Properties

Label 712.1.w.a.251.1
Level $712$
Weight $1$
Character 712.251
Analytic conductor $0.355$
Analytic rank $0$
Dimension $10$
Projective image $D_{22}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.w (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.355334288995\)
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 251.1
Root \(-0.841254 - 0.540641i\) of defining polynomial
Character \(\chi\) \(=\) 712.251
Dual form 712.1.w.a.139.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.415415 - 0.909632i) q^{2} +(-0.817178 - 0.708089i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.983568 + 0.449181i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(0.0240754 + 0.167448i) q^{9} +O(q^{10})\) \(q+(0.415415 - 0.909632i) q^{2} +(-0.817178 - 0.708089i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.983568 + 0.449181i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(0.0240754 + 0.167448i) q^{9} +(-1.84125 - 0.540641i) q^{11} +1.08128i q^{12} +(-0.142315 + 0.989821i) q^{16} +(-0.345139 - 0.755750i) q^{17} +(0.162317 + 0.0476607i) q^{18} +(0.557730 - 0.0801894i) q^{19} +(-1.25667 + 1.45027i) q^{22} +(0.983568 + 0.449181i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.485691 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{32} +(1.12181 + 1.74557i) q^{33} -0.830830 q^{34} +(0.110783 - 0.127850i) q^{36} +(0.158746 - 0.540641i) q^{38} +(0.512546 - 1.74557i) q^{43} +(0.797176 + 1.74557i) q^{44} +(0.817178 - 0.708089i) q^{48} +(-0.841254 + 0.540641i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(-0.253098 + 0.861971i) q^{51} +(0.485691 + 0.755750i) q^{54} +(-0.512546 - 0.329393i) q^{57} +(1.37491 - 1.19136i) q^{59} +(0.841254 - 0.540641i) q^{64} +(2.05384 - 0.295298i) q^{66} +(-0.186393 + 0.215109i) q^{67} +(-0.345139 + 0.755750i) q^{68} +(-0.0702757 - 0.153882i) q^{72} +(0.239446 - 1.66538i) q^{73} +(-1.07028 - 0.153882i) q^{75} +(-0.425839 - 0.368991i) q^{76} +(1.09435 - 0.321330i) q^{81} +(1.37491 - 0.627899i) q^{83} +(-1.37491 - 1.19136i) q^{86} +1.91899 q^{88} +(0.841254 + 0.540641i) q^{89} +(-0.304632 - 1.03748i) q^{96} +(0.273100 - 0.0801894i) q^{97} +(0.142315 + 0.989821i) q^{98} +(0.0462003 - 0.321330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} - 9q^{11} - q^{16} - 9q^{17} - q^{18} + 2q^{22} - q^{25} + 11q^{27} - q^{32} + 2q^{34} - q^{36} + 11q^{38} + 2q^{44} + q^{49} - q^{50} - 11q^{54} - q^{64} + 2q^{67} - 9q^{68} + 10q^{72} + 2q^{73} - q^{81} + 2q^{88} - q^{89} - 2q^{97} + q^{98} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/712\mathbb{Z}\right)^\times\).

