Properties

Label 1078.2.e.f.177.1
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.f.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +7.00000 q^{13} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -2.00000 q^{20} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(1.50000 + 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} -9.00000 q^{27} -5.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{34} +6.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(10.5000 + 18.1865i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(6.00000 + 10.3923i) q^{45} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} -3.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(3.00000 + 5.19615i) q^{53} +(4.50000 - 7.79423i) q^{54} +2.00000 q^{55} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(7.00000 - 12.1244i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +24.0000 q^{69} -2.00000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.50000 + 2.59808i) q^{75} -21.0000 q^{78} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-7.50000 - 12.9904i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-6.00000 + 10.3923i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.50000 - 2.59808i) q^{96} -7.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + 14 q^{13} + 12 q^{15} - q^{16} + 2 q^{17} - 6 q^{18} - 4 q^{20} - 2 q^{22} + 8 q^{23} + 3 q^{24} + q^{25} - 7 q^{26} - 18 q^{27} - 10 q^{29} - 6 q^{30} + 4 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} + 12 q^{36} - 4 q^{37} + 21 q^{39} + 2 q^{40} - 8 q^{41} - 16 q^{43} + q^{44} + 12 q^{45} + 8 q^{46} + 2 q^{47} - 6 q^{48} - 2 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} + 9 q^{54} + 4 q^{55} + 5 q^{58} + 3 q^{59} - 6 q^{60} + q^{61} - 8 q^{62} + 2 q^{64} + 14 q^{65} - 3 q^{66} - 9 q^{67} + 2 q^{68} + 48 q^{69} - 4 q^{71} - 6 q^{72} + 4 q^{73} - 4 q^{74} - 3 q^{75} - 42 q^{78} - 9 q^{79} + 2 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 8 q^{85} + 8 q^{86} - 15 q^{87} + q^{88} + 6 q^{89} - 24 q^{90} - 16 q^{92} - 12 q^{93} + 2 q^{94} + 3 q^{96} - 14 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) −3.00000 −1.22474
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 6.00000 1.54919
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) −3.00000 5.19615i −0.707107 1.22474i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −3.50000 + 6.06218i −0.686406 + 1.18889i
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 0 0
\(39\) 10.5000 + 18.1865i 1.68135 + 2.91218i
\(40\) 1.00000 1.73205i 0.158114 0.273861i
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 6.00000 + 10.3923i 0.894427 + 1.54919i
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) −3.00000 −0.433013
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −3.50000 6.06218i −0.485363 0.840673i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 4.50000 7.79423i 0.612372 1.06066i
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.00000 12.1244i 0.868243 1.50384i
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) −4.50000 7.79423i −0.549762 0.952217i −0.998290 0.0584478i \(-0.981385\pi\)
0.448528 0.893769i \(-0.351948\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 24.0000 2.88926
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −3.00000 + 5.19615i −0.353553 + 0.612372i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) −1.50000 + 2.59808i −0.173205 + 0.300000i
\(76\) 0 0
\(77\) 0 0
\(78\) −21.0000 −2.37778
\(79\) −4.50000 + 7.79423i −0.506290 + 0.876919i 0.493684 + 0.869641i \(0.335650\pi\)
