Properties

Label 2008.1.bd.a.83.1
Level 2008
Weight 1
Character 2008.83
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 83.1
Root \(0.947098 - 0.320944i\) of \(x^{100} - x^{75} + x^{50} - x^{25} + 1\)
Character \(\chi\) \(=\) 2008.83
Dual form 2008.1.bd.a.1379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +O(q^{10})\) \(q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +(0.0123833 + 0.0218695i) q^{11} +(0.118658 - 0.129583i) q^{12} +(-0.187381 - 0.982287i) q^{16} +(0.525944 - 0.324576i) q^{17} +(0.322545 + 0.913879i) q^{18} +(0.900801 + 1.14636i) q^{19} +(0.0145156 - 0.0205163i) q^{22} +(-0.167772 - 0.0521909i) q^{24} +(0.728969 - 0.684547i) q^{25} +(0.342054 + 0.0519751i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(-0.00197996 - 0.00394700i) q^{33} +(-0.517621 - 0.337690i) q^{34} +(0.689570 - 0.680958i) q^{36} +(0.653715 - 1.30316i) q^{38} +(0.0112688 - 0.896696i) q^{41} +(1.40325 - 0.596800i) q^{43} +(-0.0247441 - 0.00439869i) q^{44} +(0.0242101 + 0.174026i) q^{48} +(0.0125660 + 0.999921i) q^{49} +(-0.929776 - 0.368125i) q^{50} +(-0.0951582 + 0.0523137i) q^{51} +(-0.0986111 - 0.331630i) q^{54} +(-0.147953 - 0.209116i) q^{57} +(1.66770 + 1.02919i) q^{59} +(0.876307 + 0.481754i) q^{64} +(-0.00272832 + 0.00347207i) q^{66} +(1.05483 + 0.357451i) q^{67} +(-0.0851591 + 0.612139i) q^{68} +(-0.909754 - 0.334003i) q^{72} +(1.54465 - 1.24548i) q^{73} +(-0.133963 + 0.113689i) q^{75} +(-1.45748 - 0.0366381i) q^{76} +(0.890041 + 0.181404i) q^{81} +(-0.816152 + 0.371598i) q^{82} +(-0.335529 - 0.628918i) q^{83} +(-1.13747 - 1.01559i) q^{86} +(0.00655549 + 0.0242620i) q^{88} +(-0.389529 - 1.60034i) q^{89} +(0.147156 - 0.0960028i) q^{96} +(-1.94678 + 0.346074i) q^{97} +(0.899405 - 0.437116i) q^{98} +(-0.00981328 - 0.0222918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q + O(q^{10}) \) \( 100q - 25q^{22} - 25q^{32} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{47}{125}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.425779 0.904827i −0.425779 0.904827i
\(3\) −0.175480 0.00882805i −0.175480 0.00882805i −0.0376902 0.999289i \(-0.512000\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(4\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(5\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(6\) 0.0667281 + 0.162538i 0.0667281 + 0.162538i
\(7\) 0 0 −0.711536 0.702650i \(-0.752000\pi\)
0.711536 + 0.702650i \(0.248000\pi\)
\(8\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(9\) −0.964236 0.0972634i −0.964236 0.0972634i
\(10\) 0 0
\(11\) 0.0123833 + 0.0218695i 0.0123833 + 0.0218695i 0.876307 0.481754i \(-0.160000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(12\) 0.118658 0.129583i 0.118658 0.129583i
\(13\) 0 0 −0.212007 0.977268i \(-0.568000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.187381 0.982287i −0.187381 0.982287i
\(17\) 0.525944 0.324576i 0.525944 0.324576i −0.236499 0.971632i \(-0.576000\pi\)
0.762443 + 0.647056i \(0.224000\pi\)
\(18\) 0.322545 + 0.913879i 0.322545 + 0.913879i
\(19\) 0.900801 + 1.14636i 0.900801 + 1.14636i 0.988652 + 0.150226i \(0.0480000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.0145156 0.0205163i 0.0145156 0.0205163i
\(23\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(24\) −0.167772 0.0521909i −0.167772 0.0521909i
\(25\) 0.728969 0.684547i 0.728969 0.684547i
\(26\) 0 0
\(27\) 0.342054 + 0.0519751i 0.342054 + 0.0519751i
\(28\) 0 0
\(29\) 0 0 −0.793990 0.607930i \(-0.792000\pi\)
0.793990 + 0.607930i \(0.208000\pi\)
\(30\) 0 0
\(31\) 0 0 0.979855 0.199710i \(-0.0640000\pi\)
−0.979855 + 0.199710i \(0.936000\pi\)
\(32\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(33\) −0.00197996 0.00394700i −0.00197996 0.00394700i
\(34\) −0.517621 0.337690i −0.517621 0.337690i
\(35\) 0 0
\(36\) 0.689570 0.680958i 0.689570 0.680958i
