Properties

Label 2008.1.bd.a.147.1
Level 2008
Weight 1
Character 2008.147
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 147.1
Root \(0.999684 + 0.0251301i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.147
Dual form 2008.1.bd.a.683.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +O(q^{10})\) \(q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +(1.51568 + 0.644618i) q^{11} +(0.484297 + 0.807282i) q^{12} +(-0.929776 - 0.368125i) q^{16} +(-0.263152 + 1.59649i) q^{17} +(0.0952698 - 0.0621530i) q^{18} +(0.106869 - 0.0659520i) q^{19} +(-0.469445 - 1.57875i) q^{22} +(0.313319 - 0.887739i) q^{24} +(0.0627905 + 0.998027i) q^{25} +(0.605582 + 0.855927i) q^{27} +(0.309017 + 0.951057i) q^{32} +(1.46853 - 0.497642i) q^{33} +(1.39786 - 0.814879i) q^{34} +(-0.108617 - 0.0337888i) q^{36} +(-0.118938 - 0.0403044i) q^{38} +(-1.55993 - 1.07452i) q^{41} +(-1.27992 + 0.622047i) q^{43} +(-0.917210 + 1.36805i) q^{44} +(-0.883731 + 0.324450i) q^{48} +(0.823533 - 0.567269i) q^{49} +(0.728969 - 0.684547i) q^{50} +(0.816187 + 1.28611i) q^{51} +(0.273491 - 1.01220i) q^{54} +(0.0336958 - 0.113319i) q^{57} +(-0.316989 - 1.92310i) q^{59} +(0.535827 - 0.844328i) q^{64} +(-1.31952 - 0.814315i) q^{66} +(1.99369 - 0.0501174i) q^{67} +(-1.51890 - 0.557644i) q^{68} +(0.0432003 + 0.105229i) q^{72} +(0.780497 - 1.77297i) q^{73} +(0.669845 + 0.661480i) q^{75} +(0.0447586 + 0.117334i) q^{76} +(0.851064 + 0.195858i) q^{81} +(0.166407 + 1.88687i) q^{82} +(-0.0159812 + 0.423713i) q^{83} +(1.29515 + 0.589686i) q^{86} +(1.63875 - 0.165302i) q^{88} +(-0.698099 - 1.39164i) q^{89} +(0.813304 + 0.474115i) q^{96} +(-0.643272 - 0.959459i) q^{97} +(-0.962028 - 0.272952i) q^{98} +(-0.0923153 + 0.163034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{6}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.637424 0.770513i −0.637424 0.770513i
\(3\) 0.702235 0.626989i 0.702235 0.626989i −0.236499 0.971632i \(-0.576000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(4\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(5\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(6\) −0.930725 0.141424i −0.930725 0.141424i
\(7\) 0 0 0.954865 0.297042i \(-0.0960000\pi\)
−0.954865 + 0.297042i \(0.904000\pi\)
\(8\) 0.876307 0.481754i 0.876307 0.481754i
\(9\) −0.0128376 + 0.113025i −0.0128376 + 0.113025i
\(10\) 0 0
\(11\) 1.51568 + 0.644618i 1.51568 + 0.644618i 0.979855 0.199710i \(-0.0640000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(12\) 0.484297 + 0.807282i 0.484297 + 0.807282i
\(13\) 0 0 0.675333 0.737513i \(-0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.929776 0.368125i −0.929776 0.368125i
\(17\) −0.263152 + 1.59649i −0.263152 + 1.59649i 0.448383 + 0.893841i \(0.352000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(18\) 0.0952698 0.0621530i 0.0952698 0.0621530i
\(19\) 0.106869 0.0659520i 0.106869 0.0659520i −0.470704 0.882291i \(-0.656000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.469445 1.57875i −0.469445 1.57875i
\(23\) 0 0 −0.888136 0.459580i \(-0.848000\pi\)
0.888136 + 0.459580i \(0.152000\pi\)
\(24\) 0.313319 0.887739i 0.313319 0.887739i
\(25\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(26\) 0 0
\(27\) 0.605582 + 0.855927i 0.605582 + 0.855927i
\(28\) 0 0
\(29\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(30\) 0 0
\(31\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(32\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(33\) 1.46853 0.497642i 1.46853 0.497642i
\(34\) 1.39786 0.814879i 1.39786 0.814879i
\(35\) 0 0
\(36\) −0.108617 0.0337888i −0.108617 0.0337888i
