Properties

Label 405.4.b.e.244.5
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.5
Root \(-2.67506i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.e.244.12

$q$-expansion

\(f(q)\) \(=\) \(q-2.67506i q^{2} +0.844033 q^{4} +(-10.9788 - 2.11350i) q^{5} +15.4153i q^{7} -23.6584i q^{8} +O(q^{10})\) \(q-2.67506i q^{2} +0.844033 q^{4} +(-10.9788 - 2.11350i) q^{5} +15.4153i q^{7} -23.6584i q^{8} +(-5.65374 + 29.3689i) q^{10} +44.5598 q^{11} -28.0233i q^{13} +41.2370 q^{14} -56.5353 q^{16} -92.6615i q^{17} -49.5811 q^{19} +(-9.26644 - 1.78386i) q^{20} -119.200i q^{22} -0.922809i q^{23} +(116.066 + 46.4071i) q^{25} -74.9642 q^{26} +13.0110i q^{28} -189.849 q^{29} -299.180 q^{31} -38.0312i q^{32} -247.875 q^{34} +(32.5802 - 169.241i) q^{35} +57.8330i q^{37} +132.633i q^{38} +(-50.0019 + 259.739i) q^{40} -287.880 q^{41} +0.591953i q^{43} +37.6099 q^{44} -2.46857 q^{46} -598.302i q^{47} +105.368 q^{49} +(124.142 - 310.485i) q^{50} -23.6526i q^{52} +146.339i q^{53} +(-489.211 - 94.1769i) q^{55} +364.701 q^{56} +507.859i q^{58} +193.066 q^{59} -566.153 q^{61} +800.326i q^{62} -554.019 q^{64} +(-59.2272 + 307.661i) q^{65} -355.163i q^{67} -78.2093i q^{68} +(-452.731 - 87.1542i) q^{70} -320.703 q^{71} -636.782i q^{73} +154.707 q^{74} -41.8481 q^{76} +686.903i q^{77} +287.765 q^{79} +(620.688 + 119.487i) q^{80} +770.097i q^{82} +285.058i q^{83} +(-195.840 + 1017.31i) q^{85} +1.58351 q^{86} -1054.21i q^{88} +331.615 q^{89} +431.988 q^{91} -0.778881i q^{92} -1600.50 q^{94} +(544.339 + 104.789i) q^{95} +1821.63i q^{97} -281.866i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} - 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 54 q^{4} - 3 q^{5} - 10 q^{10} - 90 q^{11} + 102 q^{14} + 146 q^{16} - 4 q^{19} + 6 q^{20} - 71 q^{25} - 468 q^{26} + 516 q^{29} + 38 q^{31} - 212 q^{34} - 267 q^{35} - 44 q^{40} - 576 q^{41} + 1644 q^{44} - 290 q^{46} + 4 q^{49} - 558 q^{50} + 15 q^{55} - 2430 q^{56} + 2202 q^{59} + 20 q^{61} + 322 q^{64} - 339 q^{65} - 636 q^{70} - 2952 q^{71} + 4080 q^{74} - 396 q^{76} + 218 q^{79} + 1266 q^{80} + 704 q^{85} - 6108 q^{86} + 4074 q^{89} - 942 q^{91} + 1078 q^{94} + 1692 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67506i 0.945778i −0.881122 0.472889i \(-0.843211\pi\)
0.881122 0.472889i \(-0.156789\pi\)
\(3\) 0 0
\(4\) 0.844033 0.105504
\(5\) −10.9788 2.11350i −0.981970 0.189037i
\(6\) 0 0
\(7\) 15.4153i 0.832349i 0.909285 + 0.416175i \(0.136629\pi\)
−0.909285 + 0.416175i \(0.863371\pi\)
\(8\) 23.6584i 1.04556i
\(9\) 0 0
\(10\) −5.65374 + 29.3689i −0.178787 + 0.928726i
\(11\) 44.5598 1.22139 0.610694 0.791866i \(-0.290890\pi\)
0.610694 + 0.791866i \(0.290890\pi\)
\(12\) 0 0
\(13\) 28.0233i 0.597867i −0.954274 0.298933i \(-0.903369\pi\)
0.954274 0.298933i \(-0.0966309\pi\)
\(14\) 41.2370 0.787217
\(15\) 0 0
\(16\) −56.5353 −0.883365
\(17\) 92.6615i 1.32198i −0.750394 0.660991i \(-0.770136\pi\)
0.750394 0.660991i \(-0.229864\pi\)
\(18\) 0 0
\(19\) −49.5811 −0.598667 −0.299334 0.954149i \(-0.596764\pi\)
−0.299334 + 0.954149i \(0.596764\pi\)
\(20\) −9.26644 1.78386i −0.103602 0.0199442i
\(21\) 0 0
\(22\) 119.200i 1.15516i
\(23\) 0.922809i 0.00836604i −0.999991 0.00418302i \(-0.998668\pi\)
0.999991 0.00418302i \(-0.00133150\pi\)
\(24\) 0 0
\(25\) 116.066 + 46.4071i 0.928530 + 0.371257i
\(26\) −74.9642 −0.565449
\(27\) 0 0
\(28\) 13.0110i 0.0878163i
\(29\) −189.849 −1.21566 −0.607830 0.794067i \(-0.707960\pi\)
−0.607830 + 0.794067i \(0.707960\pi\)
\(30\) 0 0
\(31\) −299.180 −1.73337 −0.866683 0.498859i \(-0.833752\pi\)
−0.866683 + 0.498859i \(0.833752\pi\)
\(32\) 38.0312i 0.210095i
\(33\) 0 0
\(34\) −247.875 −1.25030
\(35\) 32.5802 169.241i 0.157345 0.817342i
\(36\) 0 0
\(37\) 57.8330i 0.256965i 0.991712 + 0.128482i \(0.0410105\pi\)
−0.991712 + 0.128482i \(0.958989\pi\)
\(38\) 132.633i 0.566206i
\(39\) 0 0
\(40\) −50.0019 + 259.739i −0.197650 + 1.02671i
\(41\) −287.880 −1.09657 −0.548284 0.836292i \(-0.684719\pi\)
−0.548284 + 0.836292i \(0.684719\pi\)