−0.999974 + 0.00727784i \(0.997683\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 2.00000 3.46410i 0.220863 0.382546i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) −7.50000 12.9904i −0.804084 1.39272i
\(88\) 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 \(0.0636557\pi\)
\(90\) −12.0000 −1.26491
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) −6.00000 + 10.3923i −0.622171 + 1.07763i
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) 0 0
\(96\) 1.50000 2.59808i 0.153093 0.265165i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) 9.00000 15.5885i 0.886796 1.53598i 0.0431555 0.999068i \(-0.486259\pi\)
0.843641 0.536908i \(-0.180408\pi\)
\(104\) 7.00000 0.686406
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i \(-0.864154\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(108\) 4.50000 + 7.79423i 0.433013 + 0.750000i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) −12.0000 −1.13899
\(112\) 0 0
\(113\) 5.00000 0.470360 0.235180 0.971952i \(-0.424432\pi\)
0.235180 + 0.971952i \(0.424432\pi\)
\(114\) 0 0
\(115\) −8.00000 13.8564i −0.746004 1.29212i
\(116\) 2.50000 + 4.33013i 0.232119 + 0.402042i
\(117\) −21.0000 + 36.3731i −1.94145 + 3.36269i
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) 6.00000 0.547723
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 0.500000 + 0.866025i 0.0452679 + 0.0784063i
\(123\) −6.00000 10.3923i −0.541002 0.937043i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −12.0000 20.7846i −1.05654 1.82998i
\(130\) 7.00000 + 12.1244i 0.613941 + 1.06338i
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 9.00000 0.777482
\(135\) −9.00000 + 15.5885i −0.774597 + 1.34164i
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) −12.0000 + 20.7846i −1.02151 + 1.76930i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 3.50000 + 6.06218i 0.292685 + 0.506945i
\(144\) −3.00000 5.19615i −0.250000 0.433013i
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) −1.50000 2.59808i −0.122474 0.212132i
\(151\) 1.50000 + 2.59808i 0.122068 + 0.211428i 0.920583 0.390547i \(-0.127714\pi\)
−0.798515 + 0.601975i \(0.794381\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 10.5000 18.1865i 0.840673 1.45609i
\(157\) 8.00000 + 13.8564i 0.638470 + 1.10586i 0.985769 + 0.168107i \(0.0537655\pi\)
−0.347299 + 0.937754i \(0.612901\pi\)
\(158\) −4.50000 7.79423i −0.358001 0.620076i
\(159\) −9.00000 + 15.5885i −0.713746 + 1.23625i
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) 8.50000 14.7224i 0.665771 1.15315i −0.313304 0.949653i \(-0.601436\pi\)
0.979076 0.203497i \(-0.0652307\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) 3.00000 + 5.19615i 0.233550 + 0.404520i
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) −2.00000 + 3.46410i −0.153393 + 0.265684i
\(171\) 0 0
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 12.5000 21.6506i 0.950357 1.64607i 0.205706 0.978614i \(-0.434051\pi\)
0.744652 0.667453i \(-0.232616\pi\)
\(174\) 15.0000 1.13715
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 6.00000 10.3923i 0.447214 0.774597i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 3.00000 0.221766
\(184\) 4.00000 6.92820i 0.294884 0.510754i
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) −6.00000 10.3923i −0.439941 0.762001i
\(187\) −1.00000 + 1.73205i −0.0731272 + 0.126660i
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) −1.00000 + 1.73205i −0.0723575 + 0.125327i −0.899934 0.436026i \(-0.856386\pi\)
0.827577 + 0.561353i \(0.189719\pi\)
\(192\) 1.50000 + 2.59808i 0.108253 + 0.187500i
\(193\) −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i \(-0.259632\pi\)
