Properties

Label 1440.2.q.q.481.1
Level $1440$
Weight $2$
Character 1440.481
Analytic conductor $11.498$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + x^{10} + 4 x^{8} - 21 x^{6} + 36 x^{4} + 81 x^{2} + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 481.1
Root \(1.66309 - 0.483872i\) of defining polynomial
Character \(\chi\) \(=\) 1440.481
Dual form 1440.2.q.q.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.66309 - 0.483872i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.56078 - 2.70334i) q^{7} +(2.53174 + 1.60944i) q^{9} +O(q^{10})\) \(q+(-1.66309 - 0.483872i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.56078 - 2.70334i) q^{7} +(2.53174 + 1.60944i) q^{9} +(-0.412500 - 0.714470i) q^{11} +(-3.03174 + 5.25112i) q^{13} +(-1.25059 + 1.19834i) q^{15} -2.74410 q^{17} -0.824999 q^{19} +(1.28764 + 5.25112i) q^{21} +(-1.76540 + 3.05777i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.43174 - 3.90169i) q^{27} +(3.15969 + 5.47274i) q^{29} +(3.63637 - 6.29837i) q^{31} +(0.340312 + 1.38783i) q^{33} -3.12155 q^{35} -2.06347 q^{37} +(7.58292 - 7.26611i) q^{39} +(2.78764 - 4.82833i) q^{41} +(3.73868 + 6.47558i) q^{43} +(2.65969 - 1.38783i) q^{45} +(3.75177 + 6.49826i) q^{47} +(-1.37205 + 2.37646i) q^{49} +(4.56368 + 1.32779i) q^{51} -1.48819 q^{53} -0.824999 q^{55} +(1.37205 + 0.399194i) q^{57} +(0.722686 - 1.25173i) q^{59} +(4.19142 + 7.25976i) q^{61} +(0.399409 - 9.35614i) q^{63} +(3.03174 + 5.25112i) q^{65} +(-5.91983 + 10.2534i) q^{67} +(4.41559 - 4.23111i) q^{69} -15.5751 q^{71} +13.4463 q^{73} +(0.412500 + 1.68221i) q^{75} +(-1.28764 + 2.23026i) q^{77} +(7.06811 + 12.2423i) q^{79} +(3.81938 + 8.14938i) q^{81} +(2.18115 + 3.77786i) q^{83} +(-1.37205 + 2.37646i) q^{85} +(-2.60674 - 10.6305i) q^{87} -2.83118 q^{89} +18.9275 q^{91} +(-9.09521 + 8.71522i) q^{93} +(-0.412500 + 0.714470i) q^{95} +(2.65969 + 4.60671i) q^{97} +(0.105560 - 2.47275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{5} - 2 q^{9} + O(q^{10}) \) \( 12 q + 6 q^{5} - 2 q^{9} - 4 q^{13} - 28 q^{17} - 12 q^{21} - 6 q^{25} + 8 q^{29} + 34 q^{33} + 40 q^{37} + 6 q^{41} + 2 q^{45} - 14 q^{49} - 8 q^{53} + 14 q^{57} - 12 q^{61} + 4 q^{65} + 28 q^{69} - 28 q^{73} + 12 q^{77} - 14 q^{81} - 14 q^{85} + 16 q^{89} - 12 q^{93} + 2 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.66309 0.483872i −0.960185 0.279364i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −1.56078 2.70334i −0.589918 1.02177i −0.994243 0.107153i \(-0.965827\pi\)
0.404324 0.914616i \(-0.367507\pi\)
\(8\) 0 0
\(9\) 2.53174 + 1.60944i 0.843912 + 0.536482i
\(10\) 0 0
\(11\) −0.412500 0.714470i −0.124373 0.215421i 0.797114 0.603828i \(-0.206359\pi\)
−0.921488 + 0.388407i \(0.873025\pi\)
\(12\) 0 0
\(13\) −3.03174 + 5.25112i −0.840852 + 1.45640i 0.0483227 + 0.998832i \(0.484612\pi\)
−0.889175 + 0.457567i \(0.848721\pi\)
\(14\) 0 0
\(15\) −1.25059 + 1.19834i −0.322901 + 0.309411i
\(16\) 0 0
\(17\) −2.74410 −0.665541 −0.332771 0.943008i \(-0.607983\pi\)
−0.332771 + 0.943008i \(0.607983\pi\)
\(18\) 0 0
\(19\) −0.824999 −0.189268 −0.0946339 0.995512i \(-0.530168\pi\)
−0.0946339 + 0.995512i \(0.530168\pi\)
\(20\) 0 0
\(21\) 1.28764 + 5.25112i 0.280986 + 1.14589i
\(22\) 0 0
\(23\) −1.76540 + 3.05777i −0.368112 + 0.637589i −0.989270 0.146096i \(-0.953329\pi\)
0.621158 + 0.783685i \(0.286662\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −3.43174 3.90169i −0.660439 0.750880i
\(28\) 0 0
\(29\) 3.15969 + 5.47274i 0.586739 + 1.01626i 0.994656 + 0.103243i \(0.0329220\pi\)
−0.407917 + 0.913019i \(0.633745\pi\)
\(30\) 0 0
\(31\) 3.63637 6.29837i 0.653111 1.13122i −0.329253 0.944242i \(-0.606797\pi\)
0.982364 0.186979i \(-0.0598697\pi\)
\(32\) 0 0
\(33\) 0.340312 + 1.38783i 0.0592407 + 0.241589i
\(34\) 0 0
\(35\) −3.12155 −0.527639
\(36\) 0 0
\(37\) −2.06347 −0.339233 −0.169616 0.985510i \(-0.554253\pi\)
−0.169616 + 0.985510i \(0.554253\pi\)
\(38\) 0 0
\(39\) 7.58292 7.26611i 1.21424 1.16351i
\(40\) 0 0
\(41\) 2.78764 4.82833i 0.435356 0.754059i −0.561968 0.827159i \(-0.689956\pi\)
0.997325 + 0.0730996i \(0.0232891\pi\)
\(42\) 0 0
\(43\) 3.73868 + 6.47558i 0.570143 + 0.987517i 0.996551 + 0.0829859i \(0.0264457\pi\)
−0.426407 + 0.904531i \(0.640221\pi\)
\(44\) 0 0