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{22}\right)\)

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
\(3\) −0.817178 0.708089i −0.817178 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(4\) −0.654861 0.755750i −0.654861 0.755750i
\(5\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(6\) −0.983568 + 0.449181i −0.983568 + 0.449181i
\(7\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(8\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(9\) 0.0240754 + 0.167448i 0.0240754 + 0.167448i
\(10\) 0 0
\(11\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(12\) 1.08128i 1.08128i
\(13\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(17\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(18\) 0.162317 + 0.0476607i 0.162317 + 0.0476607i
\(19\) 0.557730 0.0801894i 0.557730 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(23\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(24\) 0.983568 + 0.449181i 0.983568 + 0.449181i
\(25\) 0.841254 0.540641i 0.841254 0.540641i
\(26\) 0 0
\(27\) −0.485691 + 0.755750i −0.485691 + 0.755750i
\(28\) 0 0
\(29\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(30\) 0 0
\(31\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(32\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(33\) 1.12181 + 1.74557i 1.12181 + 1.74557i
\(34\) −0.830830 −0.830830
\(35\) 0 0
\(36\) 0.110783 0.127850i 0.110783 0.127850i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0.158746 0.540641i 0.158746 0.540641i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(42\) 0 0
\(43\) 0.512546 1.74557i 0.512546 1.74557i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(44\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(48\) 0.817178 0.708089i 0.817178 0.708089i
\(49\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(50\) −0.142315 0.989821i −0.142315 0.989821i
\(51\) −0.253098 + 0.861971i −0.253098 + 0.861971i
\(52\) 0 0
\(53\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(54\) 0.485691 + 0.755750i 0.485691 + 0.755750i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.512546 0.329393i −0.512546 0.329393i
\(58\) 0 0
\(59\) 1.37491 1.19136i 1.37491 1.19136i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(60\) 0 0
\(61\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.841254 0.540641i 0.841254 0.540641i
\(65\) 0 0
\(66\) 2.05384 0.295298i 2.05384 0.295298i
\(67\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(68\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(72\) −0.0702757 0.153882i −0.0702757 0.153882i
\(73\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(74\) 0 0
\(75\) −1.07028 0.153882i −1.07028 0.153882i
\(76\) −0.425839 0.368991i −0.425839 0.368991i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(80\) 0 0
\(81\) 1.09435 0.321330i 1.09435 0.321330i
\(82\) 0 0
\(83\) 1.37491 0.627899i 1.37491 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.37491 1.19136i −1.37491 1.19136i
\(87\) 0 0
\(88\) 1.91899 1.91899
\(89\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.304632 1.03748i −0.304632 1.03748i
\(97\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(98\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(99\) 0.0462003 0.321330i 0.0462003 0.321330i
\(100\) −0.959493 0.281733i −0.959493 0.281733i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0.678936 + 0.588302i 0.678936 + 0.588302i
\(103\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.91899 0.563465i −1.91899 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 0.281733i \(-0.909091\pi\)
\(108\) 0.889217 0.127850i 0.889217 0.127850i
\(109\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.37491 0.627899i −1.37491 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(114\) −0.512546 + 0.329393i −0.512546 + 0.329393i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.512546 1.74557i −0.512546 1.74557i
\(119\) 0 0
\(120\) 0 0
\(121\) 2.25667 + 1.45027i 2.25667 + 1.45027i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(128\) −0.142315 0.989821i −0.142315 0.989821i
\(129\) −1.65486 + 1.06351i −1.65486 + 1.06351i
\(130\) 0 0
\(131\) 1.10181 + 1.27155i 1.10181 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(132\) 0.584585 1.99091i 0.584585 1.99091i
\(133\) 0 0
\(134\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(135\) 0 0
\(136\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(137\) −1.37491 + 1.19136i −1.37491 + 1.19136i −0.415415 + 0.909632i \(0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(138\) 0 0
\(139\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.169170 −0.169170
\(145\) 0 0
\(146\) −1.41542 0.909632i −1.41542 0.909632i
\(147\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(148\) 0 0
\(149\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(150\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(151\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(152\) −0.512546 + 0.234072i −0.512546 + 0.234072i
\(153\) 0.118239 0.0759879i 0.118239 0.0759879i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.162317 1.12894i 0.162317 1.12894i
\(163\) 0.983568 + 0.449181i 0.983568 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.51150i 1.51150i
