Properties

Label 105.3.t.b.11.5
Level 105
Weight 3
Character 105.11
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 11.5
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.31825 + 1.33844i) q^{2} +(2.46021 - 1.71679i) q^{3} +(1.58287 - 2.74161i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.40557 + 7.27281i) q^{6} +(4.89419 + 5.00469i) q^{7} -2.23323i q^{8} +(3.10528 - 8.44732i) q^{9} +O(q^{10})\) \(q+(-2.31825 + 1.33844i) q^{2} +(2.46021 - 1.71679i) 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} +(3.10528 - 8.44732i) q^{9} +(2.99285 - 5.18377i) q^{10} +(15.6726 + 9.04859i) q^{11} +(-0.812567 - 9.46238i) 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} +(4.10744 + 23.7393i) q^{18} +(14.7810 + 25.6015i) q^{19} +7.07880i q^{20} +(20.6327 + 3.91032i) q^{21} -48.4441 q^{22} +(-5.66814 + 3.27250i) q^{23} +(-3.83399 - 5.49423i) 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} +(-1.53638 - 17.8913i) q^{30} +(12.6486 - 21.9079i) q^{31} +(-35.4786 - 20.4836i) q^{32} +(54.0924 - 4.64510i) 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} +(6.65740 - 4.64567i) q^{39} +(2.49683 + 4.32464i) q^{40} +38.7488i q^{41} +(-53.0656 + 18.5507i) q^{42} -63.9074 q^{43} +(49.6153 - 28.6454i) q^{44} +(3.43104 + 19.8300i) 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} +(-11.7256 + 1.00691i) q^{51} +(4.28328 - 7.41886i) q^{52} +(-0.787120 - 0.454444i) q^{53} +(50.8605 + 51.3521i) 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} +(12.1528 + 17.4153i) q^{60} +(-25.3438 - 43.8968i) q^{61} +67.7176i q^{62} +(57.4741 - 25.8018i) q^{63} +35.1002 q^{64} +(-5.24020 + 3.02543i) q^{65} +(-119.183 + 83.1683i) 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} +(-18.8648 - 6.93482i) q^{72} +(14.8601 - 25.7384i) q^{73} +(155.341 + 89.6861i) q^{74} +(-1.28338 - 14.9450i) 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} +(-61.7144 - 52.4626i) q^{81} +(-51.8631 - 89.8295i) q^{82} +78.4979i q^{83} +(43.3794 - 50.3773i) q^{84} +8.77189 q^{85} +(148.153 - 85.5364i) q^{86} +(-32.3940 - 46.4216i) 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} +(-6.49315 - 75.6131i) q^{93} +(-51.9421 + 89.9663i) q^{94} +(-57.2466 - 33.0514i) q^{95} +(-122.451 + 10.5153i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31825 + 1.33844i −1.15913 + 0.669222i −0.951095 0.308900i \(-0.900039\pi\)
−0.208032 + 0.978122i \(0.566706\pi\)
\(3\) 2.46021 1.71679i 0.820071 0.572262i
\(4\) 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
\(9\) 3.10528 8.44732i 0.345031 0.938591i
\(10\) 2.99285 5.18377i 0.299285 0.518377i
\(11\) 15.6726 + 9.04859i 1.42478 + 0.822599i 0.996703 0.0811419i \(-0.0258567\pi\)
0.428080 + 0.903741i \(0.359190\pi\)
\(12\) −0.812567 9.46238i −0.0677139 0.788532i
\(13\) 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 \(-0.370142\pi\)
−0.596582 + 0.802552i \(0.703475\pi\)
\(18\) 4.10744 + 23.7393i 0.228191 + 1.31885i
\(19\) 14.7810 + 25.6015i 0.777948 + 1.34745i 0.933122 + 0.359559i \(0.117073\pi\)
−0.155174 + 0.987887i \(0.549594\pi\)
\(20\) 7.07880i 0.353940i
\(21\) 20.6327 + 3.91032i 0.982511 + 0.186206i
\(22\) −48.4441 −2.20201
\(23\) −5.66814 + 3.27250i −0.246441 + 0.142283i −0.618133 0.786073i \(-0.712111\pi\)
0.371693 + 0.928356i \(0.378778\pi\)
\(24\) −3.83399 5.49423i −0.159750 0.228926i
\(25\) 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 \(-0.105474\pi\)
\(30\) −1.53638 17.8913i −0.0512128 0.596376i
\(31\) 12.6486 21.9079i 0.408018 0.706708i −0.586650 0.809841i \(-0.699553\pi\)
0.994668 + 0.103133i \(0.0328867\pi\)
\(32\) −35.4786 20.4836i −1.10871 0.640111i
\(33\) 54.0924 4.64510i 1.63916 0.140761i
\(34\) 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 −0.820232 0.572031i \(-0.806156\pi\)
−0.0852768 0.996357i \(-0.527177\pi\)
\(38\) −68.5323 39.5671i −1.80348 1.04124i
\(39\) 6.65740 4.64567i 0.170702 0.119120i
\(40\) 2.49683 + 4.32464i 0.0624208 + 0.108116i
\(41\) 38.7488i 0.945092i 0.881306 + 0.472546i \(0.156665\pi\)
−0.881306 + 0.472546i \(0.843335\pi\)
\(42\) −53.0656 + 18.5507i −1.26347 + 0.441682i
\(43\) −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
\(45\) 3.43104 + 19.8300i 0.0762453 + 0.440666i
\(46\) 8.76013 15.1730i 0.190438 0.329847i
\(47\) 33.6085 19.4039i 0.715075 0.412849i −0.0978620 0.995200i \(-0.531200\pi\)
