Properties

Label 690.3.b.a.599.19
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.19
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.20

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-0.996475 - 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 + 3.98905i) q^{5} +(1.40923 + 4.00176i) q^{6} -10.6805i q^{7} -2.82843 q^{8} +(-7.01408 + 5.63939i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-0.996475 - 2.82967i) q^{3} +2.00000 q^{4} +(3.01455 + 3.98905i) q^{5} +(1.40923 + 4.00176i) q^{6} -10.6805i q^{7} -2.82843 q^{8} +(-7.01408 + 5.63939i) q^{9} +(-4.26321 - 5.64137i) q^{10} +5.50721i q^{11} +(-1.99295 - 5.65934i) q^{12} +16.7611i q^{13} +15.1045i q^{14} +(8.28377 - 12.5052i) q^{15} +4.00000 q^{16} -9.80700 q^{17} +(9.91940 - 7.97530i) q^{18} +10.0985 q^{19} +(6.02910 + 7.97810i) q^{20} +(-30.2223 + 10.6429i) q^{21} -7.78837i q^{22} +4.79583 q^{23} +(2.81846 + 8.00352i) q^{24} +(-6.82500 + 24.0504i) q^{25} -23.7038i q^{26} +(22.9470 + 14.2280i) q^{27} -21.3610i q^{28} +28.0925i q^{29} +(-11.7150 + 17.6850i) q^{30} -47.2712 q^{31} -5.65685 q^{32} +(15.5836 - 5.48779i) q^{33} +13.8692 q^{34} +(42.6051 - 32.1969i) q^{35} +(-14.0282 + 11.2788i) q^{36} +63.2473i q^{37} -14.2814 q^{38} +(47.4284 - 16.7020i) q^{39} +(-8.52643 - 11.2827i) q^{40} -10.8343i q^{41} +(42.7408 - 15.0513i) q^{42} -68.8660i q^{43} +11.0144i q^{44} +(-43.6401 - 10.9793i) q^{45} -6.78233 q^{46} -48.4644 q^{47} +(-3.98590 - 11.3187i) q^{48} -65.0732 q^{49} +(9.65201 - 34.0123i) q^{50} +(9.77242 + 27.7506i) q^{51} +33.5222i q^{52} +0.337512 q^{53} +(-32.4519 - 20.1215i) q^{54} +(-21.9685 + 16.6017i) q^{55} +30.2090i q^{56} +(-10.0629 - 28.5754i) q^{57} -39.7288i q^{58} +81.8665i q^{59} +(16.5675 - 25.0103i) q^{60} +106.911 q^{61} +66.8515 q^{62} +(60.2316 + 74.9139i) q^{63} +8.00000 q^{64} +(-66.8608 + 50.5271i) q^{65} +(-22.0385 + 7.76091i) q^{66} -29.9541i q^{67} -19.6140 q^{68} +(-4.77892 - 13.5706i) q^{69} +(-60.2526 + 45.5333i) q^{70} +122.414i q^{71} +(19.8388 - 15.9506i) q^{72} +18.4676i q^{73} -89.4452i q^{74} +(74.8555 - 4.65305i) q^{75} +20.1970 q^{76} +58.8198 q^{77} +(-67.0738 + 23.6202i) q^{78} +59.0164 q^{79} +(12.0582 + 15.9562i) q^{80} +(17.3945 - 79.1102i) q^{81} +15.3220i q^{82} +94.7516 q^{83} +(-60.4446 + 21.2857i) q^{84} +(-29.5637 - 39.1206i) q^{85} +97.3913i q^{86} +(79.4926 - 27.9935i) q^{87} -15.5767i q^{88} +124.858i q^{89} +(61.7164 + 15.5270i) q^{90} +179.017 q^{91} +9.59166 q^{92} +(47.1045 + 133.762i) q^{93} +68.5391 q^{94} +(30.4424 + 40.2834i) q^{95} +(5.63691 + 16.0070i) q^{96} +148.042i q^{97} +92.0275 q^{98} +(-31.0573 - 38.6280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −0.996475 2.82967i −0.332158 0.943224i
\(4\) 2.00000 0.500000
\(5\) 3.01455 + 3.98905i 0.602910 + 0.797810i
\(6\) 1.40923 + 4.00176i 0.234871 + 0.666960i
\(7\) 10.6805i 1.52579i −0.646524 0.762893i \(-0.723778\pi\)
0.646524 0.762893i \(-0.276222\pi\)
\(8\) −2.82843 −0.353553
\(9\) −7.01408 + 5.63939i −0.779342 + 0.626599i
\(10\) −4.26321 5.64137i −0.426321 0.564137i
\(11\) 5.50721i 0.500655i 0.968161 + 0.250328i \(0.0805383\pi\)
−0.968161 + 0.250328i \(0.919462\pi\)
\(12\) −1.99295 5.65934i −0.166079 0.471612i
\(13\) 16.7611i 1.28931i 0.764472 + 0.644657i \(0.223000\pi\)
−0.764472 + 0.644657i \(0.777000\pi\)
\(14\) 15.1045i 1.07889i
\(15\) 8.28377 12.5052i 0.552252 0.833678i
\(16\) 4.00000 0.250000
\(17\) −9.80700 −0.576882 −0.288441 0.957498i \(-0.593137\pi\)
−0.288441 + 0.957498i \(0.593137\pi\)
\(18\) 9.91940 7.97530i 0.551078 0.443072i
\(19\) 10.0985 0.531500 0.265750 0.964042i \(-0.414380\pi\)
0.265750 + 0.964042i \(0.414380\pi\)
\(20\) 6.02910 + 7.97810i 0.301455 + 0.398905i
\(21\) −30.2223 + 10.6429i −1.43916 + 0.506803i
\(22\) 7.78837i 0.354017i
\(23\) 4.79583 0.208514
\(24\) 2.81846 + 8.00352i 0.117436 + 0.333480i
\(25\) −6.82500 + 24.0504i −0.273000 + 0.962014i
\(26\) 23.7038i 0.911683i
\(27\) 22.9470 + 14.2280i 0.849888 + 0.526964i
\(28\) 21.3610i 0.762893i
\(29\) 28.0925i 0.968707i 0.874872 + 0.484354i \(0.160945\pi\)
−0.874872 + 0.484354i \(0.839055\pi\)
\(30\) −11.7150 + 17.6850i −0.390501 + 0.589499i
\(31\) −47.2712 −1.52488 −0.762438 0.647061i \(-0.775998\pi\)
−0.762438 + 0.647061i \(0.775998\pi\)
\(32\) −5.65685 −0.176777
\(33\) 15.5836 5.48779i 0.472230 0.166297i
\(34\) 13.8692 0.407917
\(35\) 42.6051 32.1969i 1.21729 0.919911i
\(36\) −14.0282 + 11.2788i −0.389671 + 0.313299i
\(37\) 63.2473i 1.70939i 0.519133 + 0.854694i \(0.326255\pi\)
−0.519133 + 0.854694i \(0.673745\pi\)
\(38\) −14.2814 −0.375827
\(39\) 47.4284 16.7020i 1.21611 0.428256i
\(40\) −8.52643 11.2827i −0.213161 0.282068i
\(41\) 10.8343i 0.264252i −0.991233 0.132126i \(-0.957820\pi\)
0.991233 0.132126i \(-0.0421803\pi\)
\(42\) 42.7408 15.0513i 1.01764 0.358364i
\(43\) 68.8660i 1.60154i −0.598975 0.800768i \(-0.704425\pi\)
0.598975 0.800768i \(-0.295575\pi\)
\(44\) 11.0144i 0.250328i
\(45\) −43.6401 10.9793i −0.969779 0.243984i
\(46\) −6.78233 −0.147442
\(47\) −48.4644 −1.03116 −0.515579 0.856842i \(-0.672423\pi\)
−0.515579 + 0.856842i \(0.672423\pi\)
\(48\) −3.98590 11.3187i −0.0830395 0.235806i
