Properties

Label 735.2.i.l.361.2
Level $735$
Weight $2$
Character 735.361
Analytic conductor $5.869$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 735.361
Dual form 735.2.i.l.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 2.36603i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.73205 q^{6} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.36603 + 2.36603i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.73205 q^{6} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-2.73205 - 4.73205i) q^{12} -2.26795 q^{13} -1.00000 q^{15} +(-7.46410 - 12.9282i) q^{16} +(1.63397 - 2.83013i) q^{17} +(1.36603 - 2.36603i) q^{18} +(2.23205 + 3.86603i) q^{19} -5.46410 q^{20} -2.00000 q^{22} +(2.36603 + 4.09808i) q^{23} +(4.73205 - 8.19615i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.09808 - 5.36603i) q^{26} +1.00000 q^{27} -4.19615 q^{29} +(-1.36603 - 2.36603i) q^{30} +(-0.232051 + 0.401924i) q^{31} +(10.9282 - 18.9282i) q^{32} +(-0.366025 - 0.633975i) q^{33} +8.92820 q^{34} +5.46410 q^{36} +(1.59808 + 2.76795i) q^{37} +(-6.09808 + 10.5622i) q^{38} +(1.13397 - 1.96410i) q^{39} +(-4.73205 - 8.19615i) q^{40} +0.732051 q^{41} +3.19615 q^{43} +(-2.00000 - 3.46410i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-6.46410 + 11.1962i) q^{46} +(1.00000 + 1.73205i) q^{47} +14.9282 q^{48} -2.73205 q^{50} +(1.63397 + 2.83013i) q^{51} +(6.19615 - 10.7321i) q^{52} +(-6.19615 + 10.7321i) q^{53} +(1.36603 + 2.36603i) q^{54} -0.732051 q^{55} -4.46410 q^{57} +(-5.73205 - 9.92820i) q^{58} +(-0.0980762 + 0.169873i) q^{59} +(2.73205 - 4.73205i) q^{60} +(2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +29.8564 q^{64} +(-1.13397 - 1.96410i) q^{65} +(1.00000 - 1.73205i) q^{66} +(7.33013 - 12.6962i) q^{67} +(8.92820 + 15.4641i) q^{68} -4.73205 q^{69} +6.19615 q^{71} +(4.73205 + 8.19615i) q^{72} +(6.33013 - 10.9641i) q^{73} +(-4.36603 + 7.56218i) q^{74} +(-0.500000 - 0.866025i) q^{75} -24.3923 q^{76} +6.19615 q^{78} +(3.69615 + 6.40192i) q^{79} +(7.46410 - 12.9282i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} -15.1244 q^{83} +3.26795 q^{85} +(4.36603 + 7.56218i) q^{86} +(2.09808 - 3.63397i) q^{87} +(3.46410 - 6.00000i) q^{88} +(7.56218 + 13.0981i) q^{89} +2.73205 q^{90} -25.8564 q^{92} +(-0.232051 - 0.401924i) q^{93} +(-2.73205 + 4.73205i) q^{94} +(-2.23205 + 3.86603i) q^{95} +(10.9282 + 18.9282i) q^{96} -14.9282 q^{97} +0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 4q^{6} - 24q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 4q^{6} - 24q^{8} - 2q^{9} - 2q^{10} + 2q^{11} - 4q^{12} - 16q^{13} - 4q^{15} - 16q^{16} + 10q^{17} + 2q^{18} + 2q^{19} - 8q^{20} - 8q^{22} + 6q^{23} + 12q^{24} - 2q^{25} - 2q^{26} + 4q^{27} + 4q^{29} - 2q^{30} + 6q^{31} + 16q^{32} + 2q^{33} + 8q^{34} + 8q^{36} - 4q^{37} - 14q^{38} + 8q^{39} - 12q^{40} - 4q^{41} - 8q^{43} - 