Properties

Label 1386.2.k.f.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 462)
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.f.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} +4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(0.500000 - 2.59808i) q^{28} +1.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(1.50000 - 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +6.00000 q^{41} +1.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-0.500000 + 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(2.00000 + 1.73205i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 5.19615i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(-0.500000 + 0.866025i) q^{68} +15.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(1.50000 + 2.59808i) q^{74} -3.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(-3.00000 + 5.19615i) q^{82} +16.0000 q^{83} +(-0.500000 + 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(8.00000 + 6.92820i) q^{91} +1.00000 q^{92} +(-0.500000 - 0.866025i) q^{94} +7.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 4q^{7} + 2q^{8} - q^{11} + 8q^{13} - 5q^{14} - q^{16} - q^{17} + 3q^{19} + 2q^{22} - q^{23} + 5q^{25} - 4q^{26} + q^{28} + 2q^{29} - 6q^{31} - q^{32} + 2q^{34} + 3q^{37} + 3q^{38} + 12q^{41} + 2q^{43} - q^{44} - q^{46} - q^{47} + 2q^{49} - 10q^{50} - 4q^{52} + 4q^{56} - q^{58} + 7q^{59} - 6q^{61} + 12q^{62} + 2q^{64} + 4q^{67} - q^{68} + 30q^{71} - 12q^{73} + 3q^{74} - 6q^{76} + q^{77} - 6q^{82} + 32q^{83} - q^{86} - q^{88} - 8q^{89} + 16q^{91} + 2q^{92} - q^{94} + 14q^{97} - 13q^{98} + O(q^{100}) \)

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
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.500000 0.866025i −0.121268 0.210042i 0.799000 0.601331i \(-0.205363\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(18\) 0 0
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) 0 0
\(28\) 0.500000 2.59808i 0.0944911 0.490990i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 0 0
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) 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
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −0.500000 + 0.866025i −0.0729325 + 0.126323i −0.900185 0.435507i \(-0.856569\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 0 0
\(58\) −0.500000 + 0.866025i −0.0656532 + 0.113715i
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −0.500000 + 0.866025i −0.0606339 + 0.105021i
\(69\) 0 0
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i \(-0.918847\pi\)
0.265429 0.964130i \(-0.414486\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) 0.500000 2.59808i 0.0569803 0.296078i
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −4.00000 + 6.92820i −0.423999 + 0.734388i −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) 0 0
\(91\) 8.00000 + 6.92820i 0.838628 + 0.726273i
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) −0.500000 0.866025i −0.0515711 0.0893237i
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) 0 0
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.500000 0.866025i −0.0464238 0.0804084i
\(117\) 0 0
\(118\) −7.00000 −0.644402
\(119\) 0.500000 2.59808i 0.0458349 0.238165i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −3.00000 5.19615i −0.271607 0.470438i
\(123\) 0 0
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 + 1.73205i −0.0873704 + 0.151330i −0.906399 0.422423i \(-0.861180\pi\)
0.819028 + 0.573753i \(0.194513\pi\)
\(132\) 0 0
\(133\) 7.50000 2.59808i 0.650332 0.225282i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −0.500000 0.866025i −0.0428746 0.0742611i
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) −17.0000 −1.44192 −0.720961 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.50000 + 12.9904i −0.629386 + 1.09013i
\(143\) −2.00000 3.46410i −0.167248 0.289683i
\(144\) 0 0
\(145\) 0 0
