Properties

Label 2004.1.g.e.2003.7
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 2003.7
Root \(0.654861 + 0.755750i\) of defining polynomial
Character \(\chi\) \(=\) 2004.2003
Dual form 2004.1.g.e.2003.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.415415 - 0.909632i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{6} +1.08128i q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(q+(0.415415 - 0.909632i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{6} +1.08128i q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.959493 - 0.281733i) q^{9} +1.30972 q^{11} +(0.841254 - 0.540641i) q^{12} +(0.983568 + 0.449181i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-0.654861 + 0.755750i) q^{18} +0.563465i q^{19} +(-1.07028 - 0.153882i) q^{21} +(0.544078 - 1.19136i) q^{22} +(-0.142315 - 0.989821i) q^{24} -1.00000 q^{25} +(0.415415 - 0.909632i) q^{27} +(0.817178 - 0.708089i) q^{28} +1.08128i q^{29} +1.81926i q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.186393 + 1.29639i) q^{33} +(0.415415 + 0.909632i) q^{36} +(0.512546 + 0.234072i) q^{38} +(-0.584585 + 0.909632i) q^{42} +(-0.857685 - 0.989821i) q^{44} +1.91899 q^{47} +(-0.959493 - 0.281733i) q^{48} -0.169170 q^{49} +(-0.415415 + 0.909632i) q^{50} +(-0.654861 - 0.755750i) q^{54} +(-0.304632 - 1.03748i) q^{56} +(-0.557730 - 0.0801894i) q^{57} +(0.983568 + 0.449181i) q^{58} +0.284630 q^{61} +(1.65486 + 0.755750i) q^{62} +(0.304632 - 1.03748i) q^{63} +(0.841254 - 0.540641i) q^{64} +(1.10181 + 0.708089i) q^{66} +1.00000 q^{72} +(0.142315 - 0.989821i) q^{75} +(0.425839 - 0.368991i) q^{76} +1.41618i q^{77} +(0.841254 + 0.540641i) q^{81} +(0.584585 + 0.909632i) q^{84} +(-1.07028 - 0.153882i) q^{87} +(-1.25667 + 0.368991i) q^{88} -1.97964i q^{89} +(-1.80075 - 0.258908i) q^{93} +(0.797176 - 1.74557i) q^{94} +(-0.654861 + 0.755750i) q^{96} -1.30972 q^{97} +(-0.0702757 + 0.153882i) q^{98} +(-1.25667 - 0.368991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{3} - q^{4} - q^{6} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{3} - q^{4} - q^{6} - q^{8} - q^{9} + 2q^{11} - q^{12} - q^{16} - q^{18} + 2q^{22} - q^{24} - 10q^{25} - q^{27} - q^{32} + 2q^{33} - q^{36} - 11q^{42} - 9q^{44} + 2q^{47} - q^{48} - 12q^{49} + q^{50} - q^{54} + 2q^{61} + 11q^{62} - q^{64} + 2q^{66} + 10q^{72} + q^{75} - q^{81} + 11q^{84} + 2q^{88} + 2q^{94} - q^{96} - 2q^{97} + 10q^{98} + 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.415415 0.909632i 0.415415 0.909632i
\(3\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(4\) −0.654861 0.755750i −0.654861 0.755750i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(7\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(8\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(9\) −0.959493 0.281733i −0.959493 0.281733i
\(10\) 0 0
\(11\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(12\) 0.841254 0.540641i 0.841254 0.540641i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(15\) 0 0
\(16\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(19\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(20\) 0 0
\(21\) −1.07028 0.153882i −1.07028 0.153882i
\(22\) 0.544078 1.19136i 0.544078 1.19136i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −0.142315 0.989821i −0.142315 0.989821i
\(25\) −1.00000 −1.00000
\(26\) 0 0
\(27\) 0.415415 0.909632i 0.415415 0.909632i
\(28\) 0.817178 0.708089i 0.817178 0.708089i
\(29\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(30\) 0 0
\(31\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(32\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(33\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.512546 + 0.234072i 0.512546 + 0.234072i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −0.857685 0.989821i −0.857685 0.989821i
\(45\) 0 0
\(46\) 0 0
\(47\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(48\) −0.959493 0.281733i −0.959493 0.281733i
\(49\) −0.169170 −0.169170
\(50\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −0.654861 0.755750i −0.654861 0.755750i
\(55\) 0 0
\(56\) −0.304632 1.03748i −0.304632 1.03748i
\(57\) −0.557730 0.0801894i −0.557730 0.0801894i
\(58\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(62\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(63\) 0.304632 1.03748i 0.304632 1.03748i
\(64\) 0.841254 0.540641i 0.841254 0.540641i
\(65\) 0 0
\(66\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(67\) 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
\(75\) 0.142315 0.989821i 0.142315 0.989821i
\(76\) 0.425839 0.368991i 0.425839 0.368991i
\(77\) 1.41618i 1.41618i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(85\) 0 0
\(86\) 0 0
\(87\) −1.07028 0.153882i −1.07028 0.153882i
\(88\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(89\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.80075 0.258908i −1.80075 0.258908i
\(94\) 0.797176 1.74557i 0.797176 1.74557i
\(95\) 0 0
\(96\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(97\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) −0.0702757 + 0.153882i −0.0702757 + 0.153882i
\(99\) −1.25667 0.368991i −1.25667 0.368991i
\(100\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(101\) 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
