Properties

Label 2008.1.bd.a.67.1
Level 2008
Weight 1
Character 2008.67
Analytic conductor 1.002
Analytic rank 0
Dimension 100
Projective image \(D_{125}\)
CM discriminant -8
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2008.bd (of order \(250\), degree \(100\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00212254537\)
Analytic rank: \(0\)
Dimension: \(100\)
Coefficient field: \(\Q(\zeta_{250})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{125}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{125} - \cdots)\)

Embedding invariants

Embedding label 67.1
Root \(0.675333 - 0.737513i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.67
Dual form 2008.1.bd.a.1019.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +O(q^{10})\) \(q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +(0.751353 - 0.637644i) q^{11} +(0.763143 + 0.470959i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(-0.481116 + 0.387935i) q^{17} +(0.190822 + 0.0439145i) q^{18} +(1.44333 - 0.994203i) q^{19} +(0.111215 - 0.979159i) q^{22} +(0.878701 - 0.179093i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-1.06695 + 0.107624i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.187355 + 0.863634i) q^{33} +(-0.0851591 + 0.612139i) q^{34} +(0.169165 - 0.0986144i) q^{36} +(0.371566 - 1.71277i) q^{38} +(0.208923 - 0.368970i) q^{41} +(1.19186 - 1.17698i) q^{43} +(-0.589208 - 0.789908i) q^{44} +(0.517948 - 0.732066i) q^{48} +(0.492727 + 0.870184i) q^{49} +(0.968583 - 0.248690i) q^{50} +(-0.103853 - 0.544415i) q^{51} +(-0.704098 + 0.808831i) q^{54} +(0.177375 + 1.56164i) q^{57} +(0.591287 + 0.476768i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.727774 + 0.501308i) q^{66} +(-1.07242 - 1.17116i) q^{67} +(0.356960 + 0.504525i) q^{68} +(0.0558096 - 0.187688i) q^{72} +(-0.765896 - 0.372230i) q^{73} +(-0.751067 + 0.489988i) q^{75} +(-0.901614 - 1.50291i) q^{76} +(0.290853 - 0.708469i) q^{81} +(-0.100279 - 0.411986i) q^{82} +(-1.31392 - 0.445247i) q^{83} +(0.0631332 - 1.67387i) q^{86} +(-0.970244 - 0.172477i) q^{88} +(0.655963 + 1.71960i) q^{89} +(-0.123566 - 0.888213i) q^{96} +(-1.18977 + 1.59504i) q^{97} +(0.954865 + 0.297042i) q^{98} +(0.185635 + 0.0526693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{52}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.728969 0.684547i 0.728969 0.684547i
\(3\) −0.422111 + 0.791209i −0.422111 + 0.791209i −0.999684 0.0251301i \(-0.992000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(4\) 0.0627905 0.998027i 0.0627905 0.998027i
\(5\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(6\) 0.233914 + 0.865722i 0.233914 + 0.865722i
\(7\) 0 0 −0.863923 0.503623i \(-0.832000\pi\)
0.863923 + 0.503623i \(0.168000\pi\)
\(8\) −0.637424 0.770513i −0.637424 0.770513i
\(9\) 0.109042 + 0.162639i 0.109042 + 0.162639i
\(10\) 0 0
\(11\) 0.751353 0.637644i 0.751353 0.637644i −0.187381 0.982287i \(-0.560000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(12\) 0.763143 + 0.470959i 0.763143 + 0.470959i
\(13\) 0 0 0.617860 0.786288i \(-0.288000\pi\)
−0.617860 + 0.786288i \(0.712000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.992115 0.125333i −0.992115 0.125333i
\(17\) −0.481116 + 0.387935i −0.481116 + 0.387935i −0.837528 0.546394i \(-0.816000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(18\) 0.190822 + 0.0439145i 0.190822 + 0.0439145i
\(19\) 1.44333 0.994203i 1.44333 0.994203i 0.448383 0.893841i \(-0.352000\pi\)
0.994951 0.100362i \(-0.0320000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.111215 0.979159i 0.111215 0.979159i
\(23\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(24\) 0.878701 0.179093i 0.878701 0.179093i
