Properties

Label 2646.2.h.q.667.3
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.q.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.517638 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.517638 q^{5} +1.00000 q^{8} +(-0.258819 - 0.448288i) q^{10} +1.46410 q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.74238 + 3.01790i) q^{17} +(0.258819 - 0.448288i) q^{19} +(-0.258819 + 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} -7.92820 q^{23} -4.73205 q^{25} +(-1.22474 + 2.12132i) q^{26} +(1.36603 - 2.36603i) q^{29} +(3.67423 - 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.74238 - 3.01790i) q^{34} +(4.00000 - 6.92820i) q^{37} -0.517638 q^{38} +0.517638 q^{40} +(-2.82843 - 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-0.732051 + 1.26795i) q^{44} +(3.96410 + 6.86603i) q^{46} +(2.31079 + 4.00240i) q^{47} +(2.36603 + 4.09808i) q^{50} +2.44949 q^{52} +(3.36603 + 5.83013i) q^{53} +0.757875 q^{55} -2.73205 q^{58} +(-7.39924 + 12.8159i) q^{59} +(2.19067 + 3.79435i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-0.633975 - 1.09808i) q^{65} +(1.90192 - 3.29423i) q^{67} -3.48477 q^{68} +0.803848 q^{71} +(2.31079 + 4.00240i) q^{73} -8.00000 q^{74} +(0.258819 + 0.448288i) q^{76} +(-7.06218 - 12.2321i) q^{79} +(-0.258819 - 0.448288i) q^{80} +(-2.82843 + 4.89898i) q^{82} +(4.94975 - 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} -12.1962 q^{86} +1.46410 q^{88} +(8.05558 - 13.9527i) q^{89} +(3.96410 - 6.86603i) q^{92} +(2.31079 - 4.00240i) q^{94} +(0.133975 - 0.232051i) q^{95} +(-0.517638 + 0.896575i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.517638 0.231495 0.115747 0.993279i \(-0.463074\pi\)
0.115747 + 0.993279i \(0.463074\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.258819 0.448288i −0.0818458 0.141761i
\(11\) 1.46410 0.441443 0.220722 0.975337i \(-0.429159\pi\)
0.220722 + 0.975337i \(0.429159\pi\)
\(12\) 0 0
\(13\) −1.22474 2.12132i −0.339683 0.588348i 0.644690 0.764444i \(-0.276986\pi\)
−0.984373 + 0.176096i \(0.943653\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.74238 + 3.01790i 0.422590 + 0.731947i 0.996192 0.0871869i \(-0.0277877\pi\)
−0.573602 + 0.819134i \(0.694454\pi\)
\(18\) 0 0
\(19\) 0.258819 0.448288i 0.0593772 0.102844i −0.834809 0.550540i \(-0.814422\pi\)
0.894186 + 0.447696i \(0.147755\pi\)
\(20\) −0.258819 + 0.448288i −0.0578737 + 0.100240i
\(21\) 0 0
\(22\) −0.732051 1.26795i −0.156074 0.270328i
\(23\) −7.92820 −1.65314 −0.826572 0.562831i \(-0.809712\pi\)
−0.826572 + 0.562831i \(0.809712\pi\)
\(24\) 0 0
\(25\) −4.73205 −0.946410
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.36603 2.36603i 0.253665 0.439360i −0.710867 0.703326i \(-0.751697\pi\)
0.964532 + 0.263966i \(0.0850307\pi\)
\(30\) 0 0
\(31\) 3.67423 6.36396i 0.659912 1.14300i −0.320726 0.947172i \(-0.603927\pi\)
0.980638 0.195829i \(-0.0627398\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.74238 3.01790i 0.298816 0.517565i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) −0.517638 −0.0839720
\(39\) 0 0
\(40\) 0.517638 0.0818458
\(41\) −2.82843 4.89898i −0.441726 0.765092i 0.556092 0.831121i \(-0.312300\pi\)
−0.997818 + 0.0660290i \(0.978967\pi\)
\(42\) 0 0
\(43\) 6.09808 10.5622i 0.929948 1.61072i 0.146544 0.989204i \(-0.453185\pi\)
0.783404 0.621513i \(-0.213482\pi\)
\(44\) −0.732051 + 1.26795i −0.110361 + 0.191151i
\(45\) 0 0
\(46\) 3.96410 + 6.86603i 0.584475 + 1.01234i
\(47\) 2.31079 + 4.00240i 0.337063 + 0.583811i 0.983879 0.178836i \(-0.0572331\pi\)
−0.646816 + 0.762646i \(0.723900\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.36603 + 4.09808i 0.334607 + 0.579555i
\(51\) 0 0
\(52\) 2.44949 0.339683
\(53\) 3.36603 + 5.83013i 0.462359 + 0.800830i 0.999078 0.0429316i \(-0.0136698\pi\)
−0.536719 + 0.843761i \(0.680336\pi\)
\(54\) 0 0
\(55\) 0.757875 0.102192
\(56\) 0 0
\(57\) 0 0
\(58\) −2.73205 −0.358736
\(59\) −7.39924 + 12.8159i −0.963299 + 1.66848i −0.249180 + 0.968457i \(0.580161\pi\)
−0.714118 + 0.700025i \(0.753172\pi\)
\(60\) 0 0
\(61\) 2.19067 + 3.79435i 0.280487 + 0.485817i 0.971505 0.237020i \(-0.0761708\pi\)
−0.691018 + 0.722838i \(0.742837\pi\)
\(62\) −7.34847 −0.933257
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.633975 1.09808i −0.0786349 0.136200i
\(66\) 0 0
