Properties

Label 588.4.k.e.521.16
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 521.16
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.e.509.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.69298 + 4.44386i) q^{3} +(4.87287 + 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +O(q^{10})\) \(q+(2.69298 + 4.44386i) q^{3} +(4.87287 + 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +(42.9817 + 24.8155i) q^{11} -2.47499i q^{13} +(-24.3838 + 44.3832i) q^{15} +(-24.7602 + 42.8858i) q^{17} +(-96.0631 + 55.4620i) q^{19} +(149.767 - 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(-140.012 + 8.92575i) q^{27} +134.538i q^{29} +(-2.18514 - 1.26159i) q^{31} +(5.47234 + 257.832i) q^{33} +(58.5515 + 101.414i) q^{37} +(10.9985 - 6.66509i) q^{39} +160.696 q^{41} -442.678 q^{43} +(-262.898 + 11.1648i) q^{45} +(155.814 + 269.879i) q^{47} +(-257.257 + 5.46014i) q^{51} +(-248.907 - 143.706i) q^{53} +483.690i q^{55} +(-505.161 - 277.532i) q^{57} +(276.360 - 478.670i) q^{59} +(-504.937 + 291.525i) q^{61} +(20.8890 - 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(787.573 + 432.688i) q^{69} +984.717i q^{71} +(-178.030 - 102.786i) q^{73} +(155.957 - 3.31010i) q^{75} +(-321.643 - 557.103i) q^{79} +(-416.714 - 598.156i) q^{81} +351.902 q^{83} -482.612 q^{85} +(-597.869 + 362.309i) q^{87} +(-544.376 - 942.887i) q^{89} +(-0.278207 - 13.1079i) q^{93} +(-936.205 - 540.518i) q^{95} +1365.09i q^{97} +(-1131.03 + 718.654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 64 q^{9} + O(q^{10}) \) \( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99} + O(q^{100}) \)

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
\(3\) 2.69298 + 4.44386i 0.518264 + 0.855221i
\(4\) 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
\(9\) −12.4957 + 23.9344i −0.462804 + 0.886460i
\(10\) 0 0
\(11\) 42.9817 + 24.8155i 1.17813 + 0.680195i 0.955582 0.294726i \(-0.0952284\pi\)
0.222551 + 0.974921i \(0.428562\pi\)
\(12\) 0 0
\(13\) 2.47499i 0.0528029i −0.999651 0.0264015i \(-0.991595\pi\)
0.999651 0.0264015i \(-0.00840482\pi\)
\(14\) 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 −0.951284 0.308317i \(-0.900234\pi\)
−0.208631 + 0.977994i \(0.566901\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 149.767 86.4683i 1.35777 0.783908i 0.368446 0.929649i \(-0.379890\pi\)
0.989323 + 0.145741i \(0.0465567\pi\)
\(24\) 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 \(0.141749\pi\)
−0.902474 + 0.430744i \(0.858251\pi\)
\(30\) 0 0
\(31\) −2.18514 1.26159i −0.0126601 0.00730929i 0.493657 0.869657i \(-0.335660\pi\)
−0.506317 + 0.862348i \(0.668993\pi\)
\(32\) 0 0
\(33\) 5.47234 + 257.832i 0.0288670 + 1.36008i
\(34\) 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
\(39\) 10.9985 6.66509i 0.0451582 0.0273659i
\(40\) 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
\(45\) −262.898 + 11.1648i −0.870900 + 0.0369854i
\(46\) 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
\(51\) −257.257 + 5.46014i −0.706337 + 0.0149916i
\(52\) 0 0
\(53\) −248.907 143.706i −0.645093 0.372445i 0.141480 0.989941i \(-0.454814\pi\)
−0.786574 + 0.617496i \(0.788147\pi\)
\(54\) 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 −0.925389 0.379018i \(-0.876262\pi\)
−0.134455 + 0.990920i \(0.542928\pi\)
