Properties

Label 1470.2.i.m.361.1
Level $1470$
Weight $2$
Character 1470.361
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.m.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(-1.50000 - 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +1.00000 q^{27} -8.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.00000 q^{36} +(-5.50000 - 9.52628i) q^{37} +(1.50000 - 2.59808i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(3.50000 - 6.06218i) q^{46} +(-2.50000 - 4.33013i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(5.50000 - 9.52628i) q^{53} +(0.500000 + 0.866025i) q^{54} -1.00000 q^{55} +3.00000 q^{57} +(-4.00000 - 6.92820i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{60} -2.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(-0.500000 + 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(5.50000 - 9.52628i) q^{74} +(-0.500000 - 0.866025i) q^{75} +3.00000 q^{76} +1.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.50000 + 9.52628i) q^{82} -8.00000 q^{83} +(4.00000 + 6.92820i) q^{86} +(4.00000 - 6.92820i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-5.00000 - 8.66025i) q^{89} -1.00000 q^{90} +7.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(2.50000 - 4.33013i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(0.500000 + 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - q^{5} - 2q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - q^{5} - 2q^{6} - 2q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2q^{13} + 2q^{15} - q^{16} + q^{18} - 3q^{19} + 2q^{20} + 2q^{22} - 7q^{23} + q^{24} - q^{25} - q^{26} + 2q^{27} - 16q^{29} + q^{30} - 2q^{31} + q^{32} + q^{33} + 2q^{36} - 11q^{37} + 3q^{38} + q^{39} + q^{40} + 22q^{41} + 16q^{43} + q^{44} - q^{45} + 7q^{46} - 5q^{47} + 2q^{48} - 2q^{50} + q^{52} + 11q^{53} + q^{54} - 2q^{55} + 6q^{57} - 8q^{58} + 4q^{59} - q^{60} - 4q^{62} + 2q^{64} + q^{65} - q^{66} + 14q^{69} - 12q^{71} + q^{72} - 6q^{73} + 11q^{74} - q^{75} + 6q^{76} + 2q^{78} + 8q^{79} - q^{80} - q^{81} + 11q^{82} - 16q^{83} + 8q^{86} + 8q^{87} - q^{88} - 10q^{89} - 2q^{90} + 14q^{92} - 2q^{93} + 5q^{94} - 3q^{95} + q^{96} + 32q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −5.50000 9.52628i −0.904194 1.56611i −0.821995 0.569495i \(-0.807139\pi\)
−0.0821995 0.996616i \(-0.526194\pi\)
\(38\) 1.50000 2.59808i 0.243332 0.421464i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) −2.50000 4.33013i −0.364662 0.631614i 0.624059 0.781377i \(-0.285482\pi\)
−0.988722 + 0.149763i \(0.952149\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i \(-0.560736\pi\)
0.945134 0.326683i \(-0.105931\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) −4.00000 6.92820i −0.525226 0.909718i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(68\) 0 0
\(69\) 7.00000 0.842701
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −3.00000 + 5.19615i −0.351123 + 0.608164i −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 5.50000 9.52628i 0.639362 1.10741i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 3.00000 0.344124
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.50000 + 9.52628i 0.607373 + 1.05200i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 4.00000 6.92820i 0.428845 0.742781i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 7.00000 0.729800
\(93\) −1.00000 1.73205i −0.103695 0.179605i
\(94\) 2.50000 4.33013i 0.257855 0.446619i
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i \(-0.877647\pi\)
0.138767 0.990325i \(-0.455686\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 11.0000 1.06841
\(107\) 5.00000 + 8.66025i 0.483368 + 0.837218i 0.999818 0.0190994i \(-0.00607989\pi\)
−0.516449 + 0.856318i \(0.672747\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −3.00000 + 5.19615i −0.287348 + 0.497701i −0.973176 0.230063i \(-0.926107\pi\)
0.685828 + 0.727764i \(0.259440\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) 11.0000 1.04407
