Properties

Label 224.3.s.a.129.6
Level 224
Weight 3
Character 224.129
Analytic conductor 6.104
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.6
Root \(-0.707107 + 1.17406i\) of \(x^{16} + 36 x^{14} + 522 x^{12} + 3644 x^{10} + 12219 x^{8} + 15156 x^{6} + 15478 x^{4} - 10992 x^{2} + 11025\)
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.a.33.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.43792 + 0.830185i) q^{3} +(7.27622 - 4.20093i) q^{5} +(-3.99843 - 5.74565i) q^{7} +(-3.12159 - 5.40674i) q^{9} +O(q^{10})\) \(q+(1.43792 + 0.830185i) q^{3} +(7.27622 - 4.20093i) q^{5} +(-3.99843 - 5.74565i) q^{7} +(-3.12159 - 5.40674i) q^{9} +(2.60793 - 4.51706i) q^{11} -4.88512i q^{13} +13.9502 q^{15} +(6.68769 + 3.86114i) q^{17} +(-30.6032 + 17.6687i) q^{19} +(-0.979482 - 11.5812i) q^{21} +(13.3135 + 23.0597i) q^{23} +(22.7956 - 39.4832i) q^{25} -25.3093i q^{27} +45.1300 q^{29} +(35.0200 + 20.2188i) q^{31} +(7.50000 - 4.33013i) q^{33} +(-53.2306 - 25.0095i) q^{35} +(-3.97948 - 6.89266i) q^{37} +(4.05555 - 7.02442i) q^{39} +26.6511i q^{41} -0.403279 q^{43} +(-45.4267 - 26.2271i) q^{45} +(28.2845 - 16.3301i) q^{47} +(-17.0251 + 45.9472i) q^{49} +(6.41092 + 11.1040i) q^{51} +(-40.6118 + 70.3416i) q^{53} -43.8229i q^{55} -58.6733 q^{57} +(7.62318 + 4.40124i) q^{59} +(-25.3298 + 14.6242i) q^{61} +(-18.5838 + 39.5541i) q^{63} +(-20.5220 - 35.5452i) q^{65} +(-43.7792 + 75.8278i) q^{67} +44.2108i q^{69} +27.5210 q^{71} +(75.3481 + 43.5023i) q^{73} +(65.5567 - 37.8492i) q^{75} +(-36.3811 + 3.07693i) q^{77} +(-60.8467 - 105.390i) q^{79} +(-7.08286 + 12.2679i) q^{81} -46.6625i q^{83} +64.8815 q^{85} +(64.8934 + 37.4662i) q^{87} +(-52.7235 + 30.4399i) q^{89} +(-28.0682 + 19.5328i) q^{91} +(33.5707 + 58.1462i) q^{93} +(-148.450 + 257.123i) q^{95} +66.4681i q^{97} -32.5635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{9} + O(q^{10}) \) \( 16q + 8q^{9} + 48q^{17} + 56q^{21} + 16q^{25} + 112q^{29} + 120q^{33} + 8q^{37} - 72q^{45} - 128q^{49} - 24q^{53} - 528q^{57} - 360q^{61} - 8q^{65} + 72q^{73} + 32q^{81} + 720q^{85} + 408q^{89} - 232q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) 1.43792 + 0.830185i 0.479308 + 0.276728i 0.720128 0.693841i \(-0.244083\pi\)
−0.240820 + 0.970570i \(0.577416\pi\)
\(4\) 0 0
\(5\) 7.27622 4.20093i 1.45524 0.840186i 0.456473 0.889737i \(-0.349112\pi\)
0.998772 + 0.0495513i \(0.0157791\pi\)
\(6\) 0 0
\(7\) −3.99843 5.74565i −0.571205 0.820808i
\(8\) 0 0
\(9\) −3.12159 5.40674i −0.346843 0.600749i
\(10\) 0 0
\(11\) 2.60793 4.51706i 0.237084 0.410642i −0.722792 0.691066i \(-0.757142\pi\)
0.959876 + 0.280423i \(0.0904749\pi\)
\(12\) 0 0
\(13\) 4.88512i 0.375778i −0.982190 0.187889i \(-0.939835\pi\)
0.982190 0.187889i \(-0.0601646\pi\)
\(14\) 0 0
\(15\) 13.9502 0.930013
\(16\) 0 0
\(17\) 6.68769 + 3.86114i 0.393394 + 0.227126i 0.683629 0.729829i \(-0.260400\pi\)
−0.290236 + 0.956955i \(0.593734\pi\)
\(18\) 0 0
\(19\) −30.6032 + 17.6687i −1.61069 + 0.929934i −0.621483 + 0.783428i \(0.713469\pi\)
−0.989210 + 0.146506i \(0.953197\pi\)
\(20\) 0 0
\(21\) −0.979482 11.5812i −0.0466420 0.551488i
\(22\) 0 0
\(23\) 13.3135 + 23.0597i 0.578850 + 1.00260i 0.995612 + 0.0935814i \(0.0298315\pi\)
−0.416762 + 0.909016i \(0.636835\pi\)
\(24\) 0 0
\(25\) 22.7956 39.4832i 0.911825 1.57933i
\(26\) 0 0
\(27\) 25.3093i 0.937382i
\(28\) 0 0
\(29\) 45.1300 1.55621 0.778103 0.628137i \(-0.216182\pi\)
0.778103 + 0.628137i \(0.216182\pi\)
\(30\) 0 0
\(31\) 35.0200 + 20.2188i 1.12968 + 0.652220i 0.943854 0.330363i \(-0.107171\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(32\) 0 0
\(33\) 7.50000 4.33013i 0.227273 0.131216i
\(34\) 0 0
\(35\) −53.2306 25.0095i −1.52087 0.714558i
\(36\) 0 0
\(37\) −3.97948 6.89266i −0.107554 0.186288i 0.807225 0.590244i \(-0.200968\pi\)
−0.914779 + 0.403956i \(0.867635\pi\)
\(38\) 0 0
\(39\) 4.05555 7.02442i 0.103989 0.180113i
\(40\) 0 0
\(41\) 26.6511i 0.650027i 0.945709 + 0.325014i \(0.105369\pi\)
−0.945709 + 0.325014i \(0.894631\pi\)
\(42\) 0 0
\(43\) −0.403279 −0.00937859 −0.00468930 0.999989i \(-0.501493\pi\)
−0.00468930 + 0.999989i \(0.501493\pi\)
\(44\) 0 0
\(45\) −45.4267 26.2271i −1.00948 0.582825i
\(46\) 0 0