\(62\) 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 \(0.307695\pi\)
−0.568058 + 0.822988i \(0.692305\pi\)
\(72\) 0 0
\(73\) −178.030 102.786i −0.285436 0.164797i 0.350446 0.936583i \(-0.386030\pi\)
−0.635882 + 0.771786i \(0.719363\pi\)
\(74\) 0 0
\(75\) 155.957 3.31010i 0.240111 0.00509623i
\(76\) 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
\(81\) −416.714 598.156i −0.571624 0.820516i
\(82\) 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
\(87\) −597.869 + 362.309i −0.736762 + 0.446478i
\(88\) 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
\(93\) −0.278207 13.1079i −0.000310202 0.0146153i
\(94\) 0 0
\(95\) −936.205 540.518i −1.01108 0.583747i
\(96\) 0 0
\(97\) 1365.09i 1.42891i 0.699683 + 0.714454i \(0.253325\pi\)
−0.699683 + 0.714454i \(0.746675\pi\)
\(98\) 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 −0.921744 0.387800i \(-0.873235\pi\)
−0.125027 + 0.992153i \(0.539902\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1267.25 + 731.647i −1.14495 + 0.661037i −0.947652 0.319306i \(-0.896550\pi\)
−0.197299 + 0.980343i \(0.563217\pi\)
\(108\) 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 \(-0.962636\pi\)
0.993119 0.117114i \(-0.0373642\pi\)
\(114\) 0 0
\(115\) 1459.59 + 842.697i 1.18355 + 0.683321i
\(116\) 0 0
\(117\) 59.2374 + 30.9268i 0.0468077 + 0.0244374i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 566.115 + 980.541i 0.425331 + 0.736695i
\(122\) 0 0
\(123\) 432.752 + 714.111i 0.317235 + 0.523490i
\(124\) 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
\(129\) −1192.12 1967.20i −0.813647 1.34265i
\(130\) 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
\(135\) −757.593 1138.21i −0.482987 0.725643i
\(136\) 0 0
\(137\) 892.802 + 515.459i 0.556768 + 0.321450i 0.751847 0.659337i \(-0.229163\pi\)
−0.195079 + 0.980787i \(0.562496\pi\)
\(138\) 0 0
\(139\) 234.497i 0.143092i 0.997437 + 0.0715460i \(0.0227933\pi\)
−0.997437 + 0.0715460i \(0.977207\pi\)
\(140\) 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 0.169830 0.985473i \(-0.445678\pi\)
0.938360 + 0.345660i \(0.112345\pi\)
\(150\) 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 0.509725 0.860337i \(-0.329747\pi\)
−0.490211 + 0.871604i \(0.663080\pi\)
\(158\) 0 0
\(159\) −31.6903 1493.10i −0.0158063 0.744722i
\(160\) 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
\(165\) −2149.45 + 1302.57i −1.01415 + 0.614574i
\(166\) 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
\(171\) −127.075 2992.25i −0.0568285 1.33815i
\(172\) 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
\(177\) 2871.37 60.9433i 1.21935 0.0258801i
\(178\) 0 0
\(179\) 372.577 + 215.108i 0.155574 + 0.0898206i 0.575766 0.817615i \(-0.304704\pi\)
−0.420192 + 0.907435i \(0.638037\pi\)
\(180\) 0 0
\(181\) 2230.49i 0.915971i −0.888960 0.457986i \(-0.848571\pi\)
0.888960 0.457986i \(-0.151429\pi\)
\(182\) 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 −0.677855 0.735195i \(-0.737090\pi\)
0.297770 + 0.954638i \(0.403757\pi\)
\(192\) 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 \(-0.797863\pi\)
0.805053 0.593203i \(-0.202137\pi\)
\(198\) 0 0
\(199\) 3818.10 + 2204.38i 1.36009 + 0.785248i 0.989635 0.143603i \(-0.0458687\pi\)
0.370454 + 0.928851i \(0.379202\pi\)
\(200\) 0 0
