Properties

Label 2008.1.bd.a.27.1
Level 2008
Weight 1
Character 2008.27
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 27.1
Root \(-0.994951 - 0.100362i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.27
Dual form 2008.1.bd.a.595.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.929776 - 0.368125i) q^{2} +(0.740210 + 0.170347i) q^{3} +(0.728969 + 0.684547i) q^{4} +(-0.625521 - 0.430874i) q^{6} +(-0.425779 - 0.904827i) q^{8} +(-0.380513 - 0.184931i) q^{9} +O(q^{10})\) \(q+(-0.929776 - 0.368125i) q^{2} +(0.740210 + 0.170347i) q^{3} +(0.728969 + 0.684547i) q^{4} +(-0.625521 - 0.430874i) q^{6} +(-0.425779 - 0.904827i) q^{8} +(-0.380513 - 0.184931i) q^{9} +(0.0562293 - 1.49082i) q^{11} +(0.422979 + 0.630886i) q^{12} +(0.0627905 + 0.998027i) q^{16} +(-1.28470 - 0.983652i) q^{17} +(0.285714 + 0.312021i) q^{18} +(-1.15824 - 1.55277i) q^{19} +(-0.601089 + 1.36543i) q^{22} +(-0.161032 - 0.742292i) q^{24} +(0.968583 - 0.248690i) q^{25} +(-0.841444 - 0.678475i) q^{27} +(0.309017 - 0.951057i) q^{32} +(0.295578 - 1.09394i) q^{33} +(0.832381 + 1.38751i) q^{34} +(-0.150788 - 0.395288i) q^{36} +(0.505293 + 1.87010i) q^{38} +(-0.389145 + 0.347447i) q^{41} +(0.472849 + 1.94265i) q^{43} +(1.06153 - 1.04827i) q^{44} +(-0.123532 + 0.749445i) q^{48} +(-0.745941 - 0.666012i) q^{49} +(-0.992115 - 0.125333i) q^{50} +(-0.783388 - 0.946954i) q^{51} +(0.532592 + 0.940586i) q^{54} +(-0.592833 - 1.34668i) q^{57} +(0.981149 - 0.751231i) q^{59} +(-0.637424 + 0.770513i) q^{64} +(-0.677529 + 0.908313i) q^{66} +(1.90009 - 0.191664i) q^{67} +(-0.263152 - 1.59649i) q^{68} +(-0.00531633 + 0.423038i) q^{72} +(-0.0941461 + 1.06751i) q^{73} +(0.759318 - 0.0190878i) q^{75} +(0.218622 - 1.92479i) q^{76} +(-0.245871 - 0.312895i) q^{81} +(0.489722 - 0.179794i) q^{82} +(1.29827 + 0.197272i) q^{83} +(0.275494 - 1.98030i) q^{86} +(-1.37288 + 0.583883i) q^{88} +(0.518795 + 1.74471i) q^{89} +(0.390747 - 0.651341i) q^{96} +(1.10781 + 1.09397i) q^{97} +(0.448383 + 0.893841i) q^{98} +(-0.297095 + 0.556878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{24}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.929776 0.368125i −0.929776 0.368125i
\(3\) 0.740210 + 0.170347i 0.740210 + 0.170347i 0.577573 0.816339i \(-0.304000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(4\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(5\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(6\) −0.625521 0.430874i −0.625521 0.430874i
\(7\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(8\) −0.425779 0.904827i −0.425779 0.904827i
\(9\) −0.380513 0.184931i −0.380513 0.184931i
\(10\) 0 0
\(11\) 0.0562293 1.49082i 0.0562293 1.49082i −0.637424 0.770513i \(-0.720000\pi\)
0.693653 0.720309i \(-0.256000\pi\)
\(12\) 0.422979 + 0.630886i 0.422979 + 0.630886i
\(13\) 0 0 0.984564 0.175023i \(-0.0560000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(17\) −1.28470 0.983652i −1.28470 0.983652i −0.999684 0.0251301i \(-0.992000\pi\)
−0.285019 0.958522i \(-0.592000\pi\)
\(18\) 0.285714 + 0.312021i 0.285714 + 0.312021i
\(19\) −1.15824 1.55277i −1.15824 1.55277i −0.778462 0.627691i \(-0.784000\pi\)
−0.379779 0.925077i \(-0.624000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.601089 + 1.36543i −0.601089 + 1.36543i
\(23\) 0 0 0.332820 0.942991i \(-0.392000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(24\) −0.161032 0.742292i −0.161032 0.742292i
\(25\) 0.968583 0.248690i 0.968583 0.248690i
\(26\) 0 0
\(27\) −0.841444 0.678475i −0.841444 0.678475i
\(28\) 0 0
\(29\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(30\) 0 0
\(31\) 0 0 0.617860 0.786288i \(-0.288000\pi\)
−0.617860 + 0.786288i \(0.712000\pi\)
\(32\) 0.309017 0.951057i 0.309017 0.951057i