\(37\) 0 0 0.863923 0.503623i \(-0.168000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(38\) 0.653715 1.30316i 0.653715 1.30316i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.0112688 0.896696i 0.0112688 0.896696i −0.888136 0.459580i \(-0.848000\pi\)
0.899405 0.437116i \(-0.144000\pi\)
\(42\) 0 0
\(43\) 1.40325 0.596800i 1.40325 0.596800i 0.448383 0.893841i \(-0.352000\pi\)
0.954865 + 0.297042i \(0.0960000\pi\)
\(44\) −0.0247441 0.00439869i −0.0247441 0.00439869i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(48\) 0.0242101 + 0.174026i 0.0242101 + 0.174026i
\(49\) 0.0125660 + 0.999921i 0.0125660 + 0.999921i
\(50\) −0.929776 0.368125i −0.929776 0.368125i
\(51\) −0.0951582 + 0.0523137i −0.0951582 + 0.0523137i
\(52\) 0 0
\(53\) 0 0 0.656586 0.754251i \(-0.272000\pi\)
−0.656586 + 0.754251i \(0.728000\pi\)
\(54\) −0.0986111 0.331630i −0.0986111 0.331630i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.147953 0.209116i −0.147953 0.209116i
\(58\) 0 0
\(59\) 1.66770 + 1.02919i 1.66770 + 1.02919i 0.938734 + 0.344643i \(0.112000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(60\) 0 0
\(61\) 0 0 0.0878512 0.996134i \(-0.472000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(65\) 0 0
\(66\) −0.00272832 + 0.00347207i −0.00272832 + 0.00347207i
\(67\) 1.05483 + 0.357451i 1.05483 + 0.357451i 0.793990 0.607930i \(-0.208000\pi\)
0.260842 + 0.965382i \(0.416000\pi\)
\(68\) −0.0851591 + 0.612139i −0.0851591 + 0.612139i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(72\) −0.909754 0.334003i −0.909754 0.334003i
\(73\) 1.54465 1.24548i 1.54465 1.24548i 0.693653 0.720309i \(-0.256000\pi\)
0.850994 0.525175i \(-0.176000\pi\)
\(74\) 0 0
\(75\) −0.133963 + 0.113689i −0.133963 + 0.113689i
\(76\) −1.45748 0.0366381i −1.45748 0.0366381i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.285019 0.958522i \(-0.408000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(80\) 0 0
\(81\) 0.890041 + 0.181404i 0.890041 + 0.181404i
\(82\) −0.816152 + 0.371598i −0.816152 + 0.371598i
\(83\) −0.335529 0.628918i −0.335529 0.628918i 0.656586 0.754251i \(-0.272000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.13747 1.01559i −1.13747 1.01559i
\(87\) 0 0
\(88\) 0.00655549 + 0.0242620i 0.00655549 + 0.0242620i
\(89\) −0.389529 1.60034i −0.389529 1.60034i −0.745941 0.666012i \(-0.768000\pi\)
0.356412 0.934329i \(-0.384000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.147156 0.0960028i 0.147156 0.0960028i
\(97\) −1.94678 + 0.346074i −1.94678 + 0.346074i −0.947098 + 0.320944i \(0.896000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(98\) 0.899405 0.437116i 0.899405 0.437116i
\(99\) −0.00981328 0.0222918i −0.00981328 0.0222918i
\(100\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(101\) 0 0 −0.910106 0.414376i \(-0.864000\pi\)
0.910106 + 0.414376i \(0.136000\pi\)
\(102\) 0.0878512 + 0.0638276i 0.0878512 + 0.0638276i
\(103\) 0 0 0.162637 0.986686i \(-0.448000\pi\)
−0.162637 + 0.986686i \(0.552000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.0903883 + 1.02490i 0.0903883 + 1.02490i 0.899405 + 0.437116i \(0.144000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) −0.258081 + 0.230427i −0.258081 + 0.230427i
\(109\) 0 0 0.999684 0.0251301i \(-0.00800000\pi\)
−0.999684 + 0.0251301i \(0.992000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.234716 0.722383i −0.234716 0.722383i −0.997159 0.0753268i \(-0.976000\pi\)
0.762443 0.647056i \(-0.224000\pi\)
\(114\) −0.126219 + 0.222909i −0.126219 + 0.222909i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.221166 1.94719i 0.221166 1.94719i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.514115 0.856985i 0.514115 0.856985i
\(122\) 0 0
\(123\) −0.00989353 + 0.157253i −0.00989353 + 0.157253i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.470704 0.882291i \(-0.344000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(128\) 0.0627905 0.998027i 0.0627905 0.998027i