\(67\) 1.90192 3.29423i 0.232357 0.402454i −0.726144 0.687542i \(-0.758690\pi\)
0.958501 + 0.285088i \(0.0920229\pi\)
\(68\) −3.48477 −0.422590
\(69\) 0 0
\(70\) 0 0
\(71\) 0.803848 0.0953992 0.0476996 0.998862i \(-0.484811\pi\)
0.0476996 + 0.998862i \(0.484811\pi\)
\(72\) 0 0
\(73\) 2.31079 + 4.00240i 0.270457 + 0.468446i 0.968979 0.247143i \(-0.0794917\pi\)
−0.698522 + 0.715589i \(0.746158\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) 0.258819 + 0.448288i 0.0296886 + 0.0514221i
\(77\) 0 0
\(78\) 0 0
\(79\) −7.06218 12.2321i −0.794557 1.37621i −0.923120 0.384512i \(-0.874370\pi\)
0.128563 0.991701i \(-0.458964\pi\)
\(80\) −0.258819 0.448288i −0.0289368 0.0501201i
\(81\) 0 0
\(82\) −2.82843 + 4.89898i −0.312348 + 0.541002i
\(83\) 4.94975 8.57321i 0.543305 0.941033i −0.455406 0.890284i \(-0.650506\pi\)
0.998711 0.0507487i \(-0.0161607\pi\)
\(84\) 0 0
\(85\) 0.901924 + 1.56218i 0.0978274 + 0.169442i
\(86\) −12.1962 −1.31514
\(87\) 0 0
\(88\) 1.46410 0.156074
\(89\) 8.05558 13.9527i 0.853889 1.47898i −0.0237822 0.999717i \(-0.507571\pi\)
0.877672 0.479263i \(-0.159096\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.96410 6.86603i 0.413286 0.715833i
\(93\) 0 0
\(94\) 2.31079 4.00240i 0.238340 0.412816i
\(95\) 0.133975 0.232051i 0.0137455 0.0238079i
\(96\) 0 0
\(97\) −0.517638 + 0.896575i −0.0525582 + 0.0910334i −0.891108 0.453792i \(-0.850071\pi\)
0.838549 + 0.544826i \(0.183404\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.36603 4.09808i 0.236603 0.409808i
\(101\) 5.79555 0.576679 0.288340 0.957528i \(-0.406897\pi\)
0.288340 + 0.957528i \(0.406897\pi\)
\(102\) 0 0
\(103\) 11.2122 1.10477 0.552384 0.833590i \(-0.313718\pi\)
0.552384 + 0.833590i \(0.313718\pi\)
\(104\) −1.22474 2.12132i −0.120096 0.208013i
\(105\) 0 0
\(106\) 3.36603 5.83013i 0.326937 0.566272i
\(107\) 1.53590 2.66025i 0.148481 0.257176i −0.782185 0.623046i \(-0.785895\pi\)
0.930666 + 0.365869i \(0.119228\pi\)
\(108\) 0 0
\(109\) −5.29423 9.16987i −0.507095 0.878315i −0.999966 0.00821222i \(-0.997386\pi\)
0.492871 0.870102i \(-0.335947\pi\)
\(110\) −0.378937 0.656339i −0.0361303 0.0625794i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.33013 12.6962i −0.689560 1.19435i −0.971980 0.235063i \(-0.924470\pi\)
0.282420 0.959291i \(-0.408863\pi\)
\(114\) 0 0
\(115\) −4.10394 −0.382694
\(116\) 1.36603 + 2.36603i 0.126832 + 0.219680i
\(117\) 0 0
\(118\) 14.7985 1.36231
\(119\) 0 0
\(120\) 0 0
\(121\) −8.85641 −0.805128
\(122\) 2.19067 3.79435i 0.198334 0.343525i
\(123\) 0 0
\(124\) 3.67423 + 6.36396i 0.329956 + 0.571501i
\(125\) −5.03768 −0.450584
\(126\) 0 0
\(127\) −5.92820 −0.526043 −0.263021 0.964790i \(-0.584719\pi\)
−0.263021 + 0.964790i \(0.584719\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.633975 + 1.09808i −0.0556033 + 0.0963077i
\(131\) 12.4877 1.09105 0.545527 0.838093i \(-0.316330\pi\)
0.545527 + 0.838093i \(0.316330\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3.80385 −0.328602
\(135\) 0 0
\(136\) 1.74238 + 3.01790i 0.149408 + 0.258782i
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −10.1075 17.5068i −0.857311 1.48491i −0.874485 0.485053i \(-0.838800\pi\)
0.0171736 0.999853i \(-0.494533\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.401924 0.696152i −0.0337287 0.0584198i
\(143\) −1.79315 3.10583i −0.149951 0.259722i
\(144\) 0 0
\(145\) 0.707107 1.22474i 0.0587220 0.101710i
\(146\) 2.31079 4.00240i 0.191242 0.331241i
\(147\) 0 0
\(148\) 4.00000 + 6.92820i 0.328798 + 0.569495i
\(149\) 2.39230 0.195985 0.0979926 0.995187i \(-0.468758\pi\)
0.0979926 + 0.995187i \(0.468758\pi\)
\(150\) 0 0
\(151\) −17.3923 −1.41537 −0.707683 0.706530i \(-0.750259\pi\)
−0.707683 + 0.706530i \(0.750259\pi\)
\(152\) 0.258819 0.448288i 0.0209930 0.0363609i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.90192 3.29423i 0.152766 0.264599i
\(156\) 0 0
\(157\) −8.64256 + 14.9694i −0.689752 + 1.19469i 0.282166 + 0.959366i \(0.408947\pi\)
−0.971918 + 0.235320i \(0.924386\pi\)
\(158\) −7.06218 + 12.2321i −0.561837 + 0.973130i
\(159\) 0 0
\(160\) −0.258819 + 0.448288i −0.0204614 + 0.0354403i
\(161\) 0 0
\(162\) 0 0
\(163\) 3.53590 6.12436i 0.276953 0.479697i −0.693673 0.720290i \(-0.744009\pi\)
0.970626 + 0.240593i \(0.0773421\pi\)
\(164\) 5.65685 0.441726
\(165\) 0 0
