Properties

Label 712.1.w.a.235.1
Level $712$
Weight $1$
Character 712.235
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 235.1
Root \(0.654861 - 0.755750i\) of defining polynomial
Character \(\chi\) \(=\) 712.235
Dual form 712.1.w.a.203.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.425839 - 1.45027i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.49611 - 0.215109i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-1.08070 + 0.694523i) q^{9} +O(q^{10})\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.425839 - 1.45027i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.49611 - 0.215109i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-1.08070 + 0.694523i) q^{9} +(-0.345139 - 0.755750i) q^{11} +1.51150i q^{12} +(0.841254 + 0.540641i) q^{16} +(-0.0405070 - 0.281733i) q^{17} +(-0.533654 - 1.16854i) q^{18} +(-0.983568 - 1.53046i) q^{19} +(0.797176 - 0.234072i) q^{22} +(-1.49611 - 0.215109i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.325137 + 0.281733i) q^{27} +(-0.654861 + 0.755750i) q^{32} +(-0.949069 + 0.822373i) q^{33} +0.284630 q^{34} +(1.23259 - 0.361922i) q^{36} +(1.65486 - 0.755750i) q^{38} +(1.80075 - 0.822373i) q^{43} +(0.118239 + 0.822373i) q^{44} +(0.425839 - 1.45027i) q^{48} +(0.654861 + 0.755750i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.391340 + 0.178719i) q^{51} +(-0.325137 + 0.281733i) q^{54} +(-1.80075 + 2.07817i) q^{57} +(-0.557730 + 1.89945i) q^{59} +(-0.654861 - 0.755750i) q^{64} +(-0.678936 - 1.05645i) q^{66} +(1.61435 - 0.474017i) q^{67} +(-0.0405070 + 0.281733i) q^{68} +(0.182822 + 1.27155i) q^{72} +(1.10181 + 0.708089i) q^{73} +(-0.817178 + 1.27155i) q^{75} +(0.512546 + 1.74557i) q^{76} +(-0.263521 + 0.577031i) q^{81} +(-0.557730 + 0.0801894i) q^{83} +(0.557730 + 1.89945i) q^{86} -0.830830 q^{88} +(-0.654861 + 0.755750i) q^{89} +(1.37491 + 0.627899i) q^{96} +(0.698939 - 1.53046i) q^{97} +(-0.841254 + 0.540641i) q^{98} +(0.897877 + 0.577031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} - 9q^{11} - q^{16} - 9q^{17} - q^{18} + 2q^{22} - q^{25} + 11q^{27} - q^{32} + 2q^{34} - q^{36} + 11q^{38} + 2q^{44} + q^{49} - q^{50} - 11q^{54} - q^{64} + 2q^{67} - 9q^{68} + 10q^{72} + 2q^{73} - q^{81} + 2q^{88} - q^{89} - 2q^{97} + q^{98} - 9q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{9}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(3\) −0.425839 1.45027i −0.425839 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(6\) 1.49611 0.215109i 1.49611 0.215109i
\(7\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) −1.08070 + 0.694523i −1.08070 + 0.694523i
\(10\) 0 0
\(11\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(12\) 1.51150i 1.51150i
\(13\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(18\) −0.533654 1.16854i −0.533654 1.16854i
\(19\) −0.983568 1.53046i −0.983568 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.797176 0.234072i 0.797176 0.234072i
\(23\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(24\) −1.49611 0.215109i −1.49611 0.215109i
\(25\) −0.654861 0.755750i −0.654861 0.755750i
\(26\) 0 0
\(27\) 0.325137 + 0.281733i 0.325137 + 0.281733i
\(28\) 0 0
\(29\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(30\) 0 0
\(31\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(32\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(33\) −0.949069 + 0.822373i −0.949069 + 0.822373i
\(34\) 0.284630 0.284630
\(35\) 0 0
\(36\) 1.23259 0.361922i 1.23259 0.361922i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.65486 0.755750i 1.65486 0.755750i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(42\) 0 0
\(43\) 1.80075 0.822373i 1.80075 0.822373i 0.841254 0.540641i \(-0.181818\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(44\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(48\) 0.425839 1.45027i 0.425839 1.45027i
\(49\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(50\) 0.841254 0.540641i 0.841254 0.540641i
\(51\) −0.391340 + 0.178719i −0.391340 + 0.178719i
\(52\) 0 0
\(53\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(54\) −0.325137 + 0.281733i −0.325137 + 0.281733i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.80075 + 2.07817i −1.80075 + 2.07817i
\(58\) 0 0
\(59\) −0.557730 + 1.89945i −0.557730 + 1.89945i −0.142315 + 0.989821i \(0.545455\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) 0 0