\(25\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(26\) 0 0
\(27\) −1.06695 + 0.107624i −1.06695 + 0.107624i
\(28\) 0 0
\(29\) 0 0 0.0878512 0.996134i \(-0.472000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(32\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(33\) 0.187355 + 0.863634i 0.187355 + 0.863634i
\(34\) −0.0851591 + 0.612139i −0.0851591 + 0.612139i
\(35\) 0 0
\(36\) 0.169165 0.0986144i 0.169165 0.0986144i
\(37\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(38\) 0.371566 1.71277i 0.371566 1.71277i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.208923 0.368970i 0.208923 0.368970i −0.745941 0.666012i \(-0.768000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(42\) 0 0
\(43\) 1.19186 1.17698i 1.19186 1.17698i 0.212007 0.977268i \(-0.432000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(44\) −0.589208 0.789908i −0.589208 0.789908i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(48\) 0.517948 0.732066i 0.517948 0.732066i
\(49\) 0.492727 + 0.870184i 0.492727 + 0.870184i
\(50\) 0.968583 0.248690i 0.968583 0.248690i
\(51\) −0.103853 0.544415i −0.103853 0.544415i
\(52\) 0 0
\(53\) 0 0 0.888136 0.459580i \(-0.152000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(54\) −0.704098 + 0.808831i −0.704098 + 0.808831i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.177375 + 1.56164i 0.177375 + 1.56164i
\(58\) 0 0
\(59\) 0.591287 + 0.476768i 0.591287 + 0.476768i 0.876307 0.481754i \(-0.160000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(60\) 0 0
\(61\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(65\) 0 0
\(66\) 0.727774 + 0.501308i 0.727774 + 0.501308i
\(67\) −1.07242 1.17116i −1.07242 1.17116i −0.984564 0.175023i \(-0.944000\pi\)
−0.0878512 0.996134i \(-0.528000\pi\)
\(68\) 0.356960 + 0.504525i 0.356960 + 0.504525i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(72\) 0.0558096 0.187688i 0.0558096 0.187688i
\(73\) −0.765896 0.372230i −0.765896 0.372230i 0.0125660 0.999921i \(-0.496000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(74\) 0 0
\(75\) −0.751067 + 0.489988i −0.751067 + 0.489988i
\(76\) −0.901614 1.50291i −0.901614 1.50291i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(80\) 0 0
\(81\) 0.290853 0.708469i 0.290853 0.708469i
\(82\) −0.100279 0.411986i −0.100279 0.411986i
\(83\) −1.31392 0.445247i −1.31392 0.445247i −0.425779 0.904827i \(-0.640000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.0631332 1.67387i 0.0631332 1.67387i
\(87\) 0 0
\(88\) −0.970244 0.172477i −0.970244 0.172477i
\(89\) 0.655963 + 1.71960i 0.655963 + 1.71960i 0.693653 + 0.720309i \(0.256000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.123566 0.888213i −0.123566 0.888213i
\(97\) −1.18977 + 1.59504i −1.18977 + 1.59504i −0.514440 + 0.857527i \(0.672000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(98\) 0.954865 + 0.297042i 0.954865 + 0.297042i
\(99\) 0.185635 + 0.0526693i 0.185635 + 0.0526693i
\(100\) 0.535827 0.844328i 0.535827 0.844328i
\(101\) 0 0 0.236499 0.971632i \(-0.424000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(102\) −0.448383 0.325769i −0.448383 0.325769i
\(103\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.145848 + 0.290744i 0.145848 + 0.290744i 0.954865 0.297042i \(-0.0960000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0.0404175 + 1.07160i 0.0404175 + 1.07160i
\(109\) 0 0 0.514440 0.857527i \(-0.328000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.161209 + 0.496150i 0.161209 + 0.496150i 0.998737 0.0502443i \(-0.0160000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(114\) 1.19832 + 1.01697i 1.19832 + 1.01697i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.757400 0.0572151i 0.757400 0.0572151i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.00469681 + 0.0284946i −0.00469681 + 0.0284946i
