Properties

Label 712.1.w.a.619.1
Level $712$
Weight $1$
Character 712.619
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 619.1
Root \(0.959493 + 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 712.619
Dual form 712.1.w.a.467.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.841254 - 0.540641i) q^{2} +(0.512546 - 0.234072i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.304632 - 0.474017i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(-0.446947 + 0.515804i) q^{9} +O(q^{10})\) \(q+(0.841254 - 0.540641i) q^{2} +(0.512546 - 0.234072i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.304632 - 0.474017i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(-0.446947 + 0.515804i) q^{9} +(-0.0405070 + 0.281733i) q^{11} -0.563465i q^{12} +(-0.654861 - 0.755750i) q^{16} +(-1.41542 - 0.909632i) q^{17} +(-0.0971309 + 0.675560i) q^{18} +(1.49611 + 1.29639i) q^{19} +(0.118239 + 0.258908i) q^{22} +(-0.304632 - 0.474017i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.267092 + 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{32} +(0.0451840 + 0.153882i) q^{33} -1.68251 q^{34} +(0.283524 + 0.620830i) q^{36} +(1.95949 + 0.281733i) q^{38} +(-1.07028 - 0.153882i) q^{43} +(0.239446 + 0.153882i) q^{44} +(-0.512546 - 0.234072i) q^{48} +(0.959493 - 0.281733i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-0.938384 - 0.134919i) q^{51} +(0.267092 + 0.909632i) q^{54} +(1.07028 + 0.314261i) q^{57} +(0.983568 + 0.449181i) q^{59} +(-0.959493 + 0.281733i) q^{64} +(0.121206 + 0.105026i) q^{66} +(0.544078 + 1.19136i) q^{67} +(-1.41542 + 0.909632i) q^{68} +(0.574161 + 0.368991i) q^{72} +(-1.25667 - 1.45027i) q^{73} +(-0.425839 + 0.368991i) q^{75} +(1.80075 - 0.822373i) q^{76} +(-0.0211086 - 0.146813i) q^{81} +(0.983568 - 1.53046i) q^{83} +(-0.983568 + 0.449181i) q^{86} +0.284630 q^{88} +(-0.959493 - 0.281733i) q^{89} +(-0.557730 + 0.0801894i) q^{96} +(0.186393 + 1.29639i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.127214 - 0.146813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 10q - q^{2} - q^{4} - q^{8} - q^{9} - 9q^{11} - q^{16} - 9q^{17} - q^{18} + 2q^{22} - q^{25} + 11q^{27} - q^{32} + 2q^{34} - q^{36} + 11q^{38} + 2q^{44} + q^{49} - q^{50} - 11q^{54} - q^{64} + 2q^{67} - 9q^{68} + 10q^{72} + 2q^{73} - q^{81} + 2q^{88} - q^{89} - 2q^{97} + q^{98} - 9q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{19}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.841254 0.540641i 0.841254 0.540641i
\(3\) 0.512546 0.234072i 0.512546 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(4\) 0.415415 0.909632i 0.415415 0.909632i
\(5\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(6\) 0.304632 0.474017i 0.304632 0.474017i
\(7\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(8\) −0.142315 0.989821i −0.142315 0.989821i
\(9\) −0.446947 + 0.515804i −0.446947 + 0.515804i
\(10\) 0 0
\(11\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i 0.959493 + 0.281733i \(0.0909091\pi\)
−1.00000 \(1.00000\pi\)
\(12\) 0.563465i 0.563465i
\(13\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.654861 0.755750i −0.654861 0.755750i
\(17\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(18\) −0.0971309 + 0.675560i −0.0971309 + 0.675560i
\(19\) 1.49611 + 1.29639i 1.49611 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(23\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(24\) −0.304632 0.474017i −0.304632 0.474017i
\(25\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(26\) 0 0
\(27\) −0.267092 + 0.909632i −0.267092 + 0.909632i
\(28\) 0 0
\(29\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(30\) 0 0
\(31\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(32\) −0.959493 0.281733i −0.959493 0.281733i
\(33\) 0.0451840 + 0.153882i 0.0451840 + 0.153882i
\(34\) −1.68251 −1.68251
\(35\) 0 0
\(36\) 0.283524 + 0.620830i 0.283524 + 0.620830i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(42\) 0 0
\(43\) −1.07028 0.153882i −1.07028 0.153882i −0.415415 0.909632i \(-0.636364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(44\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(48\) −0.512546 0.234072i −0.512546 0.234072i
\(49\) 0.959493 0.281733i 0.959493 0.281733i
\(50\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(51\) −0.938384 0.134919i −0.938384 0.134919i
\(52\) 0 0
\(53\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(54\) 0.267092 + 0.909632i 0.267092 + 0.909632i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.07028 + 0.314261i 1.07028 + 0.314261i
\(58\) 0 0
\(59\) 0.983568 + 0.449181i 0.983568 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(60\) 0 0