\(45\) 2.65969 1.38783i 0.396483 0.206885i
\(46\) 0 0
\(47\) 3.75177 + 6.49826i 0.547252 + 0.947868i 0.998461 + 0.0554502i \(0.0176594\pi\)
−0.451209 + 0.892418i \(0.649007\pi\)
\(48\) 0 0
\(49\) −1.37205 + 2.37646i −0.196007 + 0.339494i
\(50\) 0 0
\(51\) 4.56368 + 1.32779i 0.639043 + 0.185928i
\(52\) 0 0
\(53\) −1.48819 −0.204419 −0.102209 0.994763i \(-0.532591\pi\)
−0.102209 + 0.994763i \(0.532591\pi\)
\(54\) 0 0
\(55\) −0.824999 −0.111243
\(56\) 0 0
\(57\) 1.37205 + 0.399194i 0.181732 + 0.0528745i
\(58\) 0 0
\(59\) 0.722686 1.25173i 0.0940857 0.162961i −0.815141 0.579263i \(-0.803341\pi\)
0.909227 + 0.416301i \(0.136674\pi\)
\(60\) 0 0
\(61\) 4.19142 + 7.25976i 0.536657 + 0.929517i 0.999081 + 0.0428582i \(0.0136464\pi\)
−0.462424 + 0.886659i \(0.653020\pi\)
\(62\) 0 0
\(63\) 0.399409 9.35614i 0.0503207 1.17876i
\(64\) 0 0
\(65\) 3.03174 + 5.25112i 0.376041 + 0.651321i
\(66\) 0 0
\(67\) −5.91983 + 10.2534i −0.723222 + 1.25266i 0.236479 + 0.971637i \(0.424006\pi\)
−0.959702 + 0.281021i \(0.909327\pi\)
\(68\) 0 0
\(69\) 4.41559 4.23111i 0.531575 0.509366i
\(70\) 0 0
\(71\) −15.5751 −1.84842 −0.924212 0.381881i \(-0.875277\pi\)
−0.924212 + 0.381881i \(0.875277\pi\)
\(72\) 0 0
\(73\) 13.4463 1.57377 0.786886 0.617098i \(-0.211692\pi\)
0.786886 + 0.617098i \(0.211692\pi\)
\(74\) 0 0
\(75\) 0.412500 + 1.68221i 0.0476314 + 0.194245i
\(76\) 0 0
\(77\) −1.28764 + 2.23026i −0.146740 + 0.254161i
\(78\) 0 0
\(79\) 7.06811 + 12.2423i 0.795224 + 1.37737i 0.922697 + 0.385526i \(0.125980\pi\)
−0.127473 + 0.991842i \(0.540687\pi\)
\(80\) 0 0
\(81\) 3.81938 + 8.14938i 0.424375 + 0.905486i
\(82\) 0 0
\(83\) 2.18115 + 3.77786i 0.239412 + 0.414674i 0.960546 0.278122i \(-0.0897119\pi\)
−0.721134 + 0.692796i \(0.756379\pi\)
\(84\) 0 0
\(85\) −1.37205 + 2.37646i −0.148820 + 0.257763i
\(86\) 0 0
\(87\) −2.60674 10.6305i −0.279472 1.13971i
\(88\) 0 0
\(89\) −2.83118 −0.300105 −0.150052 0.988678i \(-0.547944\pi\)
−0.150052 + 0.988678i \(0.547944\pi\)
\(90\) 0 0
\(91\) 18.9275 1.98414
\(92\) 0 0
\(93\) −9.09521 + 8.71522i −0.943129 + 0.903726i
\(94\) 0 0
\(95\) −0.412500 + 0.714470i −0.0423216 + 0.0733031i
\(96\) 0 0
\(97\) 2.65969 + 4.60671i 0.270050 + 0.467741i 0.968874 0.247553i \(-0.0796263\pi\)
−0.698824 + 0.715294i \(0.746293\pi\)
\(98\) 0 0
\(99\) 0.105560 2.47275i 0.0106092 0.248520i
\(100\) 0 0
\(101\) 8.06347 + 13.9663i 0.802345 + 1.38970i 0.918069 + 0.396422i \(0.129748\pi\)
−0.115723 + 0.993282i \(0.536919\pi\)
\(102\) 0 0
\(103\) −1.33981 + 2.32062i −0.132016 + 0.228658i −0.924453 0.381295i \(-0.875478\pi\)
0.792438 + 0.609953i \(0.208812\pi\)
\(104\) 0 0
\(105\) 5.19142 + 1.51043i 0.506631 + 0.147403i
\(106\) 0 0
\(107\) −16.2216 −1.56821 −0.784103 0.620631i \(-0.786877\pi\)
−0.784103 + 0.620631i \(0.786877\pi\)
\(108\) 0 0
\(109\) −9.87104 −0.945474 −0.472737 0.881204i \(-0.656734\pi\)
−0.472737 + 0.881204i \(0.656734\pi\)
\(110\) 0 0
\(111\) 3.43174 + 0.998456i 0.325726 + 0.0947693i
\(112\) 0 0
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 1.76540 + 3.05777i 0.164625 + 0.285138i
\(116\) 0 0
\(117\) −16.1269 + 8.41504i −1.49094 + 0.777971i
\(118\) 0 0
\(119\) 4.28292 + 7.41824i 0.392615 + 0.680029i
\(120\) 0 0
\(121\) 5.15969 8.93684i 0.469063 0.812440i
\(122\) 0 0
\(123\) −6.97239 + 6.68109i −0.628679 + 0.602414i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.91043 0.258259 0.129130 0.991628i \(-0.458782\pi\)
0.129130 + 0.991628i \(0.458782\pi\)
\(128\) 0 0
\(129\) −3.08441 12.5785i −0.271567 1.10748i
\(130\) 0 0
\(131\) −5.00236 + 8.66434i −0.437058 + 0.757007i −0.997461 0.0712130i \(-0.977313\pi\)
0.560403 + 0.828220i \(0.310646\pi\)
\(132\) 0 0
\(133\) 1.28764 + 2.23026i 0.111653 + 0.193388i
\(134\) 0 0
\(135\) −5.09483 + 1.02113i −0.438493 + 0.0878849i
\(136\) 0 0
\(137\) 2.34031 + 4.05354i 0.199946 + 0.346317i 0.948511 0.316745i \(-0.102590\pi\)
−0.748564 + 0.663062i \(0.769257\pi\)
\(138\) 0 0
\(139\) 8.02160 13.8938i 0.680383 1.17846i −0.294481 0.955657i \(-0.595147\pi\)
0.974864 0.222801i \(-0.0715200\pi\)
\(140\) 0 0
\(141\) −3.09521 12.6226i −0.260664 1.06301i
\(142\) 0 0
\(143\) 5.00236 0.418318
\(144\) 0 0
\(145\) 6.31938 0.524796
\(146\) 0 0
\(147\) 3.43174 3.28837i 0.283045 0.271220i
\(148\) 0 0
\(149\) −9.25490 + 16.0300i −0.758191 + 1.31322i 0.185582 + 0.982629i \(0.440583\pi\)