\(122\) 0 0
\(123\) 0.203744 + 0.321049i 0.203744 + 0.321049i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.947098 0.320944i \(-0.104000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(128\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(129\) 0.428137 + 1.43983i 0.428137 + 1.43983i
\(130\) 0 0
\(131\) −1.85720 0.0934320i −1.85720 0.0934320i −0.910106 0.414376i \(-0.864000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(132\) 0.873694 0.132758i 0.873694 0.132758i
\(133\) 0 0
\(134\) −1.58347 0.119618i −1.58347 0.119618i
\(135\) 0 0
\(136\) 0.605584 + 0.123428i 0.605584 + 0.123428i
\(137\) −1.35431 1.14935i −1.35431 1.14935i −0.974527 0.224271i \(-0.928000\pi\)
−0.379779 0.925077i \(-0.624000\pi\)
\(138\) 0 0
\(139\) −0.747469 0.572310i −0.747469 0.572310i 0.162637 0.986686i \(-0.448000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.0877979 0.175023i −0.0877979 0.175023i
\(145\) 0 0
\(146\) −0.813123 + 0.252948i −0.813123 + 0.252948i
\(147\) −0.896483 + 0.0225358i −0.896483 + 0.0225358i
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) −0.212084 + 0.871327i −0.212084 + 0.871327i
\(151\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(152\) −1.68606 0.478379i −1.68606 0.478379i
\(153\) −0.115555 0.0359471i −0.115555 0.0359471i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.272957 0.715554i −0.272957 0.715554i
\(163\) 0.172990 + 0.0307520i 0.172990 + 0.0307520i 0.260842 0.965382i \(-0.416000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(164\) −0.355124 0.231679i −0.355124 0.231679i
\(165\) 0 0
\(166\) −1.26260 + 0.574866i −1.26260 + 0.574866i
\(167\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(168\) 0 0
\(169\) −0.236499 0.971632i −0.236499 0.971632i
\(170\) 0 0
\(171\) 0.319080 + 0.126333i 0.319080 + 0.126333i
\(172\) −1.09982 1.26341i −1.09982 1.26341i
\(173\) 0 0 −0.920232 0.391374i \(-0.872000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.825346 + 0.538447i −0.825346 + 0.538447i
\(177\) −0.626813 + 0.266583i −0.626813 + 0.266583i
\(178\) 1.65532 + 0.804496i 1.65532 + 0.804496i
\(179\) −0.535114 + 1.79959i −0.535114 + 1.79959i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.114124 + 0.598257i −0.114124 + 0.598257i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.693653 0.720309i \(-0.744000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(192\) −0.698099 0.562893i −0.698099 0.562893i
\(193\) −0.292246 0.371913i −0.292246 0.371913i 0.617860 0.786288i \(-0.288000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(194\) 0.224573 + 1.97719i 0.224573 + 1.97719i
\(195\) 0 0
\(196\) 0.899405 0.437116i 0.899405 0.437116i
\(197\) 0 0 0.656586 0.754251i \(-0.272000\pi\)
−0.656586 + 0.754251i \(0.728000\pi\)
\(198\) 0.171376 0.0886814i 0.171376 0.0886814i
\(199\) 0 0 −0.745941 0.666012i \(-0.768000\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(200\) −0.187381 0.982287i −0.187381 0.982287i
\(201\) 1.37931 0.354146i 1.37931 0.354146i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.549862 + 0.0694637i −0.549862 + 0.0694637i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.450505 1.66733i 0.450505 1.66733i
\(210\) 0 0
\(211\) 0.829867 + 1.76356i 0.829867 + 1.76356i 0.617860 + 0.786288i \(0.288000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.305346 + 0.112103i 0.305346 + 0.112103i
\(215\) 0 0
\(216\) 0.763024 + 0.753495i 0.763024 + 0.753495i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.617805 0.448862i 0.617805 0.448862i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.556876 0.830596i \(-0.312000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(224\) 0 0