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) −3.00000 −0.246598
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) 0 0
\(151\) −5.50000 9.52628i −0.447584 0.775238i 0.550645 0.834740i \(-0.314382\pi\)
−0.998228 + 0.0595022i \(0.981049\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) 0 0
\(154\) 2.00000 + 1.73205i 0.161165 + 0.139573i
\(155\) 0 0
\(156\) 0 0
\(157\) 4.50000 + 7.79423i 0.359139 + 0.622047i 0.987817 0.155618i \(-0.0497370\pi\)
−0.628678 + 0.777666i \(0.716404\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.50000 + 0.866025i −0.197028 + 0.0682524i
\(162\) 0 0
\(163\) 9.00000 15.5885i 0.704934 1.22098i −0.261781 0.965127i \(-0.584310\pi\)
0.966715 0.255855i \(-0.0823569\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −2.50000 + 12.9904i −0.188982 + 0.981981i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −4.00000 6.92820i −0.299813 0.519291i
\(179\) −12.5000 21.6506i −0.934294 1.61824i −0.775888 0.630870i \(-0.782698\pi\)
−0.158406 0.987374i \(-0.550635\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −10.0000 + 3.46410i −0.741249 + 0.256776i
\(183\) 0 0
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.500000 + 0.866025i −0.0365636 + 0.0633300i
\(188\) 1.00000 0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −27.0000 −1.92367 −0.961835 0.273629i \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) 0 0
\(202\) −15.0000 −1.05540
\(203\) 2.00000 + 1.73205i 0.140372 + 0.121566i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) 0 0
\(208\) −2.00000 + 3.46410i −0.138675 + 0.240192i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.00000 + 1.73205i 0.0683586 + 0.118401i
\(215\) 0 0
\(216\) 0 0
\(217\) 3.00000 15.5885i 0.203653 1.05821i
\(218\) −18.0000 −1.21911
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 0 0
\(226\) 2.00000 3.46410i 0.133038 0.230429i
\(227\) −1.00000 1.73205i −0.0663723 0.114960i 0.830930 0.556378i \(-0.187809\pi\)
−0.897302 + 0.441417i \(0.854476\pi\)
\(228\) 0 0
\(229\) 3.00000 5.19615i 0.198246 0.343371i −0.749714 0.661762i \(-0.769809\pi\)
0.947960 + 0.318390i \(0.103142\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −5.50000 + 9.52628i −0.360317 + 0.624087i −0.988013 0.154371i \(-0.950665\pi\)
0.627696 + 0.778459i \(0.283998\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.50000 6.06218i 0.227831 0.394614i
\(237\) 0 0
\(238\) 2.00000 + 1.73205i 0.129641 + 0.112272i
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 6.00000 10.3923i 0.381771 0.661247i
\(248\) −3.00000 5.19615i −0.190500 0.329956i
\(249\) 0 0
\(250\) 0 0
\(251\) 7.00000 0.441836 0.220918 0.975292i \(-0.429095\pi\)
0.220918 + 0.975292i \(0.429095\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 3.50000 6.06218i 0.219610 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i \(-0.955440\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(258\) 0 0
\(259\) 7.50000 2.59808i 0.466027 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) −1.00000 1.73205i −0.0617802 0.107006i
\(263\) −7.00000 12.1244i −0.431638 0.747620i 0.565376 0.824833i \(-0.308731\pi\)
−0.997015 + 0.0772134i \(0.975398\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.50000 + 7.79423i −0.0919709 + 0.477895i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 8.50000 14.7224i 0.509796 0.882993i
\(279\) 0 0
\(280\) 0 0
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) 0 0
\(283\) −10.0000 17.3205i −0.594438 1.02960i −0.993626 0.112728i \(-0.964041\pi\)
0.399188 0.916869i \(-0.369292\pi\)
\(284\) −7.50000 12.9904i −0.445043 0.770837i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 12.0000 + 10.3923i 0.708338 + 0.613438i
\(288\) 0 0
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) 0 0
\(291\) 0 0
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) 15.0000 0.876309 0.438155 0.898900i \(-0.355632\pi\)
0.438155 + 0.898900i \(0.355632\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) 0 0