−0.943772 + 0.330596i \(0.892750\pi\)
\(150\) 0 0
\(151\) −1.98637 3.44049i −0.161648 0.279983i 0.773812 0.633416i \(-0.218348\pi\)
−0.935460 + 0.353433i \(0.885014\pi\)
\(152\) 0 0
\(153\) −6.94733 4.41647i −0.561658 0.357051i
\(154\) 0 0
\(155\) −3.63637 6.29837i −0.292080 0.505897i
\(156\) 0 0
\(157\) −0.511807 + 0.886476i −0.0408467 + 0.0707485i −0.885726 0.464208i \(-0.846339\pi\)
0.844879 + 0.534957i \(0.179672\pi\)
\(158\) 0 0
\(159\) 2.47500 + 0.720094i 0.196280 + 0.0571072i
\(160\) 0 0
\(161\) 11.0216 0.868624
\(162\) 0 0
\(163\) 20.6298 1.61585 0.807926 0.589284i \(-0.200590\pi\)
0.807926 + 0.589284i \(0.200590\pi\)
\(164\) 0 0
\(165\) 1.37205 + 0.399194i 0.106814 + 0.0310772i
\(166\) 0 0
\(167\) −9.57913 + 16.5915i −0.741255 + 1.28389i 0.210669 + 0.977558i \(0.432436\pi\)
−0.951924 + 0.306334i \(0.900897\pi\)
\(168\) 0 0
\(169\) −11.8828 20.5817i −0.914065 1.58321i
\(170\) 0 0
\(171\) −2.08868 1.32779i −0.159725 0.101539i
\(172\) 0 0
\(173\) −6.80757 11.7911i −0.517570 0.896457i −0.999792 0.0204082i \(-0.993503\pi\)
0.482222 0.876049i \(-0.339830\pi\)
\(174\) 0 0
\(175\) −1.56078 + 2.70334i −0.117984 + 0.204354i
\(176\) 0 0
\(177\) −1.80757 + 1.73205i −0.135865 + 0.130189i
\(178\) 0 0
\(179\) 1.86112 0.139107 0.0695533 0.997578i \(-0.477843\pi\)
0.0695533 + 0.997578i \(0.477843\pi\)
\(180\) 0 0
\(181\) 16.9581 1.26049 0.630244 0.776397i \(-0.282955\pi\)
0.630244 + 0.776397i \(0.282955\pi\)
\(182\) 0 0
\(183\) −3.45792 14.1017i −0.255617 1.04243i
\(184\) 0 0
\(185\) −1.03174 + 1.78702i −0.0758548 + 0.131384i
\(186\) 0 0
\(187\) 1.13194 + 1.96058i 0.0827756 + 0.143371i
\(188\) 0 0
\(189\) −5.19142 + 15.3668i −0.377621 + 1.11777i
\(190\) 0 0
\(191\) 4.69217 + 8.12708i 0.339514 + 0.588055i 0.984341 0.176273i \(-0.0564041\pi\)
−0.644828 + 0.764328i \(0.723071\pi\)
\(192\) 0 0
\(193\) 3.11614 5.39732i 0.224305 0.388508i −0.731806 0.681513i \(-0.761322\pi\)
0.956111 + 0.293006i \(0.0946555\pi\)
\(194\) 0 0
\(195\) −2.50118 10.2001i −0.179113 0.730441i
\(196\) 0 0
\(197\) −16.6388 −1.18546 −0.592731 0.805400i \(-0.701950\pi\)
−0.592731 + 0.805400i \(0.701950\pi\)
\(198\) 0 0
\(199\) 7.68199 0.544562 0.272281 0.962218i \(-0.412222\pi\)
0.272281 + 0.962218i \(0.412222\pi\)
\(200\) 0 0
\(201\) 14.8066 14.1880i 1.04437 1.00074i
\(202\) 0 0
\(203\) 9.86314 17.0835i 0.692256 1.19902i
\(204\) 0 0
\(205\) −2.78764 4.82833i −0.194697 0.337225i
\(206\) 0 0
\(207\) −9.39084 + 4.90014i −0.652709 + 0.340583i
\(208\) 0 0
\(209\) 0.340312 + 0.589438i 0.0235399 + 0.0407723i
\(210\) 0 0
\(211\) 0.540995 0.937031i 0.0372436 0.0645079i −0.846803 0.531907i \(-0.821476\pi\)
0.884046 + 0.467399i \(0.154809\pi\)
\(212\) 0 0
\(213\) 25.9028 + 7.53635i 1.77483 + 0.516382i
\(214\) 0 0
\(215\) 7.47736 0.509952
\(216\) 0 0
\(217\) −22.7022 −1.54113
\(218\) 0 0
\(219\) −22.3624 6.50630i −1.51111 0.439655i
\(220\) 0 0
\(221\) 8.31938 14.4096i 0.559622 0.969293i
\(222\) 0 0
\(223\) 8.54951 + 14.8082i 0.572517 + 0.991629i 0.996307 + 0.0858681i \(0.0273664\pi\)
−0.423789 + 0.905761i \(0.639300\pi\)
\(224\) 0 0
\(225\) 0.127952 2.99727i 0.00853012 0.199818i
\(226\) 0 0
\(227\) −6.86023 11.8823i −0.455330 0.788654i 0.543377 0.839489i \(-0.317145\pi\)
−0.998707 + 0.0508344i \(0.983812\pi\)
\(228\) 0 0
\(229\) −6.15969 + 10.6689i −0.407044 + 0.705020i −0.994557 0.104194i \(-0.966774\pi\)
0.587513 + 0.809214i \(0.300107\pi\)
\(230\) 0 0
\(231\) 3.22062 3.08607i 0.211901 0.203048i
\(232\) 0 0
\(233\) −9.76771 −0.639904 −0.319952 0.947434i \(-0.603667\pi\)
−0.319952 + 0.947434i \(0.603667\pi\)
\(234\) 0 0
\(235\) 7.50354 0.489477
\(236\) 0 0
\(237\) −5.83118 23.7801i −0.378776 1.54469i
\(238\) 0 0
\(239\) −11.6285 + 20.1412i −0.752188 + 1.30283i 0.194573 + 0.980888i \(0.437668\pi\)
−0.946760 + 0.321939i \(0.895665\pi\)
\(240\) 0 0
\(241\) 14.0834 + 24.3932i 0.907192 + 1.57130i 0.817948 + 0.575292i \(0.195112\pi\)
0.0892436 + 0.996010i \(0.471555\pi\)
\(242\) 0 0
\(243\) −2.40871 15.4012i −0.154519 0.987990i
\(244\) 0 0
\(245\) 1.37205 + 2.37646i 0.0876569 + 0.151826i
\(246\) 0 0
\(247\) 2.50118 4.33217i 0.159146 0.275649i
\(248\) 0 0
\(249\) −1.79945 7.33832i −0.114035 0.465047i
\(250\) 0 0
\(251\) −19.5413 −1.23344 −0.616719 0.787183i \(-0.711539\pi\)