\(129\) −0.251511 + 0.0923388i −0.251511 + 0.0923388i
\(130\) 0 0
\(131\) −1.06861 + 0.0807242i −1.06861 + 0.0807242i −0.597905 0.801567i \(-0.704000\pi\)
−0.470704 + 0.882291i \(0.656000\pi\)
\(132\) 0.00430328 0.000990327i 0.00430328 0.000990327i
\(133\) 0 0
\(134\) −0.125694 1.10664i −0.125694 1.10664i
\(135\) 0 0
\(136\) 0.590139 0.183582i 0.590139 0.183582i
\(137\) 0.647036 1.14270i 0.647036 1.14270i −0.332820 0.942991i \(-0.608000\pi\)
0.979855 0.199710i \(-0.0640000\pi\)
\(138\) 0 0
\(139\) −1.11234 + 1.65909i −1.11234 + 1.65909i −0.514440 + 0.857527i \(0.672000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.0851391 + 0.965382i 0.0851391 + 0.965382i
\(145\) 0 0
\(146\) −1.78463 0.867338i −1.78463 0.867338i
\(147\) 0.00662226 0.175578i 0.00662226 0.175578i
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) 0.159908 + 0.0728068i 0.159908 + 0.0728068i
\(151\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(152\) 0.587412 + 1.33436i 0.587412 + 1.33436i
\(153\) −0.538703 + 0.261812i −0.538703 + 0.261812i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.214821 0.882571i −0.214821 0.882571i
\(163\) 0.414211 + 1.53301i 0.414211 + 1.53301i 0.793990 + 0.607930i \(0.208000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(164\) 0.683733 + 0.580258i 0.683733 + 0.580258i
\(165\) 0 0
\(166\) −0.426201 + 0.571376i −0.426201 + 0.571376i
\(167\) 0 0 0.998737 0.0502443i \(-0.0160000\pi\)
−0.998737 + 0.0502443i \(0.984000\pi\)
\(168\) 0 0
\(169\) −0.910106 + 0.414376i −0.910106 + 0.414376i
\(170\) 0 0
\(171\) −0.757085 1.19298i −0.757085 1.19298i
\(172\) −0.434622 + 1.46164i −0.434622 + 1.46164i
\(173\) 0 0 0.823533 0.567269i \(-0.192000\pi\)
−0.823533 + 0.567269i \(0.808000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.0191618 0.0162619i 0.0191618 0.0162619i
\(177\) −0.283563 0.195325i −0.283563 0.195325i
\(178\) −1.28218 + 1.03385i −1.28218 + 1.03385i
\(179\) −1.62199 0.595490i −1.62199 0.595490i −0.637424 0.770513i \(-0.720000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.0376902 0.999289i \(-0.512000\pi\)
0.0376902 + 0.999289i \(0.488000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.0136112 + 0.00748283i 0.0136112 + 0.00748283i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(192\) −0.149522 0.0922744i −0.149522 0.0922744i
\(193\) −0.385898 + 1.77884i −0.385898 + 1.77884i 0.212007 + 0.977268i \(0.432000\pi\)
−0.597905 + 0.801567i \(0.704000\pi\)
\(194\) 1.14204 + 1.61415i 1.14204 + 1.61415i
\(195\) 0 0
\(196\) −0.778462 0.627691i −0.778462 0.627691i
\(197\) 0 0 −0.285019 0.958522i \(-0.592000\pi\)
0.285019 + 0.958522i \(0.408000\pi\)
\(198\) −0.0159919 + 0.0183707i −0.0159919 + 0.0183707i
\(199\) 0 0 −0.888136 0.459580i \(-0.848000\pi\)
0.888136 + 0.459580i \(0.152000\pi\)
\(200\) 0.876307 0.481754i 0.876307 0.481754i
\(201\) −0.181947 0.0720378i −0.181947 0.0720378i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.0203477 0.106667i 0.0203477 0.106667i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.0139155 + 0.0338957i −0.0139155 + 0.0338957i
\(210\) 0 0
\(211\) 0.660390 0.0834267i 0.660390 0.0834267i 0.212007 0.977268i \(-0.432000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.888873 0.518167i 0.888873 0.518167i
\(215\) 0 0
\(216\) 0.318382 + 0.135408i 0.318382 + 0.135408i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.282051 + 0.204922i −0.282051 + 0.204922i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.994951 0.100362i \(-0.0320000\pi\)
−0.994951 + 0.100362i \(0.968000\pi\)
\(224\) 0 0
\(225\) −0.769479 + 0.589163i −0.769479 + 0.589163i
\(226\) −0.553694 + 0.519953i −0.553694 + 0.519953i
\(227\) 1.84973 + 0.575419i 1.84973 + 0.575419i 0.998737 + 0.0502443i \(0.0160000\pi\)
0.850994 + 0.525175i \(0.176000\pi\)
