Properties

Label 462.2.i.g.331.1
Level $462$
Weight $2$
Character 462.331
Analytic conductor $3.689$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 331.1
Root \(0.500000 - 3.23735i\) of defining polynomial
Character \(\chi\) \(=\) 462.331
Dual form 462.2.i.g.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.20942 - 3.82682i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.36521 + 1.18566i) q^{14} -4.41883 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.18842 - 2.05840i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.84421 - 3.19426i) q^{19} +4.41883 q^{20} +(-0.155792 + 2.64116i) q^{21} -1.00000 q^{22} +(-2.36521 + 4.09666i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-7.26304 - 12.5800i) q^{25} -1.00000 q^{27} +(0.155792 - 2.64116i) q^{28} -6.52608 q^{29} +(2.20942 - 3.82682i) q^{30} +(1.68842 + 2.92442i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +2.37683 q^{34} +(-10.4515 + 5.23924i) q^{35} +1.00000 q^{36} +(-3.84421 + 6.65836i) q^{37} +(1.84421 + 3.19426i) q^{38} +(-2.20942 + 3.82682i) q^{40} +12.1492 q^{41} +(-2.20942 - 1.45550i) q^{42} +3.06525 q^{43} +(0.500000 - 0.866025i) q^{44} +(-2.20942 - 3.82682i) q^{45} +(-2.36521 - 4.09666i) q^{46} +(2.05362 - 3.55698i) q^{47} -1.00000 q^{48} +(2.76304 + 6.43161i) q^{49} +14.5261 q^{50} +(1.18842 - 2.05840i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.41883 q^{55} +(2.20942 + 1.45550i) q^{56} +3.68842 q^{57} +(3.26304 - 5.65175i) q^{58} +(6.26304 + 10.8479i) q^{59} +(2.20942 + 3.82682i) q^{60} +(-1.89783 + 3.28714i) q^{61} -3.37683 q^{62} +(-2.36521 + 1.18566i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-5.07462 - 8.78951i) q^{67} +(-1.18842 + 2.05840i) q^{68} -4.73042 q^{69} +(0.688417 - 11.6708i) q^{70} +0.934749 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.73042 + 6.46127i) q^{73} +(-3.84421 - 6.65836i) q^{74} +(7.26304 - 12.5800i) q^{75} -3.68842 q^{76} +(-0.155792 + 2.64116i) q^{77} +(0.209416 - 0.362720i) q^{79} +(-2.20942 - 3.82682i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.07462 + 10.5216i) q^{82} -2.14925 q^{83} +(2.36521 - 1.18566i) q^{84} +10.5028 q^{85} +(-1.53263 + 2.65458i) q^{86} +(-3.26304 - 5.65175i) q^{87} +(0.500000 + 0.866025i) q^{88} +(6.41883 - 11.1177i) q^{89} +4.41883 q^{90} +4.73042 q^{92} +(-1.68842 + 2.92442i) q^{93} +(2.05362 + 3.55698i) q^{94} +(8.14925 + 14.1149i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(-6.95146 - 0.822941i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} - 6q^{6} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} - 6q^{6} + 6q^{8} - 3q^{9} + 3q^{11} + 3q^{12} - 3q^{14} - 3q^{16} - 3q^{17} - 3q^{18} + 9q^{19} - 3q^{21} - 6q^{22} - 3q^{23} + 3q^{24} - 15q^{25} - 6q^{27} + 3q^{28} + 18q^{29} + 6q^{31} - 3q^{32} - 3q^{33} + 6q^{34} - 30q^{35} + 6q^{36} - 21q^{37} + 9q^{38} + 24q^{41} + 6q^{43} + 3q^{44} - 3q^{46} - 3q^{47} - 6q^{48} - 12q^{49} + 30q^{50} + 3q^{51} - 24q^{53} + 3q^{54} + 18q^{57} - 9q^{58} + 9q^{59} + 6q^{61} - 12q^{62} - 3q^{63} + 6q^{64} - 3q^{66} - 6q^{67} - 3q^{68} - 6q^{69} + 18q^{71} - 3q^{72} - 21q^{74} + 15q^{75} - 18q^{76} - 3q^{77} - 12q^{79} - 3q^{81} - 12q^{82} + 36q^{83} + 3q^{84} - 3q^{86} + 9q^{87} + 3q^{88} + 12q^{89} + 6q^{92} - 6q^{93} - 3q^{94} + 3q^{96} + 42q^{97} - 9q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.20942 + 3.82682i −0.988081 + 1.71141i −0.360729 + 0.932671i \(0.617472\pi\)
−0.627352 + 0.778736i \(0.715861\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.20942 + 1.45550i 0.835081 + 0.550127i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −2.20942 3.82682i −0.698679 1.21015i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.36521 + 1.18566i −0.632128 + 0.316881i
\(15\) −4.41883 −1.14094
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.18842 2.05840i −0.288233 0.499235i 0.685155 0.728398i \(-0.259735\pi\)
−0.973388 + 0.229163i \(0.926401\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 1.84421 3.19426i 0.423090 0.732814i −0.573150 0.819451i \(-0.694279\pi\)
0.996240 + 0.0866367i \(0.0276119\pi\)
\(20\) 4.41883 0.988081
\(21\) −0.155792 + 2.64116i −0.0339965 + 0.576348i
\(22\) −1.00000 −0.213201
\(23\) −2.36521 + 4.09666i −0.493180 + 0.854213i −0.999969 0.00785730i \(-0.997499\pi\)
0.506789 + 0.862070i \(0.330832\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −7.26304 12.5800i −1.45261 2.51599i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0.155792 2.64116i 0.0294418 0.499132i
\(29\) −6.52608 −1.21186 −0.605932 0.795517i \(-0.707199\pi\)
−0.605932 + 0.795517i \(0.707199\pi\)
\(30\) 2.20942 3.82682i 0.403382 0.698679i
\(31\) 1.68842 + 2.92442i 0.303249 + 0.525242i 0.976870 0.213835i \(-0.0685954\pi\)
−0.673621 + 0.739077i \(0.735262\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 2.37683 0.407624
\(35\) −10.4515 + 5.23924i −1.76662 + 0.885593i
\(36\) 1.00000 0.166667
\(37\) −3.84421 + 6.65836i −0.631984 + 1.09463i 0.355162 + 0.934805i \(0.384426\pi\)
−0.987146 + 0.159823i \(0.948908\pi\)
\(38\) 1.84421 + 3.19426i 0.299170 + 0.518178i
\(39\) 0 0
\(40\) −2.20942 + 3.82682i −0.349339 + 0.605074i
\(41\) 12.1492 1.89739 0.948697 0.316187i \(-0.102403\pi\)
0.948697 + 0.316187i \(0.102403\pi\)
\(42\) −2.20942 1.45550i −0.340920 0.224588i
\(43\) 3.06525 0.467446 0.233723 0.972303i \(-0.424909\pi\)
0.233723 + 0.972303i \(0.424909\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −2.20942 3.82682i −0.329360 0.570469i
