Properties

Label 2646.2.h.q.667.2
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 667.2
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.q.361.2

$q$-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 \(-0.536926\pi\)
−0.115747 + 0.993279i \(0.536926\pi\)
\(6\) 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 0.984373 0.176096i \(-0.0563468\pi\)
−0.644690 + 0.764444i \(0.723014\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.74238 3.01790i −0.422590 0.731947i 0.573602 0.819134i \(-0.305546\pi\)
−0.996192 + 0.0871869i \(0.972212\pi\)
\(18\) 0 0
\(19\) −0.258819 + 0.448288i −0.0593772 + 0.102844i −0.894186 0.447696i \(-0.852245\pi\)
0.834809 + 0.550540i \(0.185578\pi\)
\(20\) 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 \(0.396073\pi\)
−0.980638 + 0.195829i \(0.937260\pi\)
\(32\) −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 0.997818 0.0660290i \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 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 0.646816 0.762646i \(-0.276100\pi\)
−0.983879 + 0.178836i \(0.942767\pi\)
\(48\) 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 \(-0.419839\pi\)
0.714118 0.700025i \(-0.246828\pi\)
\(60\) 0 0
\(61\) −2.19067 3.79435i −0.280487 0.485817i 0.691018 0.722838i \(-0.257163\pi\)
−0.971505 + 0.237020i \(0.923829\pi\)
\(62\) 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 0.698522 0.715589i \(-0.253842\pi\)
−0.968979 + 0.247143i \(0.920508\pi\)
\(74\) −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 \(0.349494\pi\)
−0.998711 + 0.0507487i \(0.983839\pi\)
\(84\) 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 \(0.492429\pi\)
−0.877672 + 0.479263i \(0.840904\pi\)
\(90\) 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 −0.838549 0.544826i \(-0.816596\pi\)
0.891108 + 0.453792i \(0.149929\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.36603 4.09808i 0.236603 0.409808i
\(101\) −5.79555 −0.576679 −0.288340 0.957528i \(-0.593103\pi\)
−0.288340 + 0.957528i \(0.593103\pi\)
\(102\) 0 0
\(103\) −11.2122 −1.10477 −0.552384 0.833590i \(-0.686282\pi\)
−0.552384 + 0.833590i \(0.686282\pi\)
\(104\) 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 \(-0.683670\pi\)
−0.545527 + 0.838093i \(0.683670\pi\)
\(132\) 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 \(0.161200\pi\)
−0.0171736 + 0.999853i \(0.505467\pi\)
\(140\) 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 \(-0.591053\pi\)
0.971918 0.235320i \(-0.0756137\pi\)
\(158\) −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 \(0.00514202\pi\)
−0.485945 + 0.873989i \(0.661525\pi\)
\(168\) 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 \(-0.902324\pi\)
0.215048 0.976604i \(-0.431009\pi\)
\(174\) 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 \(-0.784503\pi\)
−0.779454 + 0.626459i \(0.784503\pi\)
\(182\) 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 0.584145 0.811649i \(-0.301430\pi\)
−0.994981 + 0.100060i \(0.968096\pi\)
\(200\) −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 −0.922110 0.386927i \(-0.873537\pi\)
0.796144 + 0.605108i \(0.206870\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.33013 + 12.6962i −0.487593 + 0.844535i
\(227\) −3.34607 −0.222086 −0.111043 0.993816i \(-0.535419\pi\)
−0.111043 + 0.993816i \(0.535419\pi\)
\(228\) 0 0
\(229\) 13.8004 0.911954 0.455977 0.889992i \(-0.349290\pi\)
0.455977 + 0.889992i \(0.349290\pi\)
\(230\) −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 \(-0.365550\pi\)
0.409939 + 0.912113i \(0.365550\pi\)
\(242\) 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 \(-0.494800\pi\)
0.0163365 + 0.999867i \(0.494800\pi\)
\(252\) 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 \(-0.537436\pi\)
−0.117339 + 0.993092i \(0.537436\pi\)
\(258\) 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 \(0.139516\pi\)
−0.0851918 + 0.996365i \(0.527150\pi\)
\(270\) 0 0
\(271\) −7.39924 + 12.8159i −0.449472 + 0.778508i −0.998352 0.0573934i \(-0.981721\pi\)
0.548880 + 0.835901i \(0.315054\pi\)
\(272\) −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 −0.973835 0.227255i \(-0.927025\pi\)
0.683726 + 0.729739i \(0.260358\pi\)
\(284\) −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 0.819431 0.573178i \(-0.194289\pi\)
−0.906102 + 0.423059i \(0.860956\pi\)
\(294\) 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 \(-0.610604\pi\)
−0.340523 + 0.940236i \(0.610604\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.80385 −0.216044
\(311\) 9.09085 15.7458i 0.515495 0.892863i −0.484343 0.874878i \(-0.660941\pi\)
0.999838 0.0179854i \(-0.00572524\pi\)
\(312\) 0 0
\(313\) 3.34607 + 5.79555i 0.189131 + 0.327584i 0.944961 0.327184i \(-0.106100\pi\)