\(225\) 0.0172021 + 0.195053i 0.0172021 + 0.195053i
\(226\) 0.457154 + 0.251323i 0.457154 + 0.251323i
\(227\) −1.24917 + 0.254600i −1.24917 + 0.254600i −0.778462 0.627691i \(-0.784000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(228\) 1.56970 0.0789682i 1.56970 0.0789682i
\(229\) 0 0 0.112856 0.993611i \(-0.464000\pi\)
−0.112856 + 0.993611i \(0.536000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.694666 0.159866i −0.694666 0.159866i −0.137790 0.990461i \(-0.544000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.512955 0.560184i 0.512955 0.560184i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(240\) 0 0
\(241\) −1.68606 + 0.926921i −1.68606 + 0.926921i −0.711536 + 0.702650i \(0.752000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(242\) 0.0160820 + 0.0239868i 0.0160820 + 0.0239868i
\(243\) −0.245775 0.297091i −0.245775 0.297091i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.368296 + 0.0945623i 0.368296 + 0.0945623i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.906903 0.851638i 0.906903 0.851638i
\(250\) 0 0
\(251\) −0.863923 + 0.503623i −0.863923 + 0.503623i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(257\) 0.397753 + 1.47210i 0.397753 + 1.47210i 0.823533 + 0.567269i \(0.192000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(258\) 1.29773 + 0.756510i 1.29773 + 0.756510i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.41780 + 1.20323i −1.41780 + 1.20323i
\(263\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(264\) 0.546017 0.694861i 0.546017 0.694861i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.63745 0.206858i −1.63745 0.206858i
\(268\) −1.23618 + 0.996762i −1.23618 + 0.996762i
\(269\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(270\) 0 0
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) 0.525944 0.324576i 0.525944 0.324576i
\(273\) 0 0
\(274\) −1.77403 + 0.0892476i −1.77403 + 0.0892476i
\(275\) 0.965603 0.196805i 0.965603 0.196805i
\(276\) 0 0
\(277\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(278\) −0.936655 + 0.0944813i −0.936655 + 0.0944813i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.0187471 1.49176i −0.0187471 1.49176i −0.675333 0.737513i \(-0.736000\pi\)
0.656586 0.754251i \(-0.272000\pi\)
\(282\) 0 0
\(283\) 1.55659 1.13093i 1.55659 1.13093i 0.617860 0.786288i \(-0.288000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.183813 0.0674845i −0.183813 0.0674845i
\(289\) −0.131028 + 0.603985i −0.131028 + 0.603985i
\(290\) 0 0
\(291\) −0.759794 1.61464i −0.759794 1.61464i
\(292\) −0.419586 + 0.741012i −0.419586 + 0.741012i
\(293\) 0 0 0.260842 0.965382i \(-0.416000\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(294\) −0.638081 + 0.630113i −0.638081 + 0.630113i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.733028 + 0.761197i −0.733028 + 0.761197i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.441861 + 0.780352i 0.441861 + 0.780352i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.55656 + 0.805466i −1.55656 + 0.805466i
\(305\) 0 0
\(306\) −0.108844 + 0.0528985i −0.108844 + 0.0528985i
\(307\) 0.200974 + 1.21927i 0.200974 + 1.21927i 0.876307 + 0.481754i \(0.160000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.693653 0.720309i \(-0.744000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(312\) 0 0
\(313\) 1.77385 + 0.807640i 1.77385 + 0.807640i 0.979855 + 0.199710i \(0.0640000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.823533 0.567269i \(-0.808000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.291603 0.00733033i −0.291603 0.00733033i
