Properties

Label 712.1.s.a.331.1
Level $712$
Weight $1$
Character 712.331
Analytic conductor $0.355$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
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.s (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: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 331.1
Root \(0.959493 + 0.281733i\) of defining polynomial
Character \(\chi\) \(=\) 712.331
Dual form 712.1.s.a.299.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.142315 - 0.989821i) q^{2} +(1.25667 + 0.368991i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.186393 - 1.29639i) q^{6} +(0.415415 + 0.909632i) q^{8} +(0.601808 + 0.386758i) q^{9} +O(q^{10})\) \(q+(-0.142315 - 0.989821i) q^{2} +(1.25667 + 0.368991i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.186393 - 1.29639i) q^{6} +(0.415415 + 0.909632i) q^{8} +(0.601808 + 0.386758i) q^{9} +(0.345139 - 0.755750i) q^{11} -1.30972 q^{12} +(0.841254 - 0.540641i) q^{16} +(0.0405070 - 0.281733i) q^{17} +(0.297176 - 0.650724i) q^{18} +(0.698939 + 0.449181i) q^{19} +(-0.797176 - 0.234072i) q^{22} +(0.186393 + 1.29639i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-0.244123 - 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{32} +(0.712591 - 0.822373i) q^{33} -0.284630 q^{34} +(-0.686393 - 0.201543i) q^{36} +(0.345139 - 0.755750i) q^{38} +(-1.91899 + 0.563465i) q^{41} +(-0.118239 + 0.258908i) q^{43} +(-0.118239 + 0.822373i) q^{44} +(1.25667 - 0.368991i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(0.841254 + 0.540641i) q^{50} +(0.154861 - 0.339098i) q^{51} +(-0.244123 + 0.281733i) q^{54} +(0.712591 + 0.822373i) q^{57} +(0.273100 - 0.0801894i) q^{59} +(-0.654861 + 0.755750i) q^{64} +(-0.915415 - 0.588302i) q^{66} +(-1.61435 - 0.474017i) q^{67} +(0.0405070 + 0.281733i) q^{68} +(-0.101808 + 0.708089i) q^{72} +(-1.10181 + 0.708089i) q^{73} +(-1.10181 + 0.708089i) q^{75} +(-0.797176 - 0.234072i) q^{76} +(-0.500000 - 1.09485i) q^{81} +(0.830830 + 1.81926i) q^{82} +(0.273100 - 1.89945i) q^{83} +(0.273100 + 0.0801894i) q^{86} +0.830830 q^{88} +(-0.654861 - 0.755750i) q^{89} +(-0.544078 - 1.19136i) q^{96} +(0.698939 + 1.53046i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.500000 - 0.321330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + O(q^{10}) \) \( 10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + 9q^{11} - 2q^{12} - q^{16} + 9q^{17} - 3q^{18} - 2q^{19} - 2q^{22} - 2q^{24} - q^{25} + 7q^{27} - q^{32} - 4q^{33} - 2q^{34} - 3q^{36} + 9q^{38} - 2q^{41} - 2q^{43} - 2q^{44} - 2q^{48} - q^{49} - q^{50} - 4q^{51} + 7q^{54} - 4q^{57} - 2q^{59} - q^{64} - 4q^{66} - 2q^{67} + 9q^{68} + 8q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 5q^{81} - 2q^{82} - 2q^{83} - 2q^{86} - 2q^{88} - q^{89} - 2q^{96} - 2q^{97} - q^{98} + 5q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{11}\right)\)

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
\(3\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(4\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(5\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(6\) 0.186393 1.29639i 0.186393 1.29639i
\(7\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(8\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(9\) 0.601808 + 0.386758i 0.601808 + 0.386758i
\(10\) 0 0
\(11\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(12\) −1.30972 −1.30972
\(13\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(14\) 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 \(-0.909091\pi\)
1.00000 \(0\)
\(18\) 0.297176 0.650724i 0.297176 0.650724i
\(19\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−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 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(24\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(25\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(26\) 0 0
\(27\) −0.244123 0.281733i −0.244123 0.281733i
\(28\) 0 0
\(29\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(30\) 0 0
\(31\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(32\) −0.654861 0.755750i −0.654861 0.755750i
\(33\) 0.712591 0.822373i 0.712591 0.822373i
\(34\) −0.284630 −0.284630
\(35\) 0 0
\(36\) −0.686393 0.201543i −0.686393 0.201543i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.345139 0.755750i 0.345139 0.755750i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.91899 + 0.563465i −1.91899 + 0.563465i −0.959493 + 0.281733i \(0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(42\) 0 0
\(43\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(44\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(48\) 1.25667 0.368991i 1.25667 0.368991i
\(49\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(50\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(51\) 0.154861 0.339098i 0.154861 0.339098i
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) −0.244123 + 0.281733i −0.244123 + 0.281733i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.712591 + 0.822373i 0.712591 + 0.822373i
\(58\) 0 0
\(59\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(60\) 0 0
\(61\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(65\) 0 0
\(66\) −0.915415 0.588302i −0.915415 0.588302i
\(67\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(68\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(72\) −0.101808 + 0.708089i −0.101808 + 0.708089i
\(73\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(74\) 0 0
\(75\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(76\) −0.797176 0.234072i −0.797176 0.234072i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(80\) 0 0