\(201\) 4683.00 99.3940i 1.64335 0.0348792i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 783.051 + 1356.28i 0.266784 + 0.462083i
\(206\) 0 0
\(207\) 198.117 + 4665.08i 0.0665221 + 1.56640i
\(208\) 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
\(213\) −4375.94 + 2651.82i −1.40767 + 0.853051i
\(214\) 0 0
\(215\) −2157.11 3736.22i −0.684249 1.18515i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −22.6664 1067.94i −0.00699386 0.329519i
\(220\) 0 0
\(221\) 106.142 + 61.2811i 0.0323072 + 0.0186525i
\(222\) 0 0
\(223\) 1134.63i 0.340718i −0.985382 0.170359i \(-0.945507\pi\)
0.985382 0.170359i \(-0.0544928\pi\)
\(224\) 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 −0.130023 0.991511i \(-0.541505\pi\)
0.793662 + 0.608359i \(0.208172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2734.14 + 1578.56i −0.768754 + 0.443840i −0.832430 0.554130i \(-0.813051\pi\)
0.0636761 + 0.997971i \(0.479718\pi\)
\(234\) 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 \(0.0890351\pi\)
−0.961135 + 0.276079i \(0.910965\pi\)
\(240\) 0 0
\(241\) 3958.64 + 2285.52i 1.05809 + 0.610886i 0.924902 0.380205i \(-0.124147\pi\)
0.133184 + 0.991091i \(0.457480\pi\)
\(242\) 0 0
\(243\) 1535.92 3462.64i 0.405470 0.914109i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 137.268 + 237.755i 0.0353609 + 0.0612469i
\(248\) 0 0
\(249\) 947.664 + 1563.80i 0.241188 + 0.397999i
\(250\) 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
\(255\) −1299.66 2144.66i −0.319169 0.526681i
\(256\) 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
\(261\) −3220.10 1681.15i −0.763675 0.398700i
\(262\) 0 0
\(263\) 4077.64 + 2354.23i 0.956038 + 0.551969i 0.894951 0.446164i \(-0.147210\pi\)
0.0610865 + 0.998132i \(0.480543\pi\)
\(264\) 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 −0.419395 0.907804i \(-0.637758\pi\)
0.576484 + 0.817109i \(0.304424\pi\)
\(272\) 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 \(-0.956280\pi\)
0.990582 0.136919i \(-0.0437198\pi\)
\(282\) 0 0
\(283\) 7466.08 + 4310.54i 1.56824 + 0.905424i 0.996374 + 0.0850780i \(0.0271139\pi\)
0.571867 + 0.820346i \(0.306219\pi\)
\(284\) 0 0
\(285\) −119.196 5615.97i −0.0247739 1.16723i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1230.37 + 2131.06i 0.250431 + 0.433760i
\(290\) 0 0
\(291\) −6066.27 + 3676.16i −1.22203 + 0.740551i
\(292\) 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
\(297\) −6239.44 3090.82i −1.21902 0.603863i
\(298\) 0 0
\(299\) −214.008 370.673i −0.0413926 0.0716941i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −6773.49 + 143.764i −1.28425 + 0.0272574i
\(304\) 0 0
\(305\) −4920.98 2841.13i −0.923850 0.533385i
\(306\) 0 0
\(307\) 3785.51i 0.703747i 0.936048 + 0.351873i \(0.114455\pi\)
−0.936048 + 0.351873i \(0.885545\pi\)
\(308\) 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 0.0200193 0.999800i \(-0.493627\pi\)
0.875861 + 0.482563i \(0.160294\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5818.71 3359.43i 1.03095 0.595219i 0.113693 0.993516i \(-0.463732\pi\)
0.917257 + 0.398297i \(0.130398\pi\)
\(318\) 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
\(327\) 11635.6 246.960i 1.96774 0.0417643i
\(328\) 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
\(333\) −3158.93 + 134.154i −0.519845 + 0.0220768i
\(334\) 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