\(61\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) 0.121206 + 0.105026i 0.121206 + 0.105026i
\(67\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(68\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(72\) 0.574161 + 0.368991i 0.574161 + 0.368991i
\(73\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(74\) 0 0
\(75\) −0.425839 + 0.368991i −0.425839 + 0.368991i
\(76\) 1.80075 0.822373i 1.80075 0.822373i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(80\) 0 0
\(81\) −0.0211086 0.146813i −0.0211086 0.146813i
\(82\) 0 0
\(83\) 0.983568 1.53046i 0.983568 1.53046i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.983568 + 0.449181i −0.983568 + 0.449181i
\(87\) 0 0
\(88\) 0.284630 0.284630
\(89\) −0.959493 0.281733i −0.959493 0.281733i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i
\(97\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) 0.654861 0.755750i 0.654861 0.755750i
\(99\) −0.127214 0.146813i −0.127214 0.146813i
\(100\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −0.862362 + 0.393828i −0.862362 + 0.393828i
\(103\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.284630 + 1.97964i −0.284630 + 1.97964i −0.142315 + 0.989821i \(0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) 0.716476 + 0.620830i 0.716476 + 0.620830i
\(109\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.983568 1.53046i −0.983568 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(114\) 1.07028 0.314261i 1.07028 0.314261i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.07028 0.153882i 1.07028 0.153882i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.881761 + 0.258908i 0.881761 + 0.258908i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(128\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(129\) −0.584585 + 0.171650i −0.584585 + 0.171650i
\(130\) 0 0
\(131\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(132\) 0.158746 + 0.0228243i 0.158746 + 0.0228243i
\(133\) 0 0
\(134\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(135\) 0 0
\(136\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(137\) −0.983568 0.449181i −0.983568 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(138\) 0 0
\(139\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.682507 0.682507
\(145\) 0 0
\(146\) −1.84125 0.540641i −1.84125 0.540641i
\(147\) 0.425839 0.368991i 0.425839 0.368991i
\(148\) 0 0
\(149\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(150\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(151\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(152\) 1.07028 1.66538i 1.07028 1.66538i
\(153\) 1.10181 0.323520i 1.10181 0.323520i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.0971309 0.112095i −0.0971309 0.112095i
\(163\) −0.304632 0.474017i −0.304632 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.81926i 1.81926i
\(167\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(168\) 0 0
\(169\) 0.654861 0.755750i 0.654861 0.755750i
\(170\) 0 0
\(171\) −1.33737 + 0.192284i −1.33737 + 0.192284i
\(172\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(173\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.239446 0.153882i 0.239446 0.153882i
\(177\) 0.609264 0.609264
\(178\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(179\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0 0
\(181\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.313607 0.361922i 0.313607 0.361922i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(192\) −0.425839 + 0.368991i −0.425839 + 0.368991i
\(193\) 0.817178 + 1.27155i 0.817178 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(194\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(195\) 0 0
\(196\) 0.142315 0.989821i 0.142315 0.989821i
\(197\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(198\) −0.186393 0.0547299i −0.186393 0.0547299i
\(199\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(200\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(201\) 0.557730 + 0.483276i 0.557730 + 0.483276i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.512546 + 0.797537i −0.512546 + 0.797537i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.425839 + 0.368991i −0.425839 + 0.368991i
\(210\) 0 0
\(211\) −0.304632 1.03748i −0.304632 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.830830 + 1.81926i 0.830830 + 1.81926i
\(215\) 0 0
\(216\) 0.938384 + 0.134919i 0.938384 + 0.134919i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.983568 0.449181i −0.983568 0.449181i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(224\) 0 0
\(225\) 0.283524 0.620830i 0.283524 0.620830i
\(226\) −1.65486 0.755750i −1.65486 0.755750i
