Properties

Label 105.3.t.b.86.14
Level $105$
Weight $3$
Character 105.86
Analytic conductor $2.861$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 86.14
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.31825 + 1.33844i) q^{2} +(0.256676 + 2.98900i) q^{3} +(1.58287 + 2.74161i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.40557 + 7.27281i) q^{6} +(4.89419 - 5.00469i) q^{7} -2.23323i q^{8} +(-8.86824 + 1.53441i) q^{9} +O(q^{10})\) \(q+(2.31825 + 1.33844i) q^{2} +(0.256676 + 2.98900i) q^{3} +(1.58287 + 2.74161i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.40557 + 7.27281i) q^{6} +(4.89419 - 5.00469i) q^{7} -2.23323i q^{8} +(-8.86824 + 1.53441i) q^{9} +(2.99285 + 5.18377i) q^{10} +(-15.6726 + 9.04859i) q^{11} +(-7.78838 + 5.43489i) q^{12} +2.70603 q^{13} +(18.0445 - 5.05154i) q^{14} +(-2.84475 + 6.07514i) q^{15} +(9.32053 - 16.1436i) q^{16} +(3.39734 - 1.96145i) q^{17} +(-22.6125 - 8.31250i) q^{18} +(14.7810 - 25.6015i) q^{19} +7.07880i q^{20} +(16.2152 + 13.3441i) q^{21} -48.4441 q^{22} +(5.66814 + 3.27250i) q^{23} +(6.67514 - 0.573217i) q^{24} +(2.50000 + 4.33013i) q^{25} +(6.27326 + 3.62187i) q^{26} +(-6.86260 - 26.1133i) q^{27} +(21.4677 + 5.49618i) q^{28} -18.8690i q^{29} +(-14.7261 + 10.2762i) q^{30} +(12.6486 + 21.9079i) q^{31} +(35.4786 - 20.4836i) q^{32} +(-31.0690 - 44.5229i) q^{33} +10.5012 q^{34} +(15.0730 - 4.21967i) q^{35} +(-18.2440 - 21.8845i) q^{36} +(-33.5038 + 58.0303i) q^{37} +(68.5323 - 39.5671i) q^{38} +(0.694571 + 8.08831i) q^{39} +(2.49683 - 4.32464i) q^{40} +38.7488i q^{41} +(19.7306 + 52.6383i) q^{42} -63.9074 q^{43} +(-49.6153 - 28.6454i) q^{44} +(-18.8888 - 6.94362i) q^{45} +(8.76013 + 15.1730i) q^{46} +(-33.6085 - 19.4039i) q^{47} +(50.6457 + 23.7154i) q^{48} +(-1.09384 - 48.9878i) q^{49} +13.3844i q^{50} +(6.73480 + 9.65119i) q^{51} +(4.28328 + 7.41886i) q^{52} +(0.787120 - 0.454444i) q^{53} +(19.0420 - 69.7225i) q^{54} -40.4665 q^{55} +(-11.1766 - 10.9299i) q^{56} +(80.3167 + 37.6092i) q^{57} +(25.2551 - 43.7430i) q^{58} +(20.6520 - 11.9234i) q^{59} +(-21.1585 + 1.81696i) q^{60} +(-25.3438 + 43.8968i) q^{61} +67.7176i q^{62} +(-35.7236 + 51.8924i) q^{63} +35.1002 q^{64} +(5.24020 + 3.02543i) q^{65} +(-12.4344 - 144.799i) q^{66} +(-34.7257 - 60.1466i) q^{67} +(10.7551 + 6.20944i) q^{68} +(-8.32663 + 17.7820i) q^{69} +(40.5908 + 10.3921i) q^{70} -55.2444i q^{71} +(3.42669 + 19.8048i) q^{72} +(14.8601 + 25.7384i) q^{73} +(-155.341 + 89.6861i) q^{74} +(-12.3011 + 8.58394i) q^{75} +93.5856 q^{76} +(-31.4193 + 122.722i) q^{77} +(-9.21556 + 19.6804i) q^{78} +(-14.9827 + 25.9507i) q^{79} +(36.0983 - 20.8413i) q^{80} +(76.2912 - 27.2150i) q^{81} +(-51.8631 + 89.8295i) q^{82} +78.4979i q^{83} +(-10.9178 + 65.5778i) q^{84} +8.77189 q^{85} +(-148.153 - 85.5364i) q^{86} +(56.3993 - 4.84320i) q^{87} +(20.2076 + 35.0006i) q^{88} +(133.421 + 77.0307i) q^{89} +(-34.4953 - 41.3787i) q^{90} +(13.2438 - 13.5428i) q^{91} +20.7198i q^{92} +(-62.2363 + 43.4298i) q^{93} +(-51.9421 - 89.9663i) q^{94} +(57.2466 - 33.0514i) q^{95} +(70.3318 + 100.788i) q^{96} +32.8490 q^{97} +(63.0316 - 115.030i) q^{98} +(125.104 - 104.293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31825 + 1.33844i 1.15913 + 0.669222i 0.951095 0.308900i \(-0.0999607\pi\)
0.208032 + 0.978122i \(0.433294\pi\)
\(3\) 0.256676 + 2.98900i 0.0855585 + 0.996333i
\(4\) 1.58287 + 2.74161i 0.395717 + 0.685402i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) −3.40557 + 7.27281i −0.567595 + 1.21213i
\(7\) 4.89419 5.00469i 0.699170 0.714956i
\(8\) 2.23323i 0.279154i
\(9\) −8.86824 + 1.53441i −0.985359 + 0.170490i
\(10\) 2.99285 + 5.18377i 0.299285 + 0.518377i
\(11\) −15.6726 + 9.04859i −1.42478 + 0.822599i −0.996703 0.0811419i \(-0.974143\pi\)
−0.428080 + 0.903741i \(0.640810\pi\)
\(12\) −7.78838 + 5.43489i −0.649032 + 0.452908i
\(13\) 2.70603 0.208156 0.104078 0.994569i \(-0.466811\pi\)
0.104078 + 0.994569i \(0.466811\pi\)
\(14\) 18.0445 5.05154i 1.28889 0.360824i
\(15\) −2.84475 + 6.07514i −0.189650 + 0.405010i
\(16\) 9.32053 16.1436i 0.582533 1.00898i
\(17\) 3.39734 1.96145i 0.199843 0.115380i −0.396739 0.917931i \(-0.629858\pi\)
0.596582 + 0.802552i \(0.296525\pi\)
\(18\) −22.6125 8.31250i −1.25625 0.461805i
\(19\) 14.7810 25.6015i 0.777948 1.34745i −0.155174 0.987887i \(-0.549594\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(20\) 7.07880i 0.353940i
\(21\) 16.2152 + 13.3441i 0.772154 + 0.635435i
\(22\) −48.4441 −2.20201
\(23\) 5.66814 + 3.27250i 0.246441 + 0.142283i 0.618133 0.786073i \(-0.287889\pi\)
−0.371693 + 0.928356i \(0.621222\pi\)
\(24\) 6.67514 0.573217i 0.278131 0.0238840i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 6.27326 + 3.62187i 0.241279 + 0.139303i
\(27\) −6.86260 26.1133i −0.254170 0.967159i
\(28\) 21.4677 + 5.49618i 0.766705 + 0.196292i
\(29\) 18.8690i 0.650654i −0.945602 0.325327i \(-0.894526\pi\)
0.945602 0.325327i \(-0.105474\pi\)
\(30\) −14.7261 + 10.2762i −0.490870 + 0.342539i
\(31\) 12.6486 + 21.9079i 0.408018 + 0.706708i 0.994668 0.103133i \(-0.0328867\pi\)
−0.586650 + 0.809841i \(0.699553\pi\)
\(32\) 35.4786 20.4836i 1.10871 0.640111i
\(33\) −31.0690 44.5229i −0.941485 1.34918i
\(34\) 10.5012 0.308859
\(35\) 15.0730 4.21967i 0.430656 0.120562i
\(36\) −18.2440 21.8845i −0.506777 0.607901i
\(37\) −33.5038 + 58.0303i −0.905509 + 1.56839i −0.0852768 + 0.996357i \(0.527177\pi\)
−0.820232 + 0.572031i \(0.806156\pi\)
\(38\) 68.5323 39.5671i 1.80348 1.04124i
\(39\) 0.694571 + 8.08831i 0.0178095 + 0.207393i
\(40\) 2.49683 4.32464i 0.0624208 0.108116i
\(41\) 38.7488i 0.945092i 0.881306 + 0.472546i \(0.156665\pi\)
−0.881306 + 0.472546i \(0.843335\pi\)
\(42\) 19.7306 + 52.6383i 0.469777 + 1.25329i
\(43\) −63.9074 −1.48622 −0.743109 0.669171i \(-0.766650\pi\)
−0.743109 + 0.669171i \(0.766650\pi\)
