Properties

Label 2008.1.bd.a.115.1
Level 2008
Weight 1
Character 2008.115
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 115.1
Root \(-0.979855 + 0.199710i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.115
Dual form 2008.1.bd.a.227.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +O(q^{10})\) \(q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +(-0.225071 + 0.0170022i) q^{11} +(0.540453 + 1.31645i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(0.161209 - 0.596639i) q^{17} +(-0.0900591 - 1.02117i) q^{18} +(-0.499529 - 1.67992i) q^{19} +(-0.152431 + 0.166466i) q^{22} +(1.29515 + 0.589686i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-0.00758238 + 0.0349517i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.277497 - 0.161766i) q^{33} +(-0.290911 - 0.545286i) q^{34} +(-0.764688 - 0.682750i) q^{36} +(-1.51412 - 0.882657i) q^{38} +(-0.194999 - 1.71681i) q^{41} +(-1.77403 - 0.917999i) q^{43} +(0.00283632 + 0.225695i) q^{44} +(1.34779 - 0.456726i) q^{48} +(0.112856 - 0.993611i) q^{49} +(0.968583 - 0.248690i) q^{50} +(0.164803 + 0.863928i) q^{51} +(0.0183988 + 0.0306692i) q^{54} +(1.68434 + 1.83943i) q^{57} +(-0.123378 - 0.456624i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.0915497 - 0.307882i) q^{66} +(1.61389 + 0.328935i) q^{67} +(-0.585339 - 0.198354i) q^{68} +(-1.02481 + 0.0257617i) q^{72} +(0.838414 - 0.149042i) q^{73} +(-1.42127 - 0.0715012i) q^{75} +(-1.70797 + 0.393060i) q^{76} +(0.230406 + 0.946599i) q^{81} +(-1.31738 - 1.11801i) q^{82} +(-0.263142 + 0.0818589i) q^{83} +(-1.92163 + 0.545214i) q^{86} +(0.156566 + 0.162583i) q^{88} +(-1.09982 - 0.717509i) q^{89} +(0.669845 - 1.25556i) q^{96} +(0.00532818 - 0.423981i) q^{97} +(-0.597905 - 0.801567i) q^{98} +(-0.128853 + 0.192188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{77}{125}\right)\) \(-1\) \(-1\)

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
\(3\) −1.27992 + 0.622047i −1.27992 + 0.622047i −0.947098 0.320944i \(-0.896000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(4\) 0.0627905 0.998027i 0.0627905 0.998027i
\(5\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(6\) −0.507200 + 1.32962i −0.507200 + 1.32962i
\(7\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(8\) −0.637424 0.770513i −0.637424 0.770513i
\(9\) 0.633388 0.806049i 0.633388 0.806049i
\(10\) 0 0
\(11\) −0.225071 + 0.0170022i −0.225071 + 0.0170022i −0.187381 0.982287i \(-0.560000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(12\) 0.540453 + 1.31645i 0.540453 + 1.31645i
\(13\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.992115 0.125333i −0.992115 0.125333i
\(17\) 0.161209 0.596639i 0.161209 0.596639i −0.837528 0.546394i \(-0.816000\pi\)
0.998737 0.0502443i \(-0.0160000\pi\)
\(18\) −0.0900591 1.02117i −0.0900591 1.02117i
\(19\) −0.499529 1.67992i −0.499529 1.67992i −0.711536 0.702650i \(-0.752000\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.152431 + 0.166466i −0.152431 + 0.166466i
\(23\) 0 0 0.778462 0.627691i \(-0.216000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(24\) 1.29515 + 0.589686i 1.29515 + 0.589686i
\(25\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(26\) 0 0
\(27\) −0.00758238 + 0.0349517i −0.00758238 + 0.0349517i
\(28\) 0 0
\(29\) 0 0 −0.920232 0.391374i \(-0.872000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(30\) 0 0
\(31\) 0 0 0.236499 0.971632i \(-0.424000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(32\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(33\) 0.277497 0.161766i 0.277497 0.161766i
\(34\) −0.290911 0.545286i −0.290911 0.545286i
\(35\) 0 0