\(49\) −65.0732 −1.32803
\(50\) 9.65201 34.0123i 0.193040 0.680247i
\(51\) 9.77242 + 27.7506i 0.191616 + 0.544129i
\(52\) 33.5222i 0.644657i
\(53\) 0.337512 0.00636816 0.00318408 0.999995i \(-0.498986\pi\)
0.00318408 + 0.999995i \(0.498986\pi\)
\(54\) −32.4519 20.1215i −0.600961 0.372620i
\(55\) −21.9685 + 16.6017i −0.399428 + 0.301850i
\(56\) 30.2090i 0.539447i
\(57\) −10.0629 28.5754i −0.176542 0.501323i
\(58\) 39.7288i 0.684980i
\(59\) 81.8665i 1.38757i 0.720183 + 0.693784i \(0.244058\pi\)
−0.720183 + 0.693784i \(0.755942\pi\)
\(60\) 16.5675 25.0103i 0.276126 0.416839i
\(61\) 106.911 1.75264 0.876318 0.481732i \(-0.159992\pi\)
0.876318 + 0.481732i \(0.159992\pi\)
\(62\) 66.8515 1.07825
\(63\) 60.2316 + 74.9139i 0.956056 + 1.18911i
\(64\) 8.00000 0.125000
\(65\) −66.8608 + 50.5271i −1.02863 + 0.777340i
\(66\) −22.0385 + 7.76091i −0.333917 + 0.117590i
\(67\) 29.9541i 0.447077i −0.974695 0.223538i \(-0.928239\pi\)
0.974695 0.223538i \(-0.0717608\pi\)
\(68\) −19.6140 −0.288441
\(69\) −4.77892 13.5706i −0.0692598 0.196676i
\(70\) −60.2526 + 45.5333i −0.860752 + 0.650476i
\(71\) 122.414i 1.72415i 0.506783 + 0.862073i \(0.330834\pi\)
−0.506783 + 0.862073i \(0.669166\pi\)
\(72\) 19.8388 15.9506i 0.275539 0.221536i
\(73\) 18.4676i 0.252980i 0.991968 + 0.126490i \(0.0403712\pi\)
−0.991968 + 0.126490i \(0.959629\pi\)
\(74\) 89.4452i 1.20872i
\(75\) 74.8555 4.65305i 0.998074 0.0620407i
\(76\) 20.1970 0.265750
\(77\) 58.8198 0.763893
\(78\) −67.0738 + 23.6202i −0.859921 + 0.302823i
\(79\) 59.0164 0.747043 0.373521 0.927622i \(-0.378150\pi\)
0.373521 + 0.927622i \(0.378150\pi\)
\(80\) 12.0582 + 15.9562i 0.150727 + 0.199452i
\(81\) 17.3945 79.1102i 0.214748 0.976670i
\(82\) 15.3220i 0.186854i
\(83\) 94.7516 1.14159 0.570793 0.821094i \(-0.306636\pi\)
0.570793 + 0.821094i \(0.306636\pi\)
\(84\) −60.4446 + 21.2857i −0.719579 + 0.253401i
\(85\) −29.5637 39.1206i −0.347808 0.460242i
\(86\) 97.3913i 1.13246i
\(87\) 79.4926 27.9935i 0.913708 0.321764i
\(88\) 15.5767i 0.177008i
\(89\) 124.858i 1.40290i 0.712717 + 0.701452i \(0.247464\pi\)
−0.712717 + 0.701452i \(0.752536\pi\)
\(90\) 61.7164 + 15.5270i 0.685738 + 0.172523i
\(91\) 179.017 1.96722
\(92\) 9.59166 0.104257
\(93\) 47.1045 + 133.762i 0.506500 + 1.43830i
\(94\) 68.5391 0.729139
\(95\) 30.4424 + 40.2834i 0.320446 + 0.424036i
\(96\) 5.63691 + 16.0070i 0.0587178 + 0.166740i
\(97\) 148.042i 1.52621i 0.646276 + 0.763103i \(0.276325\pi\)
−0.646276 + 0.763103i \(0.723675\pi\)
\(98\) 92.0275 0.939056
\(99\) −31.0573 38.6280i −0.313710 0.390182i
\(100\) −13.6500 + 48.1007i −0.136500 + 0.481007i
\(101\) 28.7770i 0.284921i −0.989800 0.142461i \(-0.954499\pi\)
0.989800 0.142461i \(-0.0455014\pi\)
\(102\) −13.8203 39.2452i −0.135493 0.384757i
\(103\) 102.710i 0.997181i −0.866838 0.498590i \(-0.833851\pi\)
0.866838 0.498590i \(-0.166149\pi\)
\(104\) 47.4075i 0.455841i
\(105\) −133.561 88.4749i −1.27201 0.842618i
\(106\) −0.477314 −0.00450297
\(107\) 142.426 1.33108 0.665540 0.746362i \(-0.268201\pi\)
0.665540 + 0.746362i \(0.268201\pi\)
\(108\) 45.8939 + 28.4560i 0.424944 + 0.263482i
\(109\) 49.1052 0.450507 0.225253 0.974300i \(-0.427679\pi\)
0.225253 + 0.974300i \(0.427679\pi\)
\(110\) 31.0682 23.4784i 0.282438 0.213440i
\(111\) 178.969 63.0243i 1.61233 0.567787i
\(112\) 42.7220i 0.381447i
\(113\) −59.1200 −0.523185 −0.261593 0.965178i \(-0.584248\pi\)
−0.261593 + 0.965178i \(0.584248\pi\)
\(114\) 14.2311 + 40.4117i 0.124834 + 0.354489i
\(115\) 14.4573 + 19.1308i 0.125715 + 0.166355i
\(116\) 56.1850i 0.484354i
\(117\) −94.5223 117.564i −0.807883 1.00482i
\(118\) 115.777i 0.981159i
\(119\) 104.744i 0.880199i
\(120\) −23.4300 + 35.3699i −0.195250 + 0.294750i
\(121\) 90.6707 0.749344
\(122\) −151.195 −1.23930
\(123\) −30.6576 + 10.7961i −0.249249 + 0.0877734i
\(124\) −94.5423 −0.762438
\(125\) −116.512 + 45.2757i −0.932098 + 0.362205i
\(126\) −85.1803 105.944i −0.676034 0.840827i
\(127\) 224.062i 1.76427i 0.471001 + 0.882133i \(0.343893\pi\)
−0.471001 + 0.882133i \(0.656107\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −194.868 + 68.6233i −1.51061 + 0.531963i
\(130\) 94.5554 71.4561i 0.727349 0.549662i
\(131\) 24.6516i 0.188180i 0.995564 + 0.0940900i \(0.0299942\pi\)
−0.995564 + 0.0940900i \(0.970006\pi\)
\(132\) 31.1672 10.9756i 0.236115 0.0831484i
\(133\) 107.857i 0.810955i
\(134\) 42.3616i 0.316131i
\(135\) 12.4185 + 134.428i 0.0919888 + 0.995760i
\(136\) 27.7384 0.203959
\(137\) 38.9946 0.284632 0.142316 0.989821i \(-0.454545\pi\)
0.142316 + 0.989821i \(0.454545\pi\)
\(138\) 6.75842 + 19.1918i 0.0489741 + 0.139071i
\(139\) −110.820 −0.797264 −0.398632 0.917111i \(-0.630515\pi\)
−0.398632 + 0.917111i \(0.630515\pi\)
\(140\) 85.2101 64.3938i 0.608644 0.459956i
\(141\) 48.2936 + 137.138i 0.342508 + 0.972613i
\(142\) 173.120i 1.21916i
\(143\) −92.3068 −0.645502
\(144\) −28.0563 + 22.5576i −0.194835 + 0.156650i
\(145\) −112.062 + 84.6862i −0.772844 + 0.584043i
\(146\) 26.1171i 0.178884i
\(147\) 64.8438 + 184.136i 0.441115 + 1.25263i
\(148\) 126.495i 0.854694i
\(149\) 86.8207i 0.582689i −0.956618 0.291345i \(-0.905897\pi\)
0.956618 0.291345i \(-0.0941026\pi\)