\(44\) −49.6153 28.6454i −1.12762 0.651032i
\(45\) −18.8888 6.94362i −0.419751 0.154303i
\(46\) 8.76013 + 15.1730i 0.190438 + 0.329847i
\(47\) −33.6085 19.4039i −0.715075 0.412849i 0.0978620 0.995200i \(-0.468800\pi\)
−0.812937 + 0.582351i \(0.802133\pi\)
\(48\) 50.6457 + 23.7154i 1.05512 + 0.494071i
\(49\) −1.09384 48.9878i −0.0223233 0.999751i
\(50\) 13.3844i 0.267689i
\(51\) 6.73480 + 9.65119i 0.132055 + 0.189239i
\(52\) 4.28328 + 7.41886i 0.0823708 + 0.142670i
\(53\) 0.787120 0.454444i 0.0148513 0.00857442i −0.492556 0.870281i \(-0.663937\pi\)
0.507407 + 0.861706i \(0.330604\pi\)
\(54\) 19.0420 69.7225i 0.352629 1.29116i
\(55\) −40.4665 −0.735755
\(56\) −11.1766 10.9299i −0.199583 0.195176i
\(57\) 80.3167 + 37.6092i 1.40907 + 0.659810i
\(58\) 25.2551 43.7430i 0.435432 0.754190i
\(59\) 20.6520 11.9234i 0.350033 0.202092i −0.314667 0.949202i \(-0.601893\pi\)
0.664700 + 0.747110i \(0.268559\pi\)
\(60\) −21.1585 + 1.81696i −0.352642 + 0.0302826i
\(61\) −25.3438 + 43.8968i −0.415472 + 0.719619i −0.995478 0.0949935i \(-0.969717\pi\)
0.580006 + 0.814612i \(0.303050\pi\)
\(62\) 67.7176i 1.09222i
\(63\) −35.7236 + 51.8924i −0.567041 + 0.823690i
\(64\) 35.1002 0.548440
\(65\) 5.24020 + 3.02543i 0.0806184 + 0.0465451i
\(66\) −12.4344 144.799i −0.188400 2.19393i
\(67\) −34.7257 60.1466i −0.518294 0.897711i −0.999774 0.0212540i \(-0.993234\pi\)
0.481481 0.876457i \(-0.340099\pi\)
\(68\) 10.7551 + 6.20944i 0.158163 + 0.0913154i
\(69\) −8.32663 + 17.7820i −0.120676 + 0.257711i
\(70\) 40.5908 + 10.3921i 0.579868 + 0.148458i
\(71\) 55.2444i 0.778090i −0.921219 0.389045i \(-0.872805\pi\)
0.921219 0.389045i \(-0.127195\pi\)
\(72\) 3.42669 + 19.8048i 0.0475929 + 0.275067i
\(73\) 14.8601 + 25.7384i 0.203563 + 0.352581i 0.949674 0.313241i \(-0.101415\pi\)
−0.746111 + 0.665821i \(0.768081\pi\)
\(74\) −155.341 + 89.6861i −2.09920 + 1.21197i
\(75\) −12.3011 + 8.58394i −0.164014 + 0.114452i
\(76\) 93.5856 1.23139
\(77\) −31.4193 + 122.722i −0.408043 + 1.59379i
\(78\) −9.21556 + 19.6804i −0.118148 + 0.252313i
\(79\) −14.9827 + 25.9507i −0.189654 + 0.328490i −0.945135 0.326680i \(-0.894070\pi\)
0.755481 + 0.655171i \(0.227403\pi\)
\(80\) 36.0983 20.8413i 0.451228 0.260517i
\(81\) 76.2912 27.2150i 0.941867 0.335987i
\(82\) −51.8631 + 89.8295i −0.632476 + 1.09548i
\(83\) 78.4979i 0.945758i 0.881127 + 0.472879i \(0.156785\pi\)
−0.881127 + 0.472879i \(0.843215\pi\)
\(84\) −10.9178 + 65.5778i −0.129974 + 0.780688i
\(85\) 8.77189 0.103199
\(86\) −148.153 85.5364i −1.72271 0.994610i
\(87\) 56.3993 4.84320i 0.648268 0.0556690i
\(88\) 20.2076 + 35.0006i 0.229632 + 0.397734i
\(89\) 133.421 + 77.0307i 1.49911 + 0.865513i 0.999999 0.00102332i \(-0.000325734\pi\)
0.499114 + 0.866537i \(0.333659\pi\)
\(90\) −34.4953 41.3787i −0.383282 0.459763i
\(91\) 13.2438 13.5428i 0.145536 0.148822i
\(92\) 20.7198i 0.225215i
\(93\) −62.2363 + 43.4298i −0.669207 + 0.466987i
\(94\) −51.9421 89.9663i −0.552575 0.957089i
\(95\) 57.2466 33.0514i 0.602596 0.347909i
\(96\) 70.3318 + 100.788i 0.732623 + 1.04987i
\(97\) 32.8490 0.338650 0.169325 0.985560i \(-0.445841\pi\)
0.169325 + 0.985560i \(0.445841\pi\)
\(98\) 63.0316 115.030i 0.643180 1.17378i
\(99\) 125.104 104.293i 1.26368 1.05347i
\(100\) −7.91434 + 13.7080i −0.0791434 + 0.137080i
\(101\) −52.7241 + 30.4403i −0.522021 + 0.301389i −0.737761 0.675062i \(-0.764117\pi\)
0.215740 + 0.976451i \(0.430784\pi\)
\(102\) 2.69540 + 31.3881i 0.0264255 + 0.307726i
\(103\) 22.1261 38.3235i 0.214816 0.372073i −0.738399 0.674364i \(-0.764418\pi\)
0.953216 + 0.302291i \(0.0977513\pi\)
\(104\) 6.04319i 0.0581076i
\(105\) 16.4815 + 43.9700i 0.156966 + 0.418762i
\(106\) 2.43299 0.0229528
\(107\) −129.731 74.9005i −1.21244 0.700004i −0.249152 0.968464i \(-0.580152\pi\)
−0.963291 + 0.268460i \(0.913485\pi\)
\(108\) 60.7298 60.1485i 0.562313 0.556930i
\(109\) 41.1471 + 71.2689i 0.377496 + 0.653843i 0.990697 0.136084i \(-0.0434517\pi\)
−0.613201 + 0.789927i \(0.710118\pi\)
\(110\) −93.8116 54.1622i −0.852833 0.492383i
\(111\) −182.052 85.2480i −1.64011 0.768000i
\(112\) −35.1774 125.656i −0.314084 1.12193i
\(113\) 56.1617i 0.497006i 0.968631 + 0.248503i \(0.0799386\pi\)
−0.968631 + 0.248503i \(0.920061\pi\)
\(114\) 135.857 + 194.687i 1.19173 + 1.70778i
\(115\) 7.31754 + 12.6743i 0.0636308 + 0.110212i
\(116\) 51.7313 29.8671i 0.445959 0.257475i
\(117\) −23.9977 + 4.15214i −0.205108 + 0.0354884i
\(118\) 63.8353 0.540977
\(119\) 6.81074 26.6024i 0.0572331 0.223549i
\(120\) 13.5672 + 6.35300i 0.113060 + 0.0529417i
\(121\) 103.254 178.841i 0.853338 1.47802i
\(122\) −117.507 + 67.8426i −0.963170 + 0.556086i
\(123\) −115.820 + 9.94586i −0.941626 + 0.0808607i
\(124\) −40.0420 + 69.3547i −0.322919 + 0.559312i
\(125\) 11.1803i 0.0894427i
\(126\) −152.271 + 72.4858i −1.20850 + 0.575284i
\(127\) 31.3811 0.247095 0.123548 0.992339i \(-0.460573\pi\)
0.123548 + 0.992339i \(0.460573\pi\)
\(128\) −60.5431 34.9546i −0.472993 0.273083i
\(129\) −16.4035 191.019i −0.127159 1.48077i
\(130\) 8.09874 + 14.0274i 0.0622980 + 0.107903i
\(131\) −0.204424 0.118024i −0.00156049 0.000900947i 0.499220 0.866476i \(-0.333620\pi\)
−0.500780 + 0.865575i \(0.666953\pi\)
\(132\) 72.8861 155.653i 0.552168 1.17919i
\(133\) −55.7864 199.273i −0.419446 1.49829i
\(134\) 185.914i 1.38741i
\(135\) 15.9062 58.2408i 0.117824 0.431413i
\(136\) −4.38039 7.58705i −0.0322087 0.0557872i
\(137\) 234.604 135.448i 1.71244 0.988675i 0.781182 0.624303i \(-0.214617\pi\)
0.931253 0.364372i \(-0.118716\pi\)
\(138\) −43.1035 + 30.0785i −0.312344 + 0.217960i
\(139\) −70.1988 −0.505027 −0.252514 0.967593i \(-0.581257\pi\)
−0.252514 + 0.967593i \(0.581257\pi\)
\(140\) 35.4272 + 34.6450i 0.253051 + 0.247464i
\(141\) 49.3718 105.436i 0.350154 0.747776i
\(142\) 73.9415 128.071i 0.520715 0.901905i
\(143\) −42.4105 + 24.4857i −0.296577 + 0.171229i
