Properties

Label 2008.1.bd.a.339.1
Level 2008
Weight 1
Character 2008.339
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 339.1
Root \(0.984564 - 0.175023i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.339
Dual form 2008.1.bd.a.1931.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +O(q^{10})\) \(q+(-0.992115 - 0.125333i) q^{2} +(0.216489 - 0.527330i) q^{3} +(0.968583 + 0.248690i) q^{4} +(-0.280874 + 0.496038i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(0.480326 + 0.474328i) q^{9} +(0.891606 + 0.302139i) q^{11} +(0.340829 - 0.456924i) q^{12} +(0.876307 + 0.481754i) q^{16} +(-0.562476 - 0.256098i) q^{17} +(-0.417090 - 0.530789i) q^{18} +(0.635213 + 0.567148i) q^{19} +(-0.846707 - 0.411504i) q^{22} +(-0.395409 + 0.410604i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(0.878680 - 0.373702i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(0.352349 - 0.404761i) q^{33} +(0.525944 + 0.324576i) q^{34} +(0.347276 + 0.578879i) q^{36} +(-0.559121 - 0.642289i) q^{38} +(-0.618115 + 1.15860i) q^{41} +(1.35024 + 0.0339424i) q^{43} +(0.788455 + 0.514380i) q^{44} +(0.443754 - 0.357808i) q^{48} +(-0.470704 - 0.882291i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.256818 + 0.241168i) q^{51} +(-0.918589 + 0.260627i) q^{54} +(0.436590 - 0.212185i) q^{57} +(-0.0228729 + 0.0104141i) q^{59} +(0.728969 + 0.684547i) q^{64} +(-0.400301 + 0.357408i) q^{66} +(1.70118 + 0.302413i) q^{67} +(-0.481116 - 0.387935i) q^{68} +(-0.271984 - 0.617839i) q^{72} +(0.0886310 - 0.364131i) q^{73} +(0.384966 + 0.420411i) q^{75} +(0.474212 + 0.707301i) q^{76} +(0.00164310 + 0.130746i) q^{81} +(0.758452 - 1.07199i) q^{82} +(-0.520201 - 1.92528i) q^{83} +(-1.33534 - 0.202905i) q^{86} +(-0.717769 - 0.609144i) q^{88} +(-0.00850716 + 0.0748988i) q^{89} +(-0.485100 + 0.299370i) q^{96} +(-1.54144 + 1.00562i) q^{97} +(0.356412 + 0.934329i) q^{98} +(0.284949 + 0.568039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{83}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.992115 0.125333i −0.992115 0.125333i
\(3\) 0.216489 0.527330i 0.216489 0.527330i −0.778462 0.627691i \(-0.784000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(4\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(5\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(6\) −0.280874 + 0.496038i −0.280874 + 0.496038i
\(7\) 0 0 0.514440 0.857527i \(-0.328000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(8\) −0.929776 0.368125i −0.929776 0.368125i
\(9\) 0.480326 + 0.474328i 0.480326 + 0.474328i
\(10\) 0 0
\(11\) 0.891606 + 0.302139i 0.891606 + 0.302139i 0.728969 0.684547i \(-0.240000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(12\) 0.340829 0.456924i 0.340829 0.456924i
\(13\) 0 0 0.888136 0.459580i \(-0.152000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(17\) −0.562476 0.256098i −0.562476 0.256098i 0.112856 0.993611i \(-0.464000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(18\) −0.417090 0.530789i −0.417090 0.530789i
\(19\) 0.635213 + 0.567148i 0.635213 + 0.567148i 0.920232 0.391374i \(-0.128000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.846707 0.411504i −0.846707 0.411504i
\(23\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(24\) −0.395409 + 0.410604i −0.395409 + 0.410604i
\(25\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(26\) 0 0
\(27\) 0.878680 0.373702i 0.878680 0.373702i
\(28\) 0 0
\(29\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(30\) 0 0
\(31\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(32\) −0.809017 0.587785i −0.809017 0.587785i
\(33\) 0.352349 0.404761i 0.352349 0.404761i
\(34\) 0.525944 + 0.324576i 0.525944 + 0.324576i
\(35\) 0 0
\(36\) 0.347276 + 0.578879i 0.347276 + 0.578879i
\(37\) 0 0 −0.162637 0.986686i \(-0.552000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(38\) −0.559121 0.642289i −0.559121 0.642289i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.618115 + 1.15860i −0.618115 + 1.15860i 0.356412 + 0.934329i \(0.384000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(42\) 0 0
