Properties

Label 462.2.i.d.331.1
Level $462$
Weight $2$
Character 462.331
Analytic conductor $3.689$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 462.331
Dual form 462.2.i.d.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.50000 - 2.59808i) q^{19} +(-0.500000 + 2.59808i) q^{21} +1.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -1.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +1.00000 q^{34} +1.00000 q^{36} +(1.50000 - 2.59808i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(2.00000 + 3.46410i) q^{39} -6.00000 q^{41} +(2.00000 + 1.73205i) q^{42} +1.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(0.500000 - 0.866025i) q^{47} -1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +5.00000 q^{50} +(-0.500000 + 0.866025i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-0.500000 + 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +3.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-3.50000 - 6.06218i) q^{59} +(-3.00000 + 5.19615i) q^{61} -6.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(2.00000 + 3.46410i) q^{67} +(0.500000 - 0.866025i) q^{68} +1.00000 q^{69} -15.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.00000 - 10.3923i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(-2.50000 + 4.33013i) q^{75} -3.00000 q^{76} +(-0.500000 + 2.59808i) q^{77} +4.00000 q^{78} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -16.0000 q^{83} +(2.50000 - 0.866025i) q^{84} +(0.500000 - 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(4.00000 - 6.92820i) q^{89} +(8.00000 + 6.92820i) q^{91} -1.00000 q^{92} +(3.00000 - 5.19615i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(6.50000 + 2.59808i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{6} + 4q^{7} - 2q^{8} - q^{9} + q^{11} + q^{12} + 8q^{13} + 5q^{14} - q^{16} + q^{17} + q^{18} + 3q^{19} - q^{21} + 2q^{22} + q^{23} - q^{24} + 5q^{25} + 4q^{26} - 2q^{27} + q^{28} - 2q^{29} - 6q^{31} + q^{32} - q^{33} + 2q^{34} + 2q^{36} + 3q^{37} - 3q^{38} + 4q^{39} - 12q^{41} + 4q^{42} + 2q^{43} + q^{44} - q^{46} + q^{47} - 2q^{48} + 2q^{49} + 10q^{50} - q^{51} - 4q^{52} - q^{54} - 4q^{56} + 6q^{57} - q^{58} - 7q^{59} - 6q^{61} - 12q^{62} - 5q^{63} + 2q^{64} + q^{66} + 4q^{67} + q^{68} + 2q^{69} - 30q^{71} + q^{72} - 12q^{73} - 3q^{74} - 5q^{75} - 6q^{76} - q^{77} + 8q^{78} - q^{81} - 6q^{82} - 32q^{83} + 5q^{84} + q^{86} - q^{87} - q^{88} + 8q^{89} + 16q^{91} - 2q^{92} + 6q^{93} - q^{94} - q^{96} + 14q^{97} + 13q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 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 0.920268 0.391289i \(-0.127971\pi\)
−0.799000 + 0.601331i \(0.794637\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 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
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 1.00000 0.213201
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 2.00000 3.46410i 0.392232 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 0.500000 2.59808i 0.0944911 0.490990i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 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
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 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
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 2.00000 + 1.73205i 0.308607 + 0.267261i
\(43\) 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 −0.827253 0.561830i \(-0.810098\pi\)
0.900185 + 0.435507i \(0.143431\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 5.00000 0.707107
\(51\) −0.500000 + 0.866025i −0.0700140 + 0.121268i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 3.00000 0.397360
\(58\) −0.500000 + 0.866025i −0.0656532 + 0.113715i
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 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
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) 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
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −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
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) −3.00000 −0.344124
\(77\) −0.500000 + 2.59808i −0.0569803 + 0.296078i
\(78\) 4.00000 0.452911
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) −16.0000 −1.75623 −0.878114 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 2.50000 0.866025i 0.272772 0.0944911i
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.0539164 0.0933859i