0.812937 + 0.582351i \(0.197867\pi\)
\(48\) 50.6457 + 23.7154i 1.05512 + 0.494071i
\(49\) −1.09384 + 48.9878i −0.0223233 + 0.999751i
\(50\) 13.3844i 0.267689i
\(51\) −11.7256 + 1.00691i −0.229913 + 0.0197434i
\(52\) 4.28328 7.41886i 0.0823708 0.142670i
\(53\) −0.787120 0.454444i −0.0148513 0.00857442i 0.492556 0.870281i \(-0.336063\pi\)
−0.507407 + 0.861706i \(0.669396\pi\)
\(54\) 50.8605 + 51.3521i 0.941860 + 0.950964i
\(55\) −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 \(-0.398107\pi\)
−0.664700 + 0.747110i \(0.731441\pi\)
\(60\) 12.1528 + 17.4153i 0.202547 + 0.290256i
\(61\) −25.3438 43.8968i −0.415472 0.719619i 0.580006 0.814612i \(-0.303050\pi\)
−0.995478 + 0.0949935i \(0.969717\pi\)
\(62\) 67.7176i 1.09222i
\(63\) 57.4741 25.8018i 0.912287 0.409552i
\(64\) 35.1002 0.548440
\(65\) −5.24020 + 3.02543i −0.0806184 + 0.0465451i
\(66\) −119.183 + 83.1683i −1.80580 + 1.26013i
\(67\) −34.7257 + 60.1466i −0.518294 + 0.897711i 0.481481 + 0.876457i \(0.340099\pi\)
−0.999774 + 0.0212540i \(0.993234\pi\)
\(68\) −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 \(-0.127195\pi\)
\(72\) −18.8648 6.93482i −0.262012 0.0963170i
\(73\) 14.8601 25.7384i 0.203563 0.352581i −0.746111 0.665821i \(-0.768081\pi\)
0.949674 + 0.313241i \(0.101415\pi\)
\(74\) 155.341 + 89.6861i 2.09920 + 1.21197i
\(75\) −1.28338 14.9450i −0.0171117 0.199267i
\(76\) 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 0.755481 0.655171i \(-0.227403\pi\)
−0.945135 + 0.326680i \(0.894070\pi\)
\(80\) −36.0983 20.8413i −0.451228 0.260517i
\(81\) −61.7144 52.4626i −0.761907 0.647687i
\(82\) −51.8631 89.8295i −0.632476 1.09548i
\(83\) 78.4979i 0.945758i 0.881127 + 0.472879i \(0.156785\pi\)
−0.881127 + 0.472879i \(0.843215\pi\)
\(84\) 43.3794 50.3773i 0.516422 0.599730i
\(85\) 8.77189 0.103199
\(86\) 148.153 85.5364i 1.72271 0.994610i
\(87\) −32.3940 46.4216i −0.372345 0.533582i
\(88\) 20.2076 35.0006i 0.229632 0.397734i
\(89\) −133.421 + 77.0307i −1.49911 + 0.865513i −0.999999 0.00102332i \(-0.999674\pi\)
−0.499114 + 0.866537i \(0.666341\pi\)
\(90\) −34.4953 41.3787i −0.383282 0.459763i
\(91\) 13.2438 + 13.5428i 0.145536 + 0.148822i
\(92\) 20.7198i 0.225215i
\(93\) −6.49315 75.6131i −0.0698188 0.813044i
\(94\) −51.9421 + 89.9663i −0.552575 + 0.957089i
\(95\) −57.2466 33.0514i −0.602596 0.347909i
\(96\) −122.451 + 10.5153i −1.27553 + 0.109534i
\(97\) 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 \(-0.235883\pi\)
−0.215740 + 0.976451i \(0.569216\pi\)
\(102\) 25.8352 18.0283i 0.253286 0.176748i
\(103\) 22.1261 + 38.3235i 0.214816 + 0.372073i 0.953216 0.302291i \(-0.0977513\pi\)
−0.738399 + 0.674364i \(0.764418\pi\)
\(104\) 6.04319i 0.0581076i
\(105\) −44.3270 + 15.4958i −0.422162 + 0.147579i
\(106\) 2.43299 0.0229528
\(107\) 129.731 74.9005i 1.21244 0.700004i 0.249152 0.968464i \(-0.419848\pi\)
0.963291 + 0.268460i \(0.0865146\pi\)
\(108\) −82.4550 22.5194i −0.763472 0.208513i
\(109\) 41.1471 71.2689i 0.377496 0.653843i −0.613201 0.789927i \(-0.710118\pi\)
0.990697 + 0.136084i \(0.0434517\pi\)
\(110\) 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 \(0.920061\pi\)
\(114\) −236.532 + 20.3118i −2.07485 + 0.178174i
\(115\) 7.31754 12.6743i 0.0636308 0.110212i
\(116\) −51.7313 29.8671i −0.445959 0.257475i
\(117\) 8.40298 22.8587i 0.0718203 0.195373i
\(118\) 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
\(123\) 66.5234 + 95.3302i 0.540840 + 0.775042i
\(124\) −40.0420 69.3547i −0.322919 0.559312i
\(125\) 11.1803i 0.0894427i
\(126\) −98.7052 + 136.741i −0.783374 + 1.08525i
\(127\) 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
\(129\) −157.226 + 109.715i −1.21880 + 0.850506i
\(130\) 8.09874 14.0274i 0.0622980 0.107903i
\(131\) 0.204424 0.118024i 0.00156049 0.000900947i −0.499220 0.866476i \(-0.666380\pi\)
0.500780 + 0.865575i \(0.333047\pi\)
\(132\) 72.8861 155.653i 0.552168 1.17919i
\(133\) −55.7864 + 199.273i −0.419446 + 1.49829i
\(134\) 185.914i 1.38741i
\(135\) 42.4849 + 42.8956i 0.314703 + 0.317745i
\(136\) −4.38039 + 7.58705i −0.0322087 + 0.0557872i
\(137\) −234.604 135.448i −1.71244 0.988675i −0.931253 0.364372i \(-0.881284\pi\)
−0.781182 0.624303i \(-0.785383\pi\)
\(138\) −4.49702 52.3680i −0.0325871 0.379478i
\(139\) −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