\(47\) 28.2845 16.3301i 0.601798 0.347448i −0.167951 0.985795i \(-0.553715\pi\)
0.769748 + 0.638347i \(0.220382\pi\)
\(48\) 0 0
\(49\) −17.0251 + 45.9472i −0.347450 + 0.937698i
\(50\) 0 0
\(51\) 6.41092 + 11.1040i 0.125704 + 0.217726i
\(52\) 0 0
\(53\) −40.6118 + 70.3416i −0.766259 + 1.32720i 0.173319 + 0.984866i \(0.444551\pi\)
−0.939578 + 0.342335i \(0.888782\pi\)
\(54\) 0 0
\(55\) 43.8229i 0.796780i
\(56\) 0 0
\(57\) −58.6733 −1.02936
\(58\) 0 0
\(59\) 7.62318 + 4.40124i 0.129206 + 0.0745973i 0.563210 0.826314i \(-0.309566\pi\)
−0.434004 + 0.900911i \(0.642900\pi\)
\(60\) 0 0
\(61\) −25.3298 + 14.6242i −0.415243 + 0.239740i −0.693040 0.720899i \(-0.743729\pi\)
0.277797 + 0.960640i \(0.410396\pi\)
\(62\) 0 0
\(63\) −18.5838 + 39.5541i −0.294981 + 0.627842i
\(64\) 0 0
\(65\) −20.5220 35.5452i −0.315724 0.546849i
\(66\) 0 0
\(67\) −43.7792 + 75.8278i −0.653421 + 1.13176i 0.328866 + 0.944376i \(0.393333\pi\)
−0.982287 + 0.187382i \(0.940000\pi\)
\(68\) 0 0
\(69\) 44.2108i 0.640737i
\(70\) 0 0
\(71\) 27.5210 0.387620 0.193810 0.981039i \(-0.437915\pi\)
0.193810 + 0.981039i \(0.437915\pi\)
\(72\) 0 0
\(73\) 75.3481 + 43.5023i 1.03217 + 0.595921i 0.917604 0.397495i \(-0.130120\pi\)
0.114562 + 0.993416i \(0.463454\pi\)
\(74\) 0 0
\(75\) 65.5567 37.8492i 0.874089 0.504656i
\(76\) 0 0
\(77\) −36.3811 + 3.07693i −0.472482 + 0.0399601i
\(78\) 0 0
\(79\) −60.8467 105.390i −0.770212 1.33405i −0.937447 0.348129i \(-0.886817\pi\)
0.167235 0.985917i \(-0.446516\pi\)
\(80\) 0 0
\(81\) −7.08286 + 12.2679i −0.0874427 + 0.151455i
\(82\) 0 0
\(83\) 46.6625i 0.562198i −0.959679 0.281099i \(-0.909301\pi\)
0.959679 0.281099i \(-0.0906990\pi\)
\(84\) 0 0
\(85\) 64.8815 0.763312
\(86\) 0 0
\(87\) 64.8934 + 37.4662i 0.745901 + 0.430646i
\(88\) 0 0
\(89\) −52.7235 + 30.4399i −0.592399 + 0.342022i −0.766045 0.642786i \(-0.777778\pi\)
0.173647 + 0.984808i \(0.444445\pi\)
\(90\) 0 0
\(91\) −28.0682 + 19.5328i −0.308442 + 0.214646i
\(92\) 0 0
\(93\) 33.5707 + 58.1462i 0.360975 + 0.625228i
\(94\) 0 0
\(95\) −148.450 + 257.123i −1.56263 + 2.70656i
\(96\) 0 0
\(97\) 66.4681i 0.685238i 0.939474 + 0.342619i \(0.111314\pi\)
−0.939474 + 0.342619i \(0.888686\pi\)
\(98\) 0 0
\(99\) −32.5635 −0.328924
\(100\) 0 0
\(101\) −83.8424 48.4064i −0.830123 0.479272i 0.0237720 0.999717i \(-0.492432\pi\)
−0.853895 + 0.520446i \(0.825766\pi\)
\(102\) 0 0
\(103\) 149.353 86.2290i 1.45003 0.837175i 0.451547 0.892247i \(-0.350872\pi\)
0.998482 + 0.0550721i \(0.0175389\pi\)
\(104\) 0 0
\(105\) −55.7789 80.1530i −0.531228 0.763362i
\(106\) 0 0
\(107\) −51.5903 89.3571i −0.482153 0.835113i 0.517638 0.855600i \(-0.326812\pi\)
−0.999790 + 0.0204873i \(0.993478\pi\)
\(108\) 0 0
\(109\) 20.7763 35.9856i 0.190608 0.330143i −0.754844 0.655905i \(-0.772287\pi\)
0.945452 + 0.325762i \(0.105621\pi\)
\(110\) 0 0
\(111\) 13.2148i 0.119052i
\(112\) 0 0
\(113\) −133.885 −1.18482 −0.592409 0.805637i \(-0.701823\pi\)
−0.592409 + 0.805637i \(0.701823\pi\)
\(114\) 0 0
\(115\) 193.745 + 111.859i 1.68474 + 0.972683i
\(116\) 0 0
\(117\) −26.4126 + 15.2493i −0.225749 + 0.130336i
\(118\) 0 0
\(119\) −4.55551 53.8637i −0.0382816 0.452636i
\(120\) 0 0
\(121\) 46.8974 + 81.2287i 0.387582 + 0.671312i
\(122\) 0 0
\(123\) −22.1254 + 38.3223i −0.179881 + 0.311563i
\(124\) 0 0
\(125\) 173.005i 1.38404i
\(126\) 0 0
\(127\) −132.489 −1.04322 −0.521610 0.853184i \(-0.674668\pi\)
−0.521610 + 0.853184i \(0.674668\pi\)
\(128\) 0 0
\(129\) −0.579885 0.334797i −0.00449523 0.00259532i
\(130\) 0 0
\(131\) 64.1188 37.0190i 0.489456 0.282588i −0.234893 0.972021i \(-0.575474\pi\)
0.724349 + 0.689434i \(0.242141\pi\)
\(132\) 0 0
\(133\) 223.883 + 105.188i 1.68333 + 0.790886i
\(134\) 0 0
\(135\) −106.323 184.156i −0.787575 1.36412i
\(136\) 0 0
\(137\) 37.1900 64.4150i 0.271460 0.470182i −0.697776 0.716316i \(-0.745827\pi\)
0.969236 + 0.246134i \(0.0791603\pi\)
\(138\) 0 0
\(139\) 123.649i 0.889560i −0.895640 0.444780i \(-0.853282\pi\)
0.895640 0.444780i \(-0.146718\pi\)
\(140\) 0 0
\(141\) 54.2279 0.384595
\(142\) 0 0
\(143\) −22.0664 12.7400i −0.154310 0.0890912i
\(144\) 0 0
\(145\) 328.376 189.588i 2.26466 1.30750i
\(146\) 0 0
\(147\) −62.6254 + 51.9346i −0.426023 + 0.353297i
