Properties

Label 2008.1.bd.a.131.1
Level 2008
Weight 1
Character 2008.131
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 131.1
Root \(-0.998737 + 0.0502443i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.131
Dual form 2008.1.bd.a.1027.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +O(q^{10})\) \(q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +(0.494453 - 0.513453i) q^{11} +(0.524247 + 0.982653i) q^{12} +(0.728969 - 0.684547i) q^{16} +(-0.585339 + 0.198354i) q^{17} +(0.0968756 + 0.220062i) q^{18} +(-0.889695 - 1.77359i) q^{19} +(-0.597010 - 0.389483i) q^{22} +(0.867013 - 0.699092i) q^{24} +(-0.992115 - 0.125333i) q^{25} +(-0.281552 - 0.797731i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-0.630356 - 0.482641i) q^{33} +(0.304522 + 0.537803i) q^{34} +(0.198012 - 0.136395i) q^{36} +(-1.57546 + 1.20627i) q^{38} +(0.565975 - 1.48370i) q^{41} +(0.0155281 + 0.0197611i) q^{43} +(-0.270716 + 0.659417i) q^{44} +(-0.849171 - 0.720659i) q^{48} +(0.356412 + 0.934329i) q^{49} +(0.0627905 + 0.998027i) q^{50} +(0.293079 + 0.622825i) q^{51} +(-0.730844 + 0.426045i) q^{54} +(-1.85088 + 1.20750i) q^{57} +(-1.70365 - 0.577317i) q^{59} +(-0.425779 + 0.904827i) q^{64} +(-0.355975 + 0.709628i) q^{66} +(1.97481 + 0.0993483i) q^{67} +(0.471215 - 0.399903i) q^{68} +(-0.171083 - 0.168946i) q^{72} +(-1.18360 + 1.29258i) q^{73} +(-0.0139954 + 1.11366i) q^{75} +(1.48012 + 1.32152i) q^{76} +(-1.06366 + 0.516946i) q^{81} +(-1.56347 - 0.277933i) q^{82} +(1.81504 - 0.137111i) q^{83} +(0.0165014 - 0.0189559i) q^{86} +(0.698464 + 0.142358i) q^{88} +(-0.253520 - 0.339876i) q^{89} +(-0.548776 + 0.969168i) q^{96} +(0.252796 + 0.615768i) q^{97} +(0.850994 - 0.525175i) q^{98} +(-0.0881711 + 0.146974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{113}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.187381 0.982287i −0.187381 0.982287i
\(3\) −0.125694 1.10664i −0.125694 1.10664i −0.888136 0.459580i \(-0.848000\pi\)
0.762443 0.647056i \(-0.224000\pi\)
\(4\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(5\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(6\) −1.06348 + 0.330830i −1.06348 + 0.330830i
\(7\) 0 0 −0.823533 0.567269i \(-0.808000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(8\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(9\) −0.234317 + 0.0539241i −0.234317 + 0.0539241i
\(10\) 0 0
\(11\) 0.494453 0.513453i 0.494453 0.513453i −0.425779 0.904827i \(-0.640000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(12\) 0.524247 + 0.982653i 0.524247 + 0.982653i
\(13\) 0 0 0.0878512 0.996134i \(-0.472000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.728969 0.684547i 0.728969 0.684547i
\(17\) −0.585339 + 0.198354i −0.585339 + 0.198354i −0.597905 0.801567i \(-0.704000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(18\) 0.0968756 + 0.220062i 0.0968756 + 0.220062i
\(19\) −0.889695 1.77359i −0.889695 1.77359i −0.556876 0.830596i \(-0.688000\pi\)
−0.332820 0.942991i \(-0.608000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.597010 0.389483i −0.597010 0.389483i
\(23\) 0 0 0.577573 0.816339i \(-0.304000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(24\) 0.867013 0.699092i 0.867013 0.699092i
\(25\) −0.992115 0.125333i −0.992115 0.125333i
\(26\) 0 0
\(27\) −0.281552 0.797731i −0.281552 0.797731i
\(28\) 0 0
\(29\) 0 0 −0.994951 0.100362i \(-0.968000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.899405 0.437116i \(-0.856000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(32\) −0.809017 0.587785i −0.809017 0.587785i
\(33\) −0.630356 0.482641i −0.630356 0.482641i