\(42\) 0 0
\(43\) 0.591953i 0.00209935i 0.999999 + 0.00104967i \(0.000334122\pi\)
−0.999999 + 0.00104967i \(0.999666\pi\)
\(44\) 37.6099 0.128862
\(45\) 0 0
\(46\) −2.46857 −0.00791242
\(47\) 598.302i 1.85684i −0.371536 0.928418i \(-0.621169\pi\)
0.371536 0.928418i \(-0.378831\pi\)
\(48\) 0 0
\(49\) 105.368 0.307195
\(50\) 124.142 310.485i 0.351127 0.878183i
\(51\) 0 0
\(52\) 23.6526i 0.0630774i
\(53\) 146.339i 0.379267i 0.981855 + 0.189634i \(0.0607301\pi\)
−0.981855 + 0.189634i \(0.939270\pi\)
\(54\) 0 0
\(55\) −489.211 94.1769i −1.19937 0.230888i
\(56\) 364.701 0.870272
\(57\) 0 0
\(58\) 507.859i 1.14975i
\(59\) 193.066 0.426018 0.213009 0.977050i \(-0.431674\pi\)
0.213009 + 0.977050i \(0.431674\pi\)
\(60\) 0 0
\(61\) −566.153 −1.18833 −0.594167 0.804341i \(-0.702518\pi\)
−0.594167 + 0.804341i \(0.702518\pi\)
\(62\) 800.326i 1.63938i
\(63\) 0 0
\(64\) −554.019 −1.08207
\(65\) −59.2272 + 307.661i −0.113019 + 0.587087i
\(66\) 0 0
\(67\) 355.163i 0.647613i −0.946123 0.323806i \(-0.895037\pi\)
0.946123 0.323806i \(-0.104963\pi\)
\(68\) 78.2093i 0.139475i
\(69\) 0 0
\(70\) −452.731 87.1542i −0.773024 0.148813i
\(71\) −320.703 −0.536062 −0.268031 0.963410i \(-0.586373\pi\)
−0.268031 + 0.963410i \(0.586373\pi\)
\(72\) 0 0
\(73\) 636.782i 1.02095i −0.859891 0.510477i \(-0.829469\pi\)
0.859891 0.510477i \(-0.170531\pi\)
\(74\) 154.707 0.243031
\(75\) 0 0
\(76\) −41.8481 −0.0631619
\(77\) 686.903i 1.01662i
\(78\) 0 0
\(79\) 287.765 0.409824 0.204912 0.978780i \(-0.434309\pi\)
0.204912 + 0.978780i \(0.434309\pi\)
\(80\) 620.688 + 119.487i 0.867438 + 0.166989i
\(81\) 0 0
\(82\) 770.097i 1.03711i
\(83\) 285.058i 0.376978i 0.982075 + 0.188489i \(0.0603590\pi\)
−0.982075 + 0.188489i \(0.939641\pi\)
\(84\) 0 0
\(85\) −195.840 + 1017.31i −0.249904 + 1.29815i
\(86\) 1.58351 0.00198552
\(87\) 0 0
\(88\) 1054.21i 1.27704i
\(89\) 331.615 0.394957 0.197478 0.980307i \(-0.436725\pi\)
0.197478 + 0.980307i \(0.436725\pi\)
\(90\) 0 0
\(91\) 431.988 0.497634
\(92\) 0.778881i 0.000882652i
\(93\) 0 0
\(94\) −1600.50 −1.75616
\(95\) 544.339 + 104.789i 0.587873 + 0.113170i
\(96\) 0 0
\(97\) 1821.63i 1.90679i 0.301730 + 0.953393i \(0.402436\pi\)
−0.301730 + 0.953393i \(0.597564\pi\)
\(98\) 281.866i 0.290538i
\(99\) 0 0
\(100\) 97.9638 + 39.1692i 0.0979638 + 0.0391692i
\(101\) −1147.37 −1.13037 −0.565184 0.824965i \(-0.691195\pi\)
−0.565184 + 0.824965i \(0.691195\pi\)
\(102\) 0 0
\(103\) 1582.54i 1.51391i −0.653467 0.756955i \(-0.726686\pi\)
0.653467 0.756955i \(-0.273314\pi\)
\(104\) −662.986 −0.625107
\(105\) 0 0
\(106\) 391.466 0.358703
\(107\) 385.387i 0.348194i −0.984728 0.174097i \(-0.944299\pi\)
0.984728 0.174097i \(-0.0557007\pi\)
\(108\) 0 0
\(109\) 203.502 0.178825 0.0894126 0.995995i \(-0.471501\pi\)
0.0894126 + 0.995995i \(0.471501\pi\)
\(110\) −251.929 + 1308.67i −0.218368 + 1.13433i
\(111\) 0 0
\(112\) 871.510i 0.735268i
\(113\) 66.0150i 0.0549573i −0.999622 0.0274786i \(-0.991252\pi\)
0.999622 0.0274786i \(-0.00874782\pi\)
\(114\) 0 0
\(115\) −1.95035 + 10.1313i −0.00158149 + 0.00821520i
\(116\) −160.239 −0.128257
\(117\) 0 0
\(118\) 516.464i 0.402918i
\(119\) 1428.41 1.10035
\(120\) 0 0
\(121\) 654.573 0.491790
\(122\) 1514.49i 1.12390i
\(123\) 0 0
\(124\) −252.518 −0.182877
\(125\) −1176.18 754.799i −0.841607 0.540090i
\(126\) 0 0
\(127\) 1821.52i 1.27270i 0.771399 + 0.636352i \(0.219557\pi\)
−0.771399 + 0.636352i \(0.780443\pi\)
\(128\) 1177.79i 0.813301i
\(129\) 0 0
\(130\) 823.013 + 158.437i 0.555254 + 0.106891i
\(131\) 238.258 0.158906 0.0794530 0.996839i \(-0.474683\pi\)
0.0794530 + 0.996839i \(0.474683\pi\)
\(132\) 0 0
\(133\) 764.308i 0.498300i
\(134\) −950.083 −0.612498
\(135\) 0 0
\(136\) −2192.22 −1.38221
\(137\) 2047.48i 1.27685i −0.769685 0.638424i \(-0.779587\pi\)
0.769685 0.638424i \(-0.220413\pi\)
\(138\) 0 0
\(139\) 2179.37 1.32987 0.664934 0.746902i \(-0.268460\pi\)
0.664934 + 0.746902i \(0.268460\pi\)
\(140\) 27.4988 142.845i 0.0166005 0.0862330i
