Properties

Label 882.4.g.g.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.g.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +(6.00000 + 10.3923i) q^{10} +(-15.0000 - 25.9808i) q^{11} -53.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(42.0000 + 72.7461i) q^{17} +(-48.5000 + 84.0045i) q^{19} -24.0000 q^{20} +60.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(44.5000 + 77.0763i) q^{25} +(53.0000 - 91.7987i) q^{26} +180.000 q^{29} +(89.5000 + 155.019i) q^{31} +(-16.0000 - 27.7128i) q^{32} -168.000 q^{34} +(72.5000 - 125.574i) q^{37} +(-97.0000 - 168.009i) q^{38} +(24.0000 - 41.5692i) q^{40} +126.000 q^{41} -325.000 q^{43} +(-60.0000 + 103.923i) q^{44} +(84.0000 + 145.492i) q^{46} +(183.000 - 316.965i) q^{47} -178.000 q^{50} +(106.000 + 183.597i) q^{52} +(-384.000 - 665.108i) q^{53} -180.000 q^{55} +(-180.000 + 311.769i) q^{58} +(132.000 + 228.631i) q^{59} +(409.000 - 708.409i) q^{61} -358.000 q^{62} +64.0000 q^{64} +(-159.000 + 275.396i) q^{65} +(261.500 + 452.931i) q^{67} +(168.000 - 290.985i) q^{68} +342.000 q^{71} +(-21.5000 - 37.2391i) q^{73} +(145.000 + 251.147i) q^{74} +388.000 q^{76} +(585.500 - 1014.12i) q^{79} +(48.0000 + 83.1384i) q^{80} +(-126.000 + 218.238i) q^{82} -810.000 q^{83} +504.000 q^{85} +(325.000 - 562.917i) q^{86} +(-120.000 - 207.846i) q^{88} +(300.000 - 519.615i) q^{89} -336.000 q^{92} +(366.000 + 633.931i) q^{94} +(291.000 + 504.027i) q^{95} -386.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 6q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 6q^{5} + 16q^{8} + 12q^{10} - 30q^{11} - 106q^{13} - 16q^{16} + 84q^{17} - 97q^{19} - 48q^{20} + 120q^{22} + 84q^{23} + 89q^{25} + 106q^{26} + 360q^{29} + 179q^{31} - 32q^{32} - 336q^{34} + 145q^{37} - 194q^{38} + 48q^{40} + 252q^{41} - 650q^{43} - 120q^{44} + 168q^{46} + 366q^{47} - 356q^{50} + 212q^{52} - 768q^{53} - 360q^{55} - 360q^{58} + 264q^{59} + 818q^{61} - 716q^{62} + 128q^{64} - 318q^{65} + 523q^{67} + 336q^{68} + 684q^{71} - 43q^{73} + 290q^{74} + 776q^{76} + 1171q^{79} + 96q^{80} - 252q^{82} - 1620q^{83} + 1008q^{85} + 650q^{86} - 240q^{88} + 600q^{89} - 672q^{92} + 732q^{94} + 582q^{95} - 772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 3.00000 5.19615i 0.268328 0.464758i −0.700102 0.714043i \(-0.746862\pi\)
0.968430 + 0.249285i \(0.0801955\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 6.00000 + 10.3923i 0.189737 + 0.328634i
\(11\) −15.0000 25.9808i −0.411152 0.712136i 0.583864 0.811851i \(-0.301540\pi\)
−0.995016 + 0.0997155i \(0.968207\pi\)
\(12\) 0 0
\(13\) −53.0000 −1.13074 −0.565368 0.824839i \(-0.691266\pi\)
−0.565368 + 0.824839i \(0.691266\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 42.0000 + 72.7461i 0.599206 + 1.03785i 0.992939 + 0.118630i \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) 0 0
\(19\) −48.5000 + 84.0045i −0.585614 + 1.01431i 0.409185 + 0.912452i \(0.365813\pi\)
−0.994799 + 0.101861i \(0.967520\pi\)
\(20\) −24.0000 −0.268328
\(21\) 0 0
\(22\) 60.0000 0.581456
\(23\) 42.0000 72.7461i 0.380765 0.659505i −0.610406 0.792088i \(-0.708994\pi\)
0.991172 + 0.132583i \(0.0423272\pi\)
\(24\) 0 0
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) 53.0000 91.7987i 0.399775 0.692431i
\(27\) 0 0
\(28\) 0 0
\(29\) 180.000 1.15259 0.576296 0.817241i \(-0.304498\pi\)
0.576296 + 0.817241i \(0.304498\pi\)
\(30\) 0 0
\(31\) 89.5000 + 155.019i 0.518538 + 0.898134i 0.999768 + 0.0215397i \(0.00685682\pi\)
−0.481230 + 0.876594i \(0.659810\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −168.000 −0.847405
\(35\) 0 0
\(36\) 0 0
\(37\) 72.5000 125.574i 0.322133 0.557951i −0.658795 0.752323i \(-0.728933\pi\)
0.980928 + 0.194372i \(0.0622668\pi\)
\(38\) −97.0000 168.009i −0.414092 0.717228i
\(39\) 0 0
\(40\) 24.0000 41.5692i 0.0948683 0.164317i
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 0 0
\(43\) −325.000 −1.15261 −0.576303 0.817236i \(-0.695505\pi\)
−0.576303 + 0.817236i \(0.695505\pi\)
\(44\) −60.0000 + 103.923i −0.205576 + 0.356068i
\(45\) 0 0
\(46\) 84.0000 + 145.492i 0.269242 + 0.466341i
\(47\) 183.000 316.965i 0.567942 0.983705i −0.428827 0.903387i \(-0.641073\pi\)
0.996769 0.0803184i \(-0.0255937\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −178.000 −0.503460
\(51\) 0 0
\(52\) 106.000 + 183.597i 0.282684 + 0.489623i