\(298\) 0.500000 + 0.866025i 0.0289642 + 0.0501675i
\(299\) −2.00000 + 3.46410i −0.115663 + 0.200334i
\(300\) 0 0
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 11.0000 0.632979
\(303\) 0 0
\(304\) 1.50000 + 2.59808i 0.0860309 + 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) −2.50000 + 0.866025i −0.142451 + 0.0493464i
\(309\) 0 0
\(310\) 0 0
\(311\) −15.5000 26.8468i −0.878924 1.52234i −0.852523 0.522690i \(-0.824928\pi\)
−0.0264017 0.999651i \(-0.508405\pi\)
\(312\) 0 0
\(313\) 16.5000 28.5788i 0.932635 1.61537i 0.153838 0.988096i \(-0.450837\pi\)
0.778798 0.627275i \(-0.215830\pi\)
\(314\) −9.00000 −0.507899
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 0 0
\(319\) −0.500000 0.866025i −0.0279946 0.0484881i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.500000 2.59808i 0.0278639 0.144785i
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) 10.0000 + 17.3205i 0.554700 + 0.960769i
\(326\) 9.00000 + 15.5885i 0.498464 + 0.863365i
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) −2.50000 + 0.866025i −0.137829 + 0.0477455i
\(330\) 0 0
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) 0 0
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 0 0
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) −1.50000 + 2.59808i −0.0815892 + 0.141317i
\(339\) 0 0
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) −10.0000 17.3205i −0.536828 0.929814i −0.999072 0.0430610i \(-0.986289\pi\)
0.462244 0.886753i \(-0.347044\pi\)
\(348\) 0 0
\(349\) 32.0000 1.71292 0.856460 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) −10.0000 8.66025i −0.534522 0.462910i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −4.00000 6.92820i −0.212899 0.368751i 0.739722 0.672913i \(-0.234957\pi\)
−0.952620 + 0.304162i \(0.901624\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) 25.0000 1.32129
\(359\) 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) −11.0000 + 19.0526i −0.578147 + 1.00138i
\(363\) 0 0
\(364\) 2.00000 10.3923i 0.104828 0.544705i
\(365\) 0 0
\(366\) 0 0
\(367\) −10.0000 17.3205i −0.521996 0.904123i −0.999673 0.0255875i \(-0.991854\pi\)
0.477677 0.878536i \(-0.341479\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −17.0000 + 29.4449i −0.880227 + 1.52460i −0.0291379 + 0.999575i \(0.509276\pi\)
−0.851089 + 0.525022i \(0.824057\pi\)
\(374\) −0.500000 0.866025i −0.0258544 0.0447811i
\(375\) 0 0
\(376\) −0.500000 + 0.866025i −0.0257855 + 0.0446619i
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −22.0000 −1.13006 −0.565032 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −12.0000 20.7846i −0.613973 1.06343i
\(383\) 14.5000 25.1147i 0.740915 1.28330i −0.211164 0.977451i \(-0.567725\pi\)
0.952079 0.305852i \(-0.0989414\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) −14.0000 24.2487i −0.709828 1.22946i −0.964921 0.262542i \(-0.915439\pi\)
0.255092 0.966917i \(-0.417894\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) 1.00000 + 6.92820i 0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 13.5000 23.3827i 0.680120 1.17800i
\(395\) 0 0
\(396\) 0 0
\(397\) −11.5000 + 19.9186i −0.577168 + 0.999685i 0.418634 + 0.908155i \(0.362509\pi\)
−0.995802 + 0.0915300i \(0.970824\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 1.00000 1.73205i 0.0499376 0.0864945i −0.839976 0.542623i \(-0.817431\pi\)
0.889914 + 0.456129i \(0.150764\pi\)
\(402\) 0 0
\(403\) −12.0000 20.7846i −0.597763 1.03536i
\(404\) 7.50000 12.9904i 0.373139 0.646296i
\(405\) 0 0
\(406\) −2.50000 + 0.866025i −0.124073 + 0.0429801i
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i \(-0.214060\pi\)
−0.930614 + 0.366002i \(0.880726\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.00000 0.197066
\(413\) −3.50000 + 18.1865i −0.172224 + 0.894901i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 0 0
