Properties

Label 1386.2.k.n.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.n.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} +5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +5.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(-2.50000 + 0.866025i) q^{56} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(3.50000 - 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} +12.0000 q^{71} +(5.00000 + 8.66025i) q^{73} +(1.00000 + 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} +(0.500000 - 0.866025i) q^{79} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(12.5000 - 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} -13.0000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 5q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 5q^{7} - 2q^{8} - q^{11} + 10q^{13} + q^{14} - q^{16} + 6q^{17} - 2q^{19} - 2q^{22} + 6q^{23} + 5q^{25} + 5q^{26} - 4q^{28} - 6q^{29} - 8q^{31} + q^{32} + 12q^{34} - 2q^{37} + 2q^{38} + 12q^{41} - 8q^{43} - q^{44} - 6q^{46} + 6q^{47} + 11q^{49} + 10q^{50} - 5q^{52} - 12q^{53} - 5q^{56} - 3q^{58} - 3q^{59} + 7q^{61} - 16q^{62} + 2q^{64} + 13q^{67} + 6q^{68} + 24q^{71} + 10q^{73} + 2q^{74} + 4q^{76} - 4q^{77} + q^{79} + 6q^{82} - 12q^{83} - 4q^{86} + q^{88} + 6q^{89} + 25q^{91} - 12q^{92} - 6q^{94} - 26q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 0 0
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 0 0
\(58\) −1.50000 + 2.59808i −0.196960 + 0.341144i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −2.00000 1.73205i −0.227921 0.197386i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 12.5000 4.33013i 1.31036 0.453921i
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 + 2.59808i −0.0472456 + 0.245495i
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) 12.0000 + 10.3923i 1.10004 + 0.952661i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −3.50000 6.06218i −0.316875 0.548844i
\(123\) 0 0
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 0 0
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 0 0
\(133\) −1.00000 + 5.19615i −0.0867110 + 0.450564i
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 7.50000 + 12.9904i 0.640768 + 1.10984i 0.985262 + 0.171054i \(0.0547174\pi\)
−0.344493 + 0.938789i \(0.611949\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) −2.50000 4.33013i −0.209061 0.362103i
\(144\) 0 0
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 0 0
\(154\) −2.50000 + 0.866025i −0.201456 + 0.0697863i
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) 0 0
\(160\) 0 0
\(161\) 3.00000 15.5885i 0.236433 1.22854i
\(162\) 0 0
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 0 0
\(175\) 10.0000 + 8.66025i 0.755929 + 0.654654i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 2.50000 12.9904i 0.185312 0.962911i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) 3.00000 5.19615i 0.219382 0.379980i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i \(0.124188\pi\)
−0.133056 + 0.991109i \(0.542479\pi\)
\(194\) −6.50000 + 11.2583i −0.466673 + 0.808301i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) 0 0
\(202\) 3.00000 0.211079
\(203\) −7.50000 + 2.59808i −0.526397 + 0.182349i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) 0 0
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −16.0000 13.8564i −1.08615 0.940634i
\(218\) −14.0000 −0.948200
\(219\) 0 0
\(220\) 0 0
\(221\) 15.0000 + 25.9808i 1.00901 + 1.74766i
\(222\) 0 0
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 2.00000 + 1.73205i 0.133631 + 0.115728i
\(225\) 0 0
\(226\) −4.50000 + 7.79423i −0.299336 + 0.518464i
\(227\) −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i \(-0.230474\pi\)
−0.948242 + 0.317547i \(0.897141\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −15.0000 + 25.9808i −0.982683 + 1.70206i −0.330870 + 0.943676i \(0.607342\pi\)
−0.651813 + 0.758380i \(0.725991\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 0 0
\(238\) 15.0000 5.19615i 0.972306 0.336817i
\(239\) −21.0000 −1.35838 −0.679189 0.733964i \(-0.737668\pi\)
−0.679189 + 0.733964i \(0.737668\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 + 8.66025i −0.318142 + 0.551039i
