Properties

Label 462.2.i.g.67.1
Level $462$
Weight $2$
Character 462.67
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 67.1
Root \(0.500000 + 3.23735i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.g.331.1

$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.627352 0.778736i \(-0.715861\pi\)
−0.360729 0.932671i \(-0.617472\pi\)
\(6\) −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 −0.973388 0.229163i \(-0.926401\pi\)
0.685155 + 0.728398i \(0.259735\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 1.84421 + 3.19426i 0.423090 + 0.732814i 0.996240 0.0866367i \(-0.0276119\pi\)
−0.573150 + 0.819451i \(0.694279\pi\)
\(20\) 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 0.506789 0.862070i \(-0.330832\pi\)
−0.999969 + 0.00785730i \(0.997499\pi\)
\(24\) 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 −0.673621 0.739077i \(-0.735262\pi\)
0.976870 + 0.213835i \(0.0685954\pi\)
\(32\) −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 −0.987146 0.159823i \(-0.948908\pi\)
0.355162 0.934805i \(-0.384426\pi\)
\(38\) 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 0.976033 0.217620i \(-0.0698295\pi\)
−0.676482 + 0.736460i \(0.736496\pi\)
\(48\) −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 0.448871 + 0.893597i \(0.351826\pi\)
−0.998313 + 0.0580651i \(0.981507\pi\)
\(54\) 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 −0.0936773 0.995603i \(-0.529862\pi\)
0.909056 0.416674i \(-0.136804\pi\)
\(60\) 2.20942 3.82682i 0.285234 0.494041i
\(61\) −1.89783 3.28714i −0.242993 0.420876i 0.718573 0.695452i \(-0.244796\pi\)
−0.961565 + 0.274576i \(0.911462\pi\)
\(62\) −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 0.369528 + 0.929220i \(0.379519\pi\)
−0.989492 + 0.144589i \(0.953814\pi\)
\(68\) −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 −0.560814 0.827942i \(-0.689512\pi\)
0.997426 + 0.0717077i \(0.0228449\pi\)
\(74\) −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 0.877566 0.479457i \(-0.159166\pi\)
−0.854004 + 0.520266i \(0.825833\pi\)
\(80\) −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 0.974860 + 0.222816i \(0.0715251\pi\)
−0.294466 + 0.955662i \(0.595142\pi\)
\(90\) 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 −0.176201 0.984354i \(-0.556381\pi\)
0.940576 0.339582i \(-0.110286\pi\)
\(102\) 1.18842 2.05840i 0.117671 0.203812i
\(103\) 1.31158 + 2.27173i 0.129234 + 0.223840i 0.923380 0.383887i \(-0.125415\pi\)
−0.794146 + 0.607727i \(0.792081\pi\)
\(104\) 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 −0.999504 0.0314773i \(-0.989979\pi\)
0.472492 0.881335i \(-0.343355\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 5.89783 10.2153i 0.564910 0.978453i −0.432148 0.901803i \(-0.642244\pi\)
0.997058 0.0766501i \(-0.0244224\pi\)
\(110\) 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 0.658695 0.752410i \(-0.271109\pi\)
−0.980954 + 0.194242i \(0.937775\pi\)
\(132\) 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 −0.613175 0.789947i \(-0.710108\pi\)
0.990702 + 0.136052i \(0.0434414\pi\)
\(138\) 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 0.991567 0.129592i \(-0.0413667\pi\)
−0.608013 + 0.793927i \(0.708033\pi\)
\(150\) 7.26304 12.5800i 0.593025 1.02715i
\(151\) 6.78404 11.7503i 0.552077 0.956226i −0.446047 0.895009i \(-0.647169\pi\)
0.998125 0.0612166i \(-0.0194980\pi\)
\(152\) 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 −0.201030 0.979585i \(-0.564429\pi\)
0.948861 0.315696i \(-0.102238\pi\)
\(158\) 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 −0.954642 0.297755i \(-0.903762\pi\)
0.219458 0.975622i \(-0.429571\pi\)
\(164\) −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 0.564604 0.825362i \(-0.309029\pi\)
−0.997086 + 0.0762805i \(0.975696\pi\)
\(174\) 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 −0.119885 + 0.992788i \(0.538253\pi\)
−0.799837 + 0.600217i \(0.795081\pi\)
\(180\) −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 0.991378 + 0.131031i \(0.0418288\pi\)
−0.382213 + 0.924074i \(0.624838\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −2.73042 + 4.72922i −0.196540 + 0.340417i −0.947404 0.320040i \(-0.896304\pi\)
0.750865 + 0.660456i \(0.229637\pi\)