\(141\) 0 0
\(142\) 857.901i 0.506996i
\(143\) 1248.71i 0.730228i
\(144\) 0 0
\(145\) 2084.31 + 401.246i 1.19374 + 0.229805i
\(146\) −1703.43 −0.965596
\(147\) 0 0
\(148\) 48.8130i 0.0271108i
\(149\) −155.948 −0.0857435 −0.0428717 0.999081i \(-0.513651\pi\)
−0.0428717 + 0.999081i \(0.513651\pi\)
\(150\) 0 0
\(151\) 1614.14 0.869914 0.434957 0.900451i \(-0.356764\pi\)
0.434957 + 0.900451i \(0.356764\pi\)
\(152\) 1173.01i 0.625943i
\(153\) 0 0
\(154\) 1837.51 0.961498
\(155\) 3284.63 + 632.316i 1.70211 + 0.327670i
\(156\) 0 0
\(157\) 988.508i 0.502494i −0.967923 0.251247i \(-0.919159\pi\)
0.967923 0.251247i \(-0.0808406\pi\)
\(158\) 769.791i 0.387603i
\(159\) 0 0
\(160\) −80.3788 + 417.535i −0.0397156 + 0.206307i
\(161\) 14.2254 0.00696347
\(162\) 0 0
\(163\) 2974.11i 1.42914i −0.699564 0.714570i \(-0.746622\pi\)
0.699564 0.714570i \(-0.253378\pi\)
\(164\) −242.980 −0.115692
\(165\) 0 0
\(166\) 762.548 0.356537
\(167\) 2438.96i 1.13013i −0.825045 0.565067i \(-0.808850\pi\)
0.825045 0.565067i \(-0.191150\pi\)
\(168\) 0 0
\(169\) 1411.69 0.642555
\(170\) 2721.36 + 523.884i 1.22776 + 0.236353i
\(171\) 0 0
\(172\) 0.499628i 0.000221490i
\(173\) 2653.59i 1.16618i −0.812409 0.583089i \(-0.801844\pi\)
0.812409 0.583089i \(-0.198156\pi\)
\(174\) 0 0
\(175\) −715.381 + 1789.20i −0.309016 + 0.772861i
\(176\) −2519.20 −1.07893
\(177\) 0 0
\(178\) 887.092i 0.373541i
\(179\) 2102.30 0.877841 0.438921 0.898526i \(-0.355361\pi\)
0.438921 + 0.898526i \(0.355361\pi\)
\(180\) 0 0
\(181\) 1597.36 0.655973 0.327987 0.944682i \(-0.393630\pi\)
0.327987 + 0.944682i \(0.393630\pi\)
\(182\) 1155.60i 0.470651i
\(183\) 0 0
\(184\) −21.8321 −0.00874721
\(185\) 122.230 634.935i 0.0485758 0.252331i
\(186\) 0 0
\(187\) 4128.97i 1.61465i
\(188\) 504.987i 0.195904i
\(189\) 0 0
\(190\) 280.318 1456.14i 0.107034 0.555997i
\(191\) −3407.43 −1.29085 −0.645426 0.763823i \(-0.723320\pi\)
−0.645426 + 0.763823i \(0.723320\pi\)
\(192\) 0 0
\(193\) 819.130i 0.305504i 0.988265 + 0.152752i \(0.0488135\pi\)
−0.988265 + 0.152752i \(0.951186\pi\)
\(194\) 4872.97 1.80340
\(195\) 0 0
\(196\) 88.9340 0.0324103
\(197\) 359.979i 0.130190i −0.997879 0.0650950i \(-0.979265\pi\)
0.997879 0.0650950i \(-0.0207350\pi\)
\(198\) 0 0
\(199\) 1338.34 0.476745 0.238372 0.971174i \(-0.423386\pi\)
0.238372 + 0.971174i \(0.423386\pi\)
\(200\) 1097.92 2745.94i 0.388172 0.970835i
\(201\) 0 0
\(202\) 3069.28i 1.06908i
\(203\) 2926.59i 1.01185i
\(204\) 0 0
\(205\) 3160.56 + 608.433i 1.07680 + 0.207292i
\(206\) −4233.41 −1.43182
\(207\) 0 0
\(208\) 1584.31i 0.528135i
\(209\) −2209.32 −0.731205
\(210\) 0 0
\(211\) 1068.23 0.348530 0.174265 0.984699i \(-0.444245\pi\)
0.174265 + 0.984699i \(0.444245\pi\)
\(212\) 123.515i 0.0400143i
\(213\) 0 0
\(214\) −1030.94 −0.329315
\(215\) 1.25109 6.49891i 0.000396855 0.00206150i
\(216\) 0 0
\(217\) 4611.96i 1.44277i
\(218\) 544.381i 0.169129i
\(219\) 0 0
\(220\) −412.910 79.4885i −0.126538 0.0243596i
\(221\) −2596.68 −0.790370
\(222\) 0 0
\(223\) 1518.83i 0.456091i −0.973650 0.228046i \(-0.926766\pi\)
0.973650 0.228046i \(-0.0732335\pi\)
\(224\) 586.263 0.174872
\(225\) 0 0
\(226\) −176.594 −0.0519774
\(227\) 4235.12i 1.23830i 0.785271 + 0.619152i \(0.212524\pi\)
−0.785271 + 0.619152i \(0.787476\pi\)
\(228\) 0 0
\(229\) 5536.52 1.59766 0.798829 0.601558i \(-0.205453\pi\)
0.798829 + 0.601558i \(0.205453\pi\)
\(230\) 27.1019 + 5.21732i 0.00776976 + 0.00149574i
\(231\) 0 0
\(232\) 4491.53i 1.27105i
\(233\) 6337.30i 1.78185i 0.454154 + 0.890923i \(0.349941\pi\)
−0.454154 + 0.890923i \(0.650059\pi\)
\(234\) 0 0
\(235\) −1264.51 + 6568.61i −0.351011 + 1.82336i
\(236\) 162.954 0.0449466
\(237\) 0 0
\(238\) 3821.08i 1.04069i
\(239\) −2542.87 −0.688220 −0.344110 0.938929i \(-0.611819\pi\)
−0.344110 + 0.938929i \(0.611819\pi\)
\(240\) 0 0
\(241\) 2051.42 0.548314 0.274157 0.961685i \(-0.411601\pi\)
0.274157 + 0.961685i \(0.411601\pi\)
\(242\) 1751.02i 0.465124i
\(243\) 0 0
\(244\) −477.852 −0.125374