\(37\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(38\) −0.118938 0.0403044i −0.118938 0.0403044i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.55993 1.07452i −1.55993 1.07452i −0.962028 0.272952i \(-0.912000\pi\)
−0.597905 0.801567i \(-0.704000\pi\)
\(42\) 0 0
\(43\) −1.27992 + 0.622047i −1.27992 + 0.622047i −0.947098 0.320944i \(-0.896000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(44\) −0.917210 + 1.36805i −0.917210 + 1.36805i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(48\) −0.883731 + 0.324450i −0.883731 + 0.324450i
\(49\) 0.823533 0.567269i 0.823533 0.567269i
\(50\) 0.728969 0.684547i 0.728969 0.684547i
\(51\) 0.816187 + 1.28611i 0.816187 + 1.28611i
\(52\) 0 0
\(53\) 0 0 0.984564 0.175023i \(-0.0560000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(54\) 0.273491 1.01220i 0.273491 1.01220i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0336958 0.113319i 0.0336958 0.113319i
\(58\) 0 0
\(59\) −0.316989 1.92310i −0.316989 1.92310i −0.379779 0.925077i \(-0.624000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.535827 0.844328i 0.535827 0.844328i
\(65\) 0 0
\(66\) −1.31952 0.814315i −1.31952 0.814315i
\(67\) 1.99369 0.0501174i 1.99369 0.0501174i 0.994951 0.100362i \(-0.0320000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(68\) −1.51890 0.557644i −1.51890 0.557644i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.492727 0.870184i \(-0.664000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(72\) 0.0432003 + 0.105229i 0.0432003 + 0.105229i
\(73\) 0.780497 1.77297i 0.780497 1.77297i 0.162637 0.986686i \(-0.448000\pi\)
0.617860 0.786288i \(-0.288000\pi\)
\(74\) 0 0
\(75\) 0.669845 + 0.661480i 0.669845 + 0.661480i
\(76\) 0.0447586 + 0.117334i 0.0447586 + 0.117334i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.260842 0.965382i \(-0.584000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(80\) 0 0
\(81\) 0.851064 + 0.195858i 0.851064 + 0.195858i
\(82\) 0.166407 + 1.88687i 0.166407 + 1.88687i
\(83\) −0.0159812 + 0.423713i −0.0159812 + 0.423713i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.29515 + 0.589686i 1.29515 + 0.589686i
\(87\) 0 0
\(88\) 1.63875 0.165302i 1.63875 0.165302i
\(89\) −0.698099 1.39164i −0.698099 1.39164i −0.910106 0.414376i \(-0.864000\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.813304 + 0.474115i 0.813304 + 0.474115i
\(97\) −0.643272 0.959459i −0.643272 0.959459i −0.999684 0.0251301i \(-0.992000\pi\)
0.356412 0.934329i \(-0.384000\pi\)
\(98\) −0.962028 0.272952i −0.962028 0.272952i
\(99\) −0.0923153 + 0.163034i −0.0923153 + 0.163034i
\(100\) −0.992115 0.125333i −0.992115 0.125333i
\(101\) 0 0 0.0878512 0.996134i \(-0.472000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(102\) 0.470704 1.44868i 0.470704 1.44868i
\(103\) 0 0 −0.0125660 0.999921i \(-0.504000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.653011 + 1.22401i −0.653011 + 1.22401i 0.309017 + 0.951057i \(0.400000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(108\) −0.954241 + 0.434470i −0.954241 + 0.434470i
\(109\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.59967 1.16223i −1.59967 1.16223i −0.888136 0.459580i \(-0.848000\pi\)
−0.711536 0.702650i \(-0.752000\pi\)
\(114\) −0.108793 + 0.0462694i −0.108793 + 0.0462694i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.27972 + 1.47008i −1.27972 + 1.47008i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.18811 + 1.23376i 1.18811 + 1.23376i
\(122\) 0 0
\(123\) −1.76915 + 0.223496i −1.76915 + 0.223496i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.0376902 0.999289i \(-0.512000\pi\)
0.0376902 + 0.999289i \(0.488000\pi\)