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.50000 + 2.59808i 0.140488 + 0.243332i
\(115\) −3.50000 + 6.06218i −0.326377 + 0.565301i
\(116\) 4.00000 6.92820i 0.371391 0.643268i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) −5.50000 + 9.52628i −0.495918 + 0.858956i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.0000 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) −0.500000 + 0.866025i −0.0438529 + 0.0759555i
\(131\) −2.50000 4.33013i −0.218426 0.378325i 0.735901 0.677089i \(-0.236759\pi\)
−0.954327 + 0.298764i \(0.903426\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) 0 0
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 0 0
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 3.50000 + 6.06218i 0.297940 + 0.516047i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 5.00000 0.421076
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −0.500000 + 0.866025i −0.0418121 + 0.0724207i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 11.0000 0.904194
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −3.00000 + 5.19615i −0.244137 + 0.422857i −0.961888 0.273442i \(-0.911838\pi\)
0.717752 + 0.696299i \(0.245171\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0.500000 + 0.866025i 0.0400320 + 0.0693375i
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 5.50000 + 9.52628i 0.436178 + 0.755483i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −8.00000 13.8564i −0.626608 1.08532i −0.988227 0.152992i \(-0.951109\pi\)
0.361619 0.932326i \(-0.382224\pi\)
\(164\) −5.50000 + 9.52628i −0.429478 + 0.743877i
\(165\) 0.500000 0.866025i 0.0389249 0.0674200i
\(166\) −4.00000 6.92820i −0.310460 0.537733i
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −1.50000 + 2.59808i −0.114708 + 0.198680i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i \(-0.973527\pi\)
0.426329 0.904568i \(-0.359807\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 2.00000 + 3.46410i 0.150329 + 0.260378i
\(178\) 5.00000 8.66025i 0.374766 0.649113i
\(179\) 9.50000 16.4545i 0.710063 1.22987i −0.254770 0.967002i \(-0.582000\pi\)
0.964833 0.262864i \(-0.0846670\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 24.0000 1.78391 0.891953 0.452128i \(-0.149335\pi\)
0.891953 + 0.452128i \(0.149335\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.50000 + 6.06218i 0.258023 + 0.446910i
\(185\) −5.50000 + 9.52628i −0.404368 + 0.700386i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) 0 0
\(188\) 5.00000 0.364662
\(189\) 0 0
\(190\) −3.00000 −0.217643
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −11.0000 + 19.0526i −0.791797 + 1.37143i 0.133056 + 0.991109i \(0.457521\pi\)
−0.924853 + 0.380325i \(0.875812\pi\)
\(194\) 8.00000 + 13.8564i 0.574367 + 0.994832i
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) −1.00000 −0.0712470 −0.0356235 0.999365i \(-0.511342\pi\)
−0.0356235 + 0.999365i \(0.511342\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i \(0.490462\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −5.50000 9.52628i −0.384137 0.665344i
\(206\) 8.00000 13.8564i 0.557386 0.965422i
\(207\) −3.50000 + 6.06218i −0.243267 + 0.421350i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 5.50000 + 9.52628i 0.377742 + 0.654268i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) −3.00000 5.19615i −0.202721 0.351123i
\(220\) 0.500000 0.866025i 0.0337100 0.0583874i
\(221\) 0 0
\(222\) 5.50000 + 9.52628i 0.369136 + 0.639362i
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 4.00000 6.92820i 0.265489 0.459841i −0.702202 0.711977i \(-0.747800\pi\)
0.967692 + 0.252136i \(0.0811332\pi\)
\(228\) −1.50000 + 2.59808i −0.0993399 + 0.172062i
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) −7.00000 −0.461566
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) −0.500000 + 0.866025i −0.0326860 + 0.0566139i
