Properties

Label 588.4.k.e.521.1
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.1
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.e.509.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.19498 - 0.110261i) q^{3} +(4.87287 + 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +O(q^{10})\) \(q+(-5.19498 - 0.110261i) q^{3} +(4.87287 + 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +(-42.9817 - 24.8155i) q^{11} +2.47499i q^{13} +(-24.3838 - 44.3832i) q^{15} +(-24.7602 + 42.8858i) q^{17} +(96.0631 - 55.4620i) q^{19} +(-149.767 + 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(-140.012 - 8.92575i) q^{27} -134.538i q^{29} +(2.18514 + 1.26159i) q^{31} +(220.553 + 133.655i) q^{33} +(58.5515 + 101.414i) q^{37} +(0.272894 - 12.8575i) q^{39} +160.696 q^{41} -442.678 q^{43} +(121.780 + 233.259i) q^{45} +(155.814 + 269.879i) q^{47} +(133.357 - 220.061i) q^{51} +(248.907 + 143.706i) q^{53} -483.690i q^{55} +(-505.161 + 277.532i) q^{57} +(276.360 - 478.670i) q^{59} +(504.937 - 291.525i) q^{61} +(-20.8890 + 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(787.573 - 432.688i) q^{69} -984.717i q^{71} +(178.030 + 102.786i) q^{73} +(-80.8451 + 133.408i) q^{75} +(-321.643 - 557.103i) q^{79} +(726.375 + 61.8069i) q^{81} +351.902 q^{83} -482.612 q^{85} +(-14.8343 + 698.924i) q^{87} +(-544.376 - 942.887i) q^{89} +(-11.2126 - 6.79487i) q^{93} +(936.205 + 540.518i) q^{95} -1365.09i q^{97} +(-1131.03 - 718.654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 64 q^{9} + O(q^{10}) \) \( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −5.19498 0.110261i −0.999775 0.0212197i
\(4\) 0 0
\(5\) 4.87287 + 8.44005i 0.435842 + 0.754901i 0.997364 0.0725609i \(-0.0231172\pi\)
−0.561522 + 0.827462i \(0.689784\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 26.9757 + 1.14560i 0.999099 + 0.0424298i
\(10\) 0 0
\(11\) −42.9817 24.8155i −1.17813 0.680195i −0.222551 0.974921i \(-0.571438\pi\)
−0.955582 + 0.294726i \(0.904772\pi\)
\(12\) 0 0
\(13\) 2.47499i 0.0528029i 0.999651 + 0.0264015i \(0.00840482\pi\)
−0.999651 + 0.0264015i \(0.991595\pi\)
\(14\) 0 0
\(15\) −24.3838 44.3832i −0.419726 0.763980i
\(16\) 0 0
\(17\) −24.7602 + 42.8858i −0.353248 + 0.611844i −0.986817 0.161843i \(-0.948256\pi\)
0.633568 + 0.773687i \(0.281590\pi\)
\(18\) 0 0
\(19\) 96.0631 55.4620i 1.15991 0.669677i 0.208631 0.977994i \(-0.433099\pi\)
0.951284 + 0.308317i \(0.0997658\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −149.767 + 86.4683i −1.35777 + 0.783908i −0.989323 0.145741i \(-0.953443\pi\)
−0.368446 + 0.929649i \(0.620110\pi\)
\(24\) 0 0
\(25\) 15.0103 25.9987i 0.120083 0.207989i
\(26\) 0 0
\(27\) −140.012 8.92575i −0.997974 0.0636208i
\(28\) 0 0
\(29\) 134.538i 0.861488i −0.902474 0.430744i \(-0.858251\pi\)
0.902474 0.430744i \(-0.141749\pi\)
\(30\) 0 0
\(31\) 2.18514 + 1.26159i 0.0126601 + 0.00730929i 0.506317 0.862348i \(-0.331007\pi\)
−0.493657 + 0.869657i \(0.664340\pi\)
\(32\) 0 0
\(33\) 220.553 + 133.655i 1.16343 + 0.705042i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 58.5515 + 101.414i 0.260157 + 0.450605i 0.966283 0.257481i \(-0.0828924\pi\)
−0.706127 + 0.708086i \(0.749559\pi\)
\(38\) 0 0
\(39\) 0.272894 12.8575i 0.00112046 0.0527910i
\(40\) 0 0
\(41\) 160.696 0.612111 0.306055 0.952014i \(-0.400991\pi\)
0.306055 + 0.952014i \(0.400991\pi\)
\(42\) 0 0
\(43\) −442.678 −1.56995 −0.784973 0.619530i \(-0.787323\pi\)
−0.784973 + 0.619530i \(0.787323\pi\)
\(44\) 0 0
\(45\) 121.780 + 233.259i 0.403420 + 0.772714i
\(46\) 0 0
\(47\) 155.814 + 269.879i 0.483572 + 0.837571i 0.999822 0.0188668i \(-0.00600584\pi\)
−0.516250 + 0.856438i \(0.672673\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 133.357 220.061i 0.366152 0.604210i
\(52\) 0 0
\(53\) 248.907 + 143.706i 0.645093 + 0.372445i 0.786574 0.617496i \(-0.211853\pi\)
−0.141480 + 0.989941i \(0.545186\pi\)
\(54\) 0 0
\(55\) 483.690i 1.18583i
\(56\) 0 0
\(57\) −505.161 + 277.532i −1.17386 + 0.644913i
\(58\) 0 0
\(59\) 276.360 478.670i 0.609814 1.05623i −0.381457 0.924387i \(-0.624577\pi\)