\(245\) −1156.81 222.695i −0.301656 0.0580712i
\(246\) 0 0
\(247\) 1389.43i 0.357923i
\(248\) 7078.11i 1.81234i
\(249\) 0 0
\(250\) −2019.13 + 3146.36i −0.510805 + 0.795974i
\(251\) −2770.89 −0.696801 −0.348401 0.937346i \(-0.613275\pi\)
−0.348401 + 0.937346i \(0.613275\pi\)
\(252\) 0 0
\(253\) 41.1201i 0.0102182i
\(254\) 4872.67 1.20370
\(255\) 0 0
\(256\) −1281.50 −0.312865
\(257\) 426.755i 0.103581i 0.998658 + 0.0517904i \(0.0164928\pi\)
−0.998658 + 0.0517904i \(0.983507\pi\)
\(258\) 0 0
\(259\) −891.514 −0.213884
\(260\) −49.9897 + 259.676i −0.0119240 + 0.0619402i
\(261\) 0 0
\(262\) 637.355i 0.150290i
\(263\) 3762.39i 0.882125i 0.897476 + 0.441063i \(0.145398\pi\)
−0.897476 + 0.441063i \(0.854602\pi\)
\(264\) 0 0
\(265\) 309.287 1606.62i 0.0716956 0.372429i
\(266\) −2044.57 −0.471281
\(267\) 0 0
\(268\) 299.769i 0.0683258i
\(269\) 1980.25 0.448839 0.224420 0.974493i \(-0.427951\pi\)
0.224420 + 0.974493i \(0.427951\pi\)
\(270\) 0 0
\(271\) 5659.70 1.26864 0.634321 0.773070i \(-0.281280\pi\)
0.634321 + 0.773070i \(0.281280\pi\)
\(272\) 5238.65i 1.16779i
\(273\) 0 0
\(274\) −5477.14 −1.20761
\(275\) 5171.89 + 2067.89i 1.13410 + 0.453449i
\(276\) 0 0
\(277\) 6169.57i 1.33824i −0.743153 0.669121i \(-0.766671\pi\)
0.743153 0.669121i \(-0.233329\pi\)
\(278\) 5829.95i 1.25776i
\(279\) 0 0
\(280\) −4003.97 770.795i −0.854581 0.164514i
\(281\) 3343.45 0.709800 0.354900 0.934904i \(-0.384515\pi\)
0.354900 + 0.934904i \(0.384515\pi\)
\(282\) 0 0
\(283\) 5103.32i 1.07195i −0.844235 0.535973i \(-0.819945\pi\)
0.844235 0.535973i \(-0.180055\pi\)
\(284\) −270.684 −0.0565568
\(285\) 0 0
\(286\) −3340.39 −0.690633
\(287\) 4437.76i 0.912727i
\(288\) 0 0
\(289\) −3673.14 −0.747638
\(290\) 1073.36 5575.67i 0.217344 1.12902i
\(291\) 0 0
\(292\) 537.465i 0.107715i
\(293\) 4130.28i 0.823527i 0.911291 + 0.411764i \(0.135087\pi\)
−0.911291 + 0.411764i \(0.864913\pi\)
\(294\) 0 0
\(295\) −2119.62 408.044i −0.418337 0.0805331i
\(296\) 1368.23 0.268672
\(297\) 0 0
\(298\) 417.172i 0.0810943i
\(299\) −25.8602 −0.00500178
\(300\) 0 0
\(301\) −9.12515 −0.00174739
\(302\) 4317.93i 0.822746i
\(303\) 0 0
\(304\) 2803.08 0.528841
\(305\) 6215.65 + 1196.56i 1.16691 + 0.224639i
\(306\) 0 0
\(307\) 3382.52i 0.628830i 0.949286 + 0.314415i \(0.101808\pi\)
−0.949286 + 0.314415i \(0.898192\pi\)
\(308\) 579.769i 0.107258i
\(309\) 0 0
\(310\) 1691.49 8786.59i 0.309903 1.60982i
\(311\) −6021.22 −1.09785 −0.548926 0.835871i \(-0.684963\pi\)
−0.548926 + 0.835871i \(0.684963\pi\)
\(312\) 0 0
\(313\) 10192.9i 1.84070i 0.391096 + 0.920350i \(0.372096\pi\)
−0.391096 + 0.920350i \(0.627904\pi\)
\(314\) −2644.32 −0.475247
\(315\) 0 0
\(316\) 242.884 0.0432382
\(317\) 5400.59i 0.956869i 0.878123 + 0.478435i \(0.158796\pi\)
−0.878123 + 0.478435i \(0.841204\pi\)
\(318\) 0 0
\(319\) −8459.65 −1.48479
\(320\) 6082.44 + 1170.92i 1.06256 + 0.204551i
\(321\) 0 0
\(322\) 38.0538i 0.00658589i
\(323\) 4594.25i 0.791428i
\(324\) 0 0
\(325\) 1300.48 3252.56i 0.221962 0.555137i
\(326\) −7955.92 −1.35165
\(327\) 0 0
\(328\) 6810.76i 1.14653i
\(329\) 9223.02 1.54554
\(330\) 0 0
\(331\) −2302.90 −0.382413 −0.191206 0.981550i \(-0.561240\pi\)
−0.191206 + 0.981550i \(0.561240\pi\)
\(332\) 240.598i 0.0397727i
\(333\) 0 0
\(334\) −6524.37 −1.06886
\(335\) −750.636 + 3899.25i −0.122423 + 0.635936i
\(336\) 0 0
\(337\) 9566.33i 1.54632i 0.634209 + 0.773162i \(0.281326\pi\)
−0.634209 + 0.773162i \(0.718674\pi\)
\(338\) 3776.37i 0.607714i
\(339\) 0 0
\(340\) −165.295 + 858.641i −0.0263659 + 0.136960i
\(341\) −13331.4 −2.11711
\(342\) 0 0
\(343\) 6911.73i 1.08804i
\(344\) 14.0046 0.00219500
\(345\) 0 0
\(346\) −7098.52 −1.10294
\(347\) 81.5218i 0.0126119i −0.999980 0.00630593i \(-0.997993\pi\)
0.999980 0.00630593i \(-0.00200725\pi\)
\(348\) 0 0
\(349\) −93.5719 −0.0143518 −0.00717591 0.999974i \(-0.502284\pi\)
−0.00717591 + 0.999974i \(0.502284\pi\)
\(350\) 4786.22 + 1913.69i 0.730955 + 0.292260i
\(351\) 0 0
\(352\) 1694.66i 0.256607i