\(128\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(129\) −0.508786 + 1.23932i −0.508786 + 1.23932i
\(130\) 0 0
\(131\) 0.756300 0.391359i 0.756300 0.391359i −0.0376902 0.999289i \(-0.512000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(132\) 0.213652 + 1.53577i 0.213652 + 1.53577i
\(133\) 0 0
\(134\) −1.30944 1.50422i −1.30944 1.50422i
\(135\) 0 0
\(136\) 0.538513 + 1.52579i 0.538513 + 1.52579i
\(137\) −1.81205 + 0.770665i −1.81205 + 0.770665i −0.837528 + 0.546394i \(0.816000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(138\) 0 0
\(139\) 1.48764 + 0.112379i 1.48764 + 0.112379i 0.793990 0.607930i \(-0.208000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.0535432 0.100362i 0.0535432 0.100362i
\(145\) 0 0
\(146\) −1.86361 + 0.528753i −1.86361 + 0.528753i
\(147\) 0.222642 0.914702i 0.222642 0.914702i
\(148\) 0 0
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0.0827038 0.937768i 0.0827038 0.937768i
\(151\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(152\) 0.0618772 0.109279i 0.0618772 0.109279i
\(153\) −0.177064 0.0502377i −0.177064 0.0502377i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.391577 0.780600i −0.391577 0.780600i
\(163\) 1.98739 0.200470i 1.98739 0.200470i 0.988652 0.150226i \(-0.0480000\pi\)
0.998737 0.0502443i \(-0.0160000\pi\)
\(164\) 1.34779 1.33096i 1.34779 1.33096i
\(165\) 0 0
\(166\) 0.336663 0.257771i 0.336663 0.257771i
\(167\) 0 0 −0.745941 0.666012i \(-0.768000\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(168\) 0 0
\(169\) −0.0878512 0.996134i −0.0878512 0.996134i
\(170\) 0 0
\(171\) 0.00608226 + 0.0129255i 0.00608226 + 0.0129255i
\(172\) −0.371196 1.37381i −0.371196 1.37381i
\(173\) 0 0 0.778462 0.627691i \(-0.216000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.17195 1.15731i −1.17195 1.15731i
\(177\) −1.42837 1.15172i −1.42837 1.15172i
\(178\) −0.627295 + 1.42496i −0.627295 + 1.42496i
\(179\) −0.744257 1.81288i −0.744257 1.81288i −0.556876 0.830596i \(-0.688000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.236499 0.971632i \(-0.576000\pi\)
0.236499 + 0.971632i \(0.424000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.42798 + 2.25014i −1.42798 + 2.25014i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.212007 0.977268i \(-0.432000\pi\)
−0.212007 + 0.977268i \(0.568000\pi\)
\(192\) −0.153108 0.928874i −0.153108 0.928874i
\(193\) 0.118658 + 0.129583i 0.118658 + 0.129583i 0.793990 0.607930i \(-0.208000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(194\) −0.329239 + 1.10723i −0.329239 + 1.10723i
\(195\) 0 0
\(196\) 0.402906 + 0.915241i 0.402906 + 0.915241i
\(197\) 0 0 0.260842 0.965382i \(-0.416000\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(198\) 0.184464 0.0327916i 0.184464 0.0327916i
\(199\) 0 0 −0.597905 0.801567i \(-0.704000\pi\)
0.597905 + 0.801567i \(0.296000\pi\)
\(200\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(201\) 1.36861 1.28521i 1.36861 1.28521i
\(202\) 0 0
\(203\) 0 0
\(204\) −1.41626 + 0.560738i −1.41626 + 0.560738i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.204493 0.0310727i 0.204493 0.0310727i
\(210\) 0 0
\(211\) −1.62243 0.416570i −1.62243 0.416570i −0.675333 0.737513i \(-0.736000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.35936 0.277059i 1.35936 0.277059i
\(215\) 0 0
\(216\) 0.943021 + 0.458313i 0.943021 + 0.458313i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.563543 1.73441i −0.563543 1.73441i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.112856 0.993611i \(-0.536000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(224\) 0 0
\(225\) −0.113608 0.00571535i −0.113608 0.00571535i