\(148\) 0 0
\(149\) −103.295 178.913i −0.693257 1.20076i −0.970765 0.240033i \(-0.922842\pi\)
0.277507 0.960724i \(-0.410492\pi\)
\(150\) 0 0
\(151\) −24.2277 + 41.9636i −0.160448 + 0.277905i −0.935030 0.354570i \(-0.884627\pi\)
0.774581 + 0.632474i \(0.217961\pi\)
\(152\) 0 0
\(153\) 48.2115i 0.315108i
\(154\) 0 0
\(155\) 339.751 2.19194
\(156\) 0 0
\(157\) 153.500 + 88.6233i 0.977708 + 0.564480i 0.901577 0.432618i \(-0.142410\pi\)
0.0761305 + 0.997098i \(0.475743\pi\)
\(158\) 0 0
\(159\) −116.793 + 67.4305i −0.734548 + 0.424091i
\(160\) 0 0
\(161\) 79.2599 168.698i 0.492298 1.04781i
\(162\) 0 0
\(163\) 63.4766 + 109.945i 0.389427 + 0.674507i 0.992373 0.123275i \(-0.0393398\pi\)
−0.602946 + 0.797782i \(0.706006\pi\)
\(164\) 0 0
\(165\) 36.3811 63.0139i 0.220492 0.381903i
\(166\) 0 0
\(167\) 191.898i 1.14909i −0.818472 0.574546i \(-0.805179\pi\)
0.818472 0.574546i \(-0.194821\pi\)
\(168\) 0 0
\(169\) 145.136 0.858791
\(170\) 0 0
\(171\) 191.061 + 110.309i 1.11731 + 0.645082i
\(172\) 0 0
\(173\) −163.288 + 94.2744i −0.943862 + 0.544939i −0.891169 0.453672i \(-0.850114\pi\)
−0.0526930 + 0.998611i \(0.516780\pi\)
\(174\) 0 0
\(175\) −318.003 + 26.8951i −1.81716 + 0.153686i
\(176\) 0 0
\(177\) 7.30769 + 12.6573i 0.0412864 + 0.0715101i
\(178\) 0 0
\(179\) −120.527 + 208.759i −0.673337 + 1.16625i 0.303615 + 0.952795i \(0.401806\pi\)
−0.976952 + 0.213459i \(0.931527\pi\)
\(180\) 0 0
\(181\) 277.790i 1.53475i −0.641198 0.767376i \(-0.721562\pi\)
0.641198 0.767376i \(-0.278438\pi\)
\(182\) 0 0
\(183\) −48.5631 −0.265372
\(184\) 0 0
\(185\) −57.9112 33.4350i −0.313033 0.180730i
\(186\) 0 0
\(187\) 34.8820 20.1392i 0.186535 0.107696i
\(188\) 0 0
\(189\) −145.419 + 101.198i −0.769410 + 0.535437i
\(190\) 0 0
\(191\) 132.188 + 228.957i 0.692085 + 1.19873i 0.971154 + 0.238455i \(0.0766408\pi\)
−0.279069 + 0.960271i \(0.590026\pi\)
\(192\) 0 0
\(193\) −105.698 + 183.075i −0.547660 + 0.948575i 0.450774 + 0.892638i \(0.351148\pi\)
−0.998434 + 0.0559370i \(0.982185\pi\)
\(194\) 0 0
\(195\) 68.1484i 0.349479i
\(196\) 0 0
\(197\) −79.4949 −0.403527 −0.201764 0.979434i \(-0.564667\pi\)
−0.201764 + 0.979434i \(0.564667\pi\)
\(198\) 0 0
\(199\) 175.765 + 101.478i 0.883241 + 0.509939i 0.871726 0.489995i \(-0.163001\pi\)
0.0115150 + 0.999934i \(0.496335\pi\)
\(200\) 0 0
\(201\) −125.902 + 72.6897i −0.626379 + 0.361640i
\(202\) 0 0
\(203\) −180.449 259.301i −0.888912 1.27735i
\(204\) 0 0
\(205\) 111.959 + 193.920i 0.546144 + 0.945949i
\(206\) 0 0
\(207\) 83.1187 143.966i 0.401540 0.695487i
\(208\) 0 0
\(209\) 184.315i 0.881891i
\(210\) 0 0
\(211\) −166.533 −0.789256 −0.394628 0.918841i \(-0.629127\pi\)
−0.394628 + 0.918841i \(0.629127\pi\)
\(212\) 0 0
\(213\) 39.5731 + 22.8476i 0.185789 + 0.107266i
\(214\) 0 0
\(215\) −2.93435 + 1.69415i −0.0136481 + 0.00787976i
\(216\) 0 0
\(217\) −23.8549 282.056i −0.109930 1.29980i
\(218\) 0 0
\(219\) 72.2299 + 125.106i 0.329817 + 0.571259i
\(220\) 0 0
\(221\) 18.8621 32.6702i 0.0853490 0.147829i
\(222\) 0 0
\(223\) 55.0782i 0.246988i −0.992345 0.123494i \(-0.960590\pi\)
0.992345 0.123494i \(-0.0394099\pi\)
\(224\) 0 0
\(225\) −284.634 −1.26504
\(226\) 0 0
\(227\) −184.119 106.301i −0.811099 0.468288i 0.0362385 0.999343i \(-0.488462\pi\)
−0.847337 + 0.531055i \(0.821796\pi\)
\(228\) 0 0
\(229\) −38.5185 + 22.2387i −0.168203 + 0.0971120i −0.581738 0.813376i \(-0.697627\pi\)
0.413535 + 0.910488i \(0.364294\pi\)
\(230\) 0 0
\(231\) −54.8677 25.7787i −0.237522 0.111596i
\(232\) 0 0
\(233\) 136.050 + 235.645i 0.583904 + 1.01135i 0.995011 + 0.0997641i \(0.0318088\pi\)
−0.411107 + 0.911587i \(0.634858\pi\)
\(234\) 0 0
\(235\) 137.203 237.642i 0.583842 1.01124i
\(236\) 0 0
\(237\) 202.056i 0.852558i
\(238\) 0 0
\(239\) 389.180 1.62837 0.814185 0.580605i \(-0.197184\pi\)
0.814185 + 0.580605i \(0.197184\pi\)
\(240\) 0 0
\(241\) −60.9363 35.1816i −0.252848 0.145982i 0.368220 0.929739i \(-0.379967\pi\)
−0.621068 + 0.783757i \(0.713301\pi\)
\(242\) 0 0
\(243\) −217.636 + 125.652i −0.895620 + 0.517087i
\(244\) 0 0
\(245\) 69.1428 + 405.843i 0.282216 + 1.65650i
\(246\) 0 0
\(247\) 86.3139 + 149.500i 0.349449 + 0.605263i
\(248\) 0 0