\(46\) −2.36521 4.09666i −0.348731 0.604020i
\(47\) 2.05362 3.55698i 0.299552 0.518839i −0.676482 0.736460i \(-0.736496\pi\)
0.976033 + 0.217620i \(0.0698295\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.76304 + 6.43161i 0.394720 + 0.918801i
\(50\) 14.5261 2.05430
\(51\) 1.18842 2.05840i 0.166412 0.288233i
\(52\) 0 0
\(53\) −4.00000 6.92820i −0.549442 0.951662i −0.998313 0.0580651i \(-0.981507\pi\)
0.448871 0.893597i \(-0.351826\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −4.41883 −0.595835
\(56\) 2.20942 + 1.45550i 0.295246 + 0.194499i
\(57\) 3.68842 0.488543
\(58\) 3.26304 5.65175i 0.428458 0.742112i
\(59\) 6.26304 + 10.8479i 0.815379 + 1.41228i 0.909056 + 0.416674i \(0.136804\pi\)
−0.0936773 + 0.995603i \(0.529862\pi\)
\(60\) 2.20942 + 3.82682i 0.285234 + 0.494041i
\(61\) −1.89783 + 3.28714i −0.242993 + 0.420876i −0.961565 0.274576i \(-0.911462\pi\)
0.718573 + 0.695452i \(0.244796\pi\)
\(62\) −3.37683 −0.428858
\(63\) −2.36521 + 1.18566i −0.297988 + 0.149379i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −5.07462 8.78951i −0.619964 1.07381i −0.989492 0.144589i \(-0.953814\pi\)
0.369528 0.929220i \(-0.379519\pi\)
\(68\) −1.18842 + 2.05840i −0.144117 + 0.249617i
\(69\) −4.73042 −0.569475
\(70\) 0.688417 11.6708i 0.0822816 1.39493i
\(71\) 0.934749 0.110934 0.0554672 0.998461i \(-0.482335\pi\)
0.0554672 + 0.998461i \(0.482335\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 3.73042 + 6.46127i 0.436612 + 0.756234i 0.997426 0.0717077i \(-0.0228449\pi\)
−0.560814 + 0.827942i \(0.689512\pi\)
\(74\) −3.84421 6.65836i −0.446880 0.774019i
\(75\) 7.26304 12.5800i 0.838664 1.45261i
\(76\) −3.68842 −0.423090
\(77\) −0.155792 + 2.64116i −0.0177541 + 0.300988i
\(78\) 0 0
\(79\) 0.209416 0.362720i 0.0235612 0.0408092i −0.854004 0.520266i \(-0.825833\pi\)
0.877566 + 0.479457i \(0.159166\pi\)
\(80\) −2.20942 3.82682i −0.247020 0.427852i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −6.07462 + 10.5216i −0.670830 + 1.16191i
\(83\) −2.14925 −0.235911 −0.117955 0.993019i \(-0.537634\pi\)
−0.117955 + 0.993019i \(0.537634\pi\)
\(84\) 2.36521 1.18566i 0.258065 0.129366i
\(85\) 10.5028 1.13919
\(86\) −1.53263 + 2.65458i −0.165267 + 0.286251i
\(87\) −3.26304 5.65175i −0.349835 0.605932i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 6.41883 11.1177i 0.680395 1.17848i −0.294466 0.955662i \(-0.595142\pi\)
0.974860 0.222816i \(-0.0715251\pi\)
\(90\) 4.41883 0.465786
\(91\) 0 0
\(92\) 4.73042 0.493180
\(93\) −1.68842 + 2.92442i −0.175081 + 0.303249i
\(94\) 2.05362 + 3.55698i 0.211815 + 0.366875i
\(95\) 8.14925 + 14.1149i 0.836095 + 1.44816i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −6.95146 0.822941i −0.702203 0.0831296i
\(99\) −1.00000 −0.100504
\(100\) −7.26304 + 12.5800i −0.726304 + 1.25800i
\(101\) 7.68187 + 13.3054i 0.764375 + 1.32394i 0.940576 + 0.339582i \(0.110286\pi\)
−0.176201 + 0.984354i \(0.556381\pi\)
\(102\) 1.18842 + 2.05840i 0.117671 + 0.203812i
\(103\) 1.31158 2.27173i 0.129234 0.223840i −0.794146 0.607727i \(-0.792081\pi\)
0.923380 + 0.383887i \(0.125415\pi\)
\(104\) 0 0
\(105\) −9.76304 6.43161i −0.952775 0.627661i
\(106\) 8.00000 0.777029
\(107\) −5.45146 + 9.44220i −0.527012 + 0.912812i 0.472492 + 0.881335i \(0.343355\pi\)
−0.999504 + 0.0314773i \(0.989979\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 5.89783 + 10.2153i 0.564910 + 0.978453i 0.997058 + 0.0766501i \(0.0244224\pi\)
−0.432148 + 0.901803i \(0.642244\pi\)
\(110\) 2.20942 3.82682i 0.210660 0.364873i
\(111\) −7.68842 −0.729752
\(112\) −2.36521 + 1.18566i −0.223491 + 0.112034i
\(113\) 5.37683 0.505810 0.252905 0.967491i \(-0.418614\pi\)
0.252905 + 0.967491i \(0.418614\pi\)
\(114\) −1.84421 + 3.19426i −0.172726 + 0.299170i
\(115\) −10.4515 18.1025i −0.974603 1.68806i
\(116\) 3.26304 + 5.65175i 0.302966 + 0.524752i
\(117\) 0 0
\(118\) −12.5261 −1.15312
\(119\) 0.370291 6.27760i 0.0339445 0.575467i
\(120\) −4.41883 −0.403382
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −1.89783 3.28714i −0.171822 0.297604i
\(123\) 6.07462 + 10.5216i 0.547730 + 0.948697i
\(124\) 1.68842 2.92442i 0.151624 0.262621i
\(125\) 42.0942 3.76502
\(126\) 0.155792 2.64116i 0.0138790 0.235293i
\(127\) 0.730416 0.0648139 0.0324070 0.999475i \(-0.489683\pi\)
0.0324070 + 0.999475i \(0.489683\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.53263 + 2.65458i 0.134940 + 0.233723i
\(130\) 0 0
\(131\) −3.68842 + 6.38853i −0.322258 + 0.558168i −0.980954 0.194242i \(-0.937775\pi\)
0.658695 + 0.752410i \(0.271109\pi\)
\(132\) 1.00000 0.0870388
\(133\) 8.72387 4.37321i 0.756456 0.379206i
\(134\) 10.1492 0.876762
\(135\) 2.20942 3.82682i 0.190156 0.329360i
\(136\) −1.18842 2.05840i −0.101906 0.176506i
\(137\) 4.41883 + 7.65364i 0.377526 + 0.653895i 0.990702 0.136052i \(-0.0434414\pi\)
−0.613175 + 0.789947i \(0.710108\pi\)
\(138\) 2.36521 4.09666i 0.201340 0.348731i
\(139\) 1.47392 0.125016 0.0625080 0.998044i \(-0.480090\pi\)
0.0625080 + 0.998044i \(0.480090\pi\)
\(140\) 9.76304 + 6.43161i 0.825128 + 0.543570i
\(141\) 4.10725 0.345893
\(142\) −0.467375 + 0.809517i −0.0392212 + 0.0679331i
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 14.4188 24.9742i 1.19742 2.07399i
\(146\) −7.46083 −0.617463
\(147\) −4.18842 + 5.60867i −0.345455 + 0.462595i
\(148\) 7.68842 0.631984
\(149\) 4.68187 8.10924i 0.383554 0.664335i −0.608013 0.793927i \(-0.708033\pi\)