\(43\) 1.35024 + 0.0339424i 1.35024 + 0.0339424i 0.693653 0.720309i \(-0.256000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(44\) 0.788455 + 0.514380i 0.788455 + 0.514380i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(48\) 0.443754 0.357808i 0.443754 0.357808i
\(49\) −0.470704 0.882291i −0.470704 0.882291i
\(50\) 0.535827 0.844328i 0.535827 0.844328i
\(51\) −0.256818 + 0.241168i −0.256818 + 0.241168i
\(52\) 0 0
\(53\) 0 0 −0.332820 0.942991i \(-0.608000\pi\)
0.332820 + 0.942991i \(0.392000\pi\)
\(54\) −0.918589 + 0.260627i −0.918589 + 0.260627i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.436590 0.212185i 0.436590 0.212185i
\(58\) 0 0
\(59\) −0.0228729 + 0.0104141i −0.0228729 + 0.0104141i −0.425779 0.904827i \(-0.640000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(60\) 0 0
\(61\) 0 0 0.285019 0.958522i \(-0.408000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(65\) 0 0
\(66\) −0.400301 + 0.357408i −0.400301 + 0.357408i
\(67\) 1.70118 + 0.302413i 1.70118 + 0.302413i 0.938734 0.344643i \(-0.112000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(68\) −0.481116 0.387935i −0.481116 0.387935i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(72\) −0.271984 0.617839i −0.271984 0.617839i
\(73\) 0.0886310 0.364131i 0.0886310 0.364131i −0.910106 0.414376i \(-0.864000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(74\) 0 0
\(75\) 0.384966 + 0.420411i 0.384966 + 0.420411i
\(76\) 0.474212 + 0.707301i 0.474212 + 0.707301i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.962028 0.272952i \(-0.912000\pi\)
0.962028 + 0.272952i \(0.0880000\pi\)
\(80\) 0 0
\(81\) 0.00164310 + 0.130746i 0.00164310 + 0.130746i
\(82\) 0.758452 1.07199i 0.758452 1.07199i
\(83\) −0.520201 1.92528i −0.520201 1.92528i −0.332820 0.942991i \(-0.608000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.33534 0.202905i −1.33534 0.202905i
\(87\) 0 0
\(88\) −0.717769 0.609144i −0.717769 0.609144i
\(89\) −0.00850716 + 0.0748988i −0.00850716 + 0.0748988i −0.997159 0.0753268i \(-0.976000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.485100 + 0.299370i −0.485100 + 0.299370i
\(97\) −1.54144 + 1.00562i −1.54144 + 1.00562i −0.556876 + 0.830596i \(0.688000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(98\) 0.356412 + 0.934329i 0.356412 + 0.934329i
\(99\) 0.284949 + 0.568039i 0.284949 + 0.568039i
\(100\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(101\) 0 0 −0.577573 0.816339i \(-0.696000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(102\) 0.285019 0.207079i 0.285019 0.207079i
\(103\) 0 0 0.0878512 0.996134i \(-0.472000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.452605 1.52211i −0.452605 1.52211i −0.809017 0.587785i \(-0.800000\pi\)
0.356412 0.934329i \(-0.384000\pi\)
\(108\) 0.944011 0.143442i 0.944011 0.143442i
\(109\) 0 0 0.556876 0.830596i \(-0.312000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.304522 0.937223i 0.304522 0.937223i −0.675333 0.737513i \(-0.736000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(114\) −0.459742 + 0.155793i −0.459742 + 0.155793i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.0239977 0.00746527i 0.0239977 0.00746527i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.0903174 0.0691528i −0.0903174 0.0691528i
\(122\) 0 0
\(123\) 0.477149 + 0.576774i 0.477149 + 0.576774i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.260842 0.965382i \(-0.416000\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(128\) −0.637424 0.770513i −0.637424 0.770513i
\(129\) 0.310210 0.704673i 0.310210 0.704673i
\(130\) 0 0
\(131\) 0.123051 + 0.0250798i 0.123051 + 0.0250798i 0.260842 0.965382i \(-0.416000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(132\) 0.441940 0.304418i 0.441940 0.304418i
\(133\) 0 0
\(134\) −1.64986 0.513242i −1.64986 0.513242i
\(135\) 0 0
\(136\) 0.428701 + 0.445175i 0.428701 + 0.445175i
\(137\) 0.630426 0.213633i 0.630426 0.213633i 0.0125660 0.999921i \(-0.496000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(138\) 0 0
\(139\) 0.656200 0.382531i 0.656200 0.382531i −0.137790 0.990461i \(-0.544000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.192404 + 0.647056i 0.192404 + 0.647056i