\(353\) 6675.41i 1.00651i −0.864139 0.503253i \(-0.832136\pi\)
0.864139 0.503253i \(-0.167864\pi\)
\(354\) 0 0
\(355\) 3520.92 + 677.805i 0.526397 + 0.101336i
\(356\) 279.894 0.0416696
\(357\) 0 0
\(358\) 5623.80i 0.830243i
\(359\) 8334.50 1.22529 0.612644 0.790359i \(-0.290106\pi\)
0.612644 + 0.790359i \(0.290106\pi\)
\(360\) 0 0
\(361\) −4400.72 −0.641598
\(362\) 4273.05i 0.620405i
\(363\) 0 0
\(364\) 364.613 0.0525025
\(365\) −1345.84 + 6991.07i −0.192998 + 1.00255i
\(366\) 0 0
\(367\) 125.761i 0.0178874i 0.999960 + 0.00894369i \(0.00284690\pi\)
−0.999960 + 0.00894369i \(0.997153\pi\)
\(368\) 52.1713i 0.00739026i
\(369\) 0 0
\(370\) −1698.49 326.973i −0.238649 0.0459419i
\(371\) −2255.86 −0.315683
\(372\) 0 0
\(373\) 1435.76i 0.199305i 0.995022 + 0.0996525i \(0.0317731\pi\)
−0.995022 + 0.0996525i \(0.968227\pi\)
\(374\) −11045.3 −1.52710
\(375\) 0 0
\(376\) −14154.8 −1.94144
\(377\) 5320.21i 0.726803i
\(378\) 0 0
\(379\) 2125.04 0.288010 0.144005 0.989577i \(-0.454002\pi\)
0.144005 + 0.989577i \(0.454002\pi\)
\(380\) 459.440 + 88.4458i 0.0620231 + 0.0119399i
\(381\) 0 0
\(382\) 9115.09i 1.22086i
\(383\) 7060.76i 0.942005i −0.882132 0.471002i \(-0.843892\pi\)
0.882132 0.471002i \(-0.156108\pi\)
\(384\) 0 0
\(385\) 1451.77 7541.34i 0.192179 0.998292i
\(386\) 2191.22 0.288939
\(387\) 0 0
\(388\) 1537.51i 0.201174i
\(389\) 9819.12 1.27982 0.639909 0.768451i \(-0.278972\pi\)
0.639909 + 0.768451i \(0.278972\pi\)
\(390\) 0 0
\(391\) −85.5088 −0.0110598
\(392\) 2492.83i 0.321191i
\(393\) 0 0
\(394\) −962.967 −0.123131
\(395\) −3159.31 608.191i −0.402435 0.0774720i
\(396\) 0 0
\(397\) 10995.5i 1.39005i −0.718987 0.695023i \(-0.755394\pi\)
0.718987 0.695023i \(-0.244606\pi\)
\(398\) 3580.14i 0.450895i
\(399\) 0 0
\(400\) −6561.85 2623.64i −0.820231 0.327956i
\(401\) −6531.81 −0.813424 −0.406712 0.913556i \(-0.633325\pi\)
−0.406712 + 0.913556i \(0.633325\pi\)
\(402\) 0 0
\(403\) 8384.02i 1.03632i
\(404\) −968.415 −0.119259
\(405\) 0 0
\(406\) −7828.82 −0.956989
\(407\) 2577.02i 0.313854i
\(408\) 0 0
\(409\) 5005.34 0.605130 0.302565 0.953129i \(-0.402157\pi\)
0.302565 + 0.953129i \(0.402157\pi\)
\(410\) 1627.60 8454.71i 0.196052 1.01841i
\(411\) 0 0
\(412\) 1335.72i 0.159724i
\(413\) 2976.17i 0.354596i
\(414\) 0 0
\(415\) 602.469 3129.58i 0.0712627 0.370181i
\(416\) −1065.76 −0.125609
\(417\) 0 0
\(418\) 5910.07i 0.691558i
\(419\) 73.4944 0.00856907 0.00428453 0.999991i \(-0.498636\pi\)
0.00428453 + 0.999991i \(0.498636\pi\)
\(420\) 0 0
\(421\) 5030.81 0.582391 0.291195 0.956664i \(-0.405947\pi\)
0.291195 + 0.956664i \(0.405947\pi\)
\(422\) 2857.58i 0.329632i
\(423\) 0 0
\(424\) 3462.13 0.396547
\(425\) 4300.15 10754.9i 0.490796 1.22750i
\(426\) 0 0
\(427\) 8727.43i 0.989110i
\(428\) 325.280i 0.0367360i
\(429\) 0 0
\(430\) −17.3850 3.34675i −0.00194972 0.000375336i
\(431\) −1951.29 −0.218075 −0.109037 0.994038i \(-0.534777\pi\)
−0.109037 + 0.994038i \(0.534777\pi\)
\(432\) 0 0
\(433\) 3805.50i 0.422357i −0.977448 0.211178i \(-0.932270\pi\)
0.977448 0.211178i \(-0.0677301\pi\)
\(434\) −12337.3 −1.36454
\(435\) 0 0
\(436\) 171.762 0.0188668
\(437\) 45.7538i 0.00500847i
\(438\) 0 0
\(439\) −11904.4 −1.29422 −0.647111 0.762395i \(-0.724023\pi\)
−0.647111 + 0.762395i \(0.724023\pi\)
\(440\) −2228.07 + 11573.9i −0.241407 + 1.25401i
\(441\) 0 0
\(442\) 6946.29i 0.747514i
\(443\) 9068.45i 0.972585i −0.873796 0.486292i \(-0.838349\pi\)
0.873796 0.486292i \(-0.161651\pi\)
\(444\) 0 0
\(445\) −3640.72 700.868i −0.387836 0.0746614i
\(446\) −4062.97 −0.431361
\(447\) 0 0
\(448\) 8540.37i 0.900658i
\(449\) −7332.48 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(450\) 0 0
\(451\) −12827.9 −1.33934
\(452\) 55.7189i 0.00579822i
\(453\) 0 0
\(454\) 11329.2 1.17116
\(455\) −4742.70 913.006i −0.488662 0.0940712i
\(456\) 0 0
\(457\) 1170.43i 0.119804i −0.998204 0.0599019i \(-0.980921\pi\)
0.998204 0.0599019i \(-0.0190788\pi\)
\(458\) 14810.5i 1.51103i
\(459\) 0 0
\(460\) −1.64616 + 8.55115i −0.000166854 + 0.000866738i