−0.973315 + 0.229475i \(0.926299\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 42.0000 3.00768
\(196\) 0 0
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 3.00000 5.19615i 0.213201 0.369274i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 13.5000 23.3827i 0.952217 1.64929i
\(202\) 9.00000 0.633238
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −4.00000 + 6.92820i −0.279372 + 0.483887i
\(206\) 9.00000 + 15.5885i 0.627060 + 1.08610i
\(207\) 24.0000 + 41.5692i 1.66812 + 2.88926i
\(208\) −3.50000 + 6.06218i −0.242681 + 0.420336i
\(209\) 0 0
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) −1.00000 1.73205i −0.0683586 0.118401i
\(215\) −8.00000 + 13.8564i −0.545595 + 0.944999i
\(216\) −9.00000 −0.612372
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −6.00000 + 10.3923i −0.405442 + 0.702247i
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) 7.00000 + 12.1244i 0.470871 + 0.815572i
\(222\) 6.00000 10.3923i 0.402694 0.697486i
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) −6.00000 −0.400000
\(226\) −2.50000 + 4.33013i −0.166298 + 0.288036i
\(227\) −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
\(229\) −14.0000 + 24.2487i −0.925146 + 1.60240i −0.133820 + 0.991006i \(0.542724\pi\)
−0.791326 + 0.611394i \(0.790609\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) −21.0000 36.3731i −1.37281 2.37778i
\(235\) −2.00000 3.46410i −0.130466 0.225973i
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) −27.0000 −1.75384
\(238\) 0 0
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) −3.00000 + 5.19615i −0.193649 + 0.335410i
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) −1.00000 −0.0640184
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) −9.00000 15.5885i −0.570352 0.987878i
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 9.50000 16.4545i 0.596083 1.03245i
\(255\) 6.00000 + 10.3923i 0.375735 + 0.650791i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 24.0000 1.49417
\(259\) 0 0
\(260\) −14.0000 −0.868243
\(261\) 15.0000 25.9808i 0.928477 1.60817i
\(262\) 0 0
\(263\) −13.5000 23.3827i −0.832446 1.44184i −0.896093 0.443866i \(-0.853607\pi\)
0.0636476 0.997972i \(-0.479727\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) −4.50000 + 7.79423i −0.274881 + 0.476108i
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) −9.00000 15.5885i −0.547723 0.948683i
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 3.00000 0.181237
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) −12.0000 20.7846i −0.722315 1.25109i
\(277\) 4.50000 + 7.79423i 0.270379 + 0.468310i 0.968959 0.247222i \(-0.0795177\pi\)
−0.698580 + 0.715532i \(0.746184\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) −24.0000 −1.43684
\(280\) 0 0
\(281\) −28.0000 −1.67034 −0.835170 0.549992i \(-0.814631\pi\)
−0.835170 + 0.549992i \(0.814631\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −7.00000 −0.413919
\(287\) 0 0
\(288\) 6.00000 0.353553
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −5.00000 8.66025i −0.293610 0.508548i
\(291\) −10.5000 18.1865i −0.615521 1.06611i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) −4.50000 7.79423i −0.261116 0.452267i
\(298\) 5.00000 + 8.66025i 0.289642 + 0.501675i
\(299\) 28.0000 48.4974i 1.61928 2.80468i
\(300\) 3.00000 0.173205
\(301\) 0 0
\(302\) −3.00000 −0.172631
\(303\) 13.5000 23.3827i 0.775555 1.34330i
\(304\) 0 0
\(305\) −1.00000 1.73205i −0.0572598 0.0991769i
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) 54.0000 3.07195