0.991271 0.131842i \(-0.0420892\pi\)
\(60\) 0 0
\(61\) 504.937 291.525i 1.05984 0.611901i 0.134455 0.990920i \(-0.457072\pi\)
0.925389 + 0.379018i \(0.123738\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −20.8890 + 12.0603i −0.0398610 + 0.0230138i
\(66\) 0 0
\(67\) 450.723 780.675i 0.821859 1.42350i −0.0824369 0.996596i \(-0.526270\pi\)
0.904296 0.426906i \(-0.140396\pi\)
\(68\) 0 0
\(69\) 787.573 432.688i 1.37410 0.754920i
\(70\) 0 0
\(71\) 984.717i 1.64598i −0.568058 0.822988i \(-0.692305\pi\)
0.568058 0.822988i \(-0.307695\pi\)
\(72\) 0 0
\(73\) 178.030 + 102.786i 0.285436 + 0.164797i 0.635882 0.771786i \(-0.280637\pi\)
−0.350446 + 0.936583i \(0.613970\pi\)
\(74\) 0 0
\(75\) −80.8451 + 133.408i −0.124469 + 0.205394i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −321.643 557.103i −0.458072 0.793405i 0.540787 0.841160i \(-0.318127\pi\)
−0.998859 + 0.0477551i \(0.984793\pi\)
\(80\) 0 0
\(81\) 726.375 + 61.8069i 0.996399 + 0.0847832i
\(82\) 0 0
\(83\) 351.902 0.465376 0.232688 0.972551i \(-0.425248\pi\)
0.232688 + 0.972551i \(0.425248\pi\)
\(84\) 0 0
\(85\) −482.612 −0.615842
\(86\) 0 0
\(87\) −14.8343 + 698.924i −0.0182805 + 0.861294i
\(88\) 0 0
\(89\) −544.376 942.887i −0.648357 1.12299i −0.983515 0.180825i \(-0.942123\pi\)
0.335159 0.942162i \(-0.391210\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −11.2126 6.79487i −0.0125021 0.00757629i
\(94\) 0 0
\(95\) 936.205 + 540.518i 1.01108 + 0.583747i
\(96\) 0 0
\(97\) 1365.09i 1.42891i −0.699683 0.714454i \(-0.746675\pi\)
0.699683 0.714454i \(-0.253325\pi\)
\(98\) 0 0
\(99\) −1131.03 718.654i −1.14821 0.729571i
\(100\) 0 0
\(101\) −651.926 + 1129.17i −0.642268 + 1.11244i 0.342658 + 0.939460i \(0.388673\pi\)
−0.984925 + 0.172980i \(0.944660\pi\)
\(102\) 0 0
\(103\) 1094.23 631.752i 1.04677 0.604354i 0.125027 0.992153i \(-0.460098\pi\)
0.921744 + 0.387800i \(0.126765\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1267.25 731.647i 1.14495 0.661037i 0.197299 0.980343i \(-0.436783\pi\)
0.947652 + 0.319306i \(0.103450\pi\)
\(108\) 0 0
\(109\) 1119.89 1939.71i 0.984093 1.70450i 0.338193 0.941077i \(-0.390184\pi\)
0.645900 0.763422i \(-0.276482\pi\)
\(110\) 0 0
\(111\) −292.992 533.300i −0.250536 0.456024i
\(112\) 0 0
\(113\) 281.355i 0.234227i 0.993119 + 0.117114i \(0.0373642\pi\)
−0.993119 + 0.117114i \(0.962636\pi\)
\(114\) 0 0
\(115\) −1459.59 842.697i −1.18355 0.683321i
\(116\) 0 0
\(117\) −2.83536 + 66.7645i −0.00224042 + 0.0527554i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 566.115 + 980.541i 0.425331 + 0.736695i
\(122\) 0 0
\(123\) −834.814 17.7185i −0.611973 0.0129888i
\(124\) 0 0
\(125\) 1510.79 1.08103
\(126\) 0 0
\(127\) −576.095 −0.402521 −0.201261 0.979538i \(-0.564504\pi\)
−0.201261 + 0.979538i \(0.564504\pi\)
\(128\) 0 0
\(129\) 2299.70 + 48.8099i 1.56959 + 0.0333137i
\(130\) 0 0
\(131\) 1142.71 + 1979.23i 0.762130 + 1.32005i 0.941750 + 0.336313i \(0.109180\pi\)
−0.179620 + 0.983736i \(0.557487\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −606.925 1225.20i −0.386932 0.781101i
\(136\) 0 0
\(137\) −892.802 515.459i −0.556768 0.321450i 0.195079 0.980787i \(-0.437504\pi\)
−0.751847 + 0.659337i \(0.770837\pi\)
\(138\) 0 0
\(139\) 234.497i 0.143092i −0.997437 0.0715460i \(-0.977207\pi\)
0.997437 0.0715460i \(-0.0227933\pi\)
\(140\) 0 0
\(141\) −779.697 1419.19i −0.465690 0.847644i
\(142\) 0 0
\(143\) 61.4180 106.379i 0.0359163 0.0622088i
\(144\) 0 0
\(145\) 1135.51 655.587i 0.650338 0.375473i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2015.55 + 1163.68i −1.10819 + 0.639814i −0.938360 0.345660i \(-0.887655\pi\)
−0.169830 + 0.985473i \(0.554322\pi\)
\(150\) 0 0
\(151\) −527.571 + 913.779i −0.284325 + 0.492466i −0.972445 0.233131i \(-0.925103\pi\)
0.688120 + 0.725597i \(0.258436\pi\)
\(152\) 0 0
\(153\) −717.052 + 1128.51i −0.378891 + 0.596305i
\(154\) 0 0
\(155\) 24.5902i 0.0127428i
\(156\) 0 0
\(157\) −38.3884 22.1635i −0.0195142 0.0112665i 0.490211 0.871604i \(-0.336920\pi\)
−0.509725 + 0.860337i \(0.670253\pi\)