\(36\) −0.764688 0.682750i −0.764688 0.682750i
\(37\) 0 0 0.0376902 0.999289i \(-0.488000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(38\) −1.51412 0.882657i −1.51412 0.882657i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.194999 1.71681i −0.194999 1.71681i −0.597905 0.801567i \(-0.704000\pi\)
0.402906 0.915241i \(-0.368000\pi\)
\(42\) 0 0
\(43\) −1.77403 0.917999i −1.77403 0.917999i −0.910106 0.414376i \(-0.864000\pi\)
−0.863923 0.503623i \(-0.832000\pi\)
\(44\) 0.00283632 + 0.225695i 0.00283632 + 0.225695i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(48\) 1.34779 0.456726i 1.34779 0.456726i
\(49\) 0.112856 0.993611i 0.112856 0.993611i
\(50\) 0.968583 0.248690i 0.968583 0.248690i
\(51\) 0.164803 + 0.863928i 0.164803 + 0.863928i
\(52\) 0 0
\(53\) 0 0 −0.162637 0.986686i \(-0.552000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(54\) 0.0183988 + 0.0306692i 0.0183988 + 0.0306692i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.68434 + 1.83943i 1.68434 + 1.83943i
\(58\) 0 0
\(59\) −0.123378 0.456624i −0.123378 0.456624i 0.876307 0.481754i \(-0.160000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.711536 0.702650i \(-0.752000\pi\)
0.711536 + 0.702650i \(0.248000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(65\) 0 0
\(66\) 0.0915497 0.307882i 0.0915497 0.307882i
\(67\) 1.61389 + 0.328935i 1.61389 + 0.328935i 0.920232 0.391374i \(-0.128000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(68\) −0.585339 0.198354i −0.585339 0.198354i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(72\) −1.02481 + 0.0257617i −1.02481 + 0.0257617i
\(73\) 0.838414 0.149042i 0.838414 0.149042i 0.260842 0.965382i \(-0.416000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(74\) 0 0
\(75\) −1.42127 0.0715012i −1.42127 0.0715012i
\(76\) −1.70797 + 0.393060i −1.70797 + 0.393060i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.514440 0.857527i \(-0.328000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(80\) 0 0
\(81\) 0.230406 + 0.946599i 0.230406 + 0.946599i
\(82\) −1.31738 1.11801i −1.31738 1.11801i
\(83\) −0.263142 + 0.0818589i −0.263142 + 0.0818589i −0.425779 0.904827i \(-0.640000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.92163 + 0.545214i −1.92163 + 0.545214i
\(87\) 0 0
\(88\) 0.156566 + 0.162583i 0.156566 + 0.162583i
\(89\) −1.09982 0.717509i −1.09982 0.717509i −0.137790 0.990461i \(-0.544000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.669845 1.25556i 0.669845 1.25556i
\(97\) 0.00532818 0.423981i 0.00532818 0.423981i −0.974527 0.224271i \(-0.928000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(98\) −0.597905 0.801567i −0.597905 0.801567i
\(99\) −0.128853 + 0.192188i −0.128853 + 0.192188i
\(100\) 0.535827 0.844328i 0.535827 0.844328i
\(101\) 0 0 0.762443 0.647056i \(-0.224000\pi\)
−0.762443 + 0.647056i \(0.776000\pi\)
\(102\) 0.711536 + 0.516961i 0.711536 + 0.516961i
\(103\) 0 0 −0.994951 0.100362i \(-0.968000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.40692 + 1.38935i −1.40692 + 1.38935i −0.597905 + 0.801567i \(0.704000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0.0344067 + 0.00976206i 0.0344067 + 0.00976206i
\(109\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.220275 + 0.677936i 0.220275 + 0.677936i 0.998737 + 0.0502443i \(0.0160000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(114\) 2.48701 + 0.187872i 2.48701 + 0.187872i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.402519 0.248407i −0.402519 0.248407i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.938284 + 0.142572i −0.938284 + 0.142572i
\(122\) 0 0
