Properties

Label 2008.1.bd.a.1339.1
Level 2008
Weight 1
Character 2008.1339
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: \(\Q(\zeta_{250})\)
Defining polynomial: \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
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 1339.1
Root \(0.470704 - 0.882291i\) of defining polynomial
Character \(\chi\) \(=\) 2008.1339
Dual form 2008.1.bd.a.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.992115 + 0.125333i) q^{2} +(-1.58347 + 0.119618i) q^{3} +(0.968583 - 0.248690i) q^{4} +(1.55599 - 0.317136i) q^{6} +(-0.929776 + 0.368125i) q^{8} +(1.50441 - 0.228596i) q^{9} +O(q^{10})\) \(q+(-0.992115 + 0.125333i) q^{2} +(-1.58347 + 0.119618i) q^{3} +(0.968583 - 0.248690i) q^{4} +(1.55599 - 0.317136i) q^{6} +(-0.929776 + 0.368125i) q^{8} +(1.50441 - 0.228596i) q^{9} +(0.0174330 + 1.38720i) q^{11} +(-1.50397 + 0.509652i) q^{12} +(0.876307 - 0.481754i) q^{16} +(-0.417379 - 0.455808i) q^{17} +(-1.46390 + 0.415346i) q^{18} +(-0.180536 + 0.832201i) q^{19} +(-0.191157 - 1.37407i) q^{22} +(1.42824 - 0.694131i) q^{24} +(-0.425779 - 0.904827i) q^{25} +(-0.807320 + 0.185791i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(-0.193538 - 2.19450i) q^{33} +(0.471215 + 0.399903i) q^{34} +(1.40030 - 0.595547i) q^{36} +(0.0748104 - 0.848266i) q^{38} +(-0.121877 + 0.126560i) q^{41} +(0.811554 + 0.559018i) q^{43} +(0.361867 + 1.33928i) q^{44} +(-1.32998 + 0.867664i) q^{48} +(0.693653 + 0.720309i) q^{49} +(0.535827 + 0.844328i) q^{50} +(0.715429 + 0.671832i) q^{51} +(0.777668 - 0.285510i) q^{54} +(0.186328 - 1.33936i) q^{57} +(-1.28970 + 1.40845i) q^{59} +(0.728969 - 0.684547i) q^{64} +(0.467055 + 2.15294i) q^{66} +(-0.936655 - 1.75567i) q^{67} +(-0.517621 - 0.337690i) q^{68} +(-1.31462 + 0.766355i) q^{72} +(-0.318921 + 0.196816i) q^{73} +(0.782442 + 1.38184i) q^{75} +(0.0320954 + 0.850954i) q^{76} +(-0.196859 + 0.0612392i) q^{81} +(0.105053 - 0.140837i) q^{82} +(-0.472401 + 0.0237655i) q^{83} +(-0.875218 - 0.452895i) q^{86} +(-0.526870 - 1.28337i) q^{88} +(-1.12464 + 0.512052i) q^{89} +(1.21074 - 1.02751i) q^{96} +(-0.508394 + 1.88158i) q^{97} +(-0.778462 - 0.627691i) q^{98} +(0.343334 + 2.08293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{117}{125}\right)\) \(-1\) \(-1\)

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
\(3\) −1.58347 + 0.119618i −1.58347 + 0.119618i −0.837528 0.546394i \(-0.816000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(4\) 0.968583 0.248690i 0.968583 0.248690i
\(5\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(6\) 1.55599 0.317136i 1.55599 0.317136i
\(7\) 0 0 −0.920232 0.391374i \(-0.872000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(8\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(9\) 1.50441 0.228596i 1.50441 0.228596i
\(10\) 0 0
\(11\) 0.0174330 + 1.38720i 0.0174330 + 1.38720i 0.728969 + 0.684547i \(0.240000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(12\) −1.50397 + 0.509652i −1.50397 + 0.509652i
\(13\) 0 0 −0.448383 0.893841i \(-0.648000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.876307 0.481754i 0.876307 0.481754i
\(17\) −0.417379 0.455808i −0.417379 0.455808i 0.492727 0.870184i \(-0.336000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(18\) −1.46390 + 0.415346i −1.46390 + 0.415346i
\(19\) −0.180536 + 0.832201i −0.180536 + 0.832201i 0.793990 + 0.607930i \(0.208000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.191157 1.37407i −0.191157 1.37407i
\(23\) 0 0 −0.112856 0.993611i \(-0.536000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(24\) 1.42824 0.694131i 1.42824 0.694131i
\(25\) −0.425779 0.904827i −0.425779 0.904827i
\(26\) 0 0
\(27\) −0.807320 + 0.185791i −0.807320 + 0.185791i
\(28\) 0 0