−0.616719 + 0.787183i \(0.711539\pi\)
\(252\) 0 0
\(253\) 2.91291 0.183133
\(254\) 0 0
\(255\) 3.43174 3.28837i 0.214904 0.205925i
\(256\) 0 0
\(257\) 9.14788 15.8446i 0.570629 0.988359i −0.425872 0.904783i \(-0.640033\pi\)
0.996501 0.0835754i \(-0.0266339\pi\)
\(258\) 0 0
\(259\) 3.22062 + 5.57828i 0.200120 + 0.346617i
\(260\) 0 0
\(261\) −0.808576 + 18.9409i −0.0500496 + 1.17241i
\(262\) 0 0
\(263\) −6.55329 11.3506i −0.404093 0.699910i 0.590122 0.807314i \(-0.299080\pi\)
−0.994215 + 0.107404i \(0.965746\pi\)
\(264\) 0 0
\(265\) −0.744096 + 1.28881i −0.0457095 + 0.0791711i
\(266\) 0 0
\(267\) 4.70851 + 1.36993i 0.288156 + 0.0838383i
\(268\) 0 0
\(269\) −4.25590 −0.259487 −0.129744 0.991548i \(-0.541415\pi\)
−0.129744 + 0.991548i \(0.541415\pi\)
\(270\) 0 0
\(271\) −28.9322 −1.75750 −0.878752 0.477278i \(-0.841623\pi\)
−0.878752 + 0.477278i \(0.841623\pi\)
\(272\) 0 0
\(273\) −31.4781 9.15846i −1.90514 0.554295i
\(274\) 0 0
\(275\) −0.412500 + 0.714470i −0.0248747 + 0.0430842i
\(276\) 0 0
\(277\) −16.1587 27.9877i −0.970881 1.68162i −0.692907 0.721027i \(-0.743671\pi\)
−0.277974 0.960589i \(-0.589663\pi\)
\(278\) 0 0
\(279\) 19.3432 10.0933i 1.15805 0.604269i
\(280\) 0 0
\(281\) −6.19142 10.7239i −0.369349 0.639732i 0.620115 0.784511i \(-0.287086\pi\)
−0.989464 + 0.144779i \(0.953753\pi\)
\(282\) 0 0
\(283\) −4.86077 + 8.41911i −0.288943 + 0.500464i −0.973558 0.228441i \(-0.926637\pi\)
0.684615 + 0.728905i \(0.259970\pi\)
\(284\) 0 0
\(285\) 1.03174 0.988632i 0.0611148 0.0585615i
\(286\) 0 0
\(287\) −17.4035 −1.02730
\(288\) 0 0
\(289\) −9.46994 −0.557055
\(290\) 0 0
\(291\) −2.19424 8.94833i −0.128629 0.524560i
\(292\) 0 0
\(293\) 6.60702 11.4437i 0.385986 0.668547i −0.605919 0.795526i \(-0.707195\pi\)
0.991905 + 0.126979i \(0.0405280\pi\)
\(294\) 0 0
\(295\) −0.722686 1.25173i −0.0420764 0.0728785i
\(296\) 0 0
\(297\) −1.37205 + 4.06132i −0.0796143 + 0.235662i
\(298\) 0 0
\(299\) −10.7045 18.5407i −0.619056 1.07224i
\(300\) 0 0
\(301\) 11.6705 20.2139i 0.672676 1.16511i
\(302\) 0 0
\(303\) −6.65236 27.1290i −0.382168 1.55852i
\(304\) 0 0
\(305\) 8.38285 0.480001
\(306\) 0 0
\(307\) 29.9486 1.70926 0.854629 0.519240i \(-0.173785\pi\)
0.854629 + 0.519240i \(0.173785\pi\)
\(308\) 0 0
\(309\) 3.35111 3.21111i 0.190638 0.182674i
\(310\) 0 0
\(311\) −11.1399 + 19.2949i −0.631686 + 1.09411i 0.355521 + 0.934668i \(0.384304\pi\)
−0.987207 + 0.159444i \(0.949030\pi\)
\(312\) 0 0
\(313\) −6.75490 11.6998i −0.381809 0.661313i 0.609512 0.792777i \(-0.291366\pi\)
−0.991321 + 0.131464i \(0.958032\pi\)
\(314\) 0 0
\(315\) −7.90295 5.02397i −0.445281 0.283069i
\(316\) 0 0
\(317\) −13.4781 23.3447i −0.757003 1.31117i −0.944372 0.328878i \(-0.893329\pi\)
0.187369 0.982290i \(-0.440004\pi\)
\(318\) 0 0
\(319\) 2.60674 4.51501i 0.145949 0.252792i
\(320\) 0 0
\(321\) 26.9781 + 7.84920i 1.50577 + 0.438099i
\(322\) 0 0
\(323\) 2.26388 0.125966
\(324\) 0 0
\(325\) 6.06347 0.336341
\(326\) 0 0
\(327\) 16.4164 + 4.77632i 0.907831 + 0.264131i
\(328\) 0 0
\(329\) 11.7114 20.2847i 0.645668 1.11833i
\(330\) 0 0
\(331\) 7.04192 + 12.1970i 0.387059 + 0.670406i 0.992053 0.125824i \(-0.0401576\pi\)
−0.604993 + 0.796231i \(0.706824\pi\)
\(332\) 0 0
\(333\) −5.22417 3.32104i −0.286283 0.181992i
\(334\) 0 0
\(335\) 5.91983 + 10.2534i 0.323435 + 0.560206i
\(336\) 0 0
\(337\) −0.403784 + 0.699375i −0.0219955 + 0.0380974i −0.876814 0.480830i \(-0.840335\pi\)
0.854818 + 0.518928i \(0.173669\pi\)
\(338\) 0 0
\(339\) −7.50354 + 7.19005i −0.407536 + 0.390510i
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −13.2850 −0.717324
\(344\) 0 0
\(345\) −1.45646 5.93957i −0.0784130 0.319776i
\(346\) 0 0
\(347\) −2.70905 + 4.69222i −0.145430 + 0.251892i −0.929533 0.368739i \(-0.879790\pi\)
0.784104 + 0.620630i \(0.213123\pi\)
\(348\) 0 0
\(349\) −1.84031 3.18751i −0.0985096 0.170624i 0.812558 0.582880i \(-0.198074\pi\)
−0.911068 + 0.412256i \(0.864741\pi\)
\(350\) 0 0
\(351\) 30.8924 6.19160i 1.64891 0.330483i
\(352\) 0 0
\(353\) 9.34031 + 16.1779i 0.497135 + 0.861062i 0.999995 0.00330547i \(-0.00105217\pi\)
−0.502860 + 0.864368i \(0.667719\pi\)
\(354\) 0 0
\(355\) −7.78755 + 13.4884i −0.413320 + 0.715891i
\(356\) 0 0
\(357\) −3.53341 14.4096i −0.187008 0.762636i