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −6.50000 + 11.2583i −0.407846 + 0.706410i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.5000 23.3827i 0.842107 1.45857i −0.0460033 0.998941i \(-0.514648\pi\)
0.888110 0.459631i \(-0.152018\pi\)
\(258\) 0 0
\(259\) −1.00000 + 5.19615i −0.0621370 + 0.322873i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i \(-0.196151\pi\)
−0.908560 + 0.417755i \(0.862817\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 + 3.46410i 0.245256 + 0.212398i
\(267\) 0 0
\(268\) 6.50000 11.2583i 0.397051 0.687712i
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) 12.5000 21.6506i 0.759321 1.31518i −0.183876 0.982949i \(-0.558865\pi\)
0.943197 0.332233i \(-0.107802\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 15.0000 0.906183
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 0 0
\(286\) −5.00000 −0.295656
\(287\) 15.0000 5.19615i 0.885422 0.306719i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 15.0000 25.9808i 0.867472 1.50251i
\(300\) 0 0
\(301\) −10.0000 + 3.46410i −0.576390 + 0.199667i
\(302\) 1.00000 0.0575435
\(303\) 0 0
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) −0.500000 + 2.59808i −0.0284901 + 0.148039i
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) 3.50000 6.06218i 0.197832 0.342655i −0.749993 0.661445i \(-0.769943\pi\)
0.947825 + 0.318791i \(0.103277\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i \(0.402086\pi\)
−0.976764 + 0.214318i \(0.931247\pi\)
\(318\) 0 0
\(319\) 1.50000 + 2.59808i 0.0839839 + 0.145464i
\(320\) 0 0
\(321\) 0 0
\(322\) −12.0000 10.3923i −0.668734 0.579141i
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 12.5000 + 21.6506i 0.693375 + 1.20096i
\(326\) 8.50000 + 14.7224i 0.470771 + 0.815400i
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 3.00000 15.5885i 0.165395 0.859419i
\(330\) 0 0
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 0 0
\(334\) −4.50000 + 7.79423i −0.246229 + 0.426481i
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) −4.00000 + 6.92820i −0.216612 + 0.375183i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 7.50000 + 12.9904i 0.403202 + 0.698367i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 12.5000 4.33013i 0.668153 0.231455i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i \(0.127637\pi\)
−0.122308 + 0.992492i \(0.539030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 9.00000 0.475665
\(359\) −4.50000 + 7.79423i −0.237501 + 0.411364i −0.959997 0.280012i \(-0.909662\pi\)
0.722496 + 0.691375i \(0.242995\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −5.00000 + 8.66025i −0.262794 + 0.455173i
\(363\) 0 0
\(364\) −10.0000 8.66025i −0.524142 0.453921i
\(365\) 0 0
\(366\) 0 0
\(367\) −19.0000 32.9090i −0.991792 1.71783i −0.606628 0.794986i \(-0.707478\pi\)
−0.385164 0.922848i \(-0.625855\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 20.7846i −1.24602 1.07908i
\(372\) 0 0
\(373\) −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) 0 0
\(388\) 6.50000 + 11.2583i 0.329988 + 0.571555i
\(389\) 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) −5.50000 + 4.33013i −0.277792 + 0.218704i
\(393\) 0 0
\(394\) 4.50000 7.79423i 0.226707 0.392668i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −14.0000 −0.701757
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −4.50000 + 7.79423i −0.224719 + 0.389225i −0.956235 0.292599i \(-0.905480\pi\)
0.731516 + 0.681824i \(0.238813\pi\)
\(402\) 0 0
\(403\) −20.0000 34.6410i −0.996271 1.72559i
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 0 0
\(406\) −1.50000 + 7.79423i −0.0744438 + 0.386821i
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) −6.00000 5.19615i −0.295241 0.255686i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) 0 0
\(418\) 1.00000 1.73205i 0.0489116 0.0847174i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) 13.0000 22.5167i 0.632830 1.09609i
\(423\) 0 0
\(424\) 6.00000 + 10.3923i 0.291386 + 0.504695i
\(425\) −15.0000 + 25.9808i −0.727607 + 1.26025i
\(426\) 0 0
\(427\) 3.50000 18.1865i 0.169377 0.880108i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −20.0000 + 6.92820i −0.960031 + 0.332564i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) 0 0
\(439\) 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i \(-0.683541\pi\)