\(150\) −105.862 + 6.58041i −0.705745 + 0.0438694i
\(151\) −114.955 −0.761291 −0.380645 0.924721i \(-0.624298\pi\)
−0.380645 + 0.924721i \(0.624298\pi\)
\(152\) −28.5629 −0.187914
\(153\) 68.7870 55.3055i 0.449588 0.361474i
\(154\) −83.1837 −0.540154
\(155\) −142.501 188.567i −0.919363 1.21656i
\(156\) 94.8567 33.4040i 0.608056 0.214128i
\(157\) 197.398i 1.25731i −0.777684 0.628655i \(-0.783606\pi\)
0.777684 0.628655i \(-0.216394\pi\)
\(158\) −83.4618 −0.528239
\(159\) −0.336322 0.955049i −0.00211523 0.00600659i
\(160\) −17.0529 22.5655i −0.106580 0.141034i
\(161\) 51.2219i 0.318149i
\(162\) −24.5996 + 111.879i −0.151849 + 0.690610i
\(163\) 13.1307i 0.0805564i 0.999189 + 0.0402782i \(0.0128244\pi\)
−0.999189 + 0.0402782i \(0.987176\pi\)
\(164\) 21.6686i 0.132126i
\(165\) 68.8685 + 45.6205i 0.417385 + 0.276488i
\(166\) −133.999 −0.807223
\(167\) −225.489 −1.35023 −0.675117 0.737711i \(-0.735907\pi\)
−0.675117 + 0.737711i \(0.735907\pi\)
\(168\) 85.4816 30.1025i 0.508819 0.179182i
\(169\) −111.934 −0.662331
\(170\) 41.8093 + 55.3248i 0.245937 + 0.325440i
\(171\) −70.8316 + 56.9494i −0.414220 + 0.333037i
\(172\) 137.732i 0.800768i
\(173\) −107.311 −0.620295 −0.310147 0.950689i \(-0.600378\pi\)
−0.310147 + 0.950689i \(0.600378\pi\)
\(174\) −112.419 + 39.5887i −0.646089 + 0.227522i
\(175\) 256.870 + 72.8945i 1.46783 + 0.416540i
\(176\) 22.0288i 0.125164i
\(177\) 231.655 81.5779i 1.30879 0.460892i
\(178\) 176.576i 0.992002i
\(179\) 352.761i 1.97073i 0.170453 + 0.985366i \(0.445477\pi\)
−0.170453 + 0.985366i \(0.554523\pi\)
\(180\) −87.2801 21.9585i −0.484890 0.121992i
\(181\) 103.600 0.572378 0.286189 0.958173i \(-0.407611\pi\)
0.286189 + 0.958173i \(0.407611\pi\)
\(182\) −253.168 −1.39103
\(183\) −106.534 302.523i −0.582153 1.65313i
\(184\) −13.5647 −0.0737210
\(185\) −252.297 + 190.662i −1.36377 + 1.03061i
\(186\) −66.6158 189.168i −0.358150 1.01703i
\(187\) 54.0092i 0.288819i
\(188\) −96.9289 −0.515579
\(189\) 151.962 245.085i 0.804034 1.29675i
\(190\) −43.0520 56.9693i −0.226590 0.299838i
\(191\) 161.577i 0.845952i −0.906141 0.422976i \(-0.860985\pi\)
0.906141 0.422976i \(-0.139015\pi\)
\(192\) −7.97180 22.6374i −0.0415198 0.117903i
\(193\) 111.785i 0.579196i −0.957148 0.289598i \(-0.906478\pi\)
0.957148 0.289598i \(-0.0935215\pi\)
\(194\) 209.363i 1.07919i
\(195\) 209.600 + 138.845i 1.07487 + 0.712026i
\(196\) −130.146 −0.664013
\(197\) −259.757 −1.31856 −0.659282 0.751896i \(-0.729139\pi\)
−0.659282 + 0.751896i \(0.729139\pi\)
\(198\) 43.9216 + 54.6282i 0.221827 + 0.275900i
\(199\) −86.0655 −0.432490 −0.216245 0.976339i \(-0.569381\pi\)
−0.216245 + 0.976339i \(0.569381\pi\)
\(200\) 19.3040 68.0247i 0.0965201 0.340123i
\(201\) −84.7604 + 29.8485i −0.421693 + 0.148500i
\(202\) 40.6969i 0.201470i
\(203\) 300.042 1.47804
\(204\) 19.5448 + 55.5011i 0.0958081 + 0.272064i
\(205\) 43.2186 32.6606i 0.210823 0.159320i
\(206\) 145.253i 0.705113i
\(207\) −33.6383 + 27.0456i −0.162504 + 0.130655i
\(208\) 67.0443i 0.322329i
\(209\) 55.6145i 0.266098i
\(210\) 188.884 + 125.122i 0.899450 + 0.595821i
\(211\) 117.720 0.557914 0.278957 0.960304i \(-0.410011\pi\)
0.278957 + 0.960304i \(0.410011\pi\)
\(212\) 0.675024 0.00318408
\(213\) 346.393 121.983i 1.62626 0.572690i
\(214\) −201.420 −0.941216
\(215\) 274.710 207.600i 1.27772 0.965581i
\(216\) −64.9038 40.2429i −0.300481 0.186310i
\(217\) 504.880i 2.32664i
\(218\) −69.4453 −0.318556
\(219\) 52.2571 18.4025i 0.238617 0.0840295i
\(220\) −43.9370 + 33.2035i −0.199714 + 0.150925i
\(221\) 164.376i 0.743782i
\(222\) −253.101 + 89.1299i −1.14009 + 0.401486i
\(223\) 316.140i 1.41767i −0.705375 0.708834i \(-0.749221\pi\)
0.705375 0.708834i \(-0.250779\pi\)
\(224\) 60.4181i 0.269724i
\(225\) −87.7582 207.180i −0.390037 0.920799i
\(226\) 83.6082 0.369948
\(227\) −447.042 −1.96935 −0.984674 0.174404i \(-0.944200\pi\)
−0.984674 + 0.174404i \(0.944200\pi\)
\(228\) −20.1258 57.1508i −0.0882710 0.250662i
\(229\) 46.2455 0.201945 0.100973 0.994889i \(-0.467805\pi\)
0.100973 + 0.994889i \(0.467805\pi\)
\(230\) −20.4457 27.0550i −0.0888942 0.117631i
\(231\) −58.6124 166.441i −0.253733 0.720522i
\(232\) 79.4576i 0.342490i
\(233\) −4.37626 −0.0187823 −0.00939113 0.999956i \(-0.502989\pi\)
−0.00939113 + 0.999956i \(0.502989\pi\)
\(234\) 133.675 + 166.260i 0.571260 + 0.710513i
\(235\) −146.098 193.327i −0.621695 0.822668i
\(236\) 163.733i 0.693784i
\(237\) −58.8083 166.997i −0.248136 0.704629i
\(238\) 148.130i 0.622395i
\(239\) 92.6709i 0.387744i −0.981027 0.193872i \(-0.937895\pi\)
0.981027 0.193872i \(-0.0621047\pi\)
\(240\) 33.1351 50.0207i 0.138063 0.208419i
\(241\) 189.935 0.788111 0.394056 0.919087i \(-0.371072\pi\)
0.394056 + 0.919087i \(0.371072\pi\)
\(242\) −128.228 −0.529866
\(243\) −241.189 + 29.6105i −0.992548 + 0.121854i
\(244\) 213.822 0.876318
\(245\) −196.166 259.580i −0.800679 1.05951i
\(246\) 43.3564 15.2680i 0.176245 0.0620652i
\(247\) 169.262i 0.685270i
\(248\) 133.703 0.539125
\(249\) −94.4176 268.116i −0.379187 1.07677i
\(250\) 164.773 64.0295i 0.659093 0.256118i
\(251\) 139.189i 0.554536i −0.960793 0.277268i \(-0.910571\pi\)
0.960793 0.277268i \(-0.0894290\pi\)