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) 17.0000 0.830504 0.415252 0.909706i \(-0.363693\pi\)
0.415252 + 0.909706i \(0.363693\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) 0 0
\(425\) 2.50000 4.33013i 0.121268 0.210042i
\(426\) 0 0
\(427\) −15.0000 + 5.19615i −0.725901 + 0.251459i
\(428\) −2.00000 −0.0966736
\(429\) 0 0
\(430\) 0 0
\(431\) −14.0000 24.2487i −0.674356 1.16802i −0.976657 0.214807i \(-0.931088\pi\)
0.302300 0.953213i \(-0.402245\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 12.0000 + 10.3923i 0.576018 + 0.498847i
\(435\) 0 0
\(436\) 9.00000 15.5885i 0.431022 0.746552i
\(437\) 1.50000 + 2.59808i 0.0717547 + 0.124283i
\(438\) 0 0
\(439\) 5.50000 9.52628i 0.262501 0.454665i −0.704405 0.709798i \(-0.748786\pi\)
0.966906 + 0.255134i \(0.0821195\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000 0.190261
\(443\) −1.50000 + 2.59808i −0.0712672 + 0.123438i −0.899457 0.437009i \(-0.856038\pi\)
0.828190 + 0.560448i \(0.189371\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 2.00000 + 3.46410i 0.0940721 + 0.162938i
\(453\) 0 0
\(454\) 2.00000 0.0938647
\(455\) 0 0
\(456\) 0 0
\(457\) −9.00000 + 15.5885i −0.421002 + 0.729197i −0.996038 0.0889312i \(-0.971655\pi\)
0.575036 + 0.818128i \(0.304988\pi\)
\(458\) 3.00000 + 5.19615i 0.140181 + 0.242800i
\(459\) 0 0
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −5.50000 9.52628i −0.254783 0.441296i
\(467\) −11.5000 + 19.9186i −0.532157 + 0.921722i 0.467139 + 0.884184i \(0.345285\pi\)
−0.999295 + 0.0375381i \(0.988048\pi\)
\(468\) 0 0
\(469\) −2.00000 + 10.3923i −0.0923514 + 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 3.50000 + 6.06218i 0.161101 + 0.279034i
\(473\) −0.500000 0.866025i −0.0229900 0.0398199i
\(474\) 0 0
\(475\) 15.0000 0.688247
\(476\) −2.50000 + 0.866025i −0.114587 + 0.0396942i
\(477\) 0 0
\(478\) 8.00000 13.8564i 0.365911 0.633777i
\(479\) 5.00000 + 8.66025i 0.228456 + 0.395697i 0.957351 0.288929i \(-0.0932990\pi\)
−0.728895 + 0.684626i \(0.759966\pi\)
\(480\) 0 0
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) −4.00000 −0.182195
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0 0
\(487\) −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i \(-0.316364\pi\)
−0.998579 + 0.0532853i \(0.983031\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) −0.500000 0.866025i −0.0225189 0.0390038i
\(494\) 6.00000 + 10.3923i 0.269953 + 0.467572i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 30.0000 + 25.9808i 1.34568 + 1.16540i
\(498\) 0 0
\(499\) −5.00000 + 8.66025i −0.223831 + 0.387686i −0.955968 0.293471i \(-0.905190\pi\)
0.732137 + 0.681157i \(0.238523\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.50000 + 6.06218i −0.156213 + 0.270568i
\(503\) −2.00000 −0.0891756 −0.0445878 0.999005i \(-0.514197\pi\)
−0.0445878 + 0.999005i \(0.514197\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.500000 + 0.866025i −0.0222277 + 0.0384995i
\(507\) 0 0
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) 2.00000 3.46410i 0.0886484 0.153544i −0.818292 0.574803i \(-0.805079\pi\)
0.906940 + 0.421260i \(0.138412\pi\)
\(510\) 0 0
\(511\) 6.00000 31.1769i 0.265424 1.37919i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −6.00000 10.3923i −0.264649 0.458385i
\(515\) 0 0
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) −1.50000 + 7.79423i −0.0659062 + 0.342459i
\(519\) 0 0
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) −22.0000 + 38.1051i −0.961993 + 1.66622i −0.244507 + 0.969648i \(0.578626\pi\)
−0.717486 + 0.696573i \(0.754707\pi\)
\(524\) 2.00000 0.0873704
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 5.19615i −0.260133 0.225282i
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) 0 0
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) −0.500000 + 0.866025i −0.0214373 + 0.0371305i
\(545\) 0 0
\(546\) 0 0
\(547\) 7.00000 0.299298 0.149649 0.988739i \(-0.452186\pi\)
0.149649 + 0.988739i \(0.452186\pi\)
