Properties

Label 712.1.w.a.443.1
Level $712$
Weight $1$
Character 712.443
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 443.1
Root \(0.142315 - 0.989821i\) of defining polynomial
Character \(\chi\) \(=\) 712.443
Dual form 712.1.w.a.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.959493 + 0.281733i) q^{2} +(-1.07028 + 1.66538i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.557730 - 1.89945i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-1.21259 - 2.65520i) q^{9} +O(q^{10})\) \(q+(-0.959493 + 0.281733i) q^{2} +(-1.07028 + 1.66538i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.557730 - 1.89945i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-1.21259 - 2.65520i) q^{9} +(-0.857685 - 0.989821i) q^{11} +1.97964i q^{12} +(0.415415 - 0.909632i) q^{16} +(-1.84125 - 0.540641i) q^{17} +(1.91153 + 2.20602i) q^{18} +(-1.37491 + 0.627899i) q^{19} +(1.10181 + 0.708089i) q^{22} +(-0.557730 - 1.89945i) q^{24} +(-0.142315 - 0.989821i) q^{25} +(3.76024 + 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{32} +(2.56639 - 0.368991i) q^{33} +1.91899 q^{34} +(-2.45561 - 1.57812i) q^{36} +(1.14231 - 0.989821i) q^{38} +(-0.425839 + 0.368991i) q^{43} +(-1.25667 - 0.368991i) q^{44} +(1.07028 + 1.66538i) q^{48} +(0.142315 + 0.989821i) q^{49} +(0.415415 + 0.909632i) q^{50} +(2.87102 - 2.48775i) q^{51} +(-3.76024 + 0.540641i) q^{54} +(0.425839 - 2.96177i) q^{57} +(-0.304632 - 0.474017i) q^{59} +(-0.142315 - 0.989821i) q^{64} +(-2.35848 + 1.07708i) q^{66} +(-0.698939 - 0.449181i) q^{67} +(-1.84125 + 0.540641i) q^{68} +(2.80075 + 0.822373i) q^{72} +(0.118239 - 0.258908i) q^{73} +(1.80075 + 0.822373i) q^{75} +(-0.817178 + 1.27155i) q^{76} +(-3.01334 + 3.47758i) q^{81} +(-0.304632 + 1.03748i) q^{83} +(0.304632 - 0.474017i) q^{86} +1.30972 q^{88} +(-0.142315 + 0.989821i) q^{89} +(-1.49611 - 1.29639i) q^{96} +(-0.544078 + 0.627899i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(-1.58816 + 3.47758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} - 9q^{11} - q^{16} - 9q^{17} - q^{18} + 2q^{22} - q^{25} + 11q^{27} - q^{32} + 2q^{34} - q^{36} + 11q^{38} + 2q^{44} + q^{49} - q^{50} - 11q^{54} - q^{64} + 2q^{67} - 9q^{68} + 10q^{72} + 2q^{73} - q^{81} + 2q^{88} - q^{89} - 2q^{97} + q^{98} - 9q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{15}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(3\) −1.07028 + 1.66538i −1.07028 + 1.66538i −0.415415 + 0.909632i \(0.636364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(4\) 0.841254 0.540641i 0.841254 0.540641i
\(5\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(6\) 0.557730 1.89945i 0.557730 1.89945i
\(7\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(8\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(9\) −1.21259 2.65520i −1.21259 2.65520i
\(10\) 0 0
\(11\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(12\) 1.97964i 1.97964i
\(13\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.415415 0.909632i 0.415415 0.909632i
\(17\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(18\) 1.91153 + 2.20602i 1.91153 + 2.20602i
\(19\) −1.37491 + 0.627899i −1.37491 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(23\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(24\) −0.557730 1.89945i −0.557730 1.89945i
\(25\) −0.142315 0.989821i −0.142315 0.989821i
\(26\) 0 0
\(27\) 3.76024 + 0.540641i 3.76024 + 0.540641i
\(28\) 0 0
\(29\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(30\) 0 0
\(31\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(32\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(33\) 2.56639 0.368991i 2.56639 0.368991i
\(34\) 1.91899 1.91899
\(35\) 0 0
\(36\) −2.45561 1.57812i −2.45561 1.57812i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.14231 0.989821i 1.14231 0.989821i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(42\) 0 0
\(43\) −0.425839 + 0.368991i −0.425839 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(44\) −1.25667 0.368991i −1.25667 0.368991i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(48\) 1.07028 + 1.66538i 1.07028 + 1.66538i
\(49\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(50\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(51\) 2.87102 2.48775i 2.87102 2.48775i
\(52\) 0 0
\(53\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(54\) −3.76024 + 0.540641i −3.76024 + 0.540641i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.425839 2.96177i 0.425839 2.96177i
\(58\) 0 0
\(59\) −0.304632 0.474017i −0.304632 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(60\) 0 0