\(235\) −2.50000 + 4.33013i −0.163082 + 0.282466i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) −5.00000 + 8.66025i −0.321412 + 0.556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) −11.0000 −0.701334
\(247\) 1.50000 + 2.59808i 0.0954427 + 0.165312i
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) 4.00000 6.92820i 0.253490 0.439057i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −13.0000 −0.820553 −0.410276 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(252\) 0 0
\(253\) −7.00000 −0.440086
\(254\) −8.50000 14.7224i −0.533337 0.923768i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −10.0000 17.3205i −0.623783 1.08042i −0.988775 0.149413i \(-0.952262\pi\)
0.364992 0.931011i \(-0.381072\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) 4.00000 + 6.92820i 0.247594 + 0.428845i
\(262\) 2.50000 4.33013i 0.154451 0.267516i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) −11.0000 −0.675725
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 0 0
\(269\) 10.0000 17.3205i 0.609711 1.05605i −0.381577 0.924337i \(-0.624619\pi\)
0.991288 0.131713i \(-0.0420477\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 16.0000 + 27.7128i 0.971931 + 1.68343i 0.689713 + 0.724083i \(0.257737\pi\)
0.282218 + 0.959350i \(0.408930\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) −3.50000 + 6.06218i −0.210675 + 0.364900i
\(277\) 11.0000 19.0526i 0.660926 1.14476i −0.319447 0.947604i \(-0.603497\pi\)
0.980373 0.197153i \(-0.0631696\pi\)
\(278\) −10.0000 17.3205i −0.599760 1.03882i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −1.00000 −0.0596550 −0.0298275 0.999555i \(-0.509496\pi\)
−0.0298275 + 0.999555i \(0.509496\pi\)
\(282\) 2.50000 + 4.33013i 0.148873 + 0.257855i
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) −1.50000 2.59808i −0.0888523 0.153897i
\(286\) −1.00000 −0.0591312
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −4.00000 + 6.92820i −0.234888 + 0.406838i
\(291\) −8.00000 + 13.8564i −0.468968 + 0.812277i
\(292\) −3.00000 5.19615i −0.175562 0.304082i
\(293\) −27.0000 −1.57736 −0.788678 0.614806i \(-0.789234\pi\)
−0.788678 + 0.614806i \(0.789234\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 5.50000 + 9.52628i 0.319681 + 0.553704i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 0 0
\(299\) 3.50000 + 6.06218i 0.202410 + 0.350585i
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −6.00000 −0.345261
\(303\) 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 \(0.693340\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 1.00000 + 1.73205i 0.0567962 + 0.0983739i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) −0.500000 + 0.866025i −0.0283069 + 0.0490290i
\(313\) −6.00000 10.3923i −0.339140 0.587408i 0.645131 0.764072i \(-0.276803\pi\)
−0.984271 + 0.176664i \(0.943469\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) −5.50000 + 9.52628i −0.308425 + 0.534207i
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −10.0000 −0.558146
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 8.00000 13.8564i 0.443079 0.767435i
\(327\) −3.00000 5.19615i −0.165900 0.287348i
\(328\) −11.0000 −0.607373
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) 4.00000 6.92820i 0.219529 0.380235i
\(333\) −5.50000 + 9.52628i −0.301398 + 0.522037i
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 0 0
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) 1.00000 + 1.73205i 0.0541530 + 0.0937958i
\(342\) −3.00000 −0.162221
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) −3.50000 6.06218i −0.188434 0.326377i
\(346\) 7.50000 12.9904i 0.403202 0.698367i
\(347\) −7.00000 + 12.1244i −0.375780 + 0.650870i −0.990443 0.137920i \(-0.955958\pi\)
0.614664 + 0.788789i \(0.289292\pi\)
\(348\) 4.00000 + 6.92820i 0.214423 + 0.371391i
\(349\) −12.0000 −0.642345 −0.321173 0.947021i \(-0.604077\pi\)
−0.321173 + 0.947021i \(0.604077\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 19.0000 1.00418