\(228\) 0.255435 + 0.0192959i 0.255435 + 0.0192959i
\(229\) 0 0 0.577573 0.816339i \(-0.304000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.157423 + 0.446033i 0.157423 + 0.446033i 0.994951 0.100362i \(-0.0320000\pi\)
−0.837528 + 0.546394i \(0.816000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.85604 + 0.628956i −1.85604 + 0.628956i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.675333 0.737513i \(-0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(240\) 0 0
\(241\) 0.587412 + 0.551617i 0.587412 + 0.551617i 0.920232 0.391374i \(-0.128000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(242\) −0.994323 0.100298i −0.994323 0.100298i
\(243\) −0.489694 0.125732i −0.489694 0.125732i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.146499 0.0580032i 0.146499 0.0580032i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.0533267 + 0.113325i 0.0533267 + 0.113325i
\(250\) 0 0
\(251\) −0.711536 + 0.702650i −0.711536 + 0.702650i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(257\) −0.374255 0.911622i −0.374255 0.911622i −0.992115 0.125333i \(-0.960000\pi\)
0.617860 0.786288i \(-0.288000\pi\)
\(258\) 0.190639 + 0.188258i 0.190639 + 0.188258i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.528033 + 0.932536i 0.528033 + 0.932536i
\(263\) 0 0 0.675333 0.737513i \(-0.264000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(264\) −0.000936174 0.00431539i −0.000936174 0.00431539i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.0542269 + 0.284267i 0.0542269 + 0.284267i
\(268\) −0.947796 + 0.584914i −0.947796 + 0.584914i
\(269\) 0 0 −0.332820 0.942991i \(-0.608000\pi\)
0.332820 + 0.942991i \(0.392000\pi\)
\(270\) 0 0
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) −0.417379 0.455808i −0.417379 0.455808i
\(273\) 0 0
\(274\) −1.30944 0.0989170i −1.30944 0.0989170i
\(275\) 0.0239977 + 0.00746527i 0.0239977 + 0.00746527i
\(276\) 0 0
\(277\) 0 0 0.793990 0.607930i \(-0.208000\pi\)
−0.793990 + 0.607930i \(0.792000\pi\)
\(278\) 1.97481 + 0.300072i 1.97481 + 0.300072i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.23212 1.27947i −1.23212 1.27947i −0.947098 0.320944i \(-0.896000\pi\)
−0.285019 0.958522i \(-0.592000\pi\)
\(282\) 0 0
\(283\) −0.651916 + 0.473645i −0.651916 + 0.473645i −0.863923 0.503623i \(-0.832000\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.837253 0.488076i 0.837253 0.488076i
\(289\) −0.277116 + 0.552424i −0.277116 + 0.552424i
\(290\) 0 0
\(291\) 0.344677 0.0435429i 0.344677 0.0435429i
\(292\) −0.0249339 + 1.98407i −0.0249339 + 1.98407i
\(293\) 0 0 0.379779 0.925077i \(-0.376000\pi\)
−0.379779 + 0.925077i \(0.624000\pi\)
\(294\) −0.161687 + 0.0687653i −0.161687 + 0.0687653i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.00309908 + 0.00812419i 0.00309908 + 0.00812419i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.00220788 0.175689i −0.00220788 0.175689i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.957261 1.09965i 0.957261 1.09965i
\(305\) 0 0
\(306\) 0.466263 + 0.375959i 0.466263 + 0.375959i
\(307\) −0.218130 0.363603i −0.218130 0.363603i 0.728969 0.684547i \(-0.240000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.356412 0.934329i \(-0.384000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(312\) 0 0
\(313\) 0.397989 + 0.533554i 0.397989 + 0.533554i 0.954865 0.297042i \(-0.0960000\pi\)
−0.556876 + 0.830596i \(0.688000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.617860 0.786288i \(-0.288000\pi\)
−0.617860 + 0.786288i \(0.712000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.00681350 0.180648i −0.00681350 0.180648i
\(322\) 0 0
\(323\) 0.845851 + 0.310542i 0.845851 + 0.310542i
\(324\) −0.707108 + 0.570157i −0.707108 + 0.570157i
\(325\) 0 0
\(326\) 1.21074 1.02751i 1.21074 1.02751i
\(327\) 0 0