\(227\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(228\) 0.730471 0.843008i 0.730471 0.843008i
\(229\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.817178 0.708089i 0.817178 0.708089i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(240\) 0 0
\(241\) 0.983568 1.53046i 0.983568 1.53046i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(242\) 0.881761 0.258908i 0.881761 0.258908i
\(243\) −0.557730 0.867845i −0.557730 0.867845i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.145886 1.01466i 0.145886 1.01466i
\(250\) 0 0
\(251\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(257\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(258\) −0.398983 + 0.460451i −0.398983 + 0.460451i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.273100 1.89945i −0.273100 1.89945i
\(263\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(264\) 0.145886 0.0666238i 0.145886 0.0666238i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i
\(268\) 1.30972 1.30972
\(269\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(270\) 0 0
\(271\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(272\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(273\) 0 0
\(274\) −1.07028 + 0.153882i −1.07028 + 0.153882i
\(275\) −0.0405070 0.281733i −0.0405070 0.281733i
\(276\) 0 0
\(277\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(278\) 0.0405070 0.281733i 0.0405070 0.281733i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.49611 + 1.29639i −1.49611 + 1.29639i −0.654861 + 0.755750i \(0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(282\) 0 0
\(283\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.574161 0.368991i 0.574161 0.368991i
\(289\) 0.760554 + 1.66538i 0.760554 + 1.66538i
\(290\) 0 0
\(291\) 0.398983 + 0.620830i 0.398983 + 0.620830i
\(292\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(293\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(294\) 0.158746 0.540641i 0.158746 0.540641i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.245454 0.112095i −0.245454 0.112095i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.97964i 1.97964i
\(305\) 0 0
\(306\) 0.751992 0.867845i 0.751992 0.867845i
\(307\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(312\) 0 0
\(313\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.317493 + 1.08128i 0.317493 + 1.08128i
\(322\) 0 0
\(323\) −0.938384 3.19584i −0.938384 3.19584i
\(324\) −0.142315 0.0417874i −0.142315 0.0417874i
\(325\) 0 0
\(326\) −0.512546 0.234072i −0.512546 0.234072i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(332\) −0.983568 1.53046i −0.983568 1.53046i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.49611 1.29639i −1.49611 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(338\) 0.142315 0.989821i 0.142315 0.989821i
\(339\) −0.862362 0.554206i −0.862362 0.554206i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.02111 + 0.884796i −1.02111 + 0.884796i
\(343\) 0 0
\(344\) 1.08128i 1.08128i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(348\) 0 0
\(349\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.118239 0.258908i 0.118239 0.258908i
\(353\) 1.37491 0.627899i 1.37491 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(354\) 0.512546 0.329393i 0.512546 0.329393i
\(355\) 0 0
\(356\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(357\) 0 0
\(358\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(359\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(360\) 0 0
\(361\) 0.415415 + 2.88927i 0.415415 + 2.88927i
\(362\) 0 0
\(363\) 0.512546 0.0736930i 0.512546 0.0736930i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(374\) 0.0681534 0.474017i 0.0681534 0.474017i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.14231 0.989821i −1.14231 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(384\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(385\) 0 0
\(386\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(387\) 0.557730 0.483276i 0.557730 0.483276i
\(388\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(389\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.415415 0.909632i −0.415415 0.909632i
\(393\) 1.08128i 1.08128i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.186393 + 0.0547299i −0.186393 + 0.0547299i
\(397\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(401\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(402\) 0.730471 + 0.105026i 0.730471 + 0.105026i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.948034i 0.948034i
\(409\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(410\) 0 0
\(411\) −0.609264 −0.609264
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.0451840 0.153882i 0.0451840 0.153882i