\(252\) 120.463 + 149.828i 0.478028 + 0.594555i
\(253\) 26.4116i 0.104394i
\(254\) 316.871i 1.24752i
\(255\) −81.2389 + 122.638i −0.318584 + 0.480934i
\(256\) 16.0000 0.0625000
\(257\) 444.315 1.72885 0.864426 0.502761i \(-0.167682\pi\)
0.864426 + 0.502761i \(0.167682\pi\)
\(258\) 275.585 97.0480i 1.06816 0.376155i
\(259\) 675.514 2.60816
\(260\) −133.722 + 101.054i −0.514314 + 0.388670i
\(261\) −158.425 197.043i −0.606991 0.754954i
\(262\) 34.8626i 0.133063i
\(263\) −353.437 −1.34387 −0.671933 0.740612i \(-0.734536\pi\)
−0.671933 + 0.740612i \(0.734536\pi\)
\(264\) −44.0770 + 15.5218i −0.166958 + 0.0587948i
\(265\) 1.01745 + 1.34635i 0.00383942 + 0.00508057i
\(266\) 152.533i 0.573432i
\(267\) 353.308 124.418i 1.32325 0.465986i
\(268\) 59.9083i 0.223538i
\(269\) 68.5693i 0.254904i −0.991845 0.127452i \(-0.959320\pi\)
0.991845 0.127452i \(-0.0406799\pi\)
\(270\) −17.5624 190.109i −0.0650459 0.704109i
\(271\) 53.4646 0.197286 0.0986431 0.995123i \(-0.468550\pi\)
0.0986431 + 0.995123i \(0.468550\pi\)
\(272\) −39.2280 −0.144221
\(273\) −178.386 506.559i −0.653428 1.85553i
\(274\) −55.1467 −0.201265
\(275\) −132.450 37.5867i −0.481637 0.136679i
\(276\) −9.55785 27.1413i −0.0346299 0.0983379i
\(277\) 323.987i 1.16963i 0.811167 + 0.584815i \(0.198833\pi\)
−0.811167 + 0.584815i \(0.801167\pi\)
\(278\) 156.723 0.563751
\(279\) 331.564 266.581i 1.18840 0.955486i
\(280\) −120.505 + 91.0666i −0.430376 + 0.325238i
\(281\) 151.475i 0.539057i −0.962992 0.269529i \(-0.913132\pi\)
0.962992 0.269529i \(-0.0868679\pi\)
\(282\) −68.2974 193.943i −0.242190 0.687741i
\(283\) 239.029i 0.844627i 0.906450 + 0.422313i \(0.138782\pi\)
−0.906450 + 0.422313i \(0.861218\pi\)
\(284\) 244.829i 0.862073i
\(285\) 83.6536 126.283i 0.293522 0.443099i
\(286\) 130.541 0.456439
\(287\) −115.716 −0.403192
\(288\) 39.6776 31.9012i 0.137769 0.110768i
\(289\) −192.823 −0.667207
\(290\) 158.480 119.764i 0.546483 0.412981i
\(291\) 418.910 147.520i 1.43955 0.506942i
\(292\) 36.9351i 0.126490i
\(293\) 283.885 0.968891 0.484446 0.874821i \(-0.339021\pi\)
0.484446 + 0.874821i \(0.339021\pi\)
\(294\) −91.7030 260.407i −0.311915 0.885740i
\(295\) −326.569 + 246.791i −1.10702 + 0.836578i
\(296\) 178.890i 0.604360i
\(297\) −78.3567 + 126.374i −0.263827 + 0.425501i
\(298\) 122.783i 0.412023i
\(299\) 80.3833i 0.268841i
\(300\) 149.711 9.30610i 0.499037 0.0310203i
\(301\) −735.524 −2.44360
\(302\) 162.571 0.538314
\(303\) −81.4295 + 28.6756i −0.268744 + 0.0946389i
\(304\) 40.3940 0.132875
\(305\) 322.288 + 426.472i 1.05668 + 1.39827i
\(306\) −97.2795 + 78.2138i −0.317907 + 0.255601i
\(307\) 332.488i 1.08302i 0.840693 + 0.541512i \(0.182148\pi\)
−0.840693 + 0.541512i \(0.817852\pi\)
\(308\) 117.640 0.381947
\(309\) −290.634 + 102.348i −0.940565 + 0.331222i
\(310\) 201.527 + 266.674i 0.650087 + 0.860238i
\(311\) 325.810i 1.04762i 0.851835 + 0.523811i \(0.175490\pi\)
−0.851835 + 0.523811i \(0.824510\pi\)
\(312\) −134.148 + 47.2404i −0.429960 + 0.151411i
\(313\) 175.258i 0.559929i −0.960010 0.279965i \(-0.909677\pi\)
0.960010 0.279965i \(-0.0903227\pi\)
\(314\) 279.163i 0.889053i
\(315\) −117.264 + 466.098i −0.372267 + 1.47968i
\(316\) 118.033 0.373521
\(317\) 137.362 0.433319 0.216659 0.976247i \(-0.430484\pi\)
0.216659 + 0.976247i \(0.430484\pi\)
\(318\) 0.475632 + 1.35064i 0.00149570 + 0.00424730i
\(319\) −154.711 −0.484988
\(320\) 24.1164 + 31.9124i 0.0753637 + 0.0997262i
\(321\) −141.924 403.018i −0.442129 1.25551i
\(322\) 72.4387i 0.224965i
\(323\) −99.0359 −0.306613
\(324\) 34.7891 158.220i 0.107374 0.488335i
\(325\) −403.110 114.394i −1.24034 0.351983i
\(326\) 18.5696i 0.0569620i
\(327\) −48.9321 138.952i −0.149639 0.424929i
\(328\) 30.6441i 0.0934271i
\(329\) 517.625i 1.57333i
\(330\) −97.3948 64.5171i −0.295136 0.195506i
\(331\) −373.059 −1.12707 −0.563533 0.826093i \(-0.690558\pi\)
−0.563533 + 0.826093i \(0.690558\pi\)
\(332\) 189.503 0.570793
\(333\) −356.676 443.622i −1.07110 1.33220i
\(334\) 318.890 0.954760
\(335\) 119.488 90.2982i 0.356682 0.269547i
\(336\) −120.889 + 42.5714i −0.359790 + 0.126701i
\(337\) 46.2129i 0.137130i −0.997647 0.0685652i \(-0.978158\pi\)
0.997647 0.0685652i \(-0.0218421\pi\)
\(338\) 158.299 0.468339
\(339\) 58.9115 + 167.290i 0.173780 + 0.493481i
\(340\) −59.1273 78.2411i −0.173904 0.230121i
\(341\) 260.332i 0.763437i
\(342\) 100.171 80.5385i 0.292898 0.235493i
\(343\) 171.670i 0.500497i
\(344\) 194.783i 0.566228i
\(345\) 39.7276 59.9727i 0.115152 0.173834i
\(346\) 151.761 0.438614
\(347\) −436.414 −1.25768 −0.628838 0.777536i \(-0.716469\pi\)
−0.628838 + 0.777536i \(0.716469\pi\)
\(348\) 158.985 55.9869i 0.456854 0.160882i
\(349\) −144.441 −0.413871 −0.206936 0.978355i \(-0.566349\pi\)
−0.206936 + 0.978355i \(0.566349\pi\)
\(350\) −363.269 103.088i −1.03791 0.294538i
\(351\) −238.477 + 384.616i −0.679422 + 1.09577i
\(352\) 31.1535i 0.0885042i
\(353\) −128.039 −0.362717 −0.181359 0.983417i \(-0.558049\pi\)
−0.181359 + 0.983417i \(0.558049\pi\)
\(354\) −327.610 + 115.369i −0.925452 + 0.325900i
\(355\) −488.317 + 369.024i −1.37554 + 1.03950i
\(356\) 249.717i 0.701452i