\(33\) 0.295578 1.09394i 0.295578 1.09394i
\(34\) 0.832381 + 1.38751i 0.832381 + 1.38751i
\(35\) 0 0
\(36\) −0.150788 0.395288i −0.150788 0.395288i
\(37\) 0 0 0.693653 0.720309i \(-0.256000\pi\)
−0.693653 + 0.720309i \(0.744000\pi\)
\(38\) 0.505293 + 1.87010i 0.505293 + 1.87010i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.389145 + 0.347447i −0.389145 + 0.347447i −0.837528 0.546394i \(-0.816000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(42\) 0 0
\(43\) 0.472849 + 1.94265i 0.472849 + 1.94265i 0.260842 + 0.965382i \(0.416000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(44\) 1.06153 1.04827i 1.06153 1.04827i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(48\) −0.123532 + 0.749445i −0.123532 + 0.749445i
\(49\) −0.745941 0.666012i −0.745941 0.666012i
\(50\) −0.992115 0.125333i −0.992115 0.125333i
\(51\) −0.783388 0.946954i −0.783388 0.946954i
\(52\) 0 0
\(53\) 0 0 0.762443 0.647056i \(-0.224000\pi\)
−0.762443 + 0.647056i \(0.776000\pi\)
\(54\) 0.532592 + 0.940586i 0.532592 + 0.940586i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.592833 1.34668i −0.592833 1.34668i
\(58\) 0 0
\(59\) 0.981149 0.751231i 0.981149 0.751231i 0.0125660 0.999921i \(-0.496000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.379779 0.925077i \(-0.624000\pi\)
0.379779 + 0.925077i \(0.376000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(65\) 0 0
\(66\) −0.677529 + 0.908313i −0.677529 + 0.908313i
\(67\) 1.90009 0.191664i 1.90009 0.191664i 0.920232 0.391374i \(-0.128000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(68\) −0.263152 1.59649i −0.263152 1.59649i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(72\) −0.00531633 + 0.423038i −0.00531633 + 0.423038i
\(73\) −0.0941461 + 1.06751i −0.0941461 + 1.06751i 0.793990 + 0.607930i \(0.208000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(74\) 0 0
\(75\) 0.759318 0.0190878i 0.759318 0.0190878i
\(76\) 0.218622 1.92479i 0.218622 1.92479i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.492727 0.870184i \(-0.336000\pi\)
−0.492727 + 0.870184i \(0.664000\pi\)
\(80\) 0 0
\(81\) −0.245871 0.312895i −0.245871 0.312895i
\(82\) 0.489722 0.179794i 0.489722 0.179794i
\(83\) 1.29827 + 0.197272i 1.29827 + 0.197272i 0.762443 0.647056i \(-0.224000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.275494 1.98030i 0.275494 1.98030i
\(87\) 0 0
\(88\) −1.37288 + 0.583883i −1.37288 + 0.583883i
\(89\) 0.518795 + 1.74471i 0.518795 + 1.74471i 0.656586 + 0.754251i \(0.272000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.390747 0.651341i 0.390747 0.651341i
\(97\) 1.10781 + 1.09397i 1.10781 + 1.09397i 0.994951 + 0.100362i \(0.0320000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(98\) 0.448383 + 0.893841i 0.448383 + 0.893841i
\(99\) −0.297095 + 0.556878i −0.297095 + 0.556878i
\(100\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(101\) 0 0 −0.938734 0.344643i \(-0.888000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(102\) 0.379779 + 1.16884i 0.379779 + 1.16884i
\(103\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.757400 1.84490i 0.757400 1.84490i 0.309017 0.951057i \(-0.400000\pi\)
0.448383 0.893841i \(-0.352000\pi\)
\(108\) −0.148938 1.07060i −0.148938 1.07060i
\(109\) 0 0 −0.112856 0.993611i \(-0.536000\pi\)
0.112856 + 0.993611i \(0.464000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.33250 + 0.968121i −1.33250 + 0.968121i −0.332820 + 0.942991i \(0.608000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(114\) 0.0554570 + 1.47035i 0.0554570 + 1.47035i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.18880 + 0.337292i −1.18880 + 0.337292i
\(119\) 0 0
\(120\) 0 0
\(121\) −1.22223 0.0923290i −1.22223 0.0923290i
\(122\) 0 0