\(158\) 0 0
\(159\) −1277.22 773.996i −0.637045 0.386050i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 126.057 + 218.337i 0.0605738 + 0.104917i 0.894722 0.446623i \(-0.147374\pi\)
−0.834148 + 0.551540i \(0.814040\pi\)
\(164\) 0 0
\(165\) −53.3320 + 2512.76i −0.0251630 + 1.18556i
\(166\) 0 0
\(167\) −1657.35 −0.767962 −0.383981 0.923341i \(-0.625447\pi\)
−0.383981 + 0.923341i \(0.625447\pi\)
\(168\) 0 0
\(169\) 2190.87 0.997212
\(170\) 0 0
\(171\) 2654.90 1386.08i 1.18728 0.619859i
\(172\) 0 0
\(173\) 1663.55 + 2881.36i 0.731084 + 1.26627i 0.956420 + 0.291994i \(0.0943186\pi\)
−0.225336 + 0.974281i \(0.572348\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1488.46 + 2456.21i −0.632090 + 1.04305i
\(178\) 0 0
\(179\) −372.577 215.108i −0.155574 0.0898206i 0.420192 0.907435i \(-0.361963\pi\)
−0.575766 + 0.817615i \(0.695296\pi\)
\(180\) 0 0
\(181\) 2230.49i 0.915971i 0.888960 + 0.457986i \(0.151429\pi\)
−0.888960 + 0.457986i \(0.848571\pi\)
\(182\) 0 0
\(183\) −2655.28 + 1458.79i −1.07259 + 0.589274i
\(184\) 0 0
\(185\) −570.627 + 988.355i −0.226775 + 0.392785i
\(186\) 0 0
\(187\) 2128.47 1228.87i 0.832346 0.480555i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1003.30 579.256i 0.380086 0.219442i −0.297770 0.954638i \(-0.596243\pi\)
0.677855 + 0.735195i \(0.262910\pi\)
\(192\) 0 0
\(193\) 1127.84 1953.48i 0.420641 0.728572i −0.575361 0.817899i \(-0.695138\pi\)
0.996002 + 0.0893276i \(0.0284718\pi\)
\(194\) 0 0
\(195\) 109.848 60.3497i 0.0403404 0.0221627i
\(196\) 0 0
\(197\) 3280.44i 1.18641i 0.805053 + 0.593203i \(0.202137\pi\)
−0.805053 + 0.593203i \(0.797863\pi\)
\(198\) 0 0
\(199\) −3818.10 2204.38i −1.36009 0.785248i −0.370454 0.928851i \(-0.620798\pi\)
−0.989635 + 0.143603i \(0.954131\pi\)
\(200\) 0 0
\(201\) −2427.58 + 4005.90i −0.851880 + 1.40574i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 783.051 + 1356.28i 0.266784 + 0.462083i
\(206\) 0 0
\(207\) −4139.14 + 2160.97i −1.38981 + 0.725592i
\(208\) 0 0
\(209\) −5505.27 −1.82204
\(210\) 0 0
\(211\) 5620.46 1.83378 0.916892 0.399135i \(-0.130689\pi\)
0.916892 + 0.399135i \(0.130689\pi\)
\(212\) 0 0
\(213\) −108.576 + 5115.59i −0.0349271 + 1.64561i
\(214\) 0 0
\(215\) −2157.11 3736.22i −0.684249 1.18515i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −913.530 553.600i −0.281875 0.170816i
\(220\) 0 0
\(221\) −106.142 61.2811i −0.0323072 0.0186525i
\(222\) 0 0
\(223\) 1134.63i 0.340718i 0.985382 + 0.170359i \(0.0544928\pi\)
−0.985382 + 0.170359i \(0.945507\pi\)
\(224\) 0 0
\(225\) 434.699 684.136i 0.128800 0.202707i
\(226\) 0 0
\(227\) 1061.60 1838.75i 0.310400 0.537629i −0.668049 0.744118i \(-0.732870\pi\)
0.978449 + 0.206488i \(0.0662035\pi\)
\(228\) 0 0
\(229\) −2299.77 + 1327.77i −0.663638 + 0.383152i −0.793662 0.608359i \(-0.791828\pi\)
0.130023 + 0.991511i \(0.458495\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2734.14 1578.56i 0.768754 0.443840i −0.0636761 0.997971i \(-0.520282\pi\)
0.832430 + 0.554130i \(0.186949\pi\)
\(234\) 0 0
\(235\) −1518.53 + 2630.16i −0.421522 + 0.730098i
\(236\) 0 0
\(237\) 1609.51 + 2929.60i 0.441133 + 0.802946i
\(238\) 0 0
\(239\) 2040.14i 0.552157i −0.961135 0.276079i \(-0.910965\pi\)
0.961135 0.276079i \(-0.0890351\pi\)
\(240\) 0 0
\(241\) −3958.64 2285.52i −1.05809 0.610886i −0.133184 0.991091i \(-0.542520\pi\)
−0.924902 + 0.380205i \(0.875853\pi\)
\(242\) 0 0
\(243\) −3766.69 401.177i −0.994376 0.105907i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 137.268 + 237.755i 0.0353609 + 0.0612469i
\(248\) 0 0
\(249\) −1828.12 38.8009i −0.465272 0.00987513i
\(250\) 0 0
\(251\) 5848.44 1.47072 0.735359 0.677678i \(-0.237014\pi\)
0.735359 + 0.677678i \(0.237014\pi\)
\(252\) 0 0
\(253\) 8583.01 2.13284
\(254\) 0 0
\(255\) 2507.16 + 53.2131i 0.615704 + 0.0130680i
\(256\) 0 0
\(257\) −3884.44 6728.05i −0.942820 1.63301i −0.760058 0.649855i \(-0.774830\pi\)
−0.182762 0.983157i \(-0.558504\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 154.128 3629.26i 0.0365527 0.860712i
\(262\) 0 0