0.991567 + 0.129592i \(0.0413667\pi\)
\(150\) 7.26304 + 12.5800i 0.593025 + 1.02715i
\(151\) 6.78404 + 11.7503i 0.552077 + 0.956226i 0.998125 + 0.0612166i \(0.0194980\pi\)
−0.446047 + 0.895009i \(0.647169\pi\)
\(152\) 1.84421 3.19426i 0.149585 0.259089i
\(153\) 2.37683 0.192156
\(154\) −2.20942 1.45550i −0.178040 0.117288i
\(155\) −14.9217 −1.19854
\(156\) 0 0
\(157\) 9.37029 + 16.2298i 0.747831 + 1.29528i 0.948861 + 0.315696i \(0.102238\pi\)
−0.201030 + 0.979585i \(0.564429\pi\)
\(158\) 0.209416 + 0.362720i 0.0166603 + 0.0288564i
\(159\) 4.00000 6.92820i 0.317221 0.549442i
\(160\) 4.41883 0.349339
\(161\) −11.1884 + 5.60867i −0.881771 + 0.442025i
\(162\) 1.00000 0.0785674
\(163\) −9.38621 + 16.2574i −0.735185 + 1.27338i 0.219458 + 0.975622i \(0.429571\pi\)
−0.954642 + 0.297755i \(0.903762\pi\)
\(164\) −6.07462 10.5216i −0.474348 0.821596i
\(165\) −2.20942 3.82682i −0.172003 0.297918i
\(166\) 1.07462 1.86130i 0.0834070 0.144465i
\(167\) −23.8898 −1.84865 −0.924325 0.381606i \(-0.875371\pi\)
−0.924325 + 0.381606i \(0.875371\pi\)
\(168\) −0.155792 + 2.64116i −0.0120196 + 0.203770i
\(169\) −13.0000 −1.00000
\(170\) −5.25142 + 9.09572i −0.402765 + 0.697610i
\(171\) 1.84421 + 3.19426i 0.141030 + 0.244271i
\(172\) −1.53263 2.65458i −0.116862 0.202410i
\(173\) −5.68842 + 9.85263i −0.432482 + 0.749081i −0.997086 0.0762805i \(-0.975696\pi\)
0.564604 + 0.825362i \(0.309029\pi\)
\(174\) 6.52608 0.494741
\(175\) 2.26304 38.3657i 0.171070 2.90018i
\(176\) −1.00000 −0.0753778
\(177\) −6.26304 + 10.8479i −0.470759 + 0.815379i
\(178\) 6.41883 + 11.1177i 0.481112 + 0.833310i
\(179\) −12.3050 21.3130i −0.919722 1.59301i −0.799837 0.600217i \(-0.795081\pi\)
−0.119885 0.992788i \(-0.538253\pi\)
\(180\) −2.20942 + 3.82682i −0.164680 + 0.285234i
\(181\) 17.4608 1.29785 0.648927 0.760851i \(-0.275218\pi\)
0.648927 + 0.760851i \(0.275218\pi\)
\(182\) 0 0
\(183\) −3.79567 −0.280584
\(184\) −2.36521 + 4.09666i −0.174365 + 0.302010i
\(185\) −16.9869 29.4222i −1.24890 2.16316i
\(186\) −1.68842 2.92442i −0.123801 0.214429i
\(187\) 1.18842 2.05840i 0.0869056 0.150525i
\(188\) −4.10725 −0.299552
\(189\) −2.20942 1.45550i −0.160711 0.105872i
\(190\) −16.2985 −1.18242
\(191\) 8.41883 14.5818i 0.609165 1.05511i −0.382213 0.924074i \(-0.624838\pi\)
0.991378 0.131031i \(-0.0418288\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −2.73042 4.72922i −0.196540 0.340417i 0.750865 0.660456i \(-0.229637\pi\)
−0.947404 + 0.320040i \(0.896304\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) 0 0
\(196\) 4.18842 5.60867i 0.299173 0.400619i
\(197\) −9.68842 −0.690271 −0.345136 0.938553i \(-0.612167\pi\)
−0.345136 + 0.938553i \(0.612167\pi\)
\(198\) 0.500000 0.866025i 0.0355335 0.0615457i
\(199\) −10.1492 17.5790i −0.719461 1.24614i −0.961214 0.275805i \(-0.911056\pi\)
0.241752 0.970338i \(-0.422278\pi\)
\(200\) −7.26304 12.5800i −0.513575 0.889537i
\(201\) 5.07462 8.78951i 0.357936 0.619964i
\(202\) −15.3637 −1.08099
\(203\) −14.4188 9.49871i −1.01200 0.666679i
\(204\) −2.37683 −0.166412
\(205\) −26.8427 + 46.4930i −1.87478 + 3.24721i
\(206\) 1.31158 + 2.27173i 0.0913823 + 0.158279i
\(207\) −2.36521 4.09666i −0.164393 0.284738i
\(208\) 0 0
\(209\) 3.68842 0.255133
\(210\) 10.4515 5.23924i 0.721219 0.361542i
\(211\) 22.5130 1.54986 0.774929 0.632048i \(-0.217785\pi\)
0.774929 + 0.632048i \(0.217785\pi\)
\(212\) −4.00000 + 6.92820i −0.274721 + 0.475831i
\(213\) 0.467375 + 0.809517i 0.0320240 + 0.0554672i
\(214\) −5.45146 9.44220i −0.372654 0.645456i
\(215\) −6.77241 + 11.7302i −0.461875 + 0.799991i
\(216\) −1.00000 −0.0680414
\(217\) −0.526082 + 8.91876i −0.0357128 + 0.605445i
\(218\) −11.7957 −0.798903
\(219\) −3.73042 + 6.46127i −0.252078 + 0.436612i
\(220\) 2.20942 + 3.82682i 0.148959 + 0.258004i
\(221\) 0 0
\(222\) 3.84421 6.65836i 0.258006 0.446880i
\(223\) −7.46083 −0.499614 −0.249807 0.968296i \(-0.580367\pi\)
−0.249807 + 0.968296i \(0.580367\pi\)
\(224\) 0.155792 2.64116i 0.0104093 0.176470i
\(225\) 14.5261 0.968405
\(226\) −2.68842 + 4.65647i −0.178831 + 0.309744i
\(227\) 1.38621 + 2.40098i 0.0920058 + 0.159359i 0.908355 0.418200i \(-0.137339\pi\)
−0.816349 + 0.577559i \(0.804005\pi\)
\(228\) −1.84421 3.19426i −0.122136 0.211545i
\(229\) 1.26958 2.19898i 0.0838965 0.145313i −0.821024 0.570894i \(-0.806597\pi\)
0.904920 + 0.425581i \(0.139930\pi\)
\(230\) 20.9029 1.37830
\(231\) −2.36521 + 1.18566i −0.155619 + 0.0780108i
\(232\) −6.52608 −0.428458
\(233\) 12.0261 20.8298i 0.787855 1.36460i −0.139424 0.990233i \(-0.544525\pi\)
0.927279 0.374372i \(-0.122142\pi\)
\(234\) 0 0
\(235\) 9.07462 + 15.7177i 0.591963 + 1.02531i
\(236\) 6.26304 10.8479i 0.407689 0.706138i
\(237\) 0.418833 0.0272061
\(238\) 5.25142 + 3.45948i 0.340399 + 0.224245i
\(239\) 7.59133 0.491042 0.245521 0.969391i \(-0.421041\pi\)
0.245521 + 0.969391i \(0.421041\pi\)
\(240\) 2.20942 3.82682i 0.142617 0.247020i
\(241\) −8.14925 14.1149i −0.524939 0.909221i −0.999578 0.0290409i \(-0.990755\pi\)
0.474639 0.880181i \(-0.342579\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 3.79567 0.242993
\(245\) −30.7173 3.63644i −1.96246 0.232324i
\(246\) −12.1492 −0.774608
\(247\) 0 0
\(248\) 1.68842 + 2.92442i 0.107215 + 0.185701i
\(249\) −1.07462 1.86130i −0.0681015 0.117955i
\(250\) −21.0471 + 36.4546i −1.33113 + 2.30559i
\(251\) −8.61008 −0.543463 −0.271732 0.962373i \(-0.587596\pi\)