\(167\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(168\) 0 0
\(169\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(170\) 0 0
\(171\) 0.0268551 + 0.0914602i 0.0268551 + 0.0914602i
\(172\) −1.65486 + 0.755750i −1.65486 + 0.755750i
\(173\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.797176 1.74557i 0.797176 1.74557i
\(177\) −1.96714 −1.96714
\(178\) 0.841254 0.540641i 0.841254 0.540641i
\(179\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) 0 0
\(181\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.226900 + 1.57812i 0.226900 + 1.57812i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(192\) −1.07028 0.153882i −1.07028 0.153882i
\(193\) −1.80075 0.822373i −1.80075 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
−0.841254 0.540641i \(-0.818182\pi\)
\(194\) 0.0405070 0.281733i 0.0405070 0.281733i
\(195\) 0 0
\(196\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(197\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(198\) −0.273100 0.175511i −0.273100 0.175511i
\(199\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(200\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(201\) 0.304632 0.0437995i 0.304632 0.0437995i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.817178 0.373193i 0.817178 0.373193i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.07028 0.153882i −1.07028 0.153882i
\(210\) 0 0
\(211\) 0.983568 + 1.53046i 0.983568 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.30972 + 1.51150i −1.30972 + 1.51150i
\(215\) 0 0
\(216\) 0.253098 0.861971i 0.253098 0.861971i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.37491 + 1.19136i −1.37491 + 1.19136i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(224\) 0 0
\(225\) 0.110783 + 0.127850i 0.110783 + 0.127850i
\(226\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(227\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(228\) 0.0867074 + 0.603063i 0.0867074 + 0.603063i
\(229\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.80075 0.258908i −1.80075 0.258908i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(240\) 0 0
\(241\) 1.37491 0.627899i 1.37491 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(242\) 2.25667 1.45027i 2.25667 1.45027i
\(243\) −0.304632 0.139121i −0.304632 0.139121i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −1.56815 0.460451i −1.56815 0.460451i
\(250\) 0 0
\(251\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.959493 0.281733i −0.959493 0.281733i
\(257\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(258\) 0.279953 + 1.94711i 0.279953 + 1.94711i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.61435 0.474017i 1.61435 0.474017i
\(263\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) −1.56815 1.35881i −1.56815 1.35881i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.304632 1.03748i −0.304632 1.03748i
\(268\) 0.284630 0.284630
\(269\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(270\) 0 0
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0.797176 0.234072i 0.797176 0.234072i
\(273\) 0 0
\(274\) 0.512546 + 1.74557i 0.512546 + 1.74557i
\(275\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(276\) 0 0
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.557730 0.0801894i −0.557730 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(282\) 0 0
\(283\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0702757 + 0.153882i −0.0702757 + 0.153882i
\(289\) 0.202824 0.234072i 0.202824 0.234072i
\(290\) 0 0
\(291\) −0.279953 0.127850i −0.279953 0.127850i
\(292\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(293\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(294\) 0.584585 0.909632i 0.584585 0.909632i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.30287 1.12894i 1.30287 1.12894i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.563465i 0.563465i
\(305\) 0 0
\(306\) −0.0200026 0.139121i −0.0200026 0.139121i
\(307\) 1.10181 0.708089i 1.10181 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(312\) 0 0
\(313\) 0.557730 1.89945i 0.557730 1.89945i 0.142315 0.989821i \(-0.454545\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.16917 + 1.81926i 1.16917 + 1.81926i
\(322\) 0 0
\(323\) −0.253098 0.393828i −0.253098 0.393828i
\(324\) −0.959493 0.616629i −0.959493 0.616629i
\(325\) 0 0
\(326\) 0.817178 0.708089i 0.817178 0.708089i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) −1.37491 0.627899i −1.37491 0.627899i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(338\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(339\) 0.678936 + 1.48666i 0.678936 + 1.48666i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.0943511 + 0.0135656i 0.0943511 + 0.0135656i
\(343\) 0 0
\(344\) 1.81926i 1.81926i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(348\) 0 0
\(349\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.25667 1.45027i −1.25667 1.45027i
\(353\) −1.49611 1.29639i −1.49611 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(354\) −0.817178 + 1.78937i −0.817178 + 1.78937i
\(355\) 0 0
\(356\) −0.142315 0.989821i −0.142315 0.989821i
\(357\) 0 0
\(358\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(359\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(360\) 0 0