\(145\) 0 0
\(146\) −0.133570 + 0.350152i −0.133570 + 0.350152i
\(147\) −0.567160 + 0.0572100i −0.567160 + 0.0572100i
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) −0.329239 0.465345i −0.329239 0.465345i
\(151\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(152\) −0.381825 0.761158i −0.381825 0.761158i
\(153\) −0.148698 0.389809i −0.148698 0.389809i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.0147567 0.129921i 0.0147567 0.129921i
\(163\) 1.43146 + 1.21483i 1.43146 + 1.21483i 0.938734 + 0.344643i \(0.112000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(164\) −0.886828 + 0.968481i −0.886828 + 0.968481i
\(165\) 0 0
\(166\) 0.274798 + 1.97529i 0.274798 + 1.97529i
\(167\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(168\) 0 0
\(169\) 0.577573 0.816339i 0.577573 0.816339i
\(170\) 0 0
\(171\) 0.0360951 + 0.573715i 0.0360951 + 0.573715i
\(172\) 1.29938 + 0.368667i 1.29938 + 0.368667i
\(173\) 0 0 0.0376902 0.999289i \(-0.488000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.635764 + 0.694301i 0.635764 + 0.694301i
\(177\) 0.000539959 0.0143161i 0.000539959 0.0143161i
\(178\) 0.0178274 0.0732420i 0.0178274 0.0732420i
\(179\) 0.131055 + 0.297704i 0.131055 + 0.297704i 0.968583 0.248690i \(-0.0800000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.994951 0.100362i \(-0.968000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.424130 0.398285i −0.424130 0.398285i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(192\) 0.518795 0.236210i 0.518795 0.236210i
\(193\) −1.02593 0.530882i −1.02593 0.530882i −0.137790 0.990461i \(-0.544000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(194\) 1.65532 0.804496i 1.65532 0.804496i
\(195\) 0 0
\(196\) −0.236499 0.971632i −0.236499 0.971632i
\(197\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(198\) −0.211508 0.599273i −0.211508 0.599273i
\(199\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(200\) 0.728969 0.684547i 0.728969 0.684547i
\(201\) 0.527757 0.831612i 0.527757 0.831612i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.308726 + 0.169723i −0.308726 + 0.169723i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.395002 + 0.697595i 0.395002 + 0.697595i
\(210\) 0 0
\(211\) −0.231551 1.21383i −0.231551 1.21383i −0.888136 0.459580i \(-0.848000\pi\)
0.656586 0.754251i \(-0.272000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.258265 + 1.56684i 0.258265 + 1.56684i
\(215\) 0 0
\(216\) −0.954545 + 0.0239954i −0.954545 + 0.0239954i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.172830 0.125568i −0.172830 0.125568i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.711536 0.702650i \(-0.248000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(224\) 0 0
\(225\) −0.633698 + 0.232653i −0.633698 + 0.232653i
\(226\) −0.419586 + 0.891666i −0.419586 + 0.891666i
\(227\) −1.28989 + 1.33945i −1.28989 + 1.33945i −0.379779 + 0.925077i \(0.624000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(228\) 0.475642 0.0969435i 0.475642 0.0969435i
\(229\) 0 0 −0.899405 0.437116i \(-0.856000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.139459 + 0.177475i 0.139459 + 0.177475i 0.850994 0.525175i \(-0.176000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.0247441 + 0.00439869i −0.0247441 + 0.00439869i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(240\) 0 0
\(241\) −0.381825 0.811419i −0.381825 0.811419i −0.999684 0.0251301i \(-0.992000\pi\)
0.617860 0.786288i \(-0.288000\pi\)
\(242\) 0.0809381 + 0.0799273i 0.0809381 + 0.0799273i
\(243\) 0.957096 + 0.378941i 0.957096 + 0.378941i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.401098 0.632029i −0.401098 0.632029i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.12787 0.142484i −1.12787 0.142484i
\(250\) 0 0
\(251\) −0.514440 0.857527i −0.514440 0.857527i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(257\) −0.933322 + 1.64830i −0.933322 + 1.64830i −0.187381 + 0.982287i \(0.560000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(258\) −0.396083 + 0.660237i −0.396083 + 0.660237i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.118938 0.0403044i −0.118938 0.0403044i