0.998595 + 0.0529862i \(0.0168739\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −5.00000 + 8.66025i −0.236757 + 0.410075i
\(447\) 0 0
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 4.50000 + 7.79423i 0.211662 + 0.366610i
\(453\) 0 0
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 10.0000 + 17.3205i 0.467269 + 0.809334i
\(459\) 0 0
\(460\) 0 0
\(461\) −39.0000 −1.81641 −0.908206 0.418524i \(-0.862547\pi\)
−0.908206 + 0.418524i \(0.862547\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) 0 0
\(466\) 15.0000 + 25.9808i 0.694862 + 1.20354i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 0 0
\(469\) 26.0000 + 22.5167i 1.20057 + 1.03972i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 0 0
\(475\) −10.0000 −0.458831
\(476\) 3.00000 15.5885i 0.137505 0.714496i
\(477\) 0 0
\(478\) −10.5000 + 18.1865i −0.480259 + 0.831833i
\(479\) −1.50000 2.59808i −0.0685367 0.118709i 0.829721 0.558179i \(-0.188500\pi\)
−0.898257 + 0.439470i \(0.855166\pi\)
\(480\) 0 0
\(481\) −5.00000 + 8.66025i −0.227980 + 0.394874i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0 0
\(487\) 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 30.0000 10.3923i 1.34568 0.466159i
\(498\) 0 0
\(499\) −4.00000 + 6.92820i −0.179065 + 0.310149i −0.941560 0.336844i \(-0.890640\pi\)
0.762496 + 0.646993i \(0.223974\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.00000 + 5.19615i −0.133366 + 0.230997i
\(507\) 0 0
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) 20.0000 + 17.3205i 0.884748 + 0.766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −13.5000 23.3827i −0.595459 1.03137i
\(515\) 0 0
\(516\) 0 0
\(517\) −6.00000 −0.263880
\(518\) 4.00000 + 3.46410i 0.175750 + 0.152204i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 0 0
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) 24.0000 41.5692i 1.04546 1.81078i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 5.00000 1.73205i 0.216777 0.0750939i
\(533\) 30.0000 1.29944
\(534\) 0 0
\(535\) 0 0
\(536\) −6.50000 11.2583i −0.280757 0.486286i
\(537\) 0 0
\(538\) −24.0000 −1.03471
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) 0 0
\(541\) −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) −12.5000 21.6506i −0.536921 0.929974i
\(543\) 0 0
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 7.50000 12.9904i 0.320384 0.554922i
\(549\) 0 0
\(550\) −2.50000 4.33013i −0.106600 0.184637i
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) 0.500000 2.59808i 0.0212622 0.110481i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i \(-0.207238\pi\)
−0.922557 + 0.385860i \(0.873905\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) 0 0
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −2.50000 + 4.33013i −0.104530 + 0.181052i
\(573\) 0 0
\(574\) 3.00000 15.5885i 0.125218 0.650650i
\(575\) 30.0000 1.25109
\(576\) 0 0
\(577\) 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) −15.0000 + 5.19615i −0.622305 + 0.215573i
\(582\) 0 0
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) 0 0
\(586\) 9.00000 15.5885i 0.371787 0.643953i
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) −15.0000 25.9808i −0.613396 1.06243i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −2.00000 + 10.3923i −0.0815139 + 0.423559i
\(603\) 0 0
\(604\) 0.500000 0.866025i 0.0203447 0.0352381i
\(605\) 0 0
\(606\) 0 0
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 15.0000 25.9808i 0.606835 1.05107i
\(612\) 0 0
\(613\) −13.0000 22.5167i −0.525065 0.909439i −0.999574 0.0291886i \(-0.990708\pi\)
0.474509 0.880251i \(-0.342626\pi\)
\(614\) 16.0000 27.7128i 0.645707 1.11840i
\(615\) 0 0
\(616\) 2.00000 + 1.73205i 0.0805823 + 0.0697863i
\(617\) −21.0000 −0.845428 −0.422714 0.906263i \(-0.638923\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 3.00000 15.5885i 0.120192 0.624538i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −3.50000 6.06218i −0.139888 0.242293i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −0.500000 + 0.866025i −0.0198889 + 0.0344486i
\(633\) 0 0
\(634\) 12.0000 + 20.7846i 0.476581 + 0.825462i
\(635\) 0 0
\(636\) 0 0
\(637\) 27.5000 21.6506i 1.08959 0.857829i
\(638\) 3.00000 0.118771
\(639\) 0 0
\(640\) 0 0
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 0 0