\(53\) −384.000 665.108i −0.995216 1.72376i −0.582217 0.813034i \(-0.697814\pi\)
−0.413000 0.910731i \(-0.635519\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) 0 0
\(57\) 0 0
\(58\) −180.000 + 311.769i −0.407503 + 0.705815i
\(59\) 132.000 + 228.631i 0.291270 + 0.504495i 0.974110 0.226073i \(-0.0725888\pi\)
−0.682840 + 0.730568i \(0.739255\pi\)
\(60\) 0 0
\(61\) 409.000 708.409i 0.858477 1.48693i −0.0149048 0.999889i \(-0.504745\pi\)
0.873382 0.487036i \(-0.161922\pi\)
\(62\) −358.000 −0.733323
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −159.000 + 275.396i −0.303408 + 0.525518i
\(66\) 0 0
\(67\) 261.500 + 452.931i 0.476826 + 0.825886i 0.999647 0.0265560i \(-0.00845402\pi\)
−0.522822 + 0.852442i \(0.675121\pi\)
\(68\) 168.000 290.985i 0.299603 0.518927i
\(69\) 0 0
\(70\) 0 0
\(71\) 342.000 0.571661 0.285831 0.958280i \(-0.407731\pi\)
0.285831 + 0.958280i \(0.407731\pi\)
\(72\) 0 0
\(73\) −21.5000 37.2391i −0.0344710 0.0597056i 0.848275 0.529556i \(-0.177641\pi\)
−0.882746 + 0.469850i \(0.844308\pi\)
\(74\) 145.000 + 251.147i 0.227783 + 0.394531i
\(75\) 0 0
\(76\) 388.000 0.585614
\(77\) 0 0
\(78\) 0 0
\(79\) 585.500 1014.12i 0.833847 1.44427i −0.0611191 0.998130i \(-0.519467\pi\)
0.894966 0.446135i \(-0.147200\pi\)
\(80\) 48.0000 + 83.1384i 0.0670820 + 0.116190i
\(81\) 0 0
\(82\) −126.000 + 218.238i −0.169687 + 0.293907i
\(83\) −810.000 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(84\) 0 0
\(85\) 504.000 0.643135
\(86\) 325.000 562.917i 0.407508 0.705824i
\(87\) 0 0
\(88\) −120.000 207.846i −0.145364 0.251778i
\(89\) 300.000 519.615i 0.357303 0.618866i −0.630207 0.776428i \(-0.717030\pi\)
0.987509 + 0.157561i \(0.0503631\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) 0 0
\(94\) 366.000 + 633.931i 0.401596 + 0.695585i
\(95\) 291.000 + 504.027i 0.314273 + 0.544337i
\(96\) 0 0
\(97\) −386.000 −0.404045 −0.202022 0.979381i \(-0.564751\pi\)
−0.202022 + 0.979381i \(0.564751\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 178.000 308.305i 0.178000 0.308305i
\(101\) −309.000 535.204i −0.304422 0.527275i 0.672710 0.739906i \(-0.265130\pi\)
−0.977133 + 0.212631i \(0.931797\pi\)
\(102\) 0 0
\(103\) 737.500 1277.39i 0.705515 1.22199i −0.260991 0.965341i \(-0.584049\pi\)
0.966505 0.256646i \(-0.0826175\pi\)
\(104\) −424.000 −0.399775
\(105\) 0 0
\(106\) 1536.00 1.40745
\(107\) 942.000 1631.59i 0.851090 1.47413i −0.0291364 0.999575i \(-0.509276\pi\)
0.880226 0.474555i \(-0.157391\pi\)
\(108\) 0 0
\(109\) −206.500 357.668i −0.181460 0.314298i 0.760918 0.648848i \(-0.224749\pi\)
−0.942378 + 0.334550i \(0.891416\pi\)
\(110\) 180.000 311.769i 0.156021 0.270237i
\(111\) 0 0
\(112\) 0 0
\(113\) 882.000 0.734262 0.367131 0.930169i \(-0.380340\pi\)
0.367131 + 0.930169i \(0.380340\pi\)
\(114\) 0 0
\(115\) −252.000 436.477i −0.204340 0.353928i
\(116\) −360.000 623.538i −0.288148 0.499087i
\(117\) 0 0
\(118\) −528.000 −0.411918
\(119\) 0 0
\(120\) 0 0
\(121\) 215.500 373.257i 0.161908 0.280433i
\(122\) 818.000 + 1416.82i 0.607035 + 1.05142i
\(123\) 0 0
\(124\) 358.000 620.074i 0.259269 0.449067i
\(125\) 1284.00 0.918756
\(126\) 0 0
\(127\) 2483.00 1.73489 0.867443 0.497536i \(-0.165762\pi\)
0.867443 + 0.497536i \(0.165762\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −318.000 550.792i −0.214542 0.371597i
\(131\) −1059.00 + 1834.24i −0.706300 + 1.22335i 0.259921 + 0.965630i \(0.416304\pi\)
−0.966220 + 0.257717i \(0.917030\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1046.00 −0.674333
\(135\) 0 0
\(136\) 336.000 + 581.969i 0.211851 + 0.366937i
\(137\) 1506.00 + 2608.47i 0.939170 + 1.62669i 0.767024 + 0.641618i \(0.221737\pi\)
0.172146 + 0.985071i \(0.444930\pi\)
\(138\) 0 0
\(139\) 37.0000 0.0225777 0.0112888 0.999936i \(-0.496407\pi\)
0.0112888 + 0.999936i \(0.496407\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −342.000 + 592.361i −0.202113 + 0.350069i
\(143\) 795.000 + 1376.98i 0.464904 + 0.805237i
\(144\) 0 0
\(145\) 540.000 935.307i 0.309273 0.535676i
\(146\) 86.0000 0.0487494
\(147\) 0 0
\(148\) −580.000 −0.322133
\(149\) −822.000 + 1423.75i −0.451952 + 0.782804i −0.998507 0.0546191i \(-0.982606\pi\)
0.546555 + 0.837423i \(0.315939\pi\)
\(150\) 0 0
\(151\) −544.000 942.236i −0.293179 0.507802i 0.681380 0.731930i \(-0.261380\pi\)
−0.974560 + 0.224128i \(0.928047\pi\)
\(152\) −388.000 + 672.036i −0.207046 + 0.358614i