\(144\) −57.8858 + 157.467i −0.401984 + 1.09352i
\(145\) 21.0961 36.5396i 0.145491 0.251997i
\(146\) 79.5575i 0.544914i
\(147\) 146.144 15.8435i 0.994175 0.107779i
\(148\) −212.129 −1.43330
\(149\) 50.9648 + 29.4245i 0.342046 + 0.197480i 0.661176 0.750231i \(-0.270058\pi\)
−0.319131 + 0.947711i \(0.603391\pi\)
\(150\) −40.0061 + 3.43546i −0.266707 + 0.0229031i
\(151\) 128.237 + 222.112i 0.849249 + 1.47094i 0.881879 + 0.471475i \(0.156278\pi\)
−0.0326304 + 0.999467i \(0.510388\pi\)
\(152\) −57.1741 33.0095i −0.376145 0.217168i
\(153\) −27.1187 + 22.6075i −0.177247 + 0.147762i
\(154\) −237.095 + 242.448i −1.53958 + 1.57434i
\(155\) 56.5661i 0.364942i
\(156\) −21.0756 + 14.7070i −0.135100 + 0.0942754i
\(157\) −36.6914 63.5513i −0.233703 0.404785i 0.725192 0.688547i \(-0.241751\pi\)
−0.958895 + 0.283761i \(0.908418\pi\)
\(158\) −69.4672 + 40.1069i −0.439666 + 0.253841i
\(159\) 1.56037 + 2.23606i 0.00981364 + 0.0140633i
\(160\) 91.6053 0.572533
\(161\) 44.1188 12.3510i 0.274030 0.0767145i
\(162\) 213.288 + 39.0204i 1.31659 + 0.240866i
\(163\) −32.3989 + 56.1166i −0.198766 + 0.344274i −0.948129 0.317887i \(-0.897027\pi\)
0.749362 + 0.662160i \(0.230360\pi\)
\(164\) −106.234 + 61.3342i −0.647768 + 0.373989i
\(165\) −10.3868 120.954i −0.0629501 0.733057i
\(166\) −105.065 + 181.978i −0.632922 + 1.09625i
\(167\) 208.422i 1.24803i −0.781411 0.624017i \(-0.785500\pi\)
0.781411 0.624017i \(-0.214500\pi\)
\(168\) 29.8006 36.2124i 0.177385 0.215550i
\(169\) −161.677 −0.956671
\(170\) 20.3355 + 11.7407i 0.119620 + 0.0690629i
\(171\) −91.7985 + 249.720i −0.536833 + 1.46035i
\(172\) −101.157 175.209i −0.588121 1.01866i
\(173\) 152.382 + 87.9780i 0.880823 + 0.508543i 0.870930 0.491408i \(-0.163518\pi\)
0.00989305 + 0.999951i \(0.496851\pi\)
\(174\) 137.230 + 64.2596i 0.788680 + 0.369308i
\(175\) 33.9064 + 8.68073i 0.193751 + 0.0496042i
\(176\) 337.351i 1.91676i
\(177\) 40.9399 + 58.6682i 0.231299 + 0.331459i
\(178\) 206.203 + 357.153i 1.15844 + 2.00648i
\(179\) 119.555 69.0248i 0.667902 0.385614i −0.127379 0.991854i \(-0.540656\pi\)
0.795281 + 0.606240i \(0.207323\pi\)
\(180\) −10.8618 62.7765i −0.0603431 0.348758i
\(181\) 220.457 1.21800 0.608998 0.793172i \(-0.291572\pi\)
0.608998 + 0.793172i \(0.291572\pi\)
\(182\) 48.8288 13.6696i 0.268290 0.0751077i
\(183\) −137.713 64.4854i −0.752527 0.352379i
\(184\) 7.30826 12.6583i 0.0397188 0.0687950i
\(185\) −129.760 + 74.9169i −0.701404 + 0.404956i
\(186\) −202.408 + 17.3814i −1.08821 + 0.0934486i
\(187\) −35.4968 + 61.4822i −0.189822 + 0.328782i
\(188\) 122.855i 0.653485i
\(189\) −164.276 93.4583i −0.869184 0.494488i
\(190\) 176.950 0.931314
\(191\) 164.995 + 95.2597i 0.863846 + 0.498742i 0.865298 0.501257i \(-0.167129\pi\)
−0.00145232 + 0.999999i \(0.500462\pi\)
\(192\) 9.00936 + 104.914i 0.0469238 + 0.546429i
\(193\) 50.5882 + 87.6213i 0.262115 + 0.453996i 0.966804 0.255520i \(-0.0822467\pi\)
−0.704689 + 0.709517i \(0.748913\pi\)
\(194\) 76.1523 + 43.9666i 0.392538 + 0.226632i
\(195\) −7.69798 + 16.4395i −0.0394768 + 0.0843051i
\(196\) 132.574 80.5401i 0.676397 0.410919i
\(197\) 73.4072i 0.372625i −0.982491 0.186313i \(-0.940346\pi\)
0.982491 0.186313i \(-0.0596537\pi\)
\(198\) 429.614 74.3330i 2.16977 0.375419i
\(199\) 39.3463 + 68.1497i 0.197720 + 0.342461i 0.947789 0.318899i \(-0.103313\pi\)
−0.750069 + 0.661360i \(0.769980\pi\)
\(200\) 9.67019 5.58309i 0.0483509 0.0279154i
\(201\) 170.865 119.233i 0.850075 0.593200i
\(202\) −162.970 −0.806784
\(203\) −94.4333 92.3482i −0.465189 0.454917i
\(204\) −15.7995 + 33.7407i −0.0774483 + 0.165396i
\(205\) −43.3224 + 75.0367i −0.211329 + 0.366032i
\(206\) 102.588 59.2291i 0.497999 0.287520i
\(207\) −55.2877 20.3241i −0.267091 0.0981840i
\(208\) 25.2216 43.6851i 0.121258 0.210024i
\(209\) 534.989i 2.55976i
\(210\) −20.6432 + 123.993i −0.0983010 + 0.590444i
\(211\) −26.1357 −0.123866 −0.0619329 0.998080i \(-0.519726\pi\)
−0.0619329 + 0.998080i \(0.519726\pi\)
\(212\) 2.49181 + 1.43865i 0.0117538 + 0.00678608i
\(213\) 165.125 14.1799i 0.775237 0.0665722i
\(214\) −200.500 347.277i −0.936917 1.62279i
\(215\) −123.756 71.4506i −0.575610 0.332328i
\(216\) −58.3171 + 15.3258i −0.269987 + 0.0709528i
\(217\) 171.547 + 43.9195i 0.790539 + 0.202394i
\(218\) 220.292i 1.01052i
\(219\) −73.1178 + 51.0231i −0.333871 + 0.232982i
\(220\) −64.0531 110.943i −0.291151 0.504288i
\(221\) 9.19329 5.30775i 0.0415986 0.0240170i
\(222\) −307.944 441.293i −1.38713 1.98781i
\(223\) −383.186 −1.71832 −0.859161 0.511705i \(-0.829014\pi\)
−0.859161 + 0.511705i \(0.829014\pi\)
\(224\) 71.1249 277.810i 0.317522 1.24022i
\(225\) −28.8148 34.5646i −0.128066 0.153620i
\(226\) −75.1693 + 130.197i −0.332608 + 0.576093i
\(227\) −207.499 + 119.799i −0.914091 + 0.527751i −0.881745 0.471726i \(-0.843631\pi\)
−0.0323460 + 0.999477i \(0.510298\pi\)
\(228\) 24.0211 + 279.727i 0.105356 + 1.22687i
\(229\) 178.359 308.927i 0.778861 1.34903i −0.153738 0.988112i \(-0.549131\pi\)
0.932599 0.360915i \(-0.117536\pi\)
\(230\) 39.1765i 0.170332i
\(231\) −374.881 62.4126i −1.62286 0.270185i
\(232\) −42.1388 −0.181633
\(233\) −51.5126 29.7408i −0.221084 0.127643i 0.385368 0.922763i \(-0.374075\pi\)
−0.606452 + 0.795120i \(0.707408\pi\)
\(234\) −61.1901 22.4938i −0.261496 0.0961275i
\(235\) −43.3884 75.1510i −0.184632 0.319791i
\(236\) 65.3786 + 37.7464i 0.277028 + 0.159942i
\(237\) −81.4124 38.1222i −0.343512 0.160853i
\(238\) 51.3948 52.5552i 0.215945 0.220820i
\(239\) 279.616i 1.16994i −0.811054 0.584971i \(-0.801106\pi\)
0.811054 0.584971i \(-0.198894\pi\)
\(240\) 71.5603 + 102.548i 0.298168 + 0.427284i
\(241\) 110.381 + 191.186i 0.458014 + 0.793304i 0.998856 0.0478204i \(-0.0152275\pi\)
−0.540842 + 0.841124i \(0.681894\pi\)
\(242\) 478.737 276.399i 1.97825 1.14215i
\(243\) 100.928 + 221.049i 0.415340 + 0.909666i