\(328\) 0.233914 0.865722i 0.233914 0.865722i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.975318 1.53686i −0.975318 1.53686i −0.837528 0.546394i \(-0.816000\pi\)
−0.137790 0.990461i \(-0.544000\pi\)
\(332\) 0.698464 + 0.142358i 0.698464 + 0.142358i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.41296 + 1.26156i 1.41296 + 1.26156i 0.920232 + 0.391374i \(0.128000\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(338\) 0.762443 + 0.647056i 0.762443 + 0.647056i
\(339\) 0.0348109 + 0.128836i 0.0348109 + 0.128836i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.757085 + 1.19298i −0.757085 + 1.19298i
\(343\) 0 0
\(344\) 1.50758 0.229077i 1.50758 0.229077i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.13122 0.737996i 1.13122 0.737996i 0.162637 0.986686i \(-0.448000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(348\) 0 0
\(349\) 0 0 0.899405 0.437116i \(-0.144000\pi\)
−0.899405 + 0.437116i \(0.856000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.0228729 0.0104141i −0.0228729 0.0104141i
\(353\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(354\) −0.0560002 + 0.339741i −0.0560002 + 0.339741i
\(355\) 0 0
\(356\) 1.48138 + 0.719958i 1.48138 + 0.719958i
\(357\) 0 0
\(358\) 0.151793 + 1.72117i 0.151793 + 1.72117i
\(359\) 0 0 0.745941 0.666012i \(-0.232000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(360\) 0 0
\(361\) −0.266199 + 1.09365i −0.266199 + 1.09365i
\(362\) 0 0
\(363\) −0.0977826 + 0.145846i −0.0977826 + 0.145846i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.974527 0.224271i \(-0.0720000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(368\) 0 0
\(369\) −0.0980815 + 0.863530i −0.0980815 + 0.863530i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.938734 0.344643i \(-0.112000\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(374\) 0.000975292 0.0155018i 0.000975292 0.0155018i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.00473317 + 0.0752316i −0.00473317 + 0.0752316i −0.999684 0.0251301i \(-0.992000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.974527 0.224271i \(-0.928000\pi\)
0.974527 + 0.224271i \(0.0720000\pi\)
\(384\) −0.0198291 + 0.174580i −0.0198291 + 0.174580i
\(385\) 0 0
\(386\) 1.77385 0.408220i 1.77385 0.408220i
\(387\) −1.41111 + 0.438971i −1.41111 + 0.438971i
\(388\) 0.974271 1.72062i 0.974271 1.72062i
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.236499 + 0.971632i −0.236499 + 0.971632i
\(393\) 0.188233 0.00473180i 0.188233 0.00473180i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.0234314 + 0.00664808i 0.0234314 + 0.00664808i
\(397\) 0 0 −0.899405 0.437116i \(-0.856000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 0.587785i −0.809017 0.587785i
\(401\) −1.26260 0.574866i −1.26260 0.574866i −0.332820 0.942991i \(-0.608000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(402\) 0.0122874 + 0.195303i 0.0122874 + 0.195303i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.105178 + 0.0270052i −0.105178 + 0.0270052i
\(409\) −1.53926 + 0.233890i −1.53926 + 0.233890i −0.863923 0.503623i \(-0.832000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(410\) 0 0
\(411\) −0.123630 + 0.194810i −0.123630 + 0.194810i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.209841 0.281319i 0.209841 0.281319i
\(418\) 0.0365947 0.00184100i 0.0365947 0.00184100i
\(419\) 0.732851 + 1.37366i 0.732851 + 1.37366i 0.920232 + 0.391374i \(0.128000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.979855 0.199710i \(-0.936000\pi\)
0.979855 + 0.199710i \(0.0640000\pi\)
\(422\) −0.356667 0.562018i −0.356667 0.562018i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.161209 0.596639i 0.161209 0.596639i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.847315 0.583651i −0.847315 0.583651i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.402906 0.915241i \(-0.368000\pi\)
−0.402906 + 0.915241i \(0.632000\pi\)