\(359\) −2.00000 3.46410i −0.105556 0.182828i 0.808409 0.588621i \(-0.200329\pi\)
−0.913965 + 0.405793i \(0.866996\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 12.0000 + 20.7846i 0.630706 + 1.09241i
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 12.5000 21.6506i 0.652495 1.13015i −0.330021 0.943974i \(-0.607056\pi\)
0.982516 0.186180i \(-0.0596109\pi\)
\(368\) −3.50000 + 6.06218i −0.182450 + 0.316013i
\(369\) −5.50000 9.52628i −0.286319 0.495918i
\(370\) −11.0000 −0.571863
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 2.50000 + 4.33013i 0.128928 + 0.223309i
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) 8.50000 14.7224i 0.435468 0.754253i
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) 17.5000 + 30.3109i 0.894208 + 1.54881i 0.834781 + 0.550581i \(0.185594\pi\)
0.0594268 + 0.998233i \(0.481073\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −8.00000 + 13.8564i −0.406138 + 0.703452i
\(389\) −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) −0.500000 0.866025i −0.0253185 0.0438529i
\(391\) 0 0
\(392\) 0 0
\(393\) 5.00000 0.252217
\(394\) −0.500000 0.866025i −0.0251896 0.0436297i
\(395\) 4.00000 6.92820i 0.201262 0.348596i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 2.50000 + 4.33013i 0.124844 + 0.216236i 0.921672 0.387970i \(-0.126824\pi\)
−0.796828 + 0.604206i \(0.793490\pi\)
\(402\) 0 0
\(403\) 1.00000 1.73205i 0.0498135 0.0862796i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −11.0000 −0.545250
\(408\) 0 0
\(409\) 1.00000 1.73205i 0.0494468 0.0856444i −0.840243 0.542211i \(-0.817588\pi\)
0.889689 + 0.456566i \(0.150921\pi\)
\(410\) 5.50000 9.52628i 0.271626 0.470469i
\(411\) 9.00000 + 15.5885i 0.443937 + 0.768922i
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) −7.00000 −0.344031
\(415\) 4.00000 + 6.92820i 0.196352 + 0.340092i
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 10.0000 17.3205i 0.489702 0.848189i
\(418\) −1.50000 2.59808i −0.0733674 0.127076i
\(419\) 5.00000 0.244266 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 2.50000 + 4.33013i 0.121698 + 0.210787i
\(423\) −2.50000 + 4.33013i −0.121554 + 0.210538i
\(424\) −5.50000 + 9.52628i −0.267104 + 0.462637i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) −0.500000 0.866025i −0.0241402 0.0418121i
\(430\) 4.00000 6.92820i 0.192897 0.334108i
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 32.0000 1.53782 0.768911 0.639356i \(-0.220799\pi\)
0.768911 + 0.639356i \(0.220799\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) −3.00000 5.19615i −0.143674 0.248851i
\(437\) −10.5000 + 18.1865i −0.502283 + 0.869980i
\(438\) 3.00000 5.19615i 0.143346 0.248282i
\(439\) 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i \(0.109922\pi\)
−0.177325 + 0.984152i \(0.556744\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) 0 0
\(443\) −8.00000 13.8564i −0.380091 0.658338i 0.610984 0.791643i \(-0.290774\pi\)
−0.991075 + 0.133306i \(0.957441\pi\)
\(444\) −5.50000 + 9.52628i −0.261018 + 0.452097i
\(445\) −5.00000 + 8.66025i −0.237023 + 0.410535i
\(446\) −6.00000 10.3923i −0.284108 0.492090i
\(447\) 0 0
\(448\) 0 0
\(449\) 11.0000 0.519122 0.259561 0.965727i \(-0.416422\pi\)
0.259561 + 0.965727i \(0.416422\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 5.50000 9.52628i 0.258985 0.448575i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −3.00000 5.19615i −0.140952 0.244137i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) −3.50000 6.06218i −0.163188 0.282650i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 4.00000 + 6.92820i 0.185695 + 0.321634i
\(465\) −1.00000 + 1.73205i −0.0463739 + 0.0803219i
\(466\) 9.00000 15.5885i 0.416917 0.722121i
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 0 0
\(470\) −5.00000 −0.230633
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) −4.00000 6.92820i −0.183726 0.318223i
\(475\) 3.00000 0.137649
\(476\) 0 0