\(322\) 0 0
\(323\) −0.308726 + 1.03825i −0.308726 + 1.03825i
\(324\) −0.688808 0.334764i −0.688808 0.334764i
\(325\) 0 0
\(326\) 0.147156 0.0960028i 0.147156 0.0960028i
\(327\) 0 0
\(328\) −0.417469 + 0.0742123i −0.417469 + 0.0742123i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.439782 + 0.174122i 0.439782 + 0.174122i 0.577573 0.816339i \(-0.304000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(332\) −0.526870 + 1.28337i −0.526870 + 1.28337i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.0509068 1.34971i 0.0509068 1.34971i −0.711536 0.702650i \(-0.752000\pi\)
0.762443 0.647056i \(-0.224000\pi\)
\(338\) −0.837528 0.546394i −0.837528 0.546394i
\(339\) −0.460607 0.0818807i −0.460607 0.0818807i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.319080 0.126333i 0.319080 0.126333i
\(343\) 0 0
\(344\) −1.66660 0.168112i −1.66660 0.168112i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.234518 1.68575i −0.234518 1.68575i −0.637424 0.770513i \(-0.720000\pi\)
0.402906 0.915241i \(-0.368000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.954865 0.297042i \(-0.904000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.233059 + 0.957499i −0.233059 + 0.957499i
\(353\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(354\) −0.274438 + 0.623413i −0.274438 + 0.623413i
\(355\) 0 0
\(356\) 1.75739 0.546694i 1.75739 0.546694i
\(357\) 0 0
\(358\) 0.841825 + 1.67816i 0.841825 + 1.67816i
\(359\) 0 0 −0.0376902 0.999289i \(-0.512000\pi\)
0.0376902 + 0.999289i \(0.488000\pi\)
\(360\) 0 0
\(361\) 0.738362 1.93561i 0.738362 1.93561i
\(362\) 0 0
\(363\) −0.0205626 0.0157440i −0.0205626 0.0157440i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.988652 0.150226i \(-0.952000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(368\) 0 0
\(369\) 0.0827903 0.00625410i 0.0827903 0.00625410i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(374\) 0.326342 + 0.514233i 0.326342 + 0.514233i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.07132 1.68812i −1.07132 1.68812i −0.556876 0.830596i \(-0.688000\pi\)
−0.514440 0.857527i \(-0.672000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.988652 0.150226i \(-0.0480000\pi\)
−0.988652 + 0.150226i \(0.952000\pi\)
\(384\) −0.894219 + 0.0675506i −0.894219 + 0.0675506i
\(385\) 0 0
\(386\) −0.467630 0.0710564i −0.467630 0.0710564i
\(387\) 0.321385 + 0.0655034i 0.321385 + 0.0655034i
\(388\) 1.51719 + 1.28758i 1.51719 + 1.28758i
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.356412 0.934329i 0.356412 0.934329i
\(393\) 0.857871 1.43000i 0.857871 1.43000i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.0642215 0.181961i 0.0642215 0.181961i
\(397\) 0 0 0.954865 0.297042i \(-0.0960000\pi\)
−0.954865 + 0.297042i \(0.904000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 0.587785i −0.809017 0.587785i
\(401\) −0.00594371 + 0.0244191i −0.00594371 + 0.0244191i −0.974527 0.224271i \(-0.928000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(402\) 0.763043 1.20236i 0.763043 1.20236i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.353281 + 0.427043i −0.353281 + 0.427043i
\(409\) 1.78973 + 0.180532i 1.78973 + 0.180532i 0.938734 0.344643i \(-0.112000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(410\) 0 0
\(411\) 1.48104 0.586386i 1.48104 0.586386i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.768332 0.349825i 0.768332 0.349825i
\(418\) −0.812963 1.52382i −0.812963 1.52382i
\(419\) −1.70365 0.577317i −1.70365 0.577317i −0.711536 0.702650i \(-0.752000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(420\) 0 0