\(432\) −0.0130401 0.345735i −0.0130401 0.345735i
\(433\) −0.124591 0.0157395i −0.124591 0.0157395i 0.0627905 0.998027i \(-0.480000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.305510 + 0.167956i 0.305510 + 0.167956i
\(439\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(440\) 0 0
\(441\) 0.0851391 0.965382i 0.0851391 0.965382i
\(442\) 0 0
\(443\) −1.37694 0.849750i −1.37694 0.849750i −0.379779 0.925077i \(-0.624000\pi\)
−0.997159 + 0.0753268i \(0.976000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.09982 + 1.26341i −1.09982 + 1.26341i −0.137790 + 0.990461i \(0.544000\pi\)
−0.962028 + 0.272952i \(0.912000\pi\)
\(450\) 0.860718 + 0.445392i 0.860718 + 0.445392i
\(451\) 0.0197499 0.0108576i 0.0197499 0.0108576i
\(452\) 0.706219 + 0.279612i 0.706219 + 0.279612i
\(453\) 0 0
\(454\) −0.266923 1.91869i −0.266923 1.91869i
\(455\) 0 0
\(456\) −0.0912996 0.239341i −0.0912996 0.239341i
\(457\) 0.819223 0.232435i 0.819223 0.232435i 0.162637 0.986686i \(-0.448000\pi\)
0.656586 + 0.754251i \(0.272000\pi\)
\(458\) 0 0
\(459\) 0.196771 0.0836866i 0.196771 0.0836866i
\(460\) 0 0
\(461\) 0 0 0.0125660 0.999921i \(-0.496000\pi\)
−0.0125660 + 0.999921i \(0.504000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.162637 0.986686i \(-0.552000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.336555 0.332352i 0.336555 0.332352i
\(467\) −0.866313 0.368442i −0.866313 0.368442i −0.0878512 0.996134i \(-0.528000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.35936 + 1.41160i 1.35936 + 1.41160i
\(473\) 0.0304285 + 0.0232980i 0.0304285 + 0.0232980i
\(474\) 0 0
\(475\) 1.44139 + 0.219019i 1.44139 + 0.219019i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.997159 0.0753268i \(-0.976000\pi\)
0.997159 + 0.0753268i \(0.0240000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.249010 0.766374i 0.249010 0.766374i
\(483\) 0 0
\(484\) 0.332609 + 0.942395i 0.332609 + 0.942395i
\(485\) 0 0
\(486\) 0.0947359 + 0.496623i 0.0947359 + 0.496623i
\(487\) 0 0 0.947098 0.320944i \(-0.104000\pi\)
−0.947098 + 0.320944i \(0.896000\pi\)
\(488\) 0 0
\(489\) −0.0591525 0.272670i −0.0591525 0.272670i
\(490\) 0 0
\(491\) −0.701186 1.23833i −0.701186 1.23833i −0.962028 0.272952i \(-0.912000\pi\)
0.260842 0.965382i \(-0.416000\pi\)
\(492\) −0.114859 0.107860i −0.114859 0.107860i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0798341 0.0965028i 0.0798341 0.0965028i
\(499\) −1.92163 0.0966728i −1.92163 0.0966728i −0.947098 0.320944i \(-0.896000\pi\)
−0.974527 + 0.224271i \(0.928000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.938734 + 0.344643i 0.938734 + 0.344643i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.163364 0.0646804i 0.163364 0.0646804i
\(508\) 0 0
\(509\) 0 0 −0.711536 0.702650i \(-0.752000\pi\)
0.711536 + 0.702650i \(0.248000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(513\) 0.248541 + 0.438936i 0.248541 + 0.438936i
\(514\) −0.665510 + 0.726786i −0.665510 + 0.726786i
\(515\) 0 0
\(516\) 0.0891710 0.252652i 0.0891710 0.252652i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.06757 1.35859i −1.06757 1.35859i −0.929776 0.368125i \(-0.880000\pi\)
−0.137790 0.990461i \(-0.544000\pi\)
\(522\) 0 0
\(523\) −1.21480 1.32665i −1.21480 1.32665i −0.929776 0.368125i \(-0.880000\pi\)
−0.285019 0.958522i \(-0.592000\pi\)
\(524\) 0.618958 0.874833i 0.618958 0.874833i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.00350608 + 0.00268448i −0.00350608 + 0.00268448i
\(529\) 0.988652 + 0.150226i 0.988652 + 0.150226i
\(530\) 0 0
\(531\) −1.50796 1.15459i −1.50796 1.15459i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.234124 0.170101i 0.234124 0.170101i
\(535\) 0 0
\(536\) 0.932798 + 0.608547i 0.932798 + 0.608547i
\(537\) 0.279370 + 0.118816i 0.279370 + 0.118816i
\(538\) 0 0
\(539\) −0.0217122 + 0.0126571i −0.0217122 + 0.0126571i
\(540\) 0 0