\(263\) −4077.64 2354.23i −0.956038 0.551969i −0.0610865 0.998132i \(-0.519457\pi\)
−0.894951 + 0.446164i \(0.852790\pi\)
\(264\) 0 0
\(265\) 2801.05i 0.649309i
\(266\) 0 0
\(267\) 2724.06 + 4958.30i 0.624381 + 1.13649i
\(268\) 0 0
\(269\) 2054.29 3558.14i 0.465622 0.806481i −0.533607 0.845732i \(-0.679164\pi\)
0.999229 + 0.0392514i \(0.0124973\pi\)
\(270\) 0 0
\(271\) −700.809 + 404.612i −0.157089 + 0.0906953i −0.576484 0.817109i \(-0.695576\pi\)
0.419395 + 0.907804i \(0.362242\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1290.34 + 744.978i −0.282947 + 0.163359i
\(276\) 0 0
\(277\) 3727.43 6456.10i 0.808518 1.40039i −0.105372 0.994433i \(-0.533603\pi\)
0.913890 0.405962i \(-0.133063\pi\)
\(278\) 0 0
\(279\) 57.5003 + 36.5355i 0.0123385 + 0.00783988i
\(280\) 0 0
\(281\) 1289.89i 0.273837i 0.990582 + 0.136919i \(0.0437198\pi\)
−0.990582 + 0.136919i \(0.956280\pi\)
\(282\) 0 0
\(283\) −7466.08 4310.54i −1.56824 0.905424i −0.996374 0.0850780i \(-0.972886\pi\)
−0.571867 0.820346i \(-0.693781\pi\)
\(284\) 0 0
\(285\) −4803.97 2911.21i −0.998466 0.605071i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1230.37 + 2131.06i 0.250431 + 0.433760i
\(290\) 0 0
\(291\) −150.516 + 7091.62i −0.0303209 + 1.42859i
\(292\) 0 0
\(293\) −6187.72 −1.23376 −0.616878 0.787059i \(-0.711603\pi\)
−0.616878 + 0.787059i \(0.711603\pi\)
\(294\) 0 0
\(295\) 5386.66 1.06313
\(296\) 0 0
\(297\) 5796.45 + 3858.10i 1.13247 + 0.753771i
\(298\) 0 0
\(299\) −214.008 370.673i −0.0413926 0.0716941i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 3511.25 5794.13i 0.665729 1.09856i
\(304\) 0 0
\(305\) 4920.98 + 2841.13i 0.923850 + 0.533385i
\(306\) 0 0
\(307\) 3785.51i 0.703747i −0.936048 0.351873i \(-0.885545\pi\)
0.936048 0.351873i \(-0.114455\pi\)
\(308\) 0 0
\(309\) −5754.15 + 3161.29i −1.05936 + 0.582005i
\(310\) 0 0
\(311\) −2998.76 + 5194.00i −0.546765 + 0.947025i 0.451728 + 0.892156i \(0.350808\pi\)
−0.998494 + 0.0548698i \(0.982526\pi\)
\(312\) 0 0
\(313\) −4960.97 + 2864.22i −0.895881 + 0.517237i −0.875861 0.482563i \(-0.839706\pi\)
−0.0200193 + 0.999800i \(0.506373\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5818.71 + 3359.43i −1.03095 + 0.595219i −0.917257 0.398297i \(-0.869602\pi\)
−0.113693 + 0.993516i \(0.536268\pi\)
\(318\) 0 0
\(319\) −3338.63 + 5782.68i −0.585980 + 1.01495i
\(320\) 0 0
\(321\) −6664.01 + 3661.17i −1.15872 + 0.636593i
\(322\) 0 0
\(323\) 5493.00i 0.946249i
\(324\) 0 0
\(325\) 64.3464 + 37.1504i 0.0109825 + 0.00634072i
\(326\) 0 0
\(327\) −6031.69 + 9953.27i −1.02004 + 1.68323i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −845.184 1463.90i −0.140349 0.243092i 0.787279 0.616597i \(-0.211489\pi\)
−0.927628 + 0.373505i \(0.878156\pi\)
\(332\) 0 0
\(333\) 1463.29 + 2802.79i 0.240803 + 0.461237i
\(334\) 0 0
\(335\) 8785.25 1.43280
\(336\) 0 0
\(337\) 4257.51 0.688194 0.344097 0.938934i \(-0.388185\pi\)
0.344097 + 0.938934i \(0.388185\pi\)
\(338\) 0 0
\(339\) 31.0224 1461.64i 0.00497023 0.234174i
\(340\) 0 0
\(341\) −62.6139 108.450i −0.00994349 0.0172226i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 7489.65 + 4538.73i 1.16878 + 0.708281i
\(346\) 0 0
\(347\) −1092.59 630.806i −0.169029 0.0975891i 0.413099 0.910686i \(-0.364446\pi\)
−0.582128 + 0.813097i \(0.697780\pi\)
\(348\) 0 0
\(349\) 10981.9i 1.68438i 0.539179 + 0.842191i \(0.318735\pi\)
−0.539179 + 0.842191i \(0.681265\pi\)
\(350\) 0 0
\(351\) 22.0911 346.528i 0.00335936 0.0526960i
\(352\) 0 0
\(353\) 3677.09 6368.90i 0.554424 0.960290i −0.443524 0.896262i \(-0.646272\pi\)
0.997948 0.0640280i \(-0.0203947\pi\)
\(354\) 0 0
\(355\) 8311.06 4798.39i 1.24255 0.717387i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −432.312 + 249.595i −0.0635559 + 0.0366940i −0.531441 0.847095i \(-0.678349\pi\)
0.467885 + 0.883789i \(0.345016\pi\)
\(360\) 0 0
\(361\) 2722.58 4715.64i 0.396935 0.687511i
\(362\) 0 0
\(363\) −2832.84 5156.31i −0.409603 0.745554i
\(364\) 0 0
\(365\) 2003.44i 0.287302i
\(366\) 0 0
\(367\) −282.908 163.337i −0.0402390 0.0232320i 0.479746 0.877408i \(-0.340729\pi\)