\(29\) 0 0 0.556876 0.830596i \(-0.312000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.954865 0.297042i \(-0.904000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(32\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(33\) −0.193538 2.19450i −0.193538 2.19450i
\(34\) 0.471215 + 0.399903i 0.471215 + 0.399903i
\(35\) 0 0
\(36\) 1.40030 0.595547i 1.40030 0.595547i
\(37\) 0 0 0.711536 0.702650i \(-0.248000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(38\) 0.0748104 0.848266i 0.0748104 0.848266i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.121877 + 0.126560i −0.121877 + 0.126560i −0.778462 0.627691i \(-0.784000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(42\) 0 0
\(43\) 0.811554 + 0.559018i 0.811554 + 0.559018i 0.899405 0.437116i \(-0.144000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(44\) 0.361867 + 1.33928i 0.361867 + 1.33928i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(48\) −1.32998 + 0.867664i −1.32998 + 0.867664i
\(49\) 0.693653 + 0.720309i 0.693653 + 0.720309i
\(50\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(51\) 0.715429 + 0.671832i 0.715429 + 0.671832i
\(52\) 0 0
\(53\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(54\) 0.777668 0.285510i 0.777668 0.285510i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.186328 1.33936i 0.186328 1.33936i
\(58\) 0 0
\(59\) −1.28970 + 1.40845i −1.28970 + 1.40845i −0.425779 + 0.904827i \(0.640000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.793990 0.607930i \(-0.792000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.728969 0.684547i 0.728969 0.684547i
\(65\) 0 0
\(66\) 0.467055 + 2.15294i 0.467055 + 2.15294i
\(67\) −0.936655 1.75567i −0.936655 1.75567i −0.556876 0.830596i \(-0.688000\pi\)
−0.379779 0.925077i \(-0.624000\pi\)
\(68\) −0.517621 0.337690i −0.517621 0.337690i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.162637 0.986686i \(-0.448000\pi\)
−0.162637 + 0.986686i \(0.552000\pi\)
\(72\) −1.31462 + 0.766355i −1.31462 + 0.766355i
\(73\) −0.318921 + 0.196816i −0.318921 + 0.196816i −0.675333 0.737513i \(-0.736000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(74\) 0 0
\(75\) 0.782442 + 1.38184i 0.782442 + 1.38184i
\(76\) 0.0320954 + 0.850954i 0.0320954 + 0.850954i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(80\) 0 0
\(81\) −0.196859 + 0.0612392i −0.196859 + 0.0612392i
\(82\) 0.105053 0.140837i 0.105053 0.140837i
\(83\) −0.472401 + 0.0237655i −0.472401 + 0.0237655i −0.285019 0.958522i \(-0.592000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.875218 0.452895i −0.875218 0.452895i
\(87\) 0 0
\(88\) −0.526870 1.28337i −0.526870 1.28337i
\(89\) −1.12464 + 0.512052i −1.12464 + 0.512052i −0.888136 0.459580i \(-0.848000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.21074 1.02751i 1.21074 1.02751i
\(97\) −0.508394 + 1.88158i −0.508394 + 1.88158i −0.0376902 + 0.999289i \(0.512000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(98\) −0.778462 0.627691i −0.778462 0.627691i
\(99\) 0.343334 + 2.08293i 0.343334 + 2.08293i
\(100\) −0.637424 0.770513i −0.637424 0.770513i
\(101\) 0 0 −0.597905 0.801567i \(-0.704000\pi\)
0.597905 + 0.801567i \(0.296000\pi\)
\(102\) −0.793990 0.576868i −0.793990 0.576868i
\(103\) 0 0 0.514440 0.857527i \(-0.328000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.58748 + 1.21548i −1.58748 + 1.21548i −0.778462 + 0.627691i \(0.784000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) −0.735752 + 0.380726i −0.735752 + 0.380726i
\(109\) 0 0 0.0376902 0.999289i \(-0.488000\pi\)
−0.0376902 + 0.999289i \(0.512000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.605584 + 1.86380i 0.605584 + 1.86380i 0.492727 + 0.870184i \(0.336000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(114\) −0.0169925 + 1.35215i −0.0169925 + 1.35215i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.10301 1.55899i 1.10301 1.55899i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.924328 + 0.0232358i −0.924328 + 0.0232358i