\(153\) 0 0
\(154\) 0 0
\(155\) 1074.00 0.556553
\(156\) 0 0
\(157\) 253.000 + 438.209i 0.128609 + 0.222757i 0.923138 0.384469i \(-0.125615\pi\)
−0.794529 + 0.607226i \(0.792282\pi\)
\(158\) 1171.00 + 2028.23i 0.589619 + 1.02125i
\(159\) 0 0
\(160\) −192.000 −0.0948683
\(161\) 0 0
\(162\) 0 0
\(163\) −922.000 + 1596.95i −0.443047 + 0.767379i −0.997914 0.0645596i \(-0.979436\pi\)
0.554867 + 0.831939i \(0.312769\pi\)
\(164\) −252.000 436.477i −0.119987 0.207824i
\(165\) 0 0
\(166\) 810.000 1402.96i 0.378724 0.655969i
\(167\) 162.000 0.0750655 0.0375327 0.999295i \(-0.488050\pi\)
0.0375327 + 0.999295i \(0.488050\pi\)
\(168\) 0 0
\(169\) 612.000 0.278562
\(170\) −504.000 + 872.954i −0.227383 + 0.393838i
\(171\) 0 0
\(172\) 650.000 + 1125.83i 0.288151 + 0.499093i
\(173\) 1362.00 2359.05i 0.598560 1.03674i −0.394473 0.918907i \(-0.629073\pi\)
0.993034 0.117830i \(-0.0375937\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 480.000 0.205576
\(177\) 0 0
\(178\) 600.000 + 1039.23i 0.252651 + 0.437605i
\(179\) −627.000 1086.00i −0.261811 0.453470i 0.704912 0.709295i \(-0.250986\pi\)
−0.966723 + 0.255825i \(0.917653\pi\)
\(180\) 0 0
\(181\) 1807.00 0.742062 0.371031 0.928620i \(-0.379004\pi\)
0.371031 + 0.928620i \(0.379004\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 336.000 581.969i 0.134621 0.233170i
\(185\) −435.000 753.442i −0.172875 0.299428i
\(186\) 0 0
\(187\) 1260.00 2182.38i 0.492729 0.853432i
\(188\) −1464.00 −0.567942
\(189\) 0 0
\(190\) −1164.00 −0.444450
\(191\) 357.000 618.342i 0.135244 0.234250i −0.790447 0.612531i \(-0.790151\pi\)
0.925691 + 0.378281i \(0.123485\pi\)
\(192\) 0 0
\(193\) 1854.50 + 3212.09i 0.691657 + 1.19799i 0.971295 + 0.237880i \(0.0764524\pi\)
−0.279637 + 0.960106i \(0.590214\pi\)
\(194\) 386.000 668.572i 0.142851 0.247426i
\(195\) 0 0
\(196\) 0 0
\(197\) 1044.00 0.377573 0.188787 0.982018i \(-0.439545\pi\)
0.188787 + 0.982018i \(0.439545\pi\)
\(198\) 0 0
\(199\) −68.0000 117.779i −0.0242231 0.0419556i 0.853660 0.520831i \(-0.174378\pi\)
−0.877883 + 0.478875i \(0.841045\pi\)
\(200\) 356.000 + 616.610i 0.125865 + 0.218005i
\(201\) 0 0
\(202\) 1236.00 0.430518
\(203\) 0 0
\(204\) 0 0
\(205\) 378.000 654.715i 0.128784 0.223060i
\(206\) 1475.00 + 2554.77i 0.498874 + 0.864076i
\(207\) 0 0
\(208\) 424.000 734.390i 0.141342 0.244811i
\(209\) 2910.00 0.963105
\(210\) 0 0
\(211\) 1484.00 0.484184 0.242092 0.970253i \(-0.422166\pi\)
0.242092 + 0.970253i \(0.422166\pi\)
\(212\) −1536.00 + 2660.43i −0.497608 + 0.861882i
\(213\) 0 0
\(214\) 1884.00 + 3263.18i 0.601811 + 1.04237i
\(215\) −975.000 + 1688.75i −0.309277 + 0.535683i
\(216\) 0 0
\(217\) 0 0
\(218\) 826.000 0.256623
\(219\) 0 0
\(220\) 360.000 + 623.538i 0.110324 + 0.191086i
\(221\) −2226.00 3855.55i −0.677543 1.17354i
\(222\) 0 0
\(223\) 2032.00 0.610192 0.305096 0.952322i \(-0.401311\pi\)
0.305096 + 0.952322i \(0.401311\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −882.000 + 1527.67i −0.259601 + 0.449642i
\(227\) −3099.00 5367.63i −0.906114 1.56944i −0.819415 0.573201i \(-0.805702\pi\)
−0.0866989 0.996235i \(-0.527632\pi\)
\(228\) 0 0
\(229\) −2295.50 + 3975.92i −0.662406 + 1.14732i 0.317576 + 0.948233i \(0.397131\pi\)
−0.979982 + 0.199088i \(0.936202\pi\)
\(230\) 1008.00 0.288981
\(231\) 0 0
\(232\) 1440.00 0.407503
\(233\) 2265.00 3923.10i 0.636846 1.10305i −0.349275 0.937020i \(-0.613572\pi\)
0.986121 0.166029i \(-0.0530946\pi\)
\(234\) 0 0
\(235\) −1098.00 1901.79i −0.304790 0.527912i
\(236\) 528.000 914.523i 0.145635 0.252247i
\(237\) 0 0
\(238\) 0 0
\(239\) −1530.00 −0.414090 −0.207045 0.978331i \(-0.566385\pi\)
−0.207045 + 0.978331i \(0.566385\pi\)
\(240\) 0 0
\(241\) 2767.00 + 4792.58i 0.739577 + 1.28099i 0.952686 + 0.303957i \(0.0983079\pi\)
−0.213108 + 0.977029i \(0.568359\pi\)
\(242\) 431.000 + 746.514i 0.114486 + 0.198296i
\(243\) 0 0
\(244\) −3272.00 −0.858477
\(245\) 0 0
\(246\) 0 0
\(247\) 2570.50 4452.24i 0.662174 1.14692i
\(248\) 716.000 + 1240.15i 0.183331 + 0.317538i
\(249\) 0 0
\(250\) −1284.00 + 2223.95i −0.324829 + 0.562621i
\(251\) −468.000 −0.117689 −0.0588444 0.998267i \(-0.518742\pi\)
−0.0588444 + 0.998267i \(0.518742\pi\)
\(252\) 0 0
\(253\) −2520.00 −0.626210
\(254\) −2483.00 + 4300.68i −0.613375 + 1.06240i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1245.00 2156.40i 0.302183 0.523396i −0.674447 0.738323i \(-0.735618\pi\)