\(61\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.142315 0.989821i −0.142315 0.989821i
\(65\) 0 0
\(66\) −2.35848 + 1.07708i −2.35848 + 1.07708i
\(67\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(68\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(72\) 2.80075 + 0.822373i 2.80075 + 0.822373i
\(73\) 0.118239 0.258908i 0.118239 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(74\) 0 0
\(75\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(76\) −0.817178 + 1.27155i −0.817178 + 1.27155i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(80\) 0 0
\(81\) −3.01334 + 3.47758i −3.01334 + 3.47758i
\(82\) 0 0
\(83\) −0.304632 + 1.03748i −0.304632 + 1.03748i 0.654861 + 0.755750i \(0.272727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.304632 0.474017i 0.304632 0.474017i
\(87\) 0 0
\(88\) 1.30972 1.30972
\(89\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −1.49611 1.29639i −1.49611 1.29639i
\(97\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(98\) −0.415415 0.909632i −0.415415 0.909632i
\(99\) −1.58816 + 3.47758i −1.58816 + 3.47758i
\(100\) −0.654861 0.755750i −0.654861 0.755750i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −2.05384 + 3.19584i −2.05384 + 3.19584i
\(103\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.30972 1.51150i −1.30972 1.51150i −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(108\) 3.45561 1.57812i 3.45561 1.57812i
\(109\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.304632 + 1.03748i 0.304632 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(114\) 0.425839 + 2.96177i 0.425839 + 2.96177i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.425839 + 0.368991i 0.425839 + 0.368991i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.101808 + 0.708089i −0.101808 + 0.708089i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(128\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(129\) −0.158746 1.10411i −0.158746 1.10411i
\(130\) 0 0
\(131\) 0.239446 0.153882i 0.239446 0.153882i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 1.95949 1.69791i 1.95949 1.69791i
\(133\) 0 0
\(134\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(135\) 0 0
\(136\) 1.61435 1.03748i 1.61435 1.03748i
\(137\) 0.304632 + 0.474017i 0.304632 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(138\) 0 0
\(139\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.91899 −2.91899
\(145\) 0 0
\(146\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(147\) −1.80075 0.822373i −1.80075 0.822373i
\(148\) 0 0
\(149\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(150\) −1.95949 0.281733i −1.95949 0.281733i
\(151\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(152\) 0.425839 1.45027i 0.425839 1.45027i
\(153\) 0.797176 + 5.54448i 0.797176 + 5.54448i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.91153 4.18567i 1.91153 4.18567i
\(163\) −0.557730 1.89945i −0.557730 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.08128i 1.08128i
\(167\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(168\) 0 0
\(169\) −0.415415 0.909632i −0.415415 0.909632i
\(170\) 0 0
\(171\) 3.33440 + 2.88927i 3.33440 + 2.88927i
\(172\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(173\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(177\) 1.11546 1.11546
\(178\) −0.142315 0.989821i −0.142315 0.989821i
\(179\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.04408 + 2.28621i 1.04408 + 2.28621i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(192\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(193\) −0.512546 1.74557i −0.512546 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(194\) 0.345139 0.755750i 0.345139 0.755750i
\(195\) 0 0
\(196\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(197\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(198\) 0.544078 3.78415i 0.544078 3.78415i
\(199\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(200\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(201\) 1.49611 0.683252i 1.49611 0.683252i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.07028 3.64502i 1.07028 3.64502i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(210\) 0 0
\(211\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.68251 + 1.08128i 1.68251 + 1.08128i
\(215\) 0 0
\(216\) −2.87102 + 2.48775i −2.87102 + 2.48775i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.304632 + 0.474017i 0.304632 + 0.474017i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(224\) 0 0
\(225\) −2.45561 + 1.57812i −2.45561 + 1.57812i
\(226\) −0.584585 0.909632i −0.584585 0.909632i