\(122\) 0 0
\(123\) 0.177849 0.214982i 0.177849 0.214982i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(128\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(129\) −1.35194 0.788111i −1.35194 0.788111i
\(130\) 0 0
\(131\) 0.0141726 0.124779i 0.0141726 0.124779i −0.984564 0.175023i \(-0.944000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(132\) −0.733207 2.07742i −0.733207 2.07742i
\(133\) 0 0
\(134\) 1.14931 + 1.62444i 1.14931 + 1.62444i
\(135\) 0 0
\(136\) 0.555863 + 0.270152i 0.555863 + 0.270152i
\(137\) −0.00716313 + 0.569994i −0.00716313 + 0.569994i 0.954865 + 0.297042i \(0.0960000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(138\) 0 0
\(139\) −1.98425 + 0.200153i −1.98425 + 0.200153i −0.984564 + 0.175023i \(0.944000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.20820 0.925077i 1.20820 0.925077i
\(145\) 0 0
\(146\) 0.291739 0.235235i 0.291739 0.235235i
\(147\) −1.18454 1.05761i −1.18454 1.05761i
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) −0.949462 1.27287i −0.949462 1.27287i
\(151\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(152\) −0.138495 0.840221i −0.138495 0.840221i
\(153\) −0.732106 0.590313i −0.732106 0.590313i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.187631 0.0854293i 0.187631 0.0854293i
\(163\) 0.422979 + 1.03031i 0.422979 + 1.03031i 0.979855 + 0.199710i \(0.0640000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(164\) −0.0865734 + 0.152893i −0.0865734 + 0.152893i
\(165\) 0 0
\(166\) 0.465697 0.0827856i 0.465697 0.0827856i
\(167\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(168\) 0 0
\(169\) −0.597905 + 0.801567i −0.597905 + 0.801567i
\(170\) 0 0
\(171\) −0.0813641 + 1.29325i −0.0813641 + 1.29325i
\(172\) 0.925080 + 0.339630i 0.925080 + 0.339630i
\(173\) 0 0 −0.617860 0.786288i \(-0.712000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.683564 + 1.20721i 0.683564 + 1.20721i
\(177\) 1.87373 2.38451i 1.87373 2.38451i
\(178\) 1.05159 0.648968i 1.05159 0.648968i
\(179\) 1.22942 0.716692i 1.22942 0.716692i 0.260842 0.965382i \(-0.416000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(180\) 0 0
\(181\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.625020 0.586932i 0.625020 0.586932i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.236499 0.971632i \(-0.424000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(192\) −1.07242 + 1.17116i −1.07242 + 1.17116i
\(193\) −0.536181 + 1.06886i −0.536181 + 1.06886i 0.448383 + 0.893841i \(0.352000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(194\) 0.268561 1.93046i 0.268561 1.93046i
\(195\) 0 0
\(196\) 0.850994 + 0.525175i 0.850994 + 0.525175i
\(197\) 0 0 0.938734 0.344643i \(-0.112000\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(198\) −0.601687 2.02348i −0.601687 2.02348i
\(199\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(200\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(201\) 1.69317 + 2.66801i 1.69317 + 2.66801i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.860030 + 0.472806i 0.860030 + 0.472806i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.15757 0.235932i −1.15757 0.235932i
\(210\) 0 0
\(211\) 0.360532 1.88998i 0.360532 1.88998i −0.0878512 0.996134i \(-0.528000\pi\)
0.448383 0.893841i \(-0.352000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.42262 1.40486i 1.42262 1.40486i
\(215\) 0 0
\(216\) 0.682233 0.469938i 0.682233 0.469938i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.481459 0.349800i 0.481459 0.349800i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.988652 0.150226i \(-0.952000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(224\) 0 0