\(34\) 0.304522 + 0.537803i 0.304522 + 0.537803i
\(35\) 0 0
\(36\) 0.198012 0.136395i 0.198012 0.136395i
\(37\) 0 0 −0.920232 0.391374i \(-0.872000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(38\) −1.57546 + 1.20627i −1.57546 + 1.20627i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.565975 1.48370i 0.565975 1.48370i −0.285019 0.958522i \(-0.592000\pi\)
0.850994 0.525175i \(-0.176000\pi\)
\(42\) 0 0
\(43\) 0.0155281 + 0.0197611i 0.0155281 + 0.0197611i 0.793990 0.607930i \(-0.208000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(44\) −0.270716 + 0.659417i −0.270716 + 0.659417i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(48\) −0.849171 0.720659i −0.849171 0.720659i
\(49\) 0.356412 + 0.934329i 0.356412 + 0.934329i
\(50\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(51\) 0.293079 + 0.622825i 0.293079 + 0.622825i
\(52\) 0 0
\(53\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(54\) −0.730844 + 0.426045i −0.730844 + 0.426045i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.85088 + 1.20750i −1.85088 + 1.20750i
\(58\) 0 0
\(59\) −1.70365 0.577317i −1.70365 0.577317i −0.711536 0.702650i \(-0.752000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(65\) 0 0
\(66\) −0.355975 + 0.709628i −0.355975 + 0.709628i
\(67\) 1.97481 + 0.0993483i 1.97481 + 0.0993483i 0.994951 0.100362i \(-0.0320000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(68\) 0.471215 0.399903i 0.471215 0.399903i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(72\) −0.171083 0.168946i −0.171083 0.168946i
\(73\) −1.18360 + 1.29258i −1.18360 + 1.29258i −0.236499 + 0.971632i \(0.576000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(74\) 0 0
\(75\) −0.0139954 + 1.11366i −0.0139954 + 1.11366i
\(76\) 1.48012 + 1.32152i 1.48012 + 1.32152i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.863923 0.503623i \(-0.832000\pi\)
0.863923 + 0.503623i \(0.168000\pi\)
\(80\) 0 0
\(81\) −1.06366 + 0.516946i −1.06366 + 0.516946i
\(82\) −1.56347 0.277933i −1.56347 0.277933i
\(83\) 1.81504 0.137111i 1.81504 0.137111i 0.876307 0.481754i \(-0.160000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.0165014 0.0189559i 0.0165014 0.0189559i
\(87\) 0 0
\(88\) 0.698464 + 0.142358i 0.698464 + 0.142358i
\(89\) −0.253520 0.339876i −0.253520 0.339876i 0.656586 0.754251i \(-0.272000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.548776 + 0.969168i −0.548776 + 0.969168i
\(97\) 0.252796 + 0.615768i 0.252796 + 0.615768i 0.998737 0.0502443i \(-0.0160000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(98\) 0.850994 0.525175i 0.850994 0.525175i
\(99\) −0.0881711 + 0.146974i −0.0881711 + 0.146974i
\(100\) 0.968583 0.248690i 0.968583 0.248690i
\(101\) 0 0 0.984564 0.175023i \(-0.0560000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(102\) 0.556876 0.404594i 0.556876 0.404594i
\(103\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.0419775 0.0626106i 0.0419775 0.0626106i −0.809017 0.587785i \(-0.800000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(108\) 0.555445 + 0.638066i 0.555445 + 0.638066i
\(109\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.590139 1.81626i 0.590139 1.81626i 0.0125660 0.999921i \(-0.496000\pi\)
0.577573 0.816339i \(-0.304000\pi\)
\(114\) 1.53293 + 1.59184i 1.53293 + 1.59184i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.247859 + 1.78165i −0.247859 + 1.78165i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0185391 + 0.491533i 0.0185391 + 0.491533i
\(122\) 0 0
\(123\) −1.71305 0.439837i −1.71305 0.439837i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(128\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(129\) 0.0199165 0.0196678i 0.0199165 0.0196678i