\(358\) 0 0
\(359\) −28.4706 −1.50262 −0.751309 0.659950i \(-0.770577\pi\)
−0.751309 + 0.659950i \(0.770577\pi\)
\(360\) 0 0
\(361\) −18.3194 −0.964178
\(362\) 0 0
\(363\) −12.9053 + 12.3661i −0.677353 + 0.649054i
\(364\) 0 0
\(365\) 6.72316 11.6449i 0.351906 0.609520i
\(366\) 0 0
\(367\) −12.5853 21.7983i −0.656946 1.13786i −0.981402 0.191963i \(-0.938514\pi\)
0.324456 0.945901i \(-0.394819\pi\)
\(368\) 0 0
\(369\) 14.8285 7.73752i 0.771941 0.402799i
\(370\) 0 0
\(371\) 2.32274 + 4.02310i 0.120590 + 0.208869i
\(372\) 0 0
\(373\) −12.8710 + 22.2933i −0.666437 + 1.15430i 0.312456 + 0.949932i \(0.398848\pi\)
−0.978894 + 0.204371i \(0.934485\pi\)
\(374\) 0 0
\(375\) 1.66309 + 0.483872i 0.0858816 + 0.0249870i
\(376\) 0 0
\(377\) −38.3174 −1.97344
\(378\) 0 0
\(379\) 7.67549 0.394264 0.197132 0.980377i \(-0.436837\pi\)
0.197132 + 0.980377i \(0.436837\pi\)
\(380\) 0 0
\(381\) −4.84031 1.40828i −0.247977 0.0721482i
\(382\) 0 0
\(383\) −1.55093 + 2.68629i −0.0792490 + 0.137263i −0.902926 0.429796i \(-0.858586\pi\)
0.823677 + 0.567059i \(0.191919\pi\)
\(384\) 0 0
\(385\) 1.28764 + 2.23026i 0.0656242 + 0.113664i
\(386\) 0 0
\(387\) −0.956742 + 22.4117i −0.0486339 + 1.13925i
\(388\) 0 0
\(389\) −2.93552 5.08447i −0.148837 0.257793i 0.781961 0.623327i \(-0.214220\pi\)
−0.930798 + 0.365534i \(0.880886\pi\)
\(390\) 0 0
\(391\) 4.84444 8.39081i 0.244994 0.424341i
\(392\) 0 0
\(393\) 12.5118 11.9891i 0.631137 0.604769i
\(394\) 0 0
\(395\) 14.1362 0.711270
\(396\) 0 0
\(397\) −9.66237 −0.484940 −0.242470 0.970159i \(-0.577958\pi\)
−0.242470 + 0.970159i \(0.577958\pi\)
\(398\) 0 0
\(399\) −1.06230 4.33217i −0.0531816 0.216880i
\(400\) 0 0
\(401\) 3.85212 6.67207i 0.192366 0.333187i −0.753668 0.657255i \(-0.771717\pi\)
0.946034 + 0.324068i \(0.105051\pi\)
\(402\) 0 0
\(403\) 22.0490 + 38.1900i 1.09834 + 1.90238i
\(404\) 0 0
\(405\) 8.96726 + 0.767012i 0.445587 + 0.0381132i
\(406\) 0 0
\(407\) 0.851182 + 1.47429i 0.0421915 + 0.0730778i
\(408\) 0 0
\(409\) 3.21135 5.56223i 0.158791 0.275034i −0.775642 0.631173i \(-0.782574\pi\)
0.934433 + 0.356139i \(0.115907\pi\)
\(410\) 0 0
\(411\) −1.93076 7.87381i −0.0952372 0.388386i
\(412\) 0 0
\(413\) −4.51181 −0.222012
\(414\) 0 0
\(415\) 4.36230 0.214137
\(416\) 0 0
\(417\) −20.0635 + 19.2252i −0.982512 + 0.941464i
\(418\) 0 0
\(419\) −4.05211 + 7.01847i −0.197959 + 0.342874i −0.947866 0.318668i \(-0.896765\pi\)
0.749908 + 0.661542i \(0.230098\pi\)
\(420\) 0 0
\(421\) −0.936528 1.62211i −0.0456436 0.0790570i 0.842301 0.539007i \(-0.181201\pi\)
−0.887945 + 0.459950i \(0.847867\pi\)
\(422\) 0 0
\(423\) −0.960092 + 22.4901i −0.0466813 + 1.09351i
\(424\) 0 0
\(425\) 1.37205 + 2.37646i 0.0665541 + 0.115275i
\(426\) 0 0
\(427\) 13.0838 22.6617i 0.633167 1.09668i
\(428\) 0 0
\(429\) −8.31938 2.42050i −0.401663 0.116863i
\(430\) 0 0
\(431\) 37.0364 1.78398 0.891990 0.452054i \(-0.149309\pi\)
0.891990 + 0.452054i \(0.149309\pi\)
\(432\) 0 0
\(433\) −30.8710 −1.48357 −0.741784 0.670639i \(-0.766020\pi\)
−0.741784 + 0.670639i \(0.766020\pi\)
\(434\) 0 0
\(435\) −10.5097 3.05777i −0.503901 0.146609i
\(436\) 0 0
\(437\) 1.45646 2.52266i 0.0696718 0.120675i
\(438\) 0 0
\(439\) −4.35581 7.54448i −0.207891 0.360078i 0.743159 0.669115i \(-0.233327\pi\)
−0.951050 + 0.309037i \(0.899993\pi\)
\(440\) 0 0
\(441\) −7.29844 + 3.80833i −0.347545 + 0.181349i
\(442\) 0 0
\(443\) 1.09591 + 1.89818i 0.0520684 + 0.0901851i 0.890885 0.454229i \(-0.150085\pi\)
−0.838816 + 0.544414i \(0.816752\pi\)
\(444\) 0 0
\(445\) −1.41559 + 2.45188i −0.0671055 + 0.116230i
\(446\) 0 0
\(447\) 23.1482 22.1811i 1.09487 1.04913i
\(448\) 0 0
\(449\) −38.9345 −1.83743 −0.918717 0.394917i \(-0.870773\pi\)
−0.918717 + 0.394917i \(0.870773\pi\)
\(450\) 0 0
\(451\) −4.59960 −0.216587
\(452\) 0 0
\(453\) 1.63875 + 6.68299i 0.0769953 + 0.313994i
\(454\) 0 0
\(455\) 9.46373 16.3917i 0.443666 0.768453i
\(456\) 0 0
\(457\) 17.6914 + 30.6424i 0.827570 + 1.43339i 0.899939 + 0.436015i \(0.143611\pi\)
−0.0723694 + 0.997378i \(0.523056\pi\)
\(458\) 0 0
\(459\) 9.41703 + 10.7066i 0.439549 + 0.499742i
\(460\) 0 0
\(461\) 19.7748 + 34.2510i 0.921005 + 1.59523i 0.797863 + 0.602839i \(0.205964\pi\)
0.123143 + 0.992389i \(0.460703\pi\)
\(462\) 0 0