\(144\) 165.313 28.6030i 1.14801 0.198632i
\(145\) 21.0961 + 36.5396i 0.145491 + 0.251997i
\(146\) 79.5575i 0.544914i
\(147\) 81.4105 + 122.398i 0.553813 + 0.832641i
\(148\) −212.129 −1.43330
\(149\) −50.9648 + 29.4245i −0.342046 + 0.197480i −0.661176 0.750231i \(-0.729942\pi\)
0.319131 + 0.947711i \(0.396609\pi\)
\(150\) 22.9782 + 32.9286i 0.153188 + 0.219524i
\(151\) 128.237 222.112i 0.849249 1.47094i −0.0326304 0.999467i \(-0.510388\pi\)
0.881879 0.471475i \(-0.156278\pi\)
\(152\) 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
\(156\) −2.19883 25.6054i −0.0140950 0.164137i
\(157\) −36.6914 + 63.5513i −0.233703 + 0.404785i −0.958895 0.283761i \(-0.908418\pi\)
0.725192 + 0.688547i \(0.241751\pi\)
\(158\) 69.4672 + 40.1069i 0.439666 + 0.253841i
\(159\) −2.71667 + 0.233289i −0.0170860 + 0.00146723i
\(160\) 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 0.749362 0.662160i \(-0.230360\pi\)
−0.948129 + 0.317887i \(0.897027\pi\)
\(164\) 106.234 + 61.3342i 0.647768 + 0.373989i
\(165\) −99.5562 + 69.4724i −0.603371 + 0.421045i
\(166\) −105.065 181.978i −0.632922 1.09625i
\(167\) 208.422i 1.24803i −0.781411 0.624017i \(-0.785500\pi\)
0.781411 0.624017i \(-0.214500\pi\)
\(168\) 8.73265 46.0777i 0.0519801 0.274272i
\(169\) −161.677 −0.956671
\(170\) −20.3355 + 11.7407i −0.119620 + 0.0690629i
\(171\) 262.163 45.3602i 1.53312 0.265264i
\(172\) −101.157 + 175.209i −0.588121 + 1.01866i
\(173\) −152.382 + 87.9780i −0.880823 + 0.508543i −0.870930 0.491408i \(-0.836482\pi\)
−0.00989305 + 0.999951i \(0.503149\pi\)
\(174\) 137.230 + 64.2596i 0.788680 + 0.369308i
\(175\) 33.9064 8.68073i 0.193751 0.0496042i
\(176\) 337.351i 1.91676i
\(177\) −71.2781 + 6.12090i −0.402701 + 0.0345813i
\(178\) 206.203 357.153i 1.15844 2.00648i
\(179\) −119.555 69.0248i −0.667902 0.385614i 0.127379 0.991854i \(-0.459344\pi\)
−0.795281 + 0.606240i \(0.792677\pi\)
\(180\) 59.7969 + 21.9817i 0.332205 + 0.122120i
\(181\) 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
\(186\) 116.257 + 166.600i 0.625036 + 0.895696i
\(187\) −35.4968 61.4822i −0.189822 0.328782i
\(188\) 122.855i 0.653485i
\(189\) 97.1021 162.149i 0.513768 0.857929i
\(190\) 176.950 0.931314
\(191\) −164.995 + 95.2597i −0.863846 + 0.498742i −0.865298 0.501257i \(-0.832871\pi\)
0.00145232 + 0.999999i \(0.499538\pi\)
\(192\) 86.3539 60.2595i 0.449760 0.313852i
\(193\) 50.5882 87.6213i 0.262115 0.453996i −0.704689 0.709517i \(-0.748913\pi\)
0.966804 + 0.255520i \(0.0822467\pi\)
\(194\) −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 \(-0.0596537\pi\)
\(198\) −150.433 + 409.223i −0.759761 + 2.06678i
\(199\) 39.3463 68.1497i 0.197720 0.342461i −0.750069 0.661360i \(-0.769980\pi\)
0.947789 + 0.318899i \(0.103313\pi\)
\(200\) −9.67019 5.58309i −0.0483509 0.0279154i
\(201\) 17.8265 + 207.590i 0.0886889 + 1.03279i
\(202\) −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
\(207\) 10.0427 + 58.0426i 0.0485154 + 0.280399i
\(208\) 25.2216 + 43.6851i 0.121258 + 0.210024i
\(209\) 534.989i 2.55976i
\(210\) 82.0209 95.2524i 0.390576 0.453583i
\(211\) −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
\(213\) −94.8429 135.913i −0.445272 0.638089i
\(214\) −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
\(219\) −7.62843 88.8334i −0.0348330 0.405632i
\(220\) −64.0531 + 110.943i −0.291151 + 0.504288i
\(221\) −9.19329 5.30775i −0.0415986 0.0240170i
\(222\) 536.143 46.0404i 2.41506 0.207389i
\(223\) −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 \(-0.156369\pi\)
0.0323460 + 0.999477i \(0.489702\pi\)
\(228\) 230.240 160.667i 1.00983 0.704678i
\(229\) 178.359 + 308.927i 0.778861 + 1.34903i 0.932599 + 0.360915i \(0.117536\pi\)
−0.153738 + 0.988112i \(0.549131\pi\)
\(230\) 39.1765i 0.170332i
\(231\) 287.986 + 247.982i 1.24669 + 1.07351i
\(232\) −42.1388 −0.181633
\(233\) 51.5126 29.7408i 0.221084 0.127643i −0.385368 0.922763i \(-0.625925\pi\)
0.606452 + 0.795120i \(0.292592\pi\)
\(234\) 11.1148 + 64.2391i 0.0474993 + 0.274526i
\(235\) −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 \(-0.198894\pi\)
\(240\) −124.590 + 10.6989i −0.519123 + 0.0445789i
\(241\) 110.381 191.186i 0.458014 0.793304i −0.540842 0.841124i \(-0.681894\pi\)
0.998856 + 0.0478204i \(0.0152275\pi\)
\(242\) −478.737 276.399i −1.97825 1.14215i