−0.519985 + 0.854176i \(0.674062\pi\)
\(368\) 0 0
\(369\) 4334.89 + 184.094i 0.611559 + 0.0259717i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 137.986 + 239.000i 0.0191546 + 0.0331767i 0.875444 0.483320i \(-0.160569\pi\)
−0.856289 + 0.516497i \(0.827236\pi\)
\(374\) 0 0
\(375\) −7848.53 166.581i −1.08079 0.0229392i
\(376\) 0 0
\(377\) 332.981 0.0454891
\(378\) 0 0
\(379\) 508.854 0.0689659 0.0344829 0.999405i \(-0.489022\pi\)
0.0344829 + 0.999405i \(0.489022\pi\)
\(380\) 0 0
\(381\) 2992.80 + 63.5206i 0.402430 + 0.00854137i
\(382\) 0 0
\(383\) 2212.79 + 3832.66i 0.295217 + 0.511331i 0.975035 0.222049i \(-0.0712746\pi\)
−0.679818 + 0.733381i \(0.737941\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11941.5 507.133i −1.56853 0.0666125i
\(388\) 0 0
\(389\) −1558.98 900.077i −0.203196 0.117315i 0.394949 0.918703i \(-0.370762\pi\)
−0.598146 + 0.801388i \(0.704096\pi\)
\(390\) 0 0
\(391\) 8563.87i 1.10766i
\(392\) 0 0
\(393\) −5718.13 10408.1i −0.733948 1.33592i
\(394\) 0 0
\(395\) 3134.65 5429.38i 0.399295 0.691599i
\(396\) 0 0
\(397\) 5601.29 3233.91i 0.708113 0.408829i −0.102249 0.994759i \(-0.532604\pi\)
0.810362 + 0.585930i \(0.199271\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2974.16 + 1717.13i −0.370381 + 0.213839i −0.673625 0.739074i \(-0.735264\pi\)
0.303244 + 0.952913i \(0.401930\pi\)
\(402\) 0 0
\(403\) −3.12242 + 5.40819i −0.000385952 + 0.000668489i
\(404\) 0 0
\(405\) 3017.88 + 6431.82i 0.370270 + 0.789135i
\(406\) 0 0
\(407\) 5811.93i 0.707829i
\(408\) 0 0
\(409\) −817.228 471.827i −0.0988003 0.0570424i 0.449786 0.893136i \(-0.351500\pi\)
−0.548586 + 0.836094i \(0.684834\pi\)
\(410\) 0 0
\(411\) 4581.26 + 2776.24i 0.549822 + 0.333192i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1714.77 + 2970.07i 0.202831 + 0.351313i
\(416\) 0 0
\(417\) −25.8558 + 1218.21i −0.00303637 + 0.143060i
\(418\) 0 0
\(419\) −10148.4 −1.18325 −0.591626 0.806213i \(-0.701514\pi\)
−0.591626 + 0.806213i \(0.701514\pi\)
\(420\) 0 0
\(421\) −6775.40 −0.784354 −0.392177 0.919890i \(-0.628278\pi\)
−0.392177 + 0.919890i \(0.628278\pi\)
\(422\) 0 0
\(423\) 3894.03 + 7458.66i 0.447598 + 0.857335i
\(424\) 0 0
\(425\) 743.317 + 1287.46i 0.0848381 + 0.146944i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −330.795 + 545.865i −0.0372283 + 0.0614327i
\(430\) 0 0
\(431\) −14439.3 8336.51i −1.61372 0.931684i −0.988497 0.151241i \(-0.951673\pi\)
−0.625227 0.780443i \(-0.714993\pi\)
\(432\) 0 0
\(433\) 2848.46i 0.316140i −0.987428 0.158070i \(-0.949473\pi\)
0.987428 0.158070i \(-0.0505271\pi\)
\(434\) 0 0
\(435\) −5971.24 + 3280.56i −0.658159 + 0.361588i
\(436\) 0 0
\(437\) −9591.41 + 16612.8i −1.04993 + 1.81853i
\(438\) 0 0
\(439\) 8042.46 4643.32i 0.874364 0.504814i 0.00556785 0.999984i \(-0.498228\pi\)
0.868796 + 0.495170i \(0.164894\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4281.76 2472.08i 0.459216 0.265128i −0.252499 0.967597i \(-0.581252\pi\)
0.711714 + 0.702469i \(0.247919\pi\)
\(444\) 0 0
\(445\) 5305.34 9189.12i 0.565163 0.978890i
\(446\) 0 0
\(447\) 10599.1 5823.05i 1.12152 0.616154i
\(448\) 0 0
\(449\) 15964.7i 1.67799i −0.544136 0.838997i \(-0.683142\pi\)
0.544136 0.838997i \(-0.316858\pi\)
\(450\) 0 0
\(451\) −6906.99 3987.75i −0.721147 0.416355i
\(452\) 0 0
\(453\) 2841.47 4688.90i 0.294711 0.486321i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4133.41 + 7159.28i 0.423092 + 0.732816i 0.996240 0.0866354i \(-0.0276115\pi\)
−0.573148 + 0.819452i \(0.694278\pi\)
\(458\) 0 0
\(459\) 3849.50 5783.53i 0.391459 0.588130i
\(460\) 0 0
\(461\) −3468.42 −0.350413 −0.175207 0.984532i \(-0.556059\pi\)
−0.175207 + 0.984532i \(0.556059\pi\)
\(462\) 0 0
\(463\) −9918.45 −0.995572 −0.497786 0.867300i \(-0.665853\pi\)
−0.497786 + 0.867300i \(0.665853\pi\)
\(464\) 0 0
\(465\) 2.71133 127.746i 0.000270398 0.0127399i
\(466\) 0 0
\(467\) 8430.55 + 14602.1i 0.835373 + 1.44691i 0.893726 + 0.448613i \(0.148082\pi\)
−0.0583529 + 0.998296i \(0.518585\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 196.983 + 119.372i 0.0192707 + 0.0116781i