\(130\) 0 0
\(131\) −0.736317 1.04071i −0.736317 1.04071i −0.997159 0.0753268i \(-0.976000\pi\)
0.260842 0.965382i \(-0.416000\pi\)
\(132\) 0.763762 + 0.216699i 0.763762 + 0.216699i
\(133\) 0 0
\(134\) −0.272453 1.95844i −0.272453 1.95844i
\(135\) 0 0
\(136\) −0.481116 0.387935i −0.481116 0.387935i
\(137\) 1.30231 + 1.35236i 1.30231 + 1.35236i 0.899405 + 0.437116i \(0.144000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(138\) 0 0
\(139\) 0.223151 0.0339078i 0.223151 0.0339078i −0.0376902 0.999289i \(-0.512000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.133896 + 0.199710i −0.133896 + 0.199710i
\(145\) 0 0
\(146\) 1.49146 + 0.920428i 1.49146 + 0.920428i
\(147\) 0.989163 0.511858i 0.989163 0.511858i
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 1.09656 0.194932i 1.09656 0.194932i
\(151\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(152\) 1.02077 1.70153i 1.02077 1.70153i
\(153\) 0.126459 0.0780416i 0.126459 0.0780416i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.707100 + 0.947957i 0.707100 + 0.947957i
\(163\) 1.94982 + 0.397403i 1.94982 + 0.397403i 0.994951 + 0.100362i \(0.0320000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(164\) 0.0199546 + 1.58786i 0.0199546 + 1.58786i
\(165\) 0 0
\(166\) −0.474787 1.75720i −0.474787 1.75720i
\(167\) 0 0 0.112856 0.993611i \(-0.464000\pi\)
−0.112856 + 0.993611i \(0.536000\pi\)
\(168\) 0 0
\(169\) −0.984564 0.175023i −0.984564 0.175023i
\(170\) 0 0
\(171\) 0.304110 + 0.367605i 0.304110 + 0.367605i
\(172\) −0.0217122 0.0126571i −0.0217122 0.0126571i
\(173\) 0 0 −0.212007 0.977268i \(-0.568000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.00895737 0.712767i 0.00895737 0.712767i
\(177\) −0.424741 + 1.95789i −0.424741 + 1.95789i
\(178\) −0.286351 + 0.312716i −0.286351 + 0.312716i
\(179\) −1.30956 1.29320i −1.30956 1.29320i −0.929776 0.368125i \(-0.880000\pi\)
−0.379779 0.925077i \(-0.624000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.888136 0.459580i \(-0.848000\pi\)
0.888136 + 0.459580i \(0.152000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.187577 + 0.398621i −0.187577 + 0.398621i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.910106 0.414376i \(-0.136000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(192\) 1.05483 + 0.357451i 1.05483 + 0.357451i
\(193\) 0.172990 + 1.96152i 0.172990 + 1.96152i 0.260842 + 0.965382i \(0.416000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(194\) 0.557491 0.363701i 0.557491 0.363701i
\(195\) 0 0
\(196\) −0.675333 0.737513i −0.675333 0.737513i
\(197\) 0 0 0.863923 0.503623i \(-0.168000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(198\) 0.160892 + 0.0590693i 0.160892 + 0.0590693i
\(199\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(200\) −0.425779 0.904827i −0.425779 0.904827i
\(201\) −0.138279 2.19788i −0.138279 2.19788i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.501775 0.471198i −0.501775 0.471198i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.35057 0.420137i −1.35057 0.420137i
\(210\) 0 0
\(211\) 0.706139 0.388203i 0.706139 0.388203i −0.0878512 0.996134i \(-0.528000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.0693674 0.0295019i −0.0693674 0.0295019i
\(215\) 0 0
\(216\) 0.522684 0.665168i 0.522684 0.665168i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.57918 + 1.14734i 1.57918 + 1.14734i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(224\) 0 0
\(225\) 0.239228 0.0241312i 0.239228 0.0241312i
\(226\) −1.89467 0.239353i −1.89467 0.239353i
