Properties

Label 224.3.s.a.129.3
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 129.3
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.33.3

$q$-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 0.240820 0.970570i \(-0.422584\pi\)
−0.720128 + 0.693841i \(0.755917\pi\)
\(4\) 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 −0.959876 0.280423i \(-0.909525\pi\)
0.722792 + 0.691066i \(0.242858\pi\)
\(12\) 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 \(-0.286531\pi\)
0.989210 0.146506i \(-0.0468028\pi\)
\(20\) 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 \(-0.970168\pi\)
0.416762 0.909016i \(-0.363165\pi\)
\(24\) 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 −0.185824 0.982583i \(-0.559495\pi\)
−0.943854 + 0.330363i \(0.892829\pi\)
\(32\) 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 \(-0.498507\pi\)
0.00468930 + 0.999989i \(0.498507\pi\)
\(44\) 0 0
\(45\) −45.4267 26.2271i −1.00948 0.582825i
\(46\) 0 0
\(47\) −28.2845 + 16.3301i −0.601798 + 0.347448i −0.769748 0.638347i \(-0.779618\pi\)
0.167951 + 0.985795i \(0.446285\pi\)
\(48\) 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 0.434004 0.900911i \(-0.357100\pi\)
−0.563210 + 0.826314i \(0.690434\pi\)
\(60\) 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 \(-0.606667\pi\)
0.982287 0.187382i \(-0.0600001\pi\)
\(68\) 0 0
\(69\) 44.2108i 0.640737i
\(70\) 0 0
\(71\) −27.5210 −0.387620 −0.193810 0.981039i \(-0.562085\pi\)
−0.193810 + 0.981039i \(0.562085\pi\)
\(72\) 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 \(0.113183\pi\)
−0.167235 + 0.985917i \(0.553484\pi\)
\(80\) 0 0
\(81\) −7.08286 + 12.2679i −0.0874427 + 0.151455i
\(82\) 0 0
\(83\) 46.6625i 0.562198i 0.959679 + 0.281099i \(0.0906990\pi\)
−0.959679 + 0.281099i \(0.909301\pi\)
\(84\) 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 −0.998482 0.0550721i \(-0.982461\pi\)
−0.451547 + 0.892247i \(0.649128\pi\)
\(104\) 0 0
\(105\) −55.7789 80.1530i −0.531228 0.763362i
\(106\) 0 0
\(107\) 51.5903 + 89.3571i 0.482153 + 0.835113i 0.999790 0.0204873i \(-0.00652177\pi\)
−0.517638 + 0.855600i \(0.673188\pi\)
\(108\) 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 \(-0.325332\pi\)
0.521610 + 0.853184i \(0.325332\pi\)
\(128\) 0 0
\(129\) −0.579885 0.334797i −0.00449523 0.00259532i
\(130\) 0 0
\(131\) −64.1188 + 37.0190i −0.489456 + 0.282588i −0.724349 0.689434i \(-0.757859\pi\)
0.234893 + 0.972021i \(0.424526\pi\)
\(132\) 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 \(0.146718\pi\)
−0.895640 + 0.444780i \(0.853282\pi\)
\(140\) 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 −0.774581 0.632474i \(-0.782039\pi\)
0.935030 + 0.354570i \(0.115373\pi\)
\(152\) 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 0.602946 0.797782i \(-0.293994\pi\)
−0.992373 + 0.123275i \(0.960660\pi\)
\(164\) 0 0
\(165\) 36.3811 63.0139i 0.220492 0.381903i
\(166\) 0 0
\(167\) 191.898i 1.14909i 0.818472 + 0.574546i \(0.194821\pi\)
−0.818472 + 0.574546i \(0.805179\pi\)
\(168\) 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 \(-0.598194\pi\)
0.976952 0.213459i \(-0.0684730\pi\)
\(180\) 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 \(-0.923359\pi\)
0.279069 0.960271i \(-0.409974\pi\)
\(192\) 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 −0.0115150 0.999934i \(-0.503665\pi\)