\(263\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(264\) −0.476608 + 0.246628i −0.476608 + 0.246628i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.0376546 + 0.0207008i 0.0376546 + 0.0207008i
\(268\) 1.57252 + 0.715978i 1.57252 + 0.715978i
\(269\) 0 0 −0.617860 0.786288i \(-0.712000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) −0.369526 0.495396i −0.369526 0.495396i
\(273\) 0 0
\(274\) −0.652230 + 0.132935i −0.652230 + 0.132935i
\(275\) −0.653011 + 0.678105i −0.653011 + 0.678105i
\(276\) 0 0
\(277\) 0 0 0.938734 0.344643i \(-0.112000\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(278\) −0.698970 + 0.297271i −0.698970 + 0.297271i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.94659 + 0.0979289i −1.94659 + 0.0979289i −0.984564 0.175023i \(-0.944000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(282\) 0 0
\(283\) −0.725499 0.527106i −0.725499 0.527106i 0.162637 0.986686i \(-0.448000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.109789 0.666068i −0.109789 0.666068i
\(289\) −0.405792 0.466153i −0.405792 0.466153i
\(290\) 0 0
\(291\) 0.196588 + 1.03055i 0.196588 + 1.03055i
\(292\) 0.176402 0.330650i 0.176402 0.330650i
\(293\) 0 0 −0.492727 0.870184i \(-0.664000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(294\) 0.569859 + 0.0143251i 0.569859 + 0.0143251i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.896346 0.0677113i 0.896346 0.0677113i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.268319 + 0.502940i 0.268319 + 0.502940i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.283415 + 0.803012i 0.283415 + 0.803012i
\(305\) 0 0
\(306\) 0.0986692 + 0.405372i 0.0986692 + 0.405372i
\(307\) −1.41034 + 1.07985i −1.41034 + 1.07985i −0.425779 + 0.904827i \(0.640000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(312\) 0 0
\(313\) −0.170270 + 1.22393i −0.170270 + 1.22393i 0.693653 + 0.720309i \(0.256000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.900640 0.0908485i −0.900640 0.0908485i
\(322\) 0 0
\(323\) −0.212046 0.481684i −0.212046 0.481684i
\(324\) −0.0309239 + 0.127047i −0.0309239 + 0.127047i
\(325\) 0 0
\(326\) −1.26792 1.38466i −1.26792 1.38466i
\(327\) 0 0
\(328\) 1.00122 0.849695i 1.00122 0.849695i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.0725322 + 1.15287i 0.0725322 + 1.15287i 0.850994 + 0.525175i \(0.176000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(332\) −0.0250607 1.99416i −0.0250607 1.99416i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.94678 0.295814i −1.94678 0.295814i −0.947098 0.320944i \(-0.896000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(338\) −0.675333 + 0.737513i −0.675333 + 0.737513i
\(339\) −0.428300 0.363482i −0.428300 0.363482i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.0360951 0.573715i 0.0360951 0.573715i
\(343\) 0 0
\(344\) −1.24293 0.528615i −1.24293 0.528615i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.01763 + 0.628009i −1.01763 + 0.628009i −0.929776 0.368125i \(-0.880000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.356412 0.934329i \(-0.616000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.543731 0.768508i −0.543731 0.768508i
\(353\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(354\) 0.00125858 0.0142709i 0.00125858 0.0142709i
\(355\) 0 0
\(356\) −0.0268665 + 0.0704301i −0.0268665 + 0.0704301i
\(357\) 0 0
\(358\) −0.0927094 0.311783i −0.0927094 0.311783i
\(359\) 0 0 0.988652 0.150226i \(-0.0480000\pi\)
−0.988652 + 0.150226i \(0.952000\pi\)
\(360\) 0 0
\(361\) −0.0310183 0.273092i −0.0310183 0.273092i
\(362\) 0 0
\(363\) −0.0560190 + 0.0326562i −0.0560190 + 0.0326562i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.823533 0.567269i \(-0.808000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(368\) 0 0
\(369\) −0.846453 + 0.263317i −0.846453 + 0.263317i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(374\) 0.370867 + 0.448302i 0.370867 + 0.448302i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.26841 1.53325i −1.26841 1.53325i −0.711536 0.702650i \(-0.752000\pi\)