\(225\) −0.847388 1.26390i −0.847388 1.26390i
\(226\) −0.834404 1.77320i −0.834404 1.77320i
\(227\) −1.67249 + 0.812840i −1.67249 + 0.812840i −0.675333 + 0.737513i \(0.736000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(228\) −0.152611 1.34362i −0.152611 1.34362i
\(229\) 0 0 −0.137790 0.990461i \(-0.544000\pi\)
0.137790 + 0.990461i \(0.456000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.75109 0.496830i 1.75109 0.496830i 0.762443 0.647056i \(-0.224000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.898917 + 1.68494i −0.898917 + 1.68494i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.947098 0.320944i \(-0.104000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(240\) 0 0
\(241\) −0.138495 + 0.294317i −0.138495 + 0.294317i −0.962028 0.272952i \(-0.912000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(242\) 0.914127 0.138902i 0.914127 0.138902i
\(243\) 1.07464 0.425481i 1.07464 0.425481i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.149502 + 0.235578i −0.149502 + 0.235578i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.745189 0.0941393i 0.745189 0.0941393i
\(250\) 0 0
\(251\) 0.920232 0.391374i 0.920232 0.391374i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.535827 0.844328i 0.535827 0.844328i
\(257\) 0.0246258 0.00501913i 0.0246258 0.00501913i −0.187381 0.982287i \(-0.560000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(258\) 1.44006 + 0.612454i 1.44006 + 0.612454i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.00157806 + 0.125571i 0.00157806 + 0.125571i
\(263\) 0 0 0.947098 0.320944i \(-0.104000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(264\) 0.987796 + 1.96915i 0.987796 + 1.96915i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.71958 0.945344i 1.71958 0.945344i
\(268\) −1.34385 1.46758i −1.34385 1.46758i
\(269\) 0 0 0.962028 0.272952i \(-0.0880000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(270\) 0 0
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) −0.585339 0.198354i −0.585339 0.198354i
\(273\) 0 0
\(274\) −0.0643325 0.566397i −0.0643325 0.566397i
\(275\) 1.24775 0.606414i 1.24775 0.606414i
\(276\) 0 0
\(277\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(278\) 1.94352 0.447267i 1.94352 0.447267i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.468030 1.22693i 0.468030 1.22693i −0.470704 0.882291i \(-0.656000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(282\) 0 0
\(283\) −0.263152 + 0.191191i −0.263152 + 0.191191i −0.711536 0.702650i \(-0.752000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.08273 + 1.06921i −1.08273 + 1.06921i
\(289\) 0.0542950 0.615644i 0.0542950 0.615644i
\(290\) 0 0
\(291\) 0.579956 3.04024i 0.579956 3.04024i
\(292\) −0.259955 + 0.269945i −0.259955 + 0.269945i
\(293\) 0 0 −0.979855 0.199710i \(-0.936000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(294\) 1.30775 + 0.900812i 1.30775 + 0.900812i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.271803 1.11667i −0.271803 1.11667i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.10151 + 1.14384i 1.10151 + 1.14384i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.242711 + 0.816237i 0.242711 + 0.816237i
\(305\) 0 0
\(306\) 0.800319 + 0.493901i 0.800319 + 0.493901i
\(307\) −0.896483 0.0225358i −0.896483 0.0225358i −0.425779 0.904827i \(-0.640000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.236499 0.971632i \(-0.424000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(312\) 0 0
\(313\) 1.89436 + 0.336754i 1.89436 + 0.336754i 0.994951 0.100362i \(-0.0320000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.212007 0.977268i \(-0.568000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 2.36833 2.11456i 2.36833 2.11456i