\(357\) 296.390 104.374i 0.830225 0.292365i
\(358\) 498.879i 1.39352i
\(359\) 223.554i 0.622713i −0.950293 0.311357i \(-0.899217\pi\)
0.950293 0.311357i \(-0.100783\pi\)
\(360\) 123.433 + 31.0541i 0.342869 + 0.0862613i
\(361\) −259.020 −0.717508
\(362\) −146.513 −0.404733
\(363\) −90.3510 256.568i −0.248901 0.706799i
\(364\) 358.034 0.983609
\(365\) −73.6680 + 55.6713i −0.201830 + 0.152524i
\(366\) 150.662 + 427.831i 0.411644 + 1.16894i
\(367\) 239.940i 0.653788i 0.945061 + 0.326894i \(0.106002\pi\)
−0.945061 + 0.326894i \(0.893998\pi\)
\(368\) 19.1833 0.0521286
\(369\) 61.0990 + 75.9928i 0.165580 + 0.205942i
\(370\) 356.801 269.637i 0.964328 0.728748i
\(371\) 3.60480i 0.00971645i
\(372\) 94.2090 + 267.524i 0.253250 + 0.719150i
\(373\) 233.984i 0.627302i 0.949538 + 0.313651i \(0.101552\pi\)
−0.949538 + 0.313651i \(0.898448\pi\)
\(374\) 76.3805i 0.204226i
\(375\) 244.217 + 284.575i 0.651245 + 0.758868i
\(376\) 137.078 0.364570
\(377\) −470.861 −1.24897
\(378\) −214.907 + 346.603i −0.568538 + 0.916939i
\(379\) 161.554 0.426263 0.213132 0.977024i \(-0.431634\pi\)
0.213132 + 0.977024i \(0.431634\pi\)
\(380\) 60.8848 + 80.5667i 0.160223 + 0.212018i
\(381\) 634.021 223.272i 1.66410 0.586015i
\(382\) 228.504i 0.598179i
\(383\) −444.654 −1.16098 −0.580488 0.814269i \(-0.697138\pi\)
−0.580488 + 0.814269i \(0.697138\pi\)
\(384\) 11.2738 + 32.0141i 0.0293589 + 0.0833700i
\(385\) 177.315 + 234.635i 0.460559 + 0.609441i
\(386\) 158.087i 0.409553i
\(387\) 388.363 + 483.032i 1.00352 + 1.24814i
\(388\) 296.084i 0.763103i
\(389\) 469.314i 1.20646i 0.797567 + 0.603231i \(0.206120\pi\)
−0.797567 + 0.603231i \(0.793880\pi\)
\(390\) −296.419 196.357i −0.760050 0.503478i
\(391\) −47.0327 −0.120288
\(392\) 184.055 0.469528
\(393\) 69.7559 24.5647i 0.177496 0.0625055i
\(394\) 367.352 0.932365
\(395\) 177.908 + 235.419i 0.450399 + 0.595998i
\(396\) −62.1146 77.2560i −0.156855 0.195091i
\(397\) 48.3846i 0.121876i 0.998142 + 0.0609378i \(0.0194091\pi\)
−0.998142 + 0.0609378i \(0.980591\pi\)
\(398\) 121.715 0.305817
\(399\) −305.200 + 107.477i −0.764912 + 0.269365i
\(400\) −27.3000 + 96.2014i −0.0682500 + 0.240504i
\(401\) 430.001i 1.07232i −0.844116 0.536161i \(-0.819874\pi\)
0.844116 0.536161i \(-0.180126\pi\)
\(402\) 119.869 42.2122i 0.298182 0.105005i
\(403\) 792.316i 1.96604i
\(404\) 57.5541i 0.142461i
\(405\) 368.011 169.094i 0.908670 0.417516i
\(406\) −424.324 −1.04513
\(407\) −348.316 −0.855814
\(408\) −27.6406 78.4905i −0.0677465 0.192379i
\(409\) 206.431 0.504722 0.252361 0.967633i \(-0.418793\pi\)
0.252361 + 0.967633i \(0.418793\pi\)
\(410\) −61.1204 + 46.1890i −0.149074 + 0.112656i
\(411\) −38.8571 110.342i −0.0945429 0.268472i
\(412\) 205.419i 0.498590i
\(413\) 874.376 2.11713
\(414\) 47.5718 38.2482i 0.114908 0.0923870i
\(415\) 285.633 + 377.969i 0.688273 + 0.910768i
\(416\) 94.8150i 0.227921i
\(417\) 110.429 + 313.583i 0.264818 + 0.751998i
\(418\) 78.6508i 0.188160i
\(419\) 78.5600i 0.187494i 0.995596 + 0.0937471i \(0.0298845\pi\)
−0.995596 + 0.0937471i \(0.970115\pi\)
\(420\) −267.123 176.950i −0.636007 0.421309i
\(421\) −129.116 −0.306688 −0.153344 0.988173i \(-0.549004\pi\)
−0.153344 + 0.988173i \(0.549004\pi\)
\(422\) −166.481 −0.394505
\(423\) 339.933 273.310i 0.803625 0.646123i
\(424\) −0.954629 −0.00225148
\(425\) 66.9328 235.862i 0.157489 0.554969i
\(426\) −489.873 + 172.510i −1.14994 + 0.404953i
\(427\) 1141.86i 2.67415i
\(428\) 284.851 0.665540
\(429\) 91.9814 + 261.198i 0.214409 + 0.608853i
\(430\) −388.499 + 293.591i −0.903485 + 0.682769i
\(431\) 221.506i 0.513935i −0.966420 0.256968i \(-0.917277\pi\)
0.966420 0.256968i \(-0.0827234\pi\)
\(432\) 91.7879 + 56.9121i 0.212472 + 0.131741i
\(433\) 374.938i 0.865907i −0.901416 0.432953i \(-0.857471\pi\)
0.901416 0.432953i \(-0.142529\pi\)
\(434\) 714.008i 1.64518i
\(435\) 351.301 + 232.712i 0.807590 + 0.534970i
\(436\) 98.2105 0.225253
\(437\) 48.4307 0.110825
\(438\) −73.9027 + 26.0250i −0.168728 + 0.0594178i
\(439\) 425.652 0.969595 0.484798 0.874626i \(-0.338893\pi\)
0.484798 + 0.874626i \(0.338893\pi\)
\(440\) 62.1363 46.9568i 0.141219 0.106720i
\(441\) 456.429 366.973i 1.03499 0.832139i
\(442\) 232.463i 0.525933i
\(443\) 779.244 1.75902 0.879508 0.475884i \(-0.157872\pi\)
0.879508 + 0.475884i \(0.157872\pi\)
\(444\) 357.938 126.049i 0.806167 0.283893i
\(445\) −498.066 + 376.392i −1.11925 + 0.845824i
\(446\) 447.090i 1.00244i
\(447\) −245.674 + 86.5146i −0.549606 + 0.193545i
\(448\) 85.4441i 0.190723i
\(449\) 521.041i 1.16045i −0.814457 0.580224i \(-0.802965\pi\)
0.814457 0.580224i \(-0.197035\pi\)
\(450\) 124.109 + 292.997i 0.275797 + 0.651103i
\(451\) 59.6669 0.132299
\(452\) −118.240 −0.261593
\(453\) 114.550 + 325.285i 0.252869 + 0.718068i
\(454\) 632.213 1.39254
\(455\) 539.655 + 714.107i 1.18605 + 1.56947i
\(456\) 28.4622 + 80.8235i 0.0624170 + 0.177244i
\(457\) 108.265i 0.236904i −0.992960 0.118452i \(-0.962207\pi\)
0.992960 0.118452i \(-0.0377932\pi\)
\(458\) −65.4010 −0.142797
\(459\) −225.041 139.534i −0.490285 0.303996i
\(460\) 28.9145 + 38.2616i 0.0628577 + 0.0831774i
\(461\) 528.878i 1.14724i 0.819121 + 0.573620i \(0.194462\pi\)