0.976630 + 0.214927i \(0.0689514\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1272.00 0.303408
\(261\) 0 0
\(262\) −2118.00 3668.48i −0.499429 0.865037i
\(263\) 786.000 + 1361.39i 0.184285 + 0.319190i 0.943335 0.331841i \(-0.107670\pi\)
−0.759051 + 0.651032i \(0.774337\pi\)
\(264\) 0 0
\(265\) −4608.00 −1.06818
\(266\) 0 0
\(267\) 0 0
\(268\) 1046.00 1811.73i 0.238413 0.412943i
\(269\) −903.000 1564.04i −0.204672 0.354503i 0.745356 0.666667i \(-0.232280\pi\)
−0.950028 + 0.312164i \(0.898946\pi\)
\(270\) 0 0
\(271\) −3056.00 + 5293.15i −0.685014 + 1.18648i 0.288418 + 0.957504i \(0.406871\pi\)
−0.973432 + 0.228975i \(0.926463\pi\)
\(272\) −1344.00 −0.299603
\(273\) 0 0
\(274\) −6024.00 −1.32819
\(275\) 1335.00 2312.29i 0.292740 0.507041i
\(276\) 0 0
\(277\) 2115.50 + 3664.15i 0.458874 + 0.794793i 0.998902 0.0468542i \(-0.0149196\pi\)
−0.540028 + 0.841647i \(0.681586\pi\)
\(278\) −37.0000 + 64.0859i −0.00798242 + 0.0138260i
\(279\) 0 0
\(280\) 0 0
\(281\) 3816.00 0.810119 0.405060 0.914290i \(-0.367251\pi\)
0.405060 + 0.914290i \(0.367251\pi\)
\(282\) 0 0
\(283\) −1998.50 3461.50i −0.419783 0.727085i 0.576135 0.817355i \(-0.304560\pi\)
−0.995917 + 0.0902699i \(0.971227\pi\)
\(284\) −684.000 1184.72i −0.142915 0.247536i
\(285\) 0 0
\(286\) −3180.00 −0.657473
\(287\) 0 0
\(288\) 0 0
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) 1080.00 + 1870.61i 0.218689 + 0.378780i
\(291\) 0 0
\(292\) −86.0000 + 148.956i −0.0172355 + 0.0298528i
\(293\) 4608.00 0.918779 0.459389 0.888235i \(-0.348068\pi\)
0.459389 + 0.888235i \(0.348068\pi\)
\(294\) 0 0
\(295\) 1584.00 0.312624
\(296\) 580.000 1004.59i 0.113891 0.197265i
\(297\) 0 0
\(298\) −1644.00 2847.49i −0.319578 0.553526i
\(299\) −2226.00 + 3855.55i −0.430545 + 0.745726i
\(300\) 0 0
\(301\) 0 0
\(302\) 2176.00 0.414618
\(303\) 0 0
\(304\) −776.000 1344.07i −0.146403 0.253578i
\(305\) −2454.00 4250.45i −0.460707 0.797968i
\(306\) 0 0
\(307\) 631.000 0.117306 0.0586532 0.998278i \(-0.481319\pi\)
0.0586532 + 0.998278i \(0.481319\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1074.00 + 1860.22i −0.196771 + 0.340818i
\(311\) −1947.00 3372.30i −0.354998 0.614874i 0.632120 0.774871i \(-0.282185\pi\)
−0.987118 + 0.159997i \(0.948852\pi\)
\(312\) 0 0
\(313\) −1092.50 + 1892.27i −0.197290 + 0.341716i −0.947649 0.319314i \(-0.896547\pi\)
0.750359 + 0.661031i \(0.229881\pi\)
\(314\) −1012.00 −0.181880
\(315\) 0 0
\(316\) −4684.00 −0.833847
\(317\) 1752.00 3034.55i 0.310417 0.537658i −0.668036 0.744129i \(-0.732865\pi\)
0.978453 + 0.206471i \(0.0661981\pi\)
\(318\) 0 0
\(319\) −2700.00 4676.54i −0.473890 0.820802i
\(320\) 192.000 332.554i 0.0335410 0.0580948i
\(321\) 0 0
\(322\) 0 0
\(323\) −8148.00 −1.40361
\(324\) 0 0
\(325\) −2358.50 4085.04i −0.402542 0.697223i
\(326\) −1844.00 3193.90i −0.313281 0.542619i
\(327\) 0 0
\(328\) 1008.00 0.169687
\(329\) 0 0
\(330\) 0 0
\(331\) −1472.50 + 2550.44i −0.244519 + 0.423520i −0.961996 0.273062i \(-0.911964\pi\)
0.717477 + 0.696582i \(0.245297\pi\)
\(332\) 1620.00 + 2805.92i 0.267798 + 0.463840i
\(333\) 0 0
\(334\) −162.000 + 280.592i −0.0265397 + 0.0459680i
\(335\) 3138.00 0.511783
\(336\) 0 0
\(337\) 4277.00 0.691344 0.345672 0.938355i \(-0.387651\pi\)
0.345672 + 0.938355i \(0.387651\pi\)
\(338\) −612.000 + 1060.02i −0.0984864 + 0.170583i
\(339\) 0 0
\(340\) −1008.00 1745.91i −0.160784 0.278486i
\(341\) 2685.00 4650.56i 0.426396 0.738539i
\(342\) 0 0
\(343\) 0 0
\(344\) −2600.00 −0.407508
\(345\) 0 0
\(346\) 2724.00 + 4718.11i 0.423246 + 0.733084i
\(347\) 3594.00 + 6224.99i 0.556012 + 0.963040i 0.997824 + 0.0659329i \(0.0210023\pi\)
−0.441812 + 0.897107i \(0.645664\pi\)
\(348\) 0 0
\(349\) 9406.00 1.44267 0.721335 0.692587i \(-0.243529\pi\)
0.721335 + 0.692587i \(0.243529\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −480.000 + 831.384i −0.0726821 + 0.125889i
\(353\) −1695.00 2935.83i −0.255569 0.442658i 0.709481 0.704724i \(-0.248929\pi\)
−0.965050 + 0.262066i \(0.915596\pi\)
\(354\) 0 0
\(355\) 1026.00 1777.08i 0.153393 0.265684i
\(356\) −2400.00 −0.357303
\(357\) 0 0
\(358\) 2508.00 0.370257
\(359\) −2406.00 + 4167.31i −0.353715 + 0.612653i −0.986897 0.161350i \(-0.948415\pi\)
0.633182 + 0.774003i \(0.281749\pi\)
\(360\) 0 0
