LMFDB - Embedded newform 363.3.h.e.245.1

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			245.1
Root			$1.42264 + 0.987975i$ of defining polynomial
Character	$\chi$	$=$	363.245
Dual form			363.3.h.e.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94946 - 2.68321i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-2.16312 + 6.65740i) q^{4} +(-3.89893 + 5.36641i) q^{5} +(5.84839 - 8.04962i) q^{6} +(-2.47214 + 7.60845i) q^{7} +(9.46289 - 3.07468i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})$	\(q+(-1.94946 - 2.68321i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-2.16312 + 6.65740i) q^{4} +(-3.89893 + 5.36641i) q^{5} +(5.84839 - 8.04962i) q^{6} +(-2.47214 + 7.60845i) q^{7} +(9.46289 - 3.07468i) q^{8} +(-7.28115 + 5.29007i) q^{9} +22.0000 q^{10} -21.0000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(25.2344 - 8.19915i) q^{14} +(-18.9258 - 6.14936i) q^{15} +(-4.04508 - 2.93893i) q^{16} +(7.79785 - 10.7328i) q^{17} +(28.3887 + 9.22404i) q^{18} +(-1.85410 - 5.70634i) q^{19} +(-27.2925 - 37.5649i) q^{20} -24.0000 q^{21} +6.63325i q^{23} +(17.5452 + 24.1489i) q^{24} +(-5.87132 - 18.0701i) q^{25} +(12.6172 + 4.09957i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(-45.3050 - 32.9160i) q^{28} +(-37.8516 - 12.2987i) q^{29} +(20.3951 + 62.7697i) q^{30} +(21.0344 - 15.2824i) q^{31} -23.2164i q^{32} -44.0000 q^{34} +(-31.1914 - 42.9313i) q^{35} +(-19.4681 - 59.9166i) q^{36} +(9.27051 - 28.5317i) q^{37} +(-11.6968 + 16.0992i) q^{38} +(-9.70820 - 7.05342i) q^{39} +(-20.3951 + 62.7697i) q^{40} +(-12.6172 + 4.09957i) q^{41} +(46.7871 + 64.3969i) q^{42} +42.0000 q^{43} -59.6992i q^{45} +(17.7984 - 12.9313i) q^{46} +(-82.0117 + 26.6472i) q^{47} +(4.63525 - 14.2658i) q^{48} +(-12.1353 - 8.81678i) q^{49} +(-37.0398 + 50.9809i) q^{50} +(37.8516 + 12.2987i) q^{51} +(-8.65248 - 26.6296i) q^{52} +(35.0903 + 48.2977i) q^{53} +89.5489i q^{54} +79.5990i q^{56} +(14.5623 - 10.5801i) q^{57} +(40.7902 + 125.539i) q^{58} +(63.0860 + 20.4979i) q^{59} +(81.8775 - 112.695i) q^{60} +(-9.70820 - 7.05342i) q^{61} +(-82.0117 - 26.6472i) q^{62} +(-22.2492 - 68.4761i) q^{63} +(-78.4746 + 57.0152i) q^{64} -26.5330i q^{65} +2.00000 q^{67} +(54.5850 + 75.1298i) q^{68} +(-18.9258 + 6.14936i) q^{69} +(-54.3870 + 167.386i) q^{70} +(-35.0903 + 48.2977i) q^{71} +(-52.6355 + 72.4466i) q^{72} +(-22.8673 + 70.3782i) q^{73} +(-94.6289 + 30.7468i) q^{74} +(46.1140 - 33.5038i) q^{75} +42.0000 q^{76} +39.7995i q^{78} +(32.3607 - 23.5114i) q^{79} +(31.5430 - 10.2489i) q^{80} +(25.0304 - 77.0356i) q^{81} +(35.5967 + 25.8626i) q^{82} +(-23.3936 + 32.1985i) q^{83} +(51.9149 - 159.777i) q^{84} +(27.1935 + 83.6930i) q^{85} +(-81.8775 - 112.695i) q^{86} -119.398i q^{87} -119.398i q^{89} +(-160.185 + 116.381i) q^{90} +(-9.88854 - 30.4338i) q^{91} +(-44.1602 - 14.3485i) q^{92} +(63.1033 + 45.8472i) q^{93} +(231.379 + 168.107i) q^{94} +(37.8516 + 12.2987i) q^{95} +(66.2402 - 21.5228i) q^{96} +(-50.1591 + 36.4427i) 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.94946	−	2.68321i	−0.974732	−	1.34160i	−0.939620	−	0.342220i	$-0.888821\pi$
$2$	−1.94946	−	2.68321i	−0.974732	−	1.34160i	−0.0351115	−	0.999383i	$-0.511179\pi$
$3$	0.927051	+	2.85317i	0.309017	+	0.951057i
$3$	0.927051	+	2.85317i	0.309017	+	0.951057i
$4$	−2.16312	+	6.65740i	−0.540780	+	1.66435i
$5$	−3.89893	+	5.36641i	−0.779785	+	1.07328i	0.215520	+	0.976499i	$0.430855\pi$
$5$	−3.89893	+	5.36641i	−0.779785	+	1.07328i	−0.995306	+	0.0967830i	$0.969145\pi$
$6$	5.84839	−	8.04962i	0.974732	−	1.34160i
$7$	−2.47214	+	7.60845i	−0.353162	+	1.08692i	0.603905	+	0.797056i	$0.293611\pi$
$7$	−2.47214	+	7.60845i	−0.353162	+	1.08692i	−0.957067	+	0.289866i	$0.906389\pi$
$8$	9.46289	−	3.07468i	1.18286	−	0.384335i
$9$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$10$	22.0000			2.20000
$11$		0			0
$11$		0			0
$12$	−21.0000			−1.75000
$13$	−3.23607	+	2.35114i	−0.248928	+	0.180857i	−0.705252	−	0.708957i	$-0.749166\pi$
$13$	−3.23607	+	2.35114i	−0.248928	+	0.180857i	0.456323	+	0.889814i	$0.349166\pi$
$14$	25.2344	−	8.19915i	1.80246	−	0.585653i
$15$	−18.9258	−	6.14936i	−1.26172	−	0.409957i
$16$	−4.04508	−	2.93893i	−0.252818	−	0.183683i
$17$	7.79785	−	10.7328i	0.458697	−	0.631343i	−0.515541	−	0.856865i	$-0.672409\pi$
$17$	7.79785	−	10.7328i	0.458697	−	0.631343i	0.974238	+	0.225523i	$0.0724089\pi$
$18$	28.3887	+	9.22404i	1.57715	+	0.512447i
$19$	−1.85410	−	5.70634i	−0.0975843	−	0.300334i	0.890334	−	0.455307i	$-0.150471\pi$
$19$	−1.85410	−	5.70634i	−0.0975843	−	0.300334i	−0.987919	+	0.154974i	$0.950471\pi$
$20$	−27.2925	−	37.5649i	−1.36462	−	1.87824i
$21$	−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	$0.953939\pi$
$24$	17.5452	+	24.1489i	0.731049	+	1.00620i
$25$	−5.87132	−	18.0701i	−0.234853	−	0.722803i
$26$	12.6172	+	4.09957i	0.485277	+	0.157676i
$27$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$28$	−45.3050	−	32.9160i	−1.61803	−	1.17557i
$29$	−37.8516	−	12.2987i	−1.30523	−	0.424094i	−0.427830	−	0.903859i	$-0.640722\pi$
$29$	−37.8516	−	12.2987i	−1.30523	−	0.424094i	−0.877397	+	0.479765i	$0.840722\pi$
$30$	20.3951	+	62.7697i	0.679837	+	2.09232i
$31$	21.0344	−	15.2824i	0.678530	−	0.492981i	−0.194339	−	0.980934i	$-0.562256\pi$
$31$	21.0344	−	15.2824i	0.678530	−	0.492981i	0.872870	+	0.487953i	$0.162256\pi$
$32$		−	23.2164i		−	0.725512i
$33$		0			0
$34$	−44.0000			−1.29412
$35$	−31.1914	−	42.9313i	−0.891183	−	1.22661i
$36$	−19.4681	−	59.9166i	−0.540780	−	1.66435i
$37$	9.27051	−	28.5317i	0.250554	−	0.771127i	−0.744119	−	0.668047i	$-0.767130\pi$
$37$	9.27051	−	28.5317i	0.250554	−	0.771127i	0.994673	−	0.103080i	$-0.0328696\pi$
$38$	−11.6968	+	16.0992i	−0.307810	+	0.423664i
$39$	−9.70820	−	7.05342i	−0.248928	−	0.180857i
$40$	−20.3951	+	62.7697i	−0.509878	+	1.56924i
$41$	−12.6172	+	4.09957i	−0.307736	+	0.0999896i	−0.458814	−	0.888532i	$-0.651726\pi$
$41$	−12.6172	+	4.09957i	−0.307736	+	0.0999896i	0.151078	+	0.988522i	$0.451726\pi$
$42$	46.7871	+	64.3969i	1.11398	+	1.53326i
$43$	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
$46$	17.7984	−	12.9313i	0.386921	−	0.281115i
$47$	−82.0117	+	26.6472i	−1.74493	+	0.566962i	−0.995469	−	0.0950856i	$-0.969688\pi$
$47$	−82.0117	+	26.6472i	−1.74493	+	0.566962i	−0.749461	+	0.662048i	$0.769688\pi$
$48$	4.63525	−	14.2658i	0.0965678	−	0.297205i
$49$	−12.1353	−	8.81678i	−0.247658	−	0.179934i
$50$	−37.0398	+	50.9809i	−0.740796	+	1.01962i
$51$	37.8516	+	12.2987i	0.742188	+	0.241151i
$52$	−8.65248	−	26.6296i	−0.166394	−	0.512107i
$53$	35.0903	+	48.2977i	0.662082	+	0.911277i	0.999548	−	0.0300602i	$-0.00956989\pi$
$53$	35.0903	+	48.2977i	0.662082	+	0.911277i	−0.337466	+	0.941338i	$0.609570\pi$
$54$			89.5489i			1.65831i
$55$		0			0
$56$			79.5990i			1.42141i
$57$	14.5623	−	10.5801i	0.255479	−	0.185616i
$58$	40.7902	+	125.539i	0.703280	+	2.16447i
$59$	63.0860	+	20.4979i	1.06925	+	0.347421i	0.790197	−	0.612853i	$-0.209978\pi$
$59$	63.0860	+	20.4979i	1.06925	+	0.347421i	0.279057	+	0.960275i	$0.409978\pi$
$60$	81.8775	−	112.695i	1.36462	−	1.87824i
$61$	−9.70820	−	7.05342i	−0.159151	−	0.115630i	0.505360	−	0.862909i	$-0.331360\pi$
$61$	−9.70820	−	7.05342i	−0.159151	−	0.115630i	−0.664510	+	0.747279i	$0.731360\pi$
$62$	−82.0117	−	26.6472i	−1.32277	−	0.429794i
$63$	−22.2492	−	68.4761i	−0.353162	−	1.08692i
$64$	−78.4746	+	57.0152i	−1.22617	+	0.890862i
$65$		−	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	$0.495249\pi$
$68$	54.5850	+	75.1298i	0.802720	+	1.10485i
$69$	−18.9258	+	6.14936i	−0.274287	+	0.0891212i
$70$	−54.3870	+	167.386i	−0.776957	+	2.39123i
$71$	−35.0903	+	48.2977i	−0.494230	+	0.680249i	−0.981161	−	0.193191i	$-0.938116\pi$
$71$	−35.0903	+	48.2977i	−0.494230	+	0.680249i	0.486931	+	0.873440i	$0.338116\pi$
$72$	−52.6355	+	72.4466i	−0.731049	+	1.00620i
$73$	−22.8673	+	70.3782i	−0.313250	+	0.964085i	0.663219	+	0.748426i	$0.269190\pi$
$73$	−22.8673	+	70.3782i	−0.313250	+	0.964085i	−0.976469	+	0.215659i	$0.930810\pi$
$74$	−94.6289	+	30.7468i	−1.27877	+	0.415497i
$75$	46.1140	−	33.5038i	0.614853	−	0.446717i