\(123\) −0.347235 + 0.190894i −0.347235 + 0.190894i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.988652 0.150226i \(-0.0480000\pi\)
−0.988652 + 0.150226i \(0.952000\pi\)
\(128\) 0.876307 0.481754i 0.876307 0.481754i
\(129\) 0.0190832 + 1.51852i 0.0190832 + 1.51852i
\(130\) 0 0
\(131\) 0.124728 + 0.353398i 0.124728 + 0.353398i 0.988652 0.150226i \(-0.0480000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(132\) 0.964323 0.595113i 0.964323 0.595113i
\(133\) 0 0
\(134\) −1.83721 0.521264i −1.83721 0.521264i
\(135\) 0 0
\(136\) −0.343035 + 1.58125i −0.343035 + 1.58125i
\(137\) −0.0574732 1.52380i −0.0574732 1.52380i −0.675333 0.737513i \(-0.736000\pi\)
0.617860 0.786288i \(-0.288000\pi\)
\(138\) 0 0
\(139\) −1.86108 0.578950i −1.86108 0.578950i −0.997159 0.0753268i \(-0.976000\pi\)
−0.863923 0.503623i \(-0.832000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.160674 0.391374i 0.160674 0.391374i
\(145\) 0 0
\(146\) 0.480511 0.957888i 0.480511 0.957888i
\(147\) −0.438700 0.620057i −0.438700 0.620057i
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) −0.713023 0.261776i −0.713023 0.261776i
\(151\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(152\) −0.911832 + 1.70914i −0.911832 + 1.70914i
\(153\) 0.306938 + 0.611874i 0.306938 + 0.611874i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.113420 + 0.381433i 0.113420 + 0.381433i
\(163\) 1.80339 0.766979i 1.80339 0.766979i 0.823533 0.567269i \(-0.192000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(164\) −0.521518 0.0131099i −0.521518 0.0131099i
\(165\) 0 0
\(166\) −1.13448 0.661344i −1.13448 0.661344i
\(167\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(168\) 0 0
\(169\) 0.938734 0.344643i 0.938734 0.344643i
\(170\) 0 0
\(171\) 0.153570 + 0.805043i 0.153570 + 0.805043i
\(172\) −0.985143 + 1.73982i −0.985143 + 1.73982i
\(173\) 0 0 −0.910106 0.414376i \(-0.864000\pi\)
0.910106 + 0.414376i \(0.136000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.49141 0.0374911i 1.49141 0.0374911i
\(177\) 0.854226 0.388933i 0.854226 0.388933i
\(178\) 0.159908 1.81317i 0.159908 1.81317i
\(179\) 0.0174330 1.38720i 0.0174330 1.38720i −0.711536 0.702650i \(-0.752000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(180\) 0 0
\(181\) 0 0 0.577573 0.816339i \(-0.304000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.53869 + 1.85995i −1.53869 + 1.85995i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(192\) −0.603082 + 0.461758i −0.603082 + 0.461758i
\(193\) −1.84849 0.328600i −1.84849 0.328600i −0.863923 0.503623i \(-0.832000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(194\) −0.627295 1.42496i −0.627295 1.42496i
\(195\) 0 0
\(196\) −0.0878512 0.996134i −0.0878512 0.996134i
\(197\) 0 0 −0.492727 0.870184i \(-0.664000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(198\) 0.481233 0.408404i 0.481233 0.408404i
\(199\) 0 0 −0.837528 0.546394i \(-0.816000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(200\) −0.637424 0.770513i −0.637424 0.770513i
\(201\) 1.43911 + 0.181802i 1.43911 + 0.181802i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.0771690 1.22657i 0.0771690 1.22657i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.38003 + 1.63942i −2.38003 + 1.63942i
\(210\) 0 0
\(211\) −0.723723 1.14040i −0.723723 1.14040i −0.984564 0.175023i \(-0.944000\pi\)
0.260842 0.965382i \(-0.416000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.38337 + 1.43653i −1.38337 + 1.43653i
\(215\) 0 0
\(216\) −0.255633 + 1.05024i −0.255633 + 1.05024i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.251535 + 0.774144i −0.251535 + 0.774144i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.899405 0.437116i \(-0.144000\pi\)
