Properties

Label 2004.1.g.e.2003.6
Level 2004
Weight 1
Character 2004.2003
Analytic conductor 1.000
Analytic rank 0
Dimension 10
Projective image \(D_{22}\)
CM discriminant -167
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2004.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00012628532\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
Defining polynomial: \(x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{22}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{22} + \cdots)\)

Embedding invariants

Embedding label 2003.6
Root \(0.959493 + 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 2004.2003
Dual form 2004.1.g.e.2003.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.142315 + 0.989821i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{6} +1.51150i q^{7} +(0.415415 - 0.909632i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.142315 + 0.989821i) q^{2} +(0.841254 + 0.540641i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{6} +1.51150i q^{7} +(0.415415 - 0.909632i) q^{8} +(0.415415 + 0.909632i) q^{9} +1.91899 q^{11} +(-0.654861 - 0.755750i) q^{12} +(-1.49611 - 0.215109i) q^{14} +(0.841254 + 0.540641i) q^{16} +(-0.959493 + 0.281733i) q^{18} -1.81926i q^{19} +(-0.817178 + 1.27155i) q^{21} +(-0.273100 + 1.89945i) q^{22} +(0.841254 - 0.540641i) q^{24} -1.00000 q^{25} +(-0.142315 + 0.989821i) q^{27} +(0.425839 - 1.45027i) q^{28} +1.51150i q^{29} -1.97964i q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.61435 + 1.03748i) q^{33} +(-0.142315 - 0.989821i) q^{36} +(1.80075 + 0.258908i) q^{38} +(-1.14231 - 0.989821i) q^{42} +(-1.84125 - 0.540641i) q^{44} -0.830830 q^{47} +(0.415415 + 0.909632i) q^{48} -1.28463 q^{49} +(0.142315 - 0.989821i) q^{50} +(-0.959493 - 0.281733i) q^{54} +(1.37491 + 0.627899i) q^{56} +(0.983568 - 1.53046i) q^{57} +(-1.49611 - 0.215109i) q^{58} -1.68251 q^{61} +(1.95949 + 0.281733i) q^{62} +(-1.37491 + 0.627899i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.25667 + 1.45027i) q^{66} +1.00000 q^{72} +(-0.841254 - 0.540641i) q^{75} +(-0.512546 + 1.74557i) q^{76} +2.90055i q^{77} +(-0.654861 + 0.755750i) q^{81} +(1.14231 - 0.989821i) q^{84} +(-0.817178 + 1.27155i) q^{87} +(0.797176 - 1.74557i) q^{88} -1.08128i q^{89} +(1.07028 - 1.66538i) q^{93} +(0.118239 - 0.822373i) q^{94} +(-0.959493 + 0.281733i) q^{96} -1.91899 q^{97} +(0.182822 - 1.27155i) q^{98} +(0.797176 + 1.74557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{3} - q^{4} - q^{6} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{3} - q^{4} - q^{6} - q^{8} - q^{9} + 2q^{11} - q^{12} - q^{16} - q^{18} + 2q^{22} - q^{24} - 10q^{25} - q^{27} - q^{32} + 2q^{33} - q^{36} - 11q^{42} - 9q^{44} + 2q^{47} - q^{48} - 12q^{49} + q^{50} - q^{54} + 2q^{61} + 11q^{62} - q^{64} + 2q^{66} + 10q^{72} + q^{75} - q^{81} + 11q^{84} + 2q^{88} + 2q^{94} - q^{96} - 2q^{97} + 10q^{98} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2004\mathbb{Z}\right)^\times\).