−0.556876 0.830596i \(-0.688000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.823533 0.567269i \(-0.192000\pi\)
−0.823533 + 0.567269i \(0.808000\pi\)
\(384\) −0.544310 + 0.169325i −0.544310 + 0.169325i
\(385\) 0 0
\(386\) 0.951300 + 0.655278i 0.951300 + 0.655278i
\(387\) 0.632456 + 0.656760i 0.632456 + 0.656760i
\(388\) −1.74310 + 0.590685i −1.74310 + 0.590685i
\(389\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.112856 + 0.993611i 0.112856 + 0.993611i
\(393\) 0.0398645 0.0594591i 0.0398645 0.0594591i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.134731 + 0.621057i 0.134731 + 0.621057i
\(397\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(401\) 1.15369 + 1.63062i 1.15369 + 1.63062i 0.617860 + 0.786288i \(0.288000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(402\) −0.627824 + 0.758909i −0.627824 + 0.758909i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.327563 0.129691i 0.327563 0.129691i
\(409\) −0.435268 0.185119i −0.435268 0.185119i 0.162637 0.986686i \(-0.448000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(410\) 0 0
\(411\) 0.0238252 0.378691i 0.0238252 0.378691i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.0596601 0.428847i −0.0596601 0.428847i
\(418\) −0.304455 0.741601i −0.304455 0.741601i
\(419\) −0.123378 0.456624i −0.123378 0.456624i 0.876307 0.481754i \(-0.160000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.0125660 0.999921i \(-0.504000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(422\) 0.0775915 + 1.23328i 0.0775915 + 1.23328i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.471215 0.399903i 0.471215 0.399903i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0598513 1.58685i −0.0598513 1.58685i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(432\) 0.950025 + 0.0958300i 0.950025 + 0.0958300i
\(433\) 0.238883 1.25227i 0.238883 1.25227i −0.637424 0.770513i \(-0.720000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.155729 + 0.146239i 0.155729 + 0.146239i
\(439\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(440\) 0 0
\(441\) 0.192404 0.647056i 0.192404 0.647056i
\(442\) 0 0
\(443\) 1.47258 0.670474i 1.47258 0.670474i 0.492727 0.870184i \(-0.336000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.566455 1.60496i −0.566455 1.60496i −0.778462 0.627691i \(-0.784000\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(450\) 0.657860 0.151395i 0.657860 0.151395i
\(451\) −0.901173 + 0.846258i −0.901173 + 0.846258i
\(452\) 0.528033 0.832047i 0.528033 0.832047i
\(453\) 0 0
\(454\) 1.44759 1.16723i 1.44759 1.16723i
\(455\) 0 0
\(456\) −0.484042 + 0.0365652i −0.484042 + 0.0365652i
\(457\) −0.420671 + 1.93912i −0.420671 + 1.93912i −0.0878512 + 0.996134i \(0.528000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(458\) 0 0
\(459\) −0.589941 0.0148300i −0.589941 0.0148300i
\(460\) 0 0
\(461\) 0 0 0.470704 0.882291i \(-0.344000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.116116 0.193555i −0.116116 0.193555i
\(467\) −0.521518 + 0.0131099i −0.521518 + 0.0131099i −0.285019 0.958522i \(-0.592000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.0251003 0.00126274i 0.0251003 0.00126274i
\(473\) 1.19363 + 0.438223i 1.19363 + 0.438223i
\(474\) 0 0
\(475\) −0.783631 + 0.333278i −0.783631 + 0.333278i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.277116 + 0.852876i 0.277116 + 0.852876i
\(483\) 0 0
\(484\) −0.0702823 0.0894413i −0.0702823 0.0894413i
\(485\) 0 0
\(486\) −0.902055 0.495909i −0.902055 0.495909i
\(487\) 0 0 0.984564 0.175023i \(-0.0560000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(488\) 0 0
\(489\) 0.950509 0.491856i 0.950509 0.491856i
\(490\) 0 0
\(491\) 0.974450 + 0.330212i 0.974450 + 0.330212i 0.762443 0.647056i \(-0.224000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(492\) 0.318721 + 0.677316i 0.318721 + 0.677316i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.10112 + 0.282720i 1.10112 + 0.282720i
\(499\) −0.161032 + 0.392246i −0.161032 + 0.392246i −0.984564 0.175023i \(-0.944000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.402906 + 0.915241i 0.402906 + 0.915241i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.305442 0.481299i −0.305442 0.481299i