\(243\) −241.898 23.1186i −0.995464 0.0951383i
\(244\) −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
\(249\) 134.764 + 193.122i 0.541222 + 0.775588i
\(250\) −14.9643 25.9189i −0.0598571 0.103675i
\(251\) 289.707i 1.15421i −0.816670 0.577106i \(-0.804182\pi\)
0.816670 0.577106i \(-0.195818\pi\)
\(252\) 20.2354 198.412i 0.0802993 0.787350i
\(253\) −118.446 −0.468166
\(254\) −72.7494 + 42.0019i −0.286415 + 0.165362i
\(255\) 21.5807 15.0595i 0.0846302 0.0590567i
\(256\) −163.770 + 283.658i −0.639726 + 1.10804i
\(257\) −135.364 + 78.1525i −0.526709 + 0.304095i −0.739675 0.672964i \(-0.765021\pi\)
0.212966 + 0.977060i \(0.431688\pi\)
\(258\) 217.641 464.786i 0.843570 1.80150i
\(259\) 126.450 451.688i 0.488223 1.74397i
\(260\) 19.1554i 0.0736747i
\(261\) −159.392 58.5934i −0.610698 0.224496i
\(262\) −0.315937 + 0.547219i −0.00120587 + 0.00208862i
\(263\) 25.0501 + 14.4627i 0.0952475 + 0.0549912i 0.546867 0.837219i \(-0.315820\pi\)
−0.451620 + 0.892211i \(0.649154\pi\)
\(264\) −10.3736 120.801i −0.0392940 0.457580i
\(265\) 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 \(-0.210318\pi\)
−0.136705 + 0.990612i \(0.543651\pi\)
\(270\) −155.904 42.5791i −0.577423 0.157700i
\(271\) 189.529 + 328.273i 0.699367 + 1.21134i 0.968686 + 0.248288i \(0.0798681\pi\)
−0.269319 + 0.963051i \(0.586799\pi\)
\(272\) 73.1272i 0.268850i
\(273\) 55.8327 + 10.5814i 0.204515 + 0.0387598i
\(274\) 725.161 2.64657
\(275\) 78.3631 45.2429i 0.284957 0.164520i
\(276\) 35.5714 + 50.9750i 0.128882 + 0.184692i
\(277\) 66.1143 114.513i 0.238680 0.413406i −0.721656 0.692252i \(-0.756619\pi\)
0.960336 + 0.278846i \(0.0899520\pi\)
\(278\) 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 \(0.981254\pi\)
\(282\) 26.6645 + 310.510i 0.0945551 + 1.10110i
\(283\) −39.7064 + 68.7735i −0.140305 + 0.243016i −0.927612 0.373546i \(-0.878142\pi\)
0.787306 + 0.616562i \(0.211475\pi\)
\(284\) −151.458 87.4445i −0.533304 0.307903i
\(285\) −197.581 + 16.9670i −0.693267 + 0.0595332i
\(286\) −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
\(291\) 80.8155 56.3947i 0.277716 0.193796i
\(292\) −47.0430 81.4809i −0.161106 0.279044i
\(293\) 127.804i 0.436192i 0.975927 + 0.218096i \(0.0699846\pi\)
−0.975927 + 0.218096i \(0.930015\pi\)
\(294\) −352.554 174.787i −1.19916 0.594513i
\(295\) 53.3231 0.180756
\(296\) −129.595 + 74.8219i −0.437822 + 0.252777i
\(297\) 128.734 471.361i 0.433447 1.58707i
\(298\) 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
\(303\) 181.972 15.6265i 0.600567 0.0515728i
\(304\) −275.534 + 477.239i −0.906361 + 1.56986i
\(305\) 98.1561 + 56.6705i 0.321823 + 0.185805i
\(306\) 32.6092 88.7069i 0.106566 0.289892i
\(307\) 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 \(-0.638210\pi\)
−0.996006 + 0.0892815i \(0.971543\pi\)
\(312\) −10.3749 14.8675i −0.0332528 0.0476523i
\(313\) 149.067 + 258.191i 0.476251 + 0.824892i 0.999630 0.0272088i \(-0.00866190\pi\)
−0.523378 + 0.852100i \(0.675329\pi\)
\(314\) 196.437i 0.625597i
\(315\) −82.4507 + 114.223i −0.261748 + 0.362612i
\(316\) −94.8623 −0.300197
\(317\) 272.046 157.066i 0.858190 0.495476i −0.00521565 0.999986i \(-0.501660\pi\)
0.863406 + 0.504510i \(0.168327\pi\)
\(318\) 5.98568 4.17693i 0.0188229 0.0131350i
\(319\) 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
\(324\) −241.518 + 86.1553i −0.745425 + 0.265912i
\(325\) 6.76507 11.7174i 0.0208156 0.0360537i
\(326\) 150.218 + 86.7284i 0.460791 + 0.266038i
\(327\) −21.1229 245.977i −0.0645961 0.752224i
\(328\) 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 0.954498 0.298217i \(-0.0963920\pi\)
−0.735513 + 0.677511i \(0.763059\pi\)
\(332\) 215.210 + 124.252i 0.648224 + 0.374253i
\(333\) −594.240 + 102.817i −1.78450 + 0.308760i
\(334\) 278.961 + 483.174i 0.835212 + 1.44663i
\(335\) 155.298i 0.463576i
\(336\) 129.181 + 369.533i 0.384468 + 1.09980i
\(337\) −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
\(339\) 96.4177 + 138.170i 0.284418 + 0.407580i
\(340\) 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
\(345\) −3.75647 43.7442i −0.0108883 0.126795i
\(346\) 235.507 407.911i 0.680657 1.17893i
\(347\) 516.443 + 298.168i 1.48831 + 0.859274i 0.999911 0.0133476i \(-0.00424878\pi\)
0.488396 + 0.872622i \(0.337582\pi\)
\(348\) −178.545 + 15.3323i −0.513061 + 0.0440583i
