Properties

Label 128.4.g.a.17.5
Level $128$
Weight $4$
Character 128.17
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 17.5
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.729459 + 1.76107i) q^{3} +(4.29822 - 1.78038i) q^{5} +(-1.47807 + 1.47807i) q^{7} +(16.5226 + 16.5226i) q^{9} +O(q^{10})\) \(q+(-0.729459 + 1.76107i) q^{3} +(4.29822 - 1.78038i) q^{5} +(-1.47807 + 1.47807i) q^{7} +(16.5226 + 16.5226i) q^{9} +(-0.854325 - 2.06252i) q^{11} +(40.9706 + 16.9706i) q^{13} +8.86818i q^{15} +73.1063i q^{17} +(18.2478 + 7.55849i) q^{19} +(-1.52480 - 3.68119i) q^{21} +(144.221 + 144.221i) q^{23} +(-73.0834 + 73.0834i) q^{25} +(-88.6990 + 36.7403i) q^{27} +(80.7690 - 194.994i) q^{29} +168.830 q^{31} +4.25544 q^{33} +(-3.72155 + 8.98462i) q^{35} +(-72.0103 + 29.8277i) q^{37} +(-59.7727 + 59.7727i) q^{39} +(-141.297 - 141.297i) q^{41} +(-161.344 - 389.519i) q^{43} +(100.434 + 41.6013i) q^{45} -239.015i q^{47} +338.631i q^{49} +(-128.745 - 53.3280i) q^{51} +(-59.8701 - 144.539i) q^{53} +(-7.34415 - 7.34415i) q^{55} +(-26.6221 + 26.6221i) q^{57} +(-582.808 + 241.407i) q^{59} +(238.297 - 575.301i) q^{61} -48.8433 q^{63} +206.315 q^{65} +(156.090 - 376.834i) q^{67} +(-359.185 + 148.780i) q^{69} +(-411.945 + 411.945i) q^{71} +(-642.439 - 642.439i) q^{73} +(-75.3937 - 182.016i) q^{75} +(4.31132 + 1.78581i) q^{77} -800.261i q^{79} +447.890i q^{81} +(1345.29 + 557.236i) q^{83} +(130.157 + 314.227i) q^{85} +(284.480 + 284.480i) q^{87} +(340.094 - 340.094i) q^{89} +(-85.6413 + 35.4738i) q^{91} +(-123.155 + 297.321i) q^{93} +91.8900 q^{95} +632.602 q^{97} +(19.9626 - 48.1940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.729459 + 1.76107i −0.140384 + 0.338918i −0.978398 0.206732i \(-0.933717\pi\)
0.838013 + 0.545650i \(0.183717\pi\)
\(4\) 0 0
\(5\) 4.29822 1.78038i 0.384444 0.159242i −0.182087 0.983282i \(-0.558285\pi\)
0.566531 + 0.824040i \(0.308285\pi\)
\(6\) 0 0
\(7\) −1.47807 + 1.47807i −0.0798085 + 0.0798085i −0.745884 0.666076i \(-0.767973\pi\)
0.666076 + 0.745884i \(0.267973\pi\)
\(8\) 0 0
\(9\) 16.5226 + 16.5226i 0.611949 + 0.611949i
\(10\) 0 0
\(11\) −0.854325 2.06252i −0.0234172 0.0565340i 0.911738 0.410771i \(-0.134741\pi\)
−0.935156 + 0.354237i \(0.884741\pi\)
\(12\) 0 0
\(13\) 40.9706 + 16.9706i 0.874092 + 0.362061i 0.774203 0.632938i \(-0.218151\pi\)
0.0998893 + 0.994999i \(0.468151\pi\)
\(14\) 0 0
\(15\) 8.86818i 0.152650i
\(16\) 0 0
\(17\) 73.1063i 1.04299i 0.853253 + 0.521496i \(0.174626\pi\)
−0.853253 + 0.521496i \(0.825374\pi\)
\(18\) 0 0
\(19\) 18.2478 + 7.55849i 0.220333 + 0.0912650i 0.490120 0.871655i \(-0.336953\pi\)
−0.269786 + 0.962920i \(0.586953\pi\)
\(20\) 0 0
\(21\) −1.52480 3.68119i −0.0158447 0.0382524i
\(22\) 0 0
\(23\) 144.221 + 144.221i 1.30748 + 1.30748i 0.923228 + 0.384253i \(0.125541\pi\)
0.384253 + 0.923228i \(0.374459\pi\)
\(24\) 0 0
\(25\) −73.0834 + 73.0834i −0.584667 + 0.584667i
\(26\) 0 0
\(27\) −88.6990 + 36.7403i −0.632227 + 0.261877i
\(28\) 0 0
\(29\) 80.7690 194.994i 0.517187 1.24860i −0.422437 0.906392i \(-0.638825\pi\)
0.939624 0.342208i \(-0.111175\pi\)
\(30\) 0 0
\(31\) 168.830 0.978153 0.489077 0.872241i \(-0.337334\pi\)
0.489077 + 0.872241i \(0.337334\pi\)
\(32\) 0 0
\(33\) 4.25544 0.0224478
\(34\) 0 0
\(35\) −3.72155 + 8.98462i −0.0179731 + 0.0433908i
\(36\) 0 0
\(37\) −72.0103 + 29.8277i −0.319958 + 0.132531i −0.536881 0.843658i \(-0.680398\pi\)
0.216924 + 0.976189i \(0.430398\pi\)
\(38\) 0 0
\(39\) −59.7727 + 59.7727i −0.245418 + 0.245418i
\(40\) 0 0
\(41\) −141.297 141.297i −0.538215 0.538215i 0.384789 0.923005i \(-0.374274\pi\)
−0.923005 + 0.384789i \(0.874274\pi\)
\(42\) 0 0
\(43\) −161.344 389.519i −0.572203 1.38142i −0.899675 0.436560i \(-0.856197\pi\)
0.327472 0.944861i \(-0.393803\pi\)
\(44\) 0 0
\(45\) 100.434 + 41.6013i 0.332708 + 0.137812i
\(46\) 0 0
\(47\) 239.015i 0.741787i −0.928675 0.370893i \(-0.879052\pi\)
0.928675 0.370893i \(-0.120948\pi\)
\(48\) 0 0
\(49\) 338.631i 0.987261i
\(50\) 0 0
\(51\) −128.745 53.3280i −0.353489 0.146420i
\(52\) 0 0
\(53\) −59.8701 144.539i −0.155166 0.374604i 0.827111 0.562038i \(-0.189983\pi\)
−0.982277 + 0.187435i \(0.939983\pi\)
\(54\) 0 0