\(421\) 0 0 0.379779 0.925077i \(-0.376000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(422\) 1.81218 + 0.717495i 1.81218 + 0.717495i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.608494 + 0.108170i −0.608494 + 0.108170i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.299328 0.127304i 0.299328 0.127304i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(432\) 1.07202 + 0.0269486i 1.07202 + 0.0269486i
\(433\) −0.456288 + 0.969661i −0.456288 + 0.969661i 0.535827 + 0.844328i \(0.320000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.143094 0.750123i 0.143094 0.750123i
\(439\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(440\) 0 0
\(441\) −0.0877979 + 0.175023i −0.0877979 + 0.175023i
\(442\) 0 0
\(443\) 1.25958 + 1.01563i 1.25958 + 1.01563i 0.998737 + 0.0502443i \(0.0160000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.244753 0.126651i 0.244753 0.126651i −0.332820 0.942991i \(-0.608000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(450\) 0.146063 + 0.130412i 0.146063 + 0.130412i
\(451\) −0.0782967 0.410446i −0.0782967 0.410446i
\(452\) 0.505293 0.129737i 0.505293 0.129737i
\(453\) 0 0
\(454\) −0.736317 + 1.04071i −0.736317 + 1.04071i
\(455\) 0 0
\(456\) 1.09020 1.13210i 1.09020 1.13210i
\(457\) −0.485230 1.37482i −0.485230 1.37482i −0.888136 0.459580i \(-0.848000\pi\)
0.402906 0.915241i \(-0.368000\pi\)
\(458\) 0 0
\(459\) 0.471575 0.465686i 0.471575 0.465686i
\(460\) 0 0
\(461\) 0 0 0.492727 0.870184i \(-0.336000\pi\)
−0.492727 + 0.870184i \(0.664000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.615825 + 0.358995i −0.615825 + 0.358995i
\(467\) 1.34779 + 1.33096i 1.34779 + 1.33096i 0.899405 + 0.437116i \(0.144000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.00954464 0.759498i −0.00954464 0.759498i
\(473\) 0.145015 1.64431i 0.145015 1.64431i
\(474\) 0 0
\(475\) 1.74376 0.175895i 1.74376 0.175895i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.594566 + 1.82989i −0.594566 + 1.82989i
\(483\) 0 0
\(484\) 0.0281434 + 0.00647673i 0.0281434 + 0.00647673i
\(485\) 0 0
\(486\) −0.382535 0.0483254i −0.382535 0.0483254i
\(487\) 0 0 0.675333 0.737513i \(-0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(488\) 0 0
\(489\) −0.0973524 + 0.123891i −0.0973524 + 0.123891i
\(490\) 0 0
\(491\) −1.31738 + 1.11801i −1.31738 + 1.11801i −0.332820 + 0.942991i \(0.608000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(492\) 0.333208 0.183183i 0.333208 0.183183i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0781171 1.24164i 0.0781171 1.24164i
\(499\) 0.313319 0.587288i 0.313319 0.587288i −0.675333 0.737513i \(-0.736000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.285019 + 0.958522i −0.285019 + 0.958522i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.868593 + 0.223017i 0.868593 + 0.223017i
\(508\) 0 0
\(509\) 0 0 −0.863923 0.503623i \(-0.832000\pi\)
0.863923 + 0.503623i \(0.168000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.876307 0.481754i 0.876307 0.481754i
\(513\) −1.43296 + 1.21610i −1.43296 + 1.21610i
\(514\) 1.29767 + 0.800831i 1.29767 + 0.800831i
\(515\) 0 0
\(516\) 1.46387 0.336885i 1.46387 0.336885i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.54616 1.06503i 1.54616 1.06503i 0.577573 0.816339i \(-0.304000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(522\) 0 0
\(523\) 1.62517 1.00294i 1.62517 1.00294i 0.656586 0.754251i \(-0.272000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(524\) −0.209862 + 1.84767i −0.209862 + 1.84767i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.0776361 0.880306i −0.0776361 0.880306i
\(529\) 0.994951 0.100362i 0.994951 0.100362i
\(530\) 0 0