\(107\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(108\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.07028 0.153882i −1.07028 0.153882i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(115\) 0 0
\(116\) 0.817178 0.708089i 0.817178 0.708089i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.715370 0.715370
\(122\) 0.118239 0.258908i 0.118239 0.258908i
\(123\) 0 0
\(124\) 1.37491 1.19136i 1.37491 1.19136i
\(125\) 0 0
\(126\) −0.817178 0.708089i −0.817178 0.708089i
\(127\) 1.51150i 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(128\) −0.142315 0.989821i −0.142315 0.989821i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 1.10181 0.708089i 1.10181 0.708089i
\(133\) −0.609264 −0.609264
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.51150i 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.415415 0.909632i 0.415415 0.909632i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.0240754 0.167448i 0.0240754 0.167448i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −0.841254 0.540641i −0.841254 0.540641i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −0.158746 0.540641i −0.158746 0.540641i
\(153\) 0 0
\(154\) 1.28820 + 0.588302i 1.28820 + 0.588302i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.841254 0.540641i 0.841254 0.540641i
\(163\) 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
\(168\) 1.07028 0.153882i 1.07028 0.153882i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0.158746 0.540641i 0.158746 0.540641i
\(172\) 0 0
\(173\) 1.51150i 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(174\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(175\) 1.08128i 1.08128i
\(176\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(177\) 0 0
\(178\) −1.80075 0.822373i −1.80075 0.822373i
\(179\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(182\) 0 0
\(183\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(184\) 0 0
\(185\) 0 0
\(186\) −0.983568 + 1.53046i −0.983568 + 1.53046i
\(187\) 0 0
\(188\) −1.25667 1.45027i −1.25667 1.45027i
\(189\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(190\) 0 0
\(191\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(192\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(195\) 0 0
\(196\) 0.110783 + 0.127850i 0.110783 + 0.127850i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(199\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(200\) 0.959493 0.281733i 0.959493 0.281733i
\(201\) 0 0
\(202\) 0 0
\(203\) −1.16917 −1.16917
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.737982i 0.737982i
\(210\) 0 0
\(211\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(215\) 0 0
\(216\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(217\) −1.96714 −1.96714
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(224\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(225\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0.304632 + 0.474017i 0.304632 + 0.474017i
\(229\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(230\) 0 0
\(231\) −1.40176 0.201543i −1.40176 0.201543i
\(232\) −0.304632 1.03748i −0.304632 1.03748i
\(233\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.297176 0.650724i 0.297176 0.650724i
\(243\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(244\) −0.186393 0.215109i −0.186393 0.215109i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.512546 1.74557i −0.512546 1.74557i
\(249\) 0 0
\(250\) 0 0
\(251\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(252\) −0.983568 + 0.449181i −0.983568 + 0.449181i
\(253\) 0 0
\(254\) −1.37491 0.627899i −1.37491 0.627899i
\(255\) 0 0
\(256\) −0.959493 0.281733i −0.959493 0.281733i
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.304632 1.03748i 0.304632 1.03748i
\(262\) 0 0
\(263\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(264\) −0.186393 1.29639i −0.186393 1.29639i
\(265\) 0 0
\(266\) −0.253098 + 0.554206i −0.253098 + 0.554206i
\(267\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(268\) 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
\(274\) −1.37491 0.627899i −1.37491 0.627899i
\(275\) −1.30972 −1.30972
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0.512546 1.74557i 0.512546 1.74557i
\(280\) 0 0
\(281\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(282\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(283\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.654861 0.755750i −0.654861 0.755750i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0.186393 1.29639i 0.186393 1.29639i
\(292\) 0 0
\(293\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(294\) −0.142315 0.0914602i −0.142315 0.0914602i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.544078 1.19136i 0.544078 1.19136i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.557730 0.0801894i −0.557730 0.0801894i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 1.07028 0.927399i 1.07028 0.927399i
\(309\) 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 \(\pi\)
\(314\) 0.345139 0.755750i 0.345139 0.755750i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(318\) 0 0
\(319\) 1.41618i 1.41618i
\(320\) 0 0
\(321\) 0.239446 1.66538i 0.239446 1.66538i
\(322\) 0 0
\(323\) 0 0
\(324\) −0.142315 0.989821i −0.142315 0.989821i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.07496i 2.07496i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.415415 0.909632i 0.415415 0.909632i