\(548\) −2.00000 + 3.46410i −0.0854358 + 0.147979i
\(549\) 0 0
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) 1.50000 2.59808i 0.0639021 0.110682i
\(552\) 0 0
\(553\) 0 0
\(554\) −16.0000 −0.679775
\(555\) 0 0
\(556\) 8.50000 + 14.7224i 0.360480 + 0.624370i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 15.0000 0.629386
\(569\) 19.5000 33.7750i 0.817483 1.41592i −0.0900490 0.995937i \(-0.528702\pi\)
0.907532 0.419984i \(-0.137964\pi\)
\(570\) 0 0
\(571\) −3.50000 6.06218i −0.146470 0.253694i 0.783450 0.621455i \(-0.213458\pi\)
−0.929921 + 0.367760i \(0.880125\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 0 0
\(574\) −15.0000 + 5.19615i −0.626088 + 0.216883i
\(575\) −5.00000 −0.208514
\(576\) 0 0
\(577\) 11.0000 + 19.0526i 0.457936 + 0.793168i 0.998852 0.0479084i \(-0.0152556\pi\)
−0.540916 + 0.841077i \(0.681922\pi\)
\(578\) 8.00000 + 13.8564i 0.332756 + 0.576351i
\(579\) 0 0
\(580\) 0 0
\(581\) 32.0000 + 27.7128i 1.32758 + 1.14972i
\(582\) 0 0
\(583\) 0 0
\(584\) −6.00000 10.3923i −0.248282 0.430037i
\(585\) 0 0
\(586\) −7.50000 + 12.9904i −0.309822 + 0.536628i
\(587\) −4.00000 −0.165098 −0.0825488 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) 0 0
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) 0 0
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −9.50000 + 16.4545i −0.390118 + 0.675705i −0.992465 0.122530i \(-0.960899\pi\)
0.602347 + 0.798235i \(0.294233\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) −2.00000 3.46410i −0.0817861 0.141658i
\(599\) −20.0000 34.6410i −0.817178 1.41539i −0.907754 0.419504i \(-0.862204\pi\)
0.0905757 0.995890i \(-0.471129\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −2.50000 + 0.866025i −0.101892 + 0.0352966i
\(603\) 0 0
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) −2.00000 + 3.46410i −0.0809113 + 0.140143i
\(612\) 0 0
\(613\) −20.0000 34.6410i −0.807792 1.39914i −0.914390 0.404835i \(-0.867329\pi\)
0.106597 0.994302i \(-0.466004\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) 0 0
\(616\) 0.500000 2.59808i 0.0201456 0.104679i
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) 15.0000 + 25.9808i 0.602901 + 1.04425i 0.992379 + 0.123219i \(0.0393219\pi\)
−0.389479 + 0.921036i \(0.627345\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 31.0000 1.24299
\(623\) −20.0000 + 6.92820i −0.801283 + 0.277573i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 16.5000 + 28.5788i 0.659473 + 1.14224i
\(627\) 0 0
\(628\) 4.50000 7.79423i 0.179570 0.311024i
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) 4.00000 + 27.7128i 0.158486 + 1.09802i
\(638\) 1.00000 0.0395904
\(639\) 0 0
\(640\) 0 0
\(641\) 17.0000 + 29.4449i 0.671460 + 1.16300i 0.977490 + 0.210981i \(0.0676657\pi\)
−0.306031 + 0.952022i \(0.599001\pi\)
\(642\) 0 0
\(643\) −10.0000 −0.394362 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) 2.00000 + 1.73205i 0.0788110 + 0.0682524i
\(645\) 0 0
\(646\) 1.50000 2.59808i 0.0590167 0.102220i
\(647\) 4.00000 + 6.92820i 0.157256 + 0.272376i 0.933878 0.357591i \(-0.116402\pi\)
−0.776622 + 0.629967i \(0.783068\pi\)
\(648\) 0 0
\(649\) 3.50000 6.06218i 0.137387 0.237961i
\(650\) −20.0000 −0.784465
\(651\) 0 0
\(652\) −18.0000 −0.704934
\(653\) 24.0000 41.5692i 0.939193 1.62673i 0.172211 0.985060i \(-0.444909\pi\)
0.766982 0.641669i \(-0.221758\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) 0.500000 2.59808i 0.0194920 0.101284i
\(659\) −50.0000 −1.94772 −0.973862 0.227142i \(-0.927062\pi\)
−0.973862 + 0.227142i \(0.927062\pi\)
\(660\) 0 0
\(661\) 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i \(0.127103\pi\)
−0.123974 + 0.992286i \(0.539564\pi\)
\(662\) −5.00000 8.66025i −0.194331 0.336590i
\(663\) 0 0
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 0 0
\(667\) −0.500000 + 0.866025i −0.0193601 + 0.0335326i