\(55\) −7.34415 7.34415i −0.0180052 0.0180052i
\(56\) 0 0
\(57\) −26.6221 + 26.6221i −0.0618627 + 0.0618627i
\(58\) 0 0
\(59\) −582.808 + 241.407i −1.28602 + 0.532686i −0.917796 0.397051i \(-0.870033\pi\)
−0.368222 + 0.929738i \(0.620033\pi\)
\(60\) 0 0
\(61\) 238.297 575.301i 0.500178 1.20754i −0.449209 0.893427i \(-0.648294\pi\)
0.949387 0.314110i \(-0.101706\pi\)
\(62\) 0 0
\(63\) −48.8433 −0.0976775
\(64\) 0 0
\(65\) 206.315 0.393695
\(66\) 0 0
\(67\) 156.090 376.834i 0.284618 0.687129i −0.715314 0.698804i \(-0.753716\pi\)
0.999932 + 0.0116744i \(0.00371618\pi\)
\(68\) 0 0
\(69\) −359.185 + 148.780i −0.626679 + 0.259579i
\(70\) 0 0
\(71\) −411.945 + 411.945i −0.688577 + 0.688577i −0.961917 0.273341i \(-0.911871\pi\)
0.273341 + 0.961917i \(0.411871\pi\)
\(72\) 0 0
\(73\) −642.439 642.439i −1.03003 1.03003i −0.999535 0.0304901i \(-0.990293\pi\)
−0.0304901 0.999535i \(-0.509707\pi\)
\(74\) 0 0
\(75\) −75.3937 182.016i −0.116076 0.280233i
\(76\) 0 0
\(77\) 4.31132 + 1.78581i 0.00638078 + 0.00264301i
\(78\) 0 0
\(79\) 800.261i 1.13970i −0.821748 0.569850i \(-0.807001\pi\)
0.821748 0.569850i \(-0.192999\pi\)
\(80\) 0 0
\(81\) 447.890i 0.614390i
\(82\) 0 0
\(83\) 1345.29 + 557.236i 1.77909 + 0.736923i 0.992902 + 0.118933i \(0.0379475\pi\)
0.786187 + 0.617989i \(0.212052\pi\)
\(84\) 0 0
\(85\) 130.157 + 314.227i 0.166088 + 0.400973i
\(86\) 0 0
\(87\) 284.480 + 284.480i 0.350568 + 0.350568i
\(88\) 0 0
\(89\) 340.094 340.094i 0.405055 0.405055i −0.474955 0.880010i \(-0.657536\pi\)
0.880010 + 0.474955i \(0.157536\pi\)
\(90\) 0 0
\(91\) −85.6413 + 35.4738i −0.0986555 + 0.0408644i
\(92\) 0 0
\(93\) −123.155 + 297.321i −0.137317 + 0.331514i
\(94\) 0 0
\(95\) 91.8900 0.0992391
\(96\) 0 0
\(97\) 632.602 0.662175 0.331088 0.943600i \(-0.392584\pi\)
0.331088 + 0.943600i \(0.392584\pi\)
\(98\) 0 0
\(99\) 19.9626 48.1940i 0.0202658 0.0489261i
\(100\) 0 0
\(101\) −1069.17 + 442.863i −1.05333 + 0.436303i −0.841078 0.540913i \(-0.818079\pi\)
−0.212249 + 0.977216i \(0.568079\pi\)
\(102\) 0 0
\(103\) −251.287 + 251.287i −0.240389 + 0.240389i −0.817011 0.576622i \(-0.804371\pi\)
0.576622 + 0.817011i \(0.304371\pi\)
\(104\) 0 0
\(105\) −13.1078 13.1078i −0.0121828 0.0121828i
\(106\) 0 0
\(107\) 539.593 + 1302.69i 0.487518 + 1.17697i 0.955965 + 0.293481i \(0.0948138\pi\)
−0.468447 + 0.883492i \(0.655186\pi\)
\(108\) 0 0
\(109\) 723.084 + 299.511i 0.635403 + 0.263192i 0.677047 0.735940i \(-0.263260\pi\)
−0.0416440 + 0.999133i \(0.513260\pi\)
\(110\) 0 0
\(111\) 148.573i 0.127045i
\(112\) 0 0
\(113\) 118.490i 0.0986425i −0.998783 0.0493213i \(-0.984294\pi\)
0.998783 0.0493213i \(-0.0157058\pi\)
\(114\) 0 0
\(115\) 876.659 + 363.124i 0.710860 + 0.294448i
\(116\) 0 0
\(117\) 396.543 + 957.340i 0.313337 + 0.756463i
\(118\) 0 0
\(119\) −108.056 108.056i −0.0832397 0.0832397i
\(120\) 0 0
\(121\) 937.635 937.635i 0.704459 0.704459i
\(122\) 0 0
\(123\) 351.903 145.763i 0.257968 0.106854i
\(124\) 0 0
\(125\) −406.560 + 981.522i −0.290910 + 0.702320i
\(126\) 0 0
\(127\) −842.166 −0.588427 −0.294213 0.955740i \(-0.595058\pi\)
−0.294213 + 0.955740i \(0.595058\pi\)
\(128\) 0 0
\(129\) 803.664 0.548517
\(130\) 0 0
\(131\) −488.895 + 1180.30i −0.326069 + 0.787199i 0.672808 + 0.739817i \(0.265088\pi\)
−0.998877 + 0.0473823i \(0.984912\pi\)
\(132\) 0 0
\(133\) −38.1436 + 15.7996i −0.0248682 + 0.0103007i
\(134\) 0 0
\(135\) −315.836 + 315.836i −0.201354 + 0.201354i
\(136\) 0 0
\(137\) 354.278 + 354.278i 0.220934 + 0.220934i 0.808892 0.587958i \(-0.200068\pi\)
−0.587958 + 0.808892i \(0.700068\pi\)
\(138\) 0 0
\(139\) −506.903 1223.77i −0.309316 0.746756i −0.999728 0.0233385i \(-0.992570\pi\)
0.690411 0.723417i \(-0.257430\pi\)
\(140\) 0 0
\(141\) 420.923 + 174.352i 0.251405 + 0.104135i
\(142\) 0 0
\(143\) 99.0012i 0.0578944i
\(144\) 0 0
\(145\) 981.925i 0.562375i
\(146\) 0 0
\(147\) −596.352 247.017i −0.334601 0.138596i
\(148\) 0 0
\(149\) 263.786 + 636.836i 0.145035 + 0.350145i 0.979657 0.200677i \(-0.0643142\pi\)
−0.834623 + 0.550822i \(0.814314\pi\)
\(150\) 0 0
\(151\) −963.930 963.930i −0.519493 0.519493i 0.397925 0.917418i \(-0.369731\pi\)
−0.917418 + 0.397925i \(0.869731\pi\)
\(152\) 0 0