\(472\) 0 0
\(473\) 19027.0 + 10985.3i 1.84960 + 1.06787i
\(474\) 0 0
\(475\) 3330.02i 0.321667i
\(476\) 0 0
\(477\) 6549.80 + 4161.72i 0.628710 + 0.399481i
\(478\) 0 0
\(479\) −1578.16 + 2733.46i −0.150539 + 0.260741i −0.931426 0.363932i \(-0.881434\pi\)
0.780887 + 0.624672i \(0.214768\pi\)
\(480\) 0 0
\(481\) −250.999 + 144.914i −0.0237932 + 0.0137370i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 11521.4 6651.91i 1.07868 0.622778i
\(486\) 0 0
\(487\) −1214.17 + 2103.01i −0.112976 + 0.195681i −0.916969 0.398958i \(-0.869372\pi\)
0.803993 + 0.594639i \(0.202705\pi\)
\(488\) 0 0
\(489\) −630.789 1148.15i −0.0583339 0.106179i
\(490\) 0 0
\(491\) 1304.86i 0.119933i 0.998200 + 0.0599667i \(0.0190995\pi\)
−0.998200 + 0.0599667i \(0.980901\pi\)
\(492\) 0 0
\(493\) 5769.79 + 3331.19i 0.527096 + 0.304319i
\(494\) 0 0
\(495\) 554.117 13047.9i 0.0503146 1.18476i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1272.72 2204.42i −0.114178 0.197762i 0.803273 0.595611i \(-0.203090\pi\)
−0.917451 + 0.397849i \(0.869757\pi\)
\(500\) 0 0
\(501\) 8609.91 + 182.741i 0.767789 + 0.0162959i
\(502\) 0 0
\(503\) −787.994 −0.0698507 −0.0349253 0.999390i \(-0.511119\pi\)
−0.0349253 + 0.999390i \(0.511119\pi\)
\(504\) 0 0
\(505\) −12707.0 −1.11971
\(506\) 0 0
\(507\) −11381.6 241.567i −0.996987 0.0211605i
\(508\) 0 0
\(509\) 1538.89 + 2665.44i 0.134008 + 0.232109i 0.925218 0.379436i \(-0.123882\pi\)
−0.791210 + 0.611544i \(0.790549\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −13945.0 + 6907.91i −1.20017 + 0.594526i
\(514\) 0 0
\(515\) 10664.0 + 6156.89i 0.912454 + 0.526806i
\(516\) 0 0
\(517\) 15466.4i 1.31569i
\(518\) 0 0
\(519\) −8324.43 15152.0i −0.704050 1.28150i
\(520\) 0 0
\(521\) −663.114 + 1148.55i −0.0557611 + 0.0965811i −0.892559 0.450931i \(-0.851092\pi\)
0.836797 + 0.547513i \(0.184425\pi\)
\(522\) 0 0
\(523\) 5799.32 3348.24i 0.484869 0.279940i −0.237574 0.971369i \(-0.576352\pi\)
0.722444 + 0.691430i \(0.243019\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −108.209 + 62.4743i −0.00894429 + 0.00516399i
\(528\) 0 0
\(529\) 8870.03 15363.3i 0.729023 1.26271i
\(530\) 0 0
\(531\) 8003.37 12595.8i 0.654080 1.02940i
\(532\) 0 0
\(533\) 397.721i 0.0323212i
\(534\) 0 0
\(535\) 12350.3 + 7130.44i 0.998036 + 0.576216i
\(536\) 0 0
\(537\) 1911.81 + 1158.56i 0.153633 + 0.0931016i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9558.74 16556.2i −0.759634 1.31573i −0.943037 0.332687i \(-0.892045\pi\)
0.183403 0.983038i \(-0.441289\pi\)
\(542\) 0 0
\(543\) 245.935 11587.3i 0.0194366 0.915765i
\(544\) 0 0
\(545\) 21828.3 1.71564
\(546\) 0 0
\(547\) −12400.5 −0.969297 −0.484649 0.874709i \(-0.661053\pi\)
−0.484649 + 0.874709i \(0.661053\pi\)
\(548\) 0 0
\(549\) 13955.0 7285.64i 1.08485 0.566381i
\(550\) 0 0
\(551\) −7461.77 12924.2i −0.576918 0.999252i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3073.37 5071.57i 0.235058 0.387885i
\(556\) 0 0
\(557\) −6062.22 3500.02i −0.461157 0.266249i 0.251374 0.967890i \(-0.419118\pi\)
−0.712531 + 0.701641i \(0.752451\pi\)
\(558\) 0 0
\(559\) 1095.62i 0.0828978i
\(560\) 0 0
\(561\) −11192.8 + 6149.27i −0.842356 + 0.462785i
\(562\) 0 0
\(563\) 10239.9 17736.1i 0.766538 1.32768i −0.172891 0.984941i \(-0.555311\pi\)
0.939430 0.342742i \(-0.111356\pi\)
\(564\) 0 0
\(565\) −2374.65 + 1371.01i −0.176818 + 0.102086i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8603.00 4966.94i 0.633843 0.365949i −0.148396 0.988928i \(-0.547411\pi\)
0.782239 + 0.622979i \(0.214078\pi\)
\(570\) 0 0
\(571\) −2929.14 + 5073.42i −0.214677 + 0.371832i −0.953173 0.302427i \(-0.902203\pi\)
0.738496 + 0.674258i \(0.235537\pi\)
\(572\) 0 0
\(573\) −5276.00 + 2898.60i −0.384656 + 0.211328i
\(574\) 0 0
\(575\) 5191.68i 0.376535i
\(576\) 0 0
\(577\) 15287.5 + 8826.26i 1.10300 + 0.636815i 0.937006 0.349313i \(-0.113585\pi\)
0.165989 + 0.986128i \(0.446918\pi\)
\(578\) 0 0
\(579\) −6074.50 + 10023.9i −0.436006 + 0.719482i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7132.28 12353.5i −0.506670 0.877579i