\(87\) −0.500000 0.866025i −0.0536056 0.0928477i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 4.00000 6.92820i 0.423999 0.734388i −0.572327 0.820025i \(-0.693959\pi\)
0.996326 + 0.0856373i \(0.0272926\pi\)
\(90\) 0 0
\(91\) 8.00000 + 6.92820i 0.838628 + 0.726273i
\(92\) −1.00000 −0.104257
\(93\) 3.00000 5.19615i 0.311086 0.538816i
\(94\) −0.500000 0.866025i −0.0515711 0.0893237i
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 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
\(99\) −1.00000 −0.100504
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0.500000 + 0.866025i 0.0495074 + 0.0857493i
\(103\) −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 −0.910306 0.413936i \(-0.864154\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 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
\(111\) 3.00000 0.284747
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 1.50000 2.59808i 0.140488 0.243332i
\(115\) 0 0
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) −2.00000 + 3.46410i −0.184900 + 0.320256i
\(118\) −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
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 0 0
\(126\) −0.500000 + 2.59808i −0.0445435 + 0.231455i
\(127\) −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
\(129\) 0.500000 + 0.866025i 0.0440225 + 0.0762493i
\(130\) 0 0
\(131\) 1.00000 1.73205i 0.0873704 0.151330i −0.819028 0.573753i \(-0.805487\pi\)
0.906399 + 0.422423i \(0.138820\pi\)
\(132\) 1.00000 0.0870388
\(133\) 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 0.938725 0.344668i \(-0.112008\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) −17.0000 −1.44192 −0.720961 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) 0 0
\(141\) 1.00000 0.0842152
\(142\) −7.50000 + 12.9904i −0.629386 + 1.09013i
\(143\) 2.00000 + 3.46410i 0.167248 + 0.289683i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −12.0000 −0.993127
\(147\) −5.50000 + 4.33013i −0.453632 + 0.357143i
\(148\) −3.00000 −0.246598
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 2.50000 + 4.33013i 0.204124 + 0.353553i
\(151\) −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
\(153\) −1.00000 −0.0808452
\(154\) 2.00000 + 1.73205i 0.161165 + 0.139573i
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 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
\(162\) −1.00000 −0.0785674
\(163\) 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 \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0.500000 2.59808i 0.0385758 0.200446i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 1.50000 + 2.59808i 0.114708 + 0.198680i
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −1.00000 −0.0758098
\(175\) −2.50000 + 12.9904i −0.188982 + 0.981981i
\(176\) −1.00000 −0.0753778
\(177\) 3.50000 6.06218i 0.263076 0.455661i
\(178\) −4.00000 6.92820i −0.299813 0.519291i
\(179\) 12.5000 + 21.6506i 0.934294 + 1.61824i 0.775888 + 0.630870i \(0.217302\pi\)
0.158406 + 0.987374i \(0.449365\pi\)
\(180\) 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
\(183\) −6.00000 −0.443533
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) −0.500000 + 0.866025i −0.0365636 + 0.0633300i
\(188\) −1.00000 −0.0729325
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) 12.0000 20.7846i 0.868290 1.50392i 0.00454614 0.999990i \(-0.498553\pi\)
0.863743 0.503932i \(-0.168114\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −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 \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) −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
\(201\) −2.00000 + 3.46410i −0.141069 + 0.244339i
\(202\) −15.0000 −1.05540
\(203\) −2.00000 1.73205i −0.140372 0.121566i
\(204\) 1.00000 0.0700140
\(205\) 0 0
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) −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
\(213\) −7.50000 12.9904i −0.513892 0.890086i
\(214\) 1.00000 + 1.73205i 0.0683586 + 0.118401i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 3.00000 15.5885i 0.203653 1.05821i
\(218\) 18.0000 1.21911
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) 0 0
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) 1.50000 2.59808i 0.100673 0.174371i
\(223\) 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
\(225\) −5.00000 −0.333333
\(226\) 2.00000 3.46410i 0.133038 0.230429i
\(227\) 1.00000 + 1.73205i 0.0663723 + 0.114960i 0.897302 0.441417i \(-0.145524\pi\)
−0.830930 + 0.556378i \(0.812191\pi\)
\(228\) −1.50000 2.59808i −0.0993399 0.172062i
\(229\) 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