\(508\) 0 0
\(509\) 0 0 0.514440 0.857527i \(-0.328000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.425779 0.904827i −0.425779 0.904827i
\(513\) 0.770093 + 0.260962i 0.770093 + 0.260962i
\(514\) 1.13255 1.51833i 1.13255 1.51833i
\(515\) 0 0
\(516\) 0.475710 0.605388i 0.475710 0.605388i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.242636 0.216637i −0.242636 0.216637i 0.535827 0.844328i \(-0.320000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(522\) 0 0
\(523\) −0.426201 0.571376i −0.426201 0.571376i 0.535827 0.844328i \(-0.320000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(524\) 0.112948 + 0.0548935i 0.112948 + 0.0548935i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.503761 0.184949i 0.503761 0.184949i
\(529\) 0.920232 0.391374i 0.920232 0.391374i
\(530\) 0 0
\(531\) −0.0159261 0.00584706i −0.0159261 0.00584706i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.0347632 0.0252570i −0.0347632 0.0252570i
\(535\) 0 0
\(536\) −1.47039 0.907421i −1.47039 0.907421i
\(537\) 0.185360 0.00465959i 0.185360 0.00465959i
\(538\) 0 0
\(539\) −0.153108 0.928874i −0.153108 0.928874i
\(540\) 0 0
\(541\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.304522 + 0.537803i 0.304522 + 0.537803i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0898940 0.414376i 0.0898940 0.414376i −0.910106 0.414376i \(-0.864000\pi\)
1.00000 \(0\)
\(548\) 0.663748 0.0501405i 0.663748 0.0501405i
\(549\) 0 0
\(550\) 0.732851 0.590914i 0.732851 0.590914i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.730716 0.207323i 0.730716 0.207323i
\(557\) 0 0 −0.236499 0.971632i \(-0.576000\pi\)
0.236499 + 0.971632i \(0.424000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.301847 + 0.137432i −0.301847 + 0.137432i
\(562\) 1.94352 + 0.146816i 1.94352 + 0.146816i
\(563\) 0.530008 1.78242i 0.530008 1.78242i −0.0878512 0.996134i \(-0.528000\pi\)
0.617860 0.786288i \(-0.288000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.653715 + 0.613879i 0.653715 + 0.613879i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.86496 + 0.331528i 1.86496 + 0.331528i 0.988652 0.150226i \(-0.0480000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(570\) 0 0
\(571\) −0.337063 + 1.76695i −0.337063 + 1.76695i 0.260842 + 0.965382i \(0.416000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.0254430 + 0.674576i 0.0254430 + 0.674576i
\(577\) −1.34385 1.46758i −1.34385 1.46758i −0.745941 0.666012i \(-0.768000\pi\)
−0.597905 0.801567i \(-0.704000\pi\)
\(578\) 0.344168 + 0.513336i 0.344168 + 0.513336i
\(579\) −0.502051 + 0.426072i −0.502051 + 0.426072i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.0658757 1.04706i −0.0658757 1.04706i
\(583\) 0 0
\(584\) −0.216453 + 0.305933i −0.216453 + 0.305933i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.265116 + 1.90570i 0.265116 + 1.90570i 0.402906 + 0.915241i \(0.368000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(588\) −0.563570 0.0856344i −0.563570 0.0856344i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.0997101 1.58485i 0.0997101 1.58485i −0.556876 0.830596i \(-0.688000\pi\)
0.656586 0.754251i \(-0.272000\pi\)
\(594\) −0.897765 0.0451646i −0.897765 0.0451646i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.837528 0.546394i \(-0.184000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(600\) −0.203169 0.532603i −0.203169 0.532603i
\(601\) 0.653715 + 1.30316i 0.653715 + 1.30316i 0.938734 + 0.344643i \(0.112000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(602\) 0 0
\(603\) 0.673677 + 0.952173i 0.673677 + 0.952173i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(608\) −0.180536 0.832201i −0.180536 0.832201i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0470845 0.414542i −0.0470845 0.414542i
\(613\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(614\) 1.53456 0.894572i 1.53456 0.894572i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.32469 + 1.37560i 1.32469 + 1.37560i 0.876307 + 0.481754i \(0.160000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(618\) 0 0