\(61\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) −0.678936 1.05645i −0.678936 1.05645i
\(67\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(68\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(72\) 0.182822 + 1.27155i 0.182822 + 1.27155i
\(73\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(74\) 0 0
\(75\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(76\) 0.512546 + 1.74557i 0.512546 + 1.74557i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(80\) 0 0
\(81\) −0.263521 + 0.577031i −0.263521 + 0.577031i
\(82\) 0 0
\(83\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.557730 + 1.89945i 0.557730 + 1.89945i
\(87\) 0 0
\(88\) −0.830830 −0.830830
\(89\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(97\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(98\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(99\) 0.897877 + 0.577031i 0.897877 + 0.577031i
\(100\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −0.121206 0.412791i −0.121206 0.412791i
\(103\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.830830 + 1.81926i 0.830830 + 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(108\) −0.232593 0.361922i −0.232593 0.361922i
\(109\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(114\) −1.80075 2.07817i −1.80075 2.07817i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.80075 0.822373i −1.80075 0.822373i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.202824 0.234072i 0.202824 0.234072i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(128\) 0.841254 0.540641i 0.841254 0.540641i
\(129\) −1.95949 2.26138i −1.95949 2.26138i
\(130\) 0 0
\(131\) −1.25667 0.368991i −1.25667 0.368991i −0.415415 0.909632i \(-0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(132\) 1.14231 0.521678i 1.14231 0.521678i
\(133\) 0 0
\(134\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(135\) 0 0
\(136\) −0.273100 0.0801894i −0.273100 0.0801894i
\(137\) 0.557730 1.89945i 0.557730 1.89945i 0.142315 0.989821i \(-0.454545\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(138\) 0 0
\(139\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.28463 −1.28463
\(145\) 0 0
\(146\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(147\) 0.817178 1.27155i 0.817178 1.27155i
\(148\) 0 0
\(149\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(150\) −1.14231 0.989821i −1.14231 0.989821i
\(151\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(152\) −1.80075 + 0.258908i −1.80075 + 0.258908i
\(153\) 0.239446 + 0.276335i 0.239446 + 0.276335i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.533654 0.342959i −0.533654 0.342959i
\(163\) −1.49611 0.215109i −1.49611 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.563465i 0.563465i
\(167\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(168\) 0 0
\(169\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(170\) 0 0
\(171\) 2.12588 + 0.970858i 2.12588 + 0.970858i
\(172\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(173\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.118239 0.822373i 0.118239 0.822373i
\(177\) 2.99223 2.99223
\(178\) −0.654861 0.755750i −0.654861 0.755750i
\(179\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(180\) 0 0
\(181\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(192\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(193\) 1.07028 + 0.153882i 1.07028 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(194\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(195\) 0 0
\(196\) −0.415415 0.909632i −0.415415 0.909632i
\(197\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(198\) −0.698939 + 0.806618i −0.698939 + 0.806618i
\(199\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(200\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(201\) −1.37491 2.13940i −1.37491 2.13940i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.425839 0.0612263i 0.425839 0.0612263i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(210\) 0 0
\(211\) −1.49611 + 1.29639i −1.49611 + 1.29639i −0.654861 + 0.755750i \(0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.91899 + 0.563465i −1.91899 + 0.563465i
\(215\) 0 0
\(216\) 0.391340 0.178719i 0.391340 0.178719i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.557730 1.89945i 0.557730 1.89945i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(224\) 0 0