\(n\) \(673\) \(1003\) \(1337\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(3\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(7\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(10\) 0 0
\(11\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(12\) −0.654861 0.755750i −0.654861 0.755750i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −1.49611 0.215109i −1.49611 0.215109i
\(15\) 0 0
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(19\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(20\) 0 0
\(21\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(22\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0.841254 0.540641i 0.841254 0.540641i
\(25\) −1.00000 −1.00000
\(26\) 0 0
\(27\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(28\) 0.425839 1.45027i 0.425839 1.45027i
\(29\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(30\) 0 0
\(31\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(32\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(33\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.142315 0.989821i −0.142315 0.989821i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −1.14231 0.989821i −1.14231 0.989821i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −1.84125 0.540641i −1.84125 0.540641i
\(45\) 0 0
\(46\) 0 0
\(47\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(48\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(49\) −1.28463 −1.28463
\(50\) 0.142315 0.989821i 0.142315 0.989821i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −0.959493 0.281733i −0.959493 0.281733i
\(55\) 0 0
\(56\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(57\) 0.983568 1.53046i 0.983568 1.53046i
\(58\) −1.49611 0.215109i −1.49611 0.215109i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(62\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(63\) −1.37491 + 0.627899i −1.37491 + 0.627899i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.00000 1.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −0.841254 0.540641i −0.841254 0.540641i
\(76\) −0.512546 + 1.74557i −0.512546 + 1.74557i
\(77\) 2.90055i 2.90055i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 1.14231 0.989821i 1.14231 0.989821i
\(85\) 0 0
\(86\) 0 0
\(87\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(88\) 0.797176 1.74557i 0.797176 1.74557i
\(89\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.07028 1.66538i 1.07028 1.66538i
\(94\) 0.118239 0.822373i 0.118239 0.822373i
\(95\) 0 0
\(96\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(97\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(98\) 0.182822 1.27155i 0.182822 1.27155i
\(99\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(100\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(108\) 0.415415 0.909632i 0.415415 0.909632i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(115\) 0 0
\(116\) 0.425839 1.45027i 0.425839 1.45027i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.68251 2.68251
\(122\) 0.239446 1.66538i 0.239446 1.66538i
\(123\) 0 0
\(124\) −0.557730 + 1.89945i −0.557730 + 1.89945i
\(125\) 0 0
\(126\) −0.425839 1.45027i −0.425839 1.45027i
\(127\) 0.563465i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(128\) 0.841254 0.540641i 0.841254 0.540641i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −1.25667 1.45027i −1.25667 1.45027i
\(133\) 2.74982 2.74982
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.563465i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.698939 0.449181i −0.698939 0.449181i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(145\) 0 0
\(146\) 0 0
\(147\) −1.08070 0.694523i −1.08070 0.694523i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0.654861 0.755750i 0.654861 0.755750i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −1.65486 0.755750i −1.65486 0.755750i
\(153\) 0 0
\(154\) −2.87102 0.412791i −2.87102 0.412791i
\(155\) 0 0
\(156\) 0 0
\(157\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.654861 0.755750i −0.654861 0.755750i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 1.00000
\(168\) 0.817178 + 1.27155i 0.817178 + 1.27155i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 1.65486 0.755750i 1.65486 0.755750i
\(172\) 0 0
\(173\) 0.563465i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(174\) −1.14231 0.989821i −1.14231 0.989821i
\(175\) 1.51150i 1.51150i
\(176\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(177\) 0 0
\(178\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(179\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(182\) 0 0
\(183\) −1.41542 0.909632i −1.41542 0.909632i
\(184\) 0 0
\(185\) 0 0
\(186\) 1.49611 + 1.29639i 1.49611 + 1.29639i
\(187\) 0 0
\(188\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(189\) −1.49611 0.215109i −1.49611 0.215109i
\(190\) 0 0
\(191\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(192\) −0.142315 0.989821i −0.142315 0.989821i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0.273100 1.89945i 0.273100 1.89945i
\(195\) 0 0
\(196\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(199\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(200\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(201\) 0 0
\(202\) 0 0
\(203\) −2.28463 −2.28463
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.49114i 3.49114i
\(210\) 0 0
\(211\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(215\) 0 0
\(216\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(217\) 2.99223 2.99223
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(224\) −1.14231 0.989821i −1.14231 0.989821i
\(225\) −0.415415 0.909632i −0.415415 0.909632i
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −1.37491 + 1.19136i −1.37491 + 1.19136i
\(229\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(230\) 0 0
\(231\) −1.56815 + 2.44009i −1.56815 + 2.44009i
\(232\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(233\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.381761 + 2.65520i −0.381761 + 2.65520i