−0.899405 + 0.437116i \(0.856000\pi\)
\(224\) 0 0
\(225\) −0.414549 0.0844916i −0.414549 0.0844916i
\(226\) 1.59532 0.409608i 1.59532 0.409608i
\(227\) −0.180536 0.832201i −0.180536 0.832201i −0.974527 0.224271i \(-0.928000\pi\)
0.793990 0.607930i \(-0.208000\pi\)
\(228\) 0.489708 1.38751i 0.489708 1.38751i
\(229\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.384966 + 0.420411i 0.384966 + 0.420411i 0.899405 0.437116i \(-0.144000\pi\)
−0.514440 + 0.857527i \(0.672000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.22948 + 0.124019i 1.22948 + 0.124019i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(240\) 0 0
\(241\) −0.911832 0.234119i −0.911832 0.234119i −0.236499 0.971632i \(-0.576000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(242\) 1.10241 + 0.535778i 1.10241 + 0.535778i
\(243\) 0.331532 + 0.704541i 0.331532 + 0.704541i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.393124 0.0496631i 0.393124 0.0496631i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.927387 + 0.367179i 0.927387 + 0.367179i
\(250\) 0 0
\(251\) 0.356412 + 0.934329i 0.356412 + 0.934329i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(257\) −0.0620782 0.0427609i −0.0620782 0.0427609i 0.535827 0.844328i \(-0.320000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(258\) 0.541260 1.41891i 0.541260 1.41891i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.0141249 0.374496i 0.0141249 0.374496i
\(263\) 0 0 −0.556876 0.830596i \(-0.688000\pi\)
0.556876 + 0.830596i \(0.312000\pi\)
\(264\) −1.11568 + 0.198331i −1.11568 + 0.198331i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.0868115 + 1.37983i 0.0868115 + 1.37983i
\(268\) 1.51631 + 1.16098i 1.51631 + 1.16098i
\(269\) 0 0 −0.675333 0.737513i \(-0.736000\pi\)
0.675333 + 0.737513i \(0.264000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0.901044 1.34393i 0.901044 1.34393i
\(273\) 0 0
\(274\) −0.507512 + 1.43795i −0.507512 + 1.43795i
\(275\) −0.316290 1.45797i −0.316290 1.45797i
\(276\) 0 0
\(277\) 0 0 −0.979855 0.199710i \(-0.936000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(278\) 1.51726 + 1.22340i 1.51726 + 1.22340i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.48768 + 0.769822i 1.48768 + 0.769822i 0.994951 0.100362i \(-0.0320000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(282\) 0 0
\(283\) −0.290911 + 0.895332i −0.290911 + 0.895332i 0.693653 + 0.720309i \(0.256000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.293465 + 0.304742i −0.293465 + 0.304742i
\(289\) 0.422050 + 1.56202i 0.422050 + 1.56202i
\(290\) 0 0
\(291\) 0.633655 + 0.998481i 0.633655 + 0.998481i
\(292\) −0.799391 + 0.713734i −0.799391 + 0.713734i
\(293\) 0 0 0.823533 0.567269i \(-0.192000\pi\)
−0.823533 + 0.567269i \(0.808000\pi\)
\(294\) 0.179635 + 0.738011i 0.179635 + 0.738011i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.05880 + 1.21629i −1.05880 + 1.21629i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.566586 + 0.505875i 0.566586 + 0.505875i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.47698 1.25346i 1.47698 1.25346i
\(305\) 0 0
\(306\) −0.0601380 0.681897i −0.0601380 0.681897i
\(307\) 1.96353 0.148328i 1.96353 0.148328i 0.968583 0.248690i \(-0.0800000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.656586 0.754251i \(-0.728000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(312\) 0 0
\(313\) 1.16687 0.680227i 1.16687 0.680227i 0.212007 0.977268i \(-0.432000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.597905 0.801567i \(-0.296000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.874907 1.23659i 0.874907 1.23659i
\(322\) 0 0
\(323\) −0.0393870 + 3.13415i −0.0393870 + 3.13415i
\(324\) 0.0349594 0.396401i 0.0349594 0.396401i