\(335\) 0 0
\(336\) 0.304632 1.03748i 0.304632 1.03748i
\(337\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(338\) 0.415415 0.909632i 0.415415 0.909632i
\(339\) 0 0
\(340\) 0 0
\(341\) 2.38273i 2.38273i
\(342\) −0.425839 0.368991i −0.425839 0.368991i
\(343\) 0.898361i 0.898361i
\(344\) 0 0
\(345\) 0 0
\(346\) −1.37491 0.627899i −1.37491 0.627899i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −0.983568 0.449181i −0.983568 0.449181i
\(351\) 0 0
\(352\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(353\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.49611 + 1.29639i −1.49611 + 1.29639i
\(357\) 0 0
\(358\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(359\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(360\) 0 0
\(361\) 0.682507 0.682507
\(362\) 0.797176 1.74557i 0.797176 1.74557i
\(363\) −0.101808 + 0.708089i −0.101808 + 0.708089i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(367\) 0.563465i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.983568 + 1.53046i 0.983568 + 1.53046i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(377\) 0 0
\(378\) 0.817178 0.708089i 0.817178 0.708089i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(382\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(383\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.162317 0.0476607i 0.162317 0.0476607i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(397\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(398\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(399\) 0.0867074 0.603063i 0.0867074 0.603063i
\(400\) 0.142315 0.989821i 0.142315 0.989821i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −0.485691 + 1.06351i −0.485691 + 1.06351i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(410\) 0 0
\(411\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0.671292 + 0.306569i 0.671292 + 0.306569i
\(419\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(422\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(423\) −1.84125 0.540641i −1.84125 0.540641i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.307765i 0.307765i
\(428\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(429\) 0 0
\(430\) 0 0
\(431\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(432\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(433\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(434\) −0.817178 + 1.78937i −0.817178 + 1.78937i
\(435\) 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
\(441\) 0.162317 + 0.0476607i 0.162317 + 0.0476607i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.80075 0.822373i −1.80075 0.822373i
\(447\) 0 0
\(448\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(449\) 0.563465i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(450\) 0.654861 0.755750i 0.654861 0.755750i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0.557730 0.0801894i 0.557730 0.0801894i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(462\) −0.765644 + 1.19136i −0.765644 + 1.19136i
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) −1.07028 0.153882i −1.07028 0.153882i
\(465\) 0 0
\(466\) −1.65486 0.755750i −1.65486 0.755750i
\(467\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.563465i 0.563465i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.118239 0.258908i 0.118239 0.258908i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.468468 0.540641i −0.468468 0.540641i
\(485\) 0 0
\(486\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(489\) 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
\(496\) −1.80075 0.258908i −1.80075 0.258908i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(502\) 0.698939 1.53046i 0.698939 1.53046i
\(503\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(504\) 1.08128i 1.08128i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(508\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(509\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(513\) 0.512546 + 0.234072i 0.512546 + 0.234072i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2.51334 2.51334
\(518\) 0 0
\(519\) 1.49611 + 0.215109i 1.49611 + 0.215109i
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −0.817178 0.708089i −0.817178 0.708089i
\(523\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(524\) 0 0
\(525\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(526\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(527\) 0 0
\(528\) −1.25667 0.368991i −1.25667 0.368991i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0.398983 + 0.460451i 0.398983 + 0.460451i
\(533\) 0 0
\(534\) 1.07028 1.66538i 1.07028 1.66538i
\(535\) 0 0
\(536\) 0 0
\(537\) 0.273100 1.89945i 0.273100 1.89945i
\(538\) 0 0
\(539\) −0.221566 −0.221566
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(549\) −0.273100 0.0801894i −0.273100 0.0801894i
\(550\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(551\) −0.609264 −0.609264
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(558\) −1.37491 1.19136i −1.37491 1.19136i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.80075 0.822373i −1.80075 0.822373i
\(563\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(564\) 1.61435 1.03748i 1.61435 1.03748i
\(565\) 0 0