\(153\) −1207.91 + 1207.91i −0.638259 + 0.638259i
\(154\) 0 0
\(155\) 725.668 300.581i 0.376045 0.155763i
\(156\) 0 0
\(157\) 439.451 1060.93i 0.223389 0.539308i −0.771957 0.635674i \(-0.780722\pi\)
0.995346 + 0.0963665i \(0.0307221\pi\)
\(158\) 0 0
\(159\) 298.217 0.148743
\(160\) 0 0
\(161\) −426.337 −0.208696
\(162\) 0 0
\(163\) 437.870 1057.11i 0.210409 0.507972i −0.783077 0.621924i \(-0.786351\pi\)
0.993486 + 0.113953i \(0.0363512\pi\)
\(164\) 0 0
\(165\) 18.2908 7.57631i 0.00862993 0.00357464i
\(166\) 0 0
\(167\) 856.325 856.325i 0.396793 0.396793i −0.480307 0.877100i \(-0.659475\pi\)
0.877100 + 0.480307i \(0.159475\pi\)
\(168\) 0 0
\(169\) −162.925 162.925i −0.0741580 0.0741580i
\(170\) 0 0
\(171\) 176.616 + 426.388i 0.0789832 + 0.190682i
\(172\) 0 0
\(173\) −2410.30 998.380i −1.05926 0.438760i −0.216071 0.976378i \(-0.569324\pi\)
−0.843189 + 0.537618i \(0.819324\pi\)
\(174\) 0 0
\(175\) 216.045i 0.0933228i
\(176\) 0 0
\(177\) 1202.46i 0.510636i
\(178\) 0 0
\(179\) −1526.52 632.305i −0.637415 0.264026i 0.0404847 0.999180i \(-0.487110\pi\)
−0.677900 + 0.735154i \(0.737110\pi\)
\(180\) 0 0
\(181\) −1487.44 3590.99i −0.610831 1.47468i −0.862089 0.506756i \(-0.830844\pi\)
0.251258 0.967920i \(-0.419156\pi\)
\(182\) 0 0
\(183\) 839.317 + 839.317i 0.339039 + 0.339039i
\(184\) 0 0
\(185\) −256.412 + 256.412i −0.101901 + 0.101901i
\(186\) 0 0
\(187\) 150.783 62.4565i 0.0589646 0.0244239i
\(188\) 0 0
\(189\) 76.7987 185.409i 0.0295571 0.0713571i
\(190\) 0 0
\(191\) −1908.11 −0.722858 −0.361429 0.932400i \(-0.617711\pi\)
−0.361429 + 0.932400i \(0.617711\pi\)
\(192\) 0 0
\(193\) −3674.63 −1.37049 −0.685247 0.728310i \(-0.740306\pi\)
−0.685247 + 0.728310i \(0.740306\pi\)
\(194\) 0 0
\(195\) −150.498 + 363.334i −0.0552687 + 0.133430i
\(196\) 0 0
\(197\) 2539.28 1051.80i 0.918356 0.380395i 0.127107 0.991889i \(-0.459431\pi\)
0.791249 + 0.611494i \(0.209431\pi\)
\(198\) 0 0
\(199\) 1751.18 1751.18i 0.623809 0.623809i −0.322694 0.946503i \(-0.604589\pi\)
0.946503 + 0.322694i \(0.104589\pi\)
\(200\) 0 0
\(201\) 549.771 + 549.771i 0.192924 + 0.192924i
\(202\) 0 0
\(203\) 168.832 + 407.597i 0.0583730 + 0.140925i
\(204\) 0 0
\(205\) −858.886 355.762i −0.292620 0.121207i
\(206\) 0 0
\(207\) 4765.80i 1.60022i
\(208\) 0 0
\(209\) 44.0939i 0.0145935i
\(210\) 0 0
\(211\) −4123.79 1708.13i −1.34547 0.557311i −0.410440 0.911887i \(-0.634625\pi\)
−0.935027 + 0.354577i \(0.884625\pi\)
\(212\) 0 0
\(213\) −424.967 1025.96i −0.136706 0.330036i
\(214\) 0 0
\(215\) −1386.98 1386.98i −0.439961 0.439961i
\(216\) 0 0
\(217\) −249.543 + 249.543i −0.0780649 + 0.0780649i
\(218\) 0 0
\(219\) 1600.01 662.747i 0.493694 0.204495i
\(220\) 0 0
\(221\) −1240.66 + 2995.21i −0.377627 + 0.911672i
\(222\) 0 0
\(223\) 4869.99 1.46242 0.731208 0.682155i \(-0.238957\pi\)
0.731208 + 0.682155i \(0.238957\pi\)
\(224\) 0 0
\(225\) −2415.06 −0.715573
\(226\) 0 0
\(227\) −11.2187 + 27.0843i −0.00328022 + 0.00791916i −0.925511 0.378720i \(-0.876364\pi\)
0.922231 + 0.386639i \(0.126364\pi\)
\(228\) 0 0
\(229\) 4258.86 1764.08i 1.22897 0.509054i 0.328716 0.944429i \(-0.393384\pi\)
0.900250 + 0.435374i \(0.143384\pi\)
\(230\) 0 0
\(231\) −6.28986 + 6.28986i −0.00179153 + 0.00179153i
\(232\) 0 0
\(233\) 4653.94 + 4653.94i 1.30854 + 1.30854i 0.922470 + 0.386069i \(0.126167\pi\)
0.386069 + 0.922470i \(0.373833\pi\)
\(234\) 0 0
\(235\) −425.538 1027.34i −0.118124 0.285176i
\(236\) 0 0
\(237\) 1409.32 + 583.757i 0.386265 + 0.159996i
\(238\) 0 0
\(239\) 630.197i 0.170561i 0.996357 + 0.0852805i \(0.0271786\pi\)
−0.996357 + 0.0852805i \(0.972821\pi\)
\(240\) 0 0
\(241\) 1523.56i 0.407224i 0.979052 + 0.203612i \(0.0652681\pi\)
−0.979052 + 0.203612i \(0.934732\pi\)
\(242\) 0 0
\(243\) −3183.64 1318.71i −0.840455 0.348128i
\(244\) 0 0
\(245\) 602.891 + 1455.51i 0.157214 + 0.379547i
\(246\) 0 0
\(247\) 619.351 + 619.351i 0.159548 + 0.159548i
\(248\) 0 0
\(249\) −1962.66 + 1962.66i −0.499513 + 0.499513i
\(250\) 0 0
\(251\) −2943.19 + 1219.11i −0.740129 + 0.306572i −0.720707 0.693240i \(-0.756183\pi\)
−0.0194224 + 0.999811i \(0.506183\pi\)
\(252\) 0 0
\(253\) 174.247 420.670i 0.0432997 0.104535i
\(254\) 0 0