\(325\) 0 0
\(326\) −1.95909 + 0.0492477i −1.95909 + 0.0492477i
\(327\) 0 0
\(328\) 0.480069 + 0.204173i 0.480069 + 0.204173i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.351802 1.84421i −0.351802 1.84421i −0.514440 0.857527i \(-0.672000\pi\)
0.162637 0.986686i \(-0.448000\pi\)
\(332\) 0.811356 + 1.03253i 0.811356 + 1.03253i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.274189 + 1.97092i −0.274189 + 1.97092i −0.0376902 + 0.999289i \(0.512000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(338\) −0.999684 0.0251301i −0.999684 0.0251301i
\(339\) −1.15125 + 0.489625i −1.15125 + 0.489625i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.153570 0.805043i 0.153570 0.805043i
\(343\) 0 0
\(344\) 1.55643 1.25499i 1.55643 1.25499i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.572958 0.955071i 0.572958 0.955071i −0.425779 0.904827i \(-0.640000\pi\)
0.998737 0.0502443i \(-0.0160000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.448383 0.893841i \(-0.648000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.40048 0.514167i −1.40048 0.514167i
\(353\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(354\) −0.937415 + 0.0471594i −0.937415 + 0.0471594i
\(355\) 0 0
\(356\) −0.816152 + 1.62698i −0.816152 + 1.62698i
\(357\) 0 0
\(358\) −0.526870 + 1.28337i −0.526870 + 1.28337i
\(359\) 0 0 −0.137790 0.990461i \(-0.544000\pi\)
0.137790 + 0.990461i \(0.456000\pi\)
\(360\) 0 0
\(361\) −0.784548 + 2.63844i −0.784548 + 2.63844i
\(362\) 0 0
\(363\) −0.888979 0.276546i −0.888979 0.276546i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.850994 0.525175i \(-0.824000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(368\) 0 0
\(369\) 0.212328 0.0602430i 0.212328 0.0602430i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.0125660 0.999921i \(-0.504000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(374\) 2.11533 1.16291i 2.11533 1.16291i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.01226 0.556496i 1.01226 0.556496i 0.112856 0.993611i \(-0.464000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.850994 0.525175i \(-0.176000\pi\)
−0.850994 + 0.525175i \(0.824000\pi\)
\(384\) 0.730716 0.207323i 0.730716 0.207323i
\(385\) 0 0
\(386\) 1.59771 + 0.985998i 1.59771 + 0.985998i
\(387\) 0.179332 0.826647i 0.179332 0.826647i
\(388\) 0.0586808 + 1.55582i 0.0586808 + 1.55582i
\(389\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.285019 + 0.958522i −0.285019 + 0.958522i
\(393\) 0.0321250 + 0.282835i 0.0321250 + 0.282835i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.597783 + 0.202571i −0.597783 + 0.202571i
\(397\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(401\) −1.66745 0.612180i −1.66745 0.612180i −0.675333 0.737513i \(-0.736000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(402\) −1.27113 0.698808i −1.27113 0.698808i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.523279 + 1.11202i −0.523279 + 1.11202i
\(409\) 0.136778 0.110287i 0.136778 0.110287i −0.556876 0.830596i \(-0.688000\pi\)
0.693653 + 0.720309i \(0.256000\pi\)
\(410\) 0 0
\(411\) 0.217032 1.13772i 0.217032 1.13772i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.27897 0.745574i −1.27897 0.745574i
\(418\) 2.81641 0.648148i 2.81641 0.648148i
\(419\) −0.173708 0.0263950i −0.173708 0.0263950i 0.0627905 0.998027i \(-0.480000\pi\)
−0.236499 + 0.971632i \(0.576000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.617860 0.786288i \(-0.712000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(422\) 0.253089 + 1.32674i 0.253089 + 1.32674i
\(423\) 0 0
\(424\) 0 0
\(425\) −1.48897 0.633256i −1.48897 0.633256i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.81504 0.826397i 1.81504 0.826397i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.470704 0.882291i \(-0.656000\pi\)