\(361\) −0.654861 + 0.192284i −0.654861 + 0.192284i
\(362\) 0 0
\(363\) −0.817178 2.78305i −0.817178 2.78305i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −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 0
\(373\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(374\) 1.52977 + 0.449181i 1.52977 + 0.449181i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.95949 + 0.281733i −1.95949 + 0.281733i −0.959493 + 0.281733i \(0.909091\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(384\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(385\) 0 0
\(386\) −1.49611 + 1.29639i −1.49611 + 1.29639i
\(387\) 0.304632 + 0.0437995i 0.304632 + 0.0437995i
\(388\) −0.239446 0.153882i −0.239446 0.153882i
\(389\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.654861 0.755750i 0.654861 0.755750i
\(393\) 1.81926i 1.81926i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.273100 + 0.175511i −0.273100 + 0.175511i
\(397\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(401\) 0.118239 + 0.258908i 0.118239 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(402\) 0.0867074 0.295298i 0.0867074 0.295298i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.898361i 0.898361i
\(409\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(410\) 0 0
\(411\) 1.96714 1.96714
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.12181 1.74557i 1.12181 1.74557i
\(418\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(419\) 1.80075 0.822373i 1.80075 0.822373i 0.841254 0.540641i \(-0.181818\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(420\) 0 0
\(421\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(422\) 1.80075 0.258908i 1.80075 0.258908i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.698939 0.449181i −0.698939 0.449181i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.830830 + 1.81926i 0.830830 + 1.81926i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(432\) −0.678936 0.588302i −0.678936 0.588302i
\(433\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.512546 + 1.74557i 0.512546 + 1.74557i
\(439\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(440\) 0 0
\(441\) −0.110783 0.127850i −0.110783 0.127850i
\(442\) 0 0
\(443\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(450\) 0.162317 0.0476607i 0.162317 0.0476607i
\(451\) 0 0
\(452\) 0.425839 + 1.45027i 0.425839 + 1.45027i
\(453\) 0 0
\(454\) −0.239446 1.66538i −0.239446 1.66538i
\(455\) 0 0
\(456\) 0.584585 + 0.171650i 0.584585 + 0.171650i
\(457\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(458\) 0 0
\(459\) 0.738788 + 0.106222i 0.738788 + 0.106222i
\(460\) 0 0
\(461\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(462\) 0 0
\(463\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.544078 1.19136i 0.544078 1.19136i
\(467\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.983568 + 1.53046i −0.983568 + 1.53046i
\(473\) −1.88745 + 2.93694i −1.88745 + 2.93694i
\(474\) 0 0
\(475\) 0.425839 0.368991i 0.425839 0.368991i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.51150i 1.51150i
\(483\) 0 0
\(484\) −0.381761 2.65520i −0.381761 2.65520i
\(485\) 0 0
\(486\) −0.253098 + 0.219310i −0.253098 + 0.219310i
\(487\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(488\) 0 0
\(489\) −0.485691 1.06351i −0.485691 1.06351i
\(490\) 0 0
\(491\) 0.158746 0.540641i 0.158746 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
1.00000 \(0\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.07028 + 1.23516i −1.07028 + 1.23516i
\(499\) −0.817178 1.27155i −0.817178 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.10181 0.708089i −1.10181 0.708089i
\(503\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.584585 0.909632i 0.584585 0.909632i
\(508\) 0 0
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(513\) −0.210281 + 0.460451i −0.210281 + 0.460451i
\(514\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(515\) 0 0
\(516\) 1.88745 + 0.554206i 1.88745 + 0.554206i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.37491 + 1.19136i 1.37491 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(522\) 0 0
\(523\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(524\) 0.239446 1.66538i 0.239446 1.66538i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.88745 + 0.861971i −1.88745 + 0.861971i
\(529\) 0.959493 0.281733i 0.959493 0.281733i
\(530\) 0 0
\(531\) 0.232593 + 0.201543i 0.232593 + 0.201543i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.07028 0.153882i −1.07028 0.153882i
\(535\) 0 0
\(536\) 0.118239 0.258908i 0.118239 0.258908i
\(537\) 0.232593 + 0.201543i 0.232593 + 0.201543i
\(538\) 0 0
\(539\) 1.84125 0.540641i 1.84125 0.540641i
\(540\) 0 0
\(541\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.118239 0.822373i 0.118239 0.822373i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.425839 + 0.368991i 0.425839 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(548\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(549\) 0 0
\(550\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.25667 1.45027i 1.25667 1.45027i
\(557\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.932034 1.45027i 0.932034 1.45027i