−0.271732 + 0.962373i \(0.587596\pi\)
\(252\) 2.20942 + 1.45550i 0.139180 + 0.0916879i
\(253\) −4.73042 −0.297399
\(254\) −0.365208 + 0.632559i −0.0229152 + 0.0396903i
\(255\) 5.25142 + 9.09572i 0.328856 + 0.569596i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.418833 + 0.725439i −0.0261261 + 0.0452517i −0.878793 0.477203i \(-0.841650\pi\)
0.852667 + 0.522455i \(0.174984\pi\)
\(258\) −3.06525 −0.190834
\(259\) −18.1847 + 9.11585i −1.12994 + 0.566432i
\(260\) 0 0
\(261\) 3.26304 5.65175i 0.201977 0.349835i
\(262\) −3.68842 6.38853i −0.227871 0.394684i
\(263\) −5.41883 9.38569i −0.334140 0.578747i 0.649180 0.760635i \(-0.275112\pi\)
−0.983319 + 0.181888i \(0.941779\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 35.3507 2.17157
\(266\) −0.574624 + 9.74170i −0.0352325 + 0.597302i
\(267\) 12.8377 0.785652
\(268\) −5.07462 + 8.78951i −0.309982 + 0.536905i
\(269\) −8.93983 15.4842i −0.545071 0.944091i −0.998602 0.0528506i \(-0.983169\pi\)
0.453531 0.891240i \(-0.350164\pi\)
\(270\) 2.20942 + 3.82682i 0.134461 + 0.232893i
\(271\) 4.41883 7.65364i 0.268425 0.464926i −0.700030 0.714113i \(-0.746830\pi\)
0.968455 + 0.249187i \(0.0801635\pi\)
\(272\) 2.37683 0.144117
\(273\) 0 0
\(274\) −8.83767 −0.533903
\(275\) 7.26304 12.5800i 0.437978 0.758600i
\(276\) 2.36521 + 4.09666i 0.142369 + 0.246590i
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) −0.736959 + 1.27645i −0.0441999 + 0.0765564i
\(279\) −3.37683 −0.202166
\(280\) −10.4515 + 5.23924i −0.624594 + 0.313104i
\(281\) −15.9217 −0.949807 −0.474903 0.880038i \(-0.657517\pi\)
−0.474903 + 0.880038i \(0.657517\pi\)
\(282\) −2.05362 + 3.55698i −0.122292 + 0.211815i
\(283\) 9.04200 + 15.6612i 0.537491 + 0.930962i 0.999038 + 0.0438462i \(0.0139611\pi\)
−0.461547 + 0.887116i \(0.652706\pi\)
\(284\) −0.467375 0.809517i −0.0277336 0.0480360i
\(285\) −8.14925 + 14.1149i −0.482720 + 0.836095i
\(286\) 0 0
\(287\) 26.8427 + 17.6832i 1.58448 + 1.04381i
\(288\) 1.00000 0.0589256
\(289\) 5.67533 9.82996i 0.333843 0.578233i
\(290\) 14.4188 + 24.9742i 0.846703 + 1.46653i
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) 3.73042 6.46127i 0.218306 0.378117i
\(293\) 25.1492 1.46923 0.734617 0.678482i \(-0.237362\pi\)
0.734617 + 0.678482i \(0.237362\pi\)
\(294\) −2.76304 6.43161i −0.161144 0.375099i
\(295\) −55.3507 −3.22264
\(296\) −3.84421 + 6.65836i −0.223440 + 0.387010i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 4.68187 + 8.10924i 0.271214 + 0.469756i
\(299\) 0 0
\(300\) −14.5261 −0.838664
\(301\) 6.77241 + 4.46147i 0.390355 + 0.257155i
\(302\) −13.5681 −0.780755
\(303\) −7.68187 + 13.3054i −0.441312 + 0.764375i
\(304\) 1.84421 + 3.19426i 0.105773 + 0.183204i
\(305\) −8.38621 14.5253i −0.480193 0.831718i
\(306\) −1.18842 + 2.05840i −0.0679373 + 0.117671i
\(307\) −3.86950 −0.220844 −0.110422 0.993885i \(-0.535220\pi\)
−0.110422 + 0.993885i \(0.535220\pi\)
\(308\) 2.36521 1.18566i 0.134770 0.0675593i
\(309\) 2.62317 0.149227
\(310\) 7.46083 12.9225i 0.423747 0.733951i
\(311\) 6.78404 + 11.7503i 0.384688 + 0.666299i 0.991726 0.128374i \(-0.0409758\pi\)
−0.607038 + 0.794673i \(0.707642\pi\)
\(312\) 0 0
\(313\) −1.26304 + 2.18765i −0.0713913 + 0.123653i −0.899511 0.436898i \(-0.856077\pi\)
0.828120 + 0.560551i \(0.189411\pi\)
\(314\) −18.7406 −1.05759
\(315\) 0.688417 11.6708i 0.0387879 0.657578i
\(316\) −0.418833 −0.0235612
\(317\) 10.0051 17.3293i 0.561941 0.973311i −0.435386 0.900244i \(-0.643388\pi\)
0.997327 0.0730670i \(-0.0232787\pi\)
\(318\) 4.00000 + 6.92820i 0.224309 + 0.388514i
\(319\) −3.26304 5.65175i −0.182695 0.316437i
\(320\) −2.20942 + 3.82682i −0.123510 + 0.213926i
\(321\) −10.9029 −0.608541
\(322\) 0.736959 12.4938i 0.0410691 0.696252i
\(323\) −8.76675 −0.487795
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −9.38621 16.2574i −0.519854 0.900413i
\(327\) −5.89783 + 10.2153i −0.326151 + 0.564910i
\(328\) 12.1492 0.670830
\(329\) 9.71450 4.86980i 0.535578 0.268481i
\(330\) 4.41883 0.243249
\(331\) 8.07462 13.9857i 0.443821 0.768721i −0.554148 0.832418i \(-0.686956\pi\)
0.997969 + 0.0636969i \(0.0202891\pi\)
\(332\) 1.07462 + 1.86130i 0.0589777 + 0.102152i
\(333\) −3.84421 6.65836i −0.210661 0.364876i
\(334\) 11.9449 20.6892i 0.653597 1.13206i
\(335\) 44.8478 2.45030
\(336\) −2.20942 1.45550i −0.120534 0.0794040i
\(337\) 23.1362 1.26031 0.630154 0.776471i \(-0.282992\pi\)
0.630154 + 0.776471i \(0.282992\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) 2.68842 + 4.65647i 0.146015 + 0.252905i
\(340\) −5.25142 9.09572i −0.284798 0.493285i
\(341\) −1.68842 + 2.92442i −0.0914329 + 0.158366i
\(342\) −3.68842 −0.199447
\(343\) −3.25650 + 18.2317i −0.175834 + 0.984420i
\(344\) 3.06525 0.165267
\(345\) 10.4515 18.1025i 0.562688 0.974603i
\(346\) −5.68842 9.85263i −0.305811 0.529681i
\(347\) −7.82829 13.5590i −0.420245 0.727885i 0.575718 0.817648i \(-0.304722\pi\)
−0.995963 + 0.0897628i \(0.971389\pi\)
\(348\) −3.26304 + 5.65175i −0.174917 + 0.302966i
\(349\) −20.0102 −1.07112 −0.535560 0.844497i \(-0.679899\pi\)
−0.535560 + 0.844497i \(0.679899\pi\)
\(350\) 32.0942 + 21.1427i 1.71551 + 1.13013i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −3.73042 6.46127i −0.198550 0.343899i 0.749508 0.661995i \(-0.230290\pi\)
−0.948058 + 0.318096i \(0.896957\pi\)
\(354\) −6.26304 10.8479i −0.332877 0.576560i
\(355\) −2.06525 + 3.57712i −0.109612 + 0.189854i
\(356\) −12.8377 −0.680395