\(339\) 1250.30 757.684i 0.200316 0.121392i
\(340\) 0 0
\(341\) −62.6139 108.450i −0.00994349 0.0172226i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 185.833 + 8755.59i 0.0289997 + 1.36633i
\(346\) 0 0
\(347\) 1092.59 + 630.806i 0.169029 + 0.0975891i 0.582128 0.813097i \(-0.302220\pi\)
−0.413099 + 0.910686i \(0.635554\pi\)
\(348\) 0 0
\(349\) 10981.9i 1.68438i −0.539179 0.842191i \(-0.681265\pi\)
0.539179 0.842191i \(-0.318735\pi\)
\(350\) 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 −0.467885 0.883789i \(-0.654984\pi\)
0.531441 + 0.847095i \(0.321651\pi\)
\(360\) 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 0.519985 0.854176i \(-0.325938\pi\)
−0.479746 + 0.877408i \(0.659271\pi\)
\(368\) 0 0
\(369\) −2008.01 + 3846.17i −0.283287 + 0.542612i
\(370\) 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
\(375\) 4068.53 + 6713.73i 0.560261 + 0.924522i
\(376\) 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
\(381\) −1551.41 2560.08i −0.208612 0.344244i
\(382\) 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
\(387\) 5531.57 10595.2i 0.726578 1.39170i
\(388\) 0 0
\(389\) 1558.98 + 900.077i 0.203196 + 0.117315i 0.598146 0.801388i \(-0.295904\pi\)
−0.394949 + 0.918703i \(0.629238\pi\)
\(390\) 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 −0.810362 0.585930i \(-0.800729\pi\)
0.102249 + 0.994759i \(0.467396\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2974.16 1717.13i 0.370381 0.213839i −0.303244 0.952913i \(-0.598070\pi\)
0.673625 + 0.739074i \(0.264736\pi\)
\(402\) 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 0.548586 0.836094i \(-0.315166\pi\)
−0.449786 + 0.893136i \(0.648500\pi\)
\(410\) 0 0
\(411\) 113.670 + 5355.61i 0.0136421 + 0.642756i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1714.77 + 2970.07i 0.202831 + 0.351313i
\(416\) 0 0
\(417\) −1042.07 + 631.496i −0.122375 + 0.0741594i
\(418\) 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
\(423\) −8406.41 + 357.004i −0.966273 + 0.0410357i
\(424\) 0 0
\(425\) 743.317 + 1287.46i 0.0848381 + 0.146944i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 638.131 13.5440i 0.0718164 0.00152426i
\(430\) 0 0
\(431\) 14439.3 + 8336.51i 1.61372 + 0.931684i 0.988497 + 0.151241i \(0.0483268\pi\)
0.625227 + 0.780443i \(0.285007\pi\)
\(432\) 0 0
\(433\) 2848.46i 0.316140i 0.987428 + 0.158070i \(0.0505271\pi\)
−0.987428 + 0.158070i \(0.949473\pi\)
\(434\) 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 −0.868796 0.495170i \(-0.835106\pi\)
−0.00556785 + 0.999984i \(0.501772\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4281.76 + 2472.08i −0.459216 + 0.265128i −0.711714 0.702469i \(-0.752081\pi\)
0.252499 + 0.967597i \(0.418748\pi\)
\(444\) 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 \(0.316858\pi\)
−0.544136 + 0.838997i \(0.683142\pi\)
\(450\) 0 0
\(451\) 6906.99 + 3987.75i 0.721147 + 0.416355i
\(452\) 0 0
\(453\) −5481.44 + 116.341i −0.568522 + 0.0120666i
\(454\) 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
\(459\) 3083.93 6225.53i 0.313607 0.633078i
\(460\) 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
\(465\) 109.275 66.2210i 0.0108979 0.00660414i
\(466\) 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
\(471\) 4.88753 + 230.278i 0.000478144 + 0.0225280i