\(244\) −160.464 −0.657637
\(245\) 52.6518 96.0874i 0.214905 0.392193i
\(246\) −281.812 131.962i −1.14558 0.536429i
\(247\) 39.9978 69.2783i 0.161934 0.280479i
\(248\) 48.9256 28.2472i 0.197281 0.113900i
\(249\) −234.630 + 20.1485i −0.942290 + 0.0809177i
\(250\) −14.9643 + 25.9189i −0.0598571 + 0.103675i
\(251\) 289.707i 1.15421i −0.816670 0.577106i \(-0.804182\pi\)
0.816670 0.577106i \(-0.195818\pi\)
\(252\) −198.814 15.8012i −0.788946 0.0627031i
\(253\) −118.446 −0.468166
\(254\) 72.7494 + 42.0019i 0.286415 + 0.165362i
\(255\) 2.25153 + 26.2192i 0.00882953 + 0.102820i
\(256\) −163.770 283.658i −0.639726 1.10804i
\(257\) 135.364 + 78.1525i 0.526709 + 0.304095i 0.739675 0.672964i \(-0.234979\pi\)
−0.212966 + 0.977060i \(0.568312\pi\)
\(258\) 217.641 464.786i 0.843570 1.80150i
\(259\) 126.450 + 451.688i 0.488223 + 1.74397i
\(260\) 19.1554i 0.0736747i
\(261\) 28.9527 + 167.334i 0.110930 + 0.641128i
\(262\) −0.315937 0.547219i −0.00120587 0.00208862i
\(263\) −25.0501 + 14.4627i −0.0952475 + 0.0549912i −0.546867 0.837219i \(-0.684180\pi\)
0.451620 + 0.892211i \(0.350846\pi\)
\(264\) −99.4300 + 69.3844i −0.376629 + 0.262820i
\(265\) 2.03234 0.00766919
\(266\) 137.389 536.632i 0.516499 2.01741i
\(267\) −195.999 + 418.567i −0.734078 + 1.56767i
\(268\) 109.932 190.408i 0.410195 0.710479i
\(269\) −175.613 + 101.390i −0.652838 + 0.376916i −0.789543 0.613696i \(-0.789682\pi\)
0.136705 + 0.990612i \(0.456349\pi\)
\(270\) 114.827 113.727i 0.425284 0.421213i
\(271\) 189.529 328.273i 0.699367 1.21134i −0.269319 0.963051i \(-0.586799\pi\)
0.968686 0.248288i \(-0.0798681\pi\)
\(272\) 73.1272i 0.268850i
\(273\) 43.8788 + 36.1096i 0.160728 + 0.132270i
\(274\) 725.161 2.64657
\(275\) −78.3631 45.2429i −0.284957 0.164520i
\(276\) −61.9313 + 5.31825i −0.224389 + 0.0192690i
\(277\) 66.1143 + 114.513i 0.238680 + 0.413406i 0.960336 0.278846i \(-0.0899520\pi\)
−0.721656 + 0.692252i \(0.756619\pi\)
\(278\) −162.739 93.9572i −0.585391 0.337975i
\(279\) −145.786 174.877i −0.522531 0.626798i
\(280\) −9.42352 33.6615i −0.0336554 0.120220i
\(281\) 33.0779i 0.117715i 0.998266 + 0.0588574i \(0.0187457\pi\)
−0.998266 + 0.0588574i \(0.981254\pi\)
\(282\) 255.577 178.347i 0.906302 0.632436i
\(283\) −39.7064 68.7735i −0.140305 0.243016i 0.787306 0.616562i \(-0.211475\pi\)
−0.927612 + 0.373546i \(0.878142\pi\)
\(284\) 151.458 87.4445i 0.533304 0.307903i
\(285\) 113.484 + 162.627i 0.398191 + 0.570620i
\(286\) −131.091 −0.458360
\(287\) 193.926 + 189.644i 0.675699 + 0.660780i
\(288\) −283.202 + 236.092i −0.983341 + 0.819762i
\(289\) −136.805 + 236.954i −0.473375 + 0.819910i
\(290\) 97.8124 56.4720i 0.337284 0.194731i
\(291\) 8.43154 + 98.1856i 0.0289744 + 0.337408i
\(292\) −47.0430 + 81.4809i −0.161106 + 0.279044i
\(293\) 127.804i 0.436192i 0.975927 + 0.218096i \(0.0699846\pi\)
−0.975927 + 0.218096i \(0.930015\pi\)
\(294\) 360.004 + 158.876i 1.22450 + 0.540395i
\(295\) 53.3231 0.180756
\(296\) 129.595 + 74.8219i 0.437822 + 0.252777i
\(297\) 343.843 + 347.167i 1.15772 + 1.16891i
\(298\) 78.7663 + 136.427i 0.264316 + 0.457809i
\(299\) 15.3381 + 8.85548i 0.0512981 + 0.0296170i
\(300\) −43.0047 20.1374i −0.143349 0.0671248i
\(301\) −312.775 + 319.836i −1.03912 + 1.06258i
\(302\) 686.550i 2.27335i
\(303\) −104.519 149.779i −0.344947 0.494320i
\(304\) −275.534 477.239i −0.906361 1.56986i
\(305\) −98.1561 + 56.6705i −0.321823 + 0.185805i
\(306\) −93.1270 + 16.1131i −0.304337 + 0.0526572i
\(307\) 178.227 0.580545 0.290273 0.956944i \(-0.406254\pi\)
0.290273 + 0.956944i \(0.406254\pi\)
\(308\) −386.188 + 108.113i −1.25386 + 0.351017i
\(309\) 120.228 + 56.2982i 0.389088 + 0.182195i
\(310\) −75.7105 + 131.135i −0.244228 + 0.423015i
\(311\) 440.590 254.375i 1.41669 0.817926i 0.420683 0.907208i \(-0.361790\pi\)
0.996006 + 0.0892815i \(0.0284571\pi\)
\(312\) 18.0631 1.55114i 0.0578945 0.00497160i
\(313\) 149.067 258.191i 0.476251 0.824892i −0.523378 0.852100i \(-0.675329\pi\)
0.999630 + 0.0272088i \(0.00866190\pi\)
\(314\) 196.437i 0.625597i
\(315\) −127.196 + 60.5491i −0.403797 + 0.192219i
\(316\) −94.8623 −0.300197
\(317\) −272.046 157.066i −0.858190 0.495476i 0.00521565 0.999986i \(-0.498340\pi\)
−0.863406 + 0.504510i \(0.831673\pi\)
\(318\) 0.624490 + 7.27222i 0.00196381 + 0.0228686i
\(319\) 170.737 + 295.726i 0.535227 + 0.927040i
\(320\) 67.9712 + 39.2432i 0.212410 + 0.122635i
\(321\) 190.579 406.992i 0.593703 1.26789i
\(322\) 118.810 + 30.4177i 0.368974 + 0.0944650i
\(323\) 115.969i 0.359038i
\(324\) 195.372 + 166.083i 0.602999 + 0.512601i
\(325\) 6.76507 + 11.7174i 0.0208156 + 0.0360537i
\(326\) −150.218 + 86.7284i −0.460791 + 0.266038i
\(327\) −202.461 + 141.282i −0.619147 + 0.432054i
\(328\) 86.5351 0.263826
\(329\) −261.597 + 73.2340i −0.795128 + 0.222596i
\(330\) 137.812 294.305i 0.417611 0.891834i
\(331\) 72.4842 125.546i 0.218985 0.379294i −0.735513 0.677511i \(-0.763059\pi\)
0.954498 + 0.298217i \(0.0963920\pi\)
\(332\) −215.210 + 124.252i −0.648224 + 0.374253i
\(333\) 208.078 566.035i 0.624858 1.69981i
\(334\) 278.961 483.174i 0.835212 1.44663i
\(335\) 155.298i 0.463576i
\(336\) 366.558 137.398i 1.09095 0.408923i
\(337\) −187.624 −0.556748 −0.278374 0.960473i \(-0.589796\pi\)
−0.278374 + 0.960473i \(0.589796\pi\)
\(338\) −374.809 216.396i −1.10890 0.640226i
\(339\) −167.867 + 14.4153i −0.495184 + 0.0425231i
\(340\) 13.8847 + 24.0491i 0.0408375 + 0.0707326i
\(341\) −396.472 228.903i −1.16267 0.671270i
\(342\) −547.049 + 456.047i −1.59956 + 1.33347i
\(343\) −250.522 234.281i −0.730385 0.683035i
\(344\) 142.720i 0.414884i
\(345\) −36.0054 + 25.1253i −0.104363 + 0.0728270i
\(346\) 235.507 + 407.911i 0.680657 + 1.17893i
\(347\) −516.443 + 298.168i −1.48831 + 0.859274i −0.999911 0.0133476i \(-0.995751\pi\)
−0.488396 + 0.872622i \(0.662418\pi\)
\(348\) 102.551 + 146.959i 0.294686 + 0.422295i