\(227\) −0.834242 + 0.672668i −0.834242 + 0.672668i −0.947098 0.320944i \(-0.896000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(228\) 1.27640 1.80406i 1.27640 1.80406i
\(229\) 0 0 −0.837528 0.546394i \(-0.816000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.481800 1.09445i −0.481800 1.09445i −0.974527 0.224271i \(-0.928000\pi\)
0.492727 0.870184i \(-0.336000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.79654 0.0903800i 1.79654 0.0903800i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(240\) 0 0
\(241\) 1.02077 0.128953i 1.02077 0.128953i 0.402906 0.915241i \(-0.368000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(242\) 0.479353 0.110315i 0.479353 0.110315i
\(243\) 0.252480 + 0.397844i 0.252480 + 0.397844i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.111052 + 1.76513i −0.111052 + 1.76513i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.379871 1.99135i −0.379871 1.99135i
\(250\) 0 0
\(251\) 0.823533 0.567269i 0.823533 0.567269i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0627905 0.998027i 0.0627905 0.998027i
\(257\) 1.32469 0.412088i 1.32469 0.412088i 0.448383 0.893841i \(-0.352000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(258\) −0.0230514 0.0158784i −0.0230514 0.0158784i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.884303 + 0.918285i −0.884303 + 0.918285i
\(263\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(264\) 0.0697458 0.790839i 0.0697458 0.790839i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.344253 + 0.323275i −0.344253 + 0.323275i
\(268\) −1.87270 + 0.634603i −1.87270 + 0.634603i
\(269\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) −0.290911 + 0.545286i −0.290911 + 0.545286i
\(273\) 0 0
\(274\) 1.08437 1.53265i 1.08437 1.53265i
\(275\) −0.554906 + 0.447433i −0.554906 + 0.447433i
\(276\) 0 0
\(277\) 0 0 0.994951 0.100362i \(-0.0320000\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(278\) −0.0751216 0.212845i −0.0751216 0.212845i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.134814 + 0.553868i 0.134814 + 0.553868i 0.998737 + 0.0502443i \(0.0160000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(282\) 0 0
\(283\) 0.832381 + 0.604760i 0.832381 + 0.604760i 0.920232 0.391374i \(-0.128000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.221262 + 0.0941026i 0.221262 + 0.0941026i
\(289\) −0.490713 + 0.375722i −0.490713 + 0.375722i
\(290\) 0 0
\(291\) 0.649656 0.357151i 0.649656 0.357151i
\(292\) 0.624652 1.63752i 0.624652 1.63752i
\(293\) 0 0 −0.954865 0.297042i \(-0.904000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(294\) −0.688142 0.875730i −0.688142 0.875730i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.548812 0.249877i −0.548812 0.249877i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.396954 1.04061i −0.396954 1.04061i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.86266 0.683851i −1.86266 0.683851i
\(305\) 0 0
\(306\) −0.100355 0.109595i −0.100355 0.109595i
\(307\) 0.00662226 0.175578i 0.00662226 0.175578i −0.992115 0.125333i \(-0.960000\pi\)
0.998737 0.0502443i \(-0.0160000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.910106 0.414376i \(-0.136000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(312\) 0 0
\(313\) 0.210189 0.777917i 0.210189 0.777917i −0.778462 0.627691i \(-0.784000\pi\)
0.988652 0.150226i \(-0.0480000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.0745635 0.0385840i −0.0745635 0.0385840i
\(322\) 0 0
\(323\) 0.872571 + 0.861675i 0.872571 + 0.861675i
\(324\) 0.798669 0.872205i 0.798669 0.872205i
\(325\) 0 0
\(326\) 0.0250052 1.98974i 0.0250052 1.98974i
\(327\) 0 0