\(349\) −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 0.996717 + 0.0809631i \(0.0257996\pi\)
0.568475 + 0.822701i \(0.307534\pi\)
\(354\) 157.048 109.592i 0.443639 0.309581i
\(355\) 61.7651 + 106.980i 0.173986 + 0.301353i
\(356\) 487.717i 1.36999i
\(357\) −62.4265 53.7548i −0.174864 0.150574i
\(358\) 369.544 1.03224
\(359\) −95.5156 + 55.1460i −0.266060 + 0.153610i −0.627096 0.778942i \(-0.715757\pi\)
0.361036 + 0.932552i \(0.382423\pi\)
\(360\) 44.2850 7.66231i 0.123014 0.0212842i
\(361\) −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
\(366\) 405.563 34.8271i 1.10809 0.0951559i
\(367\) −296.749 + 513.984i −0.808581 + 1.40050i 0.105266 + 0.994444i \(0.466430\pi\)
−0.913847 + 0.406059i \(0.866903\pi\)
\(368\) −105.660 61.0029i −0.287120 0.165769i
\(369\) 327.323 + 120.326i 0.887055 + 0.326086i
\(370\) −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 0.962658 0.270722i \(-0.0872623\pi\)
−0.715781 + 0.698325i \(0.753929\pi\)
\(374\) 164.581 + 95.0209i 0.440056 + 0.254067i
\(375\) 19.1943 + 27.5060i 0.0511847 + 0.0733493i
\(376\) −43.3335 75.0558i −0.115249 0.199616i
\(377\) 51.0599i 0.135437i
\(378\) −8.08048 + 505.868i −0.0213769 + 1.33827i
\(379\) 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
\(381\) 77.2042 53.8747i 0.202636 0.141403i
\(382\) 255.000 441.672i 0.667538 1.15621i
\(383\) −517.073 + 298.532i −1.35006 + 0.779458i −0.988258 0.152797i \(-0.951172\pi\)
−0.361803 + 0.932255i \(0.617839\pi\)
\(384\) 88.9393 189.935i 0.231613 0.494623i
\(385\) −198.051 202.522i −0.514417 0.526032i
\(386\) 270.838i 0.701653i
\(387\) −198.450 + 539.846i −0.512792 + 1.39495i
\(388\) 51.9956 90.0591i 0.134009 0.232111i
\(389\) 262.695 + 151.667i 0.675310 + 0.389890i 0.798085 0.602544i \(-0.205846\pi\)
−0.122776 + 0.992434i \(0.539180\pi\)
\(390\) −4.15750 48.4142i −0.0106602 0.124139i
\(391\) 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
\(396\) −87.9075 508.069i −0.221989 1.28300i
\(397\) −140.150 242.747i −0.353022 0.611452i 0.633755 0.773534i \(-0.281513\pi\)
−0.986777 + 0.162081i \(0.948179\pi\)
\(398\) 210.651i 0.529274i
\(399\) 204.863 + 586.027i 0.513441 + 1.46874i
\(400\) 93.2053 0.233013
\(401\) −110.748 + 63.9406i −0.276180 + 0.159453i −0.631693 0.775219i \(-0.717640\pi\)
0.355513 + 0.934671i \(0.384306\pi\)
\(402\) −319.174 457.387i −0.793965 1.13778i
\(403\) 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
\(408\) 2.24868 + 26.1860i 0.00551146 + 0.0641813i
\(409\) −48.0455 + 83.2172i −0.117471 + 0.203465i −0.918765 0.394806i \(-0.870812\pi\)
0.801294 + 0.598271i \(0.204145\pi\)
\(410\) 200.865 + 115.969i 0.489914 + 0.282852i
\(411\) −809.711 + 69.5327i −1.97010 + 0.169179i
\(412\) 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
\(417\) −172.704 + 120.516i −0.414158 + 0.289008i
\(418\) −716.053 1240.24i −1.71305 2.96708i
\(419\) 339.702i 0.810745i −0.914152 0.405373i \(-0.867142\pi\)
0.914152 0.405373i \(-0.132858\pi\)
\(420\) −27.6803 + 146.055i −0.0659056 + 0.347750i
\(421\) −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
\(423\) −59.5469 344.157i −0.140773 0.813609i
\(424\) −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
\(429\) 146.376 12.5698i 0.341202 0.0293002i
\(430\) −191.265 + 331.281i −0.444803 + 0.770421i
\(431\) 234.768 + 135.543i 0.544705 + 0.314485i 0.746984 0.664843i \(-0.231501\pi\)
−0.202279 + 0.979328i \(0.564835\pi\)
\(432\) 357.601 354.177i 0.827779 0.819855i
\(433\) 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
\(438\) 136.583 + 195.728i 0.311834 + 0.446868i
\(439\) −267.354 463.071i −0.609007 1.05483i −0.991404 0.130833i \(-0.958235\pi\)
0.382398 0.923998i \(-0.375098\pi\)
\(440\) 90.3712i 0.205389i
\(441\) 410.419 + 161.361i 0.930655 + 0.365898i
\(442\) 28.4165 0.0642907
\(443\) 174.920 100.990i 0.394854 0.227969i −0.289407 0.957206i \(-0.593458\pi\)
0.684261 + 0.729237i \(0.260125\pi\)
\(444\) −521.881 + 364.180i −1.17541 + 0.820224i
\(445\) 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 \(-0.315896\pi\)
\(450\) 113.063 + 41.5625i 0.251250 + 0.0923611i
\(451\) −350.622 + 607.294i −0.777431 + 1.34655i
\(452\) 153.973 + 88.8966i 0.340649 + 0.196674i
\(453\) −65.8304 766.598i −0.145321 1.69227i
\(454\) −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 0.857406 0.514641i \(-0.172075\pi\)