\(357\) 5.62171 2.81812i 0.297532 0.149151i
\(358\) 24.6101 1.30068
\(359\) 5.62317 9.73961i 0.296779 0.514037i −0.678618 0.734492i \(-0.737421\pi\)
0.975397 + 0.220455i \(0.0707541\pi\)
\(360\) −2.20942 3.82682i −0.116446 0.201691i
\(361\) 2.69779 + 4.67271i 0.141989 + 0.245932i
\(362\) −8.73042 + 15.1215i −0.458860 + 0.794770i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −32.9682 −1.72563
\(366\) 1.89783 3.28714i 0.0992013 0.171822i
\(367\) 2.95800 + 5.12341i 0.154406 + 0.267440i 0.932843 0.360284i \(-0.117320\pi\)
−0.778436 + 0.627724i \(0.783987\pi\)
\(368\) −2.36521 4.09666i −0.123295 0.213553i
\(369\) −6.07462 + 10.5216i −0.316232 + 0.547730i
\(370\) 33.9738 1.76622
\(371\) 1.24633 21.1293i 0.0647064 1.09698i
\(372\) 3.37683 0.175081
\(373\) 11.5630 20.0277i 0.598709 1.03700i −0.394303 0.918981i \(-0.629014\pi\)
0.993012 0.118014i \(-0.0376529\pi\)
\(374\) 1.18842 + 2.05840i 0.0614516 + 0.106437i
\(375\) 21.0471 + 36.4546i 1.08687 + 1.88251i
\(376\) 2.05362 3.55698i 0.105908 0.183437i
\(377\) 0 0
\(378\) 2.36521 1.18566i 0.121653 0.0609838i
\(379\) −6.77241 −0.347876 −0.173938 0.984757i \(-0.555649\pi\)
−0.173938 + 0.984757i \(0.555649\pi\)
\(380\) 8.14925 14.1149i 0.418048 0.724080i
\(381\) 0.365208 + 0.632559i 0.0187102 + 0.0324070i
\(382\) 8.41883 + 14.5818i 0.430745 + 0.746072i
\(383\) −12.6819 + 21.9656i −0.648013 + 1.12239i 0.335583 + 0.942011i \(0.391067\pi\)
−0.983597 + 0.180382i \(0.942267\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −9.76304 6.43161i −0.497571 0.327785i
\(386\) 5.46083 0.277949
\(387\) −1.53263 + 2.65458i −0.0779077 + 0.134940i
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) −12.6282 21.8728i −0.640278 1.10899i −0.985371 0.170425i \(-0.945486\pi\)
0.345093 0.938568i \(-0.387847\pi\)
\(390\) 0 0
\(391\) 11.2434 0.568604
\(392\) 2.76304 + 6.43161i 0.139555 + 0.324845i
\(393\) −7.37683 −0.372112
\(394\) 4.84421 8.39042i 0.244048 0.422703i
\(395\) 0.925376 + 1.60280i 0.0465607 + 0.0806455i
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) 6.73696 11.6688i 0.338118 0.585638i −0.645961 0.763371i \(-0.723543\pi\)
0.984079 + 0.177733i \(0.0568763\pi\)
\(398\) 20.2985 1.01747
\(399\) 8.14925 + 5.36849i 0.407973 + 0.268761i
\(400\) 14.5261 0.726304
\(401\) −16.9449 + 29.3495i −0.846189 + 1.46564i 0.0383962 + 0.999263i \(0.487775\pi\)
−0.884585 + 0.466379i \(0.845558\pi\)
\(402\) 5.07462 + 8.78951i 0.253099 + 0.438381i
\(403\) 0 0
\(404\) 7.68187 13.3054i 0.382188 0.661968i
\(405\) 4.41883 0.219574
\(406\) 15.4355 7.73772i 0.766053 0.384017i
\(407\) −7.68842 −0.381101
\(408\) 1.18842 2.05840i 0.0588354 0.101906i
\(409\) 2.10725 + 3.64986i 0.104197 + 0.180474i 0.913410 0.407041i \(-0.133439\pi\)
−0.809213 + 0.587515i \(0.800106\pi\)
\(410\) −26.8427 46.4930i −1.32567 2.29613i
\(411\) −4.41883 + 7.65364i −0.217965 + 0.377526i
\(412\) −2.62317 −0.129234
\(413\) −1.95146 + 33.0834i −0.0960250 + 1.62793i
\(414\) 4.73042 0.232487
\(415\) 4.74858 8.22479i 0.233099 0.403739i
\(416\) 0 0
\(417\) 0.736959 + 1.27645i 0.0360890 + 0.0625080i
\(418\) −1.84421 + 3.19426i −0.0902032 + 0.156236i
\(419\) −22.3116 −1.08999 −0.544996 0.838439i \(-0.683469\pi\)
−0.544996 + 0.838439i \(0.683469\pi\)
\(420\) −0.688417 + 11.6708i −0.0335913 + 0.569479i
\(421\) 18.3116 0.892452 0.446226 0.894920i \(-0.352768\pi\)
0.446226 + 0.894920i \(0.352768\pi\)
\(422\) −11.2565 + 19.4968i −0.547958 + 0.949091i
\(423\) 2.05362 + 3.55698i 0.0998507 + 0.172946i
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) −17.2630 + 29.9005i −0.837380 + 1.45039i
\(426\) −0.934749 −0.0452888
\(427\) −8.97754 + 4.50037i −0.434454 + 0.217788i
\(428\) 10.9029 0.527012
\(429\) 0 0
\(430\) −6.77241 11.7302i −0.326595 0.565679i
\(431\) 14.4188 + 24.9742i 0.694531 + 1.20296i 0.970339 + 0.241750i \(0.0777213\pi\)
−0.275808 + 0.961213i \(0.588945\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 7.62317 0.366346 0.183173 0.983081i \(-0.441363\pi\)
0.183173 + 0.983081i \(0.441363\pi\)
\(434\) −7.46083 4.91498i −0.358131 0.235927i
\(435\) 28.8377 1.38266
\(436\) 5.89783 10.2153i 0.282455 0.489226i
\(437\) 8.72387 + 15.1102i 0.417319 + 0.722818i
\(438\) −3.73042 6.46127i −0.178246 0.308731i
\(439\) 16.6870 28.9027i 0.796425 1.37945i −0.125505 0.992093i \(-0.540055\pi\)
0.921930 0.387356i \(-0.126611\pi\)
\(440\) −4.41883 −0.210660
\(441\) −6.95146 0.822941i −0.331022 0.0391877i
\(442\) 0 0
\(443\) 2.42538 4.20087i 0.115233 0.199590i −0.802640 0.596464i \(-0.796572\pi\)
0.917873 + 0.396874i \(0.129905\pi\)
\(444\) 3.84421 + 6.65836i 0.182438 + 0.315992i
\(445\) 28.3637 + 49.1275i 1.34457 + 2.32886i
\(446\) 3.73042 6.46127i 0.176640 0.305950i
\(447\) 9.36375 0.442890
\(448\) 2.20942 + 1.45550i 0.104385 + 0.0687659i
\(449\) 14.3450 0.676982 0.338491 0.940970i \(-0.390083\pi\)
0.338491 + 0.940970i \(0.390083\pi\)
\(450\) −7.26304 + 12.5800i −0.342383 + 0.593025i
\(451\) 6.07462 + 10.5216i 0.286043 + 0.495441i
\(452\) −2.68842 4.65647i −0.126452 0.219022i
\(453\) −6.78404 + 11.7503i −0.318742 + 0.552077i
\(454\) −2.77241 −0.130116
\(455\) 0 0
\(456\) 3.68842 0.172726
\(457\) 12.5913 21.8088i 0.588998 1.02017i −0.405366 0.914154i \(-0.632856\pi\)
0.994364 0.106020i \(-0.0338106\pi\)
\(458\) 1.26958 + 2.19898i 0.0593238 + 0.102752i
\(459\) 1.18842 + 2.05840i 0.0554705 + 0.0960778i
\(460\) −10.4515 + 18.1025i −0.487302 + 0.844031i
\(461\) 13.0187 0.606344 0.303172 0.952936i \(-0.401954\pi\)