\(349\) −44.7573 −0.128244 −0.0641221 0.997942i \(-0.520425\pi\)
−0.0641221 + 0.997942i \(0.520425\pi\)
\(350\) 66.9850 + 65.5060i 0.191386 + 0.187160i
\(351\) −18.5704 70.6633i −0.0529071 0.201320i
\(352\) −370.695 + 642.062i −1.05311 + 1.82404i
\(353\) −552.513 + 318.993i −1.56519 + 0.903664i −0.568475 + 0.822701i \(0.692466\pi\)
−0.996717 + 0.0809631i \(0.974200\pi\)
\(354\) 16.3850 + 190.804i 0.0462852 + 0.538993i
\(355\) 61.7651 106.980i 0.173986 0.301353i
\(356\) 487.717i 1.36999i
\(357\) 81.2626 + 13.5291i 0.227626 + 0.0378967i
\(358\) 369.544 1.03224
\(359\) 95.5156 + 55.1460i 0.266060 + 0.153610i 0.627096 0.778942i \(-0.284243\pi\)
−0.361036 + 0.932552i \(0.617577\pi\)
\(360\) −15.5067 + 42.1831i −0.0430743 + 0.117175i
\(361\) −256.457 444.196i −0.710407 1.23046i
\(362\) 511.076 + 295.070i 1.41181 + 0.815110i
\(363\) 561.058 + 262.722i 1.54561 + 0.723751i
\(364\) 58.0923 + 14.8728i 0.159594 + 0.0408594i
\(365\) 66.4562i 0.182072i
\(366\) −232.942 333.814i −0.636455 0.912060i
\(367\) −296.749 513.984i −0.808581 1.40050i −0.913847 0.406059i \(-0.866903\pi\)
0.105266 0.994444i \(-0.466430\pi\)
\(368\) 105.660 61.0029i 0.287120 0.165769i
\(369\) −59.4564 343.633i −0.161128 0.931255i
\(370\) −401.088 −1.08402
\(371\) 1.57796 6.16343i 0.00425327 0.0166130i
\(372\) −217.579 101.884i −0.584890 0.273881i
\(373\) 92.0852 159.496i 0.246877 0.427604i −0.715781 0.698325i \(-0.753929\pi\)
0.962658 + 0.270722i \(0.0872623\pi\)
\(374\) −164.581 + 95.0209i −0.440056 + 0.254067i
\(375\) −33.4180 + 2.86972i −0.0891147 + 0.00765259i
\(376\) −43.3335 + 75.0558i −0.115249 + 0.199616i
\(377\) 51.0599i 0.135437i
\(378\) −255.744 436.534i −0.676573 1.15485i
\(379\) 486.561 1.28380 0.641901 0.766787i \(-0.278146\pi\)
0.641901 + 0.766787i \(0.278146\pi\)
\(380\) 181.228 + 104.632i 0.476915 + 0.275347i
\(381\) 8.05477 + 93.7982i 0.0211411 + 0.246189i
\(382\) 255.000 + 441.672i 0.667538 + 1.15621i
\(383\) 517.073 + 298.532i 1.35006 + 0.779458i 0.988258 0.152797i \(-0.0488280\pi\)
0.361803 + 0.932255i \(0.382161\pi\)
\(384\) 88.9393 189.935i 0.231613 0.494623i
\(385\) −198.051 + 202.522i −0.514417 + 0.526032i
\(386\) 270.838i 0.701653i
\(387\) 566.745 98.0599i 1.46446 0.253385i
\(388\) 51.9956 + 90.0591i 0.134009 + 0.232111i
\(389\) −262.695 + 151.667i −0.675310 + 0.389890i −0.798085 0.602544i \(-0.794154\pi\)
0.122776 + 0.992434i \(0.460820\pi\)
\(390\) −39.8492 + 27.8076i −0.102177 + 0.0713016i
\(391\) 25.6755 0.0656661
\(392\) −109.401 + 2.44280i −0.279085 + 0.00623164i
\(393\) 0.300303 0.641316i 0.000764130 0.00163185i
\(394\) 98.2514 170.176i 0.249369 0.431920i
\(395\) −58.0276 + 33.5022i −0.146905 + 0.0848158i
\(396\) 483.954 + 177.904i 1.22211 + 0.449253i
\(397\) −140.150 + 242.747i −0.353022 + 0.611452i −0.986777 0.162081i \(-0.948179\pi\)
0.633755 + 0.773534i \(0.281513\pi\)
\(398\) 210.651i 0.529274i
\(399\) 581.307 217.894i 1.45691 0.546100i
\(400\) 93.2053 0.233013
\(401\) 110.748 + 63.9406i 0.276180 + 0.159453i 0.631693 0.775219i \(-0.282360\pi\)
−0.355513 + 0.934671i \(0.615694\pi\)
\(402\) 555.695 47.7195i 1.38233 0.118705i
\(403\) 34.2273 + 59.2835i 0.0849313 + 0.147105i
\(404\) −166.910 96.3658i −0.413145 0.238529i
\(405\) 178.165 + 32.5946i 0.439912 + 0.0804805i
\(406\) −95.3173 340.480i −0.234772 0.838622i
\(407\) 1212.65i 2.97948i
\(408\) 21.5534 15.0404i 0.0528269 0.0368637i
\(409\) −48.0455 83.2172i −0.117471 0.203465i 0.801294 0.598271i \(-0.204145\pi\)
−0.918765 + 0.394806i \(0.870812\pi\)
\(410\) −200.865 + 115.969i −0.489914 + 0.282852i
\(411\) 465.073 + 666.464i 1.13156 + 1.62157i
\(412\) 140.091 0.340026
\(413\) 41.4016 161.712i 0.100246 0.391555i
\(414\) −100.968 121.116i −0.243885 0.292551i
\(415\) −87.7634 + 152.011i −0.211478 + 0.366291i
\(416\) 96.0059 55.4290i 0.230783 0.133243i
\(417\) −18.0183 209.824i −0.0432094 0.503175i
\(418\) −716.053 + 1240.24i −1.71305 + 2.96708i
\(419\) 339.702i 0.810745i −0.914152 0.405373i \(-0.867142\pi\)
0.914152 0.405373i \(-0.132858\pi\)
\(420\) −94.4605 + 114.784i −0.224906 + 0.273296i
\(421\) −323.174 −0.767634 −0.383817 0.923409i \(-0.625391\pi\)
−0.383817 + 0.923409i \(0.625391\pi\)
\(422\) −60.5891 34.9811i −0.143576 0.0828937i
\(423\) 327.822 + 120.509i 0.774993 + 0.284892i
\(424\) −1.01488 1.75782i −0.00239359 0.00414581i
\(425\) 16.9867 + 9.80727i 0.0399687 + 0.0230759i
\(426\) 401.782 + 188.139i 0.943150 + 0.441640i
\(427\) 95.6523 + 341.677i 0.224010 + 0.800180i
\(428\) 474.230i 1.10801i
\(429\) −84.0735 120.480i −0.195976 0.280839i
\(430\) −191.265 331.281i −0.444803 0.770421i
\(431\) −234.768 + 135.543i −0.544705 + 0.314485i −0.746984 0.664843i \(-0.768499\pi\)
0.202279 + 0.979328i \(0.435165\pi\)
\(432\) −485.527 132.603i −1.12390 0.306950i
\(433\) 642.220 1.48319 0.741594 0.670849i \(-0.234070\pi\)
0.741594 + 0.670849i \(0.234070\pi\)
\(434\) 338.905 + 331.423i 0.780888 + 0.763646i
\(435\) 114.632 + 53.6775i 0.263521 + 0.123397i
\(436\) −130.261 + 225.618i −0.298763 + 0.517473i
\(437\) 167.562 96.7418i 0.383437 0.221377i
\(438\) −237.797 + 20.4205i −0.542916 + 0.0466221i
\(439\) −267.354 + 463.071i −0.609007 + 1.05483i 0.382398 + 0.923998i \(0.375098\pi\)
−0.991404 + 0.130833i \(0.958235\pi\)
\(440\) 90.3712i 0.205389i
\(441\) 84.8676 + 432.757i 0.192444 + 0.981308i
\(442\) 28.4165 0.0642907
\(443\) −174.920 100.990i −0.394854 0.227969i 0.289407 0.957206i \(-0.406542\pi\)
−0.684261 + 0.729237i \(0.739875\pi\)
\(444\) −54.4482 634.052i −0.122631 1.42805i
\(445\) 172.246 + 298.339i 0.387069 + 0.670424i
\(446\) −888.322 512.873i −1.99175 1.14994i
\(447\) −74.8685 + 159.886i −0.167491 + 0.357688i
\(448\) 171.787 175.666i 0.383453 0.392111i
\(449\) 751.940i 1.67470i −0.546668 0.837350i \(-0.684104\pi\)
0.546668 0.837350i \(-0.315896\pi\)
\(450\) −20.5372 118.696i −0.0456382 0.263770i