\(166\) −9.89949 −0.768350
\(167\) −6.64136 11.5032i −0.513924 0.890143i −0.999870 0.0161534i \(-0.994858\pi\)
0.485945 0.873989i \(-0.338475\pi\)
\(168\) 0 0
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) 0.901924 1.56218i 0.0691744 0.119814i
\(171\) 0 0
\(172\) 6.09808 + 10.5622i 0.464974 + 0.805359i
\(173\) 9.71003 + 16.8183i 0.738240 + 1.27867i 0.953287 + 0.302065i \(0.0976760\pi\)
−0.215048 + 0.976604i \(0.568991\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.732051 1.26795i −0.0551804 0.0955753i
\(177\) 0 0
\(178\) −16.1112 −1.20758
\(179\) −4.09808 7.09808i −0.306305 0.530535i 0.671246 0.741234i \(-0.265759\pi\)
−0.977551 + 0.210699i \(0.932426\pi\)
\(180\) 0 0
\(181\) 20.9730 1.55891 0.779454 0.626459i \(-0.215497\pi\)
0.779454 + 0.626459i \(0.215497\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −7.92820 −0.584475
\(185\) 2.07055 3.58630i 0.152230 0.263670i
\(186\) 0 0
\(187\) 2.55103 + 4.41851i 0.186549 + 0.323113i
\(188\) −4.62158 −0.337063
\(189\) 0 0
\(190\) −0.267949 −0.0194391
\(191\) −3.59808 6.23205i −0.260348 0.450935i 0.705987 0.708225i \(-0.250504\pi\)
−0.966334 + 0.257290i \(0.917171\pi\)
\(192\) 0 0
\(193\) 11.8660 20.5526i 0.854135 1.47941i −0.0233098 0.999728i \(-0.507420\pi\)
0.877445 0.479677i \(-0.159246\pi\)
\(194\) 1.03528 0.0743285
\(195\) 0 0
\(196\) 0 0
\(197\) −9.66025 −0.688265 −0.344132 0.938921i \(-0.611827\pi\)
−0.344132 + 0.938921i \(0.611827\pi\)
\(198\) 0 0
\(199\) 5.79555 + 10.0382i 0.410836 + 0.711589i 0.994981 0.100060i \(-0.0319035\pi\)
−0.584145 + 0.811649i \(0.698570\pi\)
\(200\) −4.73205 −0.334607
\(201\) 0 0
\(202\) −2.89778 5.01910i −0.203887 0.353142i
\(203\) 0 0
\(204\) 0 0
\(205\) −1.46410 2.53590i −0.102257 0.177115i
\(206\) −5.60609 9.71003i −0.390595 0.676530i
\(207\) 0 0
\(208\) −1.22474 + 2.12132i −0.0849208 + 0.147087i
\(209\) 0.378937 0.656339i 0.0262116 0.0453999i
\(210\) 0 0
\(211\) −0.633975 1.09808i −0.0436446 0.0755947i 0.843378 0.537321i \(-0.180564\pi\)
−0.887022 + 0.461726i \(0.847230\pi\)
\(212\) −6.73205 −0.462359
\(213\) 0 0
\(214\) −3.07180 −0.209984
\(215\) 3.15660 5.46739i 0.215278 0.372873i
\(216\) 0 0
\(217\) 0 0
\(218\) −5.29423 + 9.16987i −0.358570 + 0.621062i
\(219\) 0 0
\(220\) −0.378937 + 0.656339i −0.0255480 + 0.0442504i
\(221\) 4.26795 7.39230i 0.287093 0.497260i
\(222\) 0 0
\(223\) 1.88108 3.25813i 0.125967 0.218181i −0.796144 0.605108i \(-0.793130\pi\)
0.922110 + 0.386927i \(0.126463\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.33013 + 12.6962i −0.487593 + 0.844535i
\(227\) 3.34607 0.222086 0.111043 0.993816i \(-0.464581\pi\)
0.111043 + 0.993816i \(0.464581\pi\)
\(228\) 0 0
\(229\) −13.8004 −0.911954 −0.455977 0.889992i \(-0.650710\pi\)
−0.455977 + 0.889992i \(0.650710\pi\)
\(230\) 2.05197 + 3.55412i 0.135303 + 0.234351i
\(231\) 0 0
\(232\) 1.36603 2.36603i 0.0896840 0.155337i
\(233\) 0.696152 1.20577i 0.0456065 0.0789927i −0.842321 0.538976i \(-0.818811\pi\)
0.887928 + 0.459983i \(0.152145\pi\)
\(234\) 0 0
\(235\) 1.19615 + 2.07180i 0.0780284 + 0.135149i
\(236\) −7.39924 12.8159i −0.481649 0.834241i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.23205 10.7942i −0.403118 0.698221i 0.590983 0.806684i \(-0.298740\pi\)
−0.994100 + 0.108464i \(0.965407\pi\)
\(240\) 0 0
\(241\) −12.7279 −0.819878 −0.409939 0.912113i \(-0.634450\pi\)
−0.409939 + 0.912113i \(0.634450\pi\)
\(242\) 4.42820 + 7.66987i 0.284656 + 0.493038i
\(243\) 0 0
\(244\) −4.38134 −0.280487
\(245\) 0 0
\(246\) 0 0
\(247\) −1.26795 −0.0806777
\(248\) 3.67423 6.36396i 0.233314 0.404112i
\(249\) 0 0
\(250\) 2.51884 + 4.36276i 0.159305 + 0.275925i
\(251\) −0.517638 −0.0326730 −0.0163365 0.999867i \(-0.505200\pi\)
−0.0163365 + 0.999867i \(0.505200\pi\)
\(252\) 0 0
\(253\) −11.6077 −0.729770
\(254\) 2.96410 + 5.13397i 0.185984 + 0.322134i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.76217 0.234678 0.117339 0.993092i \(-0.462564\pi\)
0.117339 + 0.993092i \(0.462564\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.26795 0.0786349
\(261\) 0 0
\(262\) −6.24384 10.8147i −0.385746 0.668131i
\(263\) −2.66025 −0.164038 −0.0820191 0.996631i \(-0.526137\pi\)
−0.0820191 + 0.996631i \(0.526137\pi\)
\(264\) 0 0
\(265\) 1.74238 + 3.01790i 0.107034 + 0.185388i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.90192 + 3.29423i 0.116178 + 0.201227i