0.303172 + 0.952936i \(0.401954\pi\)
\(462\) 0.155792 2.64116i 0.00724808 0.122878i
\(463\) −14.2145 −0.660604 −0.330302 0.943875i \(-0.607151\pi\)
−0.330302 + 0.943875i \(0.607151\pi\)
\(464\) 3.26304 5.65175i 0.151483 0.262376i
\(465\) −7.46083 12.9225i −0.345988 0.599268i
\(466\) 12.0261 + 20.8298i 0.557098 + 0.964921i
\(467\) 1.19779 2.07463i 0.0554271 0.0960026i −0.836981 0.547233i \(-0.815681\pi\)
0.892408 + 0.451230i \(0.149015\pi\)
\(468\) 0 0
\(469\) 1.58117 26.8058i 0.0730115 1.23778i
\(470\) −18.1492 −0.837162
\(471\) −9.37029 + 16.2298i −0.431760 + 0.747831i
\(472\) 6.26304 + 10.8479i 0.288280 + 0.499315i
\(473\) 1.53263 + 2.65458i 0.0704702 + 0.122058i
\(474\) −0.209416 + 0.362720i −0.00961881 + 0.0166603i
\(475\) −53.5782 −2.45834
\(476\) −5.62171 + 2.81812i −0.257670 + 0.129168i
\(477\) 8.00000 0.366295
\(478\) −3.79567 + 6.57429i −0.173610 + 0.300701i
\(479\) −5.41883 9.38569i −0.247593 0.428843i 0.715265 0.698854i \(-0.246306\pi\)
−0.962857 + 0.270010i \(0.912973\pi\)
\(480\) 2.20942 + 3.82682i 0.100846 + 0.174670i
\(481\) 0 0
\(482\) 16.2985 0.742376
\(483\) −10.4515 6.88512i −0.475558 0.313284i
\(484\) 1.00000 0.0454545
\(485\) −15.4659 + 26.7877i −0.702271 + 1.21637i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 17.3217 + 30.0021i 0.784923 + 1.35953i 0.929045 + 0.369967i \(0.120631\pi\)
−0.144121 + 0.989560i \(0.546036\pi\)
\(488\) −1.89783 + 3.28714i −0.0859109 + 0.148802i
\(489\) −18.7724 −0.848918
\(490\) 18.5079 24.7838i 0.836102 1.11962i
\(491\) 38.1492 1.72165 0.860826 0.508900i \(-0.169948\pi\)
0.860826 + 0.508900i \(0.169948\pi\)
\(492\) 6.07462 10.5216i 0.273865 0.474348i
\(493\) 7.75571 + 13.4333i 0.349299 + 0.605004i
\(494\) 0 0
\(495\) 2.20942 3.82682i 0.0993059 0.172003i
\(496\) −3.37683 −0.151624
\(497\) 2.06525 + 1.36053i 0.0926392 + 0.0610280i
\(498\) 2.14925 0.0963101
\(499\) 0.311583 0.539678i 0.0139484 0.0241593i −0.858967 0.512031i \(-0.828893\pi\)
0.872915 + 0.487872i \(0.162227\pi\)
\(500\) −21.0471 36.4546i −0.941254 1.63030i
\(501\) −11.9449 20.6892i −0.533659 0.924325i
\(502\) 4.30504 7.45655i 0.192143 0.332802i
\(503\) 31.1362 1.38829 0.694146 0.719834i \(-0.255782\pi\)
0.694146 + 0.719834i \(0.255782\pi\)
\(504\) −2.36521 + 1.18566i −0.105355 + 0.0528135i
\(505\) −67.8898 −3.02106
\(506\) 2.36521 4.09666i 0.105146 0.182119i
\(507\) −6.50000 11.2583i −0.288675 0.500000i
\(508\) −0.365208 0.632559i −0.0162035 0.0280653i
\(509\) 21.0522 36.4634i 0.933121 1.61621i 0.155170 0.987888i \(-0.450408\pi\)
0.777951 0.628325i \(-0.216259\pi\)
\(510\) −10.5028 −0.465073
\(511\) −1.16233 + 19.7053i −0.0514187 + 0.871709i
\(512\) 1.00000 0.0441942
\(513\) −1.84421 + 3.19426i −0.0814238 + 0.141030i
\(514\) −0.418833 0.725439i −0.0184739 0.0319978i
\(515\) 5.79567 + 10.0384i 0.255388 + 0.442344i
\(516\) 1.53263 2.65458i 0.0674701 0.116862i
\(517\) 4.10725 0.180637
\(518\) 1.19779 20.3063i 0.0526279 0.892209i
\(519\) −11.3768 −0.499388
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 3.26304 + 5.65175i 0.142819 + 0.247371i
\(523\) 12.6333 21.8816i 0.552417 0.956814i −0.445682 0.895191i \(-0.647039\pi\)
0.998099 0.0616232i \(-0.0196277\pi\)
\(524\) 7.37683 0.322258
\(525\) 34.3572 17.2230i 1.49947 0.751674i
\(526\) 10.8377 0.472545
\(527\) 4.01309 6.95087i 0.174813 0.302785i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 0.311583 + 0.539678i 0.0135471 + 0.0234643i
\(530\) −17.6753 + 30.6146i −0.767767 + 1.32981i
\(531\) −12.5261 −0.543586
\(532\) −8.14925 5.36849i −0.353315 0.232754i
\(533\) 0 0
\(534\) −6.41883 + 11.1177i −0.277770 + 0.481112i
\(535\) −24.0891 41.7235i −1.04146 1.80386i
\(536\) −5.07462 8.78951i −0.219190 0.379649i
\(537\) 12.3050 21.3130i 0.531002 0.919722i
\(538\) 17.8797 0.770847
\(539\) −4.18842 + 5.60867i −0.180408 + 0.241582i
\(540\) −4.41883 −0.190156
\(541\) 2.20942 3.82682i 0.0949902 0.164528i −0.814614 0.580003i \(-0.803051\pi\)
0.909605 + 0.415475i \(0.136385\pi\)
\(542\) 4.41883 + 7.65364i 0.189805 + 0.328752i
\(543\) 8.73042 + 15.1215i 0.374658 + 0.648927i
\(544\) −1.18842 + 2.05840i −0.0509530 + 0.0882531i
\(545\) −52.1231 −2.23271
\(546\) 0 0
\(547\) −27.6622 −1.18275 −0.591376 0.806396i \(-0.701415\pi\)
−0.591376 + 0.806396i \(0.701415\pi\)
\(548\) 4.41883 7.65364i 0.188763 0.326947i
\(549\) −1.89783 3.28714i −0.0809975 0.140292i
\(550\) 7.26304 + 12.5800i 0.309697 + 0.536411i
\(551\) −12.0355 + 20.8460i −0.512728 + 0.888070i
\(552\) −4.73042 −0.201340
\(553\) 0.990626 0.496593i 0.0421257 0.0211173i
\(554\) −16.0000 −0.679775
\(555\) 16.9869 29.4222i 0.721054 1.24890i
\(556\) −0.736959 1.27645i −0.0312540 0.0541335i
\(557\) 3.99346 + 6.91687i 0.169208 + 0.293077i 0.938142 0.346252i \(-0.112546\pi\)
−0.768934 + 0.639329i \(0.779212\pi\)
\(558\) 1.68842 2.92442i 0.0714764 0.123801i
\(559\) 0 0
\(560\) 0.688417 11.6708i 0.0290909 0.493183i
\(561\) 2.37683 0.100350
\(562\) 7.96083 13.7886i 0.335807 0.581636i
\(563\) 13.6753 + 23.6864i 0.576346 + 0.998261i 0.995894 + 0.0905280i \(0.0288555\pi\)
−0.419547 + 0.907733i \(0.637811\pi\)
\(564\) −2.05362 3.55698i −0.0864732 0.149776i
\(565\) −11.8797 + 20.5762i −0.499781 + 0.865646i
\(566\) −18.0840 −0.760127
\(567\) 0.155792 2.64116i 0.00654263 0.110918i
\(568\) 0.934749 0.0392212
\(569\) 14.7239 25.5025i 0.617257 1.06912i −0.372727 0.927941i \(-0.621577\pi\)
0.989984 0.141179i \(-0.0450894\pi\)