\(328\) 1.55599 0.317136i 1.55599 0.317136i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.25517 + 1.51724i 1.25517 + 1.51724i 0.762443 + 0.647056i \(0.224000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(332\) −1.63711 + 0.795643i −1.63711 + 0.795643i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.31151 1.50660i 1.31151 1.50660i 0.617860 0.786288i \(-0.288000\pi\)
0.693653 0.720309i \(-0.256000\pi\)
\(338\) 0.0125660 + 0.999921i 0.0125660 + 0.999921i
\(339\) −2.08412 0.424776i −2.08412 0.424776i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.304110 0.367605i 0.304110 0.367605i
\(343\) 0 0
\(344\) −0.00836445 + 0.0236993i −0.00836445 + 0.0236993i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.463857 + 0.819198i −0.463857 + 0.819198i −0.999684 0.0251301i \(-0.992000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(348\) 0 0
\(349\) 0 0 0.850994 0.525175i \(-0.176000\pi\)
−0.850994 + 0.525175i \(0.824000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.701821 + 0.124761i −0.701821 + 0.124761i
\(353\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(354\) 2.00279 + 0.0503463i 2.00279 + 0.0503463i
\(355\) 0 0
\(356\) 0.360834 + 0.222682i 0.360834 + 0.222682i
\(357\) 0 0
\(358\) −1.02491 + 1.52868i −1.02491 + 1.52868i
\(359\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(360\) 0 0
\(361\) −1.75615 + 2.35434i −1.75615 + 2.35434i
\(362\) 0 0
\(363\) 0.541618 0.0822988i 0.541618 0.0822988i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(368\) 0 0
\(369\) −0.0526107 + 0.378175i −0.0526107 + 0.378175i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.711536 0.702650i \(-0.248000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(374\) 0.426709 + 0.109560i 0.426709 + 0.109560i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.72047 0.441741i −1.72047 0.441741i −0.745941 0.666012i \(-0.768000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.962028 0.272952i \(-0.912000\pi\)
0.962028 + 0.272952i \(0.0880000\pi\)
\(384\) 0.153464 1.10313i 0.153464 1.10313i
\(385\) 0 0
\(386\) 1.89436 0.537477i 1.89436 0.537477i
\(387\) −0.00470409 0.00379302i −0.00470409 0.00379302i
\(388\) −0.461723 0.479466i −0.461723 0.479466i
\(389\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.597905 + 0.801567i −0.597905 + 0.801567i
\(393\) −1.05913 + 0.945646i −1.05913 + 0.945646i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.0278748 0.169111i 0.0278748 0.169111i
\(397\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(401\) 0.465697 0.0827856i 0.465697 0.0827856i 0.0627905 0.998027i \(-0.480000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(402\) −2.13304 + 0.547671i −2.13304 + 0.547671i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.368829 + 0.581181i −0.368829 + 0.581181i
\(409\) 0.449528 1.27366i 0.449528 1.27366i −0.470704 0.882291i \(-0.656000\pi\)
0.920232 0.391374i \(-0.128000\pi\)
\(410\) 0 0
\(411\) 1.33287 1.61117i 1.33287 1.61117i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.0655724 0.242685i −0.0655724 0.242685i
\(418\) −0.159625 + 1.40537i −0.159625 + 1.40537i
\(419\) 1.34683 0.101741i 1.34683 0.101741i 0.617860 0.786288i \(-0.288000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(420\) 0 0
\(421\) 0 0 0.899405 0.437116i \(-0.144000\pi\)
−0.899405 + 0.437116i \(0.856000\pi\)
\(422\) −0.513644 0.620889i −0.513644 0.620889i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.605584 0.123428i 0.605584 0.123428i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0159812 + 0.0736668i −0.0159812 + 0.0736668i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(432\) −0.751327 0.388786i −0.751327 0.388786i