\(194\) −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 0.241752 + 0.970338i \(0.422278\pi\)
−0.961214 + 0.275805i \(0.911056\pi\)
\(200\) −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 −0.816349 0.577559i \(-0.804005\pi\)
0.908355 + 0.418200i \(0.137339\pi\)
\(228\) −1.84421 + 3.19426i −0.122136 + 0.211545i
\(229\) 1.26958 + 2.19898i 0.0838965 + 0.145313i 0.904920 0.425581i \(-0.139930\pi\)
−0.821024 + 0.570894i \(0.806597\pi\)
\(230\) 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 0.927279 + 0.374372i \(0.122142\pi\)
−0.139424 + 0.990233i \(0.544525\pi\)
\(234\) 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 0.474639 + 0.880181i \(0.342579\pi\)
−0.999578 + 0.0290409i \(0.990755\pi\)
\(242\) −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 0.852667 0.522455i \(-0.174984\pi\)
−0.878793 + 0.477203i \(0.841650\pi\)
\(258\) −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 −0.983319 0.181888i \(-0.941779\pi\)
0.649180 + 0.760635i \(0.275112\pi\)
\(264\) −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 0.453531 + 0.891240i \(0.350164\pi\)
−0.998602 + 0.0528506i \(0.983169\pi\)
\(270\) 2.20942 3.82682i 0.134461 0.232893i
\(271\) 4.41883 + 7.65364i 0.268425 + 0.464926i 0.968455 0.249187i \(-0.0801635\pi\)
−0.700030 + 0.714113i \(0.746830\pi\)
\(272\) 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 −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −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 −0.461547 0.887116i \(-0.652706\pi\)
0.999038 0.0438462i \(-0.0139611\pi\)
\(284\) −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 −0.607038 0.794673i \(-0.707642\pi\)
0.991726 + 0.128374i \(0.0409758\pi\)
\(312\) 0 0
\(313\) −1.26304 2.18765i −0.0713913 0.123653i 0.828120 0.560551i \(-0.189411\pi\)
−0.899511 + 0.436898i \(0.856077\pi\)
\(314\) −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 0.997327 + 0.0730670i \(0.0232787\pi\)
−0.435386 + 0.900244i \(0.643388\pi\)
\(318\) 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 0.997969 0.0636969i \(-0.0202891\pi\)
−0.554148 + 0.832418i \(0.686956\pi\)
\(332\) 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 −0.995963 0.0897628i \(-0.971389\pi\)
0.575718 + 0.817648i \(0.304722\pi\)
\(348\) −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 −0.948058 0.318096i \(-0.896957\pi\)
0.749508 + 0.661995i \(0.230290\pi\)
\(354\) −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 0.975397 0.220455i \(-0.0707541\pi\)
−0.678618 + 0.734492i \(0.737421\pi\)
\(360\) −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 −0.778436 0.627724i \(-0.783987\pi\)
0.932843 + 0.360284i \(0.117320\pi\)
\(368\) −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 0.993012 + 0.118014i \(0.0376529\pi\)
−0.394303 + 0.918981i \(0.629014\pi\)
\(374\) 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 −0.983597 0.180382i \(-0.942267\pi\)
0.335583 0.942011i \(-0.391067\pi\)
\(384\) −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 0.345093 + 0.938568i \(0.387847\pi\)
−0.985371 + 0.170425i \(0.945486\pi\)
\(390\) 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 0.984079 0.177733i \(-0.0568763\pi\)
−0.645961 + 0.763371i \(0.723543\pi\)
\(398\) 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 −0.884585 0.466379i \(-0.845558\pi\)
0.0383962 0.999263i \(-0.487775\pi\)
\(402\) 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 −0.809213 0.587515i \(-0.800106\pi\)
0.913410 + 0.407041i \(0.133439\pi\)
\(410\) −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 −0.275808 0.961213i \(-0.588945\pi\)
0.970339 0.241750i \(-0.0777213\pi\)
\(432\) 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 0.921930 + 0.387356i \(0.126611\pi\)
−0.125505 + 0.992093i \(0.540055\pi\)
\(440\) −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 0.917873 0.396874i \(-0.129905\pi\)
−0.802640 + 0.596464i \(0.796572\pi\)
\(444\) 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 0.994364 + 0.106020i \(0.0338106\pi\)
−0.405366 + 0.914154i \(0.632856\pi\)
\(458\) 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 0.892408 0.451230i \(-0.149015\pi\)
−0.836981 + 0.547233i \(0.815681\pi\)
\(468\) 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 −0.962857 0.270010i \(-0.912973\pi\)
0.715265 + 0.698854i \(0.246306\pi\)