\(418\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(419\) −0.817178 + 1.27155i −0.817178 + 1.27155i 0.142315 + 0.989821i \(0.454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(420\) 0 0
\(421\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(422\) −0.817178 0.708089i −0.817178 0.708089i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.68251 + 1.08128i 1.68251 + 1.08128i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(432\) 0.862362 0.393828i 0.862362 0.393828i
\(433\) 0.563465i 0.563465i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −1.07028 + 0.153882i −1.07028 + 0.153882i
\(439\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(440\) 0 0
\(441\) −0.283524 + 0.620830i −0.283524 + 0.620830i
\(442\) 0 0
\(443\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.345139 + 0.755750i −0.345139 + 0.755750i 0.654861 + 0.755750i \(0.272727\pi\)
−1.00000 \(\pi\)
\(450\) −0.0971309 0.675560i −0.0971309 0.675560i
\(451\) 0 0
\(452\) −1.80075 + 0.258908i −1.80075 + 0.258908i
\(453\) 0 0
\(454\) 1.25667 1.45027i 1.25667 1.45027i
\(455\) 0 0
\(456\) 0.158746 1.10411i 0.158746 1.10411i
\(457\) 1.51150i 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(458\) 0 0
\(459\) 1.20548 1.04455i 1.20548 1.04455i
\(460\) 0 0
\(461\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(462\) 0 0
\(463\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(467\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.304632 1.03748i 0.304632 1.03748i
\(473\) 0.0867074 0.295298i 0.0867074 0.295298i
\(474\) 0 0
\(475\) −1.80075 0.822373i −1.80075 0.822373i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.81926i 1.81926i
\(483\) 0 0
\(484\) 0.601808 0.694523i 0.601808 0.694523i
\(485\) 0 0
\(486\) −0.938384 0.428546i −0.938384 0.428546i
\(487\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(488\) 0 0
\(489\) −0.267092 0.171650i −0.267092 0.171650i
\(490\) 0 0
\(491\) 1.95949 + 0.281733i 1.95949 + 0.281733i 1.00000 \(0\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.425839 0.932456i −0.425839 0.932456i
\(499\) 0.512546 + 1.74557i 0.512546 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.797176 0.234072i −0.797176 0.234072i
\(503\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.158746 0.540641i 0.158746 0.540641i
\(508\) 0 0
\(509\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(513\) −1.57884 + 1.01466i −1.57884 + 1.01466i
\(514\) −0.273100 0.0801894i −0.273100 0.0801894i
\(515\) 0 0
\(516\) −0.0867074 + 0.603063i −0.0867074 + 0.603063i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.983568 0.449181i 0.983568 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(522\) 0 0
\(523\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(524\) −1.25667 1.45027i −1.25667 1.45027i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.0867074 0.134919i 0.0867074 0.134919i
\(529\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(530\) 0 0
\(531\) −0.671292 + 0.306569i −0.671292 + 0.306569i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.425839 + 0.368991i −0.425839 + 0.368991i
\(535\) 0 0
\(536\) 1.10181 0.708089i 1.10181 0.708089i
\(537\) −0.671292 + 0.306569i −0.671292 + 0.306569i
\(538\) 0 0
\(539\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(540\) 0 0
\(541\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.80075 + 0.822373i −1.80075 + 0.822373i −0.841254 + 0.540641i \(0.818182\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(548\) −0.817178 + 0.708089i −0.817178 + 0.708089i
\(549\) 0 0
\(550\) −0.186393 0.215109i −0.186393 0.215109i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.118239 0.258908i −0.118239 0.258908i
\(557\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.0760223 0.258908i 0.0760223 0.258908i
\(562\) −0.557730 + 1.89945i −0.557730 + 1.89945i
\(563\) 1.95949 0.281733i 1.95949 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
1.00000 \(0\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.425839 + 1.45027i 0.425839 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.283524 0.620830i 0.283524 0.620830i
\(577\) −1.95949 0.281733i −1.95949 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
−1.00000 \(\pi\)
\(578\) 1.54019 + 0.989821i 1.54019 + 0.989821i
\(579\) 0.716476 + 0.460451i 0.716476 + 0.460451i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.671292 + 0.306569i 0.671292 + 0.306569i
\(583\) 0 0