\(361\) −1275.00 2208.36i −0.185887 0.321966i
\(362\) −1807.00 + 3129.82i −0.262359 + 0.454418i
\(363\) 0 0
\(364\) 0 0
\(365\) −258.000 −0.0369982
\(366\) 0 0
\(367\) −3549.50 6147.91i −0.504857 0.874437i −0.999984 0.00561709i \(-0.998212\pi\)
0.495128 0.868820i \(-0.335121\pi\)
\(368\) 672.000 + 1163.94i 0.0951914 + 0.164876i
\(369\) 0 0
\(370\) 1740.00 0.244482
\(371\) 0 0
\(372\) 0 0
\(373\) −1481.50 + 2566.03i −0.205655 + 0.356204i −0.950341 0.311210i \(-0.899266\pi\)
0.744687 + 0.667414i \(0.232599\pi\)
\(374\) 2520.00 + 4364.77i 0.348412 + 0.603467i
\(375\) 0 0
\(376\) 1464.00 2535.72i 0.200798 0.347792i
\(377\) −9540.00 −1.30328
\(378\) 0 0
\(379\) −11899.0 −1.61269 −0.806346 0.591444i \(-0.798558\pi\)
−0.806346 + 0.591444i \(0.798558\pi\)
\(380\) 1164.00 2016.11i 0.157137 0.272169i
\(381\) 0 0
\(382\) 714.000 + 1236.68i 0.0956320 + 0.165639i
\(383\) −1284.00 + 2223.95i −0.171304 + 0.296707i −0.938876 0.344256i \(-0.888131\pi\)
0.767572 + 0.640963i \(0.221465\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7418.00 −0.978151
\(387\) 0 0
\(388\) 772.000 + 1337.14i 0.101011 + 0.174957i
\(389\) −5073.00 8786.69i −0.661212 1.14525i −0.980298 0.197526i \(-0.936709\pi\)
0.319086 0.947726i \(-0.396624\pi\)
\(390\) 0 0
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) 0 0
\(394\) −1044.00 + 1808.26i −0.133492 + 0.231215i
\(395\) −3513.00 6084.69i −0.447489 0.775074i
\(396\) 0 0
\(397\) −3114.50 + 5394.47i −0.393734 + 0.681967i −0.992939 0.118629i \(-0.962150\pi\)
0.599205 + 0.800596i \(0.295483\pi\)
\(398\) 272.000 0.0342566
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) −1236.00 + 2140.81i −0.153922 + 0.266601i −0.932666 0.360741i \(-0.882524\pi\)
0.778744 + 0.627342i \(0.215857\pi\)
\(402\) 0 0
\(403\) −4743.50 8215.98i −0.586329 1.01555i
\(404\) −1236.00 + 2140.81i −0.152211 + 0.263637i
\(405\) 0 0
\(406\) 0 0
\(407\) −4350.00 −0.529783
\(408\) 0 0
\(409\) −3537.50 6127.13i −0.427673 0.740751i 0.568993 0.822342i \(-0.307333\pi\)
−0.996666 + 0.0815915i \(0.974000\pi\)
\(410\) 756.000 + 1309.43i 0.0910639 + 0.157727i
\(411\) 0 0
\(412\) −5900.00 −0.705515
\(413\) 0 0
\(414\) 0 0
\(415\) −2430.00 + 4208.88i −0.287431 + 0.497846i
\(416\) 848.000 + 1468.78i 0.0999438 + 0.173108i
\(417\) 0 0
\(418\) −2910.00 + 5040.27i −0.340509 + 0.589779i
\(419\) −4158.00 −0.484801 −0.242400 0.970176i \(-0.577935\pi\)
−0.242400 + 0.970176i \(0.577935\pi\)
\(420\) 0 0
\(421\) −6595.00 −0.763469 −0.381735 0.924272i \(-0.624673\pi\)
−0.381735 + 0.924272i \(0.624673\pi\)
\(422\) −1484.00 + 2570.36i −0.171185 + 0.296501i
\(423\) 0 0
\(424\) −3072.00 5320.86i −0.351862 0.609443i
\(425\) −3738.00 + 6474.41i −0.426634 + 0.738953i
\(426\) 0 0
\(427\) 0 0
\(428\) −7536.00 −0.851090
\(429\) 0 0
\(430\) −1950.00 3377.50i −0.218692 0.378785i
\(431\) 759.000 + 1314.63i 0.0848254 + 0.146922i 0.905317 0.424737i \(-0.139633\pi\)
−0.820491 + 0.571659i \(0.806300\pi\)
\(432\) 0 0
\(433\) −8567.00 −0.950817 −0.475408 0.879765i \(-0.657700\pi\)
−0.475408 + 0.879765i \(0.657700\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −826.000 + 1430.67i −0.0907299 + 0.157149i
\(437\) 4074.00 + 7056.37i 0.445963 + 0.772431i
\(438\) 0 0
\(439\) 5320.00 9214.51i 0.578382 1.00179i −0.417283 0.908777i \(-0.637018\pi\)
0.995665 0.0930106i \(-0.0296491\pi\)
\(440\) −1440.00 −0.156021
\(441\) 0 0
\(442\) 8904.00 0.958190
\(443\) 3516.00 6089.89i 0.377088 0.653136i −0.613549 0.789657i \(-0.710259\pi\)
0.990637 + 0.136520i \(0.0435919\pi\)
\(444\) 0 0
\(445\) −1800.00 3117.69i −0.191749 0.332119i
\(446\) −2032.00 + 3519.53i −0.215735 + 0.373665i
\(447\) 0 0
\(448\) 0 0
\(449\) 14814.0 1.55705 0.778525 0.627613i \(-0.215968\pi\)
0.778525 + 0.627613i \(0.215968\pi\)
\(450\) 0 0
\(451\) −1890.00 3273.58i −0.197332 0.341789i
\(452\) −1764.00 3055.34i −0.183565 0.317945i
\(453\) 0 0
\(454\) 12396.0 1.28144
\(455\) 0 0
\(456\) 0 0
\(457\) 5625.50 9743.65i 0.575820 0.997350i −0.420132 0.907463i \(-0.638016\pi\)
0.995952 0.0898866i \(-0.0286505\pi\)
\(458\) −4591.00 7951.85i −0.468392 0.811278i
\(459\) 0 0
\(460\) −1008.00 + 1745.91i −0.102170 + 0.176964i
\(461\) −3852.00 −0.389166 −0.194583 0.980886i \(-0.562335\pi\)
−0.194583 + 0.980886i \(0.562335\pi\)
\(462\) 0 0
\(463\) −475.000 −0.0476784 −0.0238392 0.999716i \(-0.507589\pi\)
−0.0238392 + 0.999716i \(0.507589\pi\)