\(231\) −2.50000 + 0.866025i −0.164488 + 0.0569803i
\(232\) 1.00000 0.0656532
\(233\) 5.50000 9.52628i 0.360317 0.624087i −0.627696 0.778459i \(-0.716002\pi\)
0.988013 + 0.154371i \(0.0493352\pi\)
\(234\) 2.00000 + 3.46410i 0.130744 + 0.226455i
\(235\) 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 \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 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
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 6.00000 10.3923i 0.381771 0.661247i
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) −8.00000 13.8564i −0.506979 0.878114i
\(250\) 0 0
\(251\) −7.00000 −0.441836 −0.220918 0.975292i \(-0.570905\pi\)
−0.220918 + 0.975292i \(0.570905\pi\)
\(252\) 2.00000 + 1.73205i 0.125988 + 0.109109i
\(253\) 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 −0.615948 0.787787i \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) 1.00000 0.0622573
\(259\) 7.50000 2.59808i 0.466027 0.161437i
\(260\) 0 0
\(261\) 0.500000 0.866025i 0.0309492 0.0536056i
\(262\) −1.00000 1.73205i −0.0617802 0.107006i
\(263\) 7.00000 + 12.1244i 0.431638 + 0.747620i 0.997015 0.0772134i \(-0.0246023\pi\)
−0.565376 + 0.824833i \(0.691269\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) 1.50000 7.79423i 0.0919709 0.477895i
\(267\) 8.00000 0.489592
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 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
\(273\) −2.00000 + 10.3923i −0.121046 + 0.628971i
\(274\) 4.00000 0.241649
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) 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
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) 0.500000 0.866025i 0.0297746 0.0515711i
\(283\) −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
\(288\) −1.00000 −0.0589256
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) 0 0
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) −15.0000 −0.876309 −0.438155 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 0 0
\(296\) −1.50000 + 2.59808i −0.0871857 + 0.151010i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 0.500000 + 0.866025i 0.0289642 + 0.0501675i
\(299\) 2.00000 3.46410i 0.115663 0.200334i
\(300\) 5.00000 0.288675
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) −11.0000 −0.632979
\(303\) 7.50000 12.9904i 0.430864 0.746278i
\(304\) 1.50000 + 2.59808i 0.0860309 + 0.149010i
\(305\) 0 0
\(306\) −0.500000 + 0.866025i −0.0285831 + 0.0495074i
\(307\) −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
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 15.5000 + 26.8468i 0.878924 + 1.52234i 0.852523 + 0.522690i \(0.175072\pi\)
0.0264017 + 0.999651i \(0.491595\pi\)
\(312\) −2.00000 3.46410i −0.113228 0.196116i
\(313\) 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 −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) −0.500000 0.866025i −0.0279946 0.0484881i
\(320\) 0 0
\(321\) −2.00000 −0.111629
\(322\) 0.500000 2.59808i 0.0278639 0.144785i
\(323\) 3.00000 0.166924
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 10.0000 + 17.3205i 0.554700 + 0.960769i
\(326\) −9.00000 15.5885i −0.498464 0.863365i
\(327\) −9.00000 + 15.5885i −0.497701 + 0.862044i
\(328\) 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
\(333\) 1.50000 + 2.59808i 0.0821995 + 0.142374i
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 0 0
\(336\) −2.00000 1.73205i −0.109109 0.0944911i
\(337\) −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
\(339\) 2.00000 + 3.46410i 0.108625 + 0.188144i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 3.00000 0.162221
\(343\) −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 \(0.0137110\pi\)
−0.462244 + 0.886753i \(0.652956\pi\)
\(348\) −0.500000 + 0.866025i −0.0268028 + 0.0464238i
\(349\) 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
\(351\) −4.00000 −0.213504
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 4.00000 + 6.92820i 0.212899 + 0.368751i 0.952620 0.304162i \(-0.0983763\pi\)
−0.739722 + 0.672913i \(0.765043\pi\)
\(354\) −3.50000 6.06218i −0.186023 0.322201i
\(355\) 0 0
\(356\) −8.00000 −0.423999
\(357\) −2.50000 + 0.866025i −0.132314 + 0.0458349i
\(358\) 25.0000 1.32129
\(359\) −1.00000 + 1.73205i −0.0527780 + 0.0914141i −0.891207 0.453596i \(-0.850141\pi\)
0.838429 + 0.545010i \(0.183474\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) −1.00000 −0.0524864
\(364\) 2.00000 10.3923i 0.104828 0.544705i
\(365\) 0 0