\(584\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.118239 + 0.258908i 0.118239 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(588\) −0.158746 0.540641i −0.158746 0.540641i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.37491 0.627899i −1.37491 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(594\) −0.267092 + 0.0384020i −0.267092 + 0.0384020i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(600\) 0.425839 + 0.368991i 0.425839 + 0.368991i
\(601\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(602\) 0 0
\(603\) −0.857685 0.251839i −0.857685 0.251839i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(608\) −1.07028 1.66538i −1.07028 1.66538i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.163423 1.13663i 0.163423 1.13663i
\(613\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(614\) 0.544078 0.627899i 0.544078 0.627899i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.304632 + 0.474017i −0.304632 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(618\) 0 0
\(619\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.841254 0.540641i 0.841254 0.540641i
\(626\) 1.37491 0.627899i 1.37491 0.627899i
\(627\) −0.131891 + 0.288802i −0.131891 + 0.288802i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(632\) 0 0
\(633\) −0.398983 0.460451i −0.398983 0.460451i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(642\) 0.851677 + 0.737982i 0.851677 + 0.737982i
\(643\) −1.25667 0.368991i −1.25667 0.368991i −0.415415 0.909632i \(-0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.51722 2.18119i −2.51722 2.18119i
\(647\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(648\) −0.142315 + 0.0417874i −0.142315 + 0.0417874i
\(649\) −0.166390 + 0.258908i −0.166390 + 0.258908i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i
\(653\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.30972 1.30972
\(658\) 0 0
\(659\) 0.797176 + 1.74557i 0.797176 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(660\) 0 0
\(661\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(662\) 0.186393 0.215109i 0.186393 0.215109i
\(663\) 0 0
\(664\) −1.65486 0.755750i −1.65486 0.755750i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.30972 1.51150i 1.30972 1.51150i 0.654861 0.755750i \(-0.272727\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(674\) −1.95949 0.281733i −1.95949 0.281733i
\(675\) 0.948034i 0.948034i
\(676\) −0.415415 0.909632i −0.415415 0.909632i
\(677\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(678\) −1.02509 −1.02509
\(679\) 0 0
\(680\) 0 0
\(681\) 0.817178 0.708089i 0.817178 0.708089i
\(682\) 0 0
\(683\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(684\) −0.380655 + 1.29639i −0.380655 + 1.29639i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.584585 + 0.909632i 0.584585 + 0.909632i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −0.425839 + 0.194474i −0.425839 + 0.194474i
\(700\) 0 0
\(701\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.0405070 0.281733i −0.0405070 0.281733i
\(705\) 0 0
\(706\) 0.817178 1.27155i 0.817178 1.27155i
\(707\) 0 0
\(708\) 0.253098 0.554206i 0.253098 0.554206i
\(709\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.91153 + 2.20602i 1.91153 + 2.20602i
\(723\) 0.145886 1.01466i 0.145886 1.01466i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.391340 0.339098i 0.391340 0.339098i
\(727\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(728\) 0 0
\(729\) −0.364223 0.234072i −0.364223 0.234072i
\(730\) 0 0
\(731\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(732\) 0 0
\(733\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.357685 + 0.105026i −0.357685 + 0.105026i
\(738\) 0 0
\(739\) 0.425839 1.45027i 0.425839 1.45027i −0.415415 0.909632i \(-0.636364\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.349816 + 1.19136i 0.349816 + 1.19136i
\(748\) −0.198939 0.435615i −0.198939 0.435615i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(752\) 0 0
\(753\) −0.425839 0.194474i −0.425839 0.194474i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(758\) −1.49611 0.215109i −1.49611 0.215109i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(769\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(770\) 0 0
\(771\) −0.145886 0.0666238i −0.145886 0.0666238i
\(772\) 1.49611 0.215109i 1.49611 0.215109i
\(773\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(774\) 0.207914 0.708089i 0.207914 0.708089i
\(775\) 0 0
\(776\) 1.25667 0.368991i 1.25667 0.368991i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.841254 0.540641i −0.841254 0.540641i
\(785\) 0 0
\(786\) −0.584585 0.909632i −0.584585 0.909632i
\(787\) 1.37491 1.19136i 1.37491 1.19136i 0.415415 0.909632i \(-0.363636\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.127214 + 0.146813i −0.127214 + 0.146813i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(798\) 0 0
\(799\) 0 0