\(255\) −648.320 −0.159213
\(256\) 0 0
\(257\) 3355.93 0.814541 0.407270 0.913308i \(-0.366481\pi\)
0.407270 + 0.913308i \(0.366481\pi\)
\(258\) 0 0
\(259\) 62.3491 150.524i 0.0149582 0.0361124i
\(260\) 0 0
\(261\) 4556.32 1887.29i 1.08057 0.447588i
\(262\) 0 0
\(263\) 3273.56 3273.56i 0.767514 0.767514i −0.210154 0.977668i \(-0.567397\pi\)
0.977668 + 0.210154i \(0.0673966\pi\)
\(264\) 0 0
\(265\) −514.670 514.670i −0.119305 0.119305i
\(266\) 0 0
\(267\) 350.845 + 847.014i 0.0804170 + 0.194144i
\(268\) 0 0
\(269\) −1523.46 631.037i −0.345304 0.143030i 0.203290 0.979119i \(-0.434837\pi\)
−0.548594 + 0.836089i \(0.684837\pi\)
\(270\) 0 0
\(271\) 6024.40i 1.35039i 0.737639 + 0.675196i \(0.235941\pi\)
−0.737639 + 0.675196i \(0.764059\pi\)
\(272\) 0 0
\(273\) 176.697i 0.0391729i
\(274\) 0 0
\(275\) 213.173 + 88.2993i 0.0467448 + 0.0193623i
\(276\) 0 0
\(277\) 631.310 + 1524.12i 0.136938 + 0.330597i 0.977441 0.211210i \(-0.0677404\pi\)
−0.840503 + 0.541807i \(0.817740\pi\)
\(278\) 0 0
\(279\) 2789.51 + 2789.51i 0.598580 + 0.598580i
\(280\) 0 0
\(281\) 185.259 185.259i 0.0393296 0.0393296i −0.687168 0.726498i \(-0.741147\pi\)
0.726498 + 0.687168i \(0.241147\pi\)
\(282\) 0 0
\(283\) 5010.11 2075.25i 1.05237 0.435905i 0.211631 0.977350i \(-0.432123\pi\)
0.840736 + 0.541445i \(0.182123\pi\)
\(284\) 0 0
\(285\) −67.0300 + 161.825i −0.0139316 + 0.0336339i
\(286\) 0 0
\(287\) 417.694 0.0859083
\(288\) 0 0
\(289\) −431.529 −0.0878340
\(290\) 0 0
\(291\) −461.457 + 1114.06i −0.0929591 + 0.224423i
\(292\) 0 0
\(293\) −3670.99 + 1520.58i −0.731951 + 0.303184i −0.717354 0.696709i \(-0.754647\pi\)
−0.0145978 + 0.999893i \(0.504647\pi\)
\(294\) 0 0
\(295\) −2075.24 + 2075.24i −0.409577 + 0.409577i
\(296\) 0 0
\(297\) 151.556 + 151.556i 0.0296099 + 0.0296099i
\(298\) 0 0
\(299\) 3461.30 + 8356.31i 0.669471 + 1.61625i
\(300\) 0 0
\(301\) 814.216 + 337.259i 0.155916 + 0.0645824i
\(302\) 0 0
\(303\) 2205.93i 0.418242i
\(304\) 0 0
\(305\) 2897.03i 0.543880i
\(306\) 0 0
\(307\) 5184.84 + 2147.63i 0.963890 + 0.399256i 0.808434 0.588586i \(-0.200315\pi\)
0.155456 + 0.987843i \(0.450315\pi\)
\(308\) 0 0
\(309\) −259.231 625.838i −0.0477253 0.115219i
\(310\) 0 0
\(311\) −4758.86 4758.86i −0.867685 0.867685i 0.124531 0.992216i \(-0.460257\pi\)
−0.992216 + 0.124531i \(0.960257\pi\)
\(312\) 0 0
\(313\) 1629.22 1629.22i 0.294214 0.294214i −0.544529 0.838742i \(-0.683291\pi\)
0.838742 + 0.544529i \(0.183291\pi\)
\(314\) 0 0
\(315\) −209.939 + 86.9597i −0.0375515 + 0.0155544i
\(316\) 0 0
\(317\) −1717.07 + 4145.38i −0.304228 + 0.734472i 0.695642 + 0.718388i \(0.255120\pi\)
−0.999871 + 0.0160838i \(0.994880\pi\)
\(318\) 0 0
\(319\) −471.182 −0.0826994
\(320\) 0 0
\(321\) −2687.74 −0.467337
\(322\) 0 0
\(323\) −552.573 + 1334.03i −0.0951888 + 0.229806i
\(324\) 0 0
\(325\) −4234.54 + 1754.00i −0.722738 + 0.299368i
\(326\) 0 0
\(327\) −1054.92 + 1054.92i −0.178401 + 0.178401i
\(328\) 0 0
\(329\) 353.282 + 353.282i 0.0592009 + 0.0592009i
\(330\) 0 0
\(331\) −3512.87 8480.82i −0.583338 1.40830i −0.889770 0.456410i \(-0.849135\pi\)
0.306432 0.951893i \(-0.400865\pi\)
\(332\) 0 0
\(333\) −1682.63 696.969i −0.276900 0.114696i
\(334\) 0 0
\(335\) 1897.62i 0.309486i
\(336\) 0 0
\(337\) 967.017i 0.156311i −0.996941 0.0781555i \(-0.975097\pi\)
0.996941 0.0781555i \(-0.0249031\pi\)
\(338\) 0 0
\(339\) 208.669 + 86.4336i 0.0334317 + 0.0138479i
\(340\) 0 0
\(341\) −144.236 348.216i −0.0229056 0.0552989i
\(342\) 0 0
\(343\) −1007.50 1007.50i −0.158600 0.158600i
\(344\) 0 0
\(345\) −1278.97 + 1278.97i −0.199587 + 0.199587i
\(346\) 0 0
\(347\) 6675.62 2765.13i 1.03276 0.427781i 0.199049 0.979990i \(-0.436215\pi\)
0.833706 + 0.552208i \(0.186215\pi\)
\(348\) 0 0
\(349\) 1025.92 2476.80i 0.157354 0.379885i −0.825466 0.564451i \(-0.809088\pi\)
0.982820 + 0.184566i \(0.0590878\pi\)
\(350\) 0 0
\(351\) −4257.55 −0.647440
\(352\) 0 0
\(353\) 4340.88 0.654509 0.327254 0.944936i \(-0.393877\pi\)
0.327254 + 0.944936i \(0.393877\pi\)
\(354\) 0 0
\(355\) −1037.21 + 2504.05i −0.155069 + 0.374370i
\(356\) 0 0
\(357\) 269.118 111.472i 0.0398970 0.0165259i
\(358\) 0 0
\(359\) 2662.28 2662.28i 0.391392 0.391392i −0.483792 0.875183i \(-0.660741\pi\)