\(570\) −8.14925 14.1149i −0.341334 0.591209i
\(571\) 7.26304 + 12.5800i 0.303949 + 0.526455i 0.977027 0.213117i \(-0.0683615\pi\)
−0.673078 + 0.739572i \(0.735028\pi\)
\(572\) 0 0
\(573\) 16.8377 0.703404
\(574\) −28.7355 + 14.4049i −1.19940 + 0.601248i
\(575\) 68.7144 2.86559
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −6.69779 11.6009i −0.278833 0.482952i 0.692262 0.721646i \(-0.256614\pi\)
−0.971095 + 0.238694i \(0.923281\pi\)
\(578\) 5.67533 + 9.82996i 0.236063 + 0.408872i
\(579\) 2.73042 4.72922i 0.113472 0.196540i
\(580\) −28.8377 −1.19742
\(581\) −4.74858 3.12823i −0.197004 0.129781i
\(582\) −7.00000 −0.290159
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 3.73042 + 6.46127i 0.154366 + 0.267369i
\(585\) 0 0
\(586\) −12.5746 + 21.7799i −0.519453 + 0.899719i
\(587\) −11.2928 −0.466105 −0.233053 0.972464i \(-0.574871\pi\)
−0.233053 + 0.972464i \(0.574871\pi\)
\(588\) 6.95146 + 0.822941i 0.286673 + 0.0339375i
\(589\) 12.4552 0.513206
\(590\) 27.6753 47.9351i 1.13938 1.97346i
\(591\) −4.84421 8.39042i −0.199264 0.345136i
\(592\) −3.84421 6.65836i −0.157996 0.273657i
\(593\) 9.78912 16.9553i 0.401991 0.696269i −0.591975 0.805956i \(-0.701652\pi\)
0.993966 + 0.109687i \(0.0349849\pi\)
\(594\) 1.00000 0.0410305
\(595\) 23.2051 + 15.2869i 0.951317 + 0.626700i
\(596\) −9.36375 −0.383554
\(597\) 10.1492 17.5790i 0.415381 0.719461i
\(598\) 0 0
\(599\) −5.46591 9.46724i −0.223331 0.386821i 0.732486 0.680782i \(-0.238360\pi\)
−0.955817 + 0.293961i \(0.905026\pi\)
\(600\) 7.26304 12.5800i 0.296512 0.513575i
\(601\) −41.2202 −1.68141 −0.840703 0.541497i \(-0.817858\pi\)
−0.840703 + 0.541497i \(0.817858\pi\)
\(602\) −7.24995 + 3.63435i −0.295486 + 0.148125i
\(603\) 10.1492 0.413309
\(604\) 6.78404 11.7503i 0.276039 0.478113i
\(605\) −2.20942 3.82682i −0.0898255 0.155582i
\(606\) −7.68187 13.3054i −0.312055 0.540495i
\(607\) 15.6702 27.1417i 0.636036 1.10165i −0.350259 0.936653i \(-0.613906\pi\)
0.986295 0.164993i \(-0.0527603\pi\)
\(608\) −3.68842 −0.149585
\(609\) 1.01671 17.2364i 0.0411991 0.698455i
\(610\) 16.7724 0.679095
\(611\) 0 0
\(612\) −1.18842 2.05840i −0.0480389 0.0832058i
\(613\) −8.54425 14.7991i −0.345099 0.597729i 0.640273 0.768148i \(-0.278821\pi\)
−0.985372 + 0.170419i \(0.945488\pi\)
\(614\) 1.93475 3.35108i 0.0780801 0.135239i
\(615\) −53.6855 −2.16481
\(616\) −0.155792 + 2.64116i −0.00627702 + 0.106415i
\(617\) −6.96817 −0.280528 −0.140264 0.990114i \(-0.544795\pi\)
−0.140264 + 0.990114i \(0.544795\pi\)
\(618\) −1.31158 + 2.27173i −0.0527596 + 0.0913823i
\(619\) 0.00937364 + 0.0162356i 0.000376759 + 0.000652565i 0.866214 0.499674i \(-0.166547\pi\)
−0.865837 + 0.500326i \(0.833213\pi\)
\(620\) 7.46083 + 12.9225i 0.299634 + 0.518982i
\(621\) 2.36521 4.09666i 0.0949125 0.164393i
\(622\) −13.5681 −0.544030
\(623\) 30.3637 15.2211i 1.21650 0.609821i
\(624\) 0 0
\(625\) −56.6883 + 98.1871i −2.26753 + 3.92748i
\(626\) −1.26304 2.18765i −0.0504813 0.0874361i
\(627\) 1.84421 + 3.19426i 0.0736506 + 0.127567i
\(628\) 9.37029 16.2298i 0.373915 0.647640i
\(629\) 18.2741 0.728636
\(630\) 9.76304 + 6.43161i 0.388969 + 0.256241i
\(631\) −5.78550 −0.230317 −0.115159 0.993347i \(-0.536738\pi\)
−0.115159 + 0.993347i \(0.536738\pi\)
\(632\) 0.209416 0.362720i 0.00833013 0.0144282i
\(633\) 11.2565 + 19.4968i 0.447406 + 0.774929i
\(634\) 10.0051 + 17.3293i 0.397353 + 0.688235i
\(635\) −1.61379 + 2.79517i −0.0640414 + 0.110923i
\(636\) −8.00000 −0.317221
\(637\) 0 0
\(638\) 6.52608 0.258370
\(639\) −0.467375 + 0.809517i −0.0184891 + 0.0320240i
\(640\) −2.20942 3.82682i −0.0873348 0.151268i
\(641\) −7.68842 13.3167i −0.303674 0.525979i 0.673291 0.739378i \(-0.264880\pi\)
−0.976965 + 0.213398i \(0.931547\pi\)
\(642\) 5.45146 9.44220i 0.215152 0.372654i
\(643\) −35.8058 −1.41204 −0.706022 0.708190i \(-0.749512\pi\)
−0.706022 + 0.708190i \(0.749512\pi\)
\(644\) 10.4515 + 6.88512i 0.411845 + 0.271312i
\(645\) −13.5448 −0.533327
\(646\) 4.38338 7.59223i 0.172462 0.298712i
\(647\) −4.62825 8.01636i −0.181955 0.315156i 0.760591 0.649231i \(-0.224909\pi\)
−0.942546 + 0.334076i \(0.891576\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −6.26304 + 10.8479i −0.245846 + 0.425818i
\(650\) 0 0
\(651\) −7.98691 + 4.00378i −0.313032 + 0.156920i
\(652\) 18.7724 0.735185
\(653\) −12.4239 + 21.5189i −0.486185 + 0.842098i −0.999874 0.0158790i \(-0.994945\pi\)
0.513689 + 0.857977i \(0.328279\pi\)
\(654\) −5.89783 10.2153i −0.230624 0.399452i
\(655\) −16.2985 28.2298i −0.636835 1.10303i
\(656\) −6.07462 + 10.5216i −0.237174 + 0.410798i
\(657\) −7.46083 −0.291075
\(658\) −0.639875 + 10.8479i −0.0249449 + 0.422895i
\(659\) −6.60442 −0.257272 −0.128636 0.991692i \(-0.541060\pi\)
−0.128636 + 0.991692i \(0.541060\pi\)
\(660\) −2.20942 + 3.82682i −0.0860014 + 0.148959i
\(661\) 6.61662 + 11.4603i 0.257357 + 0.445755i 0.965533 0.260281i \(-0.0838151\pi\)
−0.708176 + 0.706036i \(0.750482\pi\)
\(662\) 8.07462 + 13.9857i 0.313829 + 0.543568i
\(663\) 0 0
\(664\) −2.14925 −0.0834070
\(665\) −2.53917 + 43.0469i −0.0984647 + 1.66929i
\(666\) 7.68842 0.297920
\(667\) 15.4355 26.7351i 0.597667 1.03519i
\(668\) 11.9449 + 20.6892i 0.462163 + 0.800489i
\(669\) −3.73042 6.46127i −0.144226 0.249807i
\(670\) −22.4239 + 38.8394i −0.866311 + 1.50050i
\(671\) −3.79567 −0.146530
\(672\) 2.36521 1.18566i 0.0912399 0.0457379i
\(673\) 0.130501 0.00503045 0.00251523 0.999997i \(-0.499199\pi\)