\(531\) −0.0130660 + 0.148154i −0.0130660 + 0.148154i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.33526 + 0.970120i −1.33526 + 0.970120i
\(535\) 0 0
\(536\) −0.218808 + 1.57283i −0.218808 + 1.57283i
\(537\) −1.19798 1.18302i −1.19798 1.18302i
\(538\) 0 0
\(539\) 0.925080 + 0.339630i 0.925080 + 0.339630i
\(540\) 0 0
\(541\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.161209 0.596639i 0.161209 0.596639i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.221538 + 0.627691i 0.221538 + 0.627691i 1.00000 \(0\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(548\) −1.23212 + 1.27947i −1.23212 + 1.27947i
\(549\) 0 0
\(550\) 0.569172 0.804465i 0.569172 0.804465i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.618115 + 0.710058i −0.618115 + 0.710058i
\(557\) 0 0 0.899405 0.437116i \(-0.144000\pi\)
−0.899405 + 0.437116i \(0.856000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.425173 0.342827i −0.425173 0.342827i
\(562\) −1.03485 1.07462i −1.03485 1.07462i
\(563\) −0.571620 + 1.13951i −0.571620 + 1.13951i 0.402906 + 0.915241i \(0.368000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.360532 1.88998i 0.360532 1.88998i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.02980 1.12462i −1.02980 1.12462i −0.992115 0.125333i \(-0.960000\pi\)
−0.0376902 0.999289i \(-0.512000\pi\)
\(570\) 0 0
\(571\) −0.0961038 + 0.204231i −0.0961038 + 0.204231i −0.947098 0.320944i \(-0.896000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.180191 + 0.0766349i −0.180191 + 0.0766349i
\(577\) 1.67453 1.09244i 1.67453 1.09244i 0.823533 0.567269i \(-0.192000\pi\)
0.850994 0.525175i \(-0.176000\pi\)
\(578\) 0.317941 + 0.529981i 0.317941 + 0.529981i
\(579\) 0.417621 0.0742393i 0.417621 0.0742393i
\(580\) 0 0
\(581\) 0 0
\(582\) −1.65917 0.656910i −1.65917 0.656910i
\(583\) 0 0
\(584\) 0.201393 + 0.827401i 0.201393 + 0.827401i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.19513 + 0.544146i −1.19513 + 0.544146i −0.910106 0.414376i \(-0.864000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(588\) −0.0337993 + 0.896129i −0.0337993 + 0.896129i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.302432 + 0.119741i −0.302432 + 0.119741i −0.514440 0.857527i \(-0.672000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(594\) −0.0132793 + 1.05668i −0.0132793 + 1.05668i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(600\) 0.856290 + 0.266377i 0.856290 + 0.266377i
\(601\) 0.360532 + 0.102292i 0.360532 + 0.102292i 0.448383 0.893841i \(-0.352000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(602\) 0 0
\(603\) 0.0735376 0.302122i 0.0735376 0.302122i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.954865 0.297042i \(-0.0960000\pi\)
−0.954865 + 0.297042i \(0.904000\pi\)
\(608\) −0.583304 + 1.65270i −0.583304 + 1.65270i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0431320 + 0.113070i −0.0431320 + 0.113070i
\(613\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(614\) 0.981149 + 0.751231i 0.981149 + 0.751231i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.95414 0.398285i −1.95414 0.398285i −0.992115 0.125333i \(-0.960000\pi\)
−0.962028 0.272952i \(-0.912000\pi\)
\(618\) 0 0
\(619\) −0.710799 0.0536947i −0.710799 0.0536947i −0.285019 0.958522i \(-0.592000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(626\) 1.84595 0.625536i 1.84595 0.625536i
\(627\) 1.12904 + 1.06024i 1.12904 + 1.06024i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(632\) 0 0
\(633\) −1.74564 0.0878193i −1.74564 0.0878193i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.53809 + 1.17766i 1.53809 + 1.17766i 0.920232 + 0.391374i \(0.128000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(642\) −0.217587 + 0.194272i −0.217587 + 0.194272i