\(322\) 0 0
\(323\) 0.454676 0.265053i 0.454676 0.265053i
\(324\) −0.175444 + 0.108272i −0.175444 + 0.108272i
\(325\) 0 0
\(326\) −0.548776 0.969168i −0.548776 0.969168i
\(327\) 0 0
\(328\) 0.0667281 0.162538i 0.0667281 0.162538i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0750855 + 1.19345i −0.0750855 + 1.19345i 0.762443 + 0.647056i \(0.224000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(332\) −0.451649 + 0.140500i −0.451649 + 0.140500i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.836099 + 0.432652i 0.836099 + 0.432652i 0.823533 0.567269i \(-0.192000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(338\) 0.492727 0.870184i 0.492727 0.870184i
\(339\) −1.18187 2.87882i −1.18187 2.87882i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.0813641 1.29325i −0.0813641 1.29325i
\(343\) 0 0
\(344\) −0.960352 0.221009i −0.960352 0.221009i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.44422 + 1.22565i −1.44422 + 1.22565i −0.514440 + 0.857527i \(0.672000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.778462 0.627691i \(-0.784000\pi\)
0.778462 + 0.627691i \(0.216000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.829478 1.11202i −0.829478 1.11202i
\(353\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(354\) −1.56010 + 2.60055i −1.56010 + 2.60055i
\(355\) 0 0
\(356\) −0.961961 + 0.775650i −0.961961 + 0.775650i
\(357\) 0 0
\(358\) −1.12990 + 0.865128i −1.12990 + 0.865128i
\(359\) 0 0 0.888136 0.459580i \(-0.152000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(360\) 0 0
\(361\) 0.250141 + 0.113890i 0.250141 + 0.113890i
\(362\) 0 0
\(363\) 1.46086 0.147359i 1.46086 0.147359i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.332820 0.942991i \(-0.392000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(368\) 0 0
\(369\) −0.154422 + 0.218259i −0.154422 + 0.218259i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.863923 0.503623i \(-0.832000\pi\)
0.863923 + 0.503623i \(0.168000\pi\)
\(374\) −0.546529 + 0.660640i −0.546529 + 0.660640i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.950962 1.14952i 0.950962 1.14952i −0.0376902 0.999289i \(-0.512000\pi\)
0.988652 0.150226i \(-0.0480000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.332820 0.942991i \(-0.608000\pi\)
0.332820 + 0.942991i \(0.392000\pi\)
\(384\) 0.917174 1.29633i 0.917174 1.29633i
\(385\) 0 0
\(386\) 0.397989 1.12764i 0.397989 1.12764i
\(387\) 1.34870 + 0.655477i 1.34870 + 0.655477i
\(388\) −0.0244919 + 1.94890i −0.0244919 + 1.94890i
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.910106 0.414376i −0.910106 0.414376i
\(393\) −0.00751619 + 0.199279i −0.00751619 + 0.199279i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.850552 + 1.93211i 0.850552 + 1.93211i
\(397\) 0 0 0.778462 0.627691i \(-0.216000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 0.587785i −0.809017 0.587785i
\(401\) −0.426201 0.571376i −0.426201 0.571376i 0.535827 0.844328i \(-0.320000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(402\) −2.01421 2.43476i −2.01421 2.43476i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.912507 0.361287i −0.912507 0.361287i
\(409\) −1.65863 0.381706i −1.65863 0.381706i −0.711536 0.702650i \(-0.752000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(410\) 0 0
\(411\) −0.0568386 0.903424i −0.0568386 0.903424i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 3.11805 0.554287i 3.11805 0.554287i
\(418\) 1.17802 + 0.0889890i 1.17802 + 0.0889890i
\(419\) 1.69984 0.0855153i 1.69984 0.0855153i 0.823533 0.567269i \(-0.192000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(420\) 0 0
\(421\) 0 0 0.954865 0.297042i \(-0.0960000\pi\)
−0.954865 + 0.297042i \(0.904000\pi\)