\(249\) 38.7385 67.0970i 0.155576 0.269466i
\(250\) 0 0
\(251\) 97.5325i 0.388576i −0.980945 0.194288i \(-0.937760\pi\)
0.980945 0.194288i \(-0.0622396\pi\)
\(252\) 0 0
\(253\) 138.883 0.548945
\(254\) 0 0
\(255\) 93.2946 + 53.8637i 0.365861 + 0.211230i
\(256\) 0 0
\(257\) 179.396 103.574i 0.698038 0.403013i −0.108578 0.994088i \(-0.534630\pi\)
0.806616 + 0.591075i \(0.201296\pi\)
\(258\) 0 0
\(259\) −23.6912 + 50.4246i −0.0914717 + 0.194689i
\(260\) 0 0
\(261\) −140.877 244.006i −0.539759 0.934890i
\(262\) 0 0
\(263\) −103.607 + 179.453i −0.393943 + 0.682330i −0.992966 0.118402i \(-0.962223\pi\)
0.599022 + 0.800732i \(0.295556\pi\)
\(264\) 0 0
\(265\) 682.428i 2.57520i
\(266\) 0 0
\(267\) −101.083 −0.378588
\(268\) 0 0
\(269\) −31.1550 17.9873i −0.115818 0.0668674i 0.440972 0.897521i \(-0.354634\pi\)
−0.556790 + 0.830653i \(0.687967\pi\)
\(270\) 0 0
\(271\) −66.3923 + 38.3316i −0.244990 + 0.141445i −0.617468 0.786596i \(-0.711841\pi\)
0.372478 + 0.928041i \(0.378508\pi\)
\(272\) 0 0
\(273\) −56.5758 + 4.78488i −0.207237 + 0.0175270i
\(274\) 0 0
\(275\) −118.899 205.939i −0.432359 0.748867i
\(276\) 0 0
\(277\) −134.002 + 232.098i −0.483760 + 0.837898i −0.999826 0.0186514i \(-0.994063\pi\)
0.516066 + 0.856549i \(0.327396\pi\)
\(278\) 0 0
\(279\) 252.459i 0.904871i
\(280\) 0 0
\(281\) −417.336 −1.48518 −0.742591 0.669745i \(-0.766403\pi\)
−0.742591 + 0.669745i \(0.766403\pi\)
\(282\) 0 0
\(283\) 124.538 + 71.9020i 0.440064 + 0.254071i 0.703625 0.710572i \(-0.251564\pi\)
−0.263561 + 0.964643i \(0.584897\pi\)
\(284\) 0 0
\(285\) −426.920 + 246.482i −1.49797 + 0.864851i
\(286\) 0 0
\(287\) 153.128 106.563i 0.533547 0.371299i
\(288\) 0 0
\(289\) −114.683 198.637i −0.396828 0.687326i
\(290\) 0 0
\(291\) −55.1808 + 95.5760i −0.189625 + 0.328440i
\(292\) 0 0
\(293\) 265.694i 0.906805i 0.891306 + 0.453402i \(0.149790\pi\)
−0.891306 + 0.453402i \(0.850210\pi\)
\(294\) 0 0
\(295\) 73.9572 0.250702
\(296\) 0 0
\(297\) −114.324 66.0049i −0.384929 0.222239i
\(298\) 0 0
\(299\) 112.650 65.0382i 0.376754 0.217519i
\(300\) 0 0
\(301\) 1.61249 + 2.31710i 0.00535709 + 0.00769802i
\(302\) 0 0
\(303\) −80.3726 139.209i −0.265256 0.459437i
\(304\) 0 0
\(305\) −122.870 + 212.817i −0.402853 + 0.697762i
\(306\) 0 0
\(307\) 281.617i 0.917318i 0.888612 + 0.458659i \(0.151670\pi\)
−0.888612 + 0.458659i \(0.848330\pi\)
\(308\) 0 0
\(309\) 286.344 0.926680
\(310\) 0 0
\(311\) −48.8342 28.1945i −0.157023 0.0906574i 0.419429 0.907788i \(-0.362230\pi\)
−0.576453 + 0.817131i \(0.695563\pi\)
\(312\) 0 0
\(313\) 73.0471 42.1738i 0.233377 0.134741i −0.378752 0.925498i \(-0.623647\pi\)
0.612129 + 0.790758i \(0.290313\pi\)
\(314\) 0 0
\(315\) 30.9437 + 365.873i 0.0982339 + 1.16150i
\(316\) 0 0
\(317\) −79.6930 138.032i −0.251398 0.435433i 0.712513 0.701659i \(-0.247557\pi\)
−0.963911 + 0.266225i \(0.914223\pi\)
\(318\) 0 0
\(319\) 117.696 203.855i 0.368952 0.639044i
\(320\) 0 0
\(321\) 171.318i 0.533701i
\(322\) 0 0
\(323\) −272.886 −0.844848
\(324\) 0 0
\(325\) −192.880 111.359i −0.593477 0.342644i
\(326\) 0 0
\(327\) 59.7494 34.4963i 0.182720 0.105493i
\(328\) 0 0
\(329\) −206.920 97.2182i −0.628938 0.295496i
\(330\) 0 0
\(331\) −279.794 484.617i −0.845299 1.46410i −0.885361 0.464904i \(-0.846089\pi\)
0.0400619 0.999197i \(-0.487244\pi\)
\(332\) 0 0
\(333\) −24.8446 + 43.0321i −0.0746084 + 0.129225i
\(334\) 0 0
\(335\) 735.653i 2.19598i
\(336\) 0 0
\(337\) 140.493 0.416892 0.208446 0.978034i \(-0.433159\pi\)
0.208446 + 0.978034i \(0.433159\pi\)
\(338\) 0 0
\(339\) −192.516 111.149i −0.567893 0.327873i
\(340\) 0 0
\(341\) 182.659 105.458i 0.535658 0.309262i
\(342\) 0 0
\(343\) 332.070 85.8967i 0.968135 0.250428i
\(344\) 0 0
\(345\) 185.727 + 321.688i 0.538338 + 0.932428i
\(346\) 0 0
\(347\) −194.159 + 336.294i −0.559537 + 0.969146i 0.437998 + 0.898976i \(0.355688\pi\)
−0.997535 + 0.0701703i \(0.977646\pi\)
\(348\) 0 0
\(349\) 469.369i 1.34490i −0.740144 0.672449i \(-0.765243\pi\)
0.740144 0.672449i \(-0.234757\pi\)
\(350\) 0 0
\(351\) −123.639 −0.352248
\(352\) 0 0
\(353\) 561.753 + 324.329i 1.59137 + 0.918778i 0.993072 + 0.117503i \(0.0374891\pi\)
0.598297 + 0.801274i \(0.295844\pi\)
\(354\) 0 0