\(461\) −14747.8 −1.48996 −0.744981 0.667086i \(-0.767541\pi\)
−0.744981 + 0.667086i \(0.767541\pi\)
\(462\) 0 0
\(463\) 2085.51i 0.209334i 0.994507 + 0.104667i \(0.0333777\pi\)
−0.994507 + 0.104667i \(0.966622\pi\)
\(464\) 10733.2 1.07387
\(465\) 0 0
\(466\) 16952.7 1.68523
\(467\) 9943.76i 0.985315i −0.870223 0.492658i \(-0.836025\pi\)
0.870223 0.492658i \(-0.163975\pi\)
\(468\) 0 0
\(469\) 5474.95 0.539040
\(470\) 17571.5 + 3382.64i 1.72449 + 0.331978i
\(471\) 0 0
\(472\) 4567.62i 0.445428i
\(473\) 26.3773i 0.00256412i
\(474\) 0 0
\(475\) −5754.69 2300.92i −0.555880 0.222260i
\(476\) 1205.62 0.116092
\(477\) 0 0
\(478\) 6802.34i 0.650903i
\(479\) 2664.20 0.254134 0.127067 0.991894i \(-0.459444\pi\)
0.127067 + 0.991894i \(0.459444\pi\)
\(480\) 0 0
\(481\) 1620.67 0.153631
\(482\) 5487.68i 0.518583i
\(483\) 0 0
\(484\) 552.481 0.0518859
\(485\) 3850.01 19999.2i 0.360453 1.87241i
\(486\) 0 0
\(487\) 3071.50i 0.285797i 0.989737 + 0.142898i \(0.0456422\pi\)
−0.989737 + 0.142898i \(0.954358\pi\)
\(488\) 13394.2i 1.24248i
\(489\) 0 0
\(490\) −595.723 + 3094.54i −0.0549225 + 0.285300i
\(491\) 16089.6 1.47885 0.739423 0.673241i \(-0.235098\pi\)
0.739423 + 0.673241i \(0.235098\pi\)
\(492\) 0 0
\(493\) 17591.7i 1.60708i
\(494\) 3716.80 0.338516
\(495\) 0 0
\(496\) 16914.3 1.53119
\(497\) 4943.74i 0.446191i
\(498\) 0 0
\(499\) −12060.6 −1.08197 −0.540987 0.841031i \(-0.681949\pi\)
−0.540987 + 0.841031i \(0.681949\pi\)
\(500\) −992.737 637.075i −0.0887931 0.0569817i
\(501\) 0 0
\(502\) 7412.31i 0.659019i
\(503\) 1324.90i 0.117444i 0.998274 + 0.0587222i \(0.0187026\pi\)
−0.998274 + 0.0587222i \(0.981297\pi\)
\(504\) 0 0
\(505\) 12596.7 + 2424.95i 1.10999 + 0.213681i
\(506\) −109.999 −0.00966413
\(507\) 0 0
\(508\) 1537.42i 0.134276i
\(509\) 12121.1 1.05551 0.527757 0.849395i \(-0.323033\pi\)
0.527757 + 0.849395i \(0.323033\pi\)
\(510\) 0 0
\(511\) 9816.20 0.849791
\(512\) 12850.4i 1.10920i
\(513\) 0 0
\(514\) 1141.60 0.0979644
\(515\) −3344.70 + 17374.4i −0.286185 + 1.48661i
\(516\) 0 0
\(517\) 26660.2i 2.26792i
\(518\) 2384.86i 0.202287i
\(519\) 0 0
\(520\) 7278.76 + 1401.22i 0.613836 + 0.118168i
\(521\) 17997.6 1.51342 0.756708 0.653753i \(-0.226807\pi\)
0.756708 + 0.653753i \(0.226807\pi\)
\(522\) 0 0
\(523\) 6451.03i 0.539357i 0.962950 + 0.269679i \(0.0869174\pi\)
−0.962950 + 0.269679i \(0.913083\pi\)
\(524\) 201.098 0.0167653
\(525\) 0 0
\(526\) 10064.6 0.834294
\(527\) 27722.5i 2.29148i
\(528\) 0 0
\(529\) 12166.1 0.999930
\(530\) −4297.81 827.361i −0.352235 0.0678081i
\(531\) 0 0
\(532\) 645.101i 0.0525727i
\(533\) 8067.35i 0.655602i
\(534\) 0 0
\(535\) −814.515 + 4231.07i −0.0658216 + 0.341916i
\(536\) −8402.57 −0.677119
\(537\) 0 0
\(538\) 5297.29i 0.424502i
\(539\) 4695.17 0.375204
\(540\) 0 0
\(541\) −520.899 −0.0413959 −0.0206980 0.999786i \(-0.506589\pi\)
−0.0206980 + 0.999786i \(0.506589\pi\)
\(542\) 15140.1i 1.19985i
\(543\) 0 0
\(544\) −3524.02 −0.277741
\(545\) −2234.20 430.101i −0.175601 0.0338046i
\(546\) 0 0
\(547\) 8098.33i 0.633015i −0.948590 0.316508i \(-0.897490\pi\)
0.948590 0.316508i \(-0.102510\pi\)
\(548\) 1728.14i 0.134713i
\(549\) 0 0
\(550\) 5531.74 13835.1i 0.428862 1.07260i
\(551\) 9412.94 0.727776
\(552\) 0 0
\(553\) 4436.00i 0.341117i
\(554\) −16504.0 −1.26568
\(555\) 0 0
\(556\) 1839.46 0.140307
\(557\) 6687.22i 0.508701i 0.967112 + 0.254351i \(0.0818617\pi\)
−0.967112 + 0.254351i \(0.918138\pi\)
\(558\) 0 0
\(559\) 16.5885 0.00125513
\(560\) −1841.93 + 9568.10i −0.138993 + 0.722011i
\(561\) 0 0
\(562\) 8943.95i 0.671313i
\(563\) 2427.54i 0.181720i 0.995864 + 0.0908602i \(0.0289616\pi\)
−0.995864 + 0.0908602i \(0.971038\pi\)
\(564\) 0 0
\(565\) −139.523 + 724.763i −0.0103890 + 0.0539664i
\(566\) −13651.7 −1.01382
\(567\) 0 0
\(568\) 7587.30i 0.560486i
\(569\) −2553.65 −0.188145 −0.0940727 0.995565i \(-0.529989\pi\)
−0.0940727 + 0.995565i \(0.529989\pi\)
\(570\) 0 0
\(571\) 9036.15 0.662261 0.331130 0.943585i \(-0.392570\pi\)