\(433\) 1.69755 + 0.933237i 1.69755 + 0.933237i 0.968583 + 0.248690i \(0.0800000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.831111 1.76620i 0.831111 1.76620i
\(439\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(440\) 0 0
\(441\) −0.133896 0.199710i −0.133896 0.199710i
\(442\) 0 0
\(443\) 1.53244 + 0.519298i 1.53244 + 0.519298i 0.954865 0.297042i \(-0.0960000\pi\)
0.577573 + 0.816339i \(0.304000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.925080 + 0.339630i 0.925080 + 0.339630i 0.762443 0.647056i \(-0.224000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(450\) −0.0685305 0.230469i −0.0685305 0.230469i
\(451\) −0.481961 1.02422i −0.481961 1.02422i
\(452\) 0.119913 + 1.90596i 0.119913 + 1.90596i
\(453\) 0 0
\(454\) 0.817074 + 0.693420i 0.817074 + 0.693420i
\(455\) 0 0
\(456\) −2.01128 0.915744i −2.01128 0.915744i
\(457\) −0.0609503 0.369773i −0.0609503 0.369773i −0.999684 0.0251301i \(-0.992000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(458\) 0 0
\(459\) 0.323036 + 0.411096i 0.323036 + 0.411096i
\(460\) 0 0
\(461\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(462\) 0 0
\(463\) 0 0 0.999684 0.0251301i \(-0.00800000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.984788 + 0.678346i −0.984788 + 0.678346i
\(467\) −1.23221 + 1.56811i −1.23221 + 1.56811i −0.556876 + 0.830596i \(0.688000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.425417 1.74778i −0.425417 1.74778i
\(473\) 0.0178243 + 0.00179795i 0.0178243 + 0.00179795i
\(474\) 0 0
\(475\) 0.660390 + 1.87111i 0.660390 + 1.87111i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.577573 0.816339i \(-0.304000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.317941 0.978522i −0.317941 0.978522i
\(483\) 0 0
\(484\) −0.198183 0.450191i −0.198183 0.450191i
\(485\) 0 0
\(486\) 0.343487 0.322556i 0.343487 0.322556i
\(487\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(488\) 0 0
\(489\) 0.194701 2.20769i 0.194701 2.20769i
\(490\) 0 0
\(491\) 1.14249 1.18640i 1.14249 1.18640i 0.162637 0.986686i \(-0.448000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(492\) 1.75467 0.221666i 1.75467 0.221666i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.88490 + 0.746285i −1.88490 + 0.746285i
\(499\) 0.0367093 + 0.323196i 0.0367093 + 0.323196i 0.998737 + 0.0502443i \(0.0160000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.711536 0.702650i −0.711536 0.702650i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.0699330 + 1.11155i −0.0699330 + 1.11155i
\(508\) 0 0
\(509\) 0 0 −0.823533 0.567269i \(-0.808000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(513\) −1.16435 + 1.20909i −1.16435 + 1.20909i
\(514\) −0.653011 1.22401i −0.653011 1.22401i
\(515\) 0 0
\(516\) −0.0112777 + 0.0256184i −0.0112777 + 0.0256184i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.825233 + 1.64508i 0.825233 + 1.64508i 0.762443 + 0.647056i \(0.224000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(522\) 0 0
\(523\) −0.801133 + 1.50165i −0.801133 + 1.50165i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(524\) 1.06772 + 0.696570i 1.06772 + 0.696570i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.789900 + 0.0796780i −0.789900 + 0.0796780i
\(529\) −0.332820 0.942991i −0.332820 0.942991i
\(530\) 0 0
\(531\) 0.430326 + 0.0434074i 0.430326 + 0.0434074i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.382055 + 0.277579i 0.382055 + 0.277579i
\(535\) 0 0
\(536\) 0.974271 + 1.72062i 0.974271 + 1.72062i
\(537\) −1.26650 + 1.61175i −1.26650 + 1.61175i
\(538\) 0 0
\(539\) 0.655963 + 0.278980i 0.655963 + 0.278980i