\(123\) 1.31752 + 2.07608i 1.31752 + 2.07608i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.954865 0.297042i \(-0.904000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(128\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(129\) 2.84165 + 0.0714335i 2.84165 + 0.0714335i
\(130\) 0 0
\(131\) 1.44759 + 1.16723i 1.44759 + 1.16723i 0.954865 + 0.297042i \(0.0960000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(132\) −0.144023 0.287107i −0.144023 0.287107i
\(133\) 0 0
\(134\) 1.40164 0.864997i 1.40164 0.864997i
\(135\) 0 0
\(136\) −0.562476 + 0.256098i −0.562476 + 0.256098i
\(137\) −0.324350 0.0245019i −0.324350 0.0245019i −0.0878512 0.996134i \(-0.528000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(138\) 0 0
\(139\) 1.48138 1.02041i 1.48138 1.02041i 0.492727 0.870184i \(-0.336000\pi\)
0.988652 0.150226i \(-0.0480000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.729418 + 0.720309i −0.729418 + 0.720309i
\(145\) 0 0
\(146\) 0.509151 0.682581i 0.509151 0.682581i
\(147\) 0.473626 + 1.34194i 0.473626 + 1.34194i
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) −1.08501 + 0.920807i −1.08501 + 0.920807i
\(151\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(152\) −0.975988 + 1.45571i −0.975988 + 1.45571i
\(153\) −0.378813 0.507846i −0.378813 0.507846i
\(154\) 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
\(162\) 0.815950 + 0.532317i 0.815950 + 0.532317i
\(163\) 1.27664 + 1.32570i 1.27664 + 1.32570i 0.920232 + 0.391374i \(0.128000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(164\) −1.72566 + 0.0868145i −1.72566 + 0.0868145i
\(165\) 0 0
\(166\) −0.135786 + 0.239806i −0.135786 + 0.239806i
\(167\) 0 0 −0.899405 0.437116i \(-0.856000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(168\) 0 0
\(169\) 0.762443 + 0.647056i 0.762443 + 0.647056i
\(170\) 0 0
\(171\) −1.67049 0.661395i −1.67049 0.661395i
\(172\) −1.02758 + 1.71289i −1.02758 + 1.71289i
\(173\) 0 0 0.656586 0.754251i \(-0.272000\pi\)
−0.656586 + 0.754251i \(0.728000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.225428 + 0.0113408i 0.225428 + 0.0113408i
\(177\) 0.441954 + 0.507694i 0.441954 + 0.507694i
\(178\) −1.29290 + 0.229835i −1.29290 + 0.229835i
\(179\) 0.0753566 0.00189432i 0.0753566 0.00189432i 0.0125660 0.999921i \(-0.496000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(180\) 0 0
\(181\) 0 0 0.332820 0.942991i \(-0.392000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.0261393 + 0.137027i −0.0261393 + 0.137027i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.137790 0.990461i \(-0.544000\pi\)
0.137790 + 0.990461i \(0.456000\pi\)
\(192\) −0.371196 1.37381i −0.371196 1.37381i
\(193\) 1.43146 0.525541i 1.43146 0.525541i 0.492727 0.870184i \(-0.336000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(194\) −0.286351 0.312716i −0.286351 0.312716i
\(195\) 0 0
\(196\) −0.984564 0.175023i −0.984564 0.175023i
\(197\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(198\) 0.0376319 + 0.228305i 0.0376319 + 0.228305i
\(199\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(200\) −0.187381 0.982287i −0.187381 0.982287i
\(201\) −2.27025 + 0.582902i −2.27025 + 0.582902i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.872571 0.110231i 0.872571 0.110231i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.140992 + 0.369609i 0.140992 + 0.369609i
\(210\) 0 0
\(211\) 0.0748104 + 0.158980i 0.0748104 + 0.158980i 0.938734 0.344643i \(-0.112000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.0745249 + 1.97590i −0.0745249 + 1.97590i
\(215\) 0 0