\(464\) −1440.00 + 2494.15i −0.144074 + 0.249543i
\(465\) 0 0
\(466\) 4530.00 + 7846.19i 0.450318 + 0.779974i
\(467\) −2967.00 + 5138.99i −0.293997 + 0.509217i −0.974751 0.223295i \(-0.928319\pi\)
0.680754 + 0.732512i \(0.261652\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4392.00 0.431038
\(471\) 0 0
\(472\) 1056.00 + 1829.05i 0.102980 + 0.178366i
\(473\) 4875.00 + 8443.75i 0.473896 + 0.820812i
\(474\) 0 0
\(475\) −8633.00 −0.833914
\(476\) 0 0
\(477\) 0 0
\(478\) 1530.00 2650.04i 0.146403 0.253577i
\(479\) 6684.00 + 11577.0i 0.637578 + 1.10432i 0.985963 + 0.166966i \(0.0533969\pi\)
−0.348385 + 0.937352i \(0.613270\pi\)
\(480\) 0 0
\(481\) −3842.50 + 6655.41i −0.364247 + 0.630895i
\(482\) −11068.0 −1.04592
\(483\) 0 0
\(484\) −1724.00 −0.161908
\(485\) −1158.00 + 2005.71i −0.108417 + 0.187783i
\(486\) 0 0
\(487\) −3326.50 5761.67i −0.309524 0.536111i 0.668734 0.743501i \(-0.266836\pi\)
−0.978258 + 0.207390i \(0.933503\pi\)
\(488\) 3272.00 5667.27i 0.303517 0.525708i
\(489\) 0 0
\(490\) 0 0
\(491\) −15444.0 −1.41951 −0.709754 0.704450i \(-0.751194\pi\)
−0.709754 + 0.704450i \(0.751194\pi\)
\(492\) 0 0
\(493\) 7560.00 + 13094.3i 0.690640 + 1.19622i
\(494\) 5141.00 + 8904.47i 0.468228 + 0.810994i
\(495\) 0 0
\(496\) −2864.00 −0.259269
\(497\) 0 0
\(498\) 0 0
\(499\) −341.500 + 591.495i −0.0306366 + 0.0530641i −0.880937 0.473233i \(-0.843087\pi\)
0.850301 + 0.526297i \(0.176420\pi\)
\(500\) −2568.00 4447.91i −0.229689 0.397833i
\(501\) 0 0
\(502\) 468.000 810.600i 0.0416093 0.0720694i
\(503\) 9882.00 0.875977 0.437989 0.898980i \(-0.355691\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(504\) 0 0
\(505\) −3708.00 −0.326740
\(506\) 2520.00 4364.77i 0.221399 0.383474i
\(507\) 0 0
\(508\) −4966.00 8601.36i −0.433722 0.751228i
\(509\) −2103.00 + 3642.50i −0.183131 + 0.317193i −0.942945 0.332948i \(-0.891957\pi\)
0.759814 + 0.650141i \(0.225290\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 2490.00 + 4312.81i 0.213675 + 0.370097i
\(515\) −4425.00 7664.32i −0.378619 0.655787i
\(516\) 0 0
\(517\) −10980.0 −0.934042
\(518\) 0 0
\(519\) 0 0
\(520\) −1272.00 + 2203.17i −0.107271 + 0.185799i
\(521\) −4530.00 7846.19i −0.380927 0.659785i 0.610268 0.792195i \(-0.291062\pi\)
−0.991195 + 0.132410i \(0.957728\pi\)
\(522\) 0 0
\(523\) −7839.50 + 13578.4i −0.655444 + 1.13526i 0.326338 + 0.945253i \(0.394185\pi\)
−0.981782 + 0.190010i \(0.939148\pi\)
\(524\) 8472.00 0.706300
\(525\) 0 0
\(526\) −3144.00 −0.260618
\(527\) −7518.00 + 13021.6i −0.621422 + 1.07633i
\(528\) 0 0
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) 4608.00 7981.29i 0.377658 0.654123i
\(531\) 0 0
\(532\) 0 0
\(533\) −6678.00 −0.542695
\(534\) 0 0
\(535\) −5652.00 9789.55i −0.456743 0.791101i
\(536\) 2092.00 + 3623.45i 0.168583 + 0.291995i
\(537\) 0 0
\(538\) 3612.00 0.289451
\(539\) 0 0
\(540\) 0 0
\(541\) 3855.50 6677.92i 0.306397 0.530696i −0.671174 0.741300i \(-0.734210\pi\)
0.977571 + 0.210604i \(0.0675431\pi\)
\(542\) −6112.00 10586.3i −0.484378 0.838967i
\(543\) 0 0
\(544\) 1344.00 2327.88i 0.105926 0.183469i
\(545\) −2478.00 −0.194763
\(546\) 0 0
\(547\) 4292.00 0.335489 0.167745 0.985830i \(-0.446352\pi\)
0.167745 + 0.985830i \(0.446352\pi\)
\(548\) 6024.00 10433.9i 0.469585 0.813345i
\(549\) 0 0
\(550\) 2670.00 + 4624.58i 0.206999 + 0.358532i
\(551\) −8730.00 + 15120.8i −0.674974 + 1.16909i
\(552\) 0 0
\(553\) 0 0
\(554\) −8462.00 −0.648946
\(555\) 0 0
\(556\) −74.0000 128.172i −0.00564442 0.00977643i
\(557\) −4929.00 8537.28i −0.374952 0.649436i 0.615368 0.788240i \(-0.289008\pi\)
−0.990320 + 0.138804i \(0.955674\pi\)
\(558\) 0 0
\(559\) 17225.0 1.30329
\(560\) 0 0
\(561\) 0 0
\(562\) −3816.00 + 6609.51i −0.286420 + 0.496095i
\(563\) 6945.00 + 12029.1i 0.519888 + 0.900472i 0.999733 + 0.0231188i \(0.00735960\pi\)
−0.479845 + 0.877353i \(0.659307\pi\)
\(564\) 0 0
\(565\) 2646.00 4583.01i 0.197023 0.341254i
\(566\) 7994.00 0.593662
\(567\) 0 0
\(568\) 2736.00 0.202113
\(569\) 9519.00 16487.4i 0.701331 1.21474i −0.266669 0.963788i \(-0.585923\pi\)
0.967999 0.250952i \(-0.0807437\pi\)
\(570\) 0 0
\(571\) 4026.50 + 6974.10i 0.295103 + 0.511133i 0.975009 0.222166i \(-0.0713127\pi\)
−0.679906 + 0.733299i \(0.737979\pi\)
\(572\) 3180.00 5507.92i 0.232452 0.402618i
\(573\) 0 0
\(574\) 0 0
\(575\) 7476.00 0.542210
\(576\) 0 0