\(422\) −0.120812 + 1.92026i −0.120812 + 1.92026i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.234716 + 0.571729i −0.234716 + 0.571729i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.23533 + 1.57208i −1.23533 + 1.57208i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.162637 0.986686i \(-0.448000\pi\)
−0.162637 + 0.986686i \(0.552000\pi\)
\(432\) −0.617955 + 0.551739i −0.617955 + 0.551739i
\(433\) 0.238883 + 1.25227i 0.238883 + 1.25227i 0.876307 + 0.481754i \(0.160000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.433821 + 0.407385i −0.433821 + 0.407385i
\(439\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(440\) 0 0
\(441\) 1.20820 + 0.925077i 1.20820 + 0.925077i
\(442\) 0 0
\(443\) 1.09271 1.19332i 1.09271 1.19332i 0.112856 0.993611i \(-0.464000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.434622 1.46164i −0.434622 1.46164i −0.837528 0.546394i \(-0.816000\pi\)
0.402906 0.915241i \(-0.368000\pi\)
\(450\) 0.999115 + 1.14773i 0.999115 + 1.14773i
\(451\) −0.177688 0.166860i −0.177688 0.166860i
\(452\) 1.05007 + 1.65464i 1.05007 + 1.65464i
\(453\) 0 0
\(454\) 1.55743 1.01605i 1.55743 1.01605i
\(455\) 0 0
\(456\) 0.319808 + 1.31390i 0.319808 + 1.31390i
\(457\) −0.799459 + 1.81605i −0.799459 + 1.81605i −0.285019 + 0.958522i \(0.592000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(458\) 0 0
\(459\) 0.421643 + 0.290438i 0.421643 + 0.290438i
\(460\) 0 0
\(461\) 0 0 0.693653 0.720309i \(-0.256000\pi\)
−0.693653 + 0.720309i \(0.744000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.67502 + 0.712383i −1.67502 + 0.712383i
\(467\) 1.64498 1.13310i 1.64498 1.13310i 0.793990 0.607930i \(-0.208000\pi\)
0.850994 0.525175i \(-0.176000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.680650 1.78432i 0.680650 1.78432i
\(473\) −0.761320 + 1.13553i −0.761320 + 1.13553i
\(474\) 0 0
\(475\) 0.829867 0.190980i 0.829867 0.190980i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.112856 0.993611i \(-0.536000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.100515 0.309354i 0.100515 0.309354i
\(483\) 0 0
\(484\) −0.889510 + 0.252377i −0.889510 + 0.252377i
\(485\) 0 0
\(486\) −1.01284 + 0.556814i −1.01284 + 0.556814i
\(487\) 0 0 0.470704 0.882291i \(-0.344000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(488\) 0 0
\(489\) −0.793018 1.58086i −0.793018 1.58086i
\(490\) 0 0
\(491\) 0.0231273 + 1.84032i 0.0231273 + 1.84032i 0.402906 + 0.915241i \(0.368000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(492\) 0.118798 0.252458i 0.118798 0.252458i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.727514 + 0.186794i −0.727514 + 0.186794i
\(499\) −0.803523 + 0.0606993i −0.803523 + 0.0606993i −0.470704 0.882291i \(-0.656000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.863923 + 0.503623i −0.863923 + 0.503623i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.850883 1.34078i 0.850883 1.34078i
\(508\) 0 0
\(509\) 0 0 −0.920232 0.391374i \(-0.872000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(513\) −0.00886472 0.705395i −0.00886472 0.705395i
\(514\) −0.0238026 + 0.00806598i −0.0238026 + 0.00806598i
\(515\) 0 0
\(516\) −1.50546 0.427138i −1.50546 0.427138i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.301701 + 1.39072i −0.301701 + 1.39072i 0.535827 + 0.844328i \(0.320000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(522\) 0 0
\(523\) 1.47456 + 0.499685i 1.47456 + 0.499685i 0.938734 0.344643i \(-0.112000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(524\) −0.0173038 0.124383i −0.0173038 0.124383i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.22681 1.82982i −1.22681 1.82982i
\(529\) −0.974527 + 0.224271i −0.974527 + 0.224271i
\(530\) 0 0