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) −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
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) −6.00000 −0.311086
\(373\) −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
\(378\) −2.50000 + 0.866025i −0.128586 + 0.0445435i
\(379\) −22.0000 −1.13006 −0.565032 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) 0 0
\(381\) −3.50000 6.06218i −0.179310 0.310575i
\(382\) −12.0000 20.7846i −0.613973 1.06343i
\(383\) −14.5000 + 25.1147i −0.740915 + 1.28330i 0.211164 + 0.977451i \(0.432275\pi\)
−0.952079 + 0.305852i \(0.901059\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −0.500000 + 0.866025i −0.0254164 + 0.0440225i
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) 14.0000 + 24.2487i 0.709828 + 1.22946i 0.964921 + 0.262542i \(0.0845608\pi\)
−0.255092 + 0.966917i \(0.582106\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 2.00000 0.100887
\(394\) 13.5000 23.3827i 0.680120 1.17800i
\(395\) 0 0
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) −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
\(399\) 6.00000 + 5.19615i 0.300376 + 0.260133i
\(400\) −5.00000 −0.250000
\(401\) −1.00000 + 1.73205i −0.0499376 + 0.0864945i −0.889914 0.456129i \(-0.849236\pi\)
0.839976 + 0.542623i \(0.182569\pi\)
\(402\) 2.00000 + 3.46410i 0.0997509 + 0.172774i
\(403\) −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
\(408\) 0.500000 0.866025i 0.0247537 0.0428746i
\(409\) −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
\(411\) −2.00000 + 3.46410i −0.0986527 + 0.170872i
\(412\) 4.00000 0.197066
\(413\) 3.50000 18.1865i 0.172224 0.894901i
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 2.00000 + 3.46410i 0.0980581 + 0.169842i
\(417\) −8.50000 14.7224i −0.416247 0.720961i
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) −17.0000 −0.830504 −0.415252 0.909706i \(-0.636307\pi\)
−0.415252 + 0.909706i \(0.636307\pi\)
\(420\) 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
\(423\) 0.500000 + 0.866025i 0.0243108 + 0.0421076i
\(424\) 0 0
\(425\) −2.50000 + 4.33013i −0.121268 + 0.210042i
\(426\) −15.0000 −0.726752
\(427\) −15.0000 + 5.19615i −0.725901 + 0.251459i
\(428\) 2.00000 0.0966736
\(429\) −2.00000 + 3.46410i −0.0965609 + 0.167248i
\(430\) 0 0
\(431\) 14.0000 + 24.2487i 0.674356 + 1.16802i 0.976657 + 0.214807i \(0.0689121\pi\)
−0.302300 + 0.953213i \(0.597755\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −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
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) 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
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 4.00000 0.190261
\(443\) 1.50000 2.59808i 0.0712672 0.123438i −0.828190 0.560448i \(-0.810629\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(444\) −1.50000 2.59808i −0.0711868 0.123299i
\(445\) 0 0
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) −1.00000 −0.0472984
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) −2.50000 + 4.33013i −0.117851 + 0.204124i
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) −2.00000 3.46410i −0.0940721 0.162938i
\(453\) 5.50000 9.52628i 0.258413 0.447584i
\(454\) 2.00000 0.0938647
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) −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
\(459\) −0.500000 0.866025i −0.0233380 0.0404226i
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) −0.500000 + 2.59808i −0.0232621 + 0.120873i
\(463\) −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 \(-0.654715\pi\)
0.999295 0.0375381i \(-0.0119516\pi\)
\(468\) 4.00000 0.184900
\(469\) −2.00000 + 10.3923i −0.0923514 + 0.479872i
\(470\) 0 0
\(471\) −4.50000 + 7.79423i −0.207349 + 0.359139i
\(472\) 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 0.728895 0.684626i \(-0.240034\pi\)
−0.957351 + 0.288929i \(0.906701\pi\)
\(480\) 0 0
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) 4.00000 0.182195
\(483\) 2.00000 + 1.73205i 0.0910032 + 0.0788110i
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −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
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −3.00000 + 5.19615i −0.135250 + 0.234261i
\(493\) −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
\(498\) −16.0000 −0.716977
\(499\) −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
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) −3.50000 + 6.06218i −0.156213 + 0.270568i