0.875183 + 0.483792i \(0.160741\pi\)
\(360\) 0 0
\(361\) −4574.19 4574.19i −0.666889 0.666889i
\(362\) 0 0
\(363\) 967.274 + 2335.21i 0.139859 + 0.337649i
\(364\) 0 0
\(365\) −3905.13 1617.56i −0.560011 0.231964i
\(366\) 0 0
\(367\) 11287.0i 1.60539i −0.596389 0.802695i \(-0.703399\pi\)
0.596389 0.802695i \(-0.296601\pi\)
\(368\) 0 0
\(369\) 4669.18i 0.658721i
\(370\) 0 0
\(371\) 302.132 + 125.147i 0.0422801 + 0.0175130i
\(372\) 0 0
\(373\) 16.5243 + 39.8932i 0.00229382 + 0.00553778i 0.925022 0.379913i \(-0.124046\pi\)
−0.922728 + 0.385451i \(0.874046\pi\)
\(374\) 0 0
\(375\) −1431.96 1431.96i −0.197190 0.197190i
\(376\) 0 0
\(377\) 6618.31 6618.31i 0.904138 0.904138i
\(378\) 0 0
\(379\) −10994.6 + 4554.09i −1.49011 + 0.617224i −0.971341 0.237689i \(-0.923610\pi\)
−0.518770 + 0.854914i \(0.673610\pi\)
\(380\) 0 0
\(381\) 614.326 1483.11i 0.0826060 0.199428i
\(382\) 0 0
\(383\) −11220.8 −1.49701 −0.748506 0.663128i \(-0.769229\pi\)
−0.748506 + 0.663128i \(0.769229\pi\)
\(384\) 0 0
\(385\) 21.7104 0.00287393
\(386\) 0 0
\(387\) 3770.05 9101.71i 0.495200 1.19552i
\(388\) 0 0
\(389\) −7872.36 + 3260.84i −1.02608 + 0.425016i −0.831296 0.555831i \(-0.812400\pi\)
−0.194783 + 0.980846i \(0.562400\pi\)
\(390\) 0 0
\(391\) −10543.4 + 10543.4i −1.36369 + 1.36369i
\(392\) 0 0
\(393\) −1721.96 1721.96i −0.221021 0.221021i
\(394\) 0 0
\(395\) −1424.77 3439.70i −0.181488 0.438152i
\(396\) 0 0
\(397\) 12780.9 + 5294.04i 1.61576 + 0.669270i 0.993531 0.113565i \(-0.0362269\pi\)
0.622230 + 0.782835i \(0.286227\pi\)
\(398\) 0 0
\(399\) 78.6987i 0.00987434i
\(400\) 0 0
\(401\) 1951.13i 0.242979i −0.992593 0.121490i \(-0.961233\pi\)
0.992593 0.121490i \(-0.0387671\pi\)
\(402\) 0 0
\(403\) 6917.06 + 2865.14i 0.854996 + 0.354151i
\(404\) 0 0
\(405\) 797.415 + 1925.13i 0.0978368 + 0.236199i
\(406\) 0 0
\(407\) 123.041 + 123.041i 0.0149850 + 0.0149850i
\(408\) 0 0
\(409\) 3631.15 3631.15i 0.438995 0.438995i −0.452679 0.891674i \(-0.649532\pi\)
0.891674 + 0.452679i \(0.149532\pi\)
\(410\) 0 0
\(411\) −882.339 + 365.477i −0.105894 + 0.0438629i
\(412\) 0 0
\(413\) 504.616 1218.25i 0.0601223 0.145148i
\(414\) 0 0
\(415\) 6774.43 0.801310
\(416\) 0 0
\(417\) 2524.91 0.296512
\(418\) 0 0
\(419\) −1055.57 + 2548.38i −0.123074 + 0.297128i −0.973394 0.229139i \(-0.926409\pi\)
0.850319 + 0.526267i \(0.176409\pi\)
\(420\) 0 0
\(421\) −9547.06 + 3954.52i −1.10521 + 0.457795i −0.859287 0.511493i \(-0.829092\pi\)
−0.245927 + 0.969288i \(0.579092\pi\)
\(422\) 0 0
\(423\) 3949.16 3949.16i 0.453936 0.453936i
\(424\) 0 0
\(425\) −5342.86 5342.86i −0.609804 0.609804i
\(426\) 0 0
\(427\) 498.116 + 1202.56i 0.0564532 + 0.136290i
\(428\) 0 0
\(429\) 174.348 + 72.2173i 0.0196214 + 0.00812747i
\(430\) 0 0
\(431\) 14341.1i 1.60275i −0.598162 0.801375i \(-0.704102\pi\)
0.598162 0.801375i \(-0.295898\pi\)
\(432\) 0 0
\(433\) 16123.8i 1.78951i 0.446554 + 0.894757i \(0.352651\pi\)
−0.446554 + 0.894757i \(0.647349\pi\)
\(434\) 0 0
\(435\) 1729.24 + 716.274i 0.190599 + 0.0789487i
\(436\) 0 0
\(437\) 1541.62 + 3721.80i 0.168754 + 0.407409i
\(438\) 0 0
\(439\) 8026.57 + 8026.57i 0.872637 + 0.872637i 0.992759 0.120123i \(-0.0383288\pi\)
−0.120123 + 0.992759i \(0.538329\pi\)
\(440\) 0 0
\(441\) −5595.07 + 5595.07i −0.604154 + 0.604154i
\(442\) 0 0
\(443\) −5998.55 + 2484.68i −0.643340 + 0.266480i −0.680409 0.732832i \(-0.738198\pi\)
0.0370688 + 0.999313i \(0.488198\pi\)
\(444\) 0 0
\(445\) 856.302 2067.29i 0.0912193 0.220223i
\(446\) 0 0
\(447\) −1313.93 −0.139031
\(448\) 0 0
\(449\) 10135.3 1.06529 0.532646 0.846338i \(-0.321198\pi\)
0.532646 + 0.846338i \(0.321198\pi\)
\(450\) 0 0
\(451\) −170.714 + 412.141i −0.0178240 + 0.0430310i
\(452\) 0 0
\(453\) 2400.70 994.401i 0.248995 0.103137i
\(454\) 0 0
\(455\) −304.948 + 304.948i −0.0314202 + 0.0314202i
\(456\) 0 0
\(457\) −2946.68 2946.68i −0.301619 0.301619i 0.540028 0.841647i \(-0.318414\pi\)
−0.841647 + 0.540028i \(0.818414\pi\)
\(458\) 0 0
\(459\) −2685.95 6484.45i −0.273136 0.659408i
\(460\) 0 0
\(461\) −10176.1 4215.08i −1.02809 0.425847i −0.196065 0.980591i \(-0.562816\pi\)
−0.832021 + 0.554743i \(0.812816\pi\)
\(462\) 0 0