$76$	42.0000			0.552632
$77$		0			0
$78$			39.7995i			0.510250i
$79$	32.3607	−	23.5114i	0.409629	−	0.297613i	−0.363823	−	0.931468i	$-0.618529\pi$
$79$	32.3607	−	23.5114i	0.409629	−	0.297613i	0.773452	+	0.633855i	$0.218529\pi$
$80$	31.5430	−	10.2489i	0.394287	−	0.128112i
$81$	25.0304	−	77.0356i	0.309017	−	0.951057i
$82$	35.5967	+	25.8626i	0.434107	+	0.315397i
$83$	−23.3936	+	32.1985i	−0.281850	+	0.387933i	−0.926346	−	0.376675i	$-0.877067\pi$
$83$	−23.3936	+	32.1985i	−0.281850	+	0.387933i	0.644495	+	0.764608i	$0.277067\pi$
$84$	51.9149	−	159.777i	0.618034	−	1.90211i
$85$	27.1935	+	83.6930i	0.319923	+	0.984623i
$86$	−81.8775	−	112.695i	−0.952063	−	1.31040i
$87$		−	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	$-0.234040\pi$
$90$	−160.185	+	116.381i	−1.77984	+	1.29313i
$91$	−9.88854	−	30.4338i	−0.108665	−	0.334437i
$92$	−44.1602	−	14.3485i	−0.480002	−	0.155962i
$93$	63.1033	+	45.8472i	0.678530	+	0.492981i
$94$	231.379	+	168.107i	2.46148	+	1.78837i
$95$	37.8516	+	12.2987i	0.398438	+	0.129460i
$96$	66.2402	−	21.5228i	0.690003	−	0.224195i
$97$	−50.1591	+	36.4427i	−0.517104	+	0.375698i	−0.815512	−	0.578741i	$-0.803544\pi$
$97$	−50.1591	+	36.4427i	−0.517104	+	0.375698i	0.298408	+	0.954438i	$0.403544\pi$
$98$			49.7494i			0.507647i
$99$		0			0
$100$	133.000			1.33000
$101$	−62.3828	−	85.8626i	−0.617652	−	0.850125i	0.379528	−	0.925180i	$-0.376087\pi$
$101$	−62.3828	−	85.8626i	−0.617652	−	0.850125i	−0.997179	+	0.0750558i	$0.976087\pi$
$102$	−40.7902	−	125.539i	−0.399904	−	1.23078i
$103$	22.8673	−	70.3782i	0.222012	−	0.683283i	−0.776569	−	0.630032i	$-0.783042\pi$
$103$	22.8673	−	70.3782i	0.222012	−	0.683283i	0.998581	−	0.0532510i	$-0.0169584\pi$
$104$	−23.3936	+	32.1985i	−0.224938	+	0.309601i
$105$	93.5742	−	128.794i	0.891183	−	1.22661i
$106$	61.1854	−	188.309i	0.577220	−	1.77650i
$107$	37.8516	−	12.2987i	0.353753	−	0.114941i	−0.126749	−	0.991935i	$-0.540454\pi$
$107$	37.8516	−	12.2987i	0.353753	−	0.114941i	0.480502	+	0.876993i	$0.340454\pi$
$108$	152.904	−	111.091i	1.41578	−	1.02862i
$109$	−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
$112$	32.3607	−	23.5114i	0.288935	−	0.209923i
$113$	37.8516	−	12.2987i	0.334970	−	0.108838i	−0.136703	−	0.990612i	$-0.543651\pi$
$113$	37.8516	−	12.2987i	0.334970	−	0.108838i	0.471672	+	0.881774i	$0.343651\pi$
$114$	−56.7774	−	18.4481i	−0.498047	−	0.161825i
$115$	−35.5967	−	25.8626i	−0.309537	−	0.224892i
$116$	163.755	−	225.389i	1.41168	−	1.94301i
$117$	11.1246	−	34.2380i	0.0950822	−	0.292633i
$118$	−67.9837	−	209.232i	−0.576133	−	1.77316i
$119$	62.3828	+	85.8626i	0.524225	+	0.721534i
$120$	−198.000			−1.65000
$121$		0			0
$122$			39.7995i			0.326225i
$123$	−23.3936	−	32.1985i	−0.190192	−	0.261776i
$124$	56.2411	+	173.092i	0.453557	+	1.39591i
$125$	−37.8516	−	12.2987i	−0.302813	−	0.0983898i
$126$	−140.361	+	193.191i	−1.11398	+	1.53326i
$127$	−152.095	−	110.504i	−1.19760	−	0.870107i	−0.203553	−	0.979064i	$-0.565249\pi$
$127$	−152.095	−	110.504i	−1.19760	−	0.870107i	−0.994047	+	0.108957i	$0.965249\pi$
$128$	217.647	+	70.7176i	1.70036	+	0.552482i
$129$	38.9361	+	119.833i	0.301831	+	0.928939i
$130$	−71.1935	+	51.7251i	−0.547642	+	0.397885i
$131$			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
$134$	−3.89893	−	5.36641i	−0.0290965	−	0.0400478i
$135$	170.332	−	55.3442i	1.26172	−	0.409957i
$136$	40.7902	−	125.539i	0.299928	−	0.923084i
$137$	62.3828	−	85.8626i	0.455349	−	0.626734i	−0.518187	−	0.855267i	$-0.673393\pi$
$137$	62.3828	−	85.8626i	0.455349	−	0.626734i	0.973536	+	0.228533i	$0.0733929\pi$
$138$	53.3951	+	38.7938i	0.386921	+	0.281115i
$139$	−22.8673	+	70.3782i	−0.164513	+	0.506318i	−0.999000	−	0.0447092i	$-0.985764\pi$
$139$	−22.8673	+	70.3782i	−0.164513	+	0.506318i	0.834487	+	0.551027i	$0.185764\pi$
$140$	353.281	−	114.788i	2.52344	−	0.819915i
$141$	−152.058	−	209.290i	−1.07843	−	1.48433i
$142$	198.000			1.39437
$143$		0			0
$144$	45.0000			0.312500
$145$	213.580	−	155.175i	1.47297	−	1.07017i
$146$	233.418	−	75.8421i	1.59875	−	0.519467i
$147$	13.9058	−	42.7975i	0.0945970	−	0.291140i
$148$	169.894	+	123.435i	1.14793	+	0.834020i
$149$	−54.5850	+	75.1298i	−0.366342	+	0.504227i	−0.951902	−	0.306402i	$-0.900875\pi$
$149$	−54.5850	+	75.1298i	−0.366342	+	0.504227i	0.585560	+	0.810629i	$0.300875\pi$
$150$	−179.795	−	58.4189i	−1.19863	−	0.389460i
$151$	−49.4427	−	152.169i	−0.327435	−	1.00774i	−0.970329	−	0.241787i	$-0.922266\pi$
$151$	−49.4427	−	152.169i	−0.327435	−	1.00774i	0.642894	−	0.765955i	$-0.277734\pi$
$152$	−35.0903	−	48.2977i	−0.230857	−	0.317748i
$153$			119.398i			0.780382i
$154$		0			0
$155$			172.464i			1.11267i
$156$	67.9574	−	49.3740i	0.435625	−	0.316500i
$157$	56.2411	+	173.092i	0.358224	+	1.10250i	0.954117	+	0.299435i	$0.0967982\pi$
$157$	56.2411	+	173.092i	0.358224	+	1.10250i	−0.595893	+	0.803064i	$0.703202\pi$
$158$	−126.172	−	40.9957i	−0.798556	−	0.259467i
$159$	−105.271	+	144.893i	−0.662082	+	0.911277i
$160$	124.589	+	90.5189i	0.778679	+	0.565743i
$161$	−50.4688	−	16.3983i	−0.313471	−	0.101853i
$162$	−255.498	+	83.0164i	−1.57715	+	0.512447i
$163$	234.615	−	170.458i	1.43936	−	1.04575i	0.451179	−	0.892434i	$-0.351004\pi$
$163$	234.615	−	170.458i	1.43936	−	1.04575i	0.988177	−	0.153319i	$-0.0489963\pi$
$164$		−	92.8655i		−	0.566253i
$165$		0			0
$166$	132.000			0.795181
$167$	140.361	+	193.191i	0.840487	+	1.15683i	0.985879	+	0.167457i	$0.0535556\pi$
$167$	140.361	+	193.191i	0.840487	+	1.15683i	−0.145392	+	0.989374i	$0.546444\pi$
$168$	−227.109	+	73.7923i	−1.35184	+	0.439240i
$169$	−47.2796	+	145.512i	−0.279761	+	0.861016i
$170$	171.553	−	236.122i	1.00913	−	1.38895i
$171$	43.6869	+	31.7404i	0.255479	+	0.185616i
$172$	−90.8510	+	279.611i	−0.528203	+	1.62564i
$173$	−189.258	+	61.4936i	−1.09398	+	0.355454i	−0.799782	−	0.600291i	$-0.795051\pi$
$173$	−189.258	+	61.4936i	−1.09398	+	0.355454i	−0.294195	+	0.955746i	$0.595051\pi$
$174$	−320.371	+	232.763i	−1.84121	+	1.33772i
$175$	152.000			0.868571
$176$		0			0
$177$			198.997i			1.12428i
$178$	−320.371	+	232.763i	−1.79984	+	1.30766i
$179$	−189.258	+	61.4936i	−1.05731	+	0.343540i	−0.785532	−	0.618821i	$-0.787611\pi$
$179$	−189.258	+	61.4936i	−1.05731	+	0.343540i	−0.271775	+	0.962361i	$0.587611\pi$
$180$	397.441	+	129.137i	2.20801	+	0.717425i
$181$	−8.09017	−	5.87785i	−0.0446971	−	0.0324743i	0.565212	−	0.824945i	$-0.308794\pi$
$181$	−8.09017	−	5.87785i	−0.0446971	−	0.0324743i	−0.609909	+	0.792471i	$0.708794\pi$
$182$	−62.3828	+	85.8626i	−0.342763	+	0.471772i
$183$	11.1246	−	34.2380i	0.0607902	−	0.187093i
$184$	20.3951	+	62.7697i	0.110843	+	0.341140i
$185$	116.968	+	160.992i	0.632258	+	0.870229i
$186$		−	258.697i		−	1.39084i
$187$		0			0
$188$		−	603.626i		−	3.21078i
$189$	174.748	−	126.962i	0.924591	−	0.671755i
$190$	−40.7902	−	125.539i	−0.214685	−	0.660734i
$191$	−107.246	−	34.8464i	−0.561498	−	0.182442i	0.0144971	−	0.999895i	$-0.495385\pi$
$191$	−107.246	−	34.8464i	−0.561498	−	0.182442i	−0.575995	+	0.817453i	$0.695385\pi$
$192$	−235.424	−	171.046i	−1.22617	−	0.890862i
$193$	−241.087	−	175.160i	−1.24916	−	0.907565i	−0.250983	−	0.967991i	$-0.580754\pi$
$193$	−241.087	−	175.160i	−1.24916	−	0.907565i	−0.998173	+	0.0604267i	$0.980754\pi$
$194$	195.566	+	63.5434i	1.00807	+	0.327543i
$195$	75.7031	−	24.5974i	0.388221	−	0.126141i
$196$	84.9468	−	61.7175i	0.433402	−	0.314885i
$197$			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	$0.533653\pi$
$200$	−111.119	−	152.943i	−0.555597	−	0.764714i
$201$	1.85410	+	5.70634i	0.00922439	+	0.0283897i
$202$	−108.774	+	334.772i	−0.538485	+	1.65729i
$203$	187.148	−	257.588i	0.921914	−	1.26891i
$204$	−163.755	+	225.389i	−0.802720	+	1.10485i
$205$	27.1935	−	83.6930i	0.132651	−	0.408258i
$206$	−233.418	+	75.8421i	−1.13310	+	0.368166i
$207$	−35.0903	−	48.2977i	−0.169519	−	0.233322i
$208$	20.0000			0.0961538
$209$		0			0
$210$	−528.000			−2.51429
$211$	−199.018	+	144.595i	−0.943214	+	0.685285i	−0.949192	−	0.314697i	$-0.898097\pi$
$211$	−199.018	+	144.595i	−0.943214	+	0.685285i	0.00597807	+	0.999982i	$0.498097\pi$