\(577\) −8568.50 14841.1i −0.618217 1.07078i −0.989811 0.142388i \(-0.954522\pi\)
0.371594 0.928395i \(-0.378811\pi\)
\(578\) −2143.00 3711.78i −0.154216 0.267111i
\(579\) 0 0
\(580\) −4320.00 −0.309273
\(581\) 0 0
\(582\) 0 0
\(583\) −11520.0 + 19953.2i −0.818370 + 1.41746i
\(584\) −172.000 297.913i −0.0121873 0.0211091i
\(585\) 0 0
\(586\) −4608.00 + 7981.29i −0.324837 + 0.562635i
\(587\) 18144.0 1.27578 0.637890 0.770127i \(-0.279807\pi\)
0.637890 + 0.770127i \(0.279807\pi\)
\(588\) 0 0
\(589\) −17363.0 −1.21465
\(590\) −1584.00 + 2743.57i −0.110529 + 0.191442i
\(591\) 0 0
\(592\) 1160.00 + 2009.18i 0.0805333 + 0.139488i
\(593\) 12351.0 21392.6i 0.855303 1.48143i −0.0210603 0.999778i \(-0.506704\pi\)
0.876363 0.481650i \(-0.159962\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6576.00 0.451952
\(597\) 0 0
\(598\) −4452.00 7711.09i −0.304441 0.527308i
\(599\) −1086.00 1881.01i −0.0740781 0.128307i 0.826607 0.562780i \(-0.190268\pi\)
−0.900685 + 0.434473i \(0.856935\pi\)
\(600\) 0 0
\(601\) −4175.00 −0.283364 −0.141682 0.989912i \(-0.545251\pi\)
−0.141682 + 0.989912i \(0.545251\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2176.00 + 3768.94i −0.146590 + 0.253901i
\(605\) −1293.00 2239.54i −0.0868891 0.150496i
\(606\) 0 0
\(607\) 1130.50 1958.08i 0.0755940 0.130933i −0.825750 0.564036i \(-0.809248\pi\)
0.901344 + 0.433103i \(0.142581\pi\)
\(608\) 3104.00 0.207046
\(609\) 0 0
\(610\) 9816.00 0.651538
\(611\) −9699.00 + 16799.2i −0.642192 + 1.11231i
\(612\) 0 0
\(613\) 8159.00 + 14131.8i 0.537584 + 0.931123i 0.999033 + 0.0439561i \(0.0139962\pi\)
−0.461450 + 0.887166i \(0.652670\pi\)
\(614\) −631.000 + 1092.92i −0.0414741 + 0.0718352i
\(615\) 0 0
\(616\) 0 0
\(617\) 26550.0 1.73235 0.866177 0.499737i \(-0.166570\pi\)
0.866177 + 0.499737i \(0.166570\pi\)
\(618\) 0 0
\(619\) 9962.50 + 17255.6i 0.646893 + 1.12045i 0.983861 + 0.178935i \(0.0572652\pi\)
−0.336968 + 0.941516i \(0.609401\pi\)
\(620\) −2148.00 3720.45i −0.139138 0.240995i
\(621\) 0 0
\(622\) 7788.00 0.502042
\(623\) 0 0
\(624\) 0 0
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) −2185.00 3784.53i −0.139505 0.241630i
\(627\) 0 0
\(628\) 1012.00 1752.84i 0.0643045 0.111379i
\(629\) 12180.0 0.772096
\(630\) 0 0
\(631\) −6832.00 −0.431026 −0.215513 0.976501i \(-0.569142\pi\)
−0.215513 + 0.976501i \(0.569142\pi\)
\(632\) 4684.00 8112.93i 0.294809 0.510625i
\(633\) 0 0
\(634\) 3504.00 + 6069.11i 0.219498 + 0.380181i
\(635\) 7449.00 12902.0i 0.465519 0.806303i
\(636\) 0 0
\(637\) 0 0
\(638\) 10800.0 0.670182
\(639\) 0 0
\(640\) 384.000 + 665.108i 0.0237171 + 0.0410792i
\(641\) 5106.00 + 8843.85i 0.314625 + 0.544947i 0.979358 0.202134i \(-0.0647878\pi\)
−0.664732 + 0.747082i \(0.731454\pi\)
\(642\) 0 0
\(643\) −3779.00 −0.231772 −0.115886 0.993263i \(-0.536971\pi\)
−0.115886 + 0.993263i \(0.536971\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8148.00 14112.7i 0.496252 0.859534i
\(647\) −8499.00 14720.7i −0.516430 0.894483i −0.999818 0.0190767i \(-0.993927\pi\)
0.483388 0.875406i \(-0.339406\pi\)
\(648\) 0 0
\(649\) 3960.00 6858.92i 0.239512 0.414848i
\(650\) 9434.00 0.569280
\(651\) 0 0
\(652\) 7376.00 0.443047
\(653\) −10875.0 + 18836.1i −0.651718 + 1.12881i 0.330988 + 0.943635i \(0.392618\pi\)
−0.982706 + 0.185173i \(0.940715\pi\)
\(654\) 0 0
\(655\) 6354.00 + 11005.5i 0.379040 + 0.656517i
\(656\) −1008.00 + 1745.91i −0.0599936 + 0.103912i
\(657\) 0 0
\(658\) 0 0
\(659\) 10944.0 0.646916 0.323458 0.946243i \(-0.395155\pi\)
0.323458 + 0.946243i \(0.395155\pi\)
\(660\) 0 0
\(661\) 5477.50 + 9487.31i 0.322315 + 0.558266i 0.980965 0.194184i \(-0.0622057\pi\)
−0.658650 + 0.752449i \(0.728872\pi\)
\(662\) −2945.00 5100.89i −0.172901 0.299474i
\(663\) 0 0
\(664\) −6480.00 −0.378724
\(665\) 0 0
\(666\) 0 0
\(667\) 7560.00 13094.3i 0.438867 0.760140i
\(668\) −324.000 561.184i −0.0187664 0.0325043i
\(669\) 0 0
\(670\) −3138.00 + 5435.18i −0.180943 + 0.313402i
\(671\) −24540.0 −1.41186
\(672\) 0 0
\(673\) 25103.0 1.43782 0.718908 0.695106i \(-0.244642\pi\)
0.718908 + 0.695106i \(0.244642\pi\)
\(674\) −4277.00 + 7407.98i −0.244427 + 0.423360i
\(675\) 0 0
\(676\) −1224.00 2120.03i −0.0696404 0.120621i
\(677\) 2802.00 4853.21i 0.159069 0.275515i −0.775464 0.631391i \(-0.782484\pi\)
0.934533 + 0.355876i \(0.115817\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4032.00 0.227383