\(480\) 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 −0.144121 0.989560i \(-0.546036\pi\)
0.929045 0.369967i \(-0.120631\pi\)
\(488\) −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 0.872915 0.487872i \(-0.162227\pi\)
−0.858967 + 0.512031i \(0.828893\pi\)
\(500\) −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 0.777951 + 0.628325i \(0.216259\pi\)
0.155170 + 0.987888i \(0.450408\pi\)
\(510\) −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 −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 3.26304 5.65175i 0.142819 0.247371i
\(523\) 12.6333 + 21.8816i 0.552417 + 0.956814i 0.998099 + 0.0616232i \(0.0196277\pi\)
−0.445682 + 0.895191i \(0.647039\pi\)
\(524\) 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 0.909605 0.415475i \(-0.136385\pi\)
−0.814614 + 0.580003i \(0.803051\pi\)
\(542\) 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 −0.768934 0.639329i \(-0.779212\pi\)
0.938142 + 0.346252i \(0.112546\pi\)
\(558\) 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 −0.419547 0.907733i \(-0.637811\pi\)
0.995894 0.0905280i \(-0.0288555\pi\)
\(564\) −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 0.989984 + 0.141179i \(0.0450894\pi\)
−0.372727 + 0.927941i \(0.621577\pi\)
\(570\) −8.14925 + 14.1149i −0.341334 + 0.591209i
\(571\) 7.26304 12.5800i 0.303949 0.526455i −0.673078 0.739572i \(-0.735028\pi\)
0.977027 + 0.213117i \(0.0683615\pi\)
\(572\) 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 −0.971095 0.238694i \(-0.923281\pi\)
0.692262 + 0.721646i \(0.256614\pi\)
\(578\) 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 0.993966 0.109687i \(-0.0349849\pi\)
−0.591975 + 0.805956i \(0.701652\pi\)
\(594\) 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 −0.955817 0.293961i \(-0.905026\pi\)
0.732486 + 0.680782i \(0.238360\pi\)
\(600\) 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 0.986295 + 0.164993i \(0.0527603\pi\)
−0.350259 + 0.936653i \(0.613906\pi\)
\(608\) −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 −0.985372 0.170419i \(-0.945488\pi\)
0.640273 + 0.768148i \(0.278821\pi\)
\(614\) 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 −0.865837 0.500326i \(-0.833213\pi\)
0.866214 + 0.499674i \(0.166547\pi\)
\(620\) 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 −0.976965 0.213398i \(-0.931547\pi\)
0.673291 + 0.739378i \(0.264880\pi\)
\(642\) 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 −0.942546 0.334076i \(-0.891576\pi\)
0.760591 + 0.649231i \(0.224909\pi\)
\(648\) −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 0.513689 0.857977i \(-0.328279\pi\)
−0.999874 + 0.0158790i \(0.994945\pi\)
\(654\) −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 −0.708176 0.706036i \(-0.750482\pi\)
0.965533 + 0.260281i \(0.0838151\pi\)
\(662\) 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 −0.998885 0.0472011i \(-0.984970\pi\)
0.458565 0.888661i \(-0.348363\pi\)
\(678\) −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 −0.977095 0.212804i \(-0.931741\pi\)
0.672841 + 0.739787i \(0.265074\pi\)
\(684\) 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 0.977033 0.213087i \(-0.0683518\pi\)
−0.673055 + 0.739592i \(0.735018\pi\)
\(692\) 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 0.785313 0.619099i \(-0.212502\pi\)
−0.928812 + 0.370551i \(0.879169\pi\)
\(710\) −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 0.988363 0.152111i \(-0.0486071\pi\)
−0.625914 + 0.779892i \(0.715274\pi\)
\(720\) 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 0.536610 0.843830i \(-0.319705\pi\)
−0.999084 + 0.0428026i \(0.986371\pi\)
\(734\) −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 −0.798666 0.601774i \(-0.794461\pi\)
0.920485 + 0.390778i \(0.127794\pi\)
\(740\) −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 0.947017 0.321184i \(-0.104081\pi\)
−0.751662 + 0.659549i \(0.770747\pi\)
\(752\) 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 0.993847 + 0.110761i \(0.0353289\pi\)
−0.401001 + 0.916077i \(0.631338\pi\)
\(762\) −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 −0.867857 0.496814i \(-0.834503\pi\)
0.864182 + 0.503179i \(0.167836\pi\)
\(774\) −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
\(781\) 0.467375