\(227\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(228\) −1.24302 2.72183i −1.24302 2.72183i
\(229\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.512546 0.234072i −0.512546 0.234072i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(240\) 0 0
\(241\) −0.304632 + 1.03748i −0.304632 + 1.03748i 0.654861 + 0.755750i \(0.272727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) −0.101808 0.708089i −0.101808 0.708089i
\(243\) −1.49611 5.09530i −1.49611 5.09530i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −1.40176 1.61772i −1.40176 1.61772i
\(250\) 0 0
\(251\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.654861 0.755750i −0.654861 0.755750i
\(257\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(258\) 0.463379 + 1.01466i 0.463379 + 1.01466i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(263\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(264\) −1.40176 + 2.18119i −1.40176 + 2.18119i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.49611 1.29639i −1.49611 1.29639i
\(268\) −0.830830 −0.830830
\(269\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(270\) 0 0
\(271\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(272\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(273\) 0 0
\(274\) −0.425839 0.368991i −0.425839 0.368991i
\(275\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(276\) 0 0
\(277\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(278\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.37491 + 0.627899i 1.37491 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(282\) 0 0
\(283\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.80075 0.822373i 2.80075 0.822373i
\(289\) 2.25667 + 1.45027i 2.25667 + 1.45027i
\(290\) 0 0
\(291\) −0.463379 1.57812i −0.463379 1.57812i
\(292\) −0.0405070 0.281733i −0.0405070 0.281733i
\(293\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(294\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(295\) 0 0
\(296\) 0 0
\(297\) −2.68996 4.18567i −2.68996 4.18567i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.95949 0.281733i 1.95949 0.281733i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.51150i 1.51150i
\(305\) 0 0
\(306\) −2.32694 5.09530i −2.32694 5.09530i
\(307\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(312\) 0 0
\(313\) −1.37491 + 1.19136i −1.37491 + 1.19136i −0.415415 + 0.909632i \(0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 3.91899 0.563465i 3.91899 0.563465i
\(322\) 0 0
\(323\) 2.87102 0.412791i 2.87102 0.412791i
\(324\) −0.654861 + 4.55466i −0.654861 + 4.55466i
\(325\) 0 0
\(326\) 1.07028 + 1.66538i 1.07028 + 1.66538i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(332\) 0.304632 + 1.03748i 0.304632 + 1.03748i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.37491 0.627899i 1.37491 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(338\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(339\) −2.05384 0.603063i −2.05384 0.603063i
\(340\) 0 0
\(341\) 0 0
\(342\) −4.01334 1.83283i −4.01334 1.83283i
\(343\) 0 0
\(344\) 0.563465i 0.563465i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(348\) 0 0
\(349\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.10181 0.708089i 1.10181 0.708089i
\(353\) 0.983568 1.53046i 0.983568 1.53046i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(354\) −1.07028 + 0.314261i −1.07028 + 0.314261i
\(355\) 0 0
\(356\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(357\) 0 0
\(358\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(359\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(360\) 0 0
\(361\) 0.841254 0.970858i 0.841254 0.970858i
\(362\) 0 0
\(363\) −1.07028 0.927399i −1.07028 0.927399i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(374\) −1.64589 1.89945i −1.64589 1.89945i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.65486 + 0.755750i −1.65486 + 0.755750i −0.654861 + 0.755750i \(0.727273\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(384\) −1.95949 0.281733i −1.95949 0.281733i
\(385\) 0 0
\(386\) 0.983568 + 1.53046i 0.983568 + 1.53046i
\(387\) 1.49611 + 0.683252i 1.49611 + 0.683252i
\(388\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(389\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.841254 0.540641i −0.841254 0.540641i
\(393\) 0.563465i 0.563465i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.544078 + 3.78415i 0.544078 + 3.78415i
\(397\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.959493 0.281733i −0.959493 0.281733i
\(401\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(402\) −1.24302 + 1.07708i −1.24302 + 1.07708i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 3.79891i 3.79891i