\(269\) −13.4536 23.3023i −0.820281 1.42077i −0.905473 0.424404i \(-0.860484\pi\)
0.0851918 0.996365i \(-0.472850\pi\)
\(270\) 0 0
\(271\) 7.39924 12.8159i 0.449472 0.778508i −0.548880 0.835901i \(-0.684946\pi\)
0.998352 + 0.0573934i \(0.0182789\pi\)
\(272\) 1.74238 3.01790i 0.105647 0.182987i
\(273\) 0 0
\(274\) 0 0
\(275\) −6.92820 −0.417786
\(276\) 0 0
\(277\) −16.1962 −0.973132 −0.486566 0.873644i \(-0.661751\pi\)
−0.486566 + 0.873644i \(0.661751\pi\)
\(278\) −10.1075 + 17.5068i −0.606210 + 1.04999i
\(279\) 0 0
\(280\) 0 0
\(281\) −8.69615 + 15.0622i −0.518769 + 0.898534i 0.480993 + 0.876724i \(0.340276\pi\)
−0.999762 + 0.0218099i \(0.993057\pi\)
\(282\) 0 0
\(283\) 4.88040 8.45310i 0.290109 0.502484i −0.683726 0.729739i \(-0.739642\pi\)
0.973835 + 0.227255i \(0.0729749\pi\)
\(284\) −0.401924 + 0.696152i −0.0238498 + 0.0413090i
\(285\) 0 0
\(286\) −1.79315 + 3.10583i −0.106031 + 0.183651i
\(287\) 0 0
\(288\) 0 0
\(289\) 2.42820 4.20577i 0.142835 0.247398i
\(290\) −1.41421 −0.0830455
\(291\) 0 0
\(292\) −4.62158 −0.270457
\(293\) 1.48356 + 2.56961i 0.0866707 + 0.150118i 0.906102 0.423059i \(-0.139044\pi\)
−0.819431 + 0.573178i \(0.805711\pi\)
\(294\) 0 0
\(295\) −3.83013 + 6.63397i −0.222999 + 0.386245i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) −1.19615 2.07180i −0.0692912 0.120016i
\(299\) 9.71003 + 16.8183i 0.561545 + 0.972625i
\(300\) 0 0
\(301\) 0 0
\(302\) 8.69615 + 15.0622i 0.500407 + 0.866731i
\(303\) 0 0
\(304\) −0.517638 −0.0296886
\(305\) 1.13397 + 1.96410i 0.0649312 + 0.112464i
\(306\) 0 0
\(307\) 11.9329 0.681046 0.340523 0.940236i \(-0.389396\pi\)
0.340523 + 0.940236i \(0.389396\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.80385 −0.216044
\(311\) −9.09085 + 15.7458i −0.515495 + 0.892863i 0.484343 + 0.874878i \(0.339059\pi\)
−0.999838 + 0.0179854i \(0.994275\pi\)
\(312\) 0 0
\(313\) −3.34607 5.79555i −0.189131 0.327584i 0.755830 0.654768i \(-0.227234\pi\)
−0.944961 + 0.327184i \(0.893900\pi\)
\(314\) 17.2851 0.975456
\(315\) 0 0
\(316\) 14.1244 0.794557
\(317\) 16.2942 + 28.2224i 0.915175 + 1.58513i 0.806645 + 0.591037i \(0.201281\pi\)
0.108530 + 0.994093i \(0.465386\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) 0.517638 0.0289368
\(321\) 0 0
\(322\) 0 0
\(323\) 1.80385 0.100369
\(324\) 0 0
\(325\) 5.79555 + 10.0382i 0.321480 + 0.556819i
\(326\) −7.07180 −0.391671
\(327\) 0 0
\(328\) −2.82843 4.89898i −0.156174 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) 6.02628 + 10.4378i 0.331234 + 0.573715i 0.982754 0.184917i \(-0.0592016\pi\)
−0.651520 + 0.758632i \(0.725868\pi\)
\(332\) 4.94975 + 8.57321i 0.271653 + 0.470516i
\(333\) 0 0
\(334\) −6.64136 + 11.5032i −0.363399 + 0.629426i
\(335\) 0.984508 1.70522i 0.0537894 0.0931660i
\(336\) 0 0
\(337\) 10.6603 + 18.4641i 0.580701 + 1.00580i 0.995396 + 0.0958434i \(0.0305548\pi\)
−0.414695 + 0.909960i \(0.636112\pi\)
\(338\) −7.00000 −0.380750
\(339\) 0 0
\(340\) −1.80385 −0.0978274
\(341\) 5.37945 9.31749i 0.291314 0.504570i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.09808 10.5622i 0.328786 0.569474i
\(345\) 0 0
\(346\) 9.71003 16.8183i 0.522014 0.904155i
\(347\) 10.8564 18.8038i 0.582802 1.00944i −0.412343 0.911029i \(-0.635289\pi\)
0.995145 0.0984148i \(-0.0313772\pi\)
\(348\) 0 0
\(349\) −17.2987 + 29.9623i −0.925980 + 1.60384i −0.136002 + 0.990709i \(0.543425\pi\)
−0.789978 + 0.613136i \(0.789908\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.732051 + 1.26795i −0.0390184 + 0.0675819i
\(353\) 0.101536 0.00540421 0.00270211 0.999996i \(-0.499140\pi\)
0.00270211 + 0.999996i \(0.499140\pi\)
\(354\) 0 0
\(355\) 0.416102 0.0220844
\(356\) 8.05558 + 13.9527i 0.426945 + 0.739490i
\(357\) 0 0
\(358\) −4.09808 + 7.09808i −0.216590 + 0.375145i
\(359\) −6.96410 + 12.0622i −0.367551 + 0.636617i −0.989182 0.146693i \(-0.953137\pi\)
0.621631 + 0.783310i \(0.286470\pi\)
\(360\) 0 0
\(361\) 9.36603 + 16.2224i 0.492949 + 0.853812i
\(362\) −10.4865 18.1631i −0.551157 0.954632i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.19615 + 2.07180i 0.0626095 + 0.108443i
\(366\) 0 0
\(367\) 0.277401 0.0144802 0.00724012 0.999974i \(-0.497695\pi\)
0.00724012 + 0.999974i \(0.497695\pi\)
\(368\) 3.96410 + 6.86603i 0.206643 + 0.357916i