\(463\) 11097.1i 1.11388i 0.830552 + 0.556941i \(0.188025\pi\)
−0.830552 + 0.556941i \(0.811975\pi\)
\(464\) 0 0
\(465\) 1497.21i 0.149315i
\(466\) 0 0
\(467\) 9665.86 + 4003.73i 0.957779 + 0.396725i 0.806149 0.591712i \(-0.201548\pi\)
0.151630 + 0.988437i \(0.451548\pi\)
\(468\) 0 0
\(469\) 326.277 + 787.701i 0.0321238 + 0.0775537i
\(470\) 0 0
\(471\) 1547.81 + 1547.81i 0.151421 + 0.151421i
\(472\) 0 0
\(473\) −665.552 + 665.552i −0.0646979 + 0.0646979i
\(474\) 0 0
\(475\) −1886.01 + 781.212i −0.182181 + 0.0754620i
\(476\) 0 0
\(477\) 1398.96 3377.38i 0.134285 0.324192i
\(478\) 0 0
\(479\) 19410.2 1.85151 0.925757 0.378119i \(-0.123429\pi\)
0.925757 + 0.378119i \(0.123429\pi\)
\(480\) 0 0
\(481\) −3456.50 −0.327656
\(482\) 0 0
\(483\) 310.996 750.810i 0.0292977 0.0707309i
\(484\) 0 0
\(485\) 2719.06 1126.27i 0.254570 0.105446i
\(486\) 0 0
\(487\) −10505.7 + 10505.7i −0.977530 + 0.977530i −0.999753 0.0222232i \(-0.992926\pi\)
0.0222232 + 0.999753i \(0.492926\pi\)
\(488\) 0 0
\(489\) 1542.24 + 1542.24i 0.142623 + 0.142623i
\(490\) 0 0
\(491\) 5195.37 + 12542.7i 0.477523 + 1.15284i 0.960767 + 0.277357i \(0.0894586\pi\)
−0.483243 + 0.875486i \(0.660541\pi\)
\(492\) 0 0
\(493\) 14255.3 + 5904.72i 1.30228 + 0.539422i
\(494\) 0 0
\(495\) 242.689i 0.0220365i
\(496\) 0 0
\(497\) 1217.77i 0.109908i
\(498\) 0 0
\(499\) 7506.94 + 3109.48i 0.673461 + 0.278957i 0.693090 0.720851i \(-0.256249\pi\)
−0.0196297 + 0.999807i \(0.506249\pi\)
\(500\) 0 0
\(501\) 883.395 + 2132.70i 0.0787768 + 0.190184i
\(502\) 0 0
\(503\) 2849.72 + 2849.72i 0.252610 + 0.252610i 0.822040 0.569430i \(-0.192836\pi\)
−0.569430 + 0.822040i \(0.692836\pi\)
\(504\) 0 0
\(505\) −3807.05 + 3807.05i −0.335468 + 0.335468i
\(506\) 0 0
\(507\) 405.770 168.075i 0.0355441 0.0147229i
\(508\) 0 0
\(509\) 5853.53 14131.7i 0.509731 1.23060i −0.434308 0.900764i \(-0.643007\pi\)
0.944039 0.329834i \(-0.106993\pi\)
\(510\) 0 0
\(511\) 1899.15 0.164409
\(512\) 0 0
\(513\) −1896.26 −0.163201
\(514\) 0 0
\(515\) −632.701 + 1527.47i −0.0541362 + 0.130696i
\(516\) 0 0
\(517\) −492.975 + 204.197i −0.0419362 + 0.0173705i
\(518\) 0 0
\(519\) 3516.44 3516.44i 0.297407 0.297407i
\(520\) 0 0
\(521\) −108.330 108.330i −0.00910949 0.00910949i 0.702537 0.711647i \(-0.252050\pi\)
−0.711647 + 0.702537i \(0.752050\pi\)
\(522\) 0 0
\(523\) −7209.17 17404.5i −0.602744 1.45515i −0.870745 0.491734i \(-0.836363\pi\)
0.268001 0.963419i \(-0.413637\pi\)
\(524\) 0 0
\(525\) 380.471 + 157.596i 0.0316288 + 0.0131011i
\(526\) 0 0
\(527\) 12342.5i 1.02021i
\(528\) 0 0
\(529\) 29432.1i 2.41901i
\(530\) 0 0
\(531\) −13618.2 5640.84i −1.11296 0.461001i
\(532\) 0 0
\(533\) −3391.12 8186.89i −0.275583 0.665317i
\(534\) 0 0
\(535\) 4638.58 + 4638.58i 0.374847 + 0.374847i
\(536\) 0 0
\(537\) 2227.07 2227.07i 0.178966 0.178966i
\(538\) 0 0
\(539\) 698.434 289.301i 0.0558138 0.0231189i
\(540\) 0 0
\(541\) −1014.09 + 2448.22i −0.0805895 + 0.194560i −0.959038 0.283276i \(-0.908579\pi\)
0.878449 + 0.477836i \(0.158579\pi\)
\(542\) 0 0
\(543\) 7409.02 0.585546
\(544\) 0 0
\(545\) 3641.22 0.286188
\(546\) 0 0
\(547\) 430.820 1040.09i 0.0336755 0.0813000i −0.906147 0.422963i \(-0.860990\pi\)
0.939823 + 0.341663i \(0.110990\pi\)
\(548\) 0 0
\(549\) 13442.8 5568.18i 1.04503 0.432868i
\(550\) 0 0
\(551\) 2947.71 2947.71i 0.227907 0.227907i
\(552\) 0 0
\(553\) 1182.84 + 1182.84i 0.0909578 + 0.0909578i
\(554\) 0 0
\(555\) −264.517 638.601i −0.0202309 0.0488416i
\(556\) 0 0
\(557\) 388.391 + 160.877i 0.0295452 + 0.0122380i 0.397407 0.917642i \(-0.369910\pi\)
−0.367862 + 0.929880i \(0.619910\pi\)
\(558\) 0 0
\(559\) 18696.9i 1.41466i
\(560\) 0 0
\(561\) 311.100i 0.0234129i
\(562\) 0 0
\(563\) −12187.4 5048.19i −0.912323 0.377897i −0.123378 0.992360i \(-0.539373\pi\)
−0.788946 + 0.614463i \(0.789373\pi\)
\(564\) 0 0
\(565\) −210.957 509.296i −0.0157080 0.0379226i
\(566\) 0 0
\(567\) −662.015 662.015i −0.0490335 0.0490335i
\(568\) 0 0
\(569\) −7590.98 + 7590.98i −0.559280 + 0.559280i −0.929102 0.369822i \(-0.879418\pi\)
0.369822 + 0.929102i \(0.379418\pi\)
\(570\) 0 0
\(571\) −19882.0 + 8235.38i −1.45715 + 0.603573i −0.963888 0.266306i \(-0.914197\pi\)