\(451\) −350.622 607.294i −0.777431 1.34655i
\(452\) −153.973 + 88.8966i −0.340649 + 0.196674i
\(453\) −630.978 + 440.310i −1.39289 + 0.971987i
\(454\) −641.380 −1.41273
\(455\) 40.7878 11.4185i 0.0896436 0.0250957i
\(456\) 83.9901 179.366i 0.184189 0.393347i
\(457\) −7.76422 + 13.4480i −0.0169895 + 0.0294268i −0.874395 0.485214i \(-0.838742\pi\)
0.857406 + 0.514641i \(0.172075\pi\)
\(458\) 826.964 477.448i 1.80560 1.04246i
\(459\) −74.5346 75.2551i −0.162385 0.163954i
\(460\) −23.1654 + 40.1236i −0.0503595 + 0.0872253i
\(461\) 344.491i 0.747269i 0.927576 + 0.373634i \(0.121888\pi\)
−0.927576 + 0.373634i \(0.878112\pi\)
\(462\) −785.533 646.445i −1.70029 1.39923i
\(463\) −172.651 −0.372896 −0.186448 0.982465i \(-0.559698\pi\)
−0.186448 + 0.982465i \(0.559698\pi\)
\(464\) −304.614 175.869i −0.656495 0.379027i
\(465\) −169.076 + 14.5191i −0.363604 + 0.0312239i
\(466\) −79.6129 137.894i −0.170843 0.295909i
\(467\) 593.172 + 342.468i 1.27018 + 0.733336i 0.975021 0.222113i \(-0.0712955\pi\)
0.295155 + 0.955449i \(0.404629\pi\)
\(468\) −49.3687 59.2199i −0.105489 0.126538i
\(469\) −470.969 120.578i −1.00420 0.257095i
\(470\) 232.292i 0.494239i
\(471\) 180.537 125.982i 0.383306 0.267479i
\(472\) −26.6278 46.1207i −0.0564148 0.0977133i
\(473\) 1001.60 578.271i 2.11754 1.22256i
\(474\) −137.710 197.343i −0.290528 0.416335i
\(475\) 147.810 0.311179
\(476\) 83.7137 23.4356i 0.175869 0.0492345i
\(477\) −6.28307 + 5.23788i −0.0131720 + 0.0109809i
\(478\) 374.251 648.221i 0.782951 1.35611i
\(479\) −204.293 + 117.949i −0.426499 + 0.246239i −0.697854 0.716240i \(-0.745862\pi\)
0.271355 + 0.962479i \(0.412528\pi\)
\(480\) 23.5128 + 273.808i 0.0489851 + 0.570433i
\(481\) −90.6623 + 157.032i −0.188487 + 0.326469i
\(482\) 590.958i 1.22605i
\(483\) 48.2415 + 128.701i 0.0998788 + 0.266461i
\(484\) 653.749 1.35072
\(485\) 63.6118 + 36.7263i 0.131158 + 0.0757243i
\(486\) −61.8860 + 647.533i −0.127337 + 1.33237i
\(487\) −261.107 452.251i −0.536155 0.928647i −0.999106 0.0422639i \(-0.986543\pi\)
0.462952 0.886384i \(-0.346790\pi\)
\(488\) 98.0317 + 56.5987i 0.200885 + 0.115981i
\(489\) −176.049 82.4366i −0.360017 0.168582i
\(490\) 250.668 152.283i 0.511567 0.310783i
\(491\) 907.148i 1.84755i 0.382933 + 0.923776i \(0.374914\pi\)
−0.382933 + 0.923776i \(0.625086\pi\)
\(492\) −210.595 301.790i −0.428039 0.613394i
\(493\) −37.0106 64.1042i −0.0750722 0.130029i
\(494\) 185.450 107.070i 0.375405 0.216740i
\(495\) 358.867 62.0921i 0.724983 0.125439i
\(496\) 471.565 0.950736
\(497\) −276.481 270.376i −0.556300 0.544017i
\(498\) −570.900 267.330i −1.14639 0.536808i
\(499\) −23.5236 + 40.7441i −0.0471415 + 0.0816515i −0.888633 0.458618i \(-0.848345\pi\)
0.841492 + 0.540270i \(0.181678\pi\)
\(500\) −30.6521 + 17.6970i −0.0613042 + 0.0353940i
\(501\) 622.972 53.4968i 1.24346 0.106780i
\(502\) 387.757 671.614i 0.772424 1.33788i
\(503\) 55.4203i 0.110180i −0.998481 0.0550898i \(-0.982455\pi\)
0.998481 0.0550898i \(-0.0175445\pi\)
\(504\) 115.888 + 79.7791i 0.229936 + 0.158292i
\(505\) −136.133 −0.269570
\(506\) −274.588 158.534i −0.542664 0.313307i
\(507\) −41.4987 483.254i −0.0818514 0.953163i
\(508\) 49.6722 + 86.0347i 0.0977798 + 0.169360i
\(509\) −220.030 127.035i −0.432280 0.249577i 0.268038 0.963408i \(-0.413625\pi\)
−0.700317 + 0.713832i \(0.746958\pi\)
\(510\) −29.8733 + 63.7963i −0.0585751 + 0.125091i
\(511\) 201.541 + 51.5985i 0.394404 + 0.100976i
\(512\) 597.151i 1.16631i
\(513\) −769.975 210.289i −1.50093 0.409919i
\(514\) 209.206 + 362.355i 0.407015 + 0.704970i
\(515\) 85.6940 49.4754i 0.166396 0.0960688i
\(516\) 497.735 347.330i 0.964602 0.673120i
\(517\) 702.312 1.35844
\(518\) −311.416 + 1216.37i −0.601190 + 2.34821i
\(519\) −223.853 + 478.052i −0.431317 + 0.921103i
\(520\) 6.75649 11.7026i 0.0129933 0.0225050i
\(521\) 188.089 108.593i 0.361016 0.208433i −0.308510 0.951221i \(-0.599830\pi\)
0.669526 + 0.742788i \(0.266497\pi\)
\(522\) −156.848 + 426.675i −0.300475 + 0.817385i
\(523\) 260.787 451.696i 0.498636 0.863664i −0.501362 0.865237i \(-0.667168\pi\)
0.999999 + 0.00157381i \(0.000500960\pi\)
\(524\) 0.747265i 0.00142608i
\(525\) −17.2438 + 103.574i −0.0328452 + 0.197285i
\(526\) −77.4300 −0.147205
\(527\) 85.9429 + 49.6191i 0.163079 + 0.0941540i
\(528\) −1008.34 + 86.5897i −1.90974 + 0.163996i
\(529\) −243.081 421.029i −0.459511 0.795897i
\(530\) 4.71147 + 2.72017i 0.00888957 + 0.00513239i
\(531\) −164.851 + 137.428i −0.310454 + 0.258810i
\(532\) 458.025 468.367i 0.860950 0.880389i
\(533\) 104.855i 0.196726i
\(534\) −1014.60 + 708.012i −1.90001 + 1.32587i
\(535\) −167.483 290.088i −0.313052 0.542221i
\(536\) −134.322 + 77.5506i −0.250600 + 0.144684i
\(537\) 237.002 + 339.631i 0.441344 + 0.632461i
\(538\) −542.822 −1.00896
\(539\) 460.414 + 757.869i 0.854200 + 1.40606i
\(540\) 184.851 48.5790i 0.342316 0.0899610i
\(541\) 39.6152 68.6156i 0.0732260 0.126831i −0.827087 0.562073i \(-0.810004\pi\)
0.900313 + 0.435242i \(0.143337\pi\)
\(542\) 878.750 507.347i 1.62131 0.936064i
\(543\) 56.5860 + 658.947i 0.104210 + 1.21353i
\(544\) 80.3551 139.179i 0.147712 0.255844i
\(545\) 184.015i 0.337643i
\(546\) 53.3916 + 142.441i 0.0977868 + 0.260880i
\(547\) −280.601 −0.512982 −0.256491 0.966547i \(-0.582566\pi\)
−0.256491 + 0.966547i \(0.582566\pi\)
\(548\) 742.693 + 428.794i 1.35528 + 0.782471i
\(549\) 157.399 428.174i 0.286702 0.779917i
\(550\) −121.110 209.769i −0.220201 0.381399i
\(551\) −483.073 278.902i −0.876721 0.506175i
\(552\) 39.7115 + 18.5953i 0.0719411 + 0.0336872i
\(553\) 56.5474 + 201.991i 0.102256 + 0.365265i
\(554\) 353.961i 0.638920i
\(555\) −257.233 368.623i −0.463482 0.664185i
\(556\) −111.115 192.457i −0.199848 0.346147i
\(557\) −798.395 + 460.954i −1.43338 + 0.827565i −0.997377 0.0723785i \(-0.976941\pi\)
−0.436007 + 0.899943i \(0.643608\pi\)