\(216\) 0.0317640 0.0164368i 0.0317640 0.0164368i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.980390 + 0.712295i −0.980390 + 0.712295i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.617860 0.786288i \(-0.712000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(224\) 0 0
\(225\) 0.943359 0.401210i 0.943359 0.401210i
\(226\) 0.624652 + 0.343405i 0.624652 + 0.343405i
\(227\) 1.16025 + 0.528266i 1.16025 + 0.528266i 0.899405 0.437116i \(-0.144000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(228\) 1.94156 1.56552i 1.94156 1.56552i
\(229\) 0 0 0.675333 0.737513i \(-0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.147156 + 1.66858i 0.147156 + 1.66858i 0.617860 + 0.786288i \(0.288000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.463469 + 0.0944624i −0.463469 + 0.0944624i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(240\) 0 0
\(241\) −0.975988 + 0.536554i −0.975988 + 0.536554i −0.888136 0.459580i \(-0.848000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(242\) −0.586382 + 0.746230i −0.586382 + 0.746230i
\(243\) −0.906527 1.09580i −0.906527 1.09580i
\(244\) 0 0
\(245\) 0 0
\(246\) 2.38160 + 0.611491i 2.38160 + 0.611491i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.285880 0.268459i 0.285880 0.268459i
\(250\) 0 0
\(251\) −0.745941 0.666012i −0.745941 0.666012i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(257\) −0.710799 + 1.86335i −0.710799 + 1.86335i −0.285019 + 0.958522i \(0.592000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(258\) 2.12037 1.89317i 2.12037 1.89317i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.85427 0.140074i 1.85427 0.140074i
\(263\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(264\) −0.301526 0.110701i −0.301526 0.110701i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.85400 + 0.234215i 1.85400 + 0.234215i
\(268\) 0.429623 1.59005i 0.429623 1.59005i
\(269\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(270\) 0 0
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) −0.234716 + 0.571729i −0.234716 + 0.571729i
\(273\) 0 0
\(274\) −0.253214 + 0.204172i −0.253214 + 0.204172i
\(275\) −0.205423 0.0935299i −0.205423 0.0935299i
\(276\) 0 0
\(277\) 0 0 0.920232 0.391374i \(-0.128000\pi\)
−0.920232 + 0.391374i \(0.872000\pi\)
\(278\) 0.381361 1.75792i 0.381361 1.75792i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.465416 0.657817i 0.465416 0.657817i −0.514440 0.857527i \(-0.672000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(282\) 0 0
\(283\) 0.901044 0.654647i 0.901044 0.654647i −0.0376902 0.999289i \(-0.512000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0386374 + 1.02440i −0.0386374 + 1.02440i
\(289\) 0.533934 + 0.311256i 0.533934 + 0.311256i
\(290\) 0 0
\(291\) 0.256916 + 0.545975i 0.256916 + 0.545975i
\(292\) −0.0961038 0.846118i −0.0961038 0.846118i
\(293\) 0 0 −0.356412 0.934329i \(-0.616000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(294\) 1.26388 + 0.654015i 1.26388 + 0.654015i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.00111232 0.00799556i 0.00111232 0.00799556i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.160603 + 1.41398i −0.160603 + 1.41398i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.285040 + 1.72928i 0.285040 + 1.72928i
\(305\) 0 0
\(306\) −0.623787 0.110889i −0.623787 0.110889i
\(307\) 1.85616 + 0.282044i 1.85616 + 0.282044i 0.979855 0.199710i \(-0.0640000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.137790 0.990461i \(-0.544000\pi\)
0.137790 + 0.990461i \(0.456000\pi\)
\(312\) 0 0