\(243\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(244\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −1.80075 0.822373i −1.80075 0.822373i
\(249\) 0 0
\(250\) 0 0
\(251\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(252\) 1.49611 0.215109i 1.49611 0.215109i
\(253\) 0 0
\(254\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(255\) 0 0
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.37491 + 0.627899i −1.37491 + 0.627899i
\(262\) 0 0
\(263\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) 1.61435 1.03748i 1.61435 1.03748i
\(265\) 0 0
\(266\) −0.391340 + 2.72183i −0.391340 + 2.72183i
\(267\) 0.584585 0.909632i 0.584585 0.909632i
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(275\) −1.91899 −1.91899
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 1.80075 0.822373i 1.80075 0.822373i
\(280\) 0 0
\(281\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(282\) 0.544078 0.627899i 0.544078 0.627899i
\(283\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.959493 0.281733i −0.959493 0.281733i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) −1.61435 1.03748i −1.61435 1.03748i
\(292\) 0 0
\(293\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) 0.841254 0.970858i 0.841254 0.970858i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.983568 1.53046i 0.983568 1.53046i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0.817178 2.78305i 0.817178 2.78305i
\(309\) 0 0
\(310\) 0 0
\(311\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0.0405070 0.281733i 0.0405070 0.281733i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(318\) 0 0
\(319\) 2.90055i 2.90055i
\(320\) 0 0
\(321\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.841254 0.540641i 0.841254 0.540641i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.25580i 1.25580i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(335\) 0 0
\(336\) −1.37491 + 0.627899i −1.37491 + 0.627899i
\(337\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(338\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(339\) 0 0
\(340\) 0 0
\(341\) 3.79891i 3.79891i
\(342\) 0.512546 + 1.74557i 0.512546 + 1.74557i
\(343\) 0.430218i 0.430218i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 1.14231 0.989821i 1.14231 0.989821i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(351\) 0 0
\(352\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(353\) 1.51150i 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.304632 + 1.03748i −0.304632 + 1.03748i
\(357\) 0 0
\(358\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(359\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(360\) 0 0
\(361\) −2.30972 −2.30972
\(362\) 0.118239 0.822373i 0.118239 0.822373i
\(363\) 2.25667 + 1.45027i 2.25667 + 1.45027i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.10181 1.27155i 1.10181 1.27155i
\(367\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.49611 + 1.29639i −1.49611 + 1.29639i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(377\) 0 0
\(378\) 0.425839 1.45027i 0.425839 1.45027i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0.304632 0.474017i 0.304632 0.474017i
\(382\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(383\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.533654 + 1.16854i −0.533654 + 1.16854i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.273100 1.89945i −0.273100 1.89945i
\(397\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(398\) −0.557730 0.0801894i −0.557730 0.0801894i
\(399\) 2.31329 + 1.48666i 2.31329 + 1.48666i
\(400\) −0.841254 0.540641i −0.841254 0.540641i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.325137 2.26138i 0.325137 2.26138i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(410\) 0 0
\(411\) 0.304632 0.474017i 0.304632 0.474017i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 3.45561 + 0.496841i 3.45561 + 0.496841i
\(419\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(420\) 0 0
\(421\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(422\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(423\) −0.345139 0.755750i −0.345139 0.755750i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.54311i 2.54311i
\(428\) −1.25667 0.368991i −1.25667 0.368991i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(432\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(433\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(434\) −0.425839 + 2.96177i −0.425839 + 2.96177i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −0.533654 1.16854i −0.533654 1.16854i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(447\) 0 0
\(448\) 1.14231 0.989821i 1.14231 0.989821i
\(449\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(450\) 0.959493 0.281733i 0.959493 0.281733i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) −0.983568 1.53046i −0.983568 1.53046i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(462\) −2.19209 1.89945i −2.19209 1.89945i
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(465\) 0 0
\(466\) −1.95949 0.281733i −1.95949 0.281733i
\(467\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.239446 0.153882i −0.239446 0.153882i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.81926i 1.81926i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.239446 1.66538i 0.239446 1.66538i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −2.57385 0.755750i −2.57385 0.755750i
\(485\) 0 0
\(486\) −0.142315 0.989821i −0.142315 0.989821i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(489\) 0 0
\(490\) 0 0
\(491\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.07028 1.66538i 1.07028 1.66538i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(502\) 0.186393 1.29639i 0.186393 1.29639i
\(503\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) 1.51150i 1.51150i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(508\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(509\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.59435 −1.59435
\(518\) 0 0
\(519\) 0.304632 0.474017i 0.304632 0.474017i