\(643\) 0.411708 1.07929i 0.411708 1.07929i −0.556876 0.830596i \(-0.688000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.485677 + 0.968186i 0.485677 + 0.968186i
\(647\) 0 0 0.332820 0.942991i \(-0.392000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(648\) −0.731282 + 0.227489i −0.731282 + 0.227489i
\(649\) 0.748274 0.0188101i 0.748274 0.0188101i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.0415534 0.170718i 0.0415534 0.170718i
\(653\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.253520 + 0.339876i −0.253520 + 0.339876i
\(657\) −0.0229757 0.165153i −0.0229757 0.165153i
\(658\) 0 0
\(659\) 1.18532 1.43281i 1.18532 1.43281i 0.309017 0.951057i \(-0.400000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(660\) 0 0
\(661\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(662\) 0.439782 0.174122i 0.439782 0.174122i
\(663\) 0 0
\(664\) 0.494453 + 1.29620i 0.494453 + 1.29620i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.956628 + 0.378756i 0.956628 + 0.378756i 0.793990 0.607930i \(-0.208000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(674\) −0.886828 1.01874i −0.886828 1.01874i
\(675\) −0.986822 0.419694i −0.986822 0.419694i
\(676\) −0.984564 + 0.175023i −0.984564 + 0.175023i
\(677\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(678\) −0.391819 + 0.255618i −0.391819 + 0.255618i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.325846 1.09582i 0.325846 1.09582i
\(682\) 0 0
\(683\) 1.81964 + 0.0457421i 1.81964 + 0.0457421i 0.920232 0.391374i \(-0.128000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(684\) 0.146119 0.310518i 0.146119 0.310518i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.32998 + 1.01832i −1.32998 + 1.01832i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.733375 0.333909i −0.733375 0.333909i 0.0125660 0.999921i \(-0.496000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.32493 1.06832i −1.32493 1.06832i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.0426199 + 0.258566i 0.0426199 + 0.258566i
\(698\) 0 0
\(699\) 0.419714 0.482145i 0.419714 0.482145i
\(700\) 0 0
\(701\) 0 0 −0.745941 0.666012i \(-0.768000\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.485560 + 0.857527i 0.485560 + 0.857527i
\(705\) 0 0
\(706\) −0.124591 + 0.0157395i −0.124591 + 0.0157395i
\(707\) 0 0
\(708\) 0.226699 + 0.642315i 0.226699 + 0.642315i
\(709\) 0 0 −0.597905 0.801567i \(-0.704000\pi\)
0.597905 + 0.801567i \(0.296000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.906847 1.60154i 0.906847 1.60154i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.76244 + 0.647056i 1.76244 + 0.647056i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.137790 0.990461i \(-0.456000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.786771 1.91644i −0.786771 1.91644i
\(723\) −0.0216818 1.72529i −0.0216818 1.72529i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.0257670 + 0.00259915i −0.0257670 + 0.00259915i
\(727\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(728\) 0 0
\(729\) 1.08923 0.222001i 1.08923 0.222001i
\(730\) 0 0
\(731\) −0.116834 + 1.02863i −0.116834 + 1.02863i
\(732\) 0 0
\(733\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.55254 0.196132i −1.55254 0.196132i
\(738\) 0.0560703 0.0612329i 0.0560703 0.0612329i
\(739\) 1.77385 0.408220i 1.77385 0.408220i 0.793990 0.607930i \(-0.208000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.0708572 0.262244i −0.0708572 0.262244i
\(748\) 0.589910 + 0.151463i 0.589910 + 0.151463i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(752\) 0 0
\(753\) −0.0337993 0.896129i −0.0337993 0.896129i
\(754\) 0 0
\(755\) 0