\(541\) 0 0 −0.162637 0.986686i \(-0.552000\pi\)
0.162637 + 0.986686i \(0.448000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.234716 + 0.571729i −0.234716 + 0.571729i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.85099 0.525175i 1.85099 0.525175i 0.850994 0.525175i \(-0.176000\pi\)
1.00000 \(0\)
\(548\) 0.468030 + 1.22693i 0.468030 + 1.22693i
\(549\) 0 0
\(550\) −0.00346296 0.0248924i −0.00346296 0.0248924i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.569319 1.91462i −0.569319 1.91462i
\(557\) 0 0 −0.778462 0.627691i \(-0.784000\pi\)
0.778462 + 0.627691i \(0.216000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.00232244 0.00143325i −0.00232244 0.00143325i
\(562\) −0.633085 + 1.65962i −0.633085 + 1.65962i
\(563\) −0.170182 + 1.92968i −0.170182 + 1.92968i 0.162637 + 0.986686i \(0.448000\pi\)
−0.332820 + 0.942991i \(0.608000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.706139 + 0.388203i 0.706139 + 0.388203i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.933322 0.316275i −0.933322 0.316275i −0.187381 0.982287i \(-0.560000\pi\)
−0.745941 + 0.666012i \(0.768000\pi\)
\(570\) 0 0
\(571\) −1.14604 0.144778i −1.14604 0.144778i −0.470704 0.882291i \(-0.656000\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.798109 0.549757i −0.798109 0.549757i
\(577\) −0.0574732 + 0.0487753i −0.0574732 + 0.0487753i −0.675333 0.737513i \(-0.736000\pi\)
0.617860 + 0.786288i \(0.288000\pi\)
\(578\) 0.617839 + 0.0155313i 0.617839 + 0.0155313i
\(579\) 0.0834212 0.308744i 0.0834212 0.308744i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.186155 0.293334i −0.186155 0.293334i
\(583\) 0 0
\(584\) 1.80586 0.822216i 1.80586 0.822216i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.340829 0.456924i 0.340829 0.456924i −0.597905 0.801567i \(-0.704000\pi\)
0.938734 + 0.344643i \(0.112000\pi\)
\(588\) 0.131064 + 0.117020i 0.131064 + 0.117020i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.551301 + 0.868711i −0.551301 + 0.868711i −0.999684 0.0251301i \(-0.992000\pi\)
0.448383 + 0.893841i \(0.352000\pi\)
\(594\) 0.00603146 0.00626324i 0.00603146 0.00626324i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.984564 0.175023i \(-0.0560000\pi\)
−0.984564 + 0.175023i \(0.944000\pi\)
\(600\) −0.158028 + 0.0768023i −0.158028 + 0.0768023i
\(601\) 0.706139 + 1.60406i 0.706139 + 1.60406i 0.793990 + 0.607930i \(0.208000\pi\)
−0.0878512 + 0.996134i \(0.528000\pi\)
\(602\) 0 0
\(603\) −0.982339 0.447264i −0.982339 0.447264i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.899405 0.437116i \(-0.856000\pi\)
0.899405 + 0.437116i \(0.144000\pi\)
\(608\) −1.40258 0.397947i −1.40258 0.397947i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.141652 0.581963i 0.141652 0.581963i
\(613\) 0 0 0.888136 0.459580i \(-0.152000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(614\) −0.236123 + 0.352184i −0.236123 + 0.352184i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.215525 0.0670461i 0.215525 0.0670461i −0.187381 0.982287i \(-0.560000\pi\)
0.402906 + 0.915241i \(0.368000\pi\)
\(618\) 0 0
\(619\) −0.0533808 0.469976i −0.0533808 0.469976i −0.992115 0.125333i \(-0.960000\pi\)
0.938734 0.344643i \(-0.112000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.0627905 0.998027i 0.0627905 0.998027i
\(626\) 0.313319 0.587288i 0.313319 0.587288i
\(627\) 0.00274113 0.00582520i 0.00274113 0.00582520i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.938734 0.344643i \(-0.112000\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(632\) 0 0
\(633\) −0.116622 + 0.00880980i −0.116622 + 0.00880980i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.03554 1.54454i 1.03554 1.54454i 0.212007 0.977268i \(-0.432000\pi\)
0.823533 0.567269i \(-0.192000\pi\)
\(642\) −0.160554 + 0.0830812i −0.160554 + 0.0830812i