−0.874395 + 0.485214i \(0.838742\pi\)
\(458\) −826.964 477.448i −1.80560 1.04246i
\(459\) −27.9055 + 102.176i −0.0607963 + 0.222607i
\(460\) −23.1654 40.1236i −0.0503595 0.0872253i
\(461\) 344.491i 0.747269i 0.927576 + 0.373634i \(0.121888\pi\)
−0.927576 + 0.373634i \(0.878112\pi\)
\(462\) −999.534 189.432i −2.16349 0.410026i
\(463\) −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
\(465\) 97.1119 + 139.164i 0.208843 + 0.299278i
\(466\) −79.6129 + 137.894i −0.170843 + 0.295909i
\(467\) −593.172 + 342.468i −1.27018 + 0.733336i −0.975021 0.222113i \(-0.928705\pi\)
−0.295155 + 0.955449i \(0.595371\pi\)
\(468\) −49.3687 59.2199i −0.105489 0.126538i
\(469\) −470.969 + 120.578i −1.00420 + 0.257095i
\(470\) 232.292i 0.494239i
\(471\) 18.8356 + 219.341i 0.0399906 + 0.465692i
\(472\) −26.6278 + 46.1207i −0.0564148 + 0.0977133i
\(473\) −1001.60 578.271i −2.11754 1.22256i
\(474\) 239.759 20.5889i 0.505821 0.0434366i
\(475\) 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 \(-0.254138\pi\)
−0.271355 + 0.962479i \(0.587472\pi\)
\(480\) 225.368 157.267i 0.469517 0.327639i
\(481\) −90.6623 157.032i −0.188487 0.326469i
\(482\) 590.958i 1.22605i
\(483\) −129.746 + 45.3564i −0.268625 + 0.0939056i
\(484\) 653.749 1.35072
\(485\) −63.6118 + 36.7263i −0.131158 + 0.0757243i
\(486\) 591.723 270.172i 1.21754 0.555909i
\(487\) −261.107 + 452.251i −0.536155 + 0.928647i 0.462952 + 0.886384i \(0.346790\pi\)
−0.999106 + 0.0422639i \(0.986543\pi\)
\(488\) −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 \(0.625086\pi\)
\(492\) 366.656 31.4860i 0.745235 0.0639959i
\(493\) −37.0106 + 64.1042i −0.0750722 + 0.130029i
\(494\) −185.450 107.070i −0.375405 0.216740i
\(495\) −125.660 + 341.834i −0.253858 + 0.690573i
\(496\) 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 0.841492 0.540270i \(-0.181678\pi\)
−0.888633 + 0.458618i \(0.848345\pi\)
\(500\) 30.6521 + 17.6970i 0.0613042 + 0.0353940i
\(501\) −357.816 512.762i −0.714203 1.02348i
\(502\) 387.757 + 671.614i 0.772424 + 1.33788i
\(503\) 55.4203i 0.110180i −0.998481 0.0550898i \(-0.982455\pi\)
0.998481 0.0550898i \(-0.0175445\pi\)
\(504\) −57.6215 128.353i −0.114328 0.254669i
\(505\) −136.133 −0.269570
\(506\) 274.588 158.534i 0.542664 0.313307i
\(507\) −397.761 + 277.566i −0.784538 + 0.547467i
\(508\) 49.6722 86.0347i 0.0977798 0.169360i
\(509\) 220.030 127.035i 0.432280 0.249577i −0.268038 0.963408i \(-0.586375\pi\)
0.700317 + 0.713832i \(0.253042\pi\)
\(510\) −29.8733 + 63.7963i −0.0585751 + 0.125091i
\(511\) 201.541 51.5985i 0.394404 0.100976i
\(512\) 597.151i 1.16631i
\(513\) 567.103 561.674i 1.10546 1.09488i
\(514\) 209.206 362.355i 0.407015 0.704970i
\(515\) −85.6940 49.4754i −0.166396 0.0960688i
\(516\) 51.9290 + 604.716i 0.100638 + 1.17193i
\(517\) 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 \(-0.400170\pi\)
−0.669526 + 0.742788i \(0.733503\pi\)
\(522\) 447.935 77.5030i 0.858114 0.148473i
\(523\) 260.787 + 451.696i 0.498636 + 0.863664i 0.999999 0.00157381i \(-0.000500960\pi\)
−0.501362 + 0.865237i \(0.667168\pi\)
\(524\) 0.747265i 0.00142608i
\(525\) 68.5140 79.5665i 0.130503 0.151555i
\(526\) −77.4300 −0.147205
\(527\) −85.9429 + 49.6191i −0.163079 + 0.0941540i
\(528\) 579.159 + 829.954i 1.09689 + 1.57188i
\(529\) −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
\(534\) −105.854 1232.68i −0.198229 2.30839i
\(535\) −167.483 + 290.088i −0.313052 + 0.542221i
\(536\) 134.322 + 77.5506i 0.250600 + 0.144684i
\(537\) −412.630 + 35.4340i −0.768399 + 0.0659851i
\(538\) −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 0.900313 0.435242i \(-0.143337\pi\)
−0.827087 + 0.562073i \(0.810004\pi\)
\(542\) −878.750 507.347i −1.62131 0.936064i
\(543\) 542.372 378.478i 0.998843 0.697014i
\(544\) 80.3551 + 139.179i 0.147712 + 0.255844i
\(545\) 184.015i 0.337643i
\(546\) −143.597 + 50.1986i −0.262998 + 0.0919388i
\(547\) −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
\(549\) −449.510 + 77.7754i −0.818779 + 0.141667i
\(550\) −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
\(555\) 447.853 38.4587i 0.806942 0.0692949i
\(556\) −111.115 + 192.457i −0.199848 + 0.346147i
\(557\) 798.395 + 460.954i 1.43338 + 0.827565i 0.997377 0.0723785i \(-0.0230590\pi\)
0.436007 + 0.899943i \(0.356392\pi\)