$212$	−397.441	+	129.137i	−1.87472	+	0.609135i
$213$	−170.332	−	55.3442i	−0.799681	−	0.259832i
$214$	−106.790	−	77.5877i	−0.499020	−	0.362559i
$215$	−163.755	+	225.389i	−0.761651	+	1.04832i
$216$	−255.498	−	83.0164i	−1.18286	−	0.384335i
$217$	64.2755	+	197.820i	0.296201	+	0.911612i
$218$	389.893	+	536.641i	1.78850	+	2.46166i
$219$	−222.000			−1.01370
$220$		0			0
$221$			53.0660i			0.240118i
$222$	−175.452	−	241.489i	−0.790323	−	1.08779i
$223$	−93.3231	−	287.219i	−0.418489	−	1.28798i	−0.909092	−	0.416595i	$-0.863223\pi$
$223$	−93.3231	−	287.219i	−0.418489	−	1.28798i	0.490603	−	0.871383i	$-0.336777\pi$
$224$	176.641	+	57.3940i	0.788574	+	0.256223i
$225$	138.342	+	100.511i	0.614853	+	0.446717i
$226$	−106.790	−	77.5877i	−0.472523	−	0.343308i
$227$	−189.258	−	61.4936i	−0.833735	−	0.270897i	−0.139117	−	0.990276i	$-0.544426\pi$
$227$	−189.258	−	61.4936i	−0.833735	−	0.270897i	−0.694618	+	0.719379i	$0.744426\pi$
$228$	38.9361	+	119.833i	0.170773	+	0.525584i
$229$	−121.353	+	88.1678i	−0.529924	+	0.385012i	−0.820329	−	0.571892i	$-0.806210\pi$
$229$	−121.353	+	88.1678i	−0.529924	+	0.385012i	0.290405	+	0.956904i	$0.406210\pi$
$230$			145.931i			0.634485i
$231$		0			0
$232$	−396.000			−1.70690
$233$	257.329	+	354.183i	1.10442	+	1.52010i	0.829396	+	0.558661i	$0.188685\pi$
$233$	257.329	+	354.183i	1.10442	+	1.52010i	0.275021	+	0.961438i	$0.411315\pi$
$234$	−113.555	+	36.8962i	−0.485277	+	0.157676i
$235$	176.758	−	544.004i	0.752161	−	2.31491i
$236$	−272.925	+	375.649i	−1.15646	+	1.59173i
$237$	97.0820	+	70.5342i	0.409629	+	0.297613i
$238$	108.774	−	334.772i	0.457034	−	1.40660i
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$	58.4839	+	80.4962i	0.243683	+	0.335401i
$241$	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
$244$	67.9574	−	49.3740i	0.278514	−	0.202352i
$245$	94.6289	−	30.7468i	0.386241	−	0.125497i
$246$	−40.7902	+	125.539i	−0.165814	+	0.510323i
$247$	19.4164	+	14.1068i	0.0786089	+	0.0571127i
$248$	152.058	−	209.290i	0.613138	−	0.843912i
$249$	−113.555	−	36.8962i	−0.456043	−	0.148177i
$250$	40.7902	+	125.539i	0.163161	+	0.502158i
$251$	−171.553	−	236.122i	−0.683477	−	0.940726i	0.316492	−	0.948595i	$-0.397495\pi$
$251$	−171.553	−	236.122i	−0.683477	−	0.940726i	−0.999969	+	0.00786966i	$0.997495\pi$
$252$	504.000			2.00000
$253$		0			0
$254$			623.525i			2.45482i
$255$	−213.580	+	155.175i	−0.837571	+	0.608531i
$256$	−114.645	−	352.842i	−0.447833	−	1.37829i
$257$	466.836	+	151.684i	1.81648	+	0.590211i	0.999916	+	0.0129598i	$0.00412536\pi$
$257$	466.836	+	151.684i	1.81648	+	0.590211i	0.816567	+	0.577251i	$0.195875\pi$
$258$	245.632	−	338.084i	0.952063	−	1.31040i
$259$	194.164	+	141.068i	0.749668	+	0.544666i
$260$	176.641	+	57.3940i	0.679387	+	0.220746i
$261$	340.664	−	110.688i	1.30523	−	0.424094i
$262$	106.790	−	77.5877i	0.407596	−	0.296136i
$263$			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
$266$	−93.5742	−	128.794i	−0.351783	−	0.484188i
$267$	340.664	−	110.688i	1.27590	−	0.414564i
$268$	−4.32624	+	13.3148i	−0.0161427	+	0.0496821i
$269$	42.8882	−	59.0305i	0.159436	−	0.219444i	−0.721824	−	0.692077i	$-0.756696\pi$
$269$	42.8882	−	59.0305i	0.159436	−	0.219444i	0.881260	+	0.472632i	$0.156696\pi$
$270$	−480.556	−	349.144i	−1.77984	−	1.29313i
$271$	−138.440	+	426.073i	−0.510847	+	1.57223i	0.279866	+	0.960039i	$0.409710\pi$
$271$	−138.440	+	426.073i	−0.510847	+	1.57223i	−0.790713	+	0.612187i	$0.790290\pi$
$272$	−63.0860	+	20.4979i	−0.231934	+	0.0753598i
$273$	77.6656	−	56.4274i	0.284489	−	0.206694i
$274$	−352.000			−1.28467
$275$		0			0
$276$		−	139.298i		−	0.504704i
$277$	210.344	−	152.824i	0.759366	−	0.551712i	−0.139350	−	0.990243i	$-0.544501\pi$
$277$	210.344	−	152.824i	0.759366	−	0.551712i	0.898716	+	0.438531i	$0.144501\pi$
$278$	233.418	−	75.8421i	0.839633	−	0.272813i
$279$	−72.3100	+	222.547i	−0.259176	+	0.797660i
$280$	−427.161	−	310.351i	−1.52557	−	1.10840i
$281$	−116.968	+	160.992i	−0.416255	+	0.572927i	−0.964730	−	0.263241i	$-0.915209\pi$
$281$	−116.968	+	160.992i	−0.416255	+	0.572927i	0.548475	+	0.836167i	$0.315209\pi$
$282$	−265.137	+	816.006i	−0.940201	+	2.89364i
$283$	−15.4508	−	47.5528i	−0.0545966	−	0.168031i	0.920040	−	0.391824i	$-0.128156\pi$
$283$	−15.4508	−	47.5528i	−0.0545966	−	0.168031i	−0.974637	+	0.223793i	$0.928156\pi$
$284$	−245.632	−	338.084i	−0.864903	−	1.19044i
$285$			119.398i			0.418942i
$286$		0			0
$287$		−	106.132i		−	0.369798i
$288$	122.816	+	169.042i	0.426445	+	0.586951i
$289$	34.9189	+	107.469i	0.120827	+	0.371866i
$290$	−832.735	−	270.572i	−2.87150	−	0.933006i
$291$	−150.477	−	109.328i	−0.517104	−	0.375698i
$292$	−419.071	−	304.473i	−1.43517	−	1.04271i
$293$	454.219	+	147.585i	1.55024	+	0.503702i	0.954178	−	0.299240i	$-0.0967332\pi$
$293$	454.219	+	147.585i	1.55024	+	0.503702i	0.596057	+	0.802942i	$0.296733\pi$
$294$	−141.943	+	46.1202i	−0.482801	+	0.156871i
$295$	−355.967	+	258.626i	−1.20667	+	0.876697i
$296$		−	298.496i		−	1.00843i
$297$		0			0
$298$	308.000			1.03356
$299$	−15.5957	−	21.4656i	−0.0521595	−	0.0717915i
$300$	123.298	+	379.472i	0.410993	+	1.26491i
$301$	−103.830	+	319.555i	−0.344949	+	1.06164i
$302$	−311.914	+	429.313i	−1.03283	+	1.42157i
$303$	187.148	−	257.588i	0.617652	−	0.850125i
$304$	−9.27051	+	28.5317i	−0.0304951	+	0.0938543i
$305$	75.7031	−	24.5974i	0.248207	−	0.0806474i
$306$	320.371	−	232.763i	1.04696	−	0.760663i
$307$	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
$310$	462.758	−	336.213i	1.49277	−	1.08456i
$311$	−18.9258	+	6.14936i	−0.0608546	+	0.0197729i	−0.339286	−	0.940683i	$-0.610185\pi$
$311$	−18.9258	+	6.14936i	−0.0608546	+	0.0197729i	0.278431	+	0.960456i	$0.410185\pi$
$312$	−113.555	−	36.8962i	−0.363957	−	0.118257i
$313$	−79.2837	−	57.6030i	−0.253302	−	0.184035i	0.453887	−	0.891059i	$-0.350037\pi$
$313$	−79.2837	−	57.6030i	−0.253302	−	0.184035i	−0.707189	+	0.707024i	$0.750037\pi$
$314$	354.802	−	488.343i	1.12994	−	1.55523i
$315$	454.219	+	147.585i	1.44196	+	0.468523i
$316$	86.5248	+	266.296i	0.273813	+	0.842708i
$317$	−183.250	−	252.221i	−0.578074	−	0.795651i	0.415408	−	0.909635i	$-0.363639\pi$
$317$	−183.250	−	252.221i	−0.578074	−	0.795651i	−0.993483	+	0.113984i	$0.963639\pi$
$318$	594.000			1.86792
$319$		0			0
$320$		−	643.425i		−	2.01070i
$321$	70.1807	+	96.5954i	0.218631	+	0.300920i
$322$	54.3870	+	167.386i	0.168904	+	0.519832i
$323$	−75.7031	−	24.5974i	−0.234375	−	0.0761531i
$324$	458.713	+	333.274i	1.41578	+	1.02862i
$325$	61.4853	+	44.6717i	0.189186	+	0.137451i
$326$	−914.746	−	297.219i	−2.80597	−	0.911715i
$327$	−185.410	−	570.634i	−0.567004	−	1.74506i
$328$	−106.790	+	77.5877i	−0.325580	+	0.236548i
$329$		−	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	$0.606814\pi$
$332$	−163.755	−	225.389i	−0.493238	−	0.678883i
$333$	83.4346	+	256.785i	0.250554	+	0.771127i
$334$	244.741	−	753.237i	0.732759	−	2.25520i
$335$	−7.79785	+	10.7328i	−0.0232772	+	0.0320383i
$336$	97.0820	+	70.5342i	0.288935	+	0.209923i
$337$	85.9067	−	264.394i	0.254916	−	0.784551i	−0.738930	−	0.673782i	$-0.764669\pi$
$337$	85.9067	−	264.394i	0.254916	−	0.784551i	0.993846	−	0.110769i	$-0.0353314\pi$
$338$	482.608	−	156.809i	1.42783	−	0.463931i
$339$	70.1807	+	96.5954i	0.207023	+	0.284942i
$340$	−616.000			−1.81176
$341$		0			0
$342$		−	179.098i		−	0.523678i
$343$	−220.053	+	159.878i	−0.641553	+	0.466115i
$344$	397.441	−	129.137i	1.15535	−	0.375397i
$345$	40.7902	−	125.539i	0.118233	−	0.363882i
$346$	533.951	+	387.938i	1.54321	+	1.12121i
$347$	194.946	−	268.321i	0.561805	−	0.773258i	−0.429750	−	0.902948i	$-0.641398\pi$
$347$	194.946	−	268.321i	0.561805	−	0.773258i	0.991555	+	0.129690i	$0.0413982\pi$
$348$	794.883	+	258.273i	2.28415	+	0.742164i
$349$	100.122	+	308.142i	0.286881	+	0.882929i	0.985829	+	0.167756i	$0.0536521\pi$
$349$	100.122	+	308.142i	0.286881	+	0.882929i	−0.698947	+	0.715173i	$0.746348\pi$
$350$	−296.318	−	407.847i	−0.846624	−	1.16528i
$351$	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	$0.809365\pi$
$354$	533.951	−	387.938i	1.50834	−	1.09587i