\(369\) 0 0
\(370\) −4.14110 −0.215286
\(371\) 0 0
\(372\) 0 0
\(373\) 19.1244 0.990222 0.495111 0.868830i \(-0.335127\pi\)
0.495111 + 0.868830i \(0.335127\pi\)
\(374\) 2.55103 4.41851i 0.131910 0.228476i
\(375\) 0 0
\(376\) 2.31079 + 4.00240i 0.119170 + 0.206408i
\(377\) −6.69213 −0.344662
\(378\) 0 0
\(379\) −27.5167 −1.41344 −0.706718 0.707495i \(-0.749825\pi\)
−0.706718 + 0.707495i \(0.749825\pi\)
\(380\) 0.133975 + 0.232051i 0.00687275 + 0.0119040i
\(381\) 0 0
\(382\) −3.59808 + 6.23205i −0.184094 + 0.318859i
\(383\) −34.2185 −1.74849 −0.874243 0.485489i \(-0.838641\pi\)
−0.874243 + 0.485489i \(0.838641\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −23.7321 −1.20793
\(387\) 0 0
\(388\) −0.517638 0.896575i −0.0262791 0.0455167i
\(389\) 4.87564 0.247205 0.123602 0.992332i \(-0.460555\pi\)
0.123602 + 0.992332i \(0.460555\pi\)
\(390\) 0 0
\(391\) −13.8140 23.9265i −0.698602 1.21001i
\(392\) 0 0
\(393\) 0 0
\(394\) 4.83013 + 8.36603i 0.243338 + 0.421474i
\(395\) −3.65565 6.33178i −0.183936 0.318586i
\(396\) 0 0
\(397\) 13.1948 22.8541i 0.662228 1.14701i −0.317801 0.948157i \(-0.602945\pi\)
0.980029 0.198855i \(-0.0637222\pi\)
\(398\) 5.79555 10.0382i 0.290505 0.503169i
\(399\) 0 0
\(400\) 2.36603 + 4.09808i 0.118301 + 0.204904i
\(401\) 25.0526 1.25107 0.625533 0.780198i \(-0.284882\pi\)
0.625533 + 0.780198i \(0.284882\pi\)
\(402\) 0 0
\(403\) −18.0000 −0.896644
\(404\) −2.89778 + 5.01910i −0.144170 + 0.249709i
\(405\) 0 0
\(406\) 0 0
\(407\) 5.85641 10.1436i 0.290291 0.502799i
\(408\) 0 0
\(409\) 8.90138 15.4176i 0.440145 0.762354i −0.557555 0.830140i \(-0.688260\pi\)
0.997700 + 0.0677865i \(0.0215937\pi\)
\(410\) −1.46410 + 2.53590i −0.0723068 + 0.125239i
\(411\) 0 0
\(412\) −5.60609 + 9.71003i −0.276192 + 0.478379i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.56218 4.43782i 0.125772 0.217844i
\(416\) 2.44949 0.120096
\(417\) 0 0
\(418\) −0.757875 −0.0370689
\(419\) 11.3323 + 19.6281i 0.553619 + 0.958896i 0.998010 + 0.0630626i \(0.0200868\pi\)
−0.444391 + 0.895833i \(0.646580\pi\)
\(420\) 0 0
\(421\) −14.0263 + 24.2942i −0.683599 + 1.18403i 0.290276 + 0.956943i \(0.406253\pi\)
−0.973875 + 0.227085i \(0.927080\pi\)
\(422\) −0.633975 + 1.09808i −0.0308614 + 0.0534535i
\(423\) 0 0
\(424\) 3.36603 + 5.83013i 0.163469 + 0.283136i
\(425\) −8.24504 14.2808i −0.399943 0.692722i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.53590 + 2.66025i 0.0742405 + 0.128588i
\(429\) 0 0
\(430\) −6.31319 −0.304449
\(431\) −13.3923 23.1962i −0.645085 1.11732i −0.984282 0.176604i \(-0.943489\pi\)
0.339197 0.940715i \(-0.389845\pi\)
\(432\) 0 0
\(433\) 20.2523 0.973261 0.486631 0.873608i \(-0.338226\pi\)
0.486631 + 0.873608i \(0.338226\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10.5885 0.507095
\(437\) −2.05197 + 3.55412i −0.0981590 + 0.170016i
\(438\) 0 0
\(439\) 9.14162 + 15.8338i 0.436306 + 0.755704i 0.997401 0.0720474i \(-0.0229533\pi\)
−0.561095 + 0.827751i \(0.689620\pi\)
\(440\) 0.757875 0.0361303
\(441\) 0 0
\(442\) −8.53590 −0.406011
\(443\) −18.4904 32.0263i −0.878505 1.52161i −0.852982 0.521940i \(-0.825208\pi\)
−0.0255224 0.999674i \(-0.508125\pi\)
\(444\) 0 0
\(445\) 4.16987 7.22243i 0.197671 0.342376i
\(446\) −3.76217 −0.178144
\(447\) 0 0
\(448\) 0 0
\(449\) 23.7846 1.12247 0.561233 0.827658i \(-0.310327\pi\)
0.561233 + 0.827658i \(0.310327\pi\)
\(450\) 0 0
\(451\) −4.14110 7.17260i −0.194997 0.337745i
\(452\) 14.6603 0.689560
\(453\) 0 0
\(454\) −1.67303 2.89778i −0.0785193 0.135999i
\(455\) 0 0
\(456\) 0 0
\(457\) 11.1340 + 19.2846i 0.520825 + 0.902096i 0.999707 + 0.0242164i \(0.00770906\pi\)
−0.478881 + 0.877880i \(0.658958\pi\)
\(458\) 6.90018 + 11.9515i 0.322424 + 0.558455i
\(459\) 0 0
\(460\) 2.05197 3.55412i 0.0956736 0.165712i
\(461\) −19.4894 + 33.7566i −0.907712 + 1.57220i −0.0904771 + 0.995899i \(0.528839\pi\)
−0.817235 + 0.576305i \(0.804494\pi\)
\(462\) 0 0
\(463\) −3.33013 5.76795i −0.154764 0.268059i 0.778209 0.628005i \(-0.216128\pi\)
−0.932973 + 0.359946i \(0.882795\pi\)
\(464\) −2.73205 −0.126832
\(465\) 0 0
\(466\) −1.39230 −0.0644973
\(467\) −12.2982 + 21.3011i −0.569094 + 0.985699i 0.427562 + 0.903986i \(0.359372\pi\)
−0.996656 + 0.0817131i \(0.973961\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.19615 2.07180i 0.0551744 0.0955649i