\(558\) −103.906 600.535i −0.186212 1.07623i
\(559\) −172.935 −0.309365
\(560\) 72.3672 282.662i 0.129227 0.504754i
\(561\) −192.881 90.3189i −0.343817 0.160996i
\(562\) −44.2729 + 76.6829i −0.0787774 + 0.136446i
\(563\) 210.180 121.347i 0.373321 0.215537i −0.301587 0.953439i \(-0.597516\pi\)
0.674909 + 0.737901i \(0.264183\pi\)
\(564\) 367.214 31.5339i 0.651089 0.0559112i
\(565\) −62.7907 + 108.757i −0.111134 + 0.192490i
\(566\) 212.579i 0.375581i
\(567\) 237.181 515.009i 0.418309 0.908305i
\(568\) −123.374 −0.217207
\(569\) 247.611 + 142.958i 0.435168 + 0.251245i 0.701546 0.712624i \(-0.252493\pi\)
−0.266378 + 0.963869i \(0.585827\pi\)
\(570\) 45.4187 + 528.902i 0.0796819 + 0.927899i
\(571\) 432.123 + 748.459i 0.756783 + 1.31079i 0.944483 + 0.328560i \(0.106563\pi\)
−0.187701 + 0.982226i \(0.560103\pi\)
\(572\) −134.260 77.5153i −0.234721 0.135516i
\(573\) −242.381 + 517.620i −0.423004 + 0.903350i
\(574\) 195.741 + 699.201i 0.341012 + 1.21812i
\(575\) 32.7250i 0.0569131i
\(576\) −311.277 + 53.8579i −0.540411 + 0.0935034i
\(577\) 348.257 + 603.199i 0.603566 + 1.04541i 0.992276 + 0.124046i \(0.0395872\pi\)
−0.388711 + 0.921360i \(0.627080\pi\)
\(578\) −634.299 + 366.213i −1.09740 + 0.633586i
\(579\) −248.915 + 173.698i −0.429905 + 0.299997i
\(580\) 133.570 0.230292
\(581\) 392.858 + 384.184i 0.676175 + 0.661246i
\(582\) −111.870 + 238.904i −0.192216 + 0.410489i
\(583\) −8.22416 + 14.2447i −0.0141066 + 0.0244334i
\(584\) 57.4799 33.1860i 0.0984244 0.0568254i
\(585\) −51.1135 18.7896i −0.0873736 0.0321190i
\(586\) −171.059 + 296.283i −0.291909 + 0.505602i
\(587\) 596.728i 1.01657i −0.861188 0.508287i \(-0.830279\pi\)
0.861188 0.508287i \(-0.169721\pi\)
\(588\) 274.763 + 375.591i 0.467283 + 0.638759i
\(589\) 747.834 1.26967
\(590\) 123.617 + 71.3700i 0.209520 + 0.120966i
\(591\) 219.414 18.8418i 0.371259 0.0318813i
\(592\) 624.547 + 1081.75i 1.05498 + 1.82728i
\(593\) −394.499 227.764i −0.665260 0.384088i 0.129019 0.991642i \(-0.458817\pi\)
−0.794278 + 0.607554i \(0.792151\pi\)
\(594\) 332.453 + 1265.04i 0.559685 + 2.12969i
\(595\) 42.9313 43.9006i 0.0721534 0.0737825i
\(596\) 186.301i 0.312585i
\(597\) −193.600 + 135.098i −0.324289 + 0.226295i
\(598\) 23.7051 + 41.0585i 0.0396407 + 0.0686597i
\(599\) 974.123 562.410i 1.62625 0.938915i 0.641049 0.767500i \(-0.278499\pi\)
0.985199 0.171415i \(-0.0548338\pi\)
\(600\) 19.1699 + 27.4711i 0.0319499 + 0.0457852i
\(601\) −1026.03 −1.70721 −0.853603 0.520923i \(-0.825588\pi\)
−0.853603 + 0.520923i \(0.825588\pi\)
\(602\) −1153.17 + 322.831i −1.91557 + 0.536264i
\(603\) 400.245 + 480.111i 0.663756 + 0.796204i
\(604\) −405.963 + 703.149i −0.672124 + 1.16415i
\(605\) 399.900 230.883i 0.660992 0.381624i
\(606\) −41.8305 487.118i −0.0690273 0.803826i
\(607\) 302.447 523.854i 0.498266 0.863022i −0.501732 0.865023i \(-0.667304\pi\)
0.999998 + 0.00200136i \(0.000637054\pi\)
\(608\) 1211.07i 1.99189i
\(609\) 251.790 305.965i 0.413448 0.502405i
\(610\) −303.401 −0.497379
\(611\) −90.9456 52.5075i −0.148847 0.0859369i
\(612\) −104.906 38.5642i −0.171416 0.0630133i
\(613\) −377.326 653.548i −0.615540 1.06615i −0.990289 0.139021i \(-0.955605\pi\)
0.374749 0.927126i \(-0.377729\pi\)
\(614\) 413.176 + 238.548i 0.672926 + 0.388514i
\(615\) −235.404 110.231i −0.382771 0.179237i
\(616\) 274.067 + 70.1668i 0.444914 + 0.113907i
\(617\) 145.504i 0.235825i 0.993024 + 0.117912i \(0.0376202\pi\)
−0.993024 + 0.117912i \(0.962380\pi\)
\(618\) 203.368 + 291.432i 0.329074 + 0.471573i
\(619\) 425.339 + 736.709i 0.687139 + 1.19016i 0.972759 + 0.231817i \(0.0744671\pi\)
−0.285620 + 0.958343i \(0.592200\pi\)
\(620\) −155.082 + 89.5366i −0.250132 + 0.144414i
\(621\) 46.5577 170.472i 0.0749721 0.274512i
\(622\) 1361.87 2.18950
\(623\) 1038.50 290.728i 1.66694 0.466659i
\(624\) 137.048 + 64.1745i 0.219629 + 0.102844i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 691.149 399.035i 1.10407 0.637436i
\(627\) −1599.08 + 137.319i −2.55037 + 0.219009i
\(628\) 116.155 201.187i 0.184960 0.320361i
\(629\) 262.865i 0.417909i
\(630\) −375.914 29.8765i −0.596689 0.0474230i
\(631\) −1034.07 −1.63878 −0.819390 0.573237i \(-0.805687\pi\)
−0.819390 + 0.573237i \(0.805687\pi\)
\(632\) 57.9541 + 33.4598i 0.0916995 + 0.0529427i
\(633\) −6.70839 78.1195i −0.0105978 0.123412i
\(634\) −420.448 728.238i −0.663168 1.14864i
\(635\) 60.7693 + 35.0852i 0.0956997 + 0.0552522i
\(636\) −3.66054 + 7.81730i −0.00575556 + 0.0122914i
\(637\) −2.95996 132.562i −0.00464672 0.208104i
\(638\) 914.090i 1.43274i
\(639\) 84.7673 + 489.920i 0.132656 + 0.766698i
\(640\) −78.1608 135.379i −0.122126 0.211529i
\(641\) −619.639 + 357.749i −0.966675 + 0.558110i −0.898221 0.439544i \(-0.855140\pi\)
−0.0684543 + 0.997654i \(0.521807\pi\)
\(642\) 986.546 688.433i 1.53668 1.07233i
\(643\) 47.5168 0.0738986 0.0369493 0.999317i \(-0.488236\pi\)
0.0369493 + 0.999317i \(0.488236\pi\)
\(644\) 103.696 + 101.406i 0.161019 + 0.157463i
\(645\) 181.801 388.246i 0.281861 0.601932i
\(646\) 155.218 268.846i 0.240276 0.416170i
\(647\) −790.372 + 456.321i −1.22159 + 0.705288i −0.965258 0.261299i \(-0.915849\pi\)
−0.256337 + 0.966587i \(0.582516\pi\)
\(648\) −60.7774 170.376i −0.0937923 0.262926i
\(649\) −215.780 + 373.742i −0.332481 + 0.575874i
\(650\) 36.2187i 0.0557210i
\(651\) −87.2434 + 524.027i −0.134015 + 0.804956i
\(652\) −205.133 −0.314621
\(653\) −474.633 274.029i −0.726850 0.419647i 0.0904189 0.995904i \(-0.471179\pi\)
−0.817269 + 0.576257i \(0.804513\pi\)
\(654\) −658.454 + 56.5437i −1.00681 + 0.0864583i
\(655\) −0.263910 0.457105i −0.000402916 0.000697870i
\(656\) 625.546 + 361.159i 0.953576 + 0.550547i
\(657\) −171.276 205.453i −0.260694 0.312713i
\(658\) −704.468 180.358i −1.07062 0.274101i
\(659\) 682.581i 1.03578i 0.855446 + 0.517891i \(0.173283\pi\)