\(226\) 0.124156 + 1.97340i 0.124156 + 1.97340i
\(227\) −0.583304 + 1.65270i −0.583304 + 1.65270i 0.162637 + 0.986686i \(0.448000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(228\) 0.104998 + 0.0543329i 0.104998 + 0.0543329i
\(229\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.751067 + 0.489988i −0.751067 + 0.489988i −0.863923 0.503623i \(-0.832000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.94844 + 0.0489799i 1.94844 + 0.0489799i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(240\) 0 0
\(241\) 0.0618772 0.983510i 0.0618772 0.983510i −0.837528 0.546394i \(-0.816000\pi\)
0.899405 0.437116i \(-0.144000\pi\)
\(242\) 0.193303 1.70188i 0.193303 1.70188i
\(243\) −0.198355 + 0.109047i −0.198355 + 0.109047i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.29991 + 1.22069i 1.29991 + 1.22069i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.254441 + 0.307566i 0.254441 + 0.307566i
\(250\) 0 0
\(251\) 0.954865 + 0.297042i 0.954865 + 0.297042i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(257\) 1.81958 + 0.276485i 1.81958 + 0.276485i 0.968583 0.248690i \(-0.0800000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(258\) 1.27922 0.397944i 1.27922 0.397944i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.783631 0.333278i −0.783631 0.333278i
\(263\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(264\) 1.04714 1.14356i 1.04714 1.14356i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.36277 0.539561i −1.36277 0.539561i
\(268\) −0.324350 + 1.96777i −0.324350 + 1.96777i
\(269\) 0 0 0.837528 0.546394i \(-0.184000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(270\) 0 0
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0.832381 1.38751i 0.832381 1.38751i
\(273\) 0 0
\(274\) 1.74885 + 0.904972i 1.74885 + 0.904972i
\(275\) −0.548175 + 1.55317i −0.548175 + 1.55317i
\(276\) 0 0
\(277\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(278\) −0.861670 1.21788i −0.861670 1.21788i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.738843 0.940252i −0.738843 0.940252i 0.260842 0.965382i \(-0.416000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(282\) 0 0
\(283\) 0.304522 + 0.937223i 0.304522 + 0.937223i 0.979855 + 0.199710i \(0.0640000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.111460 + 0.0227173i −0.111460 + 0.0227173i
\(289\) −1.53244 0.519298i −1.53244 0.519298i
\(290\) 0 0
\(291\) −1.05330 0.270441i −1.05330 0.270441i
\(292\) 1.59532 + 1.09889i 1.59532 + 1.09889i
\(293\) 0 0 0.988652 0.150226i \(-0.0480000\pi\)
−0.988652 + 0.150226i \(0.952000\pi\)
\(294\) −0.846707 + 0.411504i −0.846707 + 0.411504i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.366123 + 1.68768i 0.366123 + 1.68768i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.775280 + 0.534031i −0.775280 + 0.534031i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.123643 + 0.0219796i −0.123643 + 0.0219796i
\(305\) 0 0
\(306\) 0.0741563 + 0.168453i 0.0741563 + 0.168453i
\(307\) −0.936894 + 0.972897i −0.936894 + 0.972897i −0.999684 0.0251301i \(-0.992000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.212007 0.977268i \(-0.432000\pi\)
−0.212007 + 0.977268i \(0.568000\pi\)
\(312\) 0 0
\(313\) −1.32998 1.01832i −1.32998 1.01832i −0.997159 0.0753268i \(-0.976000\pi\)
−0.332820 0.942991i \(-0.608000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.308873 + 1.26897i 0.308873 + 1.26897i
\(322\) 0 0
\(323\) 0.0771690 + 0.187970i 0.0771690 + 0.187970i
\(324\) −0.351862 + 0.799289i −0.351862 + 0.799289i
\(325\) 0 0
\(326\) −1.42127 1.40352i −1.42127 1.40352i
\(327\) 0 0