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −0.425839 1.45027i −0.425839 1.45027i
\(523\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(524\) 0 0
\(525\) 0.817178 1.27155i 0.817178 1.27155i
\(526\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(527\) 0 0
\(528\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −2.63843 0.774713i −2.63843 0.774713i
\(533\) 0 0
\(534\) 0.817178 + 0.708089i 0.817178 + 0.708089i
\(535\) 0 0
\(536\) 0 0
\(537\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(538\) 0 0
\(539\) −2.46519 −2.46519
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −0.698939 0.449181i −0.698939 0.449181i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(549\) −0.698939 1.53046i −0.698939 1.53046i
\(550\) 0.273100 1.89945i 0.273100 1.89945i
\(551\) 2.74982 2.74982
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(558\) 0.557730 + 1.89945i 0.557730 + 1.89945i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(563\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(564\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(565\) 0 0
\(566\) −0.557730 0.0801894i −0.557730 0.0801894i
\(567\) −1.14231 0.989821i −1.14231 0.989821i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.415415 0.909632i 0.415415 0.909632i
\(577\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(578\) 0.142315 0.989821i 0.142315 0.989821i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 1.25667 1.45027i 1.25667 1.45027i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −1.95949 0.281733i −1.95949 0.281733i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.841254 + 0.970858i 0.841254 + 0.970858i
\(589\) −3.60149 −3.60149
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −1.84125 0.540641i −1.84125 0.540641i
\(595\) 0 0
\(596\) 0 0
\(597\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(598\) 0 0
\(599\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(600\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(601\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(609\) −1.92195 1.23516i −1.92195 1.23516i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 2.63843 + 1.20493i 2.63843 + 1.20493i
\(617\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −0.284630 + 1.97964i −0.284630 + 1.97964i
\(623\) 1.63436 1.63436
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 1.88745 2.93694i 1.88745 2.93694i
\(628\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(632\) 0 0
\(633\) 1.07028 1.66538i 1.07028 1.66538i
\(634\) −1.07028 0.153882i −1.07028 0.153882i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −2.87102 0.412791i −2.87102 0.412791i
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(649\) 0 0
\(650\) 0 0
\(651\) 2.51722 + 1.61772i 2.51722 + 1.61772i
\(652\) 0 0
\(653\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 1.24302 + 0.178719i 1.24302 + 0.178719i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.959493 0.281733i −0.959493 0.281733i
\(669\) 0.584585 0.909632i 0.584585 0.909632i
\(670\) 0 0
\(671\) −3.22871 −3.22871
\(672\) −0.425839 1.45027i −0.425839 1.45027i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(675\) 0.142315 0.989821i 0.142315 0.989821i
\(676\) −0.959493 0.281733i −0.959493 0.281733i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 2.90055i 2.90055i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.76024 + 0.540641i 3.76024 + 0.540641i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −1.80075 + 0.258908i −1.80075 + 0.258908i
\(685\) 0 0
\(686\) 0.425839 + 0.0612263i 0.425839 + 0.0612263i
\(687\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(693\) −2.63843 + 1.20493i −2.63843 + 1.20493i
\(694\) 0 0
\(695\) 0 0
\(696\) 0.817178 + 1.27155i 0.817178 + 1.27155i
\(697\) 0 0
\(698\) 0 0
\(699\) −1.07028 + 1.66538i −1.07028 + 1.66538i
\(700\) −0.425839 + 1.45027i −0.425839 + 1.45027i
\(701\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.25667 1.45027i −1.25667 1.45027i
\(705\) 0 0
\(706\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.983568 0.449181i −0.983568 0.449181i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.797176 0.234072i −0.797176 0.234072i
\(717\) −1.41542 0.909632i −1.41542 0.909632i
\(718\) 0.0405070 0.281733i 0.0405070 0.281733i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.328708 2.28621i 0.328708 2.28621i
\(723\) 0 0
\(724\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(725\) 1.51150i 1.51150i
\(726\) −1.75667 + 2.02730i −1.75667 + 2.02730i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.959493 0.281733i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(733\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(734\) −1.80075 0.258908i −1.80075 0.258908i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(744\) −1.07028 1.66538i −1.07028 1.66538i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.97964i 1.97964i
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) −0.698939 0.449181i −0.698939 0.449181i
\(753\) −1.10181 0.708089i −1.10181 0.708089i
\(754\) 0 0
\(755\) 0 0
\(756\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(757\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(762\) 0.425839 + 0.368991i 0.425839 + 0.368991i
\(763\) 0 0
\(764\) −0.273100 0.0801894i −0.273100 0.0801894i
\(765\) 0 0
\(766\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(767\) 0 0
\(768\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 1.97964i 1.97964i
\(776\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.49611 0.215109i −1.49611 0.215109i
\(784\) −1.08070 0.694523i −1.08070 0.694523i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(790\) 0 0
\(791\) 0 0
\(792\) 1.91899 1.91899
\(793\) 0 0
\(794\) 0.239446 1.66538i 0.239446 1.66538i
\(795\) 0 0
\(796\) 0.158746 0.540641i 0.158746 0.540641i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) −1.80075 + 2.07817i −1.80075 + 2.07817i
\(799\) 0 0
\(800\) 0.654861 0.755750i 0.654861 0.755750i
\(801\) 0.983568 0.449181i 0.983568 0.449181i
\(802\)