\(409\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(410\) 0 0
\(411\) −1.11546 −1.11546
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.56639 + 0.368991i 2.56639 + 0.368991i
\(418\) −1.95949 0.281733i −1.95949 0.281733i
\(419\) 0.512546 1.74557i 0.512546 1.74557i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(420\) 0 0
\(421\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(422\) 0.512546 0.234072i 0.512546 0.234072i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.91899 0.563465i −1.91899 0.563465i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(432\) 2.05384 3.19584i 2.05384 3.19584i
\(433\) 1.97964i 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.425839 0.368991i −0.425839 0.368991i
\(439\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(440\) 0 0
\(441\) 2.45561 1.57812i 2.45561 1.57812i
\(442\) 0 0
\(443\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.41542 + 0.909632i −1.41542 + 0.909632i −0.415415 + 0.909632i \(0.636364\pi\)
−1.00000 \(\pi\)
\(450\) 1.91153 2.20602i 1.91153 2.20602i
\(451\) 0 0
\(452\) 0.817178 + 0.708089i 0.817178 + 0.708089i
\(453\) 0 0
\(454\) −0.118239 0.258908i −0.118239 0.258908i
\(455\) 0 0
\(456\) 1.95949 + 2.26138i 1.95949 + 2.26138i
\(457\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(458\) 0 0
\(459\) −6.63126 3.02840i −6.63126 3.02840i
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.61435 0.474017i 1.61435 0.474017i
\(467\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(473\) 0.730471 + 0.105026i 0.730471 + 0.105026i
\(474\) 0 0
\(475\) 0.817178 + 1.27155i 0.817178 + 1.27155i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.08128i 1.08128i
\(483\) 0 0
\(484\) 0.297176 + 0.650724i 0.297176 + 0.650724i
\(485\) 0 0
\(486\) 2.87102 + 4.46740i 2.87102 + 4.46740i
\(487\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(488\) 0 0
\(489\) 3.76024 + 1.10411i 3.76024 + 1.10411i
\(490\) 0 0
\(491\) 1.14231 0.989821i 1.14231 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
1.00000 \(0\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.80075 + 1.15727i 1.80075 + 1.15727i
\(499\) −1.07028 + 0.153882i −1.07028 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(503\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(508\) 0 0
\(509\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(513\) −5.50945 + 1.61772i −5.50945 + 1.61772i
\(514\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(515\) 0 0
\(516\) −0.730471 0.843008i −0.730471 0.843008i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.304632 + 0.474017i −0.304632 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(522\) 0 0
\(523\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(524\) 0.118239 0.258908i 0.118239 0.258908i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.730471 2.48775i 0.730471 2.48775i
\(529\) 0.654861 0.755750i 0.654861 0.755750i
\(530\) 0 0
\(531\) −0.889217 + 1.38365i −0.889217 + 1.38365i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(535\) 0 0
\(536\) 0.797176 0.234072i 0.797176 0.234072i
\(537\) −0.889217 + 1.38365i −0.889217 + 1.38365i
\(538\) 0 0
\(539\) 0.857685 0.989821i 0.857685 0.989821i
\(540\) 0 0
\(541\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.797176 1.74557i 0.797176 1.74557i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.817178 1.27155i 0.817178 1.27155i −0.142315 0.989821i \(-0.545455\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(548\) 0.512546 + 0.234072i 0.512546 + 0.234072i
\(549\) 0 0
\(550\) 0.544078 1.19136i 0.544078 1.19136i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.10181 0.708089i −1.10181 0.708089i
\(557\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −4.92487 0.708089i −4.92487 0.708089i
\(562\) −1.49611 0.215109i −1.49611 0.215109i
\(563\) 1.14231 + 0.989821i 1.14231 + 0.989821i 1.00000 \(0\)
0.142315 + 0.989821i \(0.454545\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.239446 1.66538i 0.239446 1.66538i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.80075 + 0.258908i −1.80075 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −2.45561 + 1.57812i −2.45561 + 1.57812i
\(577\) −1.14231 + 0.989821i −1.14231 + 0.989821i −0.142315 + 0.989821i \(0.545455\pi\)
−1.00000 \(\pi\)
\(578\) −2.57385 0.755750i −2.57385 0.755750i
\(579\) 3.45561 + 1.01466i 3.45561 + 1.01466i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.889217 + 1.38365i 0.889217 + 1.38365i
\(583\) 0 0