−0.493265 + 0.869879i \(0.664197\pi\)
\(572\) 0 0
\(573\) 1391.89 3360.31i 0.101478 0.244990i
\(574\) 0 0
\(575\) −21080.3 −1.52888
\(576\) 0 0
\(577\) −4301.60 −0.310361 −0.155180 0.987886i \(-0.549596\pi\)
−0.155180 + 0.987886i \(0.549596\pi\)
\(578\) 0 0
\(579\) 2680.49 6471.28i 0.192396 0.464485i
\(580\) 0 0
\(581\) −2812.07 + 1164.80i −0.200799 + 0.0831737i
\(582\) 0 0
\(583\) −246.967 + 246.967i −0.0175443 + 0.0175443i
\(584\) 0 0
\(585\) 3408.86 + 3408.86i 0.240921 + 0.240921i
\(586\) 0 0
\(587\) −1724.60 4163.55i −0.121264 0.292756i 0.851578 0.524228i \(-0.175646\pi\)
−0.972842 + 0.231471i \(0.925646\pi\)
\(588\) 0 0
\(589\) 3080.77 + 1276.10i 0.215520 + 0.0892712i
\(590\) 0 0
\(591\) 5239.10i 0.364649i
\(592\) 0 0
\(593\) 19409.8i 1.34412i −0.740495 0.672062i \(-0.765409\pi\)
0.740495 0.672062i \(-0.234591\pi\)
\(594\) 0 0
\(595\) −656.832 272.069i −0.0452563 0.0187458i
\(596\) 0 0
\(597\) 1806.54 + 4361.37i 0.123847 + 0.298993i
\(598\) 0 0
\(599\) 182.514 + 182.514i 0.0124496 + 0.0124496i 0.713304 0.700855i \(-0.247198\pi\)
−0.700855 + 0.713304i \(0.747198\pi\)
\(600\) 0 0
\(601\) −2102.19 + 2102.19i −0.142679 + 0.142679i −0.774838 0.632159i \(-0.782169\pi\)
0.632159 + 0.774838i \(0.282169\pi\)
\(602\) 0 0
\(603\) 8805.31 3647.28i 0.594660 0.246316i
\(604\) 0 0
\(605\) 2360.81 5699.51i 0.158646 0.383005i
\(606\) 0 0
\(607\) 13085.1 0.874974 0.437487 0.899225i \(-0.355869\pi\)
0.437487 + 0.899225i \(0.355869\pi\)
\(608\) 0 0
\(609\) −840.964 −0.0559566
\(610\) 0 0
\(611\) 4056.23 9792.60i 0.268572 0.648390i
\(612\) 0 0
\(613\) −8687.78 + 3598.60i −0.572424 + 0.237106i −0.650069 0.759875i \(-0.725260\pi\)
0.0776446 + 0.996981i \(0.475260\pi\)
\(614\) 0 0
\(615\) 1253.04 1253.04i 0.0821587 0.0821587i
\(616\) 0 0
\(617\) −3141.32 3141.32i −0.204967 0.204967i 0.597157 0.802124i \(-0.296297\pi\)
−0.802124 + 0.597157i \(0.796297\pi\)
\(618\) 0 0
\(619\) 808.300 + 1951.41i 0.0524852 + 0.126710i 0.947947 0.318427i \(-0.103155\pi\)
−0.895462 + 0.445138i \(0.853155\pi\)
\(620\) 0 0
\(621\) −18090.9 7493.51i −1.16902 0.484226i
\(622\) 0 0
\(623\) 1005.37i 0.0646536i
\(624\) 0 0
\(625\) 7976.82i 0.510516i
\(626\) 0 0
\(627\) 77.6525 + 32.1647i 0.00494600 + 0.00204870i
\(628\) 0 0
\(629\) −2180.59 5264.41i −0.138229 0.333713i
\(630\) 0 0
\(631\) −4291.77 4291.77i −0.270765 0.270765i 0.558643 0.829408i \(-0.311322\pi\)
−0.829408 + 0.558643i \(0.811322\pi\)
\(632\) 0 0
\(633\) 6016.28 6016.28i 0.377765 0.377765i
\(634\) 0 0
\(635\) −3619.81 + 1499.38i −0.226217 + 0.0937023i
\(636\) 0 0
\(637\) −5746.75 + 13873.9i −0.357449 + 0.862957i
\(638\) 0 0
\(639\) −13612.8 −0.842748
\(640\) 0 0
\(641\) −14676.8 −0.904365 −0.452182 0.891925i \(-0.649354\pi\)
−0.452182 + 0.891925i \(0.649354\pi\)
\(642\) 0 0
\(643\) −11364.5 + 27436.3i −0.697001 + 1.68271i 0.0331742 + 0.999450i \(0.489438\pi\)
−0.730175 + 0.683260i \(0.760562\pi\)
\(644\) 0 0
\(645\) 3454.32 1430.83i 0.210874 0.0873470i
\(646\) 0 0
\(647\) 10214.4 10214.4i 0.620661 0.620661i −0.325039 0.945701i \(-0.605378\pi\)
0.945701 + 0.325039i \(0.105378\pi\)
\(648\) 0 0
\(649\) 995.815 + 995.815i 0.0602298 + 0.0602298i
\(650\) 0 0
\(651\) −257.431 621.494i −0.0154985 0.0374167i
\(652\) 0 0
\(653\) −3089.13 1279.56i −0.185125 0.0766814i 0.288195 0.957572i \(-0.406945\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(654\) 0 0
\(655\) 5943.60i 0.354558i
\(656\) 0 0
\(657\) 21229.6i 1.26065i
\(658\) 0 0
\(659\) −12234.1 5067.54i −0.723178 0.299550i −0.00943266 0.999956i \(-0.503003\pi\)
−0.713745 + 0.700405i \(0.753003\pi\)
\(660\) 0 0
\(661\) −8849.67 21365.0i −0.520745 1.25719i −0.937441 0.348144i \(-0.886812\pi\)
0.416696 0.909046i \(-0.363188\pi\)
\(662\) 0 0
\(663\) −4369.76 4369.76i −0.255969 0.255969i
\(664\) 0 0
\(665\) −135.820 + 135.820i −0.00792012 + 0.00792012i
\(666\) 0 0
\(667\) 39770.6 16473.5i 2.30873 0.956309i
\(668\) 0 0
\(669\) −3552.46 + 8576.39i −0.205300 + 0.495639i
\(670\) 0 0
\(671\) −1390.16 −0.0799797
\(672\) 0 0
\(673\) −11132.3 −0.637621 −0.318811 0.947818i \(-0.603283\pi\)
−0.318811 + 0.947818i \(0.603283\pi\)
\(674\) 0 0
\(675\) 3797.32 9167.53i 0.216532 0.522753i
\(676\) 0 0