$355$	−122.371	−	376.618i	−0.344706	−	1.06090i
$356$	794.883	+	258.273i	2.23282	+	0.725486i
$357$	−187.148	+	257.588i	−0.524225	+	0.721534i
$358$	533.951	+	387.938i	1.49148	+	1.08363i
$359$	−290.195	−	94.2902i	−0.808344	−	0.262647i	−0.124448	−	0.992226i	$-0.539716\pi$
$359$	−290.195	−	94.2902i	−0.808344	−	0.262647i	−0.683896	+	0.729579i	$0.739716\pi$
$360$	−183.556	−	564.928i	−0.509878	−	1.56924i
$361$	262.931	−	191.030i	0.728339	−	0.529170i
$362$			33.1662i			0.0916195i
$363$		0			0
$364$	224.000			0.615385
$365$	−288.521	−	397.114i	−0.790467	−	1.08798i
$366$	−113.555	+	36.8962i	−0.310259	+	0.100809i
$367$	−85.9067	+	264.394i	−0.234078	+	0.720419i	0.763164	+	0.646205i	$0.223645\pi$
$367$	−85.9067	+	264.394i	−0.234078	+	0.720419i	−0.997242	+	0.0742141i	$0.976355\pi$
$368$	19.4946	−	26.8321i	0.0529745	−	0.0729132i
$369$	70.1807	−	96.5954i	0.190192	−	0.261776i
$370$	203.951	−	627.697i	0.551220	−	1.69648i
$371$	−454.219	+	147.585i	−1.22431	+	0.397802i
$372$	−441.723	+	320.931i	−1.18743	+	0.862717i
$373$	−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
$376$	−694.137	+	504.320i	−1.84611	+	1.34128i
$377$	151.406	−	49.1949i	0.401608	−	0.130490i
$378$	−681.328	−	221.377i	−1.80246	−	0.585653i
$379$	−542.041	−	393.816i	−1.43019	−	1.03909i	−0.989982	−	0.141196i	$-0.954905\pi$
$379$	−542.041	−	393.816i	−1.43019	−	1.03909i	−0.440207	−	0.897896i	$-0.645095\pi$
$380$	−163.755	+	225.389i	−0.430934	+	0.593130i
$381$	174.286	−	536.396i	0.457442	−	1.40786i
$382$	115.572	+	355.695i	0.302545	+	0.931139i
$383$	19.4946	+	26.8321i	0.0508998	+	0.0700576i	0.833708	−	0.552205i	$-0.186214\pi$
$383$	19.4946	+	26.8321i	0.0508998	+	0.0700576i	−0.782808	+	0.622263i	$0.786214\pi$
$384$			686.541i			1.78787i
$385$		0			0
$386$			988.354i			2.56050i
$387$	−305.808	+	222.183i	−0.790203	+	0.574116i
$388$	−134.113	−	412.759i	−0.345653	−	1.06381i
$389$	−397.441	−	129.137i	−1.02170	−	0.331971i	−0.250197	−	0.968195i	$-0.580495\pi$
$389$	−397.441	−	129.137i	−1.02170	−	0.331971i	−0.771504	+	0.636224i	$0.780495\pi$
$390$	−213.580	−	155.175i	−0.547642	−	0.397885i
$391$	71.1935	+	51.7251i	0.182081	+	0.132289i
$392$	−141.943	−	46.1202i	−0.362100	−	0.117654i
$393$	−113.555	+	36.8962i	−0.288943	+	0.0938834i
$394$	355.967	−	258.626i	0.903471	−	0.656410i
$395$			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	$0.534545\pi$
$398$	81.8775	+	112.695i	0.205722	+	0.283152i
$399$	44.4984	+	136.952i	0.111525	+	0.343238i
$400$	−29.3566	+	90.3504i	−0.0733915	+	0.225876i
$401$	−148.159	+	203.924i	−0.369474	+	0.508538i	−0.952758	−	0.303731i	$-0.901768\pi$
$401$	−148.159	+	203.924i	−0.369474	+	0.508538i	0.583284	+	0.812269i	$0.301768\pi$
$402$	11.6968	−	16.0992i	0.0290965	−	0.0400478i
$403$	−32.1378	+	98.9099i	−0.0797463	+	0.245434i
$404$	706.563	−	229.576i	1.74892	−	0.568258i
$405$	315.813	+	434.679i	0.779785	+	1.07328i
$406$	−1056.00			−2.60099
$407$		0			0
$408$	396.000			0.970588
$409$	−412.599	+	299.770i	−1.00880	+	0.732935i	−0.963957	−	0.266059i	$-0.914278\pi$
$409$	−412.599	+	299.770i	−1.00880	+	0.732935i	−0.0448419	+	0.998994i	$0.514278\pi$
$410$	−277.578	+	90.1906i	−0.677020	+	0.219977i
$411$	302.813	+	98.3898i	0.736770	+	0.239391i
$412$	419.071	+	304.473i	1.01716	+	0.739012i
$413$	−311.914	+	429.313i	−0.755240	+	1.03950i
$414$	−61.1854	+	188.309i	−0.147791	+	0.454853i
$415$	−81.5805	−	251.079i	−0.196579	−	0.605009i
$416$	54.5850	+	75.1298i	0.131214	+	0.180600i
$417$	−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	$-0.218278\pi$
$420$	655.020	+	901.557i	1.55957	+	2.14656i
$421$	−52.5329	−	161.680i	−0.124781	−	0.384037i	0.869080	−	0.494672i	$-0.164712\pi$
$421$	−52.5329	−	161.680i	−0.124781	−	0.384037i	−0.993861	+	0.110635i	$0.964712\pi$
$422$	775.957	+	252.124i	1.83876	+	0.597450i
$423$	456.174	−	627.870i	1.07843	−	1.48433i
$424$	480.556	+	349.144i	1.13339	+	0.823454i
$425$	−239.727	−	77.8919i	−0.564063	−	0.183275i
$426$	183.556	+	564.928i	0.430883	+	1.32612i
$427$	77.6656	−	56.4274i	0.181887	−	0.132148i
$428$			278.596i			0.650926i
$429$		0			0
$430$	924.000			2.14884
$431$	−163.755	−	225.389i	−0.379942	−	0.522945i	0.575627	−	0.817712i	$-0.304758\pi$
$431$	−163.755	−	225.389i	−0.379942	−	0.522945i	−0.955569	+	0.294767i	$0.904758\pi$
$432$	41.7173	+	128.393i	0.0965678	+	0.297205i
$433$	−167.487	+	515.473i	−0.386806	+	1.19047i	0.548355	+	0.836246i	$0.315254\pi$
$433$	−167.487	+	515.473i	−0.386806	+	1.19047i	−0.935161	+	0.354222i	$0.884746\pi$
$434$	405.488	−	558.107i	0.934305	−	1.28596i
$435$	640.741	+	465.526i	1.47297	+	1.07017i
$436$	432.624	−	1331.48i	0.992256	−	3.05385i
$437$	37.8516	−	12.2987i	0.0866169	−	0.0281435i
$438$	432.781	+	595.672i	0.988084	+	1.35998i
$439$	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
$442$	142.387	−	103.450i	0.322143	−	0.234050i
$443$	−126.172	+	40.9957i	−0.284812	+	0.0925412i	−0.447939	−	0.894064i	$-0.647842\pi$
$443$	−126.172	+	40.9957i	−0.284812	+	0.0925412i	0.163127	+	0.986605i	$0.447842\pi$
$444$	−194.681	+	599.166i	−0.438470	+	1.34947i
$445$	640.741	+	465.526i	1.43987	+	1.04613i
$446$	−588.738	+	810.328i	−1.32004	+	1.81688i
$447$	−264.961	−	86.0910i	−0.592754	−	0.192597i
$448$	−239.797	−	738.020i	−0.535262	−	1.64737i
$449$	265.127	+	364.916i	0.590483	+	0.812730i	0.994796	−	0.101890i	$-0.0324891\pi$
$449$	265.127	+	364.916i	0.590483	+	0.812730i	−0.404312	+	0.914621i	$0.632489\pi$
$450$		−	567.143i		−	1.26032i
$451$		0			0
$452$			278.596i			0.616364i
$453$	388.328	−	282.137i	0.857237	−	0.622819i
$454$	203.951	+	627.697i	0.449232	+	1.38259i
$455$	201.875	+	65.5932i	0.443681	+	0.144161i
$456$	105.271	−	144.893i	0.230857	−	0.317748i
$457$	−276.684	−	201.023i	−0.605435	−	0.439874i	0.242369	−	0.970184i	$-0.422076\pi$
$457$	−276.684	−	201.023i	−0.605435	−	0.439874i	−0.847804	+	0.530310i	$0.822076\pi$
$458$	473.145	+	153.734i	1.03307	+	0.335664i
$459$	−340.664	+	110.688i	−0.742188	+	0.241151i
$460$	249.177	−	181.038i	0.541690	−	0.393561i
$461$		−	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	$0.529605\pi$
$464$	116.968	+	160.992i	0.252086	+	0.346966i
$465$	−492.070	+	159.883i	−1.05822	+	0.343835i
$466$	448.693	−	1380.93i	0.962860	−	2.96338i
$467$	−350.903	+	482.977i	−0.751399	+	1.03421i	0.246482	+	0.969147i	$0.420725\pi$
$467$	−350.903	+	482.977i	−0.751399	+	1.03421i	−0.997881	+	0.0650647i	$0.979275\pi$
$468$	203.872	+	148.122i	0.435625	+	0.316500i
$469$	−4.94427	+	15.2169i	−0.0105422	+	0.0324454i
$470$	−1804.26	+	586.239i	−3.83885	+	1.24732i
$471$	−441.723	+	320.931i	−0.937841	+	0.681382i
$472$	660.000			1.39831
$473$		0			0
$474$		−	397.995i		−	0.839652i
$475$	−92.2279	+	67.0075i	−0.194164	+	0.141068i
$476$	−706.563	+	229.576i	−1.48438	+	0.482303i
$477$	−510.996	−	166.033i	−1.07127	−	0.348077i
$478$		0			0
$479$	132.563	−	182.458i	0.276751	−	0.380914i	−0.647904	−	0.761722i	$-0.724354\pi$
$479$	132.563	−	182.458i	0.276751	−	0.380914i	0.924654	+	0.380808i	$0.124354\pi$
$480$	−142.766	+	439.388i	−0.297429	+	0.915392i
$481$	37.0820	+	114.127i	0.0770936	+	0.237270i
$482$	−253.430	−	348.817i	−0.525789	−	0.723686i
$483$		−	159.198i		−	0.329602i
$484$		0			0
$485$		−	411.261i		−	0.847962i
$486$	−473.720	−	652.019i	−0.974732	−	1.34160i
$487$	137.822	+	424.171i	0.283001	+	0.870988i	0.986991	+	0.160778i	$0.0514002\pi$
$487$	137.822	+	424.171i	0.283001	+	0.870988i	−0.703989	+	0.710210i	$0.748600\pi$
$488$	−113.555	−	36.8962i	−0.232694	−	0.0756069i
$489$	703.845	+	511.373i	1.43936	+	1.04575i
$490$	−266.976	−	193.969i	−0.544848	−	0.395855i
$491$	−668.711	−	217.277i	−1.36194	−	0.442520i	−0.465248	−	0.885181i	$-0.654035\pi$
$491$	−668.711	−	217.277i	−1.36194	−	0.442520i	−0.896689	+	0.442660i	$0.854035\pi$
$492$	264.961	−	86.0910i	0.538539	−	0.174982i
$493$	−427.161	+	310.351i	−0.866452	+	0.629514i
$494$		−	79.5990i		−	0.161132i
$495$		0			0
$496$	−130.000			−0.262097
$497$	−280.723	−	386.382i	−0.564834	−	0.777428i
$498$	122.371	+	376.618i	0.245724	+	0.756262i
$499$	−17.9230	+	55.1613i	−0.0359178	+	0.110544i	−0.967408	−	0.253223i	$-0.918509\pi$