\(355\) 200.249 115.614i 0.564082 0.325673i
\(356\) 0 0
\(357\) 38.1663 81.2337i 0.106909 0.227545i
\(358\) 0 0
\(359\) 140.301 + 243.008i 0.390810 + 0.676902i 0.992557 0.121785i \(-0.0388617\pi\)
−0.601747 + 0.798687i \(0.705528\pi\)
\(360\) 0 0
\(361\) 443.869 768.803i 1.22955 2.12965i
\(362\) 0 0
\(363\) 155.734i 0.429020i
\(364\) 0 0
\(365\) 731.000 2.00274
\(366\) 0 0
\(367\) −17.3213 10.0005i −0.0471971 0.0272493i 0.476216 0.879328i \(-0.342008\pi\)
−0.523413 + 0.852079i \(0.675341\pi\)
\(368\) 0 0
\(369\) 144.096 83.1938i 0.390504 0.225457i
\(370\) 0 0
\(371\) 566.542 47.9152i 1.52707 0.129151i
\(372\) 0 0
\(373\) 80.2038 + 138.917i 0.215024 + 0.372432i 0.953280 0.302089i \(-0.0976838\pi\)
−0.738256 + 0.674520i \(0.764351\pi\)
\(374\) 0 0
\(375\) 143.626 248.767i 0.383002 0.663380i
\(376\) 0 0
\(377\) 220.465i 0.584788i
\(378\) 0 0
\(379\) −397.426 −1.04862 −0.524308 0.851529i \(-0.675676\pi\)
−0.524308 + 0.851529i \(0.675676\pi\)
\(380\) 0 0
\(381\) −190.509 109.990i −0.500023 0.288689i
\(382\) 0 0
\(383\) 232.209 134.066i 0.606291 0.350042i −0.165222 0.986256i \(-0.552834\pi\)
0.771512 + 0.636214i \(0.219501\pi\)
\(384\) 0 0
\(385\) −251.791 + 175.223i −0.654003 + 0.455124i
\(386\) 0 0
\(387\) 1.25887 + 2.18043i 0.00325290 + 0.00563418i
\(388\) 0 0
\(389\) 96.3409 166.867i 0.247663 0.428965i −0.715214 0.698905i \(-0.753671\pi\)
0.962877 + 0.269941i \(0.0870041\pi\)
\(390\) 0 0
\(391\) 205.622i 0.525887i
\(392\) 0 0
\(393\) 122.930 0.312800
\(394\) 0 0
\(395\) −885.469 511.226i −2.24169 1.29424i
\(396\) 0 0
\(397\) 120.298 69.4542i 0.303018 0.174948i −0.340780 0.940143i \(-0.610691\pi\)
0.643798 + 0.765195i \(0.277358\pi\)
\(398\) 0 0
\(399\) 234.601 + 337.116i 0.587973 + 0.844903i
\(400\) 0 0
\(401\) −338.411 586.145i −0.843917 1.46171i −0.886558 0.462617i \(-0.846911\pi\)
0.0426415 0.999090i \(-0.486423\pi\)
\(402\) 0 0
\(403\) 98.7713 171.077i 0.245090 0.424508i
\(404\) 0 0
\(405\) 119.018i 0.293872i
\(406\) 0 0
\(407\) −41.5128 −0.101997
\(408\) 0 0
\(409\) 177.165 + 102.286i 0.433166 + 0.250089i 0.700695 0.713461i \(-0.252874\pi\)
−0.267528 + 0.963550i \(0.586207\pi\)
\(410\) 0 0
\(411\) 106.953 61.7492i 0.260226 0.150241i
\(412\) 0 0
\(413\) −5.19274 61.3982i −0.0125732 0.148664i
\(414\) 0 0
\(415\) −196.026 339.527i −0.472351 0.818136i
\(416\) 0 0
\(417\) 102.651 177.797i 0.246166 0.426373i
\(418\) 0 0
\(419\) 516.134i 1.23182i −0.787815 0.615911i \(-0.788788\pi\)
0.787815 0.615911i \(-0.211212\pi\)
\(420\) 0 0
\(421\) −81.4693 −0.193514 −0.0967569 0.995308i \(-0.530847\pi\)
−0.0967569 + 0.995308i \(0.530847\pi\)
\(422\) 0 0
\(423\) −176.585 101.951i −0.417458 0.241020i
\(424\) 0 0
\(425\) 304.900 176.034i 0.717412 0.414198i
\(426\) 0 0
\(427\) 185.305 + 87.0625i 0.433969 + 0.203893i
\(428\) 0 0
\(429\) −21.1532 36.6384i −0.0493081 0.0854042i
\(430\) 0 0
\(431\) 48.8226 84.5632i 0.113277 0.196202i −0.803812 0.594883i \(-0.797198\pi\)
0.917090 + 0.398681i \(0.130532\pi\)
\(432\) 0 0
\(433\) 476.427i 1.10029i 0.835068 + 0.550146i \(0.185428\pi\)
−0.835068 + 0.550146i \(0.814572\pi\)
\(434\) 0 0
\(435\) 629.572 1.44729
\(436\) 0 0
\(437\) −814.873 470.467i −1.86470 1.07658i
\(438\) 0 0
\(439\) −233.304 + 134.698i −0.531444 + 0.306829i −0.741604 0.670838i \(-0.765935\pi\)
0.210160 + 0.977667i \(0.432601\pi\)
\(440\) 0 0
\(441\) 301.570 51.3780i 0.683832 0.116503i
\(442\) 0 0
\(443\) 170.985 + 296.155i 0.385971 + 0.668522i 0.991903 0.126994i \(-0.0405330\pi\)
−0.605932 + 0.795516i \(0.707200\pi\)
\(444\) 0 0
\(445\) −255.752 + 442.975i −0.574724 + 0.995450i
\(446\) 0 0
\(447\) 343.017i 0.767376i
\(448\) 0 0
\(449\) −460.145 −1.02482 −0.512411 0.858741i \(-0.671247\pi\)
−0.512411 + 0.858741i \(0.671247\pi\)
\(450\) 0 0
\(451\) 120.385 + 69.5042i 0.266929 + 0.154111i
\(452\) 0 0
\(453\) −69.6751 + 40.2270i −0.153808 + 0.0888012i
\(454\) 0 0
\(455\) −122.174 + 260.038i −0.268515 + 0.571511i
\(456\) 0 0
\(457\) −304.687 527.733i −0.666710 1.15478i −0.978819 0.204729i \(-0.934369\pi\)
0.312108 0.950046i \(-0.398965\pi\)
\(458\) 0 0
\(459\) 97.7228 169.261i 0.212904 0.368760i
\(460\) 0 0
\(461\) 102.856i 0.223114i −0.993758 0.111557i \(-0.964416\pi\)