\(472\) 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 \(-0.980901\pi\)
0.998200 0.0599667i \(-0.0190995\pi\)
\(492\) 0 0
\(493\) −5769.79 3331.19i −0.527096 0.304319i
\(494\) 0 0
\(495\) −11576.8 6044.05i −1.05119 0.548808i
\(496\) 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
\(501\) −4463.21 7365.03i −0.398007 0.656777i
\(502\) 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
\(507\) 5899.98 + 9735.93i 0.516819 + 0.852836i
\(508\) 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
\(513\) 12954.9 8622.78i 1.11496 0.742115i
\(514\) 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 −0.722444 0.691430i \(-0.756981\pi\)
0.237574 + 0.971369i \(0.423648\pi\)
\(524\) 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
\(537\) 47.4358 + 2234.96i 0.00381193 + 0.179601i
\(538\) 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
\(543\) 9911.96 6006.66i 0.783357 0.474715i
\(544\) 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
\(549\) −667.945 15728.2i −0.0519257 1.22270i
\(550\) 0 0
\(551\) −7461.77 12924.2i −0.576918 0.999252i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −5928.79 + 125.835i −0.453447 + 0.00962417i
\(556\) 0 0
\(557\) 6062.22 + 3500.02i 0.461157 + 0.266249i 0.712531 0.701641i \(-0.247549\pi\)
−0.251374 + 0.967890i \(0.580882\pi\)
\(558\) 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 −0.782239 0.622979i \(-0.785922\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(570\) 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 −0.165989 0.986128i \(-0.553082\pi\)
−0.937006 + 0.349313i \(0.886415\pi\)
\(578\) 0 0
\(579\) 11718.2 248.713i 0.841093 0.0178517i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7132.28 12353.5i −0.506670 0.877579i
\(584\) 0 0
\(585\) 27.6326 + 650.669i 0.00195294 + 0.0459861i
\(586\) 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
\(591\) 14577.8 8834.16i 1.01464 0.614871i
\(592\) 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
\(597\) 486.113 + 22903.4i 0.0333254 + 1.57014i
\(598\) 0 0
\(599\) −23961.5 13834.2i −1.63446 0.943655i −0.982695 0.185233i \(-0.940696\pi\)
−0.651764 0.758422i \(-0.725971\pi\)
\(600\) 0 0
\(601\) 11624.0i 0.788937i 0.918909 + 0.394469i \(0.129071\pi\)
−0.918909 + 0.394469i \(0.870929\pi\)
\(602\) 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 −0.407857 0.913046i \(-0.633724\pi\)
0.586793 + 0.809737i \(0.300390\pi\)
\(608\) 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 \(-0.886639\pi\)
0.937252 0.348654i \(-0.113361\pi\)
\(618\) 0 0
\(619\) 4946.00 + 2855.58i 0.321158 + 0.185420i 0.651908 0.758298i \(-0.273969\pi\)
−0.330751 + 0.943718i \(0.607302\pi\)
\(620\) 0 0
\(621\) −20197.4 + 13443.4i −1.30514 + 0.868702i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5485.59 + 9501.31i 0.351077 + 0.608084i
\(626\) 0 0
\(627\) −14825.6 24464.6i −0.944300 1.55825i
\(628\) 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
\(633\) 15135.8 + 24976.5i 0.950385 + 1.56829i
\(634\) 0 0
\(635\) −2807.23 4862.27i −0.175436 0.303864i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −23568.6 12304.7i −1.45909 0.761765i
\(640\) 0 0
\(641\) 14083.3 + 8131.00i 0.867796 + 0.501022i 0.866615 0.498977i \(-0.166291\pi\)
0.00118054 + 0.999999i \(0.499624\pi\)
\(642\) 0 0