$499$	−17.9230	+	55.1613i	−0.0359178	+	0.110544i	0.931490	+	0.363767i	$0.118509\pi$
$500$	163.755	−	225.389i	0.327510	−	0.450779i
$501$	−421.084	+	579.572i	−0.840487	+	1.15683i
$502$	−299.128	+	920.623i	−0.595873	+	1.83391i
$503$	479.453	−	155.784i	0.953187	−	0.309709i	0.209177	−	0.977878i	$-0.432921\pi$
$503$	479.453	−	155.784i	0.953187	−	0.309709i	0.744010	+	0.668168i	$0.232921\pi$
$504$	−421.084	−	579.572i	−0.835484	−	1.14995i
$505$	704.000			1.39406
$506$		0			0
$507$	−459.000			−0.905325
$508$	1064.67	−	773.525i	2.09580	−	1.52269i
$509$	−700.254	+	227.526i	−1.37574	+	0.447007i	−0.901268	−	0.433262i	$-0.857363\pi$
$509$	−700.254	+	227.526i	−1.37574	+	0.447007i	−0.474477	+	0.880268i	$0.657363\pi$
$510$	832.735	+	270.572i	1.63281	+	0.530533i
$511$	−478.938	−	347.969i	−0.937256	−	0.680957i
$512$	−185.199	+	254.905i	−0.361717	+	0.497860i
$513$	−50.0608	+	154.071i	−0.0975843	+	0.300334i
$514$	−503.080	−	1548.32i	−0.978754	−	3.01230i
$515$	288.521	+	397.114i	0.560234	+	0.771096i
$516$	−882.000			−1.70930
$517$		0			0
$518$		−	795.990i		−	1.53666i
$519$	−350.903	−	482.977i	−0.676114	−	0.930592i
$520$	−81.5805	−	251.079i	−0.156886	−	0.482844i
$521$	264.961	+	86.0910i	0.508562	+	0.165242i	0.552048	−	0.833812i	$-0.313846\pi$
$521$	264.961	+	86.0910i	0.508562	+	0.165242i	−0.0434860	+	0.999054i	$0.513846\pi$
$522$	−961.112	−	698.289i	−1.84121	−	1.33772i
$523$	114.880	+	83.4655i	0.219657	+	0.159590i	0.692172	−	0.721733i	$-0.256654\pi$
$523$	114.880	+	83.4655i	0.219657	+	0.159590i	−0.472515	+	0.881322i	$0.656654\pi$
$524$	−264.961	−	86.0910i	−0.505651	−	0.164296i
$525$	140.912	+	433.682i	0.268403	+	0.826061i
$526$	605.145	−	439.663i	1.15047	−	0.835862i
$527$		−	344.929i		−	0.654514i
$528$		0			0
$529$	485.000			0.916824
$530$	771.987	+	1062.55i	1.45658	+	2.00481i
$531$	−567.774	+	184.481i	−1.06925	+	0.347421i
$532$	−103.830	+	319.555i	−0.195169	+	0.600667i
$533$	31.1914	−	42.9313i	0.0585205	−	0.0805465i
$534$	−961.112	−	698.289i	−1.79984	−	1.30766i
$535$	−81.5805	+	251.079i	−0.152487	+	0.469306i
$536$	18.9258	−	6.14936i	0.0353093	−	0.0114727i
$537$	−350.903	−	482.977i	−0.653451	−	0.899399i
$538$	−242.000			−0.449814
$539$		0			0
$540$			1253.68i			2.32164i
$541$	−323.607	+	235.114i	−0.598164	+	0.434592i	−0.845227	−	0.534408i	$-0.820535\pi$
$541$	−323.607	+	235.114i	−0.598164	+	0.434592i	0.247063	+	0.969000i	$0.420535\pi$
$542$	1413.13	−	459.152i	2.60724	−	0.847144i
$543$	9.27051	−	28.5317i	0.0170728	−	0.0525446i
$544$	−249.177	−	181.038i	−0.458046	−	0.332790i
$545$	779.785	−	1073.28i	1.43080	−	1.96933i
$546$	−302.813	−	98.3898i	−0.554602	−	0.180201i
$547$	52.5329	+	161.680i	0.0960382	+	0.295575i	0.987523	−	0.157476i	$-0.0503356\pi$
$547$	52.5329	+	161.680i	0.0960382	+	0.295575i	−0.891485	+	0.453051i	$0.850336\pi$
$548$	436.680	+	601.038i	0.796861	+	1.09678i
$549$	108.000			0.196721
$550$		0			0
$551$			238.797i			0.433388i
$552$	−160.185	+	116.381i	−0.290191	+	0.210836i
$553$	98.8854	+	304.338i	0.178816	+	0.550340i
$554$	−820.117	−	266.472i	−1.48036	−	0.480997i
$555$	−350.903	+	482.977i	−0.632258	+	0.870229i
$556$	−419.071	−	304.473i	−0.753724	−	0.547613i
$557$	807.500	+	262.373i	1.44973	+	0.471046i	0.924916	−	0.380170i	$-0.124135\pi$
$557$	807.500	+	262.373i	1.44973	+	0.471046i	0.524815	+	0.851217i	$0.324135\pi$
$558$	738.106	−	239.825i	1.32277	−	0.429794i
$559$	−135.915	+	98.7479i	−0.243139	+	0.176651i
$560$			265.330i			0.473804i
$561$		0			0
$562$	660.000			1.17438
$563$	413.286	+	568.840i	0.734078	+	1.01037i	0.998938	+	0.0460852i	$0.0146746\pi$
$563$	413.286	+	568.840i	0.734078	+	1.01037i	−0.264859	+	0.964287i	$0.585325\pi$
$564$	1722.25	−	559.592i	3.05363	−	0.992184i
$565$	−81.5805	+	251.079i	−0.144390	+	0.444387i
$566$	−97.4732	+	134.160i	−0.172214	+	0.237032i
$567$	524.243	+	380.885i	0.924591	+	0.671755i
$568$	−183.556	+	564.928i	−0.323162	+	0.994591i
$569$	113.555	−	36.8962i	0.199569	−	0.0648439i	−0.207527	−	0.978229i	$-0.566541\pi$
$569$	113.555	−	36.8962i	0.199569	−	0.0648439i	0.407096	+	0.913385i	$0.366541\pi$
$570$	320.371	−	232.763i	0.562054	−	0.408356i
$571$	−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
$574$	−284.774	+	206.900i	−0.496122	+	0.360454i
$575$	119.863	−	38.9460i	0.208458	−	0.0677321i
$576$	269.772	−	830.272i	0.468354	−	1.44145i
$577$	597.055	+	433.786i	1.03476	+	0.751795i	0.969255	−	0.246058i	$-0.0791353\pi$
$577$	597.055	+	433.786i	1.03476	+	0.751795i	0.0655014	+	0.997852i	$0.479135\pi$
$578$	220.289	−	303.202i	0.381123	−	0.524571i
$579$	276.261	−	850.245i	0.477135	−	1.46847i
$580$	571.063	+	1757.55i	0.984592	+	3.03026i
$581$	−187.148	−	257.588i	−0.322114	−	0.443352i
$582$			616.892i			1.05995i
$583$		0			0
$584$			736.291i			1.26077i
$585$	140.361	+	193.191i	0.239934	+	0.330241i
$586$	−489.483	−	1506.47i	−0.835295	−	2.57077i
$587$	−895.821	−	291.070i	−1.52610	−	0.495860i	−0.578599	−	0.815612i	$-0.696400\pi$
$587$	−895.821	−	291.070i	−1.52610	−	0.495860i	−0.947501	+	0.319753i	$0.896400\pi$
$588$	254.840	+	185.152i	0.433402	+	0.314885i
$589$	−126.207	−	91.6945i	−0.214273	−	0.155678i
$590$	1387.89	+	450.953i	2.35236	+	0.764327i
$591$	−378.516	+	122.987i	−0.640467	+	0.208100i
$592$	−121.353	+	88.1678i	−0.204987	+	0.148932i
$593$			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
$596$	−382.095	−	525.908i	−0.641099	−	0.882397i
$597$	−38.9361	−	119.833i	−0.0652197	−	0.200725i
$598$	−27.1935	+	83.6930i	−0.0454741	+	0.139955i
$599$	−27.2925	+	37.5649i	−0.0455634	+	0.0627127i	−0.831191	−	0.555987i	$-0.812340\pi$
$599$	−27.2925	+	37.5649i	−0.0455634	+	0.0627127i	0.785627	+	0.618700i	$0.212340\pi$
$600$	333.358	−	458.828i	0.555597	−	0.764714i
$601$	167.487	−	515.473i	0.278681	−	0.857692i	−0.709541	−	0.704664i	$-0.751098\pi$
$601$	167.487	−	515.473i	0.278681	−	0.857692i	0.988222	−	0.153027i	$-0.0489023\pi$
$602$	1059.84	−	344.364i	1.76054	−	0.572034i
$603$	−14.5623	+	10.5801i	−0.0241498	+	0.0175458i
$604$	1120.00			1.85430
$605$		0			0
$606$	−1056.00			−1.74257
$607$	566.312	−	411.450i	0.932969	−	0.677841i	−0.0137493	−	0.999905i	$-0.504377\pi$
$607$	566.312	−	411.450i	0.932969	−	0.677841i	0.946718	+	0.322064i	$0.104377\pi$
$608$	−132.480	+	43.0455i	−0.217896	+	0.0707986i
$609$	908.438	+	295.169i	1.49169	+	0.484679i
$610$	−213.580	−	155.175i	−0.350132	−	0.254386i
$611$	202.744	−	279.053i	0.331824	−	0.456716i
$612$	−794.883	−	258.273i	−1.29883	−	0.422015i
$613$	236.089	+	726.607i	0.385137	+	1.18533i	0.936381	+	0.350986i	$0.114153\pi$
$613$	236.089	+	726.607i	0.385137	+	1.18533i	−0.551244	+	0.834344i	$0.685847\pi$
$614$	−167.654	−	230.756i	−0.273052	−	0.375824i
$615$	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	$0.989732\pi$
$618$	−432.781	−	595.672i	−0.700293	−	0.963870i
$619$	−229.291	−	705.684i	−0.370421	−	1.14004i	−0.946516	−	0.322656i	$-0.895424\pi$
$619$	−229.291	−	705.684i	−0.370421	−	1.14004i	0.576095	−	0.817383i	$-0.304576\pi$
$620$	−1148.16	−	373.061i	−1.85188	−	0.601712i
$621$	105.271	−	144.893i	0.169519	−	0.233322i
$622$	53.3951	+	38.7938i	0.0858442	+	0.0623695i
$623$	908.438	+	295.169i	1.45817	+	0.473787i
$624$	18.5410	+	57.0634i	0.0297132	+	0.0914477i
$625$	597.864	−	434.373i	0.956582	−	0.694997i
$626$			325.029i			0.519216i
$627$		0			0
$628$	−1274.00			−2.02866
$629$	−233.936	−	321.985i	−0.371917	−	0.511899i
$630$	−489.483	−	1506.47i	−0.776957	−	2.39123i
$631$	−126.697	+	389.933i	−0.200788	+	0.617961i	0.799073	+	0.601235i	$0.205324\pi$
$631$	−126.697	+	389.933i	−0.200788	+	0.617961i	−0.999860	+	0.0167260i	$0.994676\pi$
$632$	233.936	−	321.985i	0.370151	−	0.509469i
$633$	−597.055	−	433.786i	−0.943214	−	0.685285i
$634$	−319.524	+	983.392i	−0.503980	+	1.55109i
$635$	1186.02	−	385.360i	1.86774	−	0.606866i
$636$	−736.897	−	1014.25i	−1.15864	−	1.59474i
$637$	60.0000			0.0941915
$638$		0			0
$639$		−	537.293i		−	0.840834i
$640$	−1228.09	+	892.258i	−1.91889	+	1.39415i
$641$	719.180	−	233.676i	1.12197	−	0.364549i	0.311448	−	0.950263i	$-0.399186\pi$
$641$	719.180	−	233.676i	1.12197	−	0.364549i	0.810517	+	0.585715i	$0.199186\pi$