\(558\) 572.032 + 210.282i 1.02515 + 0.376850i
\(559\) −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 \(-0.402484\pi\)
−0.674909 + 0.737901i \(0.735817\pi\)
\(564\) −210.916 302.250i −0.373965 0.535904i
\(565\) −62.7907 108.757i −0.111134 0.192490i
\(566\) 212.579i 0.375581i
\(567\) −39.4829 565.624i −0.0696347 0.997573i
\(568\) −123.374 −0.217207
\(569\) −247.611 + 142.958i −0.435168 + 0.251245i −0.701546 0.712624i \(-0.747507\pi\)
0.266378 + 0.963869i \(0.414173\pi\)
\(570\) 435.334 303.785i 0.763743 0.532956i
\(571\) 432.123 748.459i 0.756783 1.31079i −0.187701 0.982226i \(-0.560103\pi\)
0.944483 0.328560i \(-0.106563\pi\)
\(572\) 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
\(576\) 108.996 296.502i 0.189229 0.514761i
\(577\) 348.257 603.199i 0.603566 1.04541i −0.388711 0.921360i \(-0.627080\pi\)
0.992276 0.124046i \(-0.0395872\pi\)
\(578\) 634.299 + 366.213i 1.09740 + 0.633586i
\(579\) −25.9695 302.416i −0.0448523 0.522308i
\(580\) 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
\(585\) 9.28448 + 53.6604i 0.0158709 + 0.0917272i
\(586\) −171.059 296.283i −0.291909 0.505602i
\(587\) 596.728i 1.01657i −0.861188 0.508287i \(-0.830279\pi\)
0.861188 0.508287i \(-0.169721\pi\)
\(588\) 464.430 29.4555i 0.789847 0.0500944i
\(589\) 747.834 1.26967
\(590\) −123.617 + 71.3700i −0.209520 + 0.120966i
\(591\) −126.025 180.597i −0.213239 0.305579i
\(592\) 624.547 1081.75i 1.05498 1.82728i
\(593\) 394.499 227.764i 0.665260 0.384088i −0.129019 0.991642i \(-0.541183\pi\)
0.794278 + 0.607554i \(0.207849\pi\)
\(594\) 332.453 + 1265.04i 0.559685 + 2.12969i
\(595\) 42.9313 + 43.9006i 0.0721534 + 0.0737825i
\(596\) 186.301i 0.312585i
\(597\) −20.1985 235.212i −0.0338333 0.393990i
\(598\) 23.7051 41.0585i 0.0396407 0.0686597i
\(599\) −974.123 562.410i −1.62625 0.938915i −0.985199 0.171415i \(-0.945166\pi\)
−0.641049 0.767500i \(-0.721501\pi\)
\(600\) −33.3757 + 2.86608i −0.0556261 + 0.00477681i
\(601\) −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
\(606\) −400.942 + 279.785i −0.661620 + 0.461692i
\(607\) 302.447 + 523.854i 0.498266 + 0.863022i 0.999998 0.00200136i \(-0.000637054\pi\)
−0.501732 + 0.865023i \(0.667304\pi\)
\(608\) 1211.07i 1.99189i
\(609\) 73.7836 389.318i 0.121155 0.639274i
\(610\) −303.401 −0.497379
\(611\) 90.9456 52.5075i 0.148847 0.0859369i
\(612\) 19.0556 + 110.134i 0.0311366 + 0.179957i
\(613\) −377.326 + 653.548i −0.615540 + 1.06615i 0.374749 + 0.927126i \(0.377729\pi\)
−0.990289 + 0.139021i \(0.955605\pi\)
\(614\) −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 \(0.962380\pi\)
\(618\) −354.071 + 30.4053i −0.572931 + 0.0491996i
\(619\) 425.339 736.709i 0.687139 1.19016i −0.285620 0.958343i \(-0.592200\pi\)
0.972759 0.231817i \(-0.0744671\pi\)
\(620\) 155.082 + 89.5366i 0.250132 + 0.144414i
\(621\) 124.354 + 125.556i 0.200248 + 0.202184i
\(622\) 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
\(627\) 918.463 + 1316.19i 1.46485 + 2.09918i
\(628\) 116.155 + 201.187i 0.184960 + 0.320361i
\(629\) 262.865i 0.417909i
\(630\) 38.2607 375.153i 0.0607313 0.595482i
\(631\) −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
\(633\) −64.2993 + 44.8694i −0.101579 + 0.0708837i
\(634\) −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
\(639\) −466.667 171.549i −0.730308 0.268465i
\(640\) −78.1608 + 135.379i −0.122126 + 0.211529i
\(641\) 619.639 + 357.749i 0.966675 + 0.558110i 0.898221 0.439544i \(-0.144860\pi\)
0.0684543 + 0.997654i \(0.478193\pi\)
\(642\) 102.927 + 1198.59i 0.160323 + 1.86696i
\(643\) 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 \(-0.0841510\pi\)
0.256337 + 0.966587i \(0.417484\pi\)
\(648\) −117.161 + 137.823i −0.180805 + 0.212690i
\(649\) −215.780 373.742i −0.332481 0.575874i
\(650\) 36.2187i 0.0557210i
\(651\) 346.641 402.561i 0.532475 0.618373i
\(652\) −205.133 −0.314621
\(653\) 474.633 274.029i 0.726850 0.419647i −0.0904189 0.995904i \(-0.528821\pi\)
0.817269 + 0.576257i \(0.195487\pi\)
\(654\) 378.195 + 541.966i 0.578280 + 0.828694i
\(655\) −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 \(0.826717\pi\)
\(660\) 32.8818 + 382.910i 0.0498208 + 0.580166i
\(661\) −300.416 + 520.336i −0.454487 + 0.787195i −0.998659 0.0517791i \(-0.983511\pi\)
0.544171 + 0.838974i \(0.316844\pi\)