\(328\) −1.88463 0.190105i −1.88463 0.190105i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.0748104 + 0.158980i 0.0748104 + 0.158980i 0.938734 0.344643i \(-0.112000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(332\) −0.413213 0.0950940i −0.413213 0.0950940i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.81964 + 0.828489i 1.81964 + 0.828489i 0.920232 + 0.391374i \(0.128000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(338\) −0.711536 + 0.702650i −0.711536 + 0.702650i
\(339\) −1.85205 + 0.186818i −1.85205 + 0.186818i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.00608226 0.0129255i 0.00608226 0.0129255i
\(343\) 0 0
\(344\) −0.821927 + 1.16171i −0.821927 + 1.16171i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.888873 + 0.518167i 0.888873 + 0.518167i 0.876307 0.481754i \(-0.160000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.962028 0.272952i \(-0.912000\pi\)
0.962028 + 0.272952i \(0.0880000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.144697 + 1.64070i −0.144697 + 1.64070i
\(353\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(354\) 0.0230569 + 1.83471i 0.0230569 + 1.83471i
\(355\) 0 0
\(356\) 1.49780 0.424966i 1.49780 0.424966i
\(357\) 0 0
\(358\) −0.922443 + 1.72904i −0.922443 + 1.72904i
\(359\) 0 0 0.910106 0.414376i \(-0.136000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(360\) 0 0
\(361\) −0.441312 + 0.879745i −0.441312 + 0.879745i
\(362\) 0 0
\(363\) 1.60788 + 0.121462i 1.60788 + 0.121462i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.137790 0.990461i \(-0.456000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(368\) 0 0
\(369\) 0.141473 0.162516i 0.141473 0.162516i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.379779 0.925077i \(-0.376000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(374\) 2.64399 0.334014i 2.64399 0.334014i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.469268 0.0592824i 0.469268 0.0592824i 0.112856 0.993611i \(-0.464000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.137790 0.990461i \(-0.544000\pi\)
0.137790 + 0.990461i \(0.456000\pi\)
\(384\) −0.618115 + 0.710058i −0.618115 + 0.710058i
\(385\) 0 0
\(386\) 0.0242101 0.174026i 0.0242101 0.174026i
\(387\) −0.0538755 0.152648i −0.0538755 0.152648i
\(388\) 1.06300 0.452093i 1.06300 0.452093i
\(389\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.448383 0.893841i 0.448383 0.893841i
\(393\) 0.285723 0.749018i 0.285723 0.749018i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.142848 0.121230i −0.142848 0.121230i
\(397\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.309017 0.951057i 0.309017 0.951057i
\(401\) −0.108559 + 1.23094i −0.108559 + 1.23094i 0.728969 + 0.684547i \(0.240000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(402\) −1.86266 0.235309i −1.86266 0.235309i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.33482 + 0.733822i 1.33482 + 0.733822i
\(409\) 0.465416 0.657817i 0.465416 0.657817i −0.514440 0.857527i \(-0.672000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(410\) 0 0
\(411\) −0.789290 + 1.67733i −0.789290 + 1.67733i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.11514 0.853820i 1.11514 0.853820i
\(418\) −0.154291 0.137758i −0.154291 0.137758i
\(419\) −0.0303712 + 0.805240i −0.0303712 + 0.805240i 0.899405 + 0.437116i \(0.144000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(422\) 0.713204 + 1.51564i 0.713204 + 1.51564i
\(423\) 0 0
\(424\) 0 0
\(425\) −1.60986 0.162389i −1.60986 0.162389i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.07997 0.870800i −1.07997 0.870800i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.492727 0.870184i \(-0.664000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(432\) −0.247968 1.01875i −0.247968 1.01875i