\(313\) −0.0865734 0.152893i −0.0865734 0.152893i 0.823533 0.567269i \(-0.192000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.285019 0.958522i \(-0.408000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.936502 2.65343i 0.936502 2.65343i
\(322\) 0 0
\(323\) −1.08283 + 0.0272203i −1.08283 + 0.0272203i
\(324\) 0.959198 0.170514i 0.959198 0.170514i
\(325\) 0 0
\(326\) 1.83814 + 0.0924728i 1.83814 + 0.0924728i
\(327\) 0 0
\(328\) −1.19853 + 1.24458i −1.19853 + 1.24458i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.41780 0.561348i −1.41780 0.561348i −0.470704 0.882291i \(-0.656000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(332\) 0.0651745 + 0.267763i 0.0651745 + 0.267763i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.88530 + 0.534907i −1.88530 + 0.534907i −0.888136 + 0.459580i \(0.848000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(338\) 0.998737 0.0502443i 0.998737 0.0502443i
\(339\) −0.703641 0.730681i −0.703641 0.730681i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.67049 + 0.661395i −1.67049 + 0.661395i
\(343\) 0 0
\(344\) 0.423479 + 1.95207i 0.423479 + 1.95207i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.357527 0.670152i 0.357527 0.670152i −0.637424 0.770513i \(-0.720000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.597905 0.801567i \(-0.704000\pi\)
0.597905 + 0.801567i \(0.296000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.172093 0.146049i 0.172093 0.146049i
\(353\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(354\) 0.669711 + 0.0675545i 0.669711 + 0.0675545i
\(355\) 0 0
\(356\) −0.785152 + 1.05259i −0.785152 + 1.05259i
\(357\) 0 0
\(358\) 0.0536358 0.0529660i 0.0536358 0.0529660i
\(359\) 0 0 −0.962028 0.272952i \(-0.912000\pi\)
0.962028 + 0.272952i \(0.0880000\pi\)
\(360\) 0 0
\(361\) −1.73507 + 1.13194i −1.73507 + 1.13194i
\(362\) 0 0
\(363\) 1.11224 0.766137i 1.11224 0.766137i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(368\) 0 0
\(369\) −1.50734 0.930227i −1.50734 0.930227i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(374\) 0.0747469 + 0.117782i 0.0747469 + 0.117782i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.356667 0.562018i −0.356667 0.562018i 0.617860 0.786288i \(-0.288000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.448383 0.893841i \(-0.648000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(384\) −1.21103 0.747361i −1.21103 0.747361i
\(385\) 0 0
\(386\) 0.683733 1.36301i 0.683733 1.36301i
\(387\) −1.86360 + 0.848506i −1.86360 + 0.848506i
\(388\) −0.422810 0.0319396i −0.422810 0.0319396i
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.837528 + 0.546394i −0.837528 + 0.546394i
\(393\) −2.57887 0.593482i −2.57887 0.593482i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.183718 + 0.140666i 0.183718 + 0.140666i
\(397\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 0.587785i −0.809017 0.587785i
\(401\) 0.880732 0.747444i 0.880732 0.747444i −0.0878512 0.996134i \(-0.528000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(402\) −1.25592 + 1.97901i −1.25592 + 1.97901i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.560619 0.677671i 0.560619 0.677671i
\(409\) −0.417469 1.92437i −0.417469 1.92437i −0.379779 0.925077i \(-0.624000\pi\)
−0.0376902 0.999289i \(-0.512000\pi\)
\(410\) 0 0
\(411\) 0.430383 0.170401i 0.430383 0.170401i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.26130 + 2.22753i −1.26130 + 2.22753i
\(418\) 0.355793 + 0.172917i 0.355793 + 0.172917i
\(419\) −1.88025 + 0.584913i −1.88025 + 0.584913i −0.888136 + 0.459580i \(0.848000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.236499 0.971632i \(-0.576000\pi\)
0.236499 + 0.971632i \(0.424000\pi\)