\(81\) −0.500000 1.09485i −0.500000 1.09485i
\(82\) 0.830830 + 1.81926i 0.830830 + 1.81926i
\(83\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(87\) 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
\(96\) −0.544078 1.19136i −0.544078 1.19136i
\(97\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(99\) 0.500000 0.321330i 0.500000 0.321330i
\(100\) 0.415415 0.909632i 0.415415 0.909632i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −0.357685 0.105026i −0.357685 0.105026i
\(103\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(104\) 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 \(-0.363636\pi\)
\(108\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(109\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(114\) 0.712591 0.822373i 0.712591 0.822373i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.118239 0.258908i −0.118239 0.258908i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.202824 + 0.234072i 0.202824 + 0.234072i
\(122\) 0 0
\(123\) −2.61944 −2.61944
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(128\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(129\) −0.244123 + 0.281733i −0.244123 + 0.281733i
\(130\) 0 0
\(131\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) −0.452036 + 0.989821i −0.452036 + 0.989821i
\(133\) 0 0
\(134\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(135\) 0 0
\(136\) 0.273100 0.0801894i 0.273100 0.0801894i
\(137\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(138\) 0 0
\(139\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.715370 0.715370
\(145\) 0 0
\(146\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(147\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(148\) 0 0
\(149\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(150\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(151\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(152\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(153\) 0.133340 0.153882i 0.133340 0.153882i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.01255 + 0.650724i −1.01255 + 0.650724i
\(163\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(164\) 1.68251 1.08128i 1.68251 1.08128i
\(165\) 0 0
\(166\) −1.91899 −1.91899
\(167\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(168\) 0 0
\(169\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(170\) 0 0
\(171\) 0.246902 + 0.540641i 0.246902 + 0.540641i
\(172\) 0.0405070 0.281733i 0.0405070 0.281733i
\(173\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.118239 0.822373i −0.118239 0.822373i
\(177\) 0.372786 0.372786
\(178\) −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 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(182\) 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 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(192\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(193\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
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 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(198\) −0.389217 0.449181i −0.389217 0.449181i
\(199\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(200\) −0.959493 0.281733i −0.959493 0.281733i
\(201\) −1.85380 1.19136i −1.85380 1.19136i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.0530529 + 0.368991i −0.0530529 + 0.368991i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.580699 0.373193i 0.580699 0.373193i
\(210\) 0 0
\(211\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.91899 0.563465i −1.91899 0.563465i
\(215\) 0 0
\(216\) 0.154861 0.339098i 0.154861 0.339098i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.64589 + 0.483276i −1.64589 + 0.483276i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(224\) 0 0
\(225\) −0.686393 + 0.201543i −0.686393 + 0.201543i
\(226\) 1.84125 0.540641i 1.84125 0.540641i
\(227\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(228\) −0.915415 0.588302i −0.915415 0.588302i
\(229\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(240\) 0 0
\(241\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(242\) 0.202824 0.234072i 0.202824 0.234072i
\(243\) −0.171292 1.19136i −0.171292 1.19136i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.372786 + 2.59278i 0.372786 + 2.59278i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.04408 2.28621i 1.04408 2.28621i
\(250\) 0 0
\(251\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 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 \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(258\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.544078 1.19136i −0.544078 1.19136i
\(263\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(264\) 1.04408 + 0.306569i 1.04408 + 0.306569i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.544078 1.19136i −0.544078 1.19136i
\(268\) 1.68251 1.68251
\(269\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(270\) 0 0
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) −0.118239 0.258908i −0.118239 0.258908i
\(273\) 0 0
\(274\) −0.118239 0.258908i −0.118239 0.258908i
\(275\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(276\) 0 0
\(277\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(278\) 0.345139 0.755750i 0.345139 0.755750i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(282\) 0 0
\(283\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.101808 0.708089i −0.101808 0.708089i
\(289\) 0.881761 + 0.258908i 0.881761 + 0.258908i