−0.819121 + 0.573620i \(0.805538\pi\)
\(462\) 82.8905 + 235.383i 0.179417 + 0.509486i
\(463\) 270.858i 0.585007i −0.956264 0.292504i \(-0.905512\pi\)
0.956264 0.292504i \(-0.0944883\pi\)
\(464\) 112.370i 0.242177i
\(465\) −391.584 + 591.134i −0.842115 + 1.27126i
\(466\) 6.18897 0.0132811
\(467\) −187.502 −0.401503 −0.200751 0.979642i \(-0.564338\pi\)
−0.200751 + 0.979642i \(0.564338\pi\)
\(468\) −189.045 235.127i −0.403941 0.502408i
\(469\) −319.925 −0.682144
\(470\) 206.614 + 273.406i 0.439605 + 0.581714i
\(471\) −558.571 + 196.702i −1.18593 + 0.417626i
\(472\) 231.553i 0.490579i
\(473\) 379.260 0.801817
\(474\) 83.1675 + 236.169i 0.175459 + 0.498248i
\(475\) −68.9222 + 242.872i −0.145099 + 0.511310i
\(476\) 209.487i 0.440100i
\(477\) −2.36734 + 1.90336i −0.00496297 + 0.00399028i
\(478\) 131.056i 0.274177i
\(479\) 17.1665i 0.0358382i 0.999839 + 0.0179191i \(0.00570414\pi\)
−0.999839 + 0.0179191i \(0.994296\pi\)
\(480\) −46.8601 + 70.7399i −0.0976252 + 0.147375i
\(481\) −1060.09 −2.20394
\(482\) −268.608 −0.557279
\(483\) −144.941 + 51.0413i −0.300085 + 0.105676i
\(484\) 181.341 0.374672
\(485\) −590.547 + 446.280i −1.21762 + 0.920165i
\(486\) 341.093 41.8755i 0.701837 0.0861637i
\(487\) 128.206i 0.263257i −0.991299 0.131628i \(-0.957979\pi\)
0.991299 0.131628i \(-0.0420206\pi\)
\(488\) −302.390 −0.619651
\(489\) 37.1556 13.0844i 0.0759827 0.0267575i
\(490\) 277.421 + 367.102i 0.566166 + 0.749188i
\(491\) 457.658i 0.932094i −0.884760 0.466047i \(-0.845678\pi\)
0.884760 0.466047i \(-0.154322\pi\)
\(492\) −61.3151 + 21.5923i −0.124624 + 0.0438867i
\(493\) 275.503i 0.558830i
\(494\) 239.372i 0.484559i
\(495\) 60.4651 240.335i 0.122152 0.485525i
\(496\) −189.085 −0.381219
\(497\) 1307.45 2.63068
\(498\) 133.527 + 379.173i 0.268126 + 0.761392i
\(499\) −522.868 −1.04783 −0.523916 0.851770i \(-0.675529\pi\)
−0.523916 + 0.851770i \(0.675529\pi\)
\(500\) −233.025 + 90.5513i −0.466049 + 0.181103i
\(501\) 224.694 + 638.060i 0.448491 + 1.27357i
\(502\) 196.842i 0.392116i
\(503\) −99.9634 −0.198734 −0.0993672 0.995051i \(-0.531682\pi\)
−0.0993672 + 0.995051i \(0.531682\pi\)
\(504\) −170.361 211.889i −0.338017 0.420414i
\(505\) 114.793 86.7497i 0.227313 0.171782i
\(506\) 37.3517i 0.0738176i
\(507\) 111.539 + 316.736i 0.219999 + 0.624727i
\(508\) 448.123i 0.882133i
\(509\) 120.324i 0.236392i −0.992990 0.118196i \(-0.962289\pi\)
0.992990 0.118196i \(-0.0377112\pi\)
\(510\) 114.889 173.436i 0.225273 0.340071i
\(511\) 197.243 0.385994
\(512\) −22.6274 −0.0441942
\(513\) 231.730 + 143.682i 0.451715 + 0.280081i
\(514\) −628.356 −1.22248
\(515\) 409.714 309.623i 0.795560 0.601210i
\(516\) −389.737 + 137.247i −0.755303 + 0.265982i
\(517\) 266.904i 0.516255i
\(518\) −955.320 −1.84425
\(519\) 106.933 + 303.655i 0.206036 + 0.585077i
\(520\) 189.111 142.912i 0.363675 0.274831i
\(521\) 115.841i 0.222344i −0.993801 0.111172i \(-0.964540\pi\)
0.993801 0.111172i \(-0.0354604\pi\)
\(522\) 224.046 + 278.661i 0.429207 + 0.533833i
\(523\) 539.428i 1.03141i 0.856766 + 0.515706i \(0.172470\pi\)
−0.856766 + 0.515706i \(0.827530\pi\)
\(524\) 49.3032i 0.0940900i
\(525\) −49.6969 799.495i −0.0946608 1.52285i
\(526\) 499.835 0.950256
\(527\) 463.588 0.879674
\(528\) 62.3343 21.9512i 0.118057 0.0415742i
\(529\) 23.0000 0.0434783
\(530\) −1.43889 1.90403i −0.00271488 0.00359251i
\(531\) −461.677 574.218i −0.869449 1.08139i
\(532\) 215.714i 0.405478i
\(533\) 181.595 0.340704
\(534\) −499.653 + 175.954i −0.935680 + 0.329502i
\(535\) 429.349 + 568.143i 0.802521 + 1.06195i
\(536\) 84.7231i 0.158065i
\(537\) 998.197 351.517i 1.85884 0.654595i
\(538\) 96.9716i 0.180245i
\(539\) 358.372i 0.664883i
\(540\) 24.8370 + 268.855i 0.0459944 + 0.497880i
\(541\) 96.6585 0.178666 0.0893332 0.996002i \(-0.471526\pi\)
0.0893332 + 0.996002i \(0.471526\pi\)
\(542\) −75.6103 −0.139502
\(543\) −103.235 293.155i −0.190120 0.539881i
\(544\) 55.4767 0.101979
\(545\) 148.030 + 195.883i 0.271615 + 0.359419i
\(546\) 252.276 + 716.383i 0.462043 + 1.31206i
\(547\) 313.641i 0.573384i 0.958023 + 0.286692i \(0.0925556\pi\)
−0.958023 + 0.286692i \(0.907444\pi\)
\(548\) 77.9892 0.142316
\(549\) −749.881 + 602.912i −1.36590 + 1.09820i
\(550\) 187.313 + 53.1556i 0.340569 + 0.0966466i
\(551\) 283.692i 0.514868i
\(552\) 13.5168 + 38.3835i 0.0244870 + 0.0695354i
\(553\) 630.325i 1.13983i
\(554\) 458.187i 0.827053i
\(555\) 790.918 + 523.926i 1.42508 + 0.944012i
\(556\) −221.639 −0.398632
\(557\) 267.444 0.480150 0.240075 0.970754i \(-0.422828\pi\)
0.240075 + 0.970754i \(0.422828\pi\)
\(558\) −468.902 + 377.002i −0.840326 + 0.675631i
\(559\) 1154.27 2.06488
\(560\) 170.420 128.788i 0.304322 0.229978i
\(561\) −152.828 + 53.8188i −0.272421 + 0.0959336i
\(562\) 214.218i 0.381171i
\(563\) −543.496 −0.965358 −0.482679 0.875797i \(-0.660336\pi\)
−0.482679 + 0.875797i \(0.660336\pi\)
\(564\) 96.5872 + 274.277i 0.171254 + 0.486307i
\(565\) −178.220 235.832i −0.315434 0.417402i
\(566\) 338.039i 0.597241i
\(567\) −844.938 185.783i −1.49019 0.327659i
\(568\) 346.240i 0.609578i
\(569\) 853.988i 1.50086i 0.660951 + 0.750429i \(0.270153\pi\)
−0.660951 + 0.750429i \(0.729847\pi\)