\(225\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(226\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(227\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(228\) 2.31329 1.48666i 2.31329 1.48666i
\(229\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.07028 1.66538i 1.07028 1.66538i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(240\) 0 0
\(241\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(242\) 0.202824 + 0.234072i 0.202824 + 0.234072i
\(243\) 1.37491 + 0.197682i 1.37491 + 0.197682i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.353799 + 0.774713i 0.353799 + 0.774713i
\(250\) 0 0
\(251\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(258\) 2.51722 1.61772i 2.51722 1.61772i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.544078 1.19136i 0.544078 1.19136i
\(263\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(264\) 0.353799 + 1.20493i 0.353799 + 1.20493i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(268\) −1.68251 −1.68251
\(269\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(270\) 0 0
\(271\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(272\) 0.118239 0.258908i 0.118239 0.258908i
\(273\) 0 0
\(274\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(275\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(276\) 0 0
\(277\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(278\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.983568 1.53046i 0.983568 1.53046i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(282\) 0 0
\(283\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.182822 1.27155i 0.182822 1.27155i
\(289\) 0.881761 0.258908i 0.881761 0.258908i
\(290\) 0 0
\(291\) −2.51722 0.361922i −2.51722 0.361922i
\(292\) −0.857685 0.989821i −0.857685 0.989821i
\(293\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(294\) 1.14231 + 0.989821i 1.14231 + 0.989821i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.100702 0.342959i 0.100702 0.342959i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.14231 0.989821i 1.14231 0.989821i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.81926i 1.81926i
\(305\) 0 0
\(306\) −0.307599 + 0.197682i −0.307599 + 0.197682i
\(307\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(312\) 0 0
\(313\) −0.983568 + 0.449181i −0.983568 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 2.28463 1.97964i 2.28463 1.97964i
\(322\) 0 0
\(323\) −0.391340 + 0.339098i −0.391340 + 0.339098i
\(324\) 0.415415 0.479414i 0.415415 0.479414i
\(325\) 0 0
\(326\) 0.425839 1.45027i 0.425839 1.45027i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.983568 + 1.53046i 0.983568 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(338\) −0.415415 0.909632i −0.415415 0.909632i
\(339\) −0.121206 0.843008i −0.121206 0.843008i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.26352 + 1.96608i −1.26352 + 1.96608i
\(343\) 0 0
\(344\) 1.97964i 1.97964i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(348\) 0 0
\(349\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(353\) −0.304632 1.03748i −0.304632 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(354\) −0.425839 + 2.96177i −0.425839 + 2.96177i
\(355\) 0 0
\(356\) 0.841254 0.540641i 0.841254 0.540641i
\(357\) 0 0
\(358\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(359\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(360\) 0 0
\(361\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(362\) 0 0
\(363\) −0.425839 0.194474i −0.425839 0.194474i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(374\) −0.0982369 0.215109i −0.0982369 0.215109i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.584585 0.909632i −0.584585 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(384\) −1.14231 0.989821i −1.14231 0.989821i
\(385\) 0 0
\(386\) −0.304632 + 1.03748i −0.304632 + 1.03748i
\(387\) −1.37491 + 2.13940i −1.37491 + 2.13940i
\(388\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(389\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.959493 0.281733i 0.959493 0.281733i
\(393\) 1.97964i 1.97964i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.698939 0.806618i −0.698939 0.806618i
\(397\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.142315 0.989821i −0.142315 0.989821i
\(401\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(402\) 2.31329 1.05645i 2.31329 1.05645i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.430218i 0.430218i