\(422\) 0.163364 + 0.0646804i 0.163364 + 0.0646804i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.428701 0.445175i 0.428701 0.445175i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.29827 + 1.49138i 1.29827 + 1.49138i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(432\) 0.0119032 0.0337258i 0.0119032 0.0337258i
\(433\) −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
\(438\) −0.227074 + 1.19036i −0.227074 + 1.19036i
\(439\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(440\) 0 0
\(441\) −0.729418 0.720309i −0.729418 0.720309i
\(442\) 0 0
\(443\) −0.422050 1.56202i −0.422050 1.56202i −0.778462 0.627691i \(-0.784000\pi\)
0.356412 0.934329i \(-0.384000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.153108 0.928874i −0.153108 0.928874i −0.947098 0.320944i \(-0.896000\pi\)
0.793990 0.607930i \(-0.208000\pi\)
\(450\) 0.413032 0.938243i 0.413032 0.938243i
\(451\) 0.0730782 + 0.383089i 0.0730782 + 0.383089i
\(452\) 0.690429 0.177272i 0.690429 0.177272i
\(453\) 0 0
\(454\) 1.20741 0.409154i 1.20741 0.409154i
\(455\) 0 0
\(456\) 0.343662 2.47030i 0.343662 2.47030i
\(457\) 1.15759 0.886324i 1.15759 0.886324i 0.162637 0.986686i \(-0.448000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(458\) 0 0
\(459\) 0.0196312 + 0.0101585i 0.0196312 + 0.0101585i
\(460\) 0 0
\(461\) 0 0 −0.112856 0.993611i \(-0.536000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(462\) 0 0
\(463\) 0 0 0.994951 0.100362i \(-0.0320000\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.24949 + 1.11561i 1.24949 + 1.11561i
\(467\) −1.69610 + 0.877673i −1.69610 + 0.877673i −0.711536 + 0.702650i \(0.752000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.273191 + 0.386127i −0.273191 + 0.386127i
\(473\) 0.414891 + 0.176453i 0.414891 + 0.176453i
\(474\) 0 0
\(475\) 0.371566 1.71277i 0.371566 1.71277i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.778462 0.627691i \(-0.216000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.344168 + 1.05924i −0.344168 + 1.05924i
\(483\) 0 0
\(484\) 0.0833755 + 0.945384i 0.0833755 + 0.945384i
\(485\) 0 0
\(486\) −1.41096 0.178245i −1.41096 0.178245i
\(487\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(488\) 0 0
\(489\) −2.45865 0.902658i −2.45865 0.902658i
\(490\) 0 0
\(491\) 1.48764 0.112379i 1.48764 0.112379i 0.693653 0.720309i \(-0.256000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(492\) 2.15471 1.18456i 2.15471 1.18456i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0246246 0.391397i 0.0246246 0.391397i
\(499\) 1.42824 0.694131i 1.42824 0.694131i 0.448383 0.893841i \(-0.352000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.999684 + 0.0251301i −0.999684 + 0.0251301i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.37836 0.353903i −1.37836 0.353903i
\(508\) 0 0
\(509\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.876307 0.481754i 0.876307 0.481754i
\(513\) 0.0625037 0.00472162i 0.0625037 0.00472162i
\(514\) 0.757400 + 1.84490i 0.757400 + 1.84490i
\(515\) 0 0
\(516\) 0.249721 2.83156i 0.249721 2.83156i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.0214849 + 0.0722537i 0.0214849 + 0.0722537i 0.968583 0.248690i \(-0.0800000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(522\) 0 0
\(523\) 0.454144 1.10622i 0.454144 1.10622i −0.514440 0.857527i \(-0.672000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(524\) 1.25582 1.37144i 1.25582 1.37144i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.295583 + 0.125711i −0.295583 + 0.125711i
\(529\) 0.212007 0.977268i 0.212007 0.977268i
\(530\) 0 0
