0.290556\pi$
$839$	−276.824	−	381.015i	−0.329945	−	0.454130i	−0.941471	+	0.337094i	$0.890556\pi$
$840$	−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	$-0.0895495\pi$
$853$	17.3050	+	53.2592i	0.0202872	+	0.0624375i	−0.940400	+	0.340069i	$0.889549\pi$
$854$	−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	0.392094	−	0.919925i	$-0.371751\pi$
$863$	1078.77	−	350.514i	1.25002	−	0.406157i	0.857929	+	0.513768i	$0.171751\pi$
$864$	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	$-0.783715\pi$
$877$	−368.912	+	268.030i	−0.420652	+	0.305622i	0.357248	+	0.934010i	$0.383715\pi$
$878$	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	$-0.887423\pi$
$881$		−	610.259i		−	0.692689i	0.938107	−	0.346344i	$-0.112577\pi$
$882$	425.830	+	138.361i	0.482801	+	0.156871i
$883$	885.065	−	643.037i	1.00234	−	0.728241i	0.0397499	−	0.999210i	$-0.487344\pi$
$883$	885.065	−	643.037i	1.00234	−	0.728241i	0.962588	+	0.270968i	$0.0873439\pi$
$884$	−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	$-0.773786\pi$
$887$	85.7764	−	118.061i	0.0967039	−	0.133102i	0.854627	+	0.519242i	$0.173786\pi$
$888$	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	0.977729	−	0.209871i	$-0.0673044\pi$
$907$	57.4772	+	176.897i	0.0633706	+	0.195035i	−0.914358	+	0.404906i	$0.867304\pi$
$908$	−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	0.719475	−	0.694519i	$-0.244383\pi$
$911$	813.809	+	264.423i	0.893314	+	0.290255i	0.173839	+	0.984774i	$0.444383\pi$
$912$	−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	$-0.174809\pi$
$919$	−132.259	−	407.052i	−0.143917	−	0.442929i	−0.996870	+	0.0790573i	$0.974809\pi$
$920$	−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	−0.616256	−	0.787546i	$-0.711352\pi$
$929$	−605.625	+	196.780i	−0.651911	+	0.211819i	−0.0356543	+	0.999364i	$0.511352\pi$
$930$	−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	$-0.850543\pi$
$937$	89.6149	−	275.806i	0.0956403	−	0.294350i	0.987420	+	0.158119i	$0.0505431\pi$
$938$	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	$-0.754033\pi$
$941$	−832.735	+	270.572i	−0.884946	+	0.287537i	−0.168937	+	0.985627i	$0.554033\pi$
$942$	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	$-0.986618\pi$
$947$		−	79.5990i		−	0.0840538i	0.999116	−	0.0420269i	$-0.0133815\pi$
$948$	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	$-0.934703\pi$
$953$	−460.073	+	633.237i	−0.482763	+	0.664466i	0.496270	+	0.868168i	$0.334703\pi$
$954$	−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	$-0.423558\pi$
$967$	460.000			0.475698			0.237849	+	0.971302i	$0.423558\pi$
$968$		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	0.999862	+	0.0166321i	$0.00529440\pi$
$971$	686.211	+	944.488i	0.706705	+	0.972697i	−0.293156	+	0.956065i	$0.594706\pi$
$972$	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	0.868054	−	0.496469i	$-0.165370\pi$
$977$	1249.10	+	405.858i	1.27851	+	0.415412i	0.410453	+	0.911882i	$0.365370\pi$
$978$		−	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	−0.665589	−	0.746318i	$-0.731820\pi$