\(566\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(567\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(568\) 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
\(573\) 0.118239 0.822373i 0.118239 0.822373i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(577\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(578\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −1.10181 0.708089i −1.10181 0.708089i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −1.65486 0.755750i −1.65486 0.755750i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.142315 + 0.0914602i −0.142315 + 0.0914602i
\(589\) −1.02509 −1.02509
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −0.857685 0.989821i −0.857685 0.989821i
\(595\) 0 0
\(596\) 0 0
\(597\) −1.49611 0.215109i −1.49611 0.215109i
\(598\) 0 0
\(599\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(600\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(601\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(609\) 0.166390 1.15727i 0.166390 1.15727i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.398983 1.35881i −0.398983 1.35881i
\(617\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0.830830 1.81926i 0.830830 1.81926i
\(623\) 2.14055 2.14055
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) −0.730471 0.105026i −0.730471 0.105026i
\(628\) −0.544078 0.627899i −0.544078 0.627899i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(632\) 0 0
\(633\) −1.80075 0.258908i −1.80075 0.258908i
\(634\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 1.28820 + 0.588302i 1.28820 + 0.588302i
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) −1.41542 0.909632i −1.41542 0.909632i
\(643\) 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 \(\pi\)
\(648\) −0.959493 0.281733i −0.959493 0.281733i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.279953 1.94711i 0.279953 1.94711i
\(652\) 0 0
\(653\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 1.88745 + 0.861971i 1.88745 + 0.861971i
\(659\) 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
\(668\) −0.654861 0.755750i −0.654861 0.755750i
\(669\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(670\) 0 0
\(671\) 0.372786 0.372786
\(672\) −0.817178 0.708089i −0.817178 0.708089i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(675\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(676\) −0.654861 0.755750i −0.654861 0.755750i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 1.41618i 1.41618i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.16741 + 0.989821i 2.16741 + 0.989821i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −0.512546 + 0.234072i −0.512546 + 0.234072i
\(685\) 0 0
\(686\) 0.817178 + 0.373193i 0.817178 + 0.373193i
\(687\) 0.239446 1.66538i 0.239446 1.66538i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(693\) 0.398983 1.35881i 0.398983 1.35881i
\(694\) 0 0
\(695\) 0 0
\(696\) 1.07028 0.153882i 1.07028 0.153882i
\(697\) 0 0
\(698\) 0 0
\(699\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(700\) −0.817178 + 0.708089i −0.817178 + 0.708089i
\(701\) 1.97964i 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.10181 0.708089i 1.10181 0.708089i
\(705\) 0 0
\(706\) −0.983568 0.449181i −0.983568 0.449181i
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.557730 + 1.89945i 0.557730 + 1.89945i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(717\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(718\) 0.345139 0.755750i 0.345139 0.755750i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.283524 0.620830i 0.283524 0.620830i
\(723\) 0 0
\(724\) −1.25667 1.45027i −1.25667 1.45027i
\(725\) 1.08128i 1.08128i
\(726\) 0.601808 + 0.386758i 0.601808 + 0.386758i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −0.654861 0.755750i −0.654861 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.239446 0.153882i 0.239446 0.153882i
\(733\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(734\) −0.512546 0.234072i −0.512546 0.234072i
\(735\) 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 \(0\)
\(744\) 1.80075 0.258908i 1.80075 0.258908i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.81926i 1.81926i
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(753\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(754\) 0 0
\(755\) 0 0
\(756\) −0.304632 1.03748i −0.304632 1.03748i
\(757\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(762\) 0.817178 1.27155i 0.817178 1.27155i
\(763\) 0 0
\(764\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(765\) 0 0
\(766\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(767\) 0 0
\(768\) 0.415415 0.909632i 0.415415 0.909632i
\(769\) 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
\(775\) 1.81926i 1.81926i
\(776\) 1.25667 0.368991i 1.25667 0.368991i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(784\) 0.0240754 0.167448i 0.0240754 0.167448i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0.0405070 0.281733i 0.0405070 0.281733i
\(790\) 0 0
\(791\) 0 0
\(792\) 1.30972 1.30972
\(793\) 0 0
\(794\) 0.118239 0.258908i 0.118239 0.258908i
\(795\) 0 0
\(796\) 1.14231 0.989821i 1.14231 0.989821i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) −0.512546 0.329393i −0.512546 0.329393i
\(799\) 0 0
\(800\) −0.841254 0.540641i −0.841254 0.540641i
\(801\) −0.557730 + 1.89945i −0.557730 + 1.89945i
\(802\)