\(503\) 2.00000 0.0891756 0.0445878 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 2.50000 0.866025i 0.111359 0.0385758i
\(505\) 0 0
\(506\) 0.500000 0.866025i 0.0222277 0.0384995i
\(507\) 1.50000 + 2.59808i 0.0666173 + 0.115385i
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) −2.00000 + 3.46410i −0.0886484 + 0.153544i −0.906940 0.421260i \(-0.861588\pi\)
0.818292 + 0.574803i \(0.194921\pi\)
\(510\) 0 0
\(511\) 6.00000 31.1769i 0.265424 1.37919i
\(512\) −1.00000 −0.0441942
\(513\) −1.50000 + 2.59808i −0.0662266 + 0.114708i
\(514\) −6.00000 10.3923i −0.264649 0.458385i
\(515\) 0 0
\(516\) 0.500000 0.866025i 0.0220113 0.0381246i
\(517\) 1.00000 0.0439799
\(518\) 1.50000 7.79423i 0.0659062 0.342459i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) −0.500000 0.866025i −0.0218844 0.0379049i
\(523\) −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
\(525\) −12.5000 + 4.33013i −0.545545 + 0.188982i
\(526\) 14.0000 0.610429
\(527\) 3.00000 5.19615i 0.130682 0.226348i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 7.00000 0.303774
\(532\) −6.00000 5.19615i −0.260133 0.225282i
\(533\) −24.0000 −1.03956
\(534\) 4.00000 6.92820i 0.173097 0.299813i
\(535\) 0 0
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) −12.5000 + 21.6506i −0.539415 + 0.934294i
\(538\) 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
\(543\) 11.0000 + 19.0526i 0.472055 + 0.817624i
\(544\) −0.500000 + 0.866025i −0.0214373 + 0.0371305i
\(545\) 0 0
\(546\) 8.00000 + 6.92820i 0.342368 + 0.296500i
\(547\) 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
\(549\) −3.00000 5.19615i −0.128037 0.221766i
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) −1.50000 + 2.59808i −0.0639021 + 0.110682i
\(552\) −1.00000 −0.0425628
\(553\) 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 0.896053 0.443947i \(-0.146422\pi\)
−0.832496 + 0.554031i \(0.813089\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) −0.500000 0.866025i −0.0210538 0.0364662i
\(565\) 0 0
\(566\) −20.0000 −0.840663
\(567\) 0.500000 2.59808i 0.0209980 0.109109i
\(568\) 15.0000 0.629386
\(569\) −19.5000 + 33.7750i −0.817483 + 1.41592i 0.0900490 + 0.995937i \(0.471298\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(570\) 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
\(573\) 24.0000 1.00261
\(574\) −15.0000 + 5.19615i −0.626088 + 0.216883i
\(575\) 5.00000 0.208514
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 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
\(579\) 7.00000 12.1244i 0.290910 0.503871i
\(580\) 0 0
\(581\) −32.0000 27.7128i −1.32758 1.14972i
\(582\) 7.00000 0.290159
\(583\) 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 \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 6.50000 + 2.59808i 0.268055 + 0.107143i
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) 13.5000 + 23.3827i 0.555316 + 0.961835i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) 9.50000 16.4545i 0.390118 0.675705i −0.602347 0.798235i \(-0.705767\pi\)
0.992465 + 0.122530i \(0.0391008\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 1.00000 0.0409616
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) −2.00000 3.46410i −0.0817861 0.141658i
\(599\) 20.0000 + 34.6410i 0.817178 + 1.41539i 0.907754 + 0.419504i \(0.137796\pi\)
−0.0905757 + 0.995890i \(0.528871\pi\)
\(600\) 2.50000 4.33013i 0.102062 0.176777i
\(601\) 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
\(603\) −4.00000 −0.162893
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) 0 0
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) 3.00000 0.121666
\(609\) 0.500000 2.59808i 0.0202610 0.105279i
\(610\) 0 0
\(611\) 2.00000 3.46410i 0.0809113 0.140143i
\(612\) 0.500000 + 0.866025i 0.0202113 + 0.0350070i
\(613\) −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 \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) −2.00000 + 3.46410i −0.0804518 + 0.139347i
\(619\) 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
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 31.0000 1.24299
\(623\) 20.0000 6.92820i 0.801283 0.277573i
\(624\) −4.00000 −0.160128
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −16.5000 28.5788i −0.659473 1.14224i
\(627\) 1.50000 + 2.59808i 0.0599042 + 0.103757i
\(628\) 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
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 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
\(639\) 7.50000 12.9904i 0.296695 0.513892i
\(640\) 0 0
\(641\) −17.0000 29.4449i −0.671460 1.16300i −0.977490 0.210981i \(-0.932334\pi\)