0.993758 0.111557i \(-0.0355837\pi\)
\(462\) 0 0
\(463\) −541.601 −1.16976 −0.584882 0.811118i \(-0.698859\pi\)
−0.584882 + 0.811118i \(0.698859\pi\)
\(464\) 0 0
\(465\) 488.536 + 282.056i 1.05062 + 0.606573i
\(466\) 0 0
\(467\) −134.069 + 77.4045i −0.287085 + 0.165748i −0.636626 0.771172i \(-0.719671\pi\)
0.349542 + 0.936921i \(0.386337\pi\)
\(468\) 0 0
\(469\) 610.728 51.6522i 1.30219 0.110133i
\(470\) 0 0
\(471\) 147.148 + 254.867i 0.312415 + 0.541119i
\(472\) 0 0
\(473\) −1.05172 + 1.82164i −0.00222352 + 0.00385125i
\(474\) 0 0
\(475\) 1611.08i 3.39175i
\(476\) 0 0
\(477\) 507.092 1.06309
\(478\) 0 0
\(479\) −631.045 364.334i −1.31742 0.760614i −0.334108 0.942535i \(-0.608435\pi\)
−0.983313 + 0.181921i \(0.941768\pi\)
\(480\) 0 0
\(481\) −33.6715 + 19.4402i −0.0700031 + 0.0404163i
\(482\) 0 0
\(483\) 254.020 176.774i 0.525921 0.365992i
\(484\) 0 0
\(485\) 279.228 + 483.637i 0.575728 + 0.997189i
\(486\) 0 0
\(487\) 224.471 388.794i 0.460925 0.798346i −0.538082 0.842892i \(-0.680851\pi\)
0.999007 + 0.0445466i \(0.0141843\pi\)
\(488\) 0 0
\(489\) 210.789i 0.431062i
\(490\) 0 0
\(491\) 73.5801 0.149858 0.0749288 0.997189i \(-0.476127\pi\)
0.0749288 + 0.997189i \(0.476127\pi\)
\(492\) 0 0
\(493\) 301.815 + 174.253i 0.612201 + 0.353455i
\(494\) 0 0
\(495\) −236.939 + 136.797i −0.478665 + 0.276357i
\(496\) 0 0
\(497\) −110.041 158.126i −0.221411 0.318162i
\(498\) 0 0
\(499\) 433.207 + 750.336i 0.868149 + 1.50368i 0.863886 + 0.503688i \(0.168024\pi\)
0.00426366 + 0.999991i \(0.498643\pi\)
\(500\) 0 0
\(501\) 159.311 275.935i 0.317986 0.550768i
\(502\) 0 0
\(503\) 306.742i 0.609825i 0.952380 + 0.304913i \(0.0986272\pi\)
−0.952380 + 0.304913i \(0.901373\pi\)
\(504\) 0 0
\(505\) −813.408 −1.61071
\(506\) 0 0
\(507\) 208.694 + 120.489i 0.411625 + 0.237652i
\(508\) 0 0
\(509\) 162.588 93.8701i 0.319426 0.184421i −0.331711 0.943381i \(-0.607626\pi\)
0.651137 + 0.758961i \(0.274292\pi\)
\(510\) 0 0
\(511\) −51.3255 606.865i −0.100441 1.18760i
\(512\) 0 0
\(513\) 447.184 + 774.545i 0.871703 + 1.50983i
\(514\) 0 0
\(515\) 724.484 1254.84i 1.40677 2.43659i
\(516\) 0 0
\(517\) 170.350i 0.329498i
\(518\) 0 0
\(519\) −313.061 −0.603200
\(520\) 0 0
\(521\) −300.489 173.487i −0.576754 0.332989i 0.183088 0.983096i \(-0.441391\pi\)
−0.759842 + 0.650107i \(0.774724\pi\)
\(522\) 0 0
\(523\) −279.427 + 161.328i −0.534278 + 0.308466i −0.742757 0.669561i \(-0.766482\pi\)
0.208479 + 0.978027i \(0.433149\pi\)
\(524\) 0 0
\(525\) −479.592 225.329i −0.913509 0.429197i
\(526\) 0 0
\(527\) 156.135 + 270.434i 0.296272 + 0.513158i
\(528\) 0 0
\(529\) −90.0008 + 155.886i −0.170134 + 0.294681i
\(530\) 0 0
\(531\) 54.9554i 0.103494i
\(532\) 0 0
\(533\) 130.194 0.244266
\(534\) 0 0
\(535\) −750.765 433.455i −1.40330 0.810196i
\(536\) 0 0
\(537\) −346.618 + 200.120i −0.645471 + 0.372663i
\(538\) 0 0
\(539\) 163.146 + 196.730i 0.302683 + 0.364991i
\(540\) 0 0
\(541\) −247.471 428.632i −0.457432 0.792296i 0.541392 0.840770i \(-0.317897\pi\)
−0.998824 + 0.0484743i \(0.984564\pi\)
\(542\) 0 0
\(543\) 230.617 399.440i 0.424709 0.735618i
\(544\) 0 0
\(545\) 349.119i 0.640585i
\(546\) 0 0
\(547\) −244.584 −0.447137 −0.223569 0.974688i \(-0.571771\pi\)
−0.223569 + 0.974688i \(0.571771\pi\)
\(548\) 0 0
\(549\) 158.138 + 91.3011i 0.288048 + 0.166304i
\(550\) 0 0
\(551\) −1381.12 + 797.390i −2.50657 + 1.44717i
\(552\) 0 0
\(553\) −362.241 + 770.998i −0.655047 + 1.39421i
\(554\) 0 0
\(555\) −55.5146 96.1540i −0.100026 0.173250i
\(556\) 0 0
\(557\) −415.083 + 718.944i −0.745211 + 1.29074i 0.204885 + 0.978786i \(0.434318\pi\)
−0.950096 + 0.311958i \(0.899015\pi\)
\(558\) 0 0
\(559\) 1.97007i 0.00352427i
\(560\) 0 0
\(561\) 66.8769 0.119210
\(562\) 0 0
\(563\) 491.327 + 283.668i 0.872695 + 0.503851i 0.868243 0.496140i \(-0.165250\pi\)
0.00445194 + 0.999990i \(0.498583\pi\)
\(564\) 0 0
\(565\) −974.174 + 562.440i −1.72420 + 0.995468i
\(566\) 0 0
\(567\) 98.8073 8.35661i 0.174263 0.0147383i
\(568\) 0 0
\(569\) 324.238 + 561.596i 0.569837 + 0.986987i 0.996582 + 0.0826150i \(0.0263272\pi\)
−0.426744 + 0.904372i \(0.640339\pi\)
\(570\) 0 0
\(571\) 254.923 441.539i 0.446450 0.773274i −0.551702 0.834041i \(-0.686021\pi\)