\(662\) −336.073 194.032i −0.507664 0.293100i
\(663\) −31.7297 + 2.72474i −0.0478578 + 0.00410971i
\(664\) 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
\(669\) −942.719 + 657.849i −1.40915 + 0.983332i
\(670\) 207.858 + 360.020i 0.310235 + 0.537343i
\(671\) 917.302i 1.36707i
\(672\) −651.922 561.364i −0.970123 0.835363i
\(673\) −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
\(675\) −130.230 35.5673i −0.192934 0.0526923i
\(676\) −255.914 + 443.256i −0.378571 + 0.655704i
\(677\) −104.116 + 60.1113i −0.153790 + 0.0887907i −0.574920 0.818210i \(-0.694967\pi\)
0.421130 + 0.907000i \(0.361634\pi\)
\(678\) −408.453 191.263i −0.602438 0.282098i
\(679\) 160.769 + 164.399i 0.236773 + 0.242119i
\(680\) 19.5897i 0.0288084i
\(681\) 716.161 61.4992i 1.05163 0.0903072i
\(682\) −612.748 + 1061.31i −0.898458 + 1.55617i
\(683\) 292.871 + 169.089i 0.428801 + 0.247569i 0.698836 0.715282i \(-0.253702\pi\)
−0.270034 + 0.962851i \(0.587035\pi\)
\(684\) 290.610 790.547i 0.424868 1.15577i
\(685\) 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
\(690\) 67.2577 + 96.3824i 0.0974749 + 0.139685i
\(691\) 165.191 + 286.119i 0.239061 + 0.414065i 0.960445 0.278470i \(-0.0898272\pi\)
−0.721384 + 0.692535i \(0.756494\pi\)
\(692\) 557.030i 0.804956i
\(693\) 1134.24 + 115.677i 1.63671 + 0.166923i
\(694\) −1596.33 −2.30018
\(695\) 135.939 78.4846i 0.195596 0.112928i
\(696\) −103.670 + 72.3434i −0.148952 + 0.103942i
\(697\) 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 \(-0.106991\pi\)
\(702\) 137.630 + 138.960i 0.196054 + 0.197949i
\(703\) 990.442 1715.50i 1.40888 2.44025i
\(704\) 550.111 + 317.607i 0.781408 + 0.451146i
\(705\) 22.2735 + 259.376i 0.0315936 + 0.367909i
\(706\) −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 0.992678 0.120790i \(-0.0385427\pi\)
−0.600946 + 0.799290i \(0.705209\pi\)
\(710\) −286.374 165.338i −0.403344 0.232871i
\(711\) −265.739 + 45.9790i −0.373755 + 0.0646680i
\(712\) 172.028 + 297.961i 0.241612 + 0.418484i
\(713\) 165.570i 0.232216i
\(714\) 216.668 + 41.0630i 0.303457 + 0.0575112i
\(715\) −109.503 −0.153152
\(716\) −378.478 + 218.514i −0.528601 + 0.305188i
\(717\) −480.042 687.915i −0.669514 0.959435i
\(718\) 147.620 255.685i 0.205598 0.356107i
\(719\) 874.330 504.795i 1.21604 0.702079i 0.251968 0.967736i \(-0.418922\pi\)
0.964068 + 0.265657i \(0.0855888\pi\)
\(720\) −288.149 + 240.215i −0.400207 + 0.333632i
\(721\) −83.5081 + 298.297i −0.115823 + 0.413726i
\(722\) 1373.01i 1.90168i
\(723\) −56.6644 659.860i −0.0783741 0.912670i
\(724\) 348.955 604.407i 0.481982 0.834817i
\(725\) −81.7050 47.1724i −0.112697 0.0650654i
\(726\) −1652.31 + 141.890i −2.27591 + 0.195441i
\(727\) −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
\(732\) −394.774 + 275.482i −0.539309 + 0.376341i
\(733\) −50.8478 88.0709i −0.0693694 0.120151i 0.829254 0.558871i \(-0.188765\pi\)
−0.898624 + 0.438720i \(0.855432\pi\)
\(734\) 1588.73i 2.16448i
\(735\) −294.496 146.003i −0.400675 0.198644i
\(736\) 268.130 0.364307
\(737\) −1088.48 + 628.436i −1.47691 + 0.852695i
\(738\) −919.868 + 159.158i −1.24643 + 0.215661i
\(739\) 94.0310 162.866i 0.127241 0.220388i −0.795366 0.606130i \(-0.792721\pi\)
0.922607 + 0.385742i \(0.126055\pi\)
\(740\) 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 \(-0.0262517\pi\)
\(744\) −168.862 + 14.5007i −0.226965 + 0.0194902i
\(745\) 65.7953 113.961i 0.0883158 0.152967i
\(746\) −426.954 246.502i −0.572324 0.330431i
\(747\) 663.097 + 243.758i 0.887680 + 0.326316i
\(748\) −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 0.997678 0.0681093i \(-0.0216967\pi\)
−0.557823 + 0.829960i \(0.688363\pi\)
\(752\) 626.499 + 361.709i 0.833110 + 0.480996i
\(753\) −497.365 712.741i −0.660512 0.946535i
\(754\) 68.3408 + 118.370i 0.0906377 + 0.156989i
\(755\) 573.492i 0.759591i
\(756\) −290.848 522.876i −0.384720 0.691635i
\(757\) 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
\(759\) −291.402 + 203.347i −0.383929 + 0.267914i
\(760\) −73.8114 + 127.845i −0.0971203 + 0.168217i
\(761\) 1106.40 638.781i 1.45388 0.839396i 0.455179 0.890400i \(-0.349575\pi\)
0.998698 + 0.0510038i \(0.0162421\pi\)
\(762\) −106.871 + 228.229i −0.140250 + 0.299513i
\(763\) 558.060 142.875i 0.731403 0.187254i
\(764\) 603.134i 0.789442i
\(765\) 27.2392 74.0990i