\(531\) −0.446207 0.189771i −0.446207 0.189771i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.51184 1.09842i 1.51184 1.09842i
\(535\) 0 0
\(536\) −0.775280 1.45319i −0.775280 1.45319i
\(537\) −0.0952719 + 0.0492999i −0.0952719 + 0.0492999i
\(538\) 0 0
\(539\) −0.00850716 + 0.225552i −0.00850716 + 0.225552i
\(540\) 0 0
\(541\) 0 0 0.994951 0.100362i \(-0.0320000\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.220275 + 0.577447i 0.220275 + 0.577447i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.26084 0.965382i 1.26084 0.965382i 0.260842 0.965382i \(-0.416000\pi\)
1.00000 \(0\)
\(548\) −0.0448196 + 0.322172i −0.0448196 + 0.322172i
\(549\) 0 0
\(550\) −0.213772 + 0.0724411i −0.213772 + 0.0724411i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.925379 1.54253i −0.925379 1.54253i
\(557\) 0 0 −0.984564 0.175023i \(-0.944000\pi\)
0.984564 + 0.175023i \(0.0560000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.0517812 0.191644i −0.0517812 0.191644i
\(562\) −0.111033 0.798127i −0.111033 0.798127i
\(563\) 0.907100 + 0.895772i 0.907100 + 0.895772i 0.994951 0.100362i \(-0.0320000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.208696 1.09402i 0.208696 1.09402i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.95414 0.398285i −1.95414 0.398285i −0.992115 0.125333i \(-0.960000\pi\)
−0.962028 0.272952i \(-0.912000\pi\)
\(570\) 0 0
\(571\) 0.575085 1.22212i 0.575085 1.22212i −0.379779 0.925077i \(-0.624000\pi\)
0.954865 0.297042i \(-0.0960000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.673087 + 0.773207i 0.673087 + 0.773207i
\(577\) −0.664798 0.0334446i −0.664798 0.0334446i −0.285019 0.958522i \(-0.592000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(578\) 0.602291 0.138607i 0.602291 0.138607i
\(579\) −1.50524 + 1.56309i −1.50524 + 1.56309i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.561029 + 0.222127i 0.561029 + 0.222127i
\(583\) 0 0
\(584\) −0.649264 0.551006i −0.649264 0.551006i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.506957 + 0.895314i −0.506957 + 0.895314i 0.492727 + 0.870184i \(0.336000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(588\) 1.36903 0.388430i 1.36903 0.388430i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.83845 + 0.727894i −1.83845 + 0.727894i −0.863923 + 0.503623i \(0.832000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(594\) −0.00466249 0.00658995i −0.00466249 0.00658995i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(600\) 0.850861 + 1.14069i 0.850861 + 1.14069i
\(601\) 0.208696 0.311276i 0.208696 0.311276i −0.711536 0.702650i \(-0.752000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(602\) 0 0
\(603\) 1.28735 1.09253i 1.28735 1.09253i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(608\) 1.39156 + 1.06547i 1.39156 + 1.06547i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.530630 + 0.346177i −0.530630 + 0.346177i
\(613\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(614\) 1.54616 1.06503i 1.54616 1.06503i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.54899 + 0.705263i −1.54899 + 0.705263i −0.992115 0.125333i \(-0.960000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(618\) 0 0
\(619\) −1.42546 + 0.879697i −1.42546 + 0.879697i −0.999684 0.0251301i \(-0.992000\pi\)
−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
\(626\) −0.167772 0.0521909i −0.167772 0.0521909i
\(627\) −0.410372 0.385365i −0.410372 0.385365i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(632\) 0 0
\(633\) −0.194644 0.156946i −0.194644 0.156946i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.59532 1.09889i 1.59532 1.09889i 0.656586 0.754251i \(-0.272000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(642\) −1.13372 2.57535i −1.13372 2.57535i