−0.871726 + 0.489995i \(0.836999\pi\)
\(200\) 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 \(-0.370873\pi\)
0.394628 + 0.918841i \(0.370873\pi\)
\(212\) 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 \(0.0394099\pi\)
−0.992345 + 0.123494i \(0.960590\pi\)
\(224\) 0 0
\(225\) −284.634 −1.26504
\(226\) 0 0
\(227\) 184.119 + 106.301i 0.811099 + 0.468288i 0.847337 0.531055i \(-0.178204\pi\)
−0.0362385 + 0.999343i \(0.511538\pi\)
\(228\) 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 \(-0.802816\pi\)
−0.814185 + 0.580605i \(0.802816\pi\)
\(240\) 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 \(0.0622396\pi\)
−0.980945 + 0.194288i \(0.937760\pi\)
\(252\) 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 −0.599022 0.800732i \(-0.704444\pi\)
0.992966 + 0.118402i \(0.0377773\pi\)
\(264\) 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 −0.372478 0.928041i \(-0.621492\pi\)
0.617468 + 0.786596i \(0.288159\pi\)
\(272\) 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 0.263561 0.964643i \(-0.415103\pi\)
−0.703625 + 0.710572i \(0.748436\pi\)
\(284\) 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 \(-0.848330\pi\)
0.888612 0.458659i \(-0.151670\pi\)
\(308\) 0 0
\(309\) 286.344 0.926680
\(310\) 0 0
\(311\) 48.8342 + 28.1945i 0.157023 + 0.0906574i 0.576453 0.817131i \(-0.304437\pi\)
−0.419429 + 0.907788i \(0.637770\pi\)
\(312\) 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 \(0.153911\pi\)
−0.0400619 + 0.999197i \(0.512756\pi\)
\(332\) 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 \(-0.644312\pi\)
0.997535 0.0701703i \(-0.0223543\pi\)
\(348\) 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 0.601747 0.798687i \(-0.294472\pi\)
−0.992557 + 0.121785i \(0.961138\pi\)
\(360\) 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 0.523413 0.852079i \(-0.324659\pi\)
−0.476216 + 0.879328i \(0.657992\pi\)
\(368\) 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 \(-0.324324\pi\)
0.524308 + 0.851529i \(0.324324\pi\)
\(380\) 0 0
\(381\) −190.509 109.990i −0.500023 0.288689i
\(382\) 0 0
\(383\) −232.209 + 134.066i −0.606291 + 0.350042i −0.771512 0.636214i \(-0.780499\pi\)
0.165222 + 0.986256i \(0.447166\pi\)
\(384\) 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 \(0.211212\pi\)
−0.787815 + 0.615911i \(0.788788\pi\)
\(420\) 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 −0.917090 0.398681i \(-0.869468\pi\)
0.803812 + 0.594883i \(0.202802\pi\)
\(432\) 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 −0.210160 0.977667i \(-0.567399\pi\)
0.741604 + 0.670838i \(0.234065\pi\)
\(440\) 0 0
\(441\) 301.570 51.3780i 0.683832 0.116503i
\(442\) 0 0
\(443\) −170.985 296.155i −0.385971 0.668522i 0.605932 0.795516i \(-0.292800\pi\)
−0.991903 + 0.126994i \(0.959467\pi\)
\(444\) 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 \(-0.301141\pi\)
0.584882 + 0.811118i \(0.301141\pi\)
\(464\) 0 0
\(465\) 488.536 + 282.056i 1.05062 + 0.606573i
\(466\) 0 0
\(467\) 134.069 77.4045i 0.287085 0.165748i −0.349542 0.936921i \(-0.613663\pi\)
0.636626 + 0.771172i \(0.280329\pi\)
\(468\) 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 0.983313 0.181921i \(-0.0582316\pi\)
0.334108 + 0.942535i \(0.391565\pi\)