\(471\) 0 0
\(472\) −7.39924 + 12.8159i −0.340577 + 0.589898i
\(473\) 8.92820 15.4641i 0.410519 0.711040i
\(474\) 0 0
\(475\) −1.22474 + 2.12132i −0.0561951 + 0.0973329i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.23205 + 10.7942i −0.285047 + 0.493717i
\(479\) −13.2827 −0.606903 −0.303452 0.952847i \(-0.598139\pi\)
−0.303452 + 0.952847i \(0.598139\pi\)
\(480\) 0 0
\(481\) −19.5959 −0.893497
\(482\) 6.36396 + 11.0227i 0.289870 + 0.502070i
\(483\) 0 0
\(484\) 4.42820 7.66987i 0.201282 0.348631i
\(485\) −0.267949 + 0.464102i −0.0121669 + 0.0210738i
\(486\) 0 0
\(487\) 16.1603 + 27.9904i 0.732291 + 1.26837i 0.955902 + 0.293687i \(0.0948822\pi\)
−0.223611 + 0.974679i \(0.571784\pi\)
\(488\) 2.19067 + 3.79435i 0.0991670 + 0.171762i
\(489\) 0 0
\(490\) 0 0
\(491\) −2.53590 4.39230i −0.114443 0.198222i 0.803114 0.595826i \(-0.203175\pi\)
−0.917557 + 0.397604i \(0.869842\pi\)
\(492\) 0 0
\(493\) 9.52056 0.428784
\(494\) 0.633975 + 1.09808i 0.0285239 + 0.0494048i
\(495\) 0 0
\(496\) −7.34847 −0.329956
\(497\) 0 0
\(498\) 0 0
\(499\) 7.32051 0.327711 0.163855 0.986484i \(-0.447607\pi\)
0.163855 + 0.986484i \(0.447607\pi\)
\(500\) 2.51884 4.36276i 0.112646 0.195109i
\(501\) 0 0
\(502\) 0.258819 + 0.448288i 0.0115517 + 0.0200081i
\(503\) 28.9406 1.29040 0.645199 0.764015i \(-0.276774\pi\)
0.645199 + 0.764015i \(0.276774\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 5.80385 + 10.0526i 0.258012 + 0.446891i
\(507\) 0 0
\(508\) 2.96410 5.13397i 0.131511 0.227783i
\(509\) −7.62587 −0.338011 −0.169005 0.985615i \(-0.554056\pi\)
−0.169005 + 0.985615i \(0.554056\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −1.88108 3.25813i −0.0829710 0.143710i
\(515\) 5.80385 0.255748
\(516\) 0 0
\(517\) 3.38323 + 5.85993i 0.148794 + 0.257719i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.633975 1.09808i −0.0278016 0.0481538i
\(521\) 16.2635 + 28.1691i 0.712515 + 1.23411i 0.963910 + 0.266228i \(0.0857773\pi\)
−0.251395 + 0.967885i \(0.580889\pi\)
\(522\) 0 0
\(523\) 19.6281 33.9969i 0.858277 1.48658i −0.0152941 0.999883i \(-0.504868\pi\)
0.873571 0.486696i \(-0.161798\pi\)
\(524\) −6.24384 + 10.8147i −0.272764 + 0.472440i
\(525\) 0 0
\(526\) 1.33013 + 2.30385i 0.0579963 + 0.100453i
\(527\) 25.6077 1.11549
\(528\) 0 0
\(529\) 39.8564 1.73289
\(530\) 1.74238 3.01790i 0.0756843 0.131089i
\(531\) 0 0
\(532\) 0 0
\(533\) −6.92820 + 12.0000i −0.300094 + 0.519778i
\(534\) 0 0
\(535\) 0.795040 1.37705i 0.0343726 0.0595350i
\(536\) 1.90192 3.29423i 0.0821506 0.142289i
\(537\) 0 0
\(538\) −13.4536 + 23.3023i −0.580026 + 1.00464i
\(539\) 0 0
\(540\) 0 0
\(541\) −10.3660 + 17.9545i −0.445670 + 0.771924i −0.998099 0.0616369i \(-0.980368\pi\)
0.552428 + 0.833560i \(0.313701\pi\)
\(542\) −14.7985 −0.635649
\(543\) 0 0
\(544\) −3.48477 −0.149408
\(545\) −2.74049 4.74668i −0.117390 0.203325i
\(546\) 0 0
\(547\) 5.73205 9.92820i 0.245085 0.424499i −0.717071 0.697000i \(-0.754518\pi\)
0.962155 + 0.272501i \(0.0878509\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 3.46410 + 6.00000i 0.147710 + 0.255841i
\(551\) −0.707107 1.22474i −0.0301238 0.0521759i
\(552\) 0 0
\(553\) 0 0
\(554\) 8.09808 + 14.0263i 0.344054 + 0.595920i
\(555\) 0 0
\(556\) 20.2151 0.857311
\(557\) 1.43782 + 2.49038i 0.0609225 + 0.105521i 0.894878 0.446311i \(-0.147262\pi\)
−0.833956 + 0.551832i \(0.813929\pi\)
\(558\) 0 0
\(559\) −29.8744 −1.26355
\(560\) 0 0
\(561\) 0 0
\(562\) 17.3923 0.733650
\(563\) 0.637756 1.10463i 0.0268782 0.0465545i −0.852273 0.523097i \(-0.824777\pi\)
0.879152 + 0.476542i \(0.158110\pi\)
\(564\) 0 0
\(565\) −3.79435 6.57201i −0.159630 0.276487i
\(566\) −9.76079 −0.410277
\(567\) 0 0
\(568\) 0.803848 0.0337287
\(569\) 13.4641 + 23.3205i 0.564445 + 0.977647i 0.997101 + 0.0760878i \(0.0242429\pi\)
−0.432657 + 0.901559i \(0.642424\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 3.58630 0.149951
\(573\) 0 0
\(574\) 0 0
\(575\) 37.5167 1.56455
\(576\) 0 0
\(577\) 13.1440 + 22.7661i 0.547193 + 0.947766i 0.998465 + 0.0553797i \(0.0176369\pi\)
−0.451272 + 0.892386i \(0.649030\pi\)
\(578\) −4.85641 −0.202000
\(579\) 0 0
\(580\) 0.707107 + 1.22474i 0.0293610 + 0.0508548i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.92820 + 8.53590i 0.204105 + 0.353521i