\(463\) −9.25261 + 16.0260i −0.430005 + 0.744791i −0.996873 0.0790179i \(-0.974822\pi\)
0.566868 + 0.823809i \(0.308155\pi\)
\(464\) 0 0
\(465\) 3.00000 + 12.2343i 0.139122 + 0.567352i
\(466\) 0 0
\(467\) 37.8090 1.74959 0.874797 0.484490i \(-0.160995\pi\)
0.874797 + 0.484490i \(0.160995\pi\)
\(468\) 0 0
\(469\) 36.9581 1.70657
\(470\) 0 0
\(471\) 1.28012 1.22664i 0.0589849 0.0565206i
\(472\) 0 0
\(473\) 3.08441 5.34235i 0.141821 0.245642i
\(474\) 0 0
\(475\) 0.412500 + 0.714470i 0.0189268 + 0.0327822i
\(476\) 0 0
\(477\) −3.76771 2.39516i −0.172512 0.109667i
\(478\) 0 0
\(479\) 10.8297 + 18.7576i 0.494823 + 0.857058i 0.999982 0.00596807i \(-0.00189971\pi\)
−0.505160 + 0.863026i \(0.668566\pi\)
\(480\) 0 0
\(481\) 6.25590 10.8355i 0.285245 0.494058i
\(482\) 0 0
\(483\) −18.3299 5.33304i −0.834040 0.242662i
\(484\) 0 0
\(485\) 5.31938 0.241540
\(486\) 0 0
\(487\) 34.7267 1.57361 0.786807 0.617199i \(-0.211732\pi\)
0.786807 + 0.617199i \(0.211732\pi\)
\(488\) 0 0
\(489\) −34.3092 9.98219i −1.55152 0.451410i
\(490\) 0 0
\(491\) −15.7298 + 27.2448i −0.709875 + 1.22954i 0.255029 + 0.966933i \(0.417915\pi\)
−0.964903 + 0.262605i \(0.915418\pi\)
\(492\) 0 0
\(493\) −8.67049 15.0177i −0.390499 0.676364i
\(494\) 0 0
\(495\) −2.08868 1.32779i −0.0938792 0.0596798i
\(496\) 0 0
\(497\) 24.3092 + 42.1048i 1.09042 + 1.88866i
\(498\) 0 0
\(499\) −4.90005 + 8.48713i −0.219356 + 0.379936i −0.954611 0.297854i \(-0.903729\pi\)
0.735255 + 0.677791i \(0.237062\pi\)
\(500\) 0 0
\(501\) 23.9591 22.9582i 1.07042 1.02569i
\(502\) 0 0
\(503\) 27.8829 1.24324 0.621618 0.783321i \(-0.286476\pi\)
0.621618 + 0.783321i \(0.286476\pi\)
\(504\) 0 0
\(505\) 16.1269 0.717640
\(506\) 0 0
\(507\) 9.80334 + 39.9790i 0.435382 + 1.77553i
\(508\) 0 0
\(509\) 14.2232 24.6352i 0.630430 1.09194i −0.357033 0.934092i \(-0.616212\pi\)
0.987464 0.157846i \(-0.0504550\pi\)
\(510\) 0 0
\(511\) −20.9867 36.3500i −0.928397 1.60803i
\(512\) 0 0
\(513\) 2.83118 + 3.21889i 0.125000 + 0.142117i
\(514\) 0 0
\(515\) 1.33981 + 2.32062i 0.0590392 + 0.102259i
\(516\) 0 0
\(517\) 3.09521 5.36106i 0.136127 0.235779i
\(518\) 0 0
\(519\) 5.61624 + 22.9036i 0.246526 + 1.00536i
\(520\) 0 0
\(521\) 17.1269 0.750345 0.375173 0.926955i \(-0.377583\pi\)
0.375173 + 0.926955i \(0.377583\pi\)
\(522\) 0 0
\(523\) −24.8874 −1.08825 −0.544125 0.839004i \(-0.683138\pi\)
−0.544125 + 0.839004i \(0.683138\pi\)
\(524\) 0 0
\(525\) 3.90378 3.74069i 0.170375 0.163257i
\(526\) 0 0
\(527\) −9.97854 + 17.2833i −0.434672 + 0.752874i
\(528\) 0 0
\(529\) 5.26670 + 9.12220i 0.228987 + 0.396617i
\(530\) 0 0
\(531\) 3.84424 2.00592i 0.166826 0.0870497i
\(532\) 0 0
\(533\) 16.9028 + 29.2765i 0.732141 + 1.26810i
\(534\) 0 0
\(535\) −8.11082 + 14.0484i −0.350661 + 0.607363i
\(536\) 0 0
\(537\) −3.09521 0.900543i −0.133568 0.0388613i
\(538\) 0 0
\(539\) 2.26388 0.0975121
\(540\) 0 0
\(541\) 8.44632 0.363136 0.181568 0.983378i \(-0.441883\pi\)
0.181568 + 0.983378i \(0.441883\pi\)
\(542\) 0 0
\(543\) −28.2029 8.20556i −1.21030 0.352134i
\(544\) 0 0
\(545\) −4.93552 + 8.54857i −0.211414 + 0.366181i
\(546\) 0 0
\(547\) −15.5882 26.9995i −0.666503 1.15442i −0.978876 0.204457i \(-0.934457\pi\)
0.312373 0.949960i \(-0.398876\pi\)
\(548\) 0 0
\(549\) −1.07260 + 25.1257i −0.0457775 + 1.07234i
\(550\) 0 0
\(551\) −2.60674 4.51501i −0.111051 0.192346i
\(552\) 0 0
\(553\) 22.0635 38.2151i 0.938234 1.62507i
\(554\) 0 0
\(555\) 2.58056 2.47275i 0.109539 0.104962i
\(556\) 0 0
\(557\) −13.5354 −0.573514 −0.286757 0.958003i \(-0.592577\pi\)
−0.286757 + 0.958003i \(0.592577\pi\)
\(558\) 0 0
\(559\) −45.3388 −1.91763
\(560\) 0 0
\(561\) −0.933849 3.80833i −0.0394271 0.160788i
\(562\) 0 0
\(563\) 15.3304 26.5530i 0.646098 1.11907i −0.337949 0.941164i \(-0.609733\pi\)
0.984047 0.177910i \(-0.0569335\pi\)
\(564\) 0 0
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 0 0
\(567\) 16.0694 23.0444i 0.674851 0.967776i
\(568\) 0 0
\(569\) −2.46726 4.27341i −0.103433 0.179151i 0.809664 0.586894i \(-0.199649\pi\)
−0.913097 + 0.407743i \(0.866316\pi\)
\(570\) 0 0
\(571\) 19.4717 33.7260i 0.814865 1.41139i −0.0945596 0.995519i \(-0.530144\pi\)
0.909425 0.415869i \(-0.136522\pi\)
\(572\) 0 0
\(573\) −3.87104 15.7865i −0.161715 0.659490i
\(574\) 0 0
\(575\) 3.53081 0.147245
\(576\) 0 0