\(409\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(410\) 0 0
\(411\) −2.99223 −2.99223
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.949069 0.822373i −0.949069 0.822373i
\(418\) −1.14231 0.989821i −1.14231 0.989821i
\(419\) −1.07028 + 0.153882i −1.07028 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(422\) −1.07028 1.66538i −1.07028 1.66538i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.284630 1.97964i −0.284630 1.97964i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(432\) 0.121206 + 0.412791i 0.121206 + 0.412791i
\(433\) 1.51150i 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(439\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(440\) 0 0
\(441\) −1.23259 0.361922i −1.23259 0.361922i
\(442\) 0 0
\(443\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(450\) −0.533654 + 1.16854i −0.533654 + 1.16854i
\(451\) 0 0
\(452\) −0.512546 0.234072i −0.512546 0.234072i
\(453\) 0 0
\(454\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(455\) 0 0
\(456\) 1.14231 + 2.50132i 1.14231 + 2.50132i
\(457\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(458\) 0 0
\(459\) 0.0662029 0.103014i 0.0662029 0.103014i
\(460\) 0 0
\(461\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(462\) 0 0
\(463\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(467\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.49611 + 1.29639i 1.49611 + 1.29639i
\(473\) −1.24302 1.07708i −1.24302 1.07708i
\(474\) 0 0
\(475\) −0.512546 + 1.74557i −0.512546 + 1.74557i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.563465i 0.563465i
\(483\) 0 0
\(484\) −0.260554 + 0.167448i −0.260554 + 0.167448i
\(485\) 0 0
\(486\) −0.391340 + 1.33278i −0.391340 + 1.33278i
\(487\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(488\) 0 0
\(489\) 0.325137 + 2.26138i 0.325137 + 2.26138i
\(490\) 0 0
\(491\) 1.65486 0.755750i 1.65486 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
1.00000 \(0\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.817178 + 0.239945i −0.817178 + 0.239945i
\(499\) −0.425839 + 0.368991i −0.425839 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.25667 1.45027i 1.25667 1.45027i
\(503\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.14231 + 0.989821i 1.14231 + 0.989821i
\(508\) 0 0
\(509\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 0.111387 0.774713i 0.111387 0.774713i
\(514\) 0.544078 0.627899i 0.544078 0.627899i
\(515\) 0 0
\(516\) 1.24302 + 2.72183i 1.24302 + 2.72183i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.557730 1.89945i −0.557730 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(522\) 0 0
\(523\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(524\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.24302 + 0.178719i −1.24302 + 0.178719i
\(529\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(530\) 0 0
\(531\) −0.716476 2.44009i −0.716476 2.44009i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(535\) 0 0
\(536\) 0.239446 1.66538i 0.239446 1.66538i
\(537\) −0.716476 2.44009i −0.716476 2.44009i
\(538\) 0 0
\(539\) 0.345139 0.755750i 0.345139 0.755750i
\(540\) 0 0
\(541\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.512546 1.74557i −0.512546 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(548\) −1.07028 + 1.66538i −1.07028 + 1.66538i
\(549\) 0 0
\(550\) −0.698939 0.449181i −0.698939 0.449181i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(557\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.270133 + 0.234072i 0.270133 + 0.234072i
\(562\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(563\) 1.65486 + 0.755750i 1.65486 + 0.755750i 1.00000 \(0\)
0.654861 + 0.755750i \(0.272727\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.817178 0.708089i 0.817178 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(577\) −1.65486 + 0.755750i −1.65486 + 0.755750i −0.654861 + 0.755750i \(0.727273\pi\)
−1.00000 \(\pi\)
\(578\) 0.130785 + 0.909632i 0.130785 + 0.909632i
\(579\) −0.232593 1.61772i −0.232593 1.61772i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.716476 2.44009i 0.716476 2.44009i
\(583\) 0 0
\(584\) 1.10181 0.708089i 1.10181 0.708089i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(588\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.304632 1.03748i 0.304632 1.03748i −0.654861 0.755750i \(-0.727273\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(594\) 0.325137 + 0.148485i 0.325137 + 0.148485i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(600\) 0.817178 + 1.27155i 0.817178 + 1.27155i