\(584\) 2.31079 + 4.00240i 0.0956211 + 0.165621i
\(585\) 0 0
\(586\) 1.48356 2.56961i 0.0612855 0.106150i
\(587\) −1.76097 + 3.05008i −0.0726828 + 0.125890i −0.900076 0.435732i \(-0.856489\pi\)
0.827393 + 0.561623i \(0.189823\pi\)
\(588\) 0 0
\(589\) −1.90192 3.29423i −0.0783674 0.135736i
\(590\) 7.66025 0.315368
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 3.39683 5.88349i 0.139491 0.241606i −0.787813 0.615915i \(-0.788787\pi\)
0.927304 + 0.374309i \(0.122120\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.19615 + 2.07180i −0.0489963 + 0.0848641i
\(597\) 0 0
\(598\) 9.71003 16.8183i 0.397073 0.687750i
\(599\) −6.19615 + 10.7321i −0.253168 + 0.438500i −0.964396 0.264461i \(-0.914806\pi\)
0.711228 + 0.702961i \(0.248139\pi\)
\(600\) 0 0
\(601\) −20.9730 + 36.3262i −0.855505 + 1.48178i 0.0206704 + 0.999786i \(0.493420\pi\)
−0.876176 + 0.481992i \(0.839913\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.69615 15.0622i 0.353841 0.612871i
\(605\) −4.58441 −0.186383
\(606\) 0 0
\(607\) 21.3891 0.868156 0.434078 0.900875i \(-0.357074\pi\)
0.434078 + 0.900875i \(0.357074\pi\)
\(608\) 0.258819 + 0.448288i 0.0104965 + 0.0181805i
\(609\) 0 0
\(610\) 1.13397 1.96410i 0.0459133 0.0795241i
\(611\) 5.66025 9.80385i 0.228989 0.396621i
\(612\) 0 0
\(613\) −10.2224 17.7058i −0.412880 0.715129i 0.582323 0.812957i \(-0.302144\pi\)
−0.995203 + 0.0978280i \(0.968810\pi\)
\(614\) −5.96644 10.3342i −0.240786 0.417054i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.1962 + 36.7128i 0.853325 + 1.47800i 0.878190 + 0.478311i \(0.158751\pi\)
−0.0248653 + 0.999691i \(0.507916\pi\)
\(618\) 0 0
\(619\) 7.48717 0.300935 0.150467 0.988615i \(-0.451922\pi\)
0.150467 + 0.988615i \(0.451922\pi\)
\(620\) 1.90192 + 3.29423i 0.0763831 + 0.132299i
\(621\) 0 0
\(622\) 18.1817 0.729020
\(623\) 0 0
\(624\) 0 0
\(625\) 21.0526 0.842102
\(626\) −3.34607 + 5.79555i −0.133736 + 0.231637i
\(627\) 0 0
\(628\) −8.64256 14.9694i −0.344876 0.597343i
\(629\) 27.8781 1.11157
\(630\) 0 0
\(631\) −3.87564 −0.154287 −0.0771435 0.997020i \(-0.524580\pi\)
−0.0771435 + 0.997020i \(0.524580\pi\)
\(632\) −7.06218 12.2321i −0.280918 0.486565i
\(633\) 0 0
\(634\) 16.2942 28.2224i 0.647126 1.12086i
\(635\) −3.06866 −0.121776
\(636\) 0 0
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) −0.258819 0.448288i −0.0102307 0.0177201i
\(641\) 3.05256 0.120569 0.0602844 0.998181i \(-0.480799\pi\)
0.0602844 + 0.998181i \(0.480799\pi\)
\(642\) 0 0
\(643\) −0.845807 1.46498i −0.0333554 0.0577732i 0.848866 0.528608i \(-0.177286\pi\)
−0.882221 + 0.470835i \(0.843953\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.901924 1.56218i −0.0354857 0.0614631i
\(647\) 7.91688 + 13.7124i 0.311244 + 0.539091i 0.978632 0.205619i \(-0.0659209\pi\)
−0.667388 + 0.744711i \(0.732588\pi\)
\(648\) 0 0
\(649\) −10.8332 + 18.7637i −0.425242 + 0.736540i
\(650\) 5.79555 10.0382i 0.227320 0.393730i
\(651\) 0 0
\(652\) 3.53590 + 6.12436i 0.138476 + 0.239848i
\(653\) 41.3205 1.61700 0.808498 0.588499i \(-0.200281\pi\)
0.808498 + 0.588499i \(0.200281\pi\)
\(654\) 0 0
\(655\) 6.46410 0.252573
\(656\) −2.82843 + 4.89898i −0.110432 + 0.191273i
\(657\) 0 0
\(658\) 0 0
\(659\) −19.5622 + 33.8827i −0.762034 + 1.31988i 0.179766 + 0.983709i \(0.442466\pi\)
−0.941800 + 0.336173i \(0.890867\pi\)
\(660\) 0 0
\(661\) 10.7267 18.5792i 0.417221 0.722648i −0.578438 0.815727i \(-0.696337\pi\)
0.995659 + 0.0930785i \(0.0296708\pi\)
\(662\) 6.02628 10.4378i 0.234218 0.405677i
\(663\) 0 0
\(664\) 4.94975 8.57321i 0.192087 0.332705i
\(665\) 0 0
\(666\) 0 0
\(667\) −10.8301 + 18.7583i −0.419344 + 0.726325i
\(668\) 13.2827 0.513924
\(669\) 0 0
\(670\) −1.96902 −0.0760697
\(671\) 3.20736 + 5.55532i 0.123819 + 0.214461i
\(672\) 0 0
\(673\) 20.0885 34.7942i 0.774353 1.34122i −0.160804 0.986986i \(-0.551409\pi\)
0.935157 0.354233i \(-0.115258\pi\)
\(674\) 10.6603 18.4641i 0.410618 0.711211i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) −0.568406 0.984508i −0.0218456 0.0378377i 0.854896 0.518800i \(-0.173621\pi\)
−0.876742 + 0.480962i \(0.840288\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.901924 + 1.56218i 0.0345872 + 0.0599068i
\(681\) 0 0
\(682\) −10.7589 −0.411980
\(683\) −6.80385 11.7846i −0.260342 0.450926i 0.705991 0.708221i \(-0.250502\pi\)