\(677\) 19266.1 7980.30i 1.09373 0.453040i 0.238427 0.971160i \(-0.423368\pi\)
0.855307 + 0.518121i \(0.173368\pi\)
\(678\) 0 0
\(679\) −935.033 + 935.033i −0.0528472 + 0.0528472i
\(680\) 0 0
\(681\) −39.5138 39.5138i −0.00222345 0.00222345i
\(682\) 0 0
\(683\) 6152.93 + 14854.5i 0.344708 + 0.832199i 0.997227 + 0.0744258i \(0.0237124\pi\)
−0.652519 + 0.757773i \(0.726288\pi\)
\(684\) 0 0
\(685\) 2153.51 + 892.014i 0.120119 + 0.0497549i
\(686\) 0 0
\(687\) 8786.97i 0.487982i
\(688\) 0 0
\(689\) 6937.89i 0.383618i
\(690\) 0 0
\(691\) 3264.16 + 1352.06i 0.179703 + 0.0744353i 0.470721 0.882282i \(-0.343994\pi\)
−0.291018 + 0.956718i \(0.593994\pi\)
\(692\) 0 0
\(693\) 41.7281 + 100.740i 0.00228733 + 0.00552210i
\(694\) 0 0
\(695\) −4357.56 4357.56i −0.237830 0.237830i
\(696\) 0 0
\(697\) 10329.7 10329.7i 0.561355 0.561355i
\(698\) 0 0
\(699\) −11590.8 + 4801.05i −0.627186 + 0.259789i
\(700\) 0 0
\(701\) −9617.29 + 23218.2i −0.518174 + 1.25098i 0.420850 + 0.907130i \(0.361732\pi\)
−0.939024 + 0.343852i \(0.888268\pi\)
\(702\) 0 0
\(703\) −1539.48 −0.0825927
\(704\) 0 0
\(705\) 2119.63 0.113234
\(706\) 0 0
\(707\) 925.723 2234.89i 0.0492438 0.118885i
\(708\) 0 0
\(709\) −16496.9 + 6833.23i −0.873841 + 0.361957i −0.774105 0.633057i \(-0.781800\pi\)
−0.0997360 + 0.995014i \(0.531800\pi\)
\(710\) 0 0
\(711\) 13222.4 13222.4i 0.697439 0.697439i
\(712\) 0 0
\(713\) 24348.7 + 24348.7i 1.27892 + 1.27892i
\(714\) 0 0
\(715\) −176.260 425.529i −0.00921922 0.0222572i
\(716\) 0 0
\(717\) −1109.82 459.703i −0.0578062 0.0239441i
\(718\) 0 0
\(719\) 8307.83i 0.430918i 0.976513 + 0.215459i \(0.0691247\pi\)
−0.976513 + 0.215459i \(0.930875\pi\)
\(720\) 0 0
\(721\) 742.842i 0.0383702i
\(722\) 0 0
\(723\) −2683.09 1111.37i −0.138015 0.0571679i
\(724\) 0 0
\(725\) 8347.93 + 20153.7i 0.427633 + 1.03240i
\(726\) 0 0
\(727\) −18455.8 18455.8i −0.941524 0.941524i 0.0568585 0.998382i \(-0.481892\pi\)
−0.998382 + 0.0568585i \(0.981892\pi\)
\(728\) 0 0
\(729\) −3906.40 + 3906.40i −0.198466 + 0.198466i
\(730\) 0 0
\(731\) 28476.3 11795.3i 1.44081 0.596804i
\(732\) 0 0
\(733\) 1663.72 4016.59i 0.0838350 0.202396i −0.876403 0.481579i \(-0.840064\pi\)
0.960238 + 0.279183i \(0.0900636\pi\)
\(734\) 0 0
\(735\) −3003.04 −0.150706
\(736\) 0 0
\(737\) −910.581 −0.0455111
\(738\) 0 0
\(739\) −5023.53 + 12127.9i −0.250059 + 0.603695i −0.998208 0.0598348i \(-0.980943\pi\)
0.748149 + 0.663530i \(0.230943\pi\)
\(740\) 0 0
\(741\) −1542.51 + 638.930i −0.0764718 + 0.0316757i
\(742\) 0 0
\(743\) −2091.87 + 2091.87i −0.103289 + 0.103289i −0.756863 0.653574i \(-0.773269\pi\)
0.653574 + 0.756863i \(0.273269\pi\)
\(744\) 0 0
\(745\) 2267.62 + 2267.62i 0.111516 + 0.111516i
\(746\) 0 0
\(747\) 13020.7 + 31434.7i 0.637753 + 1.53967i
\(748\) 0 0
\(749\) −2723.03 1127.92i −0.132840 0.0550243i
\(750\) 0 0
\(751\) 24.8821i 0.00120900i 1.00000 0.000604502i \(0.000192419\pi\)
−1.00000 0.000604502i \(0.999808\pi\)
\(752\) 0 0
\(753\) 6072.45i 0.293881i
\(754\) 0 0
\(755\) −5859.34 2427.02i −0.282442 0.116991i
\(756\) 0 0
\(757\) 8933.37 + 21567.1i 0.428915 + 1.03549i 0.979632 + 0.200801i \(0.0643544\pi\)
−0.550717 + 0.834692i \(0.685646\pi\)
\(758\) 0 0
\(759\) 613.722 + 613.722i 0.0293501 + 0.0293501i
\(760\) 0 0
\(761\) −11741.7 + 11741.7i −0.559311 + 0.559311i −0.929111 0.369800i \(-0.879426\pi\)
0.369800 + 0.929111i \(0.379426\pi\)
\(762\) 0 0
\(763\) −1511.47 + 626.072i −0.0717155 + 0.0297055i
\(764\) 0 0
\(765\) −3041.32 + 7342.39i −0.143737 + 0.347012i
\(766\) 0 0
\(767\) −27974.8 −1.31696
\(768\) 0 0
\(769\) 31635.5 1.48349 0.741745 0.670682i \(-0.233998\pi\)
0.741745 + 0.670682i \(0.233998\pi\)
\(770\) 0 0
\(771\) −2448.01 + 5910.02i −0.114349 + 0.276063i
\(772\) 0 0
\(773\) 36991.4 15322.3i 1.72120 0.712944i 0.721408 0.692511i \(-0.243495\pi\)
0.999791 0.0204334i \(-0.00650462\pi\)
\(774\) 0 0
\(775\) −12338.7 + 12338.7i −0.571894 + 0.571894i
\(776\) 0 0
\(777\) 219.602 + 219.602i 0.0101392 + 0.0101392i
\(778\) 0 0
\(779\) −1510.36 3646.34i −0.0694665 0.167707i
\(780\) 0 0
\(781\) 1201.58 + 497.712i 0.0550525 + 0.0228035i
\(782\) 0 0
\(783\) 20263.2i 0.924838i
\(784\) 0 0
\(785\) 5342.49i 0.242907i
\(786\) 0 0