\(668\) −6.00000 10.3923i −0.232147 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 13.0000 22.5167i 0.500741 0.867309i
\(675\) 0 0
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) 0 0
\(679\) 14.0000 + 12.1244i 0.537271 + 0.465290i
\(680\) 0 0
\(681\) 0 0
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) −0.500000 + 0.866025i −0.0190623 + 0.0330169i
\(689\) 0 0
\(690\) 0 0
\(691\) 17.0000 29.4449i 0.646710 1.12014i −0.337193 0.941435i \(-0.609478\pi\)
0.983904 0.178700i \(-0.0571891\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) 0 0
\(696\) 0 0
\(697\) −3.00000 5.19615i −0.113633 0.196818i
\(698\) −16.0000 + 27.7128i −0.605609 + 1.04895i
\(699\) 0 0
\(700\) 12.5000 4.33013i 0.472456 0.163663i
\(701\) −29.0000 −1.09531 −0.547657 0.836703i \(-0.684480\pi\)
−0.547657 + 0.836703i \(0.684480\pi\)
\(702\) 0 0
\(703\) −4.50000 7.79423i −0.169721 0.293965i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 8.00000 0.301084
\(707\) −7.50000 + 38.9711i −0.282067 + 1.46566i
\(708\) 0 0
\(709\) 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i \(-0.779279\pi\)
0.938069 + 0.346449i \(0.112613\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −4.00000 + 6.92820i −0.149906 + 0.259645i
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) −12.5000 + 21.6506i −0.467147 + 0.809122i
\(717\) 0 0
\(718\) 1.00000 + 1.73205i 0.0373197 + 0.0646396i
\(719\) −18.5000 + 32.0429i −0.689934 + 1.19500i 0.281925 + 0.959436i \(0.409027\pi\)
−0.971859 + 0.235564i \(0.924306\pi\)
\(720\) 0 0
\(721\) −10.0000 + 3.46410i −0.372419 + 0.129010i
\(722\) −10.0000 −0.372161
\(723\) 0 0
\(724\) −11.0000 19.0526i −0.408812 0.708083i
\(725\) 2.50000 + 4.33013i 0.0928477 + 0.160817i
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 8.00000 + 6.92820i 0.296500 + 0.256776i
\(729\) 0 0
\(730\) 0 0
\(731\) −0.500000 0.866025i −0.0184932 0.0320311i
\(732\) 0 0
\(733\) 5.00000 8.66025i 0.184679 0.319874i −0.758789 0.651336i \(-0.774209\pi\)
0.943468 + 0.331463i \(0.107542\pi\)
\(734\) 20.0000 0.738213
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 2.00000 3.46410i 0.0736709 0.127602i
\(738\) 0 0
\(739\) 10.0000 + 17.3205i 0.367856 + 0.637145i 0.989230 0.146369i \(-0.0467586\pi\)
−0.621374 + 0.783514i \(0.713425\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −17.0000 29.4449i −0.622414 1.07805i
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) 5.00000 1.73205i 0.182696 0.0632878i
\(750\) 0 0
\(751\) 17.0000 29.4449i 0.620339 1.07446i −0.369084 0.929396i \(-0.620328\pi\)
0.989423 0.145062i \(-0.0463382\pi\)
\(752\) −0.500000 0.866025i −0.0182331 0.0315807i
\(753\) 0 0
\(754\) −2.00000 + 3.46410i −0.0728357 + 0.126155i
\(755\) 0 0
\(756\) 0 0
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) 11.0000 19.0526i 0.399538 0.692020i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 0 0
\(763\) −9.00000 + 46.7654i −0.325822 + 1.69302i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 14.5000 + 25.1147i 0.523906 + 0.907432i
\(767\) 14.0000 + 24.2487i 0.505511 + 0.875570i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 7.00000 + 12.1244i 0.251773 + 0.436083i 0.964014 0.265852i \(-0.0856532\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(774\) 0 0
\(775\) 15.0000 25.9808i 0.538816 0.933257i
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) 28.0000 1.00385
\(779\) 9.00000 15.5885i 0.322458 0.558514i
\(780\) 0 0
\(781\) −7.50000 12.9904i −0.268371 0.464832i
\(782\) −0.500000 + 0.866025i −0.0178800 + 0.0309690i
\(783\) 0 0
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) 0 0
\(786\) 0 0
\(787\) 5.50000 + 9.52628i 0.196054 + 0.339575i 0.947245 0.320509i \(-0.103854\pi\)
−0.751192 + 0.660084i \(0.770521\pi\)
\(788\) 13.5000 + 23.3827i 0.480918 + 0.832974i
\(789\) 0 0
\(790\) 0 0
\(791\) −8.00000 6.92820i −0.284447 0.246339i
\(792\) 0 0
\(793\) −12.0000 + 20.7846i −0.426132 + 0.738083i
\(794\) −11.5000 19.9186i −0.408120 0.706884i
\(7