\(577\) −0.633394 −0.0263686 −0.0131843 0.999913i \(-0.504197\pi\)
−0.0131843 + 0.999913i \(0.504197\pi\)
\(578\) 0 0
\(579\) −7.79404 + 7.46841i −0.323909 + 0.310377i
\(580\) 0 0
\(581\) 6.80858 11.7928i 0.282467 0.489248i
\(582\) 0 0
\(583\) 0.613879 + 1.06327i 0.0254243 + 0.0440361i
\(584\) 0 0
\(585\) −0.775832 + 18.1739i −0.0320767 + 0.751397i
\(586\) 0 0
\(587\) −1.45197 2.51489i −0.0599292 0.103800i 0.834504 0.551002i \(-0.185754\pi\)
−0.894433 + 0.447201i \(0.852421\pi\)
\(588\) 0 0
\(589\) −3.00000 + 5.19615i −0.123613 + 0.214104i
\(590\) 0 0
\(591\) 27.6717 + 8.05102i 1.13826 + 0.331175i
\(592\) 0 0
\(593\) −36.8292 −1.51239 −0.756196 0.654345i \(-0.772945\pi\)
−0.756196 + 0.654345i \(0.772945\pi\)
\(594\) 0 0
\(595\) 8.56584 0.351165
\(596\) 0 0
\(597\) −12.7758 3.71710i −0.522880 0.152131i
\(598\) 0 0
\(599\) 9.54310 16.5291i 0.389921 0.675362i −0.602518 0.798105i \(-0.705836\pi\)
0.992438 + 0.122743i \(0.0391691\pi\)
\(600\) 0 0
\(601\) 0.852119 + 1.47591i 0.0347587 + 0.0602038i 0.882881 0.469596i \(-0.155600\pi\)
−0.848123 + 0.529800i \(0.822267\pi\)
\(602\) 0 0
\(603\) −31.4898 + 16.4314i −1.28236 + 0.669138i
\(604\) 0 0
\(605\) −5.15969 8.93684i −0.209771 0.363334i
\(606\) 0 0
\(607\) −11.4664 + 19.8604i −0.465408 + 0.806111i −0.999220 0.0394928i \(-0.987426\pi\)
0.533812 + 0.845603i \(0.320759\pi\)
\(608\) 0 0
\(609\) −24.6695 + 23.6388i −0.999658 + 0.957893i
\(610\) 0 0
\(611\) −45.4975 −1.84063
\(612\) 0 0
\(613\) 5.08709 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(614\) 0 0
\(615\) 2.29980 + 9.37881i 0.0927369 + 0.378190i
\(616\) 0 0
\(617\) −7.95545 + 13.7792i −0.320274 + 0.554731i −0.980545 0.196297i \(-0.937108\pi\)
0.660270 + 0.751028i \(0.270442\pi\)
\(618\) 0 0
\(619\) 1.24399 + 2.15466i 0.0500003 + 0.0866031i 0.889942 0.456073i \(-0.150744\pi\)
−0.839942 + 0.542676i \(0.817411\pi\)
\(620\) 0 0
\(621\) 17.9889 3.60541i 0.721868 0.144680i
\(622\) 0 0
\(623\) 4.41885 + 7.65366i 0.177037 + 0.306638i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −0.280757 1.14496i −0.0112124 0.0457251i
\(628\) 0 0
\(629\) 5.66237 0.225773
\(630\) 0 0
\(631\) −8.81634 −0.350973 −0.175486 0.984482i \(-0.556150\pi\)
−0.175486 + 0.984482i \(0.556150\pi\)
\(632\) 0 0
\(633\) −1.35313 + 1.29659i −0.0537820 + 0.0515350i
\(634\) 0 0
\(635\) 1.45522 2.52051i 0.0577485 0.100023i
\(636\) 0 0
\(637\) −8.31938 14.4096i −0.329626 0.570928i
\(638\) 0 0
\(639\) −39.4320 25.0672i −1.55991 0.991645i
\(640\) 0 0
\(641\) 8.53174 + 14.7774i 0.336983 + 0.583672i 0.983864 0.178919i \(-0.0572601\pi\)
−0.646880 + 0.762591i \(0.723927\pi\)
\(642\) 0 0
\(643\) −9.88607 + 17.1232i −0.389869 + 0.675272i −0.992432 0.122799i \(-0.960813\pi\)
0.602563 + 0.798071i \(0.294146\pi\)
\(644\) 0 0
\(645\) −12.4355 3.61808i −0.489648 0.142462i
\(646\) 0 0
\(647\) −18.2744 −0.718441 −0.359220 0.933253i \(-0.616957\pi\)
−0.359220 + 0.933253i \(0.616957\pi\)
\(648\) 0 0
\(649\) −1.19243 −0.0468070
\(650\) 0 0
\(651\) 37.7558 + 10.9850i 1.47977 + 0.430535i
\(652\) 0 0
\(653\) −6.92639 + 11.9969i −0.271051 + 0.469474i −0.969131 0.246546i \(-0.920704\pi\)
0.698080 + 0.716019i \(0.254038\pi\)
\(654\) 0 0
\(655\) 5.00236 + 8.66434i 0.195458 + 0.338544i
\(656\) 0 0
\(657\) 34.0425 + 21.6411i 1.32813 + 0.844300i
\(658\) 0 0
\(659\) −19.3694 33.5488i −0.754524 1.30687i −0.945611 0.325301i \(-0.894534\pi\)
0.191087 0.981573i \(-0.438799\pi\)
\(660\) 0 0
\(661\) −13.8710 + 24.0253i −0.539521 + 0.934478i 0.459409 + 0.888225i \(0.348061\pi\)
−0.998930 + 0.0462528i \(0.985272\pi\)
\(662\) 0 0
\(663\) −20.8083 + 19.9389i −0.808126 + 0.774363i
\(664\) 0 0
\(665\) 2.57528 0.0998651
\(666\) 0 0
\(667\) −22.3125 −0.863943
\(668\) 0 0
\(669\) −7.05334 28.7642i −0.272698 1.11209i
\(670\) 0 0
\(671\) 3.45792 5.98930i 0.133492 0.231214i
\(672\) 0 0
\(673\) 22.6070 + 39.1565i 0.871436 + 1.50937i 0.860511 + 0.509432i \(0.170144\pi\)
0.0109254 + 0.999940i \(0.496522\pi\)
\(674\) 0 0
\(675\) −1.66309 + 4.92282i −0.0640124 + 0.189479i
\(676\) 0 0
\(677\) 7.28764 + 12.6226i 0.280087 + 0.485124i 0.971406 0.237425i \(-0.0763034\pi\)
−0.691319 + 0.722550i \(0.742970\pi\)
\(678\) 0 0
\(679\) 8.30236 14.3801i 0.318615 0.551858i
\(680\) 0 0
\(681\) 5.65969 + 23.0808i 0.216880 + 0.884457i
\(682\) 0 0