\(584\) 0 0
\(585\) −577.312 + 301.404i −0.0408016 + 0.0213017i
\(586\) 0 0
\(587\) 25424.1 1.78768 0.893838 0.448390i \(-0.148002\pi\)
0.893838 + 0.448390i \(0.148002\pi\)
\(588\) 0 0
\(589\) 279.881 0.0195795
\(590\) 0 0
\(591\) 361.704 17041.8i 0.0251751 1.18614i
\(592\) 0 0
\(593\) 3832.38 + 6637.89i 0.265392 + 0.459672i 0.967666 0.252235i \(-0.0811654\pi\)
−0.702275 + 0.711906i \(0.747832\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 19591.9 + 11872.7i 1.34312 + 0.813932i
\(598\) 0 0
\(599\) 23961.5 + 13834.2i 1.63446 + 0.943655i 0.982695 + 0.185233i \(0.0593041\pi\)
0.651764 + 0.758422i \(0.274029\pi\)
\(600\) 0 0
\(601\) 11624.0i 0.788937i −0.918909 0.394469i \(-0.870929\pi\)
0.918909 0.394469i \(-0.129071\pi\)
\(602\) 0 0
\(603\) 13052.9 20542.9i 0.881518 1.38735i
\(604\) 0 0
\(605\) −5517.21 + 9556.09i −0.370754 + 0.642166i
\(606\) 0 0
\(607\) −2675.97 + 1544.97i −0.178936 + 0.103309i −0.586793 0.809737i \(-0.699610\pi\)
0.407857 + 0.913046i \(0.366276\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −667.946 + 385.639i −0.0442262 + 0.0255340i
\(612\) 0 0
\(613\) 1623.78 2812.47i 0.106989 0.185310i −0.807560 0.589785i \(-0.799213\pi\)
0.914549 + 0.404475i \(0.132546\pi\)
\(614\) 0 0
\(615\) −3918.39 7132.21i −0.256918 0.467640i
\(616\) 0 0
\(617\) 10686.9i 0.697307i 0.937252 + 0.348654i \(0.113361\pi\)
−0.937252 + 0.348654i \(0.886639\pi\)
\(618\) 0 0
\(619\) −4946.00 2855.58i −0.321158 0.185420i 0.330751 0.943718i \(-0.392698\pi\)
−0.651908 + 0.758298i \(0.726031\pi\)
\(620\) 0 0
\(621\) 21741.0 10769.8i 1.40489 0.695938i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5485.59 + 9501.31i 0.351077 + 0.608084i
\(626\) 0 0
\(627\) 28599.8 + 607.014i 1.82163 + 0.0386632i
\(628\) 0 0
\(629\) −5798.97 −0.367600
\(630\) 0 0
\(631\) −13708.4 −0.864854 −0.432427 0.901669i \(-0.642343\pi\)
−0.432427 + 0.901669i \(0.642343\pi\)
\(632\) 0 0
\(633\) −29198.2 619.716i −1.83337 0.0389123i
\(634\) 0 0
\(635\) −2807.23 4862.27i −0.175436 0.303864i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1128.10 26563.4i 0.0698385 1.64449i
\(640\) 0 0
\(641\) −14083.3 8131.00i −0.867796 0.501022i −0.00118054 0.999999i \(-0.500376\pi\)
−0.866615 + 0.498977i \(0.833709\pi\)
\(642\) 0 0
\(643\) 13805.8i 0.846729i 0.905959 + 0.423365i \(0.139151\pi\)
−0.905959 + 0.423365i \(0.860849\pi\)
\(644\) 0 0
\(645\) 10794.2 + 19647.4i 0.658947 + 1.19941i
\(646\) 0 0
\(647\) −9180.08 + 15900.4i −0.557815 + 0.966163i 0.439864 + 0.898064i \(0.355027\pi\)
−0.997679 + 0.0680988i \(0.978307\pi\)
\(648\) 0 0
\(649\) −23756.8 + 13716.0i −1.43688 + 0.829585i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16302.6 + 9412.30i −0.976983 + 0.564061i −0.901358 0.433075i \(-0.857428\pi\)
−0.0756247 + 0.997136i \(0.524095\pi\)
\(654\) 0 0
\(655\) −11136.6 + 19289.1i −0.664338 + 1.15067i
\(656\) 0 0
\(657\) 4684.73 + 2976.67i 0.278187 + 0.176759i
\(658\) 0 0
\(659\) 3472.55i 0.205268i 0.994719 + 0.102634i \(0.0327270\pi\)
−0.994719 + 0.102634i \(0.967273\pi\)
\(660\) 0 0
\(661\) 11328.2 + 6540.36i 0.666592 + 0.384857i 0.794784 0.606892i \(-0.207584\pi\)
−0.128192 + 0.991749i \(0.540917\pi\)
\(662\) 0 0
\(663\) 544.649 + 330.057i 0.0319041 + 0.0193339i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 11633.3 + 20149.5i 0.675327 + 1.16970i
\(668\) 0 0
\(669\) 125.105 5894.36i 0.00722993 0.340641i
\(670\) 0 0
\(671\) −28937.3 −1.66485
\(672\) 0 0
\(673\) −13701.5 −0.784775 −0.392388 0.919800i \(-0.628351\pi\)
−0.392388 + 0.919800i \(0.628351\pi\)
\(674\) 0 0
\(675\) −2333.68 + 3506.15i −0.133072 + 0.199928i
\(676\) 0 0
\(677\) 1975.54 + 3421.74i 0.112151 + 0.194251i 0.916637 0.399720i \(-0.130893\pi\)
−0.804486 + 0.593971i \(0.797559\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5717.74 + 9435.20i −0.321739 + 0.530922i
\(682\) 0 0
\(683\) −22216.3 12826.6i −1.24463 0.718589i −0.274598 0.961559i \(-0.588545\pi\)
−0.970034 + 0.242970i \(0.921878\pi\)
\(684\) 0 0
\(685\) 10047.1i 0.560406i