0.470704 + 0.882291i \(0.344000\pi\)
\(432\) 0.624302 0.882386i 0.624302 0.882386i
\(433\) 0.939097 1.47978i 0.939097 1.47978i 0.0627905 0.998027i \(-0.480000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.518852 0.627185i 0.518852 0.627185i
\(439\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(440\) 0 0
\(441\) 0.160674 + 0.391374i 0.160674 + 0.391374i
\(442\) 0 0
\(443\) 0.490713 0.375722i 0.490713 0.375722i −0.332820 0.942991i \(-0.608000\pi\)
0.823533 + 0.567269i \(0.192000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.784461 + 0.665742i −0.784461 + 0.665742i −0.947098 0.320944i \(-0.896000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(450\) 0.354334 + 0.231164i 0.354334 + 0.231164i
\(451\) 0.496100 + 0.599682i 0.496100 + 0.599682i
\(452\) −1.63408 0.206432i −1.63408 0.206432i
\(453\) 0 0
\(454\) −0.138495 + 0.840221i −0.138495 + 0.840221i
\(455\) 0 0
\(456\) −0.966094 + 1.10980i −0.966094 + 1.10980i
\(457\) 1.76118 + 0.596812i 1.76118 + 0.596812i 0.998737 0.0502443i \(-0.0160000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(458\) 0 0
\(459\) 0.413623 + 1.69933i 0.413623 + 1.69933i
\(460\) 0 0
\(461\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.203169 0.532603i −0.203169 0.532603i
\(467\) −0.467630 + 1.92121i −0.467630 + 1.92121i −0.0878512 + 0.996134i \(0.528000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.09749 0.567912i −1.09749 0.567912i
\(473\) 2.92273 0.595699i 2.92273 0.595699i
\(474\) 0 0
\(475\) −1.50801 1.21594i −1.50801 1.21594i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.332820 0.942991i \(-0.392000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.761615 + 0.553346i 0.761615 + 0.553346i
\(483\) 0 0
\(484\) −0.827764 0.903979i −0.827764 0.903979i
\(485\) 0 0
\(486\) −0.0488917 0.777111i −0.0488917 0.777111i
\(487\) 0 0 −0.994951 0.100362i \(-0.968000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(488\) 0 0
\(489\) 1.46554 0.260524i 1.46554 0.260524i
\(490\) 0 0
\(491\) −0.0268665 + 0.712317i −0.0268665 + 0.712317i 0.920232 + 0.391374i \(0.128000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(492\) −0.383800 0.0985430i −0.383800 0.0985430i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.727095 0.682788i −0.727095 0.682788i
\(499\) 1.84595 + 0.424813i 1.84595 + 0.424813i 0.994951 0.100362i \(-0.0320000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.0125660 0.999921i 0.0125660 0.999921i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.753569 0.0951979i 0.753569 0.0951979i
\(508\) 0 0
\(509\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(513\) −0.0789192 + 2.09241i −0.0789192 + 2.09241i
\(514\) 0.0419775 + 0.0626106i 0.0419775 + 0.0626106i
\(515\) 0 0
\(516\) −1.02559 + 1.12001i −1.02559 + 1.12001i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.829478 1.11202i −0.829478 1.11202i −0.992115 0.125333i \(-0.960000\pi\)
0.162637 0.986686i \(-0.448000\pi\)
\(522\) 0 0
\(523\) −0.499387 + 0.744851i −0.499387 + 0.744851i −0.992115 0.125333i \(-0.960000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(524\) −0.150994 + 0.342998i −0.150994 + 0.342998i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1.11034 + 0.226306i 1.11034 + 0.226306i
\(529\) −0.778462 0.627691i −0.778462 0.627691i
\(530\) 0 0
\(531\) −0.512266 + 0.104408i −0.512266 + 0.104408i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.427234 1.31489i 0.427234 1.31489i
\(535\) 0 0
\(536\) −0.982440 1.63764i −0.982440 1.63764i
\(537\) 0.249208 1.02385i 0.249208 1.02385i
\(538\) 0 0
\(539\) −1.03485 + 1.07462i −1.03485 + 1.07462i
\(540\) 0 0
\(541\) 0 0 −0.998737 0.0502443i \(-0.984000\pi\)