0.306031 0.952022i \(-0.400999\pi\)
\(642\) −1.00000 + 1.73205i −0.0394669 + 0.0683586i
\(643\) −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 0.776622 0.629967i \(-0.216932\pi\)
−0.933878 + 0.357591i \(0.883598\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 3.50000 6.06218i 0.137387 0.237961i
\(650\) 20.0000 0.784465
\(651\) 15.0000 5.19615i 0.587896 0.203653i
\(652\) −18.0000 −0.704934
\(653\) −24.0000 + 41.5692i −0.939193 + 1.62673i −0.172211 + 0.985060i \(0.555091\pi\)
−0.766982 + 0.641669i \(0.778242\pi\)
\(654\) 9.00000 + 15.5885i 0.351928 + 0.609557i
\(655\) 0 0
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) 12.0000 0.468165
\(658\) 0.500000 2.59808i 0.0194920 0.101284i
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) 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
\(663\) −2.00000 + 3.46410i −0.0776736 + 0.134535i
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 3.00000 0.116248
\(667\) −0.500000 + 0.866025i −0.0193601 + 0.0335326i
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) −2.50000 + 0.866025i −0.0964396 + 0.0334077i
\(673\) −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
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 4.00000 0.153619
\(679\) 14.0000 + 12.1244i 0.537271 + 0.465290i
\(680\) 0 0
\(681\) −1.00000 + 1.73205i −0.0383201 + 0.0663723i
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) −19.5000 33.7750i −0.746147 1.29236i −0.949657 0.313291i \(-0.898568\pi\)
0.203510 0.979073i \(-0.434765\pi\)
\(684\) 1.50000 2.59808i 0.0573539 0.0993399i
\(685\) 0 0
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 6.00000 0.228914
\(688\) −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
\(693\) −2.00000 1.73205i −0.0759737 0.0657952i
\(694\) 20.0000 0.759190
\(695\) 0 0
\(696\) 0.500000 + 0.866025i 0.0189525 + 0.0328266i
\(697\) −3.00000 5.19615i −0.113633 0.196818i
\(698\) 16.0000 27.7128i 0.605609 1.04895i
\(699\) 11.0000 0.416058
\(700\) 12.5000 4.33013i 0.472456 0.163663i
\(701\) 29.0000 1.09531 0.547657 0.836703i \(-0.315520\pi\)
0.547657 + 0.836703i \(0.315520\pi\)
\(702\) −2.00000 + 3.46410i −0.0754851 + 0.130744i
\(703\) −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
\(708\) −7.00000 −0.263076
\(709\) 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
\(714\) −0.500000 + 2.59808i −0.0187120 + 0.0972306i
\(715\) 0 0
\(716\) 12.5000 21.6506i 0.467147 0.809122i
\(717\) 8.00000 + 13.8564i 0.298765 + 0.517477i
\(718\) 1.00000 + 1.73205i 0.0373197 + 0.0646396i
\(719\) 18.5000 32.0429i 0.689934 1.19500i −0.281925 0.959436i \(-0.590973\pi\)
0.971859 0.235564i \(-0.0756936\pi\)
\(720\) 0 0
\(721\) −10.0000 + 3.46410i −0.372419 + 0.129010i
\(722\) 10.0000 0.372161
\(723\) −2.00000 + 3.46410i −0.0743808 + 0.128831i
\(724\) −11.0000 19.0526i −0.408812 0.708083i
\(725\) −2.50000 4.33013i −0.0928477 0.160817i
\(726\) −0.500000 + 0.866025i −0.0185567 + 0.0321412i
\(727\) 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
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.500000 + 0.866025i 0.0184932 + 0.0320311i
\(732\) 3.00000 + 5.19615i 0.110883 + 0.192055i
\(733\) 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
\(738\) −3.00000 5.19615i −0.110432 0.191273i
\(739\) 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
\(741\) 12.0000 0.440831
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) 0 0
\(746\) 17.0000 + 29.4449i 0.622414 + 1.07805i
\(747\) 8.00000 13.8564i 0.292705 0.506979i
\(748\) 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
\(753\) −3.50000 6.06218i −0.127547 0.220918i
\(754\) −2.00000 + 3.46410i −0.0728357 + 0.126155i
\(755\) 0 0
\(756\) −0.500000 + 2.59808i −0.0181848 + 0.0944911i
\(757\) 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
\(759\) 0.500000 + 0.866025i 0.0181489 + 0.0314347i
\(760\) 0 0
\(761\) 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) −7.00000 −0.253583
\(763\) −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
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −7.00000 12.1244i −0.251773 0.436083i 0.712241 0.701935i \(-0.247680\pi\)
−0.964014 + 0.265852i \(0.914347\pi\)
\(774\) 0.500000 + 0.866025i 0.0179721 + 0.0311286i
\(775\) 15.0000 25.9808i 0.538816 0.933257i
\(776\) −7.00000 −0.251285
\(777\) 6.00000 + 5.19615i 0.215249 + 0.186411i
\(778\) 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
\(783\) 1.00000 0.0357371
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\)