\(619\) 0.215525 + 0.0670461i 0.215525 + 0.0670461i 0.402906 0.915241i \(-0.368000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.637424 0.770513i −0.637424 0.770513i
\(626\) 0.322327 1.19294i 0.322327 1.19294i
\(627\) 0.453376 0.0572747i 0.453376 0.0572747i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(632\) 0 0
\(633\) −0.690217 0.140677i −0.690217 0.140677i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.925827 + 0.539710i −0.925827 + 0.539710i −0.888136 0.459580i \(-0.848000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(642\) 0.882152 + 0.203012i 0.882152 + 0.203012i
\(643\) −0.175709 1.54698i −0.175709 1.54698i −0.711536 0.702650i \(-0.752000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.150003 + 0.504462i 0.150003 + 0.504462i
\(647\) 0 0 −0.212007 0.977268i \(-0.568000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(648\) 0.0466033 0.122170i 0.0466033 0.122170i
\(649\) −0.0235401 + 0.00237451i −0.0235401 + 0.00237451i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.08437 + 1.53265i 1.08437 + 1.53265i
\(653\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.09982 + 0.717509i −1.09982 + 0.717509i
\(657\) 0.215290 0.132862i 0.215290 0.132862i
\(658\) 0 0
\(659\) −0.116762 + 0.0462295i −0.116762 + 0.0462295i −0.425779 0.904827i \(-0.640000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(662\) 0.0725322 1.15287i 0.0725322 1.15287i
\(663\) 0 0
\(664\) −0.225071 + 1.98158i −0.225071 + 1.98158i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.0699330 1.11155i −0.0699330 1.11155i −0.863923 0.503623i \(-0.832000\pi\)
0.793990 0.607930i \(-0.208000\pi\)
\(674\) 1.89436 + 0.537477i 1.89436 + 0.537477i
\(675\) −0.0359883 + 0.954168i −0.0359883 + 0.954168i
\(676\) 0.762443 0.647056i 0.762443 0.647056i
\(677\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(678\) 0.379366 + 0.414296i 0.379366 + 0.414296i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.427088 + 0.970171i 0.427088 + 0.970171i
\(682\) 0 0
\(683\) −0.274189 0.0276577i −0.274189 0.0276577i −0.0376902 0.999289i \(-0.512000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(684\) −0.107716 + 0.564668i −0.107716 + 0.564668i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.16687 + 0.680227i 1.16687 + 0.680227i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.0242101 0.174026i 0.0242101 0.174026i −0.974527 0.224271i \(-0.928000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.08831 0.495514i 1.08831 0.495514i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.644390 0.493387i 0.644390 0.493387i
\(698\) 0 0
\(699\) 0.123779 0.0351194i 0.123779 0.0351194i
\(700\) 0 0
\(701\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.443124 + 0.830596i 0.443124 + 0.830596i
\(705\) 0 0
\(706\) 1.69755 0.933237i 1.69755 0.933237i
\(707\) 0 0
\(708\) −0.00303727 + 0.0140006i −0.00303727 + 0.0140006i
\(709\) 0 0 −0.837528 0.546394i \(-0.816000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.0354818 0.0665074i 0.0354818 0.0665074i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0529017 + 0.320944i 0.0529017 + 0.320944i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.00345375 + 0.274826i −0.00345375 + 0.274826i
\(723\) −0.510546 + 0.0256845i −0.510546 + 0.0256845i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0596702 0.0253777i 0.0596702 0.0253777i
\(727\) 0 0 0.938734 0.344643i \(-0.112000\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(728\) 0 0
\(729\) 0.316327 0.328483i 0.316327 0.328483i
\(730\) 0 0
\(731\) −0.750785 0.364886i −0.750785 0.364886i
\(732\) 0 0
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.42541 + 0.783625i 1.42541 + 0.783625i
\(738\) 0.872781 0.155152i 0.872781 0.155152i
\(739\) −0.170270 + 0.216686i −0.170270 + 0.216686i −0.863923 0.503623i \(-0.832000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.663347 1.17151i 0.663347 1.17151i
\(748\) −0.311756 0.491249i −0.311756 0.491249i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(752\) 0 0
\(753\) −0.563570 + 0.0856344i −0.563570 + 0.0856344i
\(754\) 0 0