\(433\) −1.92189 + 0.493458i −1.92189 + 0.493458i −0.929776 + 0.368125i \(0.880000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.977168 + 1.53977i −0.977168 + 1.53977i
\(439\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(440\) 0 0
\(441\) 0.0535432 + 0.100362i 0.0535432 + 0.100362i
\(442\) 0 0
\(443\) 0.100515 + 0.609805i 0.100515 + 0.609805i 0.988652 + 0.150226i \(0.0480000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.70118 0.302413i 1.70118 0.302413i 0.762443 0.647056i \(-0.224000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(450\) 0.0680124 + 0.0911792i 0.0680124 + 0.0911792i
\(451\) −1.67171 2.63419i −1.67171 2.63419i
\(452\) 1.44139 1.35356i 1.44139 1.35356i
\(453\) 0 0
\(454\) 1.64524 0.604026i 1.64524 0.604026i
\(455\) 0 0
\(456\) −0.0250641 0.115536i −0.0250641 0.115536i
\(457\) −0.971998 + 0.824898i −0.971998 + 0.824898i −0.984564 0.175023i \(-0.944000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(458\) 0 0
\(459\) −1.52584 + 0.741567i −1.52584 + 0.741567i
\(460\) 0 0
\(461\) 0 0 −0.823533 0.567269i \(-0.808000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(462\) 0 0
\(463\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.856290 + 0.266377i 0.856290 + 0.266377i
\(467\) −0.0677975 0.0329499i −0.0677975 0.0329499i 0.402906 0.915241i \(-0.368000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.20424 1.53252i −1.20424 1.53252i
\(473\) −2.34093 + 0.117767i −2.34093 + 0.117767i
\(474\) 0 0
\(475\) 0.0725322 + 0.102517i 0.0725322 + 0.102517i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.888136 0.459580i \(-0.848000\pi\)
0.888136 + 0.459580i \(0.152000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.797250 + 0.579236i −0.797250 + 0.579236i
\(483\) 0 0
\(484\) −1.43454 + 0.935877i −1.43454 + 0.935877i
\(485\) 0 0
\(486\) 0.210458 + 0.0833264i 0.210458 + 0.0833264i
\(487\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(488\) 0 0
\(489\) 1.26992 1.38685i 1.26992 1.38685i
\(490\) 0 0
\(491\) 1.75739 + 0.747418i 1.75739 + 0.747418i 0.994951 + 0.100362i \(0.0320000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(492\) 0.111969 1.77969i 0.111969 1.77969i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0747971 0.392100i 0.0747971 0.392100i
\(499\) −1.13747 + 1.01559i −1.13747 + 1.01559i −0.137790 + 0.990461i \(0.544000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.379779 0.925077i −0.379779 0.925077i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.686257 0.644438i −0.686257 0.644438i
\(508\) 0 0
\(509\) 0 0 0.954865 0.297042i \(-0.0960000\pi\)
−0.954865 + 0.297042i \(0.904000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.0627905 0.998027i 0.0627905 0.998027i
\(513\) 0.121168 + 0.0515326i 0.121168 + 0.0515326i
\(514\) −0.946807 1.57825i −0.946807 1.57825i
\(515\) 0 0
\(516\) −1.12203 0.731999i −1.12203 0.731999i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.66770 1.02919i 1.66770 1.02919i 0.728969 0.684547i \(-0.240000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(522\) 0 0
\(523\) 0.989810 1.64993i 0.989810 1.64993i 0.260842 0.965382i \(-0.416000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(524\) 0.242711 + 0.816237i 0.242711 + 0.816237i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.54860 0.0779068i −1.54860 0.0779068i
\(529\) 0.577573 + 0.816339i 0.577573 + 0.816339i
\(530\) 0 0
\(531\) 0.221427 0.0111395i 0.221427 0.0111395i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.452927 + 1.39396i 0.452927 + 1.39396i