\(477\) −11.0000 −0.503655
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) 11.0000 19.0526i 0.502603 0.870534i −0.497393 0.867526i \(-0.665709\pi\)
0.999995 0.00300810i \(-0.000957509\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 5.50000 + 9.52628i 0.250778 + 0.434361i
\(482\) 7.00000 0.318841
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) −8.00000 13.8564i −0.363261 0.629187i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) 0 0
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) −5.50000 9.52628i −0.247959 0.429478i
\(493\) 0 0
\(494\) −1.50000 + 2.59808i −0.0674882 + 0.116893i
\(495\) 0.500000 + 0.866025i 0.0224733 + 0.0389249i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 8.00000 0.358489
\(499\) 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −1.50000 + 2.59808i −0.0670151 + 0.116073i
\(502\) −6.50000 11.2583i −0.290109 0.502484i
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.50000 6.06218i −0.155594 0.269497i
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 8.50000 14.7224i 0.377127 0.653202i
\(509\) −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −1.50000 2.59808i −0.0662266 0.114708i
\(514\) 10.0000 17.3205i 0.441081 0.763975i
\(515\) −8.00000 + 13.8564i −0.352522 + 0.610586i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) −5.00000 −0.219900
\(518\) 0 0
\(519\) 15.0000 0.658427
\(520\) −0.500000 0.866025i −0.0219265 0.0379777i
\(521\) −16.5000 + 28.5788i −0.722878 + 1.25206i 0.236963 + 0.971519i \(0.423848\pi\)
−0.959841 + 0.280543i \(0.909485\pi\)
\(522\) −4.00000 + 6.92820i −0.175075 + 0.303239i
\(523\) 1.00000 + 1.73205i 0.0437269 + 0.0757373i 0.887061 0.461653i \(-0.152744\pi\)
−0.843334 + 0.537390i \(0.819410\pi\)
\(524\) 5.00000 0.218426
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) −5.50000 9.52628i −0.238905 0.413795i
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −11.0000 −0.476463
\(534\) 5.00000 + 8.66025i 0.216371 + 0.374766i
\(535\) 5.00000 8.66025i 0.216169 0.374415i
\(536\) 0 0
\(537\) 9.50000 + 16.4545i 0.409955 + 0.710063i
\(538\) 20.0000 0.862261
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) −16.0000 + 27.7128i −0.687259 + 1.19037i
\(543\) −12.0000 + 20.7846i −0.514969 + 0.891953i
\(544\) 0 0
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) 9.00000 + 15.5885i 0.384461 + 0.665906i
\(549\) 0 0
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 12.0000 + 20.7846i 0.511217 + 0.885454i
\(552\) −7.00000 −0.297940
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) −5.50000 9.52628i −0.233462 0.404368i
\(556\) 10.0000 17.3205i 0.424094 0.734553i
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 1.00000 + 1.73205i 0.0423334 + 0.0733236i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −0.500000 0.866025i −0.0210912 0.0365311i
\(563\) −19.0000 + 32.9090i −0.800755 + 1.38695i 0.118366 + 0.992970i \(0.462235\pi\)
−0.919120 + 0.393977i \(0.871099\pi\)
\(564\) −2.50000 + 4.33013i −0.105269 + 0.182331i
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654398i \(0.772922\pi\)
\(570\) 1.50000 2.59808i 0.0628281 0.108821i
\(571\) 16.0000 27.7128i 0.669579 1.15975i −0.308443 0.951243i \(-0.599808\pi\)
0.978022 0.208502i \(-0.0668588\pi\)
\(572\) −0.500000 0.866025i −0.0209061 0.0362103i
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 7.00000 0.291920
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −7.00000 + 12.1244i −0.291414 + 0.504744i −0.974144 0.225927i \(-0.927459\pi\)
0.682730 + 0.730670i \(0.260792\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) −11.0000 19.0526i −0.457144 0.791797i
\(580\) −8.00000 −0.332182
\(581\) 0 0
\(582\) −16.0000 −0.663221
\(583\) −5.50000 9.52628i −0.227787 0.394538i
\(584\) 3.00000 5.19615i 0.124141 0.215018i
\(585\) 0.500000 0.866025i 0.0206725 0.0358057i
\(586\) −13.5000 23.3827i −0.557680 0.965930i