\(584\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(588\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.983568 1.53046i −0.983568 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(594\) 3.76024 + 3.25827i 3.76024 + 3.25827i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(600\) −1.80075 + 0.822373i −1.80075 + 0.822373i
\(601\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0 0
\(603\) −0.345139 + 2.40050i −0.345139 + 2.40050i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(608\) −0.425839 1.45027i −0.425839 1.45027i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 3.66820 + 4.23333i 3.66820 + 4.23333i
\(613\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(614\) −0.698939 1.53046i −0.698939 1.53046i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.557730 + 1.89945i −0.557730 + 1.89945i −0.142315 + 0.989821i \(0.545455\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(618\) 0 0
\(619\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(626\) 0.983568 1.53046i 0.983568 1.53046i
\(627\) −3.29686 + 2.11876i −3.29686 + 2.11876i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(632\) 0 0
\(633\) 0.463379 1.01466i 0.463379 1.01466i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(642\) −3.60149 + 1.64475i −3.60149 + 1.64475i
\(643\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.63843 + 1.20493i −2.63843 + 1.20493i
\(647\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(648\) −0.654861 4.55466i −0.654861 4.55466i
\(649\) −0.207914 + 0.708089i −0.207914 + 0.708089i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.49611 1.29639i −1.49611 1.29639i
\(653\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.830830 −0.830830
\(658\) 0 0
\(659\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(660\) 0 0
\(661\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(662\) −0.544078 1.19136i −0.544078 1.19136i
\(663\) 0 0
\(664\) −0.584585 0.909632i −0.584585 0.909632i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.830830 1.81926i −0.830830 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(674\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(675\) 3.79891i 3.79891i
\(676\) −0.841254 0.540641i −0.841254 0.540641i
\(677\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(678\) 2.14055 2.14055
\(679\) 0 0
\(680\) 0 0
\(681\) −0.512546 0.234072i −0.512546 0.234072i
\(682\) 0 0
\(683\) −1.49611 1.29639i −1.49611 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(684\) 4.36714 + 0.627899i 4.36714 + 0.627899i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.10181 1.27155i −1.10181 1.27155i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 1.80075 2.80202i 1.80075 2.80202i
\(700\) 0 0
\(701\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(705\) 0 0
\(706\) −0.512546 + 1.74557i −0.512546 + 1.74557i
\(707\) 0 0
\(708\) 0.938384 0.603063i 0.938384 0.603063i
\(709\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.654861 0.755750i −0.654861 0.755750i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.698939 0.449181i 0.698939 0.449181i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.533654 + 1.16854i −0.533654 + 1.16854i
\(723\) −1.40176 1.61772i −1.40176 1.61772i
\(724\) 0 0
\(725\) 0 0
\(726\) 1.28820 + 0.588302i 1.28820 + 0.588302i
\(727\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(728\) 0 0
\(729\) 5.67177 + 1.66538i 5.67177 + 1.66538i
\(730\) 0 0
\(731\) 0.983568 0.449181i 0.983568 0.449181i
\(732\) 0 0
\(733\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.154861 + 1.07708i 0.154861 + 1.07708i
\(738\) 0 0
\(739\) −1.80075 0.258908i −1.80075 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 3.12412 0.449181i 3.12412 0.449181i
\(748\) 2.11435 + 1.35881i 2.11435 + 1.35881i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(752\) 0 0
\(753\) 1.80075 + 2.80202i 1.80075 + 2.80202i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(758\) 1.37491 1.19136i 1.37491 1.19136i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.95949 0.281733i 1.95949 0.281733i
\(769\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(770\) 0 0
\(771\) 1.40176 + 2.18119i 1.40176 + 2.18119i
\(772\) −1.37491 1.19136i −1.37491 1.19136i
\(773\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(774\) −1.62801 0.234072i −1.62801 0.234072i
\(775\) 0 0
\(776\) −0.118239 0.822373i −0.118239 0.822373i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(785\) 0 0
\(786\) −0.158746 0.540641i −0.158746 0.540641i
\(787\) 0.983568 + 0.449181i 0.983568 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1.58816 3.47758i −1.58816 3.47758i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000