\(540\) 0 0
\(541\) 0 0 0.999684 0.0251301i \(-0.00800000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.590139 + 0.183582i 0.590139 + 0.183582i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0529017 + 0.320944i 0.0529017 + 0.320944i 1.00000 \(0\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(548\) −1.70869 0.777977i −1.70869 0.777977i
\(549\) 0 0
\(550\) 0.543487 + 0.461237i 0.543487 + 0.461237i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.194999 + 0.113674i −0.194999 + 0.113674i
\(557\) 0 0 −0.675333 0.737513i \(-0.736000\pi\)
0.675333 + 0.737513i \(0.264000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.464705 + 0.157475i 0.464705 + 0.157475i
\(562\) 0.518795 0.236210i 0.518795 0.236210i
\(563\) −0.596778 0.890111i −0.596778 0.890111i 0.402906 0.915241i \(-0.368000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.438075 0.930958i 0.438075 0.930958i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.38555 + 0.0697043i 1.38555 + 0.0697043i 0.728969 0.684547i \(-0.240000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(570\) 0 0
\(571\) −1.46786 0.806964i −1.46786 0.806964i −0.470704 0.882291i \(-0.656000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.0509754 0.234976i 0.0509754 0.234976i
\(577\) −0.0223207 + 1.77613i −0.0223207 + 1.77613i 0.448383 + 0.893841i \(0.352000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(578\) 0.461017 + 0.411618i 0.461017 + 0.411618i
\(579\) 2.14894 0.437988i 2.14894 0.437988i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.472558 0.571225i −0.472558 0.571225i
\(583\) 0 0
\(584\) −1.72556 0.306748i −1.72556 0.306748i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.450694 1.66803i −0.450694 1.66803i −0.711536 0.702650i \(-0.752000\pi\)
0.260842 0.965382i \(-0.416000\pi\)
\(588\) −0.731273 + 0.840048i −0.731273 + 0.840048i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.0480493 0.0580816i 0.0480493 0.0580816i −0.745941 0.666012i \(-0.768000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(594\) −0.142614 + 0.585913i −0.142614 + 0.585913i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(600\) −0.947796 + 0.584914i −0.947796 + 0.584914i
\(601\) 0.438075 0.730234i 0.438075 0.730234i −0.556876 0.830596i \(-0.688000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(602\) 0 0
\(603\) −0.468088 + 0.0832106i −0.468088 + 0.0832106i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(608\) −0.322709 + 1.95781i −0.322709 + 1.95781i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0888494 + 0.119114i −0.0888494 + 0.119114i
\(613\) 0 0 0.285019 0.958522i \(-0.408000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(614\) −0.173708 + 0.0263950i −0.173708 + 0.0263950i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.214529 + 0.172980i 0.214529 + 0.172980i 0.728969 0.684547i \(-0.240000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(618\) 0 0
\(619\) 0.164771 + 1.18440i 0.164771 + 1.18440i 0.876307 + 0.481754i \(0.160000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(626\) −0.803523 0.0606993i −0.803523 0.0606993i
\(627\) −0.295181 + 1.54739i −0.295181 + 1.54739i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.711536 0.702650i \(-0.248000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(632\) 0 0
\(633\) −0.518357 0.732644i −0.518357 0.732644i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.124156 0.0188655i 0.124156 0.0188655i −0.0878512 0.996134i \(-0.528000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(642\) −0.0239288 + 0.0804727i −0.0239288 + 0.0804727i