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) −2.00000 3.46410i −0.0823387 0.142615i
\(591\) 0.500000 0.866025i 0.0205673 0.0356235i
\(592\) −5.50000 + 9.52628i −0.226049 + 0.391528i
\(593\) 8.00000 + 13.8564i 0.328521 + 0.569014i 0.982219 0.187741i \(-0.0601166\pi\)
−0.653698 + 0.756756i \(0.726783\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) 0 0
\(597\) −12.0000 20.7846i −0.491127 0.850657i
\(598\) −3.50000 + 6.06218i −0.143126 + 0.247901i
\(599\) −1.00000 + 1.73205i −0.0408589 + 0.0707697i −0.885732 0.464198i \(-0.846343\pi\)
0.844873 + 0.534967i \(0.179676\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.00000 5.19615i −0.122068 0.211428i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) −18.5000 32.0429i −0.750892 1.30058i −0.947391 0.320079i \(-0.896291\pi\)
0.196499 0.980504i \(-0.437043\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) 2.50000 + 4.33013i 0.101139 + 0.175178i
\(612\) 0 0
\(613\) 20.5000 35.5070i 0.827987 1.43412i −0.0716275 0.997431i \(-0.522819\pi\)
0.899615 0.436684i \(-0.143847\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 11.0000 0.443563
\(616\) 0 0
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 8.00000 + 13.8564i 0.321807 + 0.557386i
\(619\) 14.5000 25.1147i 0.582804 1.00945i −0.412341 0.911030i \(-0.635289\pi\)
0.995145 0.0984169i \(-0.0313779\pi\)
\(620\) −1.00000 + 1.73205i −0.0401610 + 0.0695608i
\(621\) −3.50000 6.06218i −0.140450 0.243267i
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 6.00000 10.3923i 0.239808 0.415360i
\(627\) 1.50000 2.59808i 0.0599042 0.103757i
\(628\) −3.50000 6.06218i −0.139665 0.241907i
\(629\) 0 0
\(630\) 0 0
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) −2.50000 + 4.33013i −0.0993661 + 0.172107i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 8.50000 + 14.7224i 0.337312 + 0.584242i
\(636\) −11.0000 −0.436178
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 1.50000 2.59808i 0.0592464 0.102618i −0.834881 0.550431i \(-0.814464\pi\)
0.894127 + 0.447813i \(0.147797\pi\)
\(642\) −5.00000 8.66025i −0.197334 0.341793i
\(643\) 10.0000 0.394362 0.197181 0.980367i \(-0.436821\pi\)
0.197181 + 0.980367i \(0.436821\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) −8.50000 + 14.7224i −0.334169 + 0.578799i −0.983325 0.181857i \(-0.941789\pi\)
0.649155 + 0.760656i \(0.275122\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −2.00000 3.46410i −0.0785069 0.135978i
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) −3.50000 6.06218i −0.136966 0.237231i 0.789381 0.613904i \(-0.210402\pi\)
−0.926347 + 0.376672i \(0.877068\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) −2.50000 + 4.33013i −0.0976831 + 0.169192i
\(656\) −5.50000 9.52628i −0.214739 0.371939i
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0.500000 + 0.866025i 0.0194625 + 0.0337100i
\(661\) −12.0000 + 20.7846i −0.466746 + 0.808428i −0.999278 0.0379819i \(-0.987907\pi\)
0.532533 + 0.846410i \(0.321240\pi\)
\(662\) −6.50000 + 11.2583i −0.252630 + 0.437567i
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) −11.0000 −0.426241
\(667\) 28.0000 + 48.4974i 1.08416 + 1.87783i
\(668\) −1.50000 + 2.59808i −0.0580367 + 0.100523i
\(669\) 6.00000 10.3923i 0.231973 0.401790i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) −6.00000 10.3923i −0.231111 0.400297i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −6.50000 11.2583i −0.249815 0.432693i 0.713659 0.700493i \(-0.247037\pi\)
−0.963474 + 0.267800i \(0.913703\pi\)
\(678\) −6.00000 −0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) −1.00000 + 1.73205i −0.0382920 + 0.0663237i
\(683\) −2.00000 + 3.46410i −0.0765279 + 0.132550i −0.901750 0.432259i \(-0.857717\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(684\) −1.50000 2.59808i −0.0573539 0.0993399i
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) −5.50000 + 9.52628i −0.209533 + 0.362922i
\(690\) 3.50000 6.06218i 0.133243 0.230783i