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) −5.00000 8.66025i −0.283524 0.491078i 0.688726 0.725022i \(-0.258170\pi\)
−0.972250 + 0.233944i \(0.924837\pi\)
\(312\) 10.5000 + 18.1865i 0.594445 + 1.02961i
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) −16.0000 −0.902932
\(315\) 0 0
\(316\) 9.00000 0.506290
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) −9.00000 15.5885i −0.504695 0.874157i
\(319\) −2.50000 4.33013i −0.139973 0.242441i
\(320\) 1.00000 1.73205i 0.0559017 0.0968246i
\(321\) −6.00000 −0.334887
\(322\) 0 0
\(323\) 0 0
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 3.50000 + 6.06218i 0.194145 + 0.336269i
\(326\) 8.50000 + 14.7224i 0.470771 + 0.815400i
\(327\) −3.00000 + 5.19615i −0.165900 + 0.287348i
\(328\) −4.00000 −0.220863
\(329\) 0 0
\(330\) −6.00000 −0.330289
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) −12.0000 20.7846i −0.657596 1.13899i
\(334\) 9.50000 16.4545i 0.519817 0.900349i
\(335\) −18.0000 −0.983445
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) −18.0000 + 31.1769i −0.979071 + 1.69580i
\(339\) 7.50000 + 12.9904i 0.407344 + 0.705541i
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 0 0
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 24.0000 41.5692i 1.29212 2.23801i
\(346\) 12.5000 + 21.6506i 0.672004 + 1.16395i
\(347\) 11.0000 + 19.0526i 0.590511 + 1.02279i 0.994164 + 0.107883i \(0.0344071\pi\)
−0.403653 + 0.914912i \(0.632260\pi\)
\(348\) −7.50000 + 12.9904i −0.402042 + 0.696358i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −63.0000 −3.36269
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) −4.50000 7.79423i −0.239172 0.414259i
\(355\) −2.00000 + 3.46410i −0.106149 + 0.183855i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 19.0000 1.00418
\(359\) 9.50000 16.4545i 0.501391 0.868434i −0.498608 0.866828i \(-0.666155\pi\)
0.999999 0.00160673i \(-0.000511438\pi\)
\(360\) 6.00000 + 10.3923i 0.316228 + 0.547723i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −11.0000 + 19.0526i −0.578147 + 1.00138i
\(363\) −3.00000 −0.157459
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) −1.50000 + 2.59808i −0.0784063 + 0.135804i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 4.00000 + 6.92820i 0.208514 + 0.361158i
\(369\) 12.0000 20.7846i 0.624695 1.08200i
\(370\) −8.00000 −0.415900
\(371\) 0 0
\(372\) 12.0000 0.622171
\(373\) −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) −1.00000 1.73205i −0.0517088 0.0895622i
\(375\) 18.0000 + 31.1769i 0.929516 + 1.60997i
\(376\) 1.00000 1.73205i 0.0515711 0.0893237i
\(377\) −35.0000 −1.80259
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) −28.5000 49.3634i −1.46010 2.52897i
\(382\) −1.00000 1.73205i −0.0511645 0.0886194i
\(383\) 13.0000 22.5167i 0.664269 1.15055i −0.315214 0.949021i \(-0.602076\pi\)
0.979483 0.201527i \(-0.0645904\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) 24.0000 41.5692i 1.21999 2.11308i
\(388\) 3.50000 + 6.06218i 0.177686 + 0.307760i
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) −21.0000 + 36.3731i −1.06338 + 1.84182i
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) −7.50000 + 12.9904i −0.377845 + 0.654446i
\(395\) 9.00000 + 15.5885i 0.452839 + 0.784340i
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 3.00000 5.19615i 0.150566 0.260787i −0.780870 0.624694i \(-0.785224\pi\)
0.931436 + 0.363906i \(0.118557\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 4.50000 7.79423i 0.224719 0.389225i −0.731516 0.681824i \(-0.761187\pi\)
0.956235 + 0.292599i \(0.0945202\pi\)
\(402\) 13.5000 + 23.3827i 0.673319 + 1.16622i