\(535\) 0 0
\(536\) 1.72294 1.00438i 1.72294 1.00438i
\(537\) −1.65930 0.806429i −1.65930 0.806429i
\(538\) 0 0
\(539\) 1.61389 0.328935i 1.61389 0.328935i
\(540\) 0 0
\(541\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.59967 + 0.243070i −1.59967 + 0.243070i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.16264 0.986686i 1.16264 0.986686i 0.162637 0.986686i \(-0.448000\pi\)
1.00000 \(0\)
\(548\) −0.417469 1.92437i −0.417469 1.92437i
\(549\) 0 0
\(550\) 1.54616 0.567649i 1.54616 0.567649i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.389145 + 1.44024i −0.389145 + 1.44024i
\(557\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.408034 + 2.47546i 0.408034 + 2.47546i
\(562\) −0.253520 + 1.16863i −0.253520 + 1.16863i
\(563\) −0.824962 1.54632i −0.824962 1.54632i −0.837528 0.546394i \(-0.816000\pi\)
0.0125660 0.999921i \(-0.496000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.528033 0.832047i 0.528033 0.832047i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.83988 + 0.0462510i −1.83988 + 0.0462510i −0.929776 0.368125i \(-0.880000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(570\) 0 0
\(571\) −0.552130 + 0.141763i −0.552130 + 0.141763i −0.514440 0.857527i \(-0.672000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.0885510 + 0.0714007i 0.0885510 + 0.0714007i
\(577\) 0.336555 + 0.332352i 0.336555 + 0.332352i 0.850994 0.525175i \(-0.176000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(578\) 0.576687 + 1.51178i 0.576687 + 1.51178i
\(579\) 0.164572 + 0.0166006i 0.164572 + 0.0166006i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.463019 + 0.983966i 0.463019 + 0.983966i
\(583\) 0 0
\(584\) −0.170182 1.92968i −0.170182 1.92968i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.414211 0.317147i 0.414211 0.317147i −0.379779 0.925077i \(-0.624000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(588\) 0.856781 + 0.390096i 0.856781 + 0.390096i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.590686 + 1.25527i −0.590686 + 1.25527i 0.356412 + 0.934329i \(0.384000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(594\) 1.06701 1.35787i 1.06701 1.35787i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(600\) 0.905660 + 0.256959i 0.905660 + 0.256959i
\(601\) 0.528033 0.932536i 0.528033 0.932536i −0.470704 0.882291i \(-0.656000\pi\)
0.998737 0.0502443i \(-0.0160000\pi\)
\(602\) 0 0
\(603\) −0.0199296 + 0.225979i −0.0199296 + 0.225979i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(608\) 0.0957483 + 0.0812580i 0.0957483 + 0.0812580i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.0825264 0.164515i 0.0825264 0.164515i
\(613\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(614\) 1.34683 + 0.101741i 1.34683 + 0.101741i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.437049 1.23831i −0.437049 1.23831i −0.929776 0.368125i \(-0.880000\pi\)
0.492727 0.870184i \(-0.336000\pi\)
\(618\) 0 0
\(619\) 0.588804 + 0.676387i 0.588804 + 0.676387i 0.968583 0.248690i \(-0.0800000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(626\) 0.0631332 + 1.67387i 0.0631332 + 1.67387i
\(627\) 0.124120 0.150035i 0.124120 0.150035i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.379779 0.925077i \(-0.376000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(632\) 0 0
\(633\) −1.40051 + 0.724717i −1.40051 + 0.724717i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.45380 0.109822i −1.45380 0.109822i −0.675333 0.737513i \(-0.736000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(642\) 0.780877 1.04686i 0.780877 1.04686i