\(691\) −6.00000 10.3923i −0.228251 0.395342i 0.729039 0.684472i \(-0.239967\pi\)
−0.957290 + 0.289130i \(0.906634\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) −14.0000 −0.531433
\(695\) 10.0000 + 17.3205i 0.379322 + 0.657004i
\(696\) −4.00000 + 6.92820i −0.151620 + 0.262613i
\(697\) 0 0
\(698\) −6.00000 10.3923i −0.227103 0.393355i
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −0.500000 0.866025i −0.0188713 0.0326860i
\(703\) −16.5000 + 28.5788i −0.622309 + 1.07787i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −2.50000 4.33013i −0.0941554 0.163082i
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) −3.00000 + 5.19615i −0.112588 + 0.195008i
\(711\) 4.00000 6.92820i 0.150012 0.259828i
\(712\) 5.00000 + 8.66025i 0.187383 + 0.324557i
\(713\) 14.0000 0.524304
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 9.50000 + 16.4545i 0.355032 + 0.614933i
\(717\) 9.00000 15.5885i 0.336111 0.582162i
\(718\) 2.00000 3.46410i 0.0746393 0.129279i
\(719\) 1.00000 + 1.73205i 0.0372937 + 0.0645946i 0.884070 0.467355i \(-0.154793\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 10.0000 0.372161
\(723\) 3.50000 + 6.06218i 0.130166 + 0.225455i
\(724\) −12.0000 + 20.7846i −0.445976 + 0.772454i
\(725\) 4.00000 6.92820i 0.148556 0.257307i
\(726\) −5.00000 8.66025i −0.185567 0.321412i
\(727\) −11.0000 −0.407967 −0.203984 0.978974i \(-0.565389\pi\)
−0.203984 + 0.978974i \(0.565389\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.00000 + 5.19615i 0.111035 + 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) 5.50000 + 9.52628i 0.203147 + 0.351861i 0.949541 0.313644i \(-0.101550\pi\)
−0.746394 + 0.665505i \(0.768216\pi\)
\(734\) 25.0000 0.922767
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 0 0
\(738\) 5.50000 9.52628i 0.202458 0.350667i
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) −5.50000 9.52628i −0.202184 0.350193i
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) 49.0000 1.79764 0.898818 0.438322i \(-0.144427\pi\)
0.898818 + 0.438322i \(0.144427\pi\)
\(744\) 1.00000 + 1.73205i 0.0366618 + 0.0635001i
\(745\) 0 0
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) 4.00000 + 6.92820i 0.146352 + 0.253490i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i \(-0.323993\pi\)
−0.999570 + 0.0293387i \(0.990660\pi\)
\(752\) −2.50000 + 4.33013i −0.0911656 + 0.157903i
\(753\) 6.50000 11.2583i 0.236873 0.410276i
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −9.50000 16.4545i −0.345056 0.597654i
\(759\) 3.50000 6.06218i 0.127042 0.220043i
\(760\) 1.50000 2.59808i 0.0544107 0.0942421i
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 17.0000 0.615845
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) −17.5000 + 30.3109i −0.632301 + 1.09518i
\(767\) −2.00000 + 3.46410i −0.0722158 + 0.125081i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) −11.0000 19.0526i −0.395899 0.685717i
\(773\) 16.5000 28.5788i 0.593464 1.02791i −0.400298 0.916385i \(-0.631093\pi\)
0.993762 0.111524i \(-0.0355733\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) −1.00000 1.73205i −0.0359211 0.0622171i
\(776\) −16.0000 −0.574367
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) −16.5000 28.5788i −0.591174 1.02394i
\(780\) 0.500000 0.866025i 0.0179029 0.0310087i
\(781\) −3.00000 + 5.19615i −0.107348 + 0.185933i
\(782\) 0 0
\(783\) −8.00000 −0.285897
\(784\) 0 0
\(785\) 7.00000 0.249841
\(786\) 2.50000 + 4.33013i 0.0891720 + 0.154451i
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) 0.500000 0.866025i 0.0178118 0.0308509i
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) 8.00000 0.284627
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) 0 0
\(794\) −7.00000 + 12.1244i −0.248421 + 0.430277i
\(795\) 5.50000 9.52628i 0.195065 0.337862i
\(796\) −12.0000 20.7846i −0.425329 0.736691i
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −5.00000 + 8.66025i −0.176666 +