\(403\) 14.0000 + 24.2487i 0.697390 + 1.20791i
\(404\) −4.50000 + 7.79423i −0.223883 + 0.387777i
\(405\) −18.0000 −0.894427
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) −3.00000 + 5.19615i −0.148522 + 0.257248i
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) −4.00000 6.92820i −0.197546 0.342160i
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −18.0000 −0.886796
\(413\) 0 0
\(414\) −48.0000 −2.35907
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) −3.50000 6.06218i −0.171602 0.297223i
\(417\) 6.00000 + 10.3923i 0.293821 + 0.508913i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 6.00000 + 10.3923i 0.291730 + 0.505291i
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) 2.00000 0.0966736
\(429\) −10.5000 + 18.1865i −0.506945 + 0.878054i
\(430\) −8.00000 13.8564i −0.385794 0.668215i
\(431\) −12.5000 21.6506i −0.602104 1.04287i −0.992502 0.122228i \(-0.960996\pi\)
0.390398 0.920646i \(-0.372337\pi\)
\(432\) 4.50000 7.79423i 0.216506 0.375000i
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) −30.0000 −1.43839
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 0 0
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) −2.50000 + 4.33013i −0.119318 + 0.206666i −0.919498 0.393095i \(-0.871404\pi\)
0.800179 + 0.599761i \(0.204738\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 6.00000 + 10.3923i 0.284747 + 0.493197i
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 30.0000 1.41895
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 3.00000 5.19615i 0.141421 0.244949i
\(451\) −2.00000 3.46410i −0.0941763 0.163118i
\(452\) −2.50000 4.33013i −0.117590 0.203672i
\(453\) −4.50000 + 7.79423i −0.211428 + 0.366205i
\(454\) 2.00000 0.0938647
\(455\) 0 0
\(456\) 0 0
\(457\) −7.00000 + 12.1244i −0.327446 + 0.567153i −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) −14.0000 24.2487i −0.654177 1.13307i
\(459\) −9.00000 15.5885i −0.420084 0.727607i
\(460\) −8.00000 + 13.8564i −0.373002 + 0.646058i
\(461\) −27.0000 −1.25752 −0.628758 0.777601i \(-0.716436\pi\)
−0.628758 + 0.777601i \(0.716436\pi\)
\(462\) 0 0
\(463\) −2.00000 −0.0929479 −0.0464739 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) 2.50000 4.33013i 0.116060 0.201021i
\(465\) 12.0000 + 20.7846i 0.556487 + 0.963863i
\(466\) 0 0
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 42.0000 1.94145
\(469\) 0 0
\(470\) 4.00000 0.184506
\(471\) −24.0000 + 41.5692i −1.10586 + 1.91541i
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 13.5000 23.3827i 0.620076 1.07400i
\(475\) 0 0
\(476\) 0 0
\(477\) −36.0000 −1.64833
\(478\) 2.50000 4.33013i 0.114347 0.198055i
\(479\) −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i \(-0.173939\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(480\) −3.00000 5.19615i −0.136931 0.237171i
\(481\) −14.0000 + 24.2487i −0.638345 + 1.10565i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −7.00000 + 12.1244i −0.317854 + 0.550539i
\(486\) 0 0
\(487\) 20.0000 + 34.6410i 0.906287 + 1.56973i 0.819181 + 0.573535i \(0.194428\pi\)
0.0871056 + 0.996199i \(0.472238\pi\)
\(488\) 0.500000 0.866025i 0.0226339 0.0392031i
\(489\) 51.0000 2.30630
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) −5.00000 8.66025i −0.225189 0.390038i
\(494\) 0 0
\(495\) −6.00000 + 10.3923i −0.269680 + 0.467099i
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 18.0000 0.806599
\(499\) −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i \(-0.981076\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) −28.5000 49.3634i −1.27329 2.20540i
\(502\) −12.0000 + 20.7846i −0.535586 + 0.927663i