\(570\) −118.304 + 178.592i −0.207551 + 0.313319i
\(571\) −434.281 −0.760563 −0.380281 0.924871i \(-0.624173\pi\)
−0.380281 + 0.924871i \(0.624173\pi\)
\(572\) −184.614 −0.322751
\(573\) −457.209 + 161.007i −0.797922 + 0.280990i
\(574\) 163.647 0.285100
\(575\) −32.7316 + 115.341i −0.0569245 + 0.200594i
\(576\) −56.1126 + 45.1151i −0.0974177 + 0.0783249i
\(577\) 383.820i 0.665200i −0.943068 0.332600i \(-0.892074\pi\)
0.943068 0.332600i \(-0.107926\pi\)
\(578\) 272.693 0.471787
\(579\) −316.314 + 111.391i −0.546311 + 0.192385i
\(580\) −224.125 + 169.372i −0.386422 + 0.292021i
\(581\) 1012.00i 1.74182i
\(582\) −592.429 + 208.625i −1.01792 + 0.358462i
\(583\) 1.85875i 0.00318825i
\(584\) 52.2341i 0.0894420i
\(585\) 184.025 731.455i 0.314572 1.25035i
\(586\) −401.474 −0.685110
\(587\) 1110.21 1.89133 0.945663 0.325149i \(-0.105415\pi\)
0.945663 + 0.325149i \(0.105415\pi\)
\(588\) 129.688 + 368.272i 0.220557 + 0.626313i
\(589\) −477.368 −0.810471
\(590\) 461.839 349.015i 0.782778 0.591550i
\(591\) 258.841 + 735.027i 0.437972 + 1.24370i
\(592\) 252.989i 0.427347i
\(593\) 29.9752 0.0505484 0.0252742 0.999681i \(-0.491954\pi\)
0.0252742 + 0.999681i \(0.491954\pi\)
\(594\) 110.813 178.719i 0.186554 0.300874i
\(595\) −417.828 + 315.755i −0.702231 + 0.530680i
\(596\) 173.641i 0.291345i
\(597\) 85.7621 + 243.537i 0.143655 + 0.407935i
\(598\) 113.679i 0.190099i
\(599\) 382.745i 0.638973i −0.947591 0.319487i \(-0.896490\pi\)
0.947591 0.319487i \(-0.103510\pi\)
\(600\) −211.723 + 13.1608i −0.352872 + 0.0219347i
\(601\) 961.642 1.60007 0.800035 0.599954i \(-0.204814\pi\)
0.800035 + 0.599954i \(0.204814\pi\)
\(602\) 1040.19 1.72789
\(603\) 168.923 + 210.101i 0.280138 + 0.348426i
\(604\) −229.910 −0.380645
\(605\) 273.331 + 361.690i 0.451787 + 0.597834i
\(606\) 115.159 40.5534i 0.190031 0.0669198i
\(607\) 229.123i 0.377468i −0.982028 0.188734i \(-0.939562\pi\)
0.982028 0.188734i \(-0.0604383\pi\)
\(608\) −57.1257 −0.0939568
\(609\) −298.985 849.021i −0.490943 1.39412i
\(610\) −455.784 603.123i −0.747187 0.988727i
\(611\) 812.317i 1.32949i
\(612\) 137.574 110.611i 0.224794 0.180737i
\(613\) 1083.98i 1.76831i 0.467191 + 0.884156i \(0.345266\pi\)
−0.467191 + 0.884156i \(0.654734\pi\)
\(614\) 470.210i 0.765814i
\(615\) −135.485 89.7491i −0.220301 0.145933i
\(616\) −166.367 −0.270077
\(617\) −1155.91 −1.87344 −0.936721 0.350076i \(-0.886156\pi\)
−0.936721 + 0.350076i \(0.886156\pi\)
\(618\) 411.019 144.741i 0.665080 0.234209i
\(619\) −85.6341 −0.138343 −0.0691713 0.997605i \(-0.522036\pi\)
−0.0691713 + 0.997605i \(0.522036\pi\)
\(620\) −285.002 377.134i −0.459681 0.608280i
\(621\) 110.050 + 68.2352i 0.177214 + 0.109880i
\(622\) 460.765i 0.740780i
\(623\) 1333.55 2.14053
\(624\) 189.713 66.8080i 0.304028 0.107064i
\(625\) −531.839 328.287i −0.850942 0.525260i
\(626\) 247.852i 0.395930i
\(627\) 157.371 55.4184i 0.250990 0.0883867i
\(628\) 394.796i 0.628655i
\(629\) 620.266i 0.986115i
\(630\) 165.837 659.162i 0.263233 1.04629i
\(631\) 630.139 0.998636 0.499318 0.866419i \(-0.333584\pi\)
0.499318 + 0.866419i \(0.333584\pi\)
\(632\) −166.924 −0.264120
\(633\) −117.305 333.108i −0.185316 0.526238i
\(634\) −194.259 −0.306403
\(635\) −893.793 + 675.445i −1.40755 + 1.06369i
\(636\) −0.672645 1.91010i −0.00105762 0.00300330i
\(637\) 1090.70i 1.71224i
\(638\) 218.795 0.342939
\(639\) −690.343 858.624i −1.08035 1.34370i
\(640\) −34.1057 45.1309i −0.0532902 0.0705171i
\(641\) 283.428i 0.442165i −0.975255 0.221083i \(-0.929041\pi\)
0.975255 0.221083i \(-0.0709591\pi\)
\(642\) 200.710 + 569.953i 0.312633 + 0.887778i
\(643\) 1037.58i 1.61366i 0.590785 + 0.806829i \(0.298818\pi\)
−0.590785 + 0.806829i \(0.701182\pi\)
\(644\) 102.444i 0.159074i
\(645\) −861.181 570.471i −1.33516 0.884451i
\(646\) 140.058 0.216808
\(647\) −1085.51 −1.67776 −0.838878 0.544320i \(-0.816788\pi\)
−0.838878 + 0.544320i \(0.816788\pi\)
\(648\) −49.1992 + 223.758i −0.0759247 + 0.345305i
\(649\) −450.856 −0.694693
\(650\) 570.084 + 161.778i 0.877052 + 0.248889i
\(651\) 1428.64 503.100i 2.19454 0.772811i
\(652\) 26.2614i 0.0402782i
\(653\) 1104.68 1.69170 0.845851 0.533420i \(-0.179093\pi\)
0.845851 + 0.533420i \(0.179093\pi\)
\(654\) 69.2005 + 196.507i 0.105811 + 0.300470i
\(655\) −98.3364 + 74.3134i −0.150132 + 0.113456i
\(656\) 43.3373i 0.0660629i
\(657\) −104.146 129.533i −0.158517 0.197158i
\(658\) 732.032i 1.11251i
\(659\) 1185.91i 1.79955i −0.436351 0.899777i \(-0.643729\pi\)
0.436351 0.899777i \(-0.356271\pi\)
\(660\) 137.737 + 91.2409i 0.208693 + 0.138244i
\(661\) 3.97567 0.00601463 0.00300732 0.999995i \(-0.499043\pi\)
0.00300732 + 0.999995i \(0.499043\pi\)
\(662\) 527.585 0.796957
\(663\) −465.130 + 163.796i −0.701553 + 0.247053i
\(664\) −267.998 −0.403612
\(665\) 430.247 325.140i 0.646988 0.488933i
\(666\) 504.417 + 627.376i 0.757382 + 0.942006i
\(667\) 134.727i 0.201989i
\(668\) −450.978 −0.675117
\(669\) −894.572 + 315.026i −1.33718 + 0.470890i
\(670\) −168.982 + 127.701i −0.252212 + 0.190598i
\(671\) 588.780i 0.877467i
\(672\) 170.963 60.2051i 0.254410 0.0895909i
\(673\) 549.345i 0.816263i −0.912923 0.408131i \(-0.866181\pi\)