\(531\) −1.61828 + 2.41371i −1.61828 + 2.41371i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.58753 + 1.15341i −1.58753 + 1.15341i
\(535\) 0 0
\(536\) 1.51719 + 1.28758i 1.51719 + 1.28758i
\(537\) −1.86103 + 1.28192i −1.86103 + 1.28192i
\(538\) 0 0
\(539\) −0.987118 + 0.974791i −0.987118 + 0.974791i
\(540\) 0 0
\(541\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.605584 + 0.123428i 0.605584 + 0.123428i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.324667 0.737513i 0.324667 0.737513i −0.675333 0.737513i \(-0.736000\pi\)
1.00000 \(0\)
\(548\) 0.134814 + 0.553868i 0.134814 + 0.553868i
\(549\) 0 0
\(550\) −1.16191 + 0.758016i −1.16191 + 0.758016i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.87213 + 0.687328i −1.87213 + 0.687328i
\(557\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.919492 + 1.00415i −0.919492 + 1.00415i
\(562\) −0.310564 + 1.27592i −0.310564 + 1.27592i
\(563\) −1.47647 1.13048i −1.47647 1.13048i −0.962028 0.272952i \(-0.912000\pi\)
−0.514440 0.857527i \(-0.672000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.237115 0.222666i 0.237115 0.222666i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0118298 0.0221738i −0.0118298 0.0221738i 0.876307 0.481754i \(-0.160000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(570\) 0 0
\(571\) 0.0516387 + 0.270699i 0.0516387 + 0.270699i 0.998737 0.0502443i \(-0.0160000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.940186 1.19648i 0.940186 1.19648i
\(577\) −0.735091 1.29821i −0.735091 1.29821i −0.947098 0.320944i \(-0.896000\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(578\) 0.0232938 + 0.617595i 0.0232938 + 0.617595i
\(579\) 0.721171 1.75665i 0.721171 1.75665i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.194340 + 3.08895i −0.194340 + 3.08895i
\(583\) 0 0
\(584\) 0.224072 0.300397i 0.224072 0.300397i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.84849 + 0.328600i −1.84849 + 0.328600i −0.984564 0.175023i \(-0.944000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(588\) −1.41034 0.729804i −1.41034 0.729804i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.125541 1.99542i −0.125541 1.99542i −0.0878512 0.996134i \(-0.528000\pi\)
−0.0376902 0.999289i \(-0.512000\pi\)
\(594\) 0.409616 + 1.07380i 0.409616 + 1.07380i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.260842 0.965382i \(-0.416000\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(600\) −1.23618 0.996762i −1.23618 0.996762i
\(601\) 0.237115 + 1.43853i 0.237115 + 1.43853i 0.793990 + 0.607930i \(0.208000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(602\) 0 0
\(603\) −1.81046 2.42714i −1.81046 2.42714i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.778462 0.627691i \(-0.216000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(608\) −0.343098 0.779381i −0.343098 0.779381i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.855911 0.389700i −0.855911 0.389700i
\(613\) 0 0 0.656586 0.754251i \(-0.272000\pi\)
−0.656586 + 0.754251i \(0.728000\pi\)
\(614\) 0.892239 0.0900010i 0.892239 0.0900010i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.03894 + 0.504932i 1.03894 + 0.504932i 0.876307 0.481754i \(-0.160000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(618\) 0 0
\(619\) −1.05130 1.48591i −1.05130 1.48591i −0.863923 0.503623i \(-0.832000\pi\)
−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
\(626\) −1.92163 0.0966728i −1.92163 0.0966728i
\(627\) 1.86120 + 0.235125i 1.86120 + 0.235125i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.863923 0.503623i \(-0.832000\pi\)
0.863923 + 0.503623i \(0.168000\pi\)
\(632\) 0 0
\(633\) −0.344817 + 3.03584i −0.344817 + 3.03584i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.06624 0.107553i 1.06624 0.107553i 0.448383 0.893841i \(-0.352000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(642\) −2.08463 + 2.39472i −2.08463 + 2.39472i