0.998737 + 0.0502443i \(0.0160000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.33250 + 0.917860i −1.33250 + 0.917860i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.79399 + 0.607930i 1.79399 + 0.607930i 1.00000 \(0\)
0.793990 + 0.607930i \(0.208000\pi\)
\(548\) 1.00122 1.15015i 1.00122 1.15015i
\(549\) 0 0
\(550\) −0.242636 + 1.47202i −0.242636 + 1.47202i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.960352 1.69603i −0.960352 1.69603i
\(557\) 0 0 −0.0878512 0.996134i \(-0.528000\pi\)
0.0878512 + 0.996134i \(0.472000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −1.45579 + 1.11465i −1.45579 + 1.11465i
\(562\) −1.09982 1.26341i −1.09982 1.26341i
\(563\) 0.323404 + 0.787757i 0.323404 + 0.787757i 0.998737 + 0.0502443i \(0.0160000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.600076 0.725367i 0.600076 0.725367i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0749998 + 0.00756530i −0.0749998 + 0.00756530i −0.137790 0.990461i \(-0.544000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(570\) 0 0
\(571\) 0.431776 0.680370i 0.431776 0.680370i −0.556876 0.830596i \(-0.688000\pi\)
0.988652 + 0.150226i \(0.0480000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.385040 0.175310i 0.385040 0.175310i
\(577\) −1.15478 + 0.0290289i −1.15478 + 0.0290289i −0.597905 0.801567i \(-0.704000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(578\) 0.182605 1.60770i 0.182605 1.60770i
\(579\) −1.31229 0.558117i −1.31229 0.558117i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.221592 1.16163i −0.221592 1.16163i
\(583\) 0 0
\(584\) 1.00600 0.369338i 1.00600 0.369338i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.851357 0.496298i −0.851357 0.496298i 0.0125660 0.999921i \(-0.496000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(588\) 0.104660 0.752313i 0.104660 0.752313i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.373698 1.95899i 0.373698 1.95899i 0.112856 0.993611i \(-0.464000\pi\)
0.260842 0.965382i \(-0.416000\pi\)
\(594\) 1.43219 0.741111i 1.43219 0.741111i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.711536 0.702650i \(-0.752000\pi\)
0.711536 + 0.702650i \(0.248000\pi\)
\(600\) −0.340573 0.678925i −0.340573 0.678925i
\(601\) 0.600076 1.12479i 0.600076 1.12479i −0.379779 0.925077i \(-0.624000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(602\) 0 0
\(603\) −0.758452 0.278455i −0.758452 0.278455i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.448383 0.893841i \(-0.352000\pi\)
−0.448383 + 0.893841i \(0.648000\pi\)
\(608\) −1.83469 + 0.621721i −1.83469 + 0.621721i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.195108 + 0.656150i −0.195108 + 0.656150i
\(613\) 0 0 0.837528 0.546394i \(-0.184000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(614\) −1.88025 0.584913i −1.88025 0.584913i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.407913 + 1.88032i −0.407913 + 1.88032i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(618\) 0 0
\(619\) 0.548393 + 0.155593i 0.548393 + 0.155593i 0.535827 0.844328i \(-0.320000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.876307 0.481754i 0.876307 0.481754i
\(626\) −1.33534 + 0.202905i −1.33534 + 0.202905i
\(627\) −2.04099 + 0.808085i −2.04099 + 0.808085i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.0125660 0.999921i \(-0.504000\pi\)
0.0125660 + 0.999921i \(0.496000\pi\)
\(632\) 0 0
\(633\) −0.341443 0.967423i −0.341443 0.967423i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.89467 0.589399i −1.89467 0.589399i −0.984564 0.175023i \(-0.944000\pi\)
−0.910106 0.414376i \(-0.864000\pi\)
\(642\) −1.26869 + 0.827678i −1.26869 + 0.827678i