−0.966333 + 0.257295i \(0.917169\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −12.1962 −0.464974
\(689\) 8.24504 14.2808i 0.314111 0.544057i
\(690\) 0 0
\(691\) −18.4913 32.0279i −0.703442 1.21840i −0.967251 0.253822i \(-0.918312\pi\)
0.263809 0.964575i \(-0.415021\pi\)
\(692\) −19.4201 −0.738240
\(693\) 0 0
\(694\) −21.7128 −0.824207
\(695\) −5.23205 9.06218i −0.198463 0.343748i
\(696\) 0 0
\(697\) 9.85641 17.0718i 0.373338 0.646640i
\(698\) 34.5975 1.30953
\(699\) 0 0
\(700\) 0 0
\(701\) −20.5359 −0.775630 −0.387815 0.921737i \(-0.626770\pi\)
−0.387815 + 0.921737i \(0.626770\pi\)
\(702\) 0 0
\(703\) −2.07055 3.58630i −0.0780924 0.135260i
\(704\) 1.46410 0.0551804
\(705\) 0 0
\(706\) −0.0507680 0.0879327i −0.00191068 0.00330939i
\(707\) 0 0
\(708\) 0 0
\(709\) 11.2679 + 19.5167i 0.423177 + 0.732964i 0.996248 0.0865418i \(-0.0275816\pi\)
−0.573072 + 0.819505i \(0.694248\pi\)
\(710\) −0.208051 0.360355i −0.00780802 0.0135239i
\(711\) 0 0
\(712\) 8.05558 13.9527i 0.301895 0.522898i
\(713\) −29.1301 + 50.4548i −1.09093 + 1.88955i
\(714\) 0 0
\(715\) −0.928203 1.60770i −0.0347128 0.0601244i
\(716\) 8.19615 0.306305
\(717\) 0 0
\(718\) 13.9282 0.519796
\(719\) 17.0077 29.4582i 0.634281 1.09861i −0.352386 0.935855i \(-0.614629\pi\)
0.986667 0.162752i \(-0.0520372\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.36603 16.2224i 0.348567 0.603736i
\(723\) 0 0
\(724\) −10.4865 + 18.1631i −0.389727 + 0.675027i
\(725\) −6.46410 + 11.1962i −0.240071 + 0.415815i
\(726\) 0 0
\(727\) −14.8864 + 25.7840i −0.552106 + 0.956276i 0.446016 + 0.895025i \(0.352842\pi\)
−0.998122 + 0.0612512i \(0.980491\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.19615 2.07180i 0.0442716 0.0766806i
\(731\) 42.5007 1.57195
\(732\) 0 0
\(733\) −30.1146 −1.11231 −0.556154 0.831079i \(-0.687723\pi\)
−0.556154 + 0.831079i \(0.687723\pi\)
\(734\) −0.138701 0.240237i −0.00511954 0.00886730i
\(735\) 0 0
\(736\) 3.96410 6.86603i 0.146119 0.253085i
\(737\) 2.78461 4.82309i 0.102572 0.177661i
\(738\) 0 0
\(739\) 8.07180 + 13.9808i 0.296926 + 0.514291i 0.975431 0.220305i \(-0.0707052\pi\)
−0.678505 + 0.734596i \(0.737372\pi\)
\(740\) 2.07055 + 3.58630i 0.0761150 + 0.131835i
\(741\) 0 0
\(742\) 0 0
\(743\) −14.1244 24.4641i −0.518172 0.897501i −0.999777 0.0211123i \(-0.993279\pi\)
0.481605 0.876389i \(-0.340054\pi\)
\(744\) 0 0
\(745\) 1.23835 0.0453696
\(746\) −9.56218 16.5622i −0.350096 0.606384i
\(747\) 0 0
\(748\) −5.10205 −0.186549
\(749\) 0 0
\(750\) 0 0
\(751\) −50.1769 −1.83098 −0.915491 0.402339i \(-0.868197\pi\)
−0.915491 + 0.402339i \(0.868197\pi\)
\(752\) 2.31079 4.00240i 0.0842658 0.145953i
\(753\) 0 0
\(754\) 3.34607 + 5.79555i 0.121857 + 0.211062i
\(755\) −9.00292 −0.327650
\(756\) 0 0
\(757\) 20.2487 0.735952 0.367976 0.929835i \(-0.380051\pi\)
0.367976 + 0.929835i \(0.380051\pi\)
\(758\) 13.7583 + 23.8301i 0.499725 + 0.865549i
\(759\) 0 0
\(760\) 0.133975 0.232051i 0.00485977 0.00841737i
\(761\) −39.7738 −1.44180 −0.720900 0.693039i \(-0.756271\pi\)
−0.720900 + 0.693039i \(0.756271\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 7.19615 0.260348
\(765\) 0 0
\(766\) 17.1093 + 29.6341i 0.618183 + 1.07072i
\(767\) 36.2487 1.30887
\(768\) 0 0
\(769\) 14.9372 + 25.8719i 0.538648 + 0.932966i 0.998977 + 0.0452178i \(0.0143982\pi\)
−0.460329 + 0.887748i \(0.652268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.8660 + 20.5526i 0.427068 + 0.739703i
\(773\) −6.76148 11.7112i −0.243194 0.421224i 0.718429 0.695601i \(-0.244862\pi\)
−0.961622 + 0.274377i \(0.911528\pi\)
\(774\) 0 0
\(775\) −17.3867 + 30.1146i −0.624547 + 1.08175i
\(776\) −0.517638 + 0.896575i −0.0185821 + 0.0321852i
\(777\) 0 0
\(778\) −2.43782 4.22243i −0.0874002 0.151382i
\(779\) −2.92820 −0.104914
\(780\) 0 0
\(781\) 1.17691 0.0421133
\(782\) −13.8140 + 23.9265i −0.493986 + 0.855610i
\(783\) 0 0
\(784\) 0 0
\(785\) −4.47372 + 7.74871i −0.159674 + 0.276563i
\(786\) 0 0
\(787\) −18.0938 + 31.3393i −0.644973 + 1.11713i 0.339334 + 0.940666i \(0.389798\pi\)
−0.984308 + 0.176461i \(0.943535\pi\)
\(788\) 4.83013 8.36603i 0.172066 0.298027i
\(789\) 0 0
\(790\) −3.65565 + 6.33178i −0.130062 + 0.225274i
\(791\) 0 0
\(792\) 0 0
\(793\) 5.36603 9.29423i 0.190553 0.330048i
\(794\) −26.3896 −0.936531
\(795\) 0