\(681\) 0 0
\(682\) 5370.00 + 9301.11i 0.301507 + 0.522226i
\(683\) 5484.00 + 9498.57i 0.307232 + 0.532141i 0.977756 0.209747i \(-0.0672639\pi\)
−0.670524 + 0.741888i \(0.733931\pi\)
\(684\) 0 0
\(685\) 18072.0 1.00802
\(686\) 0 0
\(687\) 0 0
\(688\) 2600.00 4503.33i 0.144076 0.249546i
\(689\) 20352.0 + 35250.7i 1.12533 + 1.94912i
\(690\) 0 0
\(691\) 4202.50 7278.94i 0.231361 0.400729i −0.726848 0.686799i \(-0.759015\pi\)
0.958209 + 0.286069i \(0.0923487\pi\)
\(692\) −10896.0 −0.598560
\(693\) 0 0
\(694\) −14376.0 −0.786319
\(695\) 111.000 192.258i 0.00605823 0.0104932i
\(696\) 0 0
\(697\) 5292.00 + 9166.01i 0.287588 + 0.498117i
\(698\) −9406.00 + 16291.7i −0.510061 + 0.883451i
\(699\) 0 0
\(700\) 0 0
\(701\) −468.000 −0.0252156 −0.0126078 0.999921i \(-0.504013\pi\)
−0.0126078 + 0.999921i \(0.504013\pi\)
\(702\) 0 0
\(703\) 7032.50 + 12180.6i 0.377291 + 0.653488i
\(704\) −960.000 1662.77i −0.0513940 0.0890170i
\(705\) 0 0
\(706\) 6780.00 0.361429
\(707\) 0 0
\(708\) 0 0
\(709\) 12533.0 21707.8i 0.663874 1.14986i −0.315715 0.948854i \(-0.602244\pi\)
0.979589 0.201010i \(-0.0644222\pi\)
\(710\) 2052.00 + 3554.17i 0.108465 + 0.187867i
\(711\) 0 0
\(712\) 2400.00 4156.92i 0.126326 0.218802i
\(713\) 15036.0 0.789765
\(714\) 0 0
\(715\) 9540.00 0.498987
\(716\) −2508.00 + 4343.98i −0.130906 + 0.226735i
\(717\) 0 0
\(718\) −4812.00 8334.63i −0.250115 0.433211i
\(719\) −5541.00 + 9597.29i −0.287405 + 0.497801i −0.973190 0.230004i \(-0.926126\pi\)
0.685784 + 0.727805i \(0.259459\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5100.00 0.262884
\(723\) 0 0
\(724\) −3614.00 6259.63i −0.185516 0.321322i
\(725\) 8010.00 + 13873.7i 0.410323 + 0.710700i
\(726\) 0 0
\(727\) −13481.0 −0.687734 −0.343867 0.939018i \(-0.611737\pi\)
−0.343867 + 0.939018i \(0.611737\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 258.000 446.869i 0.0130808 0.0226567i
\(731\) −13650.0 23642.5i −0.690648 1.19624i
\(732\) 0 0
\(733\) 12158.5 21059.1i 0.612666 1.06117i −0.378123 0.925755i \(-0.623430\pi\)
0.990789 0.135414i \(-0.0432364\pi\)
\(734\) 14198.0 0.713975
\(735\) 0 0
\(736\) −2688.00 −0.134621
\(737\) 7845.00 13587.9i 0.392095 0.679129i
\(738\) 0 0
\(739\) 9108.50 + 15776.4i 0.453399 + 0.785309i 0.998595 0.0529992i \(-0.0168781\pi\)
−0.545196 + 0.838309i \(0.683545\pi\)
\(740\) −1740.00 + 3013.77i −0.0864374 + 0.149714i
\(741\) 0 0
\(742\) 0 0
\(743\) −19782.0 −0.976758 −0.488379 0.872632i \(-0.662412\pi\)
−0.488379 + 0.872632i \(0.662412\pi\)
\(744\) 0 0
\(745\) 4932.00 + 8542.47i 0.242543 + 0.420097i
\(746\) −2963.00 5132.07i −0.145420 0.251874i
\(747\) 0 0
\(748\) −10080.0 −0.492729
\(749\) 0 0
\(750\) 0 0
\(751\) 2460.50 4261.71i 0.119554 0.207073i −0.800037 0.599951i \(-0.795187\pi\)
0.919591 + 0.392877i \(0.128520\pi\)
\(752\) 2928.00 + 5071.44i 0.141986 + 0.245926i
\(753\) 0 0
\(754\) 9540.00 16523.8i 0.460778 0.798090i
\(755\) −6528.00 −0.314673
\(756\) 0 0
\(757\) 18098.0 0.868934 0.434467 0.900688i \(-0.356937\pi\)
0.434467 + 0.900688i \(0.356937\pi\)
\(758\) 11899.0 20609.7i 0.570173 0.987569i
\(759\) 0 0
\(760\) 2328.00 + 4032.21i 0.111112 + 0.192452i
\(761\) 12234.0 21189.9i 0.582762 1.00937i −0.412388 0.911008i \(-0.635305\pi\)
0.995150 0.0983657i \(-0.0313615\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2856.00 −0.135244
\(765\) 0 0
\(766\) −2568.00 4447.91i −0.121130 0.209803i
\(767\) −6996.00 12117.4i −0.329349 0.570450i
\(768\) 0 0
\(769\) −21719.0 −1.01847 −0.509237 0.860626i \(-0.670072\pi\)
−0.509237 + 0.860626i \(0.670072\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7418.00 12848.4i 0.345829 0.598993i
\(773\) 15153.0 + 26245.8i 0.705065 + 1.22121i 0.966668 + 0.256033i \(0.0824157\pi\)
−0.261603 + 0.965176i \(0.584251\pi\)
\(774\) 0 0
\(775\) −7965.50 + 13796.7i −0.369199 + 0.639471i
\(776\) −3088.00 −0.142851
\(777\) 0 0
\(778\) 20292.0 0.935094
\(779\) −6111.00 + 10584.6i −0.281065 + 0.486818i
\(780\) 0 0
\(781\) −5130.00 8885.42i −0.235039 0.407100i
\(782\) −7056.00 + 12221.4i −0.322662 + 0.558868i
\(783\) 0 0
\(784\) 0 0
\(785\) 3036.00 0.138038
\(786\) 0 0
\(787\) 13648.0 + 23639.0i 0.618169 + 1.07070i 0.989820 + 0.142327i \(0.0454584\pi\)
−0.371651 + 0.928372i \(0.621208\pi\)
\(788\) −2088.00 3616.52i −0.0943933 0.163494i
\(789\) 0 0
\(790\) 14052.0 0.632845
\(791\)