\(643\) 0.841825 1.67816i 0.841825 1.67816i 0.112856 0.993611i \(-0.464000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.0956444 0.179277i 0.0956444 0.179277i
\(647\) 0 0 −0.762443 0.647056i \(-0.776000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(648\) 0.840148 0.238371i 0.840148 0.238371i
\(649\) 0.759213 3.11915i 0.759213 3.11915i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.175480 + 1.98975i −0.175480 + 1.98975i
\(653\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.05483 + 1.57331i 1.05483 + 1.57331i
\(657\) 0.190370 + 0.110976i 0.190370 + 0.110976i
\(658\) 0 0
\(659\) −0.746226 0.410241i −0.746226 0.410241i 0.0627905 0.998027i \(-0.480000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(660\) 0 0
\(661\) 0 0 0.617860 0.786288i \(-0.288000\pi\)
−0.617860 + 0.786288i \(0.712000\pi\)
\(662\) 0.0748104 0.158980i 0.0748104 0.158980i
\(663\) 0 0
\(664\) 0.190121 + 0.379001i 0.190121 + 0.379001i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.303506 0.644982i −0.303506 0.644982i 0.693653 0.720309i \(-0.256000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(674\) −0.521518 1.93015i −0.521518 1.93015i
\(675\) −0.816213 + 0.658131i −0.816213 + 0.658131i
\(676\) 0.994951 + 0.100362i 0.994951 + 0.100362i
\(677\) 0 0 −0.356412 0.934329i \(-0.616000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(678\) 1.32449 + 1.30795i 1.32449 + 1.30795i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.626607 + 1.52631i 0.626607 + 1.52631i
\(682\) 0 0
\(683\) −0.375556 1.54293i −0.375556 1.54293i −0.778462 0.627691i \(-0.784000\pi\)
0.402906 0.915241i \(-0.368000\pi\)
\(684\) −0.0138362 + 0.00355253i −0.0138362 + 0.00355253i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.41903 0.107195i 1.41903 0.107195i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.0199546 + 0.0152786i 0.0199546 + 0.0152786i 0.617860 0.786288i \(-0.288000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.167334 1.01518i −0.167334 1.01518i
\(695\) 0 0
\(696\) 0 0
\(697\) 2.12596 2.20766i 2.12596 2.20766i
\(698\) 0 0
\(699\) −0.220208 + 0.814997i −0.220208 + 0.814997i
\(700\) 0 0
\(701\) 0 0 −0.597905 0.801567i \(-0.704000\pi\)
0.597905 + 0.801567i \(0.296000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.35641 0.934329i 1.35641 0.934329i
\(705\) 0 0
\(706\) 0.348445 0.137959i 0.348445 0.137959i
\(707\) 0 0
\(708\) 1.39897 1.18725i 1.39897 1.18725i
\(709\) 0 0 0.556876 0.830596i \(-0.312000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.28218 0.883195i −1.28218 0.883195i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.92023 0.391374i 1.92023 0.391374i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.863923 0.503623i \(-0.168000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.959158 0.220734i 0.959158 0.220734i
\(723\) −0.573198 0.729451i −0.573198 0.729451i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.931316 1.31632i −0.931316 1.31632i
\(727\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(728\) 0 0
\(729\) −0.361575 + 1.02447i −0.361575 + 1.02447i
\(730\) 0 0
\(731\) −0.656279 2.20707i −0.656279 2.20707i
\(732\) 0 0
\(733\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.05410 + 1.20921i 3.05410 + 1.20921i
\(738\) −0.215399 0.00541471i −0.215399 0.00541471i
\(739\) −1.32998 0.867664i −1.32998 0.867664i −0.332820 0.942991i \(-0.608000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.0476848 0.00724570i −0.0476848 0.00724570i
\(748\) −1.94271 1.82432i −1.94271 1.82432i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(752\) 0 0
\(753\) 0.856781 0.390096i 0.856781 0.390096i
\(754\) 0 0
\(755\) 0