0.998152 + 0.0607673i \(0.0193547\pi\)
\(572\) 0 0
\(573\) 438.963i 0.766078i
\(574\) 0 0
\(575\) 1213.96 2.11124
\(576\) 0 0
\(577\) −360.612 208.200i −0.624978 0.360831i 0.153827 0.988098i \(-0.450840\pi\)
−0.778804 + 0.627267i \(0.784174\pi\)
\(578\) 0 0
\(579\) −303.972 + 175.498i −0.524995 + 0.303106i
\(580\) 0 0
\(581\) −268.106 + 186.577i −0.461457 + 0.321130i
\(582\) 0 0
\(583\) 211.825 + 366.892i 0.363336 + 0.629317i
\(584\) 0 0
\(585\) −128.123 + 221.915i −0.219013 + 0.379342i
\(586\) 0 0
\(587\) 581.897i 0.991307i −0.868520 0.495654i \(-0.834929\pi\)
0.868520 0.495654i \(-0.165071\pi\)
\(588\) 0 0
\(589\) −1428.96 −2.42608
\(590\) 0 0
\(591\) −114.308 65.9955i −0.193414 0.111667i
\(592\) 0 0
\(593\) −480.511 + 277.423i −0.810305 + 0.467830i −0.847062 0.531495i \(-0.821631\pi\)
0.0367569 + 0.999324i \(0.488297\pi\)
\(594\) 0 0
\(595\) −259.424 372.787i −0.436007 0.626532i
\(596\) 0 0
\(597\) 168.491 + 291.835i 0.282229 + 0.488835i
\(598\) 0 0
\(599\) −33.3932 + 57.8387i −0.0557482 + 0.0965587i −0.892553 0.450943i \(-0.851088\pi\)
0.836805 + 0.547502i \(0.184421\pi\)
\(600\) 0 0
\(601\) 215.249i 0.358151i −0.983835 0.179076i \(-0.942689\pi\)
0.983835 0.179076i \(-0.0573107\pi\)
\(602\) 0 0
\(603\) 546.642 0.906537
\(604\) 0 0
\(605\) 682.472 + 394.025i 1.12805 + 0.651282i
\(606\) 0 0
\(607\) 542.576 313.256i 0.893864 0.516073i 0.0186599 0.999826i \(-0.494060\pi\)
0.875205 + 0.483753i \(0.160727\pi\)
\(608\) 0 0
\(609\) −44.2040 522.661i −0.0725845 0.858229i
\(610\) 0 0
\(611\) −79.7743 138.173i −0.130563 0.226142i
\(612\) 0 0
\(613\) −60.4201 + 104.651i −0.0985647 + 0.170719i −0.911091 0.412206i \(-0.864758\pi\)
0.812526 + 0.582925i \(0.198092\pi\)
\(614\) 0 0
\(615\) 371.788i 0.604534i
\(616\) 0 0
\(617\) 537.102 0.870506 0.435253 0.900308i \(-0.356659\pi\)
0.435253 + 0.900308i \(0.356659\pi\)
\(618\) 0 0
\(619\) −211.462 122.088i −0.341619 0.197234i 0.319369 0.947630i \(-0.396529\pi\)
−0.660988 + 0.750397i \(0.729862\pi\)
\(620\) 0 0
\(621\) 583.626 336.957i 0.939816 0.542603i
\(622\) 0 0
\(623\) 385.709 + 181.219i 0.619115 + 0.290881i
\(624\) 0 0
\(625\) −156.890 271.741i −0.251024 0.434786i
\(626\) 0 0
\(627\) −153.016 + 265.031i −0.244044 + 0.422697i
\(628\) 0 0
\(629\) 61.4613i 0.0977128i
\(630\) 0 0
\(631\) −873.683 −1.38460 −0.692300 0.721609i \(-0.743403\pi\)
−0.692300 + 0.721609i \(0.743403\pi\)
\(632\) 0 0
\(633\) −239.462 138.253i −0.378297 0.218410i
\(634\) 0 0
\(635\) −964.019 + 556.577i −1.51814 + 0.876499i
\(636\) 0 0
\(637\) 224.458 + 83.1695i 0.352367 + 0.130564i
\(638\) 0 0
\(639\) −85.9093 148.799i −0.134443 0.232863i
\(640\) 0 0
\(641\) −232.688 + 403.028i −0.363008 + 0.628749i −0.988454 0.151518i \(-0.951584\pi\)
0.625446 + 0.780267i \(0.284917\pi\)
\(642\) 0 0
\(643\) 82.1402i 0.127745i −0.997958 0.0638726i \(-0.979655\pi\)
0.997958 0.0638726i \(-0.0203451\pi\)
\(644\) 0 0
\(645\) −5.62583 −0.00872221
\(646\) 0 0
\(647\) 155.391 + 89.7147i 0.240171 + 0.138663i 0.615255 0.788328i \(-0.289053\pi\)
−0.375084 + 0.926991i \(0.622386\pi\)
\(648\) 0 0
\(649\) 39.7614 22.9563i 0.0612656 0.0353717i
\(650\) 0 0
\(651\) 199.858 425.379i 0.307001 0.653424i
\(652\) 0 0
\(653\) −122.281 211.796i −0.187260 0.324344i 0.757076 0.653327i \(-0.226627\pi\)
−0.944336 + 0.328983i \(0.893294\pi\)
\(654\) 0 0
\(655\) 311.028 538.717i 0.474852 0.822468i
\(656\) 0 0
\(657\) 543.184i 0.826764i
\(658\) 0 0
\(659\) −128.978 −0.195718 −0.0978590 0.995200i \(-0.531199\pi\)
−0.0978590 + 0.995200i \(0.531199\pi\)
\(660\) 0 0
\(661\) −394.437 227.729i −0.596728 0.344521i 0.171025 0.985267i \(-0.445292\pi\)
−0.767753 + 0.640745i \(0.778625\pi\)
\(662\) 0 0
\(663\) 54.2446 31.3181i 0.0818168 0.0472370i
\(664\) 0 0
\(665\) 2070.91 175.147i 3.11415 0.263379i
\(666\) 0 0
\(667\) 600.840 + 1040.68i 0.900809 + 1.56025i
\(668\) 0 0
\(669\) 45.7251 79.1983i 0.0683485 0.118383i
\(670\) 0 0
\(671\) 152.555i 0.227355i
\(672\) 0 0
\(673\) 690.223 1.02559 0.512795 0.858511i \(-0.328610\pi\)
0.512795 + 0.858511i \(0.328610\pi\)
\(674\) 0 0
\(675\) −999.292 576.941i −1.48043 0.854728i
\(676\) 0 0
\(677\) 355.820 205.433i 0.525583 0.303445i −0.213633 0.976914i \(-0.568530\pi\)