\(686\) 0 0
\(687\) 12093.7 6644.19i 0.671619 0.368983i
\(688\) 0 0
\(689\) −355.671 + 616.041i −0.0196662 + 0.0340628i
\(690\) 0 0
\(691\) 7142.53 4123.74i 0.393219 0.227025i −0.290335 0.956925i \(-0.593767\pi\)
0.683554 + 0.729900i \(0.260433\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1979.17 1142.67i 0.108020 0.0623655i
\(696\) 0 0
\(697\) −3978.86 + 6891.59i −0.216227 + 0.374516i
\(698\) 0 0
\(699\) −14377.9 + 7899.11i −0.777999 + 0.427428i
\(700\) 0 0
\(701\) 25364.7i 1.36663i −0.730122 0.683317i \(-0.760537\pi\)
0.730122 0.683317i \(-0.239463\pi\)
\(702\) 0 0
\(703\) 11249.3 + 6494.77i 0.603519 + 0.348442i
\(704\) 0 0
\(705\) 8178.72 13496.2i 0.436920 0.720989i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −14695.0 25452.5i −0.778397 1.34822i −0.932865 0.360225i \(-0.882700\pi\)
0.154469 0.987998i \(-0.450633\pi\)
\(710\) 0 0
\(711\) −8038.33 15396.7i −0.423996 0.812126i
\(712\) 0 0
\(713\) −436.350 −0.0229193
\(714\) 0 0
\(715\) 1197.13 0.0626154
\(716\) 0 0
\(717\) −224.947 + 10598.5i −0.0117166 + 0.552033i
\(718\) 0 0
\(719\) −1802.02 3121.19i −0.0934687 0.161893i 0.815500 0.578757i \(-0.196462\pi\)
−0.908968 + 0.416865i \(0.863129\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 20313.1 + 12309.7i 1.04488 + 0.633201i
\(724\) 0 0
\(725\) −3497.82 2019.47i −0.179180 0.103450i
\(726\) 0 0
\(727\) 35634.9i 1.81792i 0.416887 + 0.908958i \(0.363121\pi\)
−0.416887 + 0.908958i \(0.636879\pi\)
\(728\) 0 0
\(729\) 19523.7 + 2499.42i 0.991905 + 0.126984i
\(730\) 0 0
\(731\) 10960.8 18984.6i 0.554581 0.960562i
\(732\) 0 0
\(733\) −10831.6 + 6253.60i −0.545802 + 0.315119i −0.747427 0.664344i \(-0.768711\pi\)
0.201625 + 0.979463i \(0.435378\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −38745.6 + 22369.8i −1.93652 + 1.11805i
\(738\) 0 0
\(739\) −4972.17 + 8612.05i −0.247502 + 0.428687i −0.962832 0.270100i \(-0.912943\pi\)
0.715330 + 0.698787i \(0.246276\pi\)
\(740\) 0 0
\(741\) −686.889 1250.27i −0.0340533 0.0619835i
\(742\) 0 0
\(743\) 12175.9i 0.601198i −0.953751 0.300599i \(-0.902813\pi\)
0.953751 0.300599i \(-0.0971866\pi\)
\(744\) 0 0
\(745\) −19643.0 11340.9i −0.965992 0.557716i
\(746\) 0 0
\(747\) 9492.79 + 403.140i 0.464957 + 0.0197458i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7950.95 + 13771.4i 0.386331 + 0.669144i 0.991953 0.126608i \(-0.0404091\pi\)
−0.605622 + 0.795752i \(0.707076\pi\)
\(752\) 0 0
\(753\) −30382.5 644.853i −1.47039 0.0312081i
\(754\) 0 0
\(755\) −10283.1 −0.495684
\(756\) 0 0
\(757\) 39209.6 1.88256 0.941279 0.337630i \(-0.109625\pi\)
0.941279 + 0.337630i \(0.109625\pi\)
\(758\) 0 0
\(759\) −44588.6 946.368i −2.13236 0.0452582i
\(760\) 0 0
\(761\) −5888.86 10199.8i −0.280514 0.485864i 0.690998 0.722857i \(-0.257171\pi\)
−0.971511 + 0.236993i \(0.923838\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −13018.8 552.882i −0.615288 0.0261301i
\(766\) 0 0
\(767\) 1184.70 + 683.988i 0.0557720 + 0.0322000i
\(768\) 0 0
\(769\) 5932.67i 0.278202i 0.990278 + 0.139101i \(0.0444213\pi\)
−0.990278 + 0.139101i \(0.955579\pi\)
\(770\) 0 0
\(771\) 19437.8 + 35380.4i 0.907956 + 1.65265i
\(772\) 0 0
\(773\) 12154.4 21052.1i 0.565543 0.979550i −0.431456 0.902134i \(-0.642000\pi\)
0.996999 0.0774157i \(-0.0246668\pi\)
\(774\) 0 0
\(775\) 65.5993 37.8738i 0.00304051 0.00175544i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 15437.0 8912.54i 0.709996 0.409916i
\(780\) 0 0
\(781\) −24436.2 + 42324.8i −1.11959 + 1.93918i
\(782\) 0 0
\(783\) −1200.86 + 18837.0i −0.0548085 + 0.859742i
\(784\) 0 0
\(785\) 432.000i 0.0196417i
\(786\) 0 0
\(787\) 32642.3 + 18846.0i 1.47849 + 0.853606i 0.999704 0.0243259i \(-0.00774392\pi\)
0.478785 + 0.877932i \(0.341077\pi\)
\(788\) 0 0
\(789\) 20923.7 + 12679.8i 0.944110 + 0.572131i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 721.521 + 1249.71i 0.0323102 + 0.0559629i
\(794\) 0 0
\(795\) 308.845 14551.4i 0.0137781 0.649163i
\(796\) 0 0
\(797\) 5364.15 0.238404 0.119202 0.992870i \(-0.461966\pi\)
0.119202 + 0.992870i \(0.461966\pi\)
\(798\) 0