\(683\) 15.7274 0.601790 0.300895 0.953657i \(-0.402715\pi\)
0.300895 + 0.953657i \(0.402715\pi\)
\(684\) 0 0
\(685\) 4.68062 0.178837
\(686\) 0 0
\(687\) 15.4065 14.7628i 0.587794 0.563237i
\(688\) 0 0
\(689\) 4.51181 7.81468i 0.171886 0.297716i
\(690\) 0 0
\(691\) −14.1362 24.4846i −0.537767 0.931440i −0.999024 0.0441730i \(-0.985935\pi\)
0.461257 0.887267i \(-0.347399\pi\)
\(692\) 0 0
\(693\) −6.84944 + 3.57404i −0.260189 + 0.135767i
\(694\) 0 0
\(695\) −8.02160 13.8938i −0.304277 0.527023i
\(696\) 0 0
\(697\) −7.64955 + 13.2494i −0.289747 + 0.501857i
\(698\) 0 0
\(699\) 16.2446 + 4.72632i 0.614427 + 0.178766i
\(700\) 0 0
\(701\) −2.97840 −0.112493 −0.0562463 0.998417i \(-0.517913\pi\)
−0.0562463 + 0.998417i \(0.517913\pi\)
\(702\) 0 0
\(703\) 1.70236 0.0642059
\(704\) 0 0
\(705\) −12.4791 3.63075i −0.469989 0.136742i
\(706\) 0 0
\(707\) 25.1706 43.5967i 0.946636 1.63962i
\(708\) 0 0
\(709\) 7.35011 + 12.7308i 0.276039 + 0.478114i 0.970397 0.241516i \(-0.0776448\pi\)
−0.694358 + 0.719630i \(0.744311\pi\)
\(710\) 0 0
\(711\) −1.80875 + 42.3700i −0.0678336 + 1.58900i
\(712\) 0 0
\(713\) 12.8393 + 22.2383i 0.480836 + 0.832832i
\(714\) 0 0
\(715\) 2.50118 4.33217i 0.0935388 0.162014i
\(716\) 0 0
\(717\) 29.0851 27.8699i 1.08620 1.04082i
\(718\) 0 0
\(719\) 17.8848 0.666992 0.333496 0.942752i \(-0.391772\pi\)
0.333496 + 0.942752i \(0.391772\pi\)
\(720\) 0 0
\(721\) 8.36459 0.311514
\(722\) 0 0
\(723\) −11.6188 47.3826i −0.432108 1.76218i
\(724\) 0 0
\(725\) 3.15969 5.47274i 0.117348 0.203252i
\(726\) 0 0
\(727\) 9.94251 + 17.2209i 0.368747 + 0.638689i 0.989370 0.145420i \(-0.0464534\pi\)
−0.620623 + 0.784109i \(0.713120\pi\)
\(728\) 0 0
\(729\) −3.44632 + 26.7791i −0.127642 + 0.991820i
\(730\) 0 0
\(731\) −10.2593 17.7696i −0.379454 0.657233i
\(732\) 0 0
\(733\) 8.38285 14.5195i 0.309628 0.536291i −0.668653 0.743574i \(-0.733129\pi\)
0.978281 + 0.207284i \(0.0664623\pi\)
\(734\) 0 0
\(735\) −1.13194 4.61616i −0.0417522 0.170270i
\(736\) 0 0
\(737\) 9.76771 0.359798
\(738\) 0 0
\(739\) −40.1188 −1.47579 −0.737897 0.674914i \(-0.764181\pi\)
−0.737897 + 0.674914i \(0.764181\pi\)
\(740\) 0 0
\(741\) −6.25590 + 5.99454i −0.229816 + 0.220215i
\(742\) 0 0
\(743\) 13.8294 23.9532i 0.507351 0.878757i −0.492613 0.870248i \(-0.663958\pi\)
0.999964 0.00850866i \(-0.00270842\pi\)
\(744\) 0 0
\(745\) 9.25490 + 16.0300i 0.339073 + 0.587292i
\(746\) 0 0
\(747\) −0.558164 + 13.0750i −0.0204222 + 0.478389i
\(748\) 0 0
\(749\) 25.3184 + 43.8527i 0.925113 + 1.60234i
\(750\) 0 0
\(751\) 7.53055 13.0433i 0.274794 0.475957i −0.695289 0.718730i \(-0.744724\pi\)
0.970083 + 0.242773i \(0.0780571\pi\)
\(752\) 0 0
\(753\) 32.4990 + 9.45550i 1.18433 + 0.344578i
\(754\) 0 0
\(755\) −3.97274 −0.144583
\(756\) 0 0
\(757\) −4.57528 −0.166291 −0.0831457 0.996537i \(-0.526497\pi\)
−0.0831457 + 0.996537i \(0.526497\pi\)
\(758\) 0 0
\(759\) −4.84444 1.40948i −0.175842 0.0511608i
\(760\) 0 0
\(761\) −17.7350 + 30.7179i −0.642892 + 1.11352i 0.341892 + 0.939739i \(0.388932\pi\)
−0.984784 + 0.173782i \(0.944401\pi\)
\(762\) 0 0
\(763\) 15.4065 + 26.6848i 0.557752 + 0.966056i
\(764\) 0 0
\(765\) −7.29844 + 3.80833i −0.263876 + 0.137690i
\(766\) 0 0
\(767\) 4.38199 + 7.58983i 0.158224 + 0.274053i
\(768\) 0 0
\(769\) −9.54254 + 16.5282i −0.344113 + 0.596021i −0.985192 0.171454i \(-0.945154\pi\)
0.641079 + 0.767474i \(0.278487\pi\)
\(770\) 0 0
\(771\) −22.8805 + 21.9246i −0.824021 + 0.789595i
\(772\) 0 0
\(773\) 15.7893 0.567902 0.283951 0.958839i \(-0.408355\pi\)
0.283951 + 0.958839i \(0.408355\pi\)
\(774\) 0 0
\(775\) −7.27273 −0.261244
\(776\) 0 0
\(777\) −2.65701 10.8355i −0.0953197 0.388723i
\(778\) 0 0
\(779\) −2.29980 + 3.98337i −0.0823989 + 0.142719i
\(780\) 0 0
\(781\) 6.42472 + 11.1279i 0.229895 + 0.398189i
\(782\) 0 0
\(783\) 10.5097 31.1091i 0.375586 1.11175i
\(784\) 0 0
\(785\) 0.511807 + 0.886476i 0.0182672 + 0.0316397i
\(786\) 0 0
\(787\) −1.80143 + 3.12017i −0.0642140 + 0.111222i −0.896345 0.443357i \(-0.853787\pi\)
0.832131 + 0.554579i \(0.187121\pi\)
\(788\) 0 0
\(789\) 5.40646 + 22.0481i 0.192475 + 0.784933i
\(790\) 0 0
\(791\) −18.7293 −0.665938
\(792\) 0 0
\(793\) −50.8292 −1.80500
\(794\) 0 0
\(795\) 1.86112 1.78336i 0.0660071 0.0632494i
\(796\) 0 0
\(797\) 17.9264