0.00251523 + 0.999997i \(0.499199\pi\)
\(674\) −11.5681 + 20.0365i −0.445586 + 0.771777i
\(675\) 7.26304 + 12.5800i 0.279555 + 0.484203i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −14.0587 + 24.3504i −0.540320 + 0.935862i 0.458565 + 0.888661i \(0.348363\pi\)
−0.998885 + 0.0472011i \(0.984970\pi\)
\(678\) −5.37683 −0.206496
\(679\) 15.4659 + 10.1885i 0.593527 + 0.390999i
\(680\) 10.5028 0.402765
\(681\) −1.38621 + 2.40098i −0.0531196 + 0.0920058i
\(682\) −1.68842 2.92442i −0.0646528 0.111982i
\(683\) −7.95146 13.7723i −0.304254 0.526984i 0.672841 0.739787i \(-0.265074\pi\)
−0.977095 + 0.212804i \(0.931741\pi\)
\(684\) 1.84421 3.19426i 0.0705151 0.122136i
\(685\) −39.0522 −1.49211
\(686\) −14.1609 11.9361i −0.540665 0.455721i
\(687\) 2.53917 0.0968753
\(688\) −1.53263 + 2.65458i −0.0584308 + 0.101205i
\(689\) 0 0
\(690\) 10.4515 + 18.1025i 0.397880 + 0.689149i
\(691\) 7.99063 13.8402i 0.303978 0.526505i −0.673055 0.739592i \(-0.735018\pi\)
0.977033 + 0.213087i \(0.0683518\pi\)
\(692\) 11.3768 0.432482
\(693\) −2.20942 1.45550i −0.0839288 0.0552899i
\(694\) 15.6566 0.594316
\(695\) −3.25650 + 5.64042i −0.123526 + 0.213953i
\(696\) −3.26304 5.65175i −0.123685 0.214229i
\(697\) −14.4384 25.0080i −0.546892 0.947245i
\(698\) 10.0051 17.3293i 0.378698 0.655924i
\(699\) 24.0522 0.909736
\(700\) −34.3572 + 17.2230i −1.29858 + 0.650968i
\(701\) 13.9869 0.528278 0.264139 0.964485i \(-0.414912\pi\)
0.264139 + 0.964485i \(0.414912\pi\)
\(702\) 0 0
\(703\) 14.1790 + 24.5588i 0.534773 + 0.926254i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) −9.07462 + 15.7177i −0.341770 + 0.591963i
\(706\) 7.46083 0.280792
\(707\) −2.39354 + 40.5781i −0.0900184 + 1.52610i
\(708\) 12.5261 0.470759
\(709\) −3.82096 + 6.61809i −0.143499 + 0.248548i −0.928812 0.370551i \(-0.879169\pi\)
0.785313 + 0.619099i \(0.212502\pi\)
\(710\) −2.06525 3.57712i −0.0775075 0.134247i
\(711\) 0.209416 + 0.362720i 0.00785373 + 0.0136031i
\(712\) 6.41883 11.1177i 0.240556 0.416655i
\(713\) −15.9738 −0.598225
\(714\) −0.370291 + 6.27760i −0.0138578 + 0.234933i
\(715\) 0 0
\(716\) −12.3050 + 21.3130i −0.459861 + 0.796503i
\(717\) 3.79567 + 6.57429i 0.141752 + 0.245521i
\(718\) 5.62317 + 9.73961i 0.209855 + 0.363479i
\(719\) 9.71879 16.8334i 0.362450 0.627781i −0.625914 0.779892i \(-0.715274\pi\)
0.988363 + 0.152111i \(0.0486071\pi\)
\(720\) 4.41883 0.164680
\(721\) 6.20433 3.11019i 0.231061 0.115829i
\(722\) −5.39558 −0.200803
\(723\) 8.14925 14.1149i 0.303074 0.524939i
\(724\) −8.73042 15.1215i −0.324463 0.561987i
\(725\) 47.3992 + 82.0978i 1.76036 + 3.04904i
\(726\) 0.500000 0.866025i 0.0185567 0.0321412i
\(727\) −44.9217 −1.66605 −0.833026 0.553234i \(-0.813394\pi\)
−0.833026 + 0.553234i \(0.813394\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 16.4841 28.5513i 0.610103 1.05673i
\(731\) −3.64280 6.30951i −0.134734 0.233366i
\(732\) 1.89783 + 3.28714i 0.0701459 + 0.121496i
\(733\) −12.5210 + 21.6870i −0.462474 + 0.801028i −0.999084 0.0428026i \(-0.986371\pi\)
0.536610 + 0.843830i \(0.319705\pi\)
\(734\) −5.91600 −0.218364
\(735\) −12.2094 28.4202i −0.450351 1.04830i
\(736\) 4.73042 0.174365
\(737\) 5.07462 8.78951i 0.186926 0.323766i
\(738\) −6.07462 10.5216i −0.223610 0.387304i
\(739\) 3.31158 + 5.73583i 0.121819 + 0.210996i 0.920485 0.390778i \(-0.127794\pi\)
−0.798666 + 0.601774i \(0.794461\pi\)
\(740\) −16.9869 + 29.4222i −0.624451 + 1.08158i
\(741\) 0 0
\(742\) 17.6753 + 11.6440i 0.648882 + 0.427465i
\(743\) −39.3972 −1.44534 −0.722671 0.691192i \(-0.757086\pi\)
−0.722671 + 0.691192i \(0.757086\pi\)
\(744\) −1.68842 + 2.92442i −0.0619004 + 0.107215i
\(745\) 20.6884 + 35.8334i 0.757965 + 1.31283i
\(746\) 11.5630 + 20.0277i 0.423351 + 0.733266i
\(747\) 1.07462 1.86130i 0.0393184 0.0681015i
\(748\) −2.37683 −0.0869056
\(749\) −25.7877 + 12.9272i −0.942261 + 0.472348i
\(750\) −42.0942 −1.53706
\(751\) 5.35358 9.27268i 0.195355 0.338365i −0.751662 0.659549i \(-0.770747\pi\)
0.947017 + 0.321184i \(0.104081\pi\)
\(752\) 2.05362 + 3.55698i 0.0748880 + 0.129710i
\(753\) −4.30504 7.45655i −0.156884 0.271732i
\(754\) 0 0
\(755\) −59.9551 −2.18199
\(756\) −0.155792 + 2.64116i −0.00566608 + 0.0960581i
\(757\) −17.2797 −0.628043 −0.314022 0.949416i \(-0.601676\pi\)
−0.314022 + 0.949416i \(0.601676\pi\)
\(758\) 3.38621 5.86508i 0.122993 0.213029i
\(759\) −2.36521 4.09666i −0.0858516 0.148699i
\(760\) 8.14925 + 14.1149i 0.295604 + 0.512002i
\(761\) 16.3544 28.3266i 0.592846 1.02684i −0.401001 0.916077i \(-0.631338\pi\)
0.993847 0.110761i \(-0.0353289\pi\)
\(762\) −0.730416 −0.0264602
\(763\) −1.83767 + 31.1542i −0.0665280 + 1.12786i
\(764\) −16.8377 −0.609165
\(765\) −5.25142 + 9.09572i −0.189865 + 0.328856i
\(766\) −12.6819 21.9656i −0.458215 0.793651i
\(767\) 0 0
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 12.2145 0.440466 0.220233 0.975447i \(-0.429318\pi\)
0.220233 + 0.975447i \(0.429318\pi\)
\(770\) 10.4515 5.23924i 0.376644 0.188809i
\(771\) −0.837665 −0.0301678
\(772\) −2.73042 + 4.72922i −0.0982698 + 0.170208i
\(773\) −0.102167 0.176958i −0.00367468 0.00636474i 0.864182 0.503179i \(-0.167836\pi\)
−0.867857 + 0.496814i \(0.834503\pi\)
\(774\) −1.53263 2.65458i −0.0550891 0.0954171i
\(775\) 24.5261 42.4804i 0.881003 1.52594i
\(776\) 7.00000 0.251285
\(777\) −16.9869 11.1905i −0.609402 0.401457i
\(778\) 25.2565 0.905489
\(779\) 22.4057 38.8079i 0.802769 1.39044i
\(780\) 0 0