\(643\) 1.52448 + 0.694102i 1.52448 + 0.694102i 0.988652 0.150226i \(-0.0480000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.417871 + 0.319949i −0.417871 + 0.319949i
\(647\) 0 0 −0.402906 0.915241i \(-0.632000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(648\) 0.160491 0.129407i 0.160491 0.129407i
\(649\) −1.97628 1.76452i −1.97628 1.76452i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.665917 + 0.892746i 0.665917 + 0.892746i
\(653\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.0458305 + 0.169620i −0.0458305 + 0.169620i
\(657\) −0.434798 + 0.368997i −0.434798 + 0.368997i
\(658\) 0 0
\(659\) −0.116762 0.0462295i −0.116762 0.0462295i 0.309017 0.951057i \(-0.400000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(660\) 0 0
\(661\) 0 0 −0.356412 0.934329i \(-0.616000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(662\) −0.0750855 1.19345i −0.0750855 1.19345i
\(663\) 0 0
\(664\) 0.430478 0.195999i 0.430478 0.195999i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.00473317 + 0.0752316i −0.00473317 + 0.0752316i −0.999684 0.0251301i \(-0.992000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(674\) −0.883731 0.324450i −0.883731 0.324450i
\(675\) 0.511849 + 0.651379i 0.511849 + 0.651379i
\(676\) −0.379779 + 0.925077i −0.379779 + 0.925077i
\(677\) 0 0 −0.0376902 0.999289i \(-0.512000\pi\)
0.0376902 + 0.999289i \(0.488000\pi\)
\(678\) 1.53336 + 2.70800i 1.53336 + 2.70800i
\(679\) 0 0
\(680\) 0 0
\(681\) 2.55111 1.48717i 2.55111 1.48717i
\(682\) 0 0
\(683\) 1.46885 1.31146i 1.46885 1.31146i 0.617860 0.786288i \(-0.288000\pi\)
0.850994 0.525175i \(-0.176000\pi\)
\(684\) 0.242809 + 1.27285i 0.242809 + 1.27285i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.980479 + 0.0989019i 0.980479 + 0.0989019i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.01300 + 0.180078i 1.01300 + 0.180078i 0.656586 0.754251i \(-0.272000\pi\)
0.356412 + 0.934329i \(0.384000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.27921 1.39699i 1.27921 1.39699i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.108556 + 0.00272888i 0.108556 + 0.00272888i
\(698\) 0 0
\(699\) −2.71337 + 0.996177i −2.71337 + 0.996177i
\(700\) 0 0
\(701\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.962310 + 0.999289i 0.962310 + 0.999289i
\(705\) 0 0
\(706\) 1.69755 + 0.933237i 1.69755 + 0.933237i
\(707\) 0 0
\(708\) 1.22186 2.77557i 1.22186 2.77557i
\(709\) 0 0 −0.260842 0.965382i \(-0.584000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.857161 0.890100i 0.857161 0.890100i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.01257 0.999921i 1.01257 0.999921i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.762443 0.647056i \(-0.776000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.262443 0.0816413i −0.262443 0.0816413i
\(723\) 0.184097 0.482608i 0.184097 0.482608i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.43088 + 0.329292i −1.43088 + 0.329292i
\(727\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(728\) 0 0
\(729\) −1.46534 + 0.712164i −1.46534 + 0.712164i
\(730\) 0 0
\(731\) −0.0839204 0.603235i −0.0839204 0.603235i
\(732\) 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
\(737\) 2.41914 1.32993i 2.41914 1.32993i
\(738\) 0.125849 0.235892i 0.125849 0.235892i
\(739\) 1.89436 + 0.537477i 1.89436 + 0.537477i 0.994951 + 0.100362i \(0.0320000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.705254 + 0.143742i −0.705254 + 0.143742i
\(748\) 0.459419 0.723929i 0.459419 0.723929i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(752\) 0 0
\(753\) −1.41034 + 0.729804i −1.41034 + 0.729804i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0