$983$	245.632	−	338.084i	0.249880	−	0.343931i	0.915469	+	0.402388i	$0.131820\pi$
$984$	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	$-0.291698\pi$
$997$	42.0689	+	30.5648i	0.0421955	+	0.0306568i	−0.566488	+	0.824070i	$0.691698\pi$
$998$	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.e.251.2		8
3.2	odd	2	inner	363.3.h.e.251.1		8
11.2	odd	10		363.3.h.d.245.2		8
11.3	even	5	inner	363.3.h.e.323.2		8
11.4	even	5		33.3.b.a.23.2	yes	2
11.5	even	5	inner	363.3.h.e.269.1		8
11.6	odd	10		363.3.h.d.269.2		8
11.7	odd	10		363.3.b.d.122.1		2
11.8	odd	10		363.3.h.d.323.1		8
11.9	even	5	inner	363.3.h.e.245.1		8
11.10	odd	2		363.3.h.d.251.1		8
33.2	even	10		363.3.h.d.245.1		8
33.5	odd	10	inner	363.3.h.e.269.2		8
33.8	even	10		363.3.h.d.323.2		8
33.14	odd	10	inner	363.3.h.e.323.1		8
33.17	even	10		363.3.h.d.269.1		8
33.20	odd	10	inner	363.3.h.e.245.2		8
33.26	odd	10		33.3.b.a.23.1	✓	2
33.29	even	10		363.3.b.d.122.2		2
33.32	even	2		363.3.h.d.251.2		8
44.15	odd	10		528.3.i.a.353.1		2
132.59	even	10		528.3.i.a.353.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.a.23.1	✓	2	33.26	odd	10
33.3.b.a.23.2	yes	2	11.4	even	5
363.3.b.d.122.1		2	11.7	odd	10
363.3.b.d.122.2		2	33.29	even	10
363.3.h.d.245.1		8	33.2	even	10
363.3.h.d.245.2		8	11.2	odd	10
363.3.h.d.251.1		8	11.10	odd	2
363.3.h.d.251.2		8	33.32	even	2
363.3.h.d.269.1		8	33.17	even	10
363.3.h.d.269.2		8	11.6	odd	10
363.3.h.d.323.1		8	11.8	odd	10
363.3.h.d.323.2		8	33.8	even	10
363.3.h.e.245.1		8	11.9	even	5	inner
363.3.h.e.245.2		8	33.20	odd	10	inner
363.3.h.e.251.1		8	3.2	odd	2	inner
363.3.h.e.251.2		8	1.1	even	1	trivial
363.3.h.e.269.1		8	11.5	even	5	inner
363.3.h.e.269.2		8	33.5	odd	10	inner
363.3.h.e.323.1		8	33.14	odd	10	inner
363.3.h.e.323.2		8	11.3	even	5	inner
528.3.i.a.353.1		2	44.15	odd	10
528.3.i.a.353.2		2	132.59	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)

\(f(q)\)	\(=\)	\(q+(3.15430 + 1.02489i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(5.66312 + 4.11450i) q^{4} +(6.30860 - 2.04979i) q^{5} +(-9.46289 + 3.07468i) q^{6} +(6.47214 + 4.70228i) q^{7} +(5.84839 + 8.04962i) q^{8} +(2.78115 - 8.55951i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 14 q^{4} + 16 q^{7} - 18 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 14 * q^4 + 16 * q^7 - 18 * q^9	\( 8 q - 6 q^{3} + 14 q^{4} + 16 q^{7} - 18 q^{9} + 176 q^{10} - 168 q^{12} - 8 q^{13} - 10 q^{16} + 12 q^{19} - 192 q^{21} + 38 q^{25} - 54 q^{27} - 112 q^{28} - 132 q^{30} + 52 q^{31} - 352 q^{34} + 126 q^{36} - 60 q^{37} - 24 q^{39} + 132 q^{40} + 336 q^{43} + 44 q^{46} - 30 q^{48} - 30 q^{49} + 56 q^{52} + 36 q^{57} - 264 q^{58} - 24 q^{61} + 144 q^{63} - 194 q^{64} + 16 q^{67} + 352 q^{70} + 148 q^{73} + 114 q^{75} + 336 q^{76} + 80 q^{79} - 162 q^{81} + 88 q^{82} - 336 q^{84} - 176 q^{85} - 396 q^{90} + 64 q^{91} + 156 q^{93} + 572 q^{94} - 124 q^{97}+O(q^{100}) \) 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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