$642$	122.371	−	376.618i	0.190609	−	0.586633i
$643$	−720.025	−	523.129i	−1.11979	−	0.813575i	−0.135613	−	0.990762i	$-0.543300\pi$
$643$	−720.025	−	523.129i	−1.11979	−	0.813575i	−0.984177	+	0.177187i	$0.943300\pi$
$644$	218.340	−	300.519i	0.339037	−	0.466644i
$645$	−794.883	−	258.273i	−1.23238	−	0.400423i
$646$	81.5805	+	251.079i	0.126286	+	0.388667i
$647$	−284.622	−	391.748i	−0.439910	−	0.605484i	0.530282	−	0.847821i	$-0.322086\pi$
$647$	−284.622	−	391.748i	−0.439910	−	0.605484i	−0.970192	+	0.242337i	$0.922086\pi$
$648$		−	805.940i		−	1.24373i
$649$		0			0
$650$		−	252.063i		−	0.387790i
$651$	−504.827	+	366.778i	−0.775463	+	0.563407i
$652$	627.304	+	1930.64i	0.962123	+	2.96111i
$653$	372.207	+	120.937i	0.569996	+	0.185203i	0.579814	−	0.814749i	$-0.303125\pi$
$653$	372.207	+	120.937i	0.569996	+	0.185203i	−0.00981822	+	0.999952i	$0.503125\pi$
$654$	−1169.68	+	1609.92i	−1.78850	+	2.46166i
$655$	−213.580	−	155.175i	−0.326077	−	0.236909i
$656$	63.0860	+	20.4979i	0.0961676	+	0.0312468i
$657$	−205.805	−	633.404i	−0.313250	−	0.964085i
$658$	−1851.03	+	1344.85i	−2.81312	+	2.04385i
$659$		−	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	$0.690853\pi$
$662$	424.983	+	584.939i	0.641968	+	0.883593i
$663$	−151.406	+	49.1949i	−0.228365	+	0.0742004i
$664$	−122.371	+	376.618i	−0.184293	+	0.567196i
$665$	−187.148	+	257.588i	−0.281426	+	0.387350i
$666$	526.355	−	724.466i	0.790323	−	1.08779i
$667$	81.5805	−	251.079i	0.122310	−	0.376430i
$668$	−1589.77	+	516.546i	−2.37989	+	0.773273i
$669$	732.969	−	532.533i	1.09562	−	0.796014i
$670$	44.0000			0.0656716
$671$		0			0
$672$			557.193i			0.829156i
$673$	512.917	−	372.656i	0.762135	−	0.553723i	−0.137430	−	0.990512i	$-0.543884\pi$
$673$	512.917	−	372.656i	0.762135	−	0.553723i	0.899564	+	0.436788i	$0.143884\pi$
$674$	−876.895	+	284.920i	−1.30103	+	0.422731i
$675$	−158.526	+	487.892i	−0.234853	+	0.722803i
$676$	−866.457	−	629.518i	−1.28174	−	0.931240i
$677$	467.871	−	643.969i	0.691095	−	0.951210i	−0.308905	−	0.951093i	$-0.599963\pi$
$677$	467.871	−	643.969i	0.691095	−	0.951210i	1.00000		0.000117512i	$-3.74052e-5\pi$
$678$	122.371	−	376.618i	0.180488	−	0.555484i
$679$	−153.272	−	471.724i	−0.225733	−	0.694733i
$680$	514.658	+	708.366i	0.756850	+	1.04172i
$681$		−	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	$-0.107118\pi$
$684$	−305.808	+	222.183i	−0.447088	+	0.324829i
$685$	217.548	+	669.544i	0.317588	+	0.977436i
$686$	857.969	+	278.771i	1.25068	+	0.406372i
$687$	−364.058	−	264.503i	−0.529924	−	0.385012i
$688$	−169.894	−	123.435i	−0.246938	−	0.179411i
$689$	−227.109	−	73.7923i	−0.329622	−	0.107101i
$690$	−416.367	+	135.286i	−0.603431	+	0.196067i
$691$	−370.530	+	269.206i	−0.536223	+	0.389588i	−0.822680	−	0.568504i	$-0.807522\pi$
$691$	−370.530	+	269.206i	−0.536223	+	0.389588i	0.286458	+	0.958093i	$0.407522\pi$
$692$		−	1392.98i		−	2.01298i
$693$		0			0
$694$	−1100.00			−1.58501
$695$	−288.521	−	397.114i	−0.415137	−	0.571388i
$696$	−367.112	−	1129.86i	−0.527460	−	1.62336i
$697$	−54.3870	+	167.386i	−0.0780301	+	0.240152i
$698$	631.626	−	869.359i	0.904908	−	1.24550i
$699$	−771.987	+	1062.55i	−1.10442	+	1.52010i
$700$	−328.794	+	1011.92i	−0.469706	+	1.44561i
$701$	−479.453	+	155.784i	−0.683956	+	0.222231i	−0.630327	−	0.776330i	$-0.717079\pi$
$701$	−479.453	+	155.784i	−0.683956	+	0.222231i	−0.0536295	+	0.998561i	$0.517079\pi$
$702$	−210.542	−	289.786i	−0.299917	−	0.412801i
$703$	−180.000			−0.256046
$704$		0			0
$705$	1716.00			2.43404
$706$	1067.90	−	775.877i	1.51261	−	1.09898i
$707$	807.500	−	262.373i	1.14215	−	0.371107i
$708$	−1324.80	−	430.455i	−1.87119	−	0.607988i
$709$	454.668	+	330.335i	0.641280	+	0.465917i	0.860290	−	0.509805i	$-0.170283\pi$
$709$	454.668	+	330.335i	0.641280	+	0.465917i	−0.219010	+	0.975723i	$0.570283\pi$
$710$	−771.987	+	1062.55i	−1.08731	+	1.49655i
$711$	−111.246	+	342.380i	−0.156464	+	0.481548i
$712$	−367.112	−	1129.86i	−0.515607	−	1.58688i
$713$	101.372	+	139.527i	0.142177	+	0.195690i
$714$	1056.00			1.47899
$715$		0			0
$716$		−	1392.98i		−	1.94551i
$717$		0			0
$718$	312.725	+	962.469i	0.435550	+	1.34049i
$719$	321.738	+	104.539i	0.447480	+	0.145395i	0.524084	−	0.851666i	$-0.324408\pi$
$719$	321.738	+	104.539i	0.447480	+	0.145395i	−0.0766039	+	0.997062i	$0.524408\pi$
$720$	−175.452	+	241.489i	−0.243683	+	0.335401i
$721$	478.938	+	347.969i	0.664269	+	0.482620i
$722$	−1025.15	−	333.090i	−1.41987	−	0.461344i
$723$	120.517	+	370.912i	0.166690	+	0.513018i
$724$	56.6312	−	41.1450i	0.0782199	−	0.0568301i
$725$			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	$0.509196\pi$
$728$	−187.148	−	257.588i	−0.257072	−	0.353829i
$729$	225.273	+	693.320i	0.309017	+	0.951057i
$730$	−503.080	+	1548.32i	−0.689150	+	2.12099i
$731$	327.510	−	450.779i	0.448030	−	0.616660i
$732$	203.872	+	148.122i	0.278514	+	0.202352i
$733$	−192.827	+	593.459i	−0.263065	+	0.809631i	0.729068	+	0.684441i	$0.239954\pi$
$733$	−192.827	+	593.459i	−0.263065	+	0.809631i	−0.992133	+	0.125189i	$0.960046\pi$
$734$	876.895	−	284.920i	1.19468	−	0.388175i
$735$	175.452	+	241.489i	0.238710	+	0.328556i
$736$	154.000			0.209239
$737$		0			0
$738$	−396.000			−0.536585
$739$	−554.986	+	403.221i	−0.750995	+	0.545630i	−0.896135	−	0.443781i	$-0.853637\pi$
$739$	−554.986	+	403.221i	−0.750995	+	0.545630i	0.145140	+	0.989411i	$0.453637\pi$
$740$	−1324.80	+	430.455i	−1.79028	+	0.581696i
$741$	−22.2492	+	68.4761i	−0.0300259	+	0.0924103i
$742$	1281.48	+	931.052i	1.72707	+	1.25479i
$743$	−506.860	+	697.634i	−0.682181	+	0.938941i	−0.999957	−	0.00922416i	$-0.997064\pi$
$743$	−506.860	+	697.634i	−0.682181	+	0.938941i	0.317777	+	0.948166i	$0.397064\pi$
$744$	738.106	+	239.825i	0.992077	+	0.322346i
$745$	−190.354	−	585.851i	−0.255509	−	0.786377i
$746$	132.563	+	182.458i	0.177699	+	0.244582i
$747$		−	358.195i		−	0.479512i
$748$		0			0
$749$			318.396i			0.425095i
$750$	−320.371	+	232.763i	−0.427161	+	0.310351i
$751$	29.0476	+	89.3993i	0.0386786	+	0.119040i	0.968531	−	0.248891i	$-0.0800661\pi$
$751$	29.0476	+	89.3993i	0.0386786	+	0.119040i	−0.929853	+	0.367931i	$0.880066\pi$
$752$	410.059	+	133.236i	0.545291	+	0.177176i
$753$	514.658	−	708.366i	0.683477	−	0.940726i
$754$	−427.161	−	310.351i	−0.566526	−	0.411606i
$755$	1009.38	+	327.966i	1.33692	+	0.434392i
$756$	467.234	+	1438.00i	0.618034	+	1.90211i
$757$	−904.481	+	657.144i	−1.19482	+	0.868090i	−0.993766	−	0.111490i	$-0.964438\pi$
$757$	−904.481	+	657.144i	−1.19482	+	0.868090i	−0.201057	+	0.979579i	$0.564438\pi$
$758$			2222.14i			2.93158i
$759$		0			0
$760$	396.000			0.521053
$761$	678.413	+	933.756i	0.891476	+	1.22701i	0.973108	+	0.230349i	$0.0739867\pi$
$761$	678.413	+	933.756i	0.891476	+	1.22701i	−0.0816322	+	0.996663i	$0.526013\pi$
$762$	−1779.02	+	578.040i	−2.33468	+	0.758583i
$763$	494.427	−	1521.69i	0.648004	−	1.99435i
$764$	463.972	−	638.603i	0.607293	−	0.835868i
$765$	−640.741	−	465.526i	−0.837571	−	0.608531i
$766$	33.9919	−	104.616i	0.0443758	−	0.136575i
$767$	−252.344	+	81.9915i	−0.329001	+	0.106899i
$768$	900.436	−	654.205i	1.17244	−	0.851829i
$769$	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
$772$	1687.61	−	1226.12i	2.18602	−	1.58824i
$773$	889.512	−	289.020i	1.15073	−	0.373894i	0.329310	−	0.944222i	$-0.393184\pi$
$773$	889.512	−	289.020i	1.15073	−	0.373894i	0.821417	+	0.570328i	$0.193184\pi$
$774$	1192.32	+	387.410i	1.54047	+	0.500529i
$775$	−399.654	−	290.366i	−0.515683	−	0.374666i
$776$	−362.600	+	499.076i	−0.467268	+	0.643140i
$777$	−222.492	+	684.761i	−0.286348	+	0.881288i
$778$	428.298	+	1318.16i	0.550511	+	1.69430i
$779$	46.7871	+	64.3969i	0.0600605	+	0.0826662i
$780$			557.193i			0.714350i
$781$		0			0
$782$		−	291.863i		−	0.373226i
$783$	631.626	+	869.359i	0.806674	+	1.11029i
$784$	23.1763	+	71.3292i	0.0295616	+	0.0909812i
$785$	−1148.16	−	373.061i	−1.46263	−	0.475237i
$786$	320.371	+	232.763i	0.407596	+	0.296136i
$787$	−241.087	−	175.160i	−0.306337	−	0.222567i	0.423986	−	0.905669i	$-0.360630\pi$
$787$	−241.087	−	175.160i	−0.306337	−	0.222567i	−0.730323	+	0.683102i	$0.760630\pi$