0.331130 + 0.943585i \(0.392570\pi\)
\(572\) 1053.95i 0.0770421i
\(573\) 0 0
\(574\) −11871.3 −0.863237
\(575\) 42.8249 107.107i 0.00310595 0.00776812i
\(576\) 0 0
\(577\) 5427.02i 0.391560i −0.980648 0.195780i \(-0.937276\pi\)
0.980648 0.195780i \(-0.0627238\pi\)
\(578\) 9825.90i 0.707099i
\(579\) 0 0
\(580\) 1759.23 + 338.665i 0.125945 + 0.0242454i
\(581\) −4394.26 −0.313777
\(582\) 0 0
\(583\) 6520.82i 0.463233i
\(584\) −15065.2 −1.06747
\(585\) 0 0
\(586\) 11048.8 0.778874
\(587\) 5339.38i 0.375434i −0.982223 0.187717i \(-0.939891\pi\)
0.982223 0.187717i \(-0.0601088\pi\)
\(588\) 0 0
\(589\) 14833.7 1.03771
\(590\) −1091.54 + 5670.13i −0.0761664 + 0.395654i
\(591\) 0 0
\(592\) 3269.61i 0.226993i
\(593\) 4617.67i 0.319772i 0.987135 + 0.159886i \(0.0511127\pi\)
−0.987135 + 0.159886i \(0.948887\pi\)
\(594\) 0 0
\(595\) −15682.1 3018.93i −1.08051 0.208007i
\(596\) −131.626 −0.00904629
\(597\) 0 0
\(598\) 69.1776i 0.00473057i
\(599\) −10888.4 −0.742716 −0.371358 0.928490i \(-0.621108\pi\)
−0.371358 + 0.928490i \(0.621108\pi\)
\(600\) 0 0
\(601\) −11273.2 −0.765131 −0.382566 0.923928i \(-0.624959\pi\)
−0.382566 + 0.923928i \(0.624959\pi\)
\(602\) 24.4104i 0.00165264i
\(603\) 0 0
\(604\) 1362.39 0.0917795
\(605\) −7186.39 1383.44i −0.482923 0.0929665i
\(606\) 0 0
\(607\) 10224.7i 0.683702i −0.939754 0.341851i \(-0.888946\pi\)
0.939754 0.341851i \(-0.111054\pi\)
\(608\) 1885.63i 0.125777i
\(609\) 0 0
\(610\) 3200.88 16627.3i 0.212459 1.10364i
\(611\) −16766.4 −1.11014
\(612\) 0 0
\(613\) 7119.74i 0.469109i −0.972103 0.234554i \(-0.924637\pi\)
0.972103 0.234554i \(-0.0753631\pi\)
\(614\) 9048.46 0.594733
\(615\) 0 0
\(616\) 16251.0 1.06294
\(617\) 5358.95i 0.349665i −0.984598 0.174832i \(-0.944062\pi\)
0.984598 0.174832i \(-0.0559384\pi\)
\(618\) 0 0
\(619\) 21597.2 1.40237 0.701183 0.712981i \(-0.252656\pi\)
0.701183 + 0.712981i \(0.252656\pi\)
\(620\) 2772.33 + 533.696i 0.179580 + 0.0345706i
\(621\) 0 0
\(622\) 16107.1i 1.03832i
\(623\) 5111.96i 0.328742i
\(624\) 0 0
\(625\) 11317.8 + 10772.6i 0.724336 + 0.689447i
\(626\) 27266.8 1.74089
\(627\) 0 0
\(628\) 834.333i 0.0530152i
\(629\) 5358.89 0.339703
\(630\) 0 0
\(631\) −1384.23 −0.0873305 −0.0436652 0.999046i \(-0.513903\pi\)
−0.0436652 + 0.999046i \(0.513903\pi\)
\(632\) 6808.06i 0.428497i
\(633\) 0 0
\(634\) 14446.9 0.904986
\(635\) 3849.77 19998.0i 0.240588 1.24976i
\(636\) 0 0
\(637\) 2952.76i 0.183662i
\(638\) 22630.1i 1.40429i
\(639\) 0 0
\(640\) 2489.25 12930.6i 0.153744 0.798637i
\(641\) −1623.14 −0.100016 −0.0500080 0.998749i \(-0.515925\pi\)
−0.0500080 + 0.998749i \(0.515925\pi\)
\(642\) 0 0
\(643\) 28170.8i 1.72776i 0.503699 + 0.863879i \(0.331972\pi\)
−0.503699 + 0.863879i \(0.668028\pi\)
\(644\) 12.0067 0.000734675
\(645\) 0 0
\(646\) 12289.9 0.748515
\(647\) 16695.3i 1.01447i 0.861808 + 0.507235i \(0.169332\pi\)
−0.861808 + 0.507235i \(0.830668\pi\)
\(648\) 0 0
\(649\) 8602.97 0.520333
\(650\) −8700.81 3478.87i −0.525037 0.209927i
\(651\) 0 0
\(652\) 2510.24i 0.150780i
\(653\) 4489.96i 0.269075i 0.990909 + 0.134537i \(0.0429548\pi\)
−0.990909 + 0.134537i \(0.957045\pi\)
\(654\) 0 0
\(655\) −2615.78 503.558i −0.156041 0.0300391i
\(656\) 16275.4 0.968669
\(657\) 0 0
\(658\) 24672.2i 1.46173i
\(659\) 15300.9 0.904459 0.452229 0.891902i \(-0.350629\pi\)
0.452229 + 0.891902i \(0.350629\pi\)
\(660\) 0 0
\(661\) −20634.9 −1.21423 −0.607113 0.794615i \(-0.707673\pi\)
−0.607113 + 0.794615i \(0.707673\pi\)
\(662\) 6160.39i 0.361678i
\(663\) 0 0
\(664\) 6744.00 0.394154
\(665\) −1615.36 + 8391.15i −0.0941971 + 0.489316i
\(666\) 0 0
\(667\) 175.195i 0.0101703i
\(668\) 2058.56i 0.119234i
\(669\) 0 0
\(670\) 10430.7 + 2008.00i 0.601454 + 0.115785i
\(671\) −25227.6 −1.45142
\(672\) 0 0
\(673\) 17553.8i 1.00542i −0.864454 0.502712i \(-0.832336\pi\)
0.864454 0.502712i \(-0.167664\pi\)
\(674\) 25590.5 1.46248
\(675\) 0 0
\(676\) 1191.52 0.0677922
\(677\) 15182.6i 0.861915i −0.902372 0.430958i \(-0.858176\pi\)
0.902372 0.430958i \(-0.141824\pi\)