0.912923 0.408131i \(-0.133819\pi\)
\(674\) 65.3549i 0.0969658i
\(675\) −498.802 + 454.776i −0.738966 + 0.673743i
\(676\) −223.868 −0.331166
\(677\) −262.064 −0.387096 −0.193548 0.981091i \(-0.562000\pi\)
−0.193548 + 0.981091i \(0.562000\pi\)
\(678\) −83.3135 236.584i −0.122881 0.348944i
\(679\) 1581.16 2.32867
\(680\) 83.6186 + 110.650i 0.122969 + 0.162720i
\(681\) 445.466 + 1264.98i 0.654135 + 1.85754i
\(682\) 368.165i 0.539832i
\(683\) 420.062 0.615024 0.307512 0.951544i \(-0.400504\pi\)
0.307512 + 0.951544i \(0.400504\pi\)
\(684\) −141.663 + 113.899i −0.207110 + 0.166519i
\(685\) 117.551 + 155.551i 0.171607 + 0.227082i
\(686\) 242.779i 0.353905i
\(687\) −46.0825 130.860i −0.0670778 0.190480i
\(688\) 275.464i 0.400384i
\(689\) 5.65707i 0.00821055i
\(690\) −56.1833 + 84.8141i −0.0814250 + 0.122919i
\(691\) 495.971 0.717758 0.358879 0.933384i \(-0.383159\pi\)
0.358879 + 0.933384i \(0.383159\pi\)
\(692\) −214.622 −0.310147
\(693\) −412.566 + 331.708i −0.595334 + 0.478655i
\(694\) 617.182 0.889311
\(695\) −334.071 442.065i −0.480678 0.636065i
\(696\) −224.839 + 79.1775i −0.323044 + 0.113761i
\(697\) 106.252i 0.152442i
\(698\) 204.270 0.292651
\(699\) 4.36084 + 12.3834i 0.00623868 + 0.0177159i
\(700\) 513.740 + 145.789i 0.733914 + 0.208270i
\(701\) 29.5797i 0.0421964i −0.999777 0.0210982i \(-0.993284\pi\)
0.999777 0.0210982i \(-0.00671627\pi\)
\(702\) 337.258 543.929i 0.480424 0.774828i
\(703\) 638.703i 0.908539i
\(704\) 44.0577i 0.0625819i
\(705\) −401.468 + 606.056i −0.569459 + 0.859654i
\(706\) 181.075 0.256480
\(707\) −307.353 −0.434729
\(708\) 463.311 163.156i 0.654394 0.230446i
\(709\) −912.295 −1.28673 −0.643367 0.765558i \(-0.722463\pi\)
−0.643367 + 0.765558i \(0.722463\pi\)
\(710\) 690.585 521.879i 0.972654 0.735041i
\(711\) −413.946 + 332.816i −0.582202 + 0.468096i
\(712\) 353.153i 0.496001i
\(713\) −226.705 −0.317959
\(714\) −419.159 + 147.608i −0.587057 + 0.206734i
\(715\) −278.263 368.216i −0.389179 0.514988i
\(716\) 705.522i 0.985366i
\(717\) −262.228 + 92.3442i −0.365730 + 0.128792i
\(718\) 316.153i 0.440325i
\(719\) 55.2032i 0.0767777i −0.999263 0.0383889i \(-0.987777\pi\)
0.999263 0.0383889i \(-0.0122226\pi\)
\(720\) −174.560 43.9171i −0.242445 0.0609960i
\(721\) −1096.99 −1.52149
\(722\) 366.310 0.507355
\(723\) −189.265 537.453i −0.261778 0.743365i
\(724\) 207.201 0.286189
\(725\) −675.635 191.731i −0.931910 0.264457i
\(726\) 127.776 + 362.842i 0.175999 + 0.499783i
\(727\) 262.617i 0.361234i 0.983554 + 0.180617i \(0.0578094\pi\)
−0.983554 + 0.180617i \(0.942191\pi\)
\(728\) −506.336 −0.695517
\(729\) 324.127 + 652.980i 0.444618 + 0.895720i
\(730\) 104.182 78.7312i 0.142715 0.107851i
\(731\) 675.369i 0.923897i
\(732\) −213.068 605.045i −0.291076 0.826564i
\(733\) 889.774i 1.21388i −0.794748 0.606940i \(-0.792397\pi\)
0.794748 0.606940i \(-0.207603\pi\)
\(734\) 339.326i 0.462298i
\(735\) −539.052 + 813.752i −0.733404 + 1.10714i
\(736\) −27.1293 −0.0368605
\(737\) 164.964 0.223831
\(738\) −86.4070 107.470i −0.117083 0.145623i
\(739\) −1099.71 −1.48811 −0.744053 0.668121i \(-0.767099\pi\)
−0.744053 + 0.668121i \(0.767099\pi\)
\(740\) −504.593 + 381.324i −0.681883 + 0.515303i
\(741\) 478.955 168.665i 0.646363 0.227618i
\(742\) 5.09796i 0.00687057i
\(743\) 589.255 0.793076 0.396538 0.918018i \(-0.370212\pi\)
0.396538 + 0.918018i \(0.370212\pi\)
\(744\) −133.232 378.336i −0.179075 0.508516i
\(745\) 346.332 261.725i 0.464875 0.351309i
\(746\) 330.903i 0.443570i
\(747\) −664.595 + 534.342i −0.889686 + 0.715317i
\(748\) 108.018i 0.144410i
\(749\) 1521.18i 2.03095i
\(750\) −345.375 402.450i −0.460500 0.536601i
\(751\) 1379.99 1.83753 0.918766 0.394802i \(-0.129187\pi\)
0.918766 + 0.394802i \(0.129187\pi\)
\(752\) −193.858 −0.257790
\(753\) −393.858 + 138.698i −0.523052 + 0.184194i
\(754\) 665.898 0.883154
\(755\) −346.537 458.561i −0.458990 0.607365i
\(756\) 303.925 490.171i 0.402017 0.648374i
\(757\) 878.486i 1.16048i 0.814444 + 0.580242i \(0.197042\pi\)
−0.814444 + 0.580242i \(0.802958\pi\)
\(758\) −228.471 −0.301413
\(759\) 74.7363 26.3185i 0.0984667 0.0346753i
\(760\) −86.1041 113.939i −0.113295 0.149919i
\(761\) 722.402i 0.949280i 0.880180 + 0.474640i \(0.157422\pi\)
−0.880180 + 0.474640i \(0.842578\pi\)
\(762\) −896.641 + 315.754i −1.17669 + 0.414375i
\(763\) 524.469i 0.687377i
\(764\) 323.154i 0.422976i
\(765\) 427.978 + 107.674i 0.559448 + 0.140750i
\(766\) 628.836 0.820934
\(767\) −1372.17 −1.78901
\(768\) −15.9436 45.2747i −0.0207599 0.0589515i
\(769\) 800.009 1.04032 0.520162 0.854068i \(-0.325872\pi\)
0.520162 + 0.854068i \(0.325872\pi\)
\(770\) −250.761 331.824i −0.325664 0.430940i
\(771\) −442.748 1257.26i −0.574252 1.63069i
\(772\) 223.569i 0.289598i
\(773\) −615.477 −0.796219 −0.398109 0.917338i \(-0.630334\pi\)
−0.398109 + 0.917338i \(0.630334\pi\)
\(774\) −549.228 683.110i −0.709596 0.882571i
\(775\) 322.626 1136.89i 0.416291 1.46695i
\(776\) 418.726i 0.539596i
\(777\) −673.132 1911.48i −0.866322 2.46008i
\(778\) 663.710i 0.853097i
\(779\) 109.410i 0.140450i
\(780\) 419.200 + 277.690i 0.537436 + 0.356013i
\(781\) −674.162 −0.863203
\(782\) 66.5143 0.0850566
\(783\) −399.701 +