\(643\) −19.0000 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(644\) −15.0000 + 5.19615i −0.591083 + 0.204757i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) 18.0000 + 31.1769i 0.707653 + 1.22569i 0.965726 + 0.259565i \(0.0835793\pi\)
−0.258073 + 0.966126i \(0.583087\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 25.0000 0.980581
\(651\) 0 0
\(652\) 17.0000 0.665771
\(653\) −15.0000 + 25.9808i −0.586995 + 1.01671i 0.407628 + 0.913148i \(0.366356\pi\)
−0.994623 + 0.103558i \(0.966977\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) −12.0000 10.3923i −0.467809 0.405134i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 17.0000 + 29.4449i 0.661223 + 1.14527i 0.980294 + 0.197542i \(0.0632958\pi\)
−0.319071 + 0.947731i \(0.603371\pi\)
\(662\) −6.50000 11.2583i −0.252630 0.437567i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) −9.00000 + 15.5885i −0.348481 + 0.603587i
\(668\) 4.50000 + 7.79423i 0.174110 + 0.301568i
\(669\) 0 0
\(670\) 0 0
\(671\) −7.00000 −0.270232
\(672\) 0 0
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) −32.5000 + 11.2583i −1.24724 + 0.432055i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.00000 + 6.92820i 0.153168 + 0.265295i
\(683\) −22.5000 38.9711i −0.860939 1.49119i −0.871024 0.491240i \(-0.836544\pi\)
0.0100856 0.999949i \(-0.496790\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −30.0000 51.9615i −1.14291 1.97958i
\(690\) 0 0
\(691\) −17.5000 + 30.3109i −0.665731 + 1.15308i 0.313355 + 0.949636i \(0.398547\pi\)
−0.979086 + 0.203445i \(0.934786\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) −17.0000 + 29.4449i −0.643459 + 1.11450i
\(699\) 0 0
\(700\) 2.50000 12.9904i 0.0944911 0.490990i
\(701\) 3.00000 0.113308 0.0566542 0.998394i \(-0.481957\pi\)
0.0566542 + 0.998394i \(0.481957\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) 6.00000 + 5.19615i 0.225653 + 0.195421i
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −48.0000 −1.79761
\(714\) 0 0
\(715\) 0 0
\(716\) 4.50000 7.79423i 0.168173 0.291284i
\(717\) 0 0
\(718\) 4.50000 + 7.79423i 0.167939 + 0.290878i
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) 2.00000 10.3923i 0.0744839 0.387030i
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) −7.50000 12.9904i −0.278543 0.482451i
\(726\) 0 0
\(727\) 50.0000 1.85440 0.927199 0.374570i \(-0.122210\pi\)
0.927199 + 0.374570i \(0.122210\pi\)
\(728\) −12.5000 + 4.33013i −0.463281 + 0.160485i
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) 21.5000 37.2391i 0.794121 1.37546i −0.129275 0.991609i \(-0.541265\pi\)
0.923396 0.383849i \(-0.125402\pi\)
\(734\) −38.0000 −1.40261
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 6.50000 11.2583i 0.239431 0.414706i
\(738\) 0 0
\(739\) −1.00000 1.73205i −0.0367856 0.0637145i 0.847046 0.531519i \(-0.178379\pi\)
−0.883832 + 0.467804i \(0.845045\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −30.0000 + 10.3923i −1.10133 + 0.381514i
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 5.50000 + 9.52628i 0.201369 + 0.348782i
\(747\) 0 0
\(748\) −6.00000 −0.219382
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −7.50000 + 12.9904i −0.273134 + 0.473082i
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) −12.5000 + 21.6506i −0.454020 + 0.786386i
\(759\) 0 0
\(760\) 0 0
\(761\) 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) 0 0
\(763\) −28.0000 24.2487i −1.01367 0.877862i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) −6.00000 10.3923i −0.216789 0.375489i
\(767\) −7.50000 12.9904i −0.270809 0.469055i
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.0000 19.0526i 0.395899 0.685717i
\(773\) −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i \(-0.308721\pi\)
−0.997012 + 0.0772449i \(0.975388\pi\)
\(774\) 0 0
\(775\) 20.0000 34.6410i 0.718421 1.24434i
\(776\) 13.0000 0.466673
\(777\) 0 0
\(778\) 12.0000 0.430221
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 18.0000 31.1769i 0.643679 1.11488i
\(783\) 0 0
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 12.1244i −0.249523 0.432187i 0.713871 0.700278i \(-0.246941\pi\)
−0.963394 + 0.268091i \(0.913607\pi\)
\(788\) −4.50000 7.79423i −0.160306 0.277658i
\(789\) 0 0
\(790\) 0 0
\(791\) −22.5000 + 7.79423i −0.800008 + 0.277131i
\(792\) 0 0
\(793\) 17.5000 30.3109i 0.621443 1.07637i
\(794\) 1.00000 +