\(290\) 0 0
\(291\) 0.313607 + 2.18119i 0.313607 + 2.18119i
\(292\) 0.857685 0.989821i 0.857685 0.989821i
\(293\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.297176 + 0.0872586i −0.297176 + 0.0872586i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.857685 0.989821i 0.857685 0.989821i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.830830 0.830830
\(305\) 0 0
\(306\) −0.171292 0.110083i −0.171292 0.110083i
\(307\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(312\) 0 0
\(313\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.71537 1.97964i 1.71537 1.97964i
\(322\) 0 0
\(323\) 0.154861 0.178719i 0.154861 0.178719i
\(324\) 0.788201 + 0.909632i 0.788201 + 0.909632i
\(325\) 0 0
\(326\) 1.25667 0.368991i 1.25667 0.368991i
\(327\) 0 0
\(328\) −1.30972 1.51150i −1.30972 1.51150i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(332\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(338\) 0.415415 0.909632i 0.415415 0.909632i
\(339\) −0.357685 + 2.48775i −0.357685 + 2.48775i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.500000 0.321330i 0.500000 0.321330i
\(343\) 0 0
\(344\) −0.284630 −0.284630
\(345\) 0 0
\(346\) 0 0
\(347\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(348\) 0 0
\(349\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(353\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(354\) −0.0530529 0.368991i −0.0530529 0.368991i
\(355\) 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 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) 0 0
\(361\) −0.128663 0.281733i −0.128663 0.281733i
\(362\) 0 0
\(363\) 0.168513 + 0.368991i 0.168513 + 0.368991i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(368\) 0 0
\(369\) −1.37279 0.403086i −1.37279 0.403086i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(374\) −0.0982369 + 0.215109i −0.0982369 + 0.215109i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(384\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(385\) 0 0
\(386\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(387\) −0.171292 + 0.110083i −0.171292 + 0.110083i
\(388\) −1.10181 1.27155i −1.10181 1.27155i
\(389\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.959493 0.281733i −0.959493 0.281733i
\(393\) 1.71537 1.71537
\(394\) 0 0
\(395\) 0 0
\(396\) −0.389217 + 0.449181i −0.389217 + 0.449181i
\(397\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(401\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(402\) −0.915415 + 2.00448i −0.915415 + 2.00448i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.372786 0.372786
\(409\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(410\) 0 0
\(411\) 0.372786 0.372786
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.712591 + 0.822373i 0.712591 + 0.822373i
\(418\) −0.452036 0.521678i −0.452036 0.521678i
\(419\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(420\) 0 0
\(421\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(422\) −0.239446 0.153882i −0.239446 0.153882i
\(423\) 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 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(432\) −0.357685 0.105026i −0.357685 0.105026i
\(433\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.712591 + 1.56036i 0.712591 + 1.56036i
\(439\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(440\) 0 0
\(441\) −0.686393 + 0.201543i −0.686393 + 0.201543i
\(442\) 0 0
\(443\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 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 \(-0.181818\pi\)
1.00000 \(0\)
\(450\) 0.297176 + 0.650724i 0.297176 + 0.650724i
\(451\) −0.236479 + 1.64475i −0.236479 + 1.64475i
\(452\) −0.797176 1.74557i −0.797176 1.74557i
\(453\) 0 0
\(454\) −1.10181 0.708089i −1.10181 0.708089i
\(455\) 0 0
\(456\) −0.452036 + 0.989821i −0.452036 + 0.989821i
\(457\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(458\) 0 0
\(459\) −0.0892619 + 0.0573652i −0.0892619 + 0.0573652i
\(460\) 0 0
\(461\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(462\) 0 0
\(463\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(467\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(473\) 0.154861 + 0.178719i 0.154861 + 0.178719i
\(474\) 0 0
\(475\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.91899 −1.91899
\(483\) 0 0
\(484\) −0.260554 0.167448i −0.260554 0.167448i
\(485\) 0 0
\(486\) −1.15486 + 0.339098i −1.15486 + 0.339098i
\(487\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(488\) 0 0
\(489\) −0.244123 + 1.69791i −0.244123 + 1.69791i
\(490\) 0 0
\(491\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(492\) 2.51334 0.737982i 2.51334 0.737982i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −2.41153 0.708089i −2.41153 0.708089i
\(499\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(503\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(508\) 0 0
\(509\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 0.281733i −0.959493 0.281733i
\(513\) −0.0440780 0.306569i −0.0440780 0.306569i
\(514\) −0.544078 0.627899i −0.544078 0.627899i
\(515\) 0 0
\(516\) 0.154861 0.339098i 0.154861 0.339098i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(522\) 0 0
\(523\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(524\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.154861 1.07708i 0.154861 1.07708i
\(529\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(530\) 0 0
\(531\) 0.195368 + 0.0573652i 0.195368 + 0.0573652i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(535\) 0 0
\(536\) −0.239446 1.66538i −0.239446 1.66538i