\(601\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(602\) 0 0
\(603\) −1.41542 + 1.63348i −1.41542 + 1.63348i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(608\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.151894 0.332601i −0.151894 0.332601i
\(613\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(614\) 1.61435 1.03748i 1.61435 1.03748i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.49611 + 0.215109i −1.49611 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 0 0
\(619\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(626\) −0.304632 1.03748i −0.304632 1.03748i
\(627\) 2.19209 + 0.643655i 2.19209 + 0.643655i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(632\) 0 0
\(633\) 2.51722 + 1.61772i 2.51722 + 1.61772i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(642\) 1.63436 + 2.54311i 1.63436 + 2.54311i
\(643\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.279953 0.435615i −0.279953 0.435615i
\(647\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(648\) 0.415415 + 0.479414i 0.415415 + 0.479414i
\(649\) 1.62801 0.234072i 1.62801 0.234072i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(653\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.68251 −1.68251
\(658\) 0 0
\(659\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(660\) 0 0
\(661\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(662\) 0.698939 0.449181i 0.698939 0.449181i
\(663\) 0 0
\(664\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.68251 + 1.08128i −1.68251 + 1.08128i −0.841254 + 0.540641i \(0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(674\) −1.65486 + 0.755750i −1.65486 + 0.755750i
\(675\) 0.430218i 0.430218i
\(676\) 0.959493 0.281733i 0.959493 0.281733i
\(677\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(678\) 0.851677 0.851677
\(679\) 0 0
\(680\) 0 0
\(681\) 1.07028 1.66538i 1.07028 1.66538i
\(682\) 0 0
\(683\) 1.37491 + 0.627899i 1.37491 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(684\) −1.76625 1.53046i −1.76625 1.53046i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.797176 1.74557i −0.797176 1.74557i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −0.817178 2.78305i −0.817178 2.78305i
\(700\) 0 0
\(701\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(705\) 0 0
\(706\) 1.07028 0.153882i 1.07028 0.153882i
\(707\) 0 0
\(708\) −2.87102 0.843008i −2.87102 0.843008i
\(709\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.61435 0.474017i −1.61435 0.474017i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.94306 1.24873i −1.94306 1.24873i
\(723\) 0.353799 + 0.774713i 0.353799 + 0.774713i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.253098 0.393828i 0.253098 0.393828i
\(727\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(728\) 0 0
\(729\) −0.208518 1.45027i −0.208518 1.45027i
\(730\) 0 0
\(731\) −0.304632 0.474017i −0.304632 0.474017i
\(732\) 0 0
\(733\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.915415 1.05645i −0.915415 1.05645i
\(738\) 0 0
\(739\) 0.817178 + 0.708089i 0.817178 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.547045 0.474017i 0.547045 0.474017i
\(748\) 0.226900 0.0666238i 0.226900 0.0666238i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(752\) 0 0
\(753\) −0.817178 + 2.78305i −0.817178 + 2.78305i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(758\) 0.983568 0.449181i 0.983568 0.449181i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−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
\(768\) 1.14231 0.989821i 1.14231 0.989821i
\(769\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(770\) 0 0
\(771\) −0.353799 + 1.20493i −0.353799 + 1.20493i
\(772\) −0.983568 0.449181i −0.983568 0.449181i
\(773\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(774\) −1.92195 1.66538i −1.92195 1.66538i
\(775\) 0 0
\(776\) −1.10181 1.27155i −1.10181 1.27155i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(785\) 0 0
\(786\) −1.95949 0.281733i −1.95949 0.281733i
\(787\) −0.304632 + 0.474017i −0.304632 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.897877 0.577031i 0.897877 0.577031i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000