$788$	−883.203	−	286.970i	−1.12082	−	0.364175i
$789$	−643.477	+	209.078i	−0.815560	+	0.264991i
$790$	711.935	−	517.251i	0.901183	−	0.654748i
$791$			318.396i			0.402523i
$792$		0			0
$793$	48.0000			0.0605296
$794$	167.654	+	230.756i	0.211151	+	0.290624i
$795$	−367.112	−	1129.86i	−0.461776	−	1.42120i
$796$	90.8510	−	279.611i	0.114134	−	0.351270i
$797$	308.015	−	423.947i	0.386468	−	0.531928i	−0.570815	−	0.821078i	$-0.693373\pi$
$797$	308.015	−	423.947i	0.386468	−	0.531928i	0.957284	+	0.289151i	$0.0933728\pi$
$798$	280.723	−	386.382i	0.351783	−	0.484188i
$799$	−353.515	+	1088.01i	−0.442447	+	1.36171i
$800$	−419.522	+	136.311i	−0.524402	+	0.170389i
$801$	631.626	+	869.359i	0.788547	+	1.08534i
$802$	836.000			1.04239
$803$		0			0
$804$	−42.0000			−0.0522388
$805$	284.774	−	206.900i	0.353756	−	0.257019i
$806$	328.047	−	106.589i	0.407006	−	0.132244i
$807$	208.184	+	67.6430i	0.257972	+	0.0838203i
$808$	−854.322	−	620.701i	−1.05733	−	0.768195i
$809$	−538.052	+	740.565i	−0.665083	+	0.915408i	−0.999636	−	0.0269690i	$-0.991414\pi$
$809$	−538.052	+	740.565i	−0.665083	+	0.915408i	0.334554	+	0.942377i	$0.391414\pi$
$810$	550.668	−	1694.78i	0.679837	−	2.09232i
$811$	−56.2411	−	173.092i	−0.0693478	−	0.213431i	0.910377	−	0.413781i	$-0.135792\pi$
$811$	−56.2411	−	173.092i	−0.0693478	−	0.213431i	−0.979724	+	0.200350i	$0.935792\pi$
$812$	1310.04	+	1803.11i	1.61335	+	2.22058i
$813$	−1344.00			−1.65314
$814$		0			0
$815$			1923.64i			2.36030i
$816$	−116.968	−	160.992i	−0.143343	−	0.197295i
$817$	−77.8723	−	239.666i	−0.0953149	−	0.293349i
$818$	1608.69	+	522.696i	1.96662	+	0.638992i
$819$	232.997	+	169.282i	0.284489	+	0.206694i
$820$	498.354	+	362.076i	0.607749	+	0.441556i
$821$	−782.266	−	254.174i	−0.952821	−	0.309590i	−0.208959	−	0.977924i	$-0.567008\pi$
$821$	−782.266	−	254.174i	−0.952821	−	0.309590i	−0.743861	+	0.668334i	$0.767008\pi$
$822$	−326.322	−	1004.32i	−0.396985	−	1.22180i
$823$	199.018	−	144.595i	0.241820	−	0.175693i	−0.460274	−	0.887777i	$-0.652249\pi$
$823$	199.018	−	144.595i	0.241820	−	0.175693i	0.702094	+	0.712084i	$0.252249\pi$
$824$		−	736.291i		−	0.893557i
$825$		0			0
$826$	1760.00			2.13075
$827$	−319.712	−	440.046i	−0.386592	−	0.532099i	0.570724	−	0.821142i	$-0.306663\pi$
$827$	−319.712	−	440.046i	−0.386592	−	0.532099i	−0.957316	+	0.289043i	$0.906663\pi$
$828$	397.441	−	129.137i	0.480002	−	0.155962i
$829$	77.2542	−	237.764i	0.0931897	−	0.286808i	−0.893588	−	0.448888i	$-0.851820\pi$
$829$	77.2542	−	237.764i	0.0931897	−	0.286808i	0.986778	+	0.162080i	$0.0518202\pi$
$830$	−514.658	+	708.366i	−0.620070	+	0.853453i
$831$	631.033	+	458.472i	0.759366	+	0.551712i
$832$	119.899	−	369.010i	0.144109	−	0.443522i
$833$	−189.258	+	61.4936i	−0.227200	+	0.0738219i
$834$	432.781	+	595.672i	0.518922	+	0.714235i
$835$	−1584.00			−1.89701
$836$		0			0
$837$	−702.000			−0.838710
$838$	−1423.87	+	1034.50i	−1.69913	+	1.23449i
$839$	−447.910	+	145.535i	−0.533862	+	0.173462i	−0.563527	−	0.826098i	$-0.690556\pi$
$839$	−447.910	+	145.535i	−0.533862	+	0.173462i	0.0296650	+	0.999560i	$0.490556\pi$
$840$	489.483	−	1506.47i	0.582718	−	1.79342i
$841$	601.100	+	436.724i	0.714744	+	0.519292i
$842$	−331.409	+	456.145i	−0.393597	+	0.541740i
$843$	−567.774	−	184.481i	−0.673516	−	0.218838i
$844$	−532.127	−	1637.72i	−0.630483	−	1.94043i
$845$	−596.536	−	821.061i	−0.705959	−	0.971670i
$846$	−2574.00			−3.04255
$847$		0			0
$848$		−	298.496i		−	0.352000i
$849$	121.353	−	88.1678i	0.142936	−	0.103849i
$850$	258.338	+	795.083i	0.303927	+	0.935392i
$851$	189.258	+	61.4936i	0.222395	+	0.0722604i
$852$	736.897	−	1014.25i	0.864903	−	1.19044i
$853$	−45.3050	−	32.9160i	−0.0531125	−	0.0385885i	0.560912	−	0.827875i	$-0.310451\pi$
$853$	−45.3050	−	32.9160i	−0.0531125	−	0.0385885i	−0.614025	+	0.789287i	$0.710451\pi$
$854$	−302.813	−	98.3898i	−0.354581	−	0.115211i
$855$	−340.664	+	110.688i	−0.398438	+	0.129460i
$856$	320.371	−	232.763i	0.374265	−	0.271919i
$857$		−	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	$0.232979\pi$
$860$	−1146.28	−	1577.73i	−1.33289	−	1.83456i
$861$	302.813	−	98.3898i	0.351699	−	0.114274i
$862$	−285.532	+	878.776i	−0.331243	+	1.01946i
$863$	−666.716	+	917.656i	−0.772557	+	1.06333i	0.223508	+	0.974702i	$0.428249\pi$
$863$	−666.716	+	917.656i	−0.772557	+	1.06333i	−0.996065	+	0.0886309i	$0.971751\pi$
$864$	−368.449	+	507.126i	−0.426445	+	0.586951i
$865$	407.902	−	1255.39i	0.471564	−	1.45132i
$866$	1709.63	−	555.492i	1.97417	−	0.641446i
$867$	−274.257	+	199.259i	−0.316328	+	0.229826i
$868$	−1456.00			−1.67742
$869$		0			0
$870$		−	2626.77i		−	3.01927i
$871$	−6.47214	+	4.70228i	−0.00743070	+	0.00539872i
$872$	−1892.58	+	614.936i	−2.17039	+	0.705202i
$873$	172.431	−	530.690i	0.197516	−	0.607892i
$874$	−106.790	−	77.5877i	−0.122186	−	0.0887731i
$875$	187.148	−	257.588i	0.213884	−	0.294386i
$876$	480.212	−	1477.94i	0.548188	−	1.68715i
$877$	140.912	+	433.682i	0.160675	+	0.494506i	0.998692	−	0.0511384i	$-0.0162850\pi$
$877$	140.912	+	433.682i	0.160675	+	0.494506i	−0.838017	+	0.545644i	$0.816285\pi$
$878$	−639.424	−	880.092i	−0.728273	−	1.00238i
$879$			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	$-0.112577\pi$
$882$	−263.178	−	362.233i	−0.298387	−	0.410695i
$883$	−338.065	−	1040.46i	−0.382859	−	1.17832i	−0.938021	−	0.346577i	$-0.887344\pi$
$883$	−338.065	−	1040.46i	−0.382859	−	1.17832i	0.555162	−	0.831742i	$-0.312656\pi$
$884$	−353.281	−	114.788i	−0.399640	−	0.129851i
$885$	−1067.90	−	775.877i	−1.20667	−	0.876697i
$886$	355.967	+	258.626i	0.401769	+	0.291902i
$887$	138.789	+	45.0953i	0.156470	+	0.0508403i	0.386205	−	0.922413i	$-0.373786\pi$
$887$	138.789	+	45.0953i	0.156470	+	0.0508403i	−0.229735	+	0.973253i	$0.573786\pi$
$888$	851.660	−	276.721i	0.959077	−	0.311623i
$889$	1216.76	−	884.029i	1.36869	−	0.994408i
$890$		−	2626.77i		−	2.95142i
$891$		0			0
$892$	2114.00			2.36996
$893$	304.116	+	418.580i	0.340556	+	0.468735i
$894$	285.532	+	878.776i	0.319387	+	0.982971i
$895$	407.902	−	1255.39i	0.455757	−	1.40268i
$896$	−1076.10	+	1481.13i	−1.20101	+	1.65305i
$897$	46.7871	−	64.3969i	0.0521595	−	0.0717915i
$898$	462.289	−	1422.78i	0.514799	−	1.58439i
$899$	−984.141	+	319.767i	−1.09471	+	0.355692i
$900$	−968.393	+	703.579i	−1.07599	+	0.781754i
$901$	792.000			0.879023
$902$		0			0
$903$	−1008.00			−1.11628
$904$	320.371	−	232.763i	0.354392	−	0.257481i
$905$	63.0860	−	20.4979i	0.0697082	−	0.0226496i
$906$	−1514.06	−	491.949i	−1.67115	−	0.542990i
$907$	−150.477	−	109.328i	−0.165906	−	0.120538i	0.501734	−	0.865022i	$-0.332696\pi$
$907$	−150.477	−	109.328i	−0.165906	−	0.120538i	−0.667640	+	0.744484i	$0.732696\pi$
$908$	818.775	−	1126.95i	0.901734	−	1.24113i
$909$	908.438	+	295.169i	0.999381	+	0.324719i
$910$	−217.548	−	669.544i	−0.239064	−	0.735762i
$911$	−502.961	−	692.267i	−0.552098	−	0.759898i	0.438197	−	0.898879i	$-0.355617\pi$
$911$	−502.961	−	692.267i	−0.552098	−	0.759898i	−0.990295	+	0.138981i	$0.955617\pi$
$912$	−90.0000			−0.0986842
$913$		0			0
$914$			1134.29i			1.24101i
$915$	140.361	+	193.191i	0.153400	+	0.211138i
$916$	−324.468	−	998.609i	−0.354223	−	1.09018i
$917$	−302.813	−	98.3898i	−0.330221	−	0.107295i
$918$	961.112	+	698.289i	1.04696	+	0.760663i
$919$	346.259	+	251.572i	0.376778	+	0.273745i	0.760016	−	0.649904i	$-0.225191\pi$
$919$	346.259	+	251.572i	0.376778	+	0.273745i	−0.383238	+	0.923650i	$0.625191\pi$
$920$	−416.367	−	135.286i	−0.452573	−	0.147050i
$921$	79.7264	+	245.373i	0.0865650	+	0.266420i
$922$	−213.580	+	155.175i	−0.231649	+	0.168303i
$923$		−	238.797i		−	0.258718i
$924$		0			0
$925$	−570.000			−0.616216
$926$	167.654	+	230.756i	0.181052	+	0.249196i
$927$	205.805	+	633.404i	0.222012	+	0.683283i
$928$	−285.532	+	878.776i	−0.307685	+	0.946957i
$929$	374.297	−	515.176i	0.402903	−	0.554548i	−0.558567	−	0.829460i	$-0.688648\pi$
$929$	374.297	−	515.176i	0.402903	−	0.554548i	0.961470	+	0.274911i	$0.0886485\pi$
$930$	1388.27	+	1008.64i	1.49277	+	1.08456i
$931$	−27.8115	+	85.5951i	−0.0298727	+	0.0919389i
$932$	−2914.57	+	947.002i	−3.12722	+	1.01610i