\(643\) 1.58644 1.03498i 1.58644 1.03498i 0.617860 0.786288i \(-0.288000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.770717 + 0.761093i −0.770717 + 0.761093i
\(647\) 0 0 −0.793990 0.607930i \(-0.792000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(648\) 0.582501 0.780916i 0.582501 0.780916i
\(649\) 0.0355324 + 0.100675i 0.0355324 + 0.100675i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.40325 1.19088i 1.40325 1.19088i
\(653\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.0217122 + 1.72771i −0.0217122 + 1.72771i
\(657\) 0.410906 0.770205i 0.410906 0.770205i
\(658\) 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 −0.577573 0.816339i \(-0.696000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(662\) −1.41780 + 0.561348i −1.41780 + 0.561348i
\(663\) 0 0
\(664\) 0.230806 + 0.150576i 0.230806 + 0.150576i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.81218 + 0.717495i 1.81218 + 0.717495i 0.988652 + 0.150226i \(0.0480000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(674\) −1.00815 + 1.68050i −1.00815 + 1.68050i
\(675\) −0.0234826 + 0.0269756i −0.0234826 + 0.0269756i
\(676\) 0.693653 0.720309i 0.693653 0.720309i
\(677\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(678\) −1.01312 0.0509678i −1.01312 0.0509678i
\(679\) 0 0
\(680\) 0 0
\(681\) −1.81363 + 0.0455910i −1.81363 + 0.0455910i
\(682\) 0 0
\(683\) −0.327979 + 0.929274i −0.327979 + 0.929274i 0.656586 + 0.754251i \(0.272000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(684\) −0.764981 + 1.62567i −0.764981 + 1.62567i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.64498 + 1.13310i 1.64498 + 1.13310i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.980479 + 1.73158i 0.980479 + 1.73158i 0.577573 + 0.816339i \(0.304000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.198124 0.733264i −0.198124 0.733264i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.05575 0.160421i −1.05575 0.160421i
\(698\) 0 0
\(699\) −1.22628 2.04411i −1.22628 2.04411i
\(700\) 0 0
\(701\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.0254731 0.224271i 0.0254731 0.224271i
\(705\) 0 0
\(706\) −0.124591 + 0.0157395i −0.124591 + 0.0157395i
\(707\) 0 0
\(708\) 0.534443 0.409204i 0.534443 0.409204i
\(709\) 0 0 −0.0125660 0.999921i \(-0.504000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.148200 + 1.30478i 0.148200 + 1.30478i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.00284110 0.0753268i 0.00284110 0.0753268i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.489944 + 2.01288i −0.489944 + 2.01288i
\(723\) 0.915422 1.29385i 0.915422 1.29385i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.286331 1.31987i 0.286331 1.31987i
\(727\) 0 0 0.920232 0.391374i \(-0.128000\pi\)
−0.920232 + 0.391374i \(0.872000\pi\)
\(728\) 0 0
\(729\) 0.955262 + 0.434936i 0.955262 + 0.434936i
\(730\) 0 0
\(731\) −0.833703 + 0.910465i −0.833703 + 0.910465i
\(732\) 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
\(737\) −0.368832 0.0465943i −0.368832 0.0465943i
\(738\) −1.73559 + 0.353741i −1.73559 + 0.353741i
\(739\) −0.0865734 + 0.981645i −0.0865734 + 0.981645i 0.823533 + 0.567269i \(0.192000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(740\) 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
\(747\) −0.100689 + 0.263954i −0.100689 + 0.263954i
\(748\) 0.135116 + 0.0346918i 0.135116 + 0.0346918i
\(749\) 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
\(753\) 1.36903 + 0.388430i 1.36903 + 0.388430i
\(754\) 0 0
\(755\) 0