\(503\) −3.00000 −0.133763 −0.0668817 0.997761i \(-0.521305\pi\)
−0.0668817 + 0.997761i \(0.521305\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) −4.00000 + 6.92820i −0.177822 + 0.307996i
\(507\) 54.0000 + 93.5307i 2.39822 + 4.15385i
\(508\) 9.50000 + 16.4545i 0.421494 + 0.730050i
\(509\) −11.0000 + 19.0526i −0.487566 + 0.844490i −0.999898 0.0142980i \(-0.995449\pi\)
0.512331 + 0.858788i \(0.328782\pi\)
\(510\) −12.0000 −0.531369
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 1.50000 + 2.59808i 0.0661622 + 0.114596i
\(515\) −18.0000 31.1769i −0.793175 1.37382i
\(516\) −12.0000 + 20.7846i −0.528271 + 0.914991i
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) 75.0000 3.29213
\(520\) 7.00000 12.1244i 0.306970 0.531688i
\(521\) 5.00000 + 8.66025i 0.219054 + 0.379413i 0.954519 0.298150i \(-0.0963696\pi\)
−0.735465 + 0.677563i \(0.763036\pi\)
\(522\) 15.0000 + 25.9808i 0.656532 + 1.13715i
\(523\) −5.00000 + 8.66025i −0.218635 + 0.378686i −0.954391 0.298560i \(-0.903494\pi\)
0.735756 + 0.677247i \(0.236827\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 27.0000 1.17726
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) −1.50000 2.59808i −0.0652791 0.113067i
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) −6.00000 + 10.3923i −0.260623 + 0.451413i
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) −28.0000 −1.21281
\(534\) −9.00000 + 15.5885i −0.389468 + 0.674579i
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) −4.50000 7.79423i −0.194370 0.336659i
\(537\) 28.5000 49.3634i 1.22987 2.13019i
\(538\) 24.0000 1.03471
\(539\) 0 0
\(540\) 18.0000 0.774597
\(541\) −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) −5.50000 9.52628i −0.236245 0.409189i
\(543\) 33.0000 + 57.1577i 1.41617 + 2.45287i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 30.0000 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) 0 0
\(552\) 24.0000 1.02151
\(553\) 0 0
\(554\) −9.00000 −0.382373
\(555\) −12.0000 + 20.7846i −0.509372 + 0.882258i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 12.0000 20.7846i 0.508001 0.879883i
\(559\) −56.0000 −2.36855
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 14.0000 24.2487i 0.590554 1.02287i
\(563\) 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 5.00000 8.66025i 0.210352 0.364340i
\(566\) 0 0
\(567\) 0 0
\(568\) −2.00000 −0.0839181
\(569\) 6.00000 10.3923i 0.251533 0.435668i −0.712415 0.701758i \(-0.752399\pi\)
0.963948 + 0.266090i \(0.0857319\pi\)
\(570\) 0 0
\(571\) −11.0000 19.0526i −0.460336 0.797325i 0.538642 0.842535i \(-0.318938\pi\)
−0.998978 + 0.0452101i \(0.985604\pi\)
\(572\) 3.50000 6.06218i 0.146342 0.253472i
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) −3.00000 + 5.19615i −0.125000 + 0.216506i
\(577\) −21.5000 37.2391i −0.895057 1.55028i −0.833734 0.552166i \(-0.813802\pi\)
−0.0613223 0.998118i \(-0.519532\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 12.0000 20.7846i 0.498703 0.863779i
\(580\) 10.0000 0.415227
\(581\) 0 0
\(582\) 21.0000 0.870478
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 42.0000 + 72.7461i 1.73649 + 3.00768i
\(586\) −9.00000 + 15.5885i −0.371787 + 0.643953i
\(587\) −27.0000 −1.11441 −0.557205 0.830375i \(-0.688126\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −3.00000 + 5.19615i −0.123508 + 0.213922i
\(591\) 22.5000 + 38.9711i 0.925526 + 1.60306i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 9.00000 0.369274
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) 28.0000 + 48.4974i 1.14501 + 1.98321i