\(643\) 13805.8i 0.846729i −0.905959 0.423365i \(-0.860849\pi\)
0.905959 0.423365i \(-0.139151\pi\)
\(644\) 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 0.0756247 0.997136i \(-0.475905\pi\)
0.901358 + 0.433075i \(0.142572\pi\)
\(654\) 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 \(-0.967273\pi\)
0.994719 0.102634i \(-0.0327270\pi\)
\(660\) 0 0
\(661\) −11328.2 6540.36i −0.666592 0.384857i 0.128192 0.991749i \(-0.459083\pi\)
−0.794784 + 0.606892i \(0.792416\pi\)
\(662\) 0 0
\(663\) 13.5138 + 636.708i 0.000791602 + 0.0372967i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 11633.3 + 20149.5i 0.675327 + 1.16970i
\(668\) 0 0
\(669\) 5042.11 3055.52i 0.291389 0.176582i
\(670\) 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
\(675\) −1869.57 + 3774.10i −0.106607 + 0.215208i
\(676\) 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
\(681\) 11030.0 234.106i 0.620661 0.0131732i
\(682\) 0 0
\(683\) 22216.3 + 12826.6i 1.24463 + 0.718589i 0.970034 0.242970i \(-0.0781218\pi\)
0.274598 + 0.961559i \(0.411455\pi\)
\(684\) 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 −0.683554 0.729900i \(-0.739567\pi\)
0.290335 + 0.956925i \(0.406233\pi\)
\(692\) 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 \(0.239463\pi\)
−0.730122 + 0.683317i \(0.760537\pi\)
\(702\) 0 0
\(703\) −11249.3 6494.77i −0.603519 0.348442i
\(704\) 0 0
\(705\) −15777.4 + 334.867i −0.842855 + 0.0178891i
\(706\) 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
\(711\) 17353.1 736.952i 0.915320 0.0388718i
\(712\) 0 0
\(713\) −436.350 −0.0229193
\(714\) 0 0
\(715\) 1197.13 0.0626154
\(716\) 0 0
\(717\) −9066.09 + 5494.05i −0.472216 + 0.286163i
\(718\) 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
\(723\) 504.007 + 23746.5i 0.0259256 + 1.22150i
\(724\) 0 0
\(725\) 3497.82 + 2019.47i 0.179180 + 0.103450i
\(726\) 0 0
\(727\) 35634.9i 1.81792i −0.416887 0.908958i \(-0.636879\pi\)
0.416887 0.908958i \(-0.363121\pi\)
\(728\) 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 −0.201625 0.979463i \(-0.564622\pi\)
0.747427 + 0.664344i \(0.231289\pi\)
\(734\) 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 \(0.0971866\pi\)
−0.953751 + 0.300599i \(0.902813\pi\)
\(744\) 0 0
\(745\) 19643.0 + 11340.9i 0.965992 + 0.557716i
\(746\) 0 0
\(747\) −4397.27 + 8422.57i −0.215378 + 0.412538i
\(748\) 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
\(753\) 15749.7 + 25989.6i 0.762220 + 1.25779i
\(754\) 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
\(759\) 23113.9 + 38141.6i 1.10538 + 1.82405i
\(760\) 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
\(765\) 6030.58 11551.0i 0.285015 0.545920i
\(766\) 0 0
\(767\) −1184.70 683.988i −0.0557720 0.0322000i
\(768\) 0 0
\(769\) 5932.67i 0.278202i −0.990278 0.139101i \(-0.955579\pi\)
0.990278 0.139101i \(-0.0444213\pi\)
\(770\) 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 −0.478785 0.877932i \(-0.658923\pi\)
−0.999704 + 0.0243259i \(0.992256\pi\)
\(788\) 0 0
\(789\) 519.157 + 24460.3i 0.0234252 + 1.10369i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 721.521 + 1249.71i 0.0323102 + 0.0559629i
\(794\) 0 0
\(795\) 12447.4 7543.16i 0.555303 0.336514i
\(796\) 0 0
\(797\) 5364.15 0.238404 0.119202 0.992870i \(-0.461966\pi\)
0.119202 + 0.992870i \(0.461966\pi\)
\(798\) 0 0