−0.855446 + 0.517891i \(0.826717\pi\)
\(660\) 315.168 219.931i 0.477528 0.333229i
\(661\) −300.416 520.336i −0.454487 0.787195i 0.544171 0.838974i \(-0.316844\pi\)
−0.998659 + 0.0517791i \(0.983511\pi\)
\(662\) 336.073 194.032i 0.507664 0.293100i
\(663\) 18.2245 + 26.1164i 0.0274880 + 0.0393912i
\(664\) 175.304 0.264012
\(665\) 114.764 448.261i 0.172577 0.674077i
\(666\) 1239.98 1033.71i 1.86184 1.55212i
\(667\) 61.7487 106.952i 0.0925768 0.160348i
\(668\) 571.410 329.904i 0.855405 0.493868i
\(669\) −98.3545 1145.34i −0.147017 1.71202i
\(670\) 207.858 360.020i 0.310235 0.537343i
\(671\) 917.302i 1.36707i
\(672\) 848.629 + 141.285i 1.26284 + 0.210246i
\(673\) −161.729 −0.240310 −0.120155 0.992755i \(-0.538339\pi\)
−0.120155 + 0.992755i \(0.538339\pi\)
\(674\) −434.961 251.125i −0.645342 0.372588i
\(675\) 95.9174 94.9992i 0.142100 0.140740i
\(676\) −255.914 443.256i −0.378571 0.655704i
\(677\) 104.116 + 60.1113i 0.153790 + 0.0887907i 0.574920 0.818210i \(-0.305033\pi\)
−0.421130 + 0.907000i \(0.638366\pi\)
\(678\) −408.453 191.263i −0.602438 0.282098i
\(679\) 160.769 164.399i 0.236773 0.242119i
\(680\) 19.5897i 0.0288084i
\(681\) −411.340 589.464i −0.604024 0.865586i
\(682\) −612.748 1061.31i −0.898458 1.55617i
\(683\) −292.871 + 169.089i −0.428801 + 0.247569i −0.698836 0.715282i \(-0.746298\pi\)
0.270034 + 0.962851i \(0.412965\pi\)
\(684\) −829.939 + 143.598i −1.21336 + 0.209939i
\(685\) 605.744 0.884298
\(686\) −267.202 878.433i −0.389507 1.28051i
\(687\) 969.163 + 453.821i 1.41072 + 0.660584i
\(688\) −595.650 + 1031.70i −0.865771 + 1.49956i
\(689\) 2.12997 1.22974i 0.00309139 0.00178482i
\(690\) −117.098 + 10.0556i −0.169708 + 0.0145734i
\(691\) 165.191 286.119i 0.239061 0.414065i −0.721384 0.692535i \(-0.756494\pi\)
0.960445 + 0.278470i \(0.0898272\pi\)
\(692\) 557.030i 0.804956i
\(693\) 90.3286 1136.54i 0.130344 1.64003i
\(694\) −1596.33 −2.30018
\(695\) −135.939 78.4846i −0.195596 0.112928i
\(696\) −10.8160 125.953i −0.0155402 0.180967i
\(697\) 76.0039 + 131.643i 0.109044 + 0.188870i
\(698\) −103.759 59.9051i −0.148651 0.0858239i
\(699\) 75.6732 161.605i 0.108259 0.231194i
\(700\) 29.8702 + 106.699i 0.0426717 + 0.152426i
\(701\) 462.419i 0.659656i −0.944041 0.329828i \(-0.893009\pi\)
0.944041 0.329828i \(-0.106991\pi\)
\(702\) 51.5280 188.671i 0.0734018 0.268762i
\(703\) 990.442 + 1715.50i 1.40888 + 2.44025i
\(704\) −550.111 + 317.607i −0.781408 + 0.451146i
\(705\) 213.490 148.977i 0.302822 0.211316i
\(706\) −1707.82 −2.41901
\(707\) −105.697 + 412.848i −0.149501 + 0.583943i
\(708\) −96.0428 + 205.105i −0.135654 + 0.289697i
\(709\) 277.738 481.056i 0.391732 0.678500i −0.600946 0.799290i \(-0.705209\pi\)
0.992678 + 0.120790i \(0.0385427\pi\)
\(710\) 286.374 165.338i 0.403344 0.232871i
\(711\) 93.0508 253.127i 0.130873 0.356015i
\(712\) 172.028 297.961i 0.241612 0.418484i
\(713\) 165.570i 0.232216i
\(714\) 170.279 + 140.129i 0.238486 + 0.196260i
\(715\) −109.503 −0.153152
\(716\) 378.478 + 218.514i 0.528601 + 0.305188i
\(717\) 835.773 71.7707i 1.16565 0.100099i
\(718\) 147.620 + 255.685i 0.205598 + 0.356107i
\(719\) −874.330 504.795i −1.21604 0.702079i −0.251968 0.967736i \(-0.581078\pi\)
−0.964068 + 0.265657i \(0.914411\pi\)
\(720\) −288.149 + 240.215i −0.400207 + 0.333632i
\(721\) −83.5081 298.297i −0.115823 0.413726i
\(722\) 1373.01i 1.90168i
\(723\) −543.123 + 379.003i −0.751208 + 0.524209i
\(724\) 348.955 + 604.407i 0.481982 + 0.834817i
\(725\) 81.7050 47.1724i 0.112697 0.0650654i
\(726\) 949.037 + 1360.00i 1.30721 + 1.87328i
\(727\) −448.687 −0.617177 −0.308588 0.951196i \(-0.599857\pi\)
−0.308588 + 0.951196i \(0.599857\pi\)
\(728\) −30.2443 29.5765i −0.0415444 0.0406271i
\(729\) −634.809 + 358.410i −0.870795 + 0.491647i
\(730\) −88.9480 + 154.062i −0.121847 + 0.211044i
\(731\) −217.115 + 125.351i −0.297011 + 0.171479i
\(732\) −41.1871 479.625i −0.0562665 0.655226i
\(733\) −50.8478 + 88.0709i −0.0693694 + 0.120151i −0.898624 0.438720i \(-0.855432\pi\)
0.829254 + 0.558871i \(0.188765\pi\)
\(734\) 1588.73i 2.16448i
\(735\) 300.720 + 132.713i 0.409142 + 0.180562i
\(736\) 268.130 0.364307
\(737\) 1088.48 + 628.436i 1.47691 + 0.852695i
\(738\) 322.099 876.208i 0.436448 1.18727i
\(739\) 94.0310 + 162.866i 0.127241 + 0.220388i 0.922607 0.385742i \(-0.126055\pi\)
−0.795366 + 0.606130i \(0.792721\pi\)
\(740\) −410.785 237.167i −0.555115 0.320496i
\(741\) 217.339 + 101.771i 0.293305 + 0.137343i
\(742\) 11.9075 12.1764i 0.0160479 0.0164102i
\(743\) 122.415i 0.164757i −0.996601 0.0823786i \(-0.973748\pi\)
0.996601 0.0823786i \(-0.0262517\pi\)
\(744\) 96.9888 + 138.988i 0.130361 + 0.186812i
\(745\) 65.7953 + 113.961i 0.0883158 + 0.152967i
\(746\) 426.954 246.502i 0.572324 0.330431i
\(747\) −120.448 696.138i −0.161242 0.931912i
\(748\) −224.747 −0.300464
\(749\) −1009.78 + 282.689i −1.34818 + 0.377421i
\(750\) −81.3124 38.0754i −0.108417 0.0507673i
\(751\) 330.331 572.150i 0.439855 0.761850i −0.557823 0.829960i \(-0.688363\pi\)
0.997678 + 0.0681093i \(0.0216967\pi\)
\(752\) −626.499 + 361.709i −0.833110 + 0.480996i
\(753\) 865.934 74.3607i 1.14998 0.0987526i
\(754\) 68.3408 118.370i 0.0906377 0.156989i
\(755\) 573.492i 0.759591i
\(756\) −3.80112 598.312i −0.00502793 0.791418i
\(757\) 225.258 0.297567 0.148783 0.988870i \(-0.452464\pi\)
0.148783 + 0.988870i \(0.452464\pi\)
\(758\) 1127.97 + 651.235i 1.48809 + 0.859149i
\(759\) −30.4022 354.035i −0.0400556 0.466450i
\(760\) −73.8114 127.845i −0.0971203 0.168217i
\(761\) −1106.40 638.781i −1.45388 0.839396i −0.455179 0.890400i \(-0.650425\pi\)
−0.998698 + 0.0510038i \(0.983758\pi\)
\(762\) −106.871 + 228.229i −0.140250 + 0.299513i
\(763\) 558.060 + 142.875i 0.731403 + 0.187254i
\(764\) 603.134i 0.789442i
\(765\) −77.7912 + 13.4596i −0.101688 + 0.0175943i
\(766\) 799.138 + 1384.15i 1.04326 + 1.80698i