\(643\) −0.0927094 + 0.311783i −0.0927094 + 0.311783i −0.992115 0.125333i \(-0.960000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.19038 2.89956i 1.19038 2.89956i
\(647\) 0 0 0.947098 0.320944i \(-0.104000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(648\) −0.178429 + 0.355695i −0.178429 + 0.355695i
\(649\) −1.06478 1.50496i −1.06478 1.50496i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.83965 + 0.675400i 1.83965 + 0.675400i
\(653\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.371196 0.366561i −0.371196 0.366561i
\(657\) 0.233240 0.388791i 0.233240 0.388791i
\(658\) 0 0
\(659\) 0.159566 0.339095i 0.159566 0.339095i −0.809017 0.587785i \(-0.800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(660\) 0 0
\(661\) 0 0 0.888136 0.459580i \(-0.152000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(662\) −0.351802 + 1.84421i −0.351802 + 1.84421i
\(663\) 0 0
\(664\) −0.374279 1.25870i −0.374279 1.25870i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.0422944 0.221715i −0.0422944 0.221715i 0.954865 0.297042i \(-0.0960000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(674\) 0.980479 1.73158i 0.980479 1.73158i
\(675\) −0.983739 0.447901i −0.983739 0.447901i
\(676\) 0.920232 + 0.391374i 0.920232 + 0.391374i
\(677\) 0 0 0.112856 0.993611i \(-0.464000\pi\)
−0.112856 + 0.993611i \(0.536000\pi\)
\(678\) 1.25065 0.0314388i 1.25065 0.0314388i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.00812782 0.646757i 0.00812782 0.646757i
\(682\) 0 0
\(683\) −0.997957 + 1.41051i −0.997957 + 1.41051i −0.0878512 + 0.996134i \(0.528000\pi\)
−0.910106 + 0.414376i \(0.864000\pi\)
\(684\) −0.439142 + 0.691977i −0.439142 + 0.691977i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.90913 + 0.593896i −1.90913 + 0.593896i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.72566 + 1.00597i −1.72566 + 1.00597i −0.837528 + 0.546394i \(0.816000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.884308 + 0.677083i −0.884308 + 0.677083i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.841703 0.0635834i 0.841703 0.0635834i
\(698\) 0 0
\(699\) 0.213340 + 0.376770i 0.213340 + 0.376770i
\(700\) 0 0
\(701\) 0 0 −0.837528 0.546394i \(-0.816000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.11286 + 0.993611i 1.11286 + 0.993611i
\(705\) 0 0
\(706\) 0.0915446 1.45506i 0.0915446 1.45506i
\(707\) 0 0
\(708\) 0.888947 + 0.301238i 0.888947 + 0.301238i
\(709\) 0 0 0.711536 0.702650i \(-0.248000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.35777 1.21228i 1.35777 1.21228i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.962310 0.999289i 0.962310 0.999289i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.514440 0.857527i \(-0.672000\pi\)
0.514440 + 0.857527i \(0.328000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.70073 2.16435i 1.70073 2.16435i
\(723\) −0.635066 0.328624i −0.635066 0.328624i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.724749 + 0.584381i 0.724749 + 0.584381i
\(727\) 0 0 −0.979855 0.199710i \(-0.936000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(728\) 0 0
\(729\) 0.209753 + 0.966877i 0.209753 + 0.966877i
\(730\) 0 0
\(731\) 1.30342 2.96085i 1.30342 2.96085i
\(732\) 0 0
\(733\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.178896 2.84347i −0.178896 2.84347i
\(738\) −0.219595 0.0221507i −0.219595 0.0221507i
\(739\) 1.16687 1.27431i 1.16687 1.27431i 0.212007 0.977268i \(-0.432000\pi\)
0.954865 0.297042i \(-0.0960000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.457526 0.315155i −0.457526 0.315155i
\(748\) −2.39488 + 0.302544i −2.39488 + 0.302544i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(752\) 0 0
\(753\) 0.104660 + 0.752313i 0.104660 + 0.752313i
\(754\) 0 0
\(755\) 0