0.739216 + 0.673469i \(0.235196\pi\)
\(678\) 0 0
\(679\) 381.903 265.768i 0.562449 0.391411i
\(680\) 0 0
\(681\) −176.500 305.706i −0.259177 0.448908i
\(682\) 0 0
\(683\) 182.112 315.428i 0.266636 0.461827i −0.701355 0.712812i \(-0.747421\pi\)
0.967991 + 0.250985i \(0.0807546\pi\)
\(684\) 0 0
\(685\) 624.930i 0.912307i
\(686\) 0 0
\(687\) −73.8488 −0.107495
\(688\) 0 0
\(689\) 343.627 + 198.393i 0.498733 + 0.287944i
\(690\) 0 0
\(691\) 901.670 520.579i 1.30488 0.753371i 0.323641 0.946180i \(-0.395093\pi\)
0.981236 + 0.192809i \(0.0617597\pi\)
\(692\) 0 0
\(693\) 130.203 + 187.099i 0.187883 + 0.269983i
\(694\) 0 0
\(695\) −519.440 899.696i −0.747396 1.29453i
\(696\) 0 0
\(697\) −102.904 + 178.234i −0.147638 + 0.255717i
\(698\) 0 0
\(699\) 451.785i 0.646331i
\(700\) 0 0
\(701\) −366.854 −0.523330 −0.261665 0.965159i \(-0.584272\pi\)
−0.261665 + 0.965159i \(0.584272\pi\)
\(702\) 0 0
\(703\) 243.569 + 140.625i 0.346471 + 0.200035i
\(704\) 0 0
\(705\) 394.574 227.808i 0.559680 0.323131i
\(706\) 0 0
\(707\) 57.1116 + 675.279i 0.0807802 + 0.955133i
\(708\) 0 0
\(709\) 32.6520 + 56.5549i 0.0460536 + 0.0797672i 0.888133 0.459586i \(-0.152002\pi\)
−0.842080 + 0.539353i \(0.818669\pi\)
\(710\) 0 0
\(711\) −379.877 + 657.966i −0.534285 + 0.925409i
\(712\) 0 0
\(713\) 1076.74i 1.51015i
\(714\) 0 0
\(715\) −214.080 −0.299413
\(716\) 0 0
\(717\) 559.611 + 323.092i 0.780490 + 0.450616i
\(718\) 0 0
\(719\) 588.230 339.615i 0.818123 0.472344i −0.0316457 0.999499i \(-0.510075\pi\)
0.849769 + 0.527156i \(0.176741\pi\)
\(720\) 0 0
\(721\) −1092.62 513.350i −1.51542 0.711997i
\(722\) 0 0
\(723\) −58.4145 101.177i −0.0807946 0.139940i
\(724\) 0 0
\(725\) 1028.77 1781.87i 1.41899 2.45776i
\(726\) 0 0
\(727\) 1079.11i 1.48433i 0.670217 + 0.742166i \(0.266201\pi\)
−0.670217 + 0.742166i \(0.733799\pi\)
\(728\) 0 0
\(729\) −289.766 −0.397485
\(730\) 0 0
\(731\) −2.69701 1.55712i −0.00368948 0.00213012i
\(732\) 0 0
\(733\) 301.601 174.129i 0.411460 0.237557i −0.279957 0.960013i \(-0.590320\pi\)
0.691417 + 0.722456i \(0.256987\pi\)
\(734\) 0 0
\(735\) −237.503 + 640.973i −0.323133 + 0.872072i
\(736\) 0 0
\(737\) 228.346 + 395.507i 0.309832 + 0.536644i
\(738\) 0 0
\(739\) −270.743 + 468.941i −0.366364 + 0.634561i −0.988994 0.147955i \(-0.952731\pi\)
0.622630 + 0.782516i \(0.286064\pi\)
\(740\) 0 0
\(741\) 286.626i 0.386810i
\(742\) 0 0
\(743\) −702.388 −0.945340 −0.472670 0.881240i \(-0.656710\pi\)
−0.472670 + 0.881240i \(0.656710\pi\)
\(744\) 0 0
\(745\) −1503.20 867.873i −2.01772 1.16493i
\(746\) 0 0
\(747\) −252.292 + 145.661i −0.337740 + 0.194995i
\(748\) 0 0
\(749\) −307.134 + 653.708i −0.410059 + 0.872775i
\(750\) 0 0
\(751\) −19.0291 32.9593i −0.0253383 0.0438872i 0.853078 0.521783i \(-0.174733\pi\)
−0.878416 + 0.477896i \(0.841400\pi\)
\(752\) 0 0
\(753\) 80.9701 140.244i 0.107530 0.186247i
\(754\) 0 0
\(755\) 407.115i 0.539226i
\(756\) 0 0
\(757\) −451.849 −0.596895 −0.298447 0.954426i \(-0.596469\pi\)
−0.298447 + 0.954426i \(0.596469\pi\)
\(758\) 0 0
\(759\) 199.703 + 115.299i 0.263113 + 0.151909i
\(760\) 0 0
\(761\) 9.01729 5.20613i 0.0118493 0.00684117i −0.494064 0.869426i \(-0.664489\pi\)
0.505913 + 0.862585i \(0.331156\pi\)
\(762\) 0 0
\(763\) −289.833 + 24.5126i −0.379860 + 0.0321266i
\(764\) 0 0
\(765\) −202.533 350.798i −0.264749 0.458559i
\(766\) 0 0
\(767\) 21.5006 37.2401i 0.0280321 0.0485529i
\(768\) 0 0
\(769\) 1421.57i 1.84860i −0.381666 0.924300i \(-0.624649\pi\)
0.381666 0.924300i \(-0.375351\pi\)
\(770\) 0 0
\(771\) 343.943 0.446100
\(772\) 0 0
\(773\) 729.548 + 421.205i 0.943788 + 0.544897i 0.891146 0.453717i \(-0.149902\pi\)
0.0526426 + 0.998613i \(0.483236\pi\)
\(774\) 0 0
\(775\) 1596.61 921.801i 2.06014 1.18942i
\(776\) 0 0
\(777\) −75.9278 + 52.8386i −0.0977192 + 0.0680033i
\(778\) 0 0
\(779\) −470.892 815.609i −0.604482 1.04699i
\(780\) 0 0
\(781\) 71.7729 124.314i 0.0918987 0.159173i
\(782\) 0 0
\(783\) 1142.21i 1.45876i
\(784\) 0 0
\(785\) 1489.20 1.89707
\(786\) 0 0
\(787\) −419.051 241.939i −0.532466 0.307419i 0.209554 0.977797i \(-0.432799\pi\)
−0.742020 + 0.670378i \(0.766132\pi\)
\(788\) 0 0
\(789\) −297.958 + 172.026i −0.377640 + 0.218031i
\(790\) 0 0
\(791\)