\(537\) 2.11435 + 0.620830i 2.11435 + 0.620830i
\(538\) 0 0
\(539\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(540\) 0 0
\(541\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(548\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(549\) 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 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.202824 0.234072i −0.202824 0.234072i
\(562\) −0.544078 0.627899i −0.544078 0.627899i
\(563\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 0 0
\(571\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.686393 + 0.201543i −0.686393 + 0.201543i
\(577\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(578\) 0.130785 0.909632i 0.130785 0.909632i
\(579\) 0.313607 2.18119i 0.313607 2.18119i
\(580\) 0 0
\(581\) 0 0
\(582\) 2.11435 0.620830i 2.11435 0.620830i
\(583\) 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 \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(588\) 0.857685 0.989821i 0.857685 0.989821i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) 0.128663 + 0.281733i 0.128663 + 0.281733i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(600\) −1.10181 0.708089i −1.10181 0.708089i
\(601\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0 0
\(603\) −0.788201 0.909632i −0.788201 0.909632i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(608\) −0.118239 0.822373i −0.118239 0.822373i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0845850 + 0.185215i −0.0845850 + 0.185215i
\(613\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(614\) −1.61435 1.03748i −1.61435 1.03748i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(618\) 0 0
\(619\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 0.989821i −0.142315 0.989821i
\(626\) −1.61435 0.474017i −1.61435 0.474017i
\(627\) 0.867451 0.254707i 0.867451 0.254707i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(632\) 0 0
\(633\) 0.313607 0.201543i 0.313607 0.201543i
\(634\) 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 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(642\) −2.20362 1.41618i −2.20362 1.41618i
\(643\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.198939 0.127850i −0.198939 0.127850i
\(647\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(648\) 0.788201 0.909632i 0.788201 0.909632i
\(649\) 0.0336545 0.234072i 0.0336545 0.234072i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.544078 1.19136i −0.544078 1.19136i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.30972 + 1.51150i −1.30972 + 1.51150i
\(657\) −0.936936 −0.936936
\(658\) 0 0
\(659\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(660\) 0 0
\(661\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(662\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(663\) 0 0
\(664\) 1.84125 0.540641i 1.84125 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 \(0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(674\) 0.345139 0.755750i 0.345139 0.755750i
\(675\) 0.372786 0.372786
\(676\) −0.959493 0.281733i −0.959493 0.281733i
\(677\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(678\) 2.51334 2.51334
\(679\) 0 0
\(680\) 0 0
\(681\) 1.44306 0.927399i 1.44306 0.927399i
\(682\) 0 0
\(683\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(684\) −0.389217 0.449181i −0.389217 0.449181i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.0810141 + 0.563465i 0.0810141 + 0.563465i
\(698\) 0 0
\(699\) −2.41153 0.708089i −2.41153 0.708089i
\(700\) 0 0
\(701\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(705\) 0 0
\(706\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(707\) 0 0
\(708\) −0.357685 + 0.105026i −0.357685 + 0.105026i
\(709\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(710\) 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 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.260554 + 0.167448i −0.260554 + 0.167448i
\(723\) 1.04408 2.28621i 1.04408 2.28621i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.341254 0.219310i 0.341254 0.219310i
\(727\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(728\) 0 0
\(729\) 0.0530529 0.368991i 0.0530529 0.368991i
\(730\) 0 0
\(731\) 0.0681534 + 0.0437995i 0.0681534 + 0.0437995i
\(732\) 0 0
\(733\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(738\) −0.203616 + 1.41618i −0.203616 + 1.41618i
\(739\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.898983 1.03748i 0.898983 1.03748i
\(748\) 0.226900 + 0.0666238i 0.226900 + 0.0666238i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(752\) 0 0
\(753\) −2.41153 + 0.708089i −2.41153 + 0.708089i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(758\) 0.698939 1.53046i 0.698939 1.53046i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
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
\(768\) 0.857685 0.989821i 0.857685 0.989821i
\(769\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(770\) 0 0
\(771\) 1.04408 0.306569i 1.04408 0.306569i
\(772\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(773\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(774\) 0.133340 + 0.153882i 0.133340 + 0.153882i
\(775\) 0 0
\(776\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(777\) 0 0
\(778\) 0 0
\(779\) −1.59435 0.468144i −1.59435 0.468144i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(785\) 0 0
\(786\) −0.244123 1.69791i −0.244123 1.69791i
\(787\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.500000 + 0.321330i 0.500000 + 0.321330i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(798\) 0 0
\(799\) 0 0