\(480\) 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 −0.999007 0.0445466i \(-0.985816\pi\)
0.538082 + 0.842892i \(0.319149\pi\)
\(488\) 0 0
\(489\) 210.789i 0.431062i
\(490\) 0 0
\(491\) −73.5801 −0.149858 −0.0749288 0.997189i \(-0.523873\pi\)
−0.0749288 + 0.997189i \(0.523873\pi\)
\(492\) 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 \(-0.831976\pi\)
−0.00426366 0.999991i \(-0.501357\pi\)
\(500\) 0 0
\(501\) 159.311 275.935i 0.317986 0.550768i
\(502\) 0 0
\(503\) 306.742i 0.609825i −0.952380 0.304913i \(-0.901373\pi\)
0.952380 0.304913i \(-0.0986272\pi\)
\(504\) 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 −0.208479 0.978027i \(-0.566851\pi\)
0.742757 + 0.669561i \(0.233518\pi\)
\(524\) 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 \(-0.428229\pi\)
0.223569 + 0.974688i \(0.428229\pi\)
\(548\) 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 −0.00445194 0.999990i \(-0.501417\pi\)
−0.868243 + 0.496140i \(0.834750\pi\)
\(564\) 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 −0.998152 0.0607673i \(-0.980645\pi\)
0.551702 + 0.834041i \(0.313979\pi\)
\(572\) 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 \(0.165071\pi\)
−0.868520 + 0.495654i \(0.834929\pi\)
\(588\) 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 −0.836805 0.547502i \(-0.815579\pi\)
0.892553 + 0.450943i \(0.148912\pi\)
\(600\) 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 −0.875205 0.483753i \(-0.839273\pi\)
−0.0186599 + 0.999826i \(0.505940\pi\)
\(608\) 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 0.660988 0.750397i \(-0.270138\pi\)
−0.319369 + 0.947630i \(0.603471\pi\)
\(620\) 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 \(-0.256597\pi\)
0.692300 + 0.721609i \(0.256597\pi\)
\(632\) 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 \(0.0203451\pi\)
−0.997958 + 0.0638726i \(0.979655\pi\)
\(644\) 0 0
\(645\) −5.62583 −0.00872221
\(646\) 0 0
\(647\) −155.391 89.7147i −0.240171 0.138663i 0.375084 0.926991i \(-0.377614\pi\)
−0.615255 + 0.788328i \(0.710947\pi\)
\(648\) 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 \(-0.468801\pi\)
0.0978590 + 0.995200i \(0.468801\pi\)
\(660\) 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 −0.967991 0.250985i \(-0.919245\pi\)
0.701355 + 0.712812i \(0.252579\pi\)
\(684\) 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 −0.981236 0.192809i \(-0.938240\pi\)
−0.323641 + 0.946180i \(0.604907\pi\)
\(692\) 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 −0.849769 0.527156i \(-0.823259\pi\)
0.0316457 + 0.999499i \(0.489925\pi\)
\(720\) 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 \(-0.733799\pi\)
0.670217 0.742166i \(-0.266201\pi\)
\(728\) 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 −0.622630 0.782516i \(-0.713936\pi\)
0.988994 + 0.147955i \(0.0472691\pi\)
\(740\) 0 0
\(741\) 286.626i 0.386810i
\(742\) 0 0
\(743\) 702.388 0.945340 0.472670 0.881240i \(-0.343290\pi\)
0.472670 + 0.881240i \(0.343290\pi\)
\(744\) 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 0.878416 0.477896i \(-0.158600\pi\)
−0.853078 + 0.521783i \(0.825267\pi\)
\(752\) 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 0.742020 0.670378i \(-0.233868\pi\)
−0.209554 + 0.977797i \(0.567201\pi\)
\(788\) 0 0
\(789\) −297.958 + 172.026i −0.377640 + 0.218031i
\(790\) 0 0
\(791\) −535.328