−0.755830 + 0.654768i \(0.772766\pi\)
\(314\) −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 \(-0.456575\pi\)
0.789978 0.613136i \(-0.210092\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.732051 + 1.26795i −0.0390184 + 0.0675819i
\(353\) −0.101536 −0.00540421 −0.00270211 0.999996i \(-0.500860\pi\)
−0.00270211 + 0.999996i \(0.500860\pi\)
\(354\) 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 \(-0.502305\pi\)
−0.00724012 + 0.999974i \(0.502305\pi\)
\(368\) 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 \(-0.161359\pi\)
0.874243 + 0.485489i \(0.161359\pi\)
\(384\) 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 \(0.397055\pi\)
−0.980029 + 0.198855i \(0.936278\pi\)
\(398\) −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 −0.997700 0.0677865i \(-0.978406\pi\)
0.557555 + 0.830140i \(0.311740\pi\)
\(410\) −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 \(-0.979913\pi\)
0.444391 0.895833i \(-0.353420\pi\)
\(420\) 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 \(-0.661774\pi\)
−0.486631 + 0.873608i \(0.661774\pi\)
\(434\) 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 0.561095 0.827751i \(-0.310380\pi\)
−0.997401 + 0.0720474i \(0.977047\pi\)
\(440\) −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 \(-0.471161\pi\)
0.817235 0.576305i \(-0.195506\pi\)
\(462\) 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 \(-0.640628\pi\)
0.996656 0.0817131i \(-0.0260391\pi\)
\(468\) 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 \(-0.401861\pi\)
0.303452 + 0.952847i \(0.401861\pi\)
\(480\) 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 \(-0.723226\pi\)
−0.645199 + 0.764015i \(0.723226\pi\)
\(504\) 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 \(-0.445944\pi\)
0.169005 + 0.985615i \(0.445944\pi\)
\(510\) 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 \(-0.914223\pi\)
0.251395 0.967885i \(-0.419111\pi\)
\(522\) 0 0
\(523\) −19.6281 + 33.9969i −0.858277 + 1.48658i 0.0152941 + 0.999883i \(0.495132\pi\)
−0.873571 + 0.486696i \(0.838202\pi\)
\(524\) 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 −0.879152 0.476542i \(-0.841890\pi\)
0.852273 + 0.523097i \(0.175223\pi\)
\(564\) 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 \(-0.982363\pi\)
0.451272 0.892386i \(-0.350970\pi\)
\(578\) −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 −0.827393 0.561623i \(-0.810177\pi\)
0.900076 + 0.435732i \(0.143511\pi\)
\(588\) 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 −0.927304 0.374309i \(-0.877880\pi\)
0.787813 + 0.615915i \(0.211213\pi\)
\(594\) 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 \(-0.506580\pi\)
0.876176 0.481992i \(-0.160087\pi\)
\(602\) 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 \(-0.642926\pi\)
−0.434078 + 0.900875i \(0.642926\pi\)
\(608\) −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 \(-0.548078\pi\)
−0.150467 + 0.988615i \(0.548078\pi\)
\(620\) 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 0.882221 0.470835i \(-0.156047\pi\)
−0.848866 + 0.528608i \(0.822714\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.901924 1.56218i −0.0354857 0.0614631i
\(647\) −7.91688 13.7124i −0.311244 0.539091i 0.667388 0.744711i \(-0.267412\pi\)
−0.978632 + 0.205619i \(0.934079\pi\)
\(648\) 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 −0.995659 0.0930785i \(-0.970329\pi\)
0.578438 + 0.815727i \(0.303663\pi\)
\(662\) 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 0.876742 0.480962i \(-0.159712\pi\)
−0.854896 + 0.518800i \(0.826379\pi\)
\(678\) 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 \(0.0816878\pi\)
−0.263809 + 0.964575i \(0.584979\pi\)
\(692\) 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 \(0.385371\pi\)
−0.986667 + 0.162752i \(0.947963\pi\)
\(720\) 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 \(-0.647158\pi\)
0.998122 0.0612512i \(-0.0195091\pi\)
\(728\) 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 \(-0.312277\pi\)
0.556154 + 0.831079i \(0.312277\pi\)
\(734\) 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 \(-0.243729\pi\)
0.720900 + 0.693039i \(0.243729\pi\)
\(762\) 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 \(-0.985602\pi\)
0.460329 0.887748i \(-0.347732\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.8660 + 20.5526i 0.427068 + 0.739703i
\(773\) 6.76148 + 11.7112i 0.243194 + 0.421224i 0.961622 0.274377i \(-0.0884716\pi\)
−0.718429 + 0.695601i \(0.755138\pi\)
\(774\) 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 \(-0.610202\pi\)
0.984308 0.176461i \(-0.0564649\pi\)
\(788\) 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