\(643\) −0.911736 + 1.22230i −0.911736 + 1.22230i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.682908 1.01858i 0.682908 1.01858i
\(647\) 0 0 0.162637 0.986686i \(-0.448000\pi\)
−0.162637 + 0.986686i \(0.552000\pi\)
\(648\) −1.00641 0.621087i −1.00641 0.621087i
\(649\) −1.13880 + 0.589289i −1.13880 + 0.589289i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.95919 + 0.348279i −1.95919 + 0.348279i
\(653\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.603082 1.46900i −0.603082 1.46900i
\(657\) 0.207636 0.366697i 0.207636 0.366697i
\(658\) 0 0
\(659\) −0.683098 + 1.07639i −0.683098 + 1.07639i 0.309017 + 0.951057i \(0.400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(660\) 0 0
\(661\) 0 0 0.236499 0.971632i \(-0.424000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(662\) 1.25517 1.51724i 1.25517 1.51724i
\(663\) 0 0
\(664\) 1.08831 + 1.45902i 1.08831 + 1.45902i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.950962 + 1.14952i 0.950962 + 1.14952i 0.988652 + 0.150226i \(0.0480000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(674\) −1.72566 1.00597i −1.72566 1.00597i
\(675\) 0.179349 + 0.826729i 0.179349 + 0.826729i
\(676\) 0.979855 0.199710i 0.979855 0.199710i
\(677\) 0 0 −0.745941 0.666012i \(-0.768000\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(678\) −0.0267275 + 2.12680i −0.0267275 + 2.12680i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.849257 + 0.838652i 0.849257 + 0.838652i
\(682\) 0 0
\(683\) −0.463326 0.239755i −0.463326 0.239755i 0.212007 0.977268i \(-0.432000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(684\) −0.418079 0.229841i −0.418079 0.229841i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.0248469 + 0.00377548i 0.0248469 + 0.00377548i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.521518 + 1.93015i −0.521518 + 1.93015i −0.236499 + 0.971632i \(0.576000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.891606 + 0.302139i 0.891606 + 0.302139i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.0369901 + 0.980729i −0.0369901 + 0.980729i
\(698\) 0 0
\(699\) −1.15060 + 0.670743i −1.15060 + 0.670743i
\(700\) 0 0
\(701\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.254059 + 0.666012i 0.254059 + 0.666012i
\(705\) 0 0
\(706\) −1.35556 1.27295i −1.35556 1.27295i
\(707\) 0 0
\(708\) −0.325832 1.97675i −0.325832 1.97675i
\(709\) 0 0 0.379779 0.925077i \(-0.376000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.151124 0.396169i 0.151124 0.396169i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.69365 + 0.720309i 1.69365 + 0.720309i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.492727 0.870184i \(-0.664000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.64170 + 1.28388i 2.64170 + 1.28388i
\(723\) −0.271008 1.11341i −0.271008 1.11341i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.182330 0.516603i −0.182330 0.516603i
\(727\) 0 0 0.994951 0.100362i \(-0.0320000\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(728\) 0 0
\(729\) −0.512099 + 0.412917i −0.512099 + 0.412917i
\(730\) 0 0
\(731\) −0.0130089 0.00848686i −0.0130089 0.00848686i
\(732\) 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
\(737\) 1.02746 0.964848i 1.02746 0.964848i
\(738\) 0.381335 0.0191841i 0.381335 0.0191841i
\(739\) 0.210189 0.477466i 0.210189 0.477466i −0.778462 0.627691i \(-0.784000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.417901 + 0.130002i −0.417901 + 0.130002i
\(748\) 0.0276623 0.439680i 0.0276623 0.439680i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(752\) 0 0
\(753\) −0.731273 0.840048i −0.731273 0.840048i
\(754\) 0 0
\(755\)