\(643\) 0.0651745 0.267763i 0.0651745 0.267763i −0.929776 0.368125i \(-0.880000\pi\)
0.994951 + 0.100362i \(0.0320000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.0791587 0.897571i −0.0791587 0.897571i
\(647\) 0 0 −0.962028 0.272952i \(-0.912000\pi\)
0.962028 + 0.272952i \(0.0880000\pi\)
\(648\) 0.816965 + 0.397049i 0.816965 + 0.397049i
\(649\) −0.00185630 + 0.0492166i −0.00185630 + 0.0492166i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.44523 0.658020i −1.44523 0.658020i
\(653\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.882924 + 0.156955i −0.882924 + 0.156955i
\(657\) −1.61054 + 1.05070i −1.61054 + 1.05070i
\(658\) 0 0
\(659\) 1.03799 0.266509i 1.03799 0.266509i 0.309017 0.951057i \(-0.400000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(660\) 0 0
\(661\) 0 0 0.693653 0.720309i \(-0.256000\pi\)
−0.693653 + 0.720309i \(0.744000\pi\)
\(662\) −0.975318 + 1.53686i −0.975318 + 1.53686i
\(663\) 0 0
\(664\) −0.168582 0.692602i −0.168582 0.692602i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.07132 1.68812i −1.07132 1.68812i −0.556876 0.830596i \(-0.688000\pi\)
−0.514440 0.857527i \(-0.672000\pi\)
\(674\) 0.539883 1.81563i 0.539883 1.81563i
\(675\) 0.284926 0.196264i 0.284926 0.196264i
\(676\) 0.260842 0.965382i 0.260842 0.965382i
\(677\) 0 0 −0.999684 0.0251301i \(-0.992000\pi\)
0.999684 + 0.0251301i \(0.00800000\pi\)
\(678\) 0.101753 0.0863536i 0.101753 0.0863536i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.319512 0.117304i −0.319512 0.117304i
\(682\) 0 0
\(683\) 0.0450703 + 1.19496i 0.0450703 + 1.19496i 0.823533 + 0.567269i \(0.192000\pi\)
−0.778462 + 0.627691i \(0.784000\pi\)
\(684\) 1.40179 + 0.177087i 1.40179 + 0.177087i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.849171 1.26656i −0.849171 1.26656i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.194483 0.260729i −0.194483 0.260729i 0.693653 0.720309i \(-0.256000\pi\)
−0.888136 + 0.459580i \(0.848000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.14941 0.709335i −1.14941 0.709335i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.285119 0.475269i −0.285119 0.475269i
\(698\) 0 0
\(699\) −0.0236871 0.0796598i −0.0236871 0.0796598i
\(700\) 0 0
\(701\) 0 0 −0.888136 0.459580i \(-0.848000\pi\)
0.888136 + 0.459580i \(0.152000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.000315811 0.0251301i 0.000315811 0.0251301i
\(705\) 0 0
\(706\) 0.238883 1.25227i 0.238883 1.25227i
\(707\) 0 0
\(708\) 0.331251 0.0939844i 0.331251 0.0939844i
\(709\) 0 0 −0.984564 0.175023i \(-0.944000\pi\)
0.984564 + 0.175023i \(0.0560000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.0206971 1.64694i 0.0206971 1.64694i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.49273 0.870184i 1.49273 0.870184i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.837528 0.546394i \(-0.816000\pi\)
0.837528 + 0.546394i \(0.184000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.10291 0.224790i 1.10291 0.224790i
\(723\) −0.0982097 0.101984i −0.0982097 0.101984i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.173599 + 0.0263783i 0.173599 + 0.0263783i
\(727\) 0 0 0.793990 0.607930i \(-0.208000\pi\)
−0.793990 + 0.607930i \(0.792000\pi\)
\(728\) 0 0
\(729\) −0.782519 0.243428i −0.782519 0.243428i
\(730\) 0 0
\(731\) 0.544322 0.769343i 0.544322 0.769343i
\(732\) 0 0
\(733\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.00524497 + 0.0274951i 0.00524497 + 0.0274951i
\(738\) 0.823106 0.278926i 0.823106 0.278926i
\(739\) 0.397989 1.12764i 0.397989 1.12764i −0.556876 0.830596i \(-0.688000\pi\)
0.954865 0.297042i \(-0.0960000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.262358 + 0.639060i 0.262358 + 0.639060i
\(748\) −0.0144417 + 0.00571789i −0.0144417 + 0.00571789i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(752\) 0 0
\(753\) 0.131064 0.117020i 0.131064 0.117020i
\(754\) 0 0