\(599\) −18.0000 31.1769i −0.735460 1.27385i −0.954521 0.298143i \(-0.903633\pi\)
0.219061 0.975711i \(-0.429701\pi\)
\(600\) −1.50000 + 2.59808i −0.0612372 + 0.106066i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 54.0000 2.19905
\(604\) 1.50000 2.59808i 0.0610341 0.105714i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 13.5000 + 23.3827i 0.548400 + 0.949857i
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) 7.00000 12.1244i 0.283190 0.490499i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i \(0.111785\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(614\) 1.00000 1.73205i 0.0403567 0.0698999i
\(615\) −24.0000 −0.967773
\(616\) 0 0
\(617\) −15.0000 −0.603877 −0.301939 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) −27.0000 + 46.7654i −1.08610 + 1.88118i
\(619\) −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) −4.00000 6.92820i −0.160644 0.278243i
\(621\) −36.0000 + 62.3538i −1.44463 + 2.50217i
\(622\) 10.0000 0.400963
\(623\) 0 0
\(624\) −21.0000 −0.840673
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) 0 0
\(628\) 8.00000 13.8564i 0.319235 0.552931i
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) −4.50000 + 7.79423i −0.179000 + 0.310038i
\(633\) −30.0000 51.9615i −1.19239 2.06529i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) −19.0000 + 32.9090i −0.753992 + 1.30595i
\(636\) 18.0000 0.713746
\(637\) 0 0
\(638\) 5.00000 0.197952
\(639\) 6.00000 10.3923i 0.237356 0.411113i
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i \(0.0123508\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(642\) 3.00000 5.19615i 0.118401 0.205076i
\(643\) −31.0000 −1.22252 −0.611260 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) 0 0
\(645\) −48.0000 −1.89000
\(646\) 0 0
\(647\) 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i \(0.0340916\pi\)
−0.404559 + 0.914512i \(0.632575\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) −7.00000 −0.274563
\(651\) 0 0
\(652\) −17.0000 −0.665771
\(653\) −20.0000 + 34.6410i −0.782660 + 1.35561i 0.147726 + 0.989028i \(0.452805\pi\)
−0.930387 + 0.366579i \(0.880529\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) 0 0
\(656\) 2.00000 3.46410i 0.0780869 0.135250i
\(657\) −24.0000 −0.936329
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 3.00000 5.19615i 0.116775 0.202260i
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) −6.50000 11.2583i −0.252630 0.437567i
\(663\) −21.0000 + 36.3731i −0.815572 + 1.41261i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 24.0000 0.929981
\(667\) −20.0000 + 34.6410i −0.774403 + 1.34131i
\(668\) 9.50000 + 16.4545i 0.367566 + 0.636643i
\(669\) −6.00000 10.3923i −0.231973 0.401790i
\(670\) 9.00000 15.5885i 0.347700 0.602235i
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 6.00000 10.3923i 0.231111 0.400297i
\(675\) −4.50000 7.79423i −0.173205 0.300000i
\(676\) −18.0000 31.1769i −0.692308 1.19911i
\(677\) 7.00000 12.1244i 0.269032 0.465977i −0.699580 0.714554i \(-0.746630\pi\)
0.968612 + 0.248577i \(0.0799630\pi\)
\(678\) −15.0000 −0.576072
\(679\) 0 0
\(680\) 4.00000 0.153393
\(681\) 3.00000 5.19615i 0.114960 0.199117i
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −10.5000 18.1865i −0.401771 0.695888i 0.592168 0.805814i \(-0.298272\pi\)
−0.993940 + 0.109926i \(0.964939\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) −84.0000 −3.20480
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 21.0000 + 36.3731i 0.800036 + 1.38570i
\(690\) 24.0000 + 41.5692i 0.913664 + 1.58251i
\(691\) 16.5000 28.5788i 0.627690 1.08719i −0.360325 0.932827i \(-0.617334\pi\)