\(562\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(563\) 0.158746 + 0.540641i 0.158746 + 0.540641i 1.00000 \(0\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.07028 + 1.66538i 1.07028 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.110783 + 0.127850i 0.110783 + 0.127850i
\(577\) −0.158746 + 0.540641i −0.158746 + 0.540641i 0.841254 + 0.540641i \(0.181818\pi\)
−1.00000 \(\pi\)
\(578\) −0.128663 0.281733i −0.128663 0.281733i
\(579\) 0.889217 + 1.94711i 0.889217 + 1.94711i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.232593 + 0.201543i −0.232593 + 0.201543i
\(583\) 0 0
\(584\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(588\) −0.584585 0.909632i −0.584585 0.909632i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.49611 1.29639i 1.49611 1.29639i 0.654861 0.755750i \(-0.272727\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(594\) −0.485691 1.65411i −0.485691 1.65411i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(600\) 1.07028 0.153882i 1.07028 0.153882i
\(601\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(602\) 0 0
\(603\) −0.0405070 0.0260323i −0.0405070 0.0260323i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(608\) 0.512546 + 0.234072i 0.512546 + 0.234072i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.134858 0.0395979i −0.134858 0.0395979i
\(613\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(614\) −0.186393 1.29639i −0.186393 1.29639i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.983568 0.449181i 0.983568 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(618\) 0 0
\(619\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.415415 0.909632i
\(626\) −1.49611 1.29639i −1.49611 1.29639i
\(627\) 0.765644 + 0.883600i 0.765644 + 0.883600i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(632\) 0 0
\(633\) 0.279953 1.94711i 0.279953 1.94711i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(642\) 2.14055 0.307765i 2.14055 0.307765i
\(643\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.463379 + 0.0666238i −0.463379 + 0.0666238i
\(647\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(648\) −0.959493 + 0.616629i −0.959493 + 0.616629i
\(649\) −3.17565 + 1.45027i −3.17565 + 1.45027i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.304632 1.03748i −0.304632 1.03748i
\(653\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.284630 0.284630
\(658\) 0 0
\(659\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(660\) 0 0
\(661\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(662\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(663\) 0 0
\(664\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.284630 + 1.97964i 0.284630 + 1.97964i 0.142315 + 0.989821i \(0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(674\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(675\) 0.898361i 0.898361i
\(676\) 0.654861 0.755750i 0.654861 0.755750i
\(677\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(678\) 1.63436 1.63436
\(679\) 0 0
\(680\) 0 0
\(681\) −1.80075 0.258908i −1.80075 0.258908i
\(682\) 0 0
\(683\) −0.304632 1.03748i −0.304632 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(684\) 0.0515346 0.0801894i 0.0515346 0.0801894i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.65486 + 0.755750i 1.65486 + 0.755750i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −1.07028 0.927399i −1.07028 0.927399i
\(700\) 0 0
\(701\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(705\) 0 0
\(706\) −1.80075 + 0.822373i −1.80075 + 0.822373i
\(707\) 0 0
\(708\) 1.28820 + 1.48666i 1.28820 + 1.48666i
\(709\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.959493 0.281733i −0.959493 0.281733i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.0971309 + 0.675560i −0.0971309 + 0.675560i
\(723\) −1.56815 0.460451i −1.56815 0.460451i
\(724\) 0 0
\(725\) 0 0
\(726\) −2.87102 0.412791i −2.87102 0.412791i
\(727\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(728\) 0 0
\(729\) −0.323373 0.708089i −0.323373 0.708089i
\(730\) 0 0
\(731\) −1.49611 + 0.215109i −1.49611 + 0.215109i
\(732\) 0 0
\(733\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.459493 0.295298i 0.459493 0.295298i
\(738\) 0 0
\(739\) 1.07028 1.66538i 1.07028 1.66538i 0.415415 0.909632i \(-0.363636\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.138242 + 0.215109i 0.138242 + 0.215109i
\(748\) 1.04408 1.20493i 1.04408 1.20493i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(752\) 0 0
\(753\) −1.07028 + 0.927399i −1.07028 + 0.927399i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(758\) −0.557730 + 1.89945i −0.557730 + 1.89945i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(769\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(770\) 0 0
\(771\) 1.56815 1.35881i 1.56815 1.35881i
\(772\) 0.557730 + 1.89945i 0.557730 + 1.89945i
\(773\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(774\) 0.166390 0.258908i 0.166390 0.258908i
\(775\) 0 0
\(776\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.415415 0.909632i −0.415415 0.909632i
\(785\) 0 0
\(786\) −1.65486 0.755750i −1.65486 0.755750i
\(787\) −1.49611 0.215109i −1.49611 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.0462003 + 0.321330i 0.0462003 + 0.321330i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000