\(678\) 0 0
\(679\) −28081.0 −1.58711
\(680\) 24067.8 + 4633.25i 1.35729 + 0.261289i
\(681\) 0 0
\(682\) 35662.3i 2.00232i
\(683\) 1735.90i 0.0972510i 0.998817 + 0.0486255i \(0.0154841\pi\)
−0.998817 + 0.0486255i \(0.984516\pi\)
\(684\) 0 0
\(685\) −4327.34 + 22478.8i −0.241371 + 1.25383i
\(686\) 18489.3 1.02905
\(687\) 0 0
\(688\) 33.4663i 0.00185449i
\(689\) 4100.90 0.226751
\(690\) 0 0
\(691\) −27648.0 −1.52211 −0.761055 0.648687i \(-0.775318\pi\)
−0.761055 + 0.648687i \(0.775318\pi\)
\(692\) 2239.72i 0.123037i
\(693\) 0 0
\(694\) −218.076 −0.0119280
\(695\) −23926.8 4606.09i −1.30589 0.251394i
\(696\) 0 0
\(697\) 26675.4i 1.44964i
\(698\) 250.311i 0.0135736i
\(699\) 0 0
\(700\) −603.805 + 1510.14i −0.0326024 + 0.0815401i
\(701\) 19116.9 1.03001 0.515005 0.857187i \(-0.327790\pi\)
0.515005 + 0.857187i \(0.327790\pi\)
\(702\) 0 0
\(703\) 2867.42i 0.153836i
\(704\) −24686.9 −1.32162
\(705\) 0 0
\(706\) −17857.2 −0.951931
\(707\) 17687.0i 0.940861i
\(708\) 0 0
\(709\) 10045.3 0.532099 0.266050 0.963959i \(-0.414281\pi\)
0.266050 + 0.963959i \(0.414281\pi\)
\(710\) 1813.17 9418.68i 0.0958410 0.497855i
\(711\) 0 0
\(712\) 7845.47i 0.412952i
\(713\) 276.086i 0.0145014i
\(714\) 0 0
\(715\) −2639.15 + 13709.3i −0.138040 + 0.717062i
\(716\) 1774.41 0.0926159
\(717\) 0 0
\(718\) 22295.3i 1.15885i
\(719\) −22559.7 −1.17014 −0.585072 0.810981i \(-0.698934\pi\)
−0.585072 + 0.810981i \(0.698934\pi\)
\(720\) 0 0
\(721\) 24395.4 1.26010
\(722\) 11772.2i 0.606809i
\(723\) 0 0
\(724\) 1348.23 0.0692079
\(725\) −22035.1 8810.37i −1.12878 0.451323i
\(726\) 0 0
\(727\) 3668.07i 0.187127i −0.995613 0.0935635i \(-0.970174\pi\)
0.995613 0.0935635i \(-0.0298258\pi\)
\(728\) 10220.1i 0.520307i
\(729\) 0 0
\(730\) 18701.6 + 3600.20i 0.948187 + 0.182533i
\(731\) 54.8513 0.00277530
\(732\) 0 0
\(733\) 31428.4i 1.58368i −0.610731 0.791838i \(-0.709124\pi\)
0.610731 0.791838i \(-0.290876\pi\)
\(734\) 336.419 0.0169175
\(735\) 0 0
\(736\) −35.0955 −0.00175766
\(737\) 15826.0i 0.790987i
\(738\) 0 0
\(739\) −17467.0 −0.869465 −0.434732 0.900560i \(-0.643157\pi\)
−0.434732 + 0.900560i \(0.643157\pi\)
\(740\) 103.166 535.906i 0.00512495 0.0266220i
\(741\) 0 0
\(742\) 6034.57i 0.298566i
\(743\) 24993.4i 1.23408i −0.786933 0.617038i \(-0.788332\pi\)
0.786933 0.617038i \(-0.211668\pi\)
\(744\) 0 0
\(745\) 1712.12 + 329.596i 0.0841975 + 0.0162087i
\(746\) 3840.74 0.188498
\(747\) 0 0
\(748\) 3484.99i 0.170353i
\(749\) 5940.87 0.289819
\(750\) 0 0
\(751\) −9348.04 −0.454214 −0.227107 0.973870i \(-0.572927\pi\)
−0.227107 + 0.973870i \(0.572927\pi\)
\(752\) 33825.2i 1.64026i
\(753\) 0 0
\(754\) 14231.9 0.687395
\(755\) −17721.3 3411.48i −0.854230 0.164446i
\(756\) 0 0
\(757\) 11708.4i 0.562153i 0.959685 + 0.281076i \(0.0906915\pi\)
−0.959685 + 0.281076i \(0.909309\pi\)
\(758\) 5684.61i 0.272394i
\(759\) 0 0
\(760\) 2479.15 12878.2i 0.118326 0.614658i
\(761\) 19410.7 0.924621 0.462310 0.886718i \(-0.347021\pi\)
0.462310 + 0.886718i \(0.347021\pi\)
\(762\) 0 0
\(763\) 3137.05i 0.148845i
\(764\) −2875.98 −0.136190
\(765\) 0 0
\(766\) −18888.0 −0.890927
\(767\) 5410.35i 0.254702i
\(768\) 0 0
\(769\) 9857.66 0.462258 0.231129 0.972923i \(-0.425758\pi\)
0.231129 + 0.972923i \(0.425758\pi\)
\(770\) −20173.6 3883.57i −0.944162 0.181759i
\(771\) 0 0
\(772\) 691.373i 0.0322319i
\(773\) 27574.5i 1.28303i −0.767108 0.641517i \(-0.778305\pi\)
0.767108 0.641517i \(-0.221695\pi\)
\(774\) 0 0
\(775\) −34724.7 13884.1i −1.60948 0.643525i
\(776\) 43096.7 1.99366
\(777\) 0 0
\(778\) 26266.8i 1.21042i
\(779\) 14273.4 0.656479
\(780\) 0 0
\(781\) −14290.4 −0.654741
\(782\) 228.741i 0.0104601i
\(783\) 0 0
\(784\) −5957.01 −0.271365
\(785\) −2089.21 + 10852.6i −0.0949899 + 0.493434i
\(786\) 0 0
\(787\) 11777.0i 0.533425i −0.963776 0.266712i \(-0.914063\pi\)
0.963776 0.266712i \(-0.0859374\pi\)
\(788\) 303.834i 0.0137356i
\(789\) 0 0
\(790\) −1626.95 + 8451.35i −0.0732713 + 0.380614i
\(791\) 1017.64 0.0457436
\(792\) 0