0.988014 0.154363i \(-0.0493326\pi\)
\(692\) −25.0000 −0.950357
\(693\) 0 0
\(694\) −22.0000 −0.835109
\(695\) 4.00000 6.92820i 0.151729 0.262802i
\(696\) −7.50000 12.9904i −0.284287 0.492399i
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 1.00000 1.73205i 0.0378506 0.0655591i
\(699\) 0 0
\(700\) 0 0
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 31.5000 54.5596i 1.18889 2.05922i
\(703\) 0 0
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 6.00000 10.3923i 0.225973 0.391397i
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) 9.00000 0.338241
\(709\) 24.0000 41.5692i 0.901339 1.56116i 0.0755813 0.997140i \(-0.475919\pi\)
0.825758 0.564025i \(-0.190748\pi\)
\(710\) −2.00000 3.46410i −0.0750587 0.130005i
\(711\) −27.0000 46.7654i −1.01258 1.75384i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 14.0000 0.523570
\(716\) −9.50000 + 16.4545i −0.355032 + 0.614933i
\(717\) −7.50000 12.9904i −0.280093 0.485135i
\(718\) 9.50000 + 16.4545i 0.354537 + 0.614076i
\(719\) −19.0000 + 32.9090i −0.708580 + 1.22730i 0.256803 + 0.966464i \(0.417331\pi\)
−0.965384 + 0.260834i \(0.916003\pi\)
\(720\) −12.0000 −0.447214
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) −11.0000 19.0526i −0.408812 0.708083i
\(725\) −2.50000 4.33013i −0.0928477 0.160817i
\(726\) 1.50000 2.59808i 0.0556702 0.0964237i
\(727\) 22.0000 0.815935 0.407967 0.912996i \(-0.366238\pi\)
0.407967 + 0.912996i \(0.366238\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −4.00000 + 6.92820i −0.148047 + 0.256424i
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) −1.50000 2.59808i −0.0554416 0.0960277i
\(733\) −9.50000 + 16.4545i −0.350891 + 0.607760i −0.986406 0.164328i \(-0.947454\pi\)
0.635515 + 0.772088i \(0.280788\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 4.50000 7.79423i 0.165760 0.287104i
\(738\) 12.0000 + 20.7846i 0.441726 + 0.765092i
\(739\) −21.0000 36.3731i −0.772497 1.33800i −0.936190 0.351494i \(-0.885674\pi\)
0.163693 0.986511i \(-0.447659\pi\)
\(740\) 4.00000 6.92820i 0.147043 0.254686i
\(741\) 0 0
\(742\) 0 0
\(743\) 12.0000 0.440237 0.220119 0.975473i \(-0.429356\pi\)
0.220119 + 0.975473i \(0.429356\pi\)
\(744\) −6.00000 + 10.3923i −0.219971 + 0.381000i
\(745\) −10.0000 17.3205i −0.366372 0.634574i
\(746\) −5.50000 9.52628i −0.201369 0.348782i
\(747\) 18.0000 31.1769i 0.658586 1.14070i
\(748\) 2.00000 0.0731272
\(749\) 0 0
\(750\) −36.0000 −1.31453
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) 1.00000 + 1.73205i 0.0364662 + 0.0631614i
\(753\) 36.0000 + 62.3538i 1.31191 + 2.27230i
\(754\) 17.5000 30.3109i 0.637312 1.10386i
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) 12.0000 + 20.7846i 0.435572 + 0.754434i
\(760\) 0 0
\(761\) −3.00000 + 5.19615i −0.108750 + 0.188360i −0.915264 0.402854i \(-0.868018\pi\)
0.806514 + 0.591215i \(0.201351\pi\)
\(762\) 57.0000 2.06489
\(763\) 0 0
\(764\) 2.00000 0.0723575
\(765\) −12.0000 + 20.7846i −0.433861 + 0.751469i
\(766\) 13.0000 + 22.5167i 0.469709 + 0.813560i
\(767\) 10.5000 + 18.1865i 0.379133 + 0.656678i
\(768\) 1.50000 2.59808i 0.0541266 0.0937500i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 9.00000 0.324127
\(772\) −4.00000 + 6.92820i −0.143963 + 0.249351i
\(773\) 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i \(-0.0246123\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(774\) 24.0000 + 41.5692i 0.862662 + 1.49417i
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) 0 0
\(780\) −21.0000 36.3731i −0.751921 1.30236i
\(781\) −1.00000 1.73205i −0.0357828 0.0619777i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) 45.0000