$933$	−35.0903	−	48.2977i	−0.0376102	−	0.0517660i
$934$	1980.00			2.11991
$935$		0			0
$936$		−	358.195i		−	0.382687i
$937$	−234.615	+	170.458i	−0.250389	+	0.181919i	−0.705899	−	0.708312i	$-0.749457\pi$
$937$	−234.615	+	170.458i	−0.250389	+	0.181919i	0.455510	+	0.890231i	$0.349457\pi$
$938$	50.4688	−	16.3983i	0.0538047	−	0.0174822i
$939$	90.8510	−	279.611i	0.0967529	−	0.297775i
$940$	3239.30	+	2353.49i	3.44607	+	2.50372i
$941$	514.658	−	708.366i	0.546927	−	0.752780i	−0.442664	−	0.896687i	$-0.645967\pi$
$941$	514.658	−	708.366i	0.546927	−	0.752780i	0.989591	+	0.143907i	$0.0459666\pi$
$942$	1722.25	+	559.592i	1.82829	+	0.594047i
$943$	−27.1935	−	83.6930i	−0.0288372	−	0.0887518i
$944$	−194.946	−	268.321i	−0.206511	−	0.284238i
$945$			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	$-0.0133815\pi$
$948$	−679.574	+	493.740i	−0.716851	+	0.520822i
$949$	−91.4690	−	281.513i	−0.0963846	−	0.296641i
$950$	359.590	+	116.838i	0.378516	+	0.122987i
$951$	549.749	−	756.664i	0.578074	−	0.795651i
$952$	854.322	+	620.701i	0.897397	+	0.651997i
$953$	−744.414	−	241.875i	−0.781127	−	0.253804i	−0.108806	−	0.994063i	$-0.534703\pi$
$953$	−744.414	−	241.875i	−0.781127	−	0.253804i	−0.672321	+	0.740259i	$0.734703\pi$
$954$	550.668	+	1694.78i	0.577220	+	1.77650i
$955$	605.145	−	439.663i	0.633659	−	0.460380i
$956$		0			0
$957$		0			0
$958$	−748.000			−0.780793
$959$	499.063	+	686.901i	0.520399	+	0.716268i
$960$	1835.80	−	596.488i	1.91229	−	0.621342i
$961$	−88.0698	+	271.051i	−0.0916440	+	0.282051i
$962$	233.936	−	321.985i	0.243176	−	0.334703i
$963$	−210.542	+	289.786i	−0.218631	+	0.300920i
$964$	−281.205	+	865.461i	−0.291707	+	0.897782i
$965$	1879.96	−	610.836i	1.94815	−	0.632991i
$966$	−427.161	+	310.351i	−0.442196	+	0.321274i
$967$	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
$970$	−1103.50	+	801.739i	−1.13763	+	0.826535i
$971$	1110.31	−	360.762i	1.14347	−	0.371537i	0.324792	−	0.945785i	$-0.394706\pi$
$971$	1110.31	−	360.762i	1.14347	−	0.371537i	0.818681	+	0.574248i	$0.194706\pi$
$972$	−525.638	+	1617.75i	−0.540780	+	1.66435i
$973$	−478.938	−	347.969i	−0.492228	−	0.357625i
$974$	869.461	−	1196.71i	0.892670	−	1.22865i
$975$	−70.4559	+	216.841i	−0.0722624	+	0.222401i
$976$	18.5410	+	57.0634i	0.0189969	+	0.0584666i
$977$	−771.987	−	1062.55i	−0.790161	−	1.08756i	−0.994088	−	0.108577i	$-0.965370\pi$
$977$	−771.987	−	1062.55i	−0.790161	−	1.08756i	0.203927	−	0.978986i	$-0.434630\pi$
$978$		−	2885.46i		−	2.95037i
$979$		0			0
$980$			696.491i			0.710705i
$981$	1456.23	−	1058.01i	1.48443	−	1.07851i
$982$	720.628	+	2217.86i	0.733837	+	2.25852i
$983$	397.441	+	129.137i	0.404315	+	0.131370i	0.504113	−	0.863638i	$-0.331820\pi$
$983$	397.441	+	129.137i	0.404315	+	0.131370i	−0.0997979	+	0.995008i	$0.531820\pi$
$984$	−320.371	−	232.763i	−0.325580	−	0.236548i
$985$	−711.935	−	517.251i	−0.722777	−	0.525128i
$986$	1665.47	+	541.144i	1.68912	+	0.548827i
$987$	1968.28	−	639.533i	1.99421	−	0.647957i
$988$	−135.915	+	98.7479i	−0.137566	+	0.0999473i
$989$			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	$0.361045\pi$
$992$	−354.802	−	488.343i	−0.357664	−	0.492282i
$993$	−202.097	−	621.991i	−0.203522	−	0.626376i
$994$	−489.483	+	1506.47i	−0.492438	+	1.51557i
$995$	163.755	−	225.389i	0.164578	−	0.226522i
$996$	491.265	−	676.168i	0.493238	−	0.678883i
$997$	−16.0689	+	49.4549i	−0.0161172	+	0.0496038i	−0.958792	−	0.284110i	$-0.908302\pi$
$997$	−16.0689	+	49.4549i	−0.0161172	+	0.0496038i	0.942674	+	0.333714i	$0.108302\pi$
$998$	182.949	−	59.4438i	0.183316	−	0.0595629i
$999$	−655.304	+	476.106i	−0.655960	+	0.476583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.e.245.1		8
3.2	odd	2	inner	363.3.h.e.245.2		8
11.2	odd	10		363.3.b.d.122.1		2
11.3	even	5	inner	363.3.h.e.269.1		8
11.4	even	5	inner	363.3.h.e.323.2		8
11.5	even	5	inner	363.3.h.e.251.2		8
11.6	odd	10		363.3.h.d.251.1		8
11.7	odd	10		363.3.h.d.323.1		8
11.8	odd	10		363.3.h.d.269.2		8
11.9	even	5		33.3.b.a.23.2	yes	2
11.10	odd	2		363.3.h.d.245.2		8
33.2	even	10		363.3.b.d.122.2		2
33.5	odd	10	inner	363.3.h.e.251.1		8
33.8	even	10		363.3.h.d.269.1		8
33.14	odd	10	inner	363.3.h.e.269.2		8
33.17	even	10		363.3.h.d.251.2		8
33.20	odd	10		33.3.b.a.23.1	✓	2
33.26	odd	10	inner	363.3.h.e.323.1		8
33.29	even	10		363.3.h.d.323.2		8
33.32	even	2		363.3.h.d.245.1		8
44.31	odd	10		528.3.i.a.353.1		2
132.119	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	33.20	odd	10
33.3.b.a.23.2	yes	2	11.9	even	5
363.3.b.d.122.1		2	11.2	odd	10
363.3.b.d.122.2		2	33.2	even	10
363.3.h.d.245.1		8	33.32	even	2
363.3.h.d.245.2		8	11.10	odd	2
363.3.h.d.251.1		8	11.6	odd	10
363.3.h.d.251.2		8	33.17	even	10
363.3.h.d.269.1		8	33.8	even	10
363.3.h.d.269.2		8	11.8	odd	10
363.3.h.d.323.1		8	11.7	odd	10
363.3.h.d.323.2		8	33.29	even	10
363.3.h.e.245.1		8	1.1	even	1	trivial
363.3.h.e.245.2		8	3.2	odd	2	inner
363.3.h.e.251.1		8	33.5	odd	10	inner
363.3.h.e.251.2		8	11.5	even	5	inner
363.3.h.e.269.1		8	11.3	even	5	inner
363.3.h.e.269.2		8	33.14	odd	10	inner
363.3.h.e.323.1		8	33.26	odd	10	inner
363.3.h.e.323.2		8	11.4	even	5	inner
528.3.i.a.353.1		2	44.31	odd	10
528.3.i.a.353.2		2	132.119	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)

\(f(q)\)	\(=\)	\(q+(-1.94946 - 2.68321i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-2.16312 + 6.65740i) q^{4} +(-3.89893 + 5.36641i) q^{5} +(5.84839 - 8.04962i) q^{6} +(-2.47214 + 7.60845i) q^{7} +(9.46289 - 3.07468i) q^{8} +(-7.28115 + 5.29007i) q^{9} +O(q^{10})\)	\(q+(-1.94946 - 2.68321i) q^{2} +(0.927051 + 2.85317i) q^{3} +(-2.16312 + 6.65740i) q^{4} +(-3.89893 + 5.36641i) q^{5} +(5.84839 - 8.04962i) q^{6} +(-2.47214 + 7.60845i) q^{7} +(9.46289 - 3.07468i) q^{8} +(-7.28115 + 5.29007i) q^{9} +22.0000 q^{10} -21.0000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(25.2344 - 8.19915i) q^{14} +(-18.9258 - 6.14936i) q^{15} +(-4.04508 - 2.93893i) q^{16} +(7.79785 - 10.7328i) q^{17} +(28.3887 + 9.22404i) q^{18} +(-1.85410 - 5.70634i) q^{19} +(-27.2925 - 37.5649i) q^{20} -24.0000 q^{21} +6.63325i q^{23} +(17.5452 + 24.1489i) q^{24} +(-5.87132 - 18.0701i) q^{25} +(12.6172 + 4.09957i) q^{26} +(-21.8435 - 15.8702i) q^{27} +(-45.3050 - 32.9160i) q^{28} +(-37.8516 - 12.2987i) q^{29} +(20.3951 + 62.7697i) q^{30} +(21.0344 - 15.2824i) q^{31} -23.2164i q^{32} -44.0000 q^{34} +(-31.1914 - 42.9313i) q^{35} +(-19.4681 - 59.9166i) q^{36} +(9.27051 - 28.5317i) q^{37} +(-11.6968 + 16.0992i) q^{38} +(-9.70820 - 7.05342i) q^{39} +(-20.3951 + 62.7697i) q^{40} +(-12.6172 + 4.09957i) q^{41} +(46.7871 + 64.3969i) q^{42} +42.0000 q^{43} -59.6992i q^{45} +(17.7984 - 12.9313i) q^{46} +(-82.0117 + 26.6472i) q^{47} +(4.63525 - 14.2658i) q^{48} +(-12.1353 - 8.81678i) q^{49} +(-37.0398 + 50.9809i) q^{50} +(37.8516 + 12.2987i) q^{51} +(-8.65248 - 26.6296i) q^{52} +(35.0903 + 48.2977i) q^{53} +89.5489i q^{54} +79.5990i q^{56} +(14.5623 - 10.5801i) q^{57} +(40.7902 + 125.539i) q^{58} +(63.0860 + 20.4979i) q^{59} +(81.8775 - 112.695i) q^{60} +(-9.70820 - 7.05342i) q^{61} +(-82.0117 - 26.6472i) q^{62} +(-22.2492 - 68.4761i) q^{63} +(-78.4746 + 57.0152i) q^{64} -26.5330i q^{65} +2.00000 q^{67} +(54.5850 + 75.1298i) q^{68} +(-18.9258 + 6.14936i) q^{69} +(-54.3870 + 167.386i) q^{70} +(-35.0903 + 48.2977i) q^{71} +(-52.6355 + 72.4466i) q^{72} +(-22.8673 + 70.3782i) q^{73} +(-94.6289 + 30.7468i) q^{74} +(46.1140 - 33.5038i) q^{75} +42.0000 q^{76} +39.7995i q^{78} +(32.3607 - 23.5114i) q^{79} +(31.5430 - 10.2489i) q^{80} +(25.0304 - 77.0356i) q^{81} +(35.5967 + 25.8626i) q^{82} +(-23.3936 + 32.1985i) q^{83} +(51.9149 - 159.777i) q^{84} +(27.1935 + 83.6930i) q^{85} +(-81.8775 - 112.695i) q^{86} -119.398i q^{87} -119.398i q^{89} +(-160.185 + 116.381i) q^{90} +(-9.88854 - 30.4338i) q^{91} +(-44.1602 - 14.3485i) q^{92} +(63.1033 + 45.8472i) q^{93} +(231.379 + 168.107i) q^{94} +(37.8516 + 12.2987i) q^{95} +(66.2402 - 21.5228i) q^{96} +(-50.1591 + 36.4427i) 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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