8q^{44} + 2q^{45} - 12q^{46} + 4q^{47} + 32q^{48} - 4q^{50} + 10q^{51} + 4q^{52} - 4q^{53} + 2q^{54} + 4q^{55} - 4q^{57} - 16q^{58} + 10q^{59} + 4q^{60} + 8q^{61} - 12q^{62} + 64q^{64} - 8q^{65} + 4q^{66} + 12q^{67} + 8q^{68} - 12q^{69} + 4q^{71} + 12q^{72} + 8q^{73} - 14q^{74} - 2q^{75} - 56q^{76} + 4q^{78} - 6q^{79} + 16q^{80} - 2q^{81} + 4q^{82} - 12q^{83} + 20q^{85} + 14q^{86} - 2q^{87} + 6q^{89} + 4q^{90} - 48q^{92} + 6q^{93} - 4q^{94} - 2q^{95} + 16q^{96} - 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 2.36603i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −2.73205 + 4.73205i −1.36603 + 2.36603i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −2.73205 −1.11536
\(7\) 0 0
\(8\) −9.46410 −3.34607
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.36603 + 2.36603i −0.431975 + 0.748203i
\(11\) −0.366025 + 0.633975i −0.110361 + 0.191151i −0.915916 0.401371i \(-0.868534\pi\)
0.805555 + 0.592521i \(0.201867\pi\)
\(12\) −2.73205 4.73205i −0.788675 1.36603i
\(13\) −2.26795 −0.629016 −0.314508 0.949255i \(-0.601840\pi\)
−0.314508 + 0.949255i \(0.601840\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −7.46410 12.9282i −1.86603 3.23205i
\(17\) 1.63397 2.83013i 0.396297 0.686407i −0.596969 0.802264i \(-0.703628\pi\)
0.993266 + 0.115858i \(0.0369617\pi\)
\(18\) 1.36603 2.36603i 0.321975 0.557678i
\(19\) 2.23205 + 3.86603i 0.512068 + 0.886927i 0.999902 + 0.0139909i \(0.00445360\pi\)
−0.487835 + 0.872936i \(0.662213\pi\)
\(20\) −5.46410 −1.22181
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 2.36603 + 4.09808i 0.493350 + 0.854508i 0.999971 0.00766135i \(-0.00243871\pi\)
−0.506620 + 0.862169i \(0.669105\pi\)
\(24\) 4.73205 8.19615i 0.965926 1.67303i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.09808 5.36603i −0.607583 1.05236i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.19615 −0.779206 −0.389603 0.920983i \(-0.627388\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(30\) −1.36603 2.36603i −0.249401 0.431975i
\(31\) −0.232051 + 0.401924i −0.0416776 + 0.0721876i −0.886112 0.463472i \(-0.846604\pi\)
0.844434 + 0.535659i \(0.179937\pi\)
\(32\) 10.9282 18.9282i 1.93185 3.34607i
\(33\) −0.366025 0.633975i −0.0637168 0.110361i
\(34\) 8.92820 1.53117
\(35\) 0 0
\(36\) 5.46410 0.910684
\(37\) 1.59808 + 2.76795i 0.262722 + 0.455048i 0.966964 0.254912i \(-0.0820464\pi\)
−0.704242 + 0.709960i \(0.748713\pi\)
\(38\) −6.09808 + 10.5622i −0.989239 + 1.71341i
\(39\) 1.13397 1.96410i 0.181581 0.314508i
\(40\) −4.73205 8.19615i −0.748203 1.29593i
\(41\) 0.732051 0.114327 0.0571636 0.998365i \(-0.481794\pi\)
0.0571636 + 0.998365i \(0.481794\pi\)
\(42\) 0 0
\(43\) 3.19615 0.487409 0.243704 0.969850i \(-0.421637\pi\)
0.243704 + 0.969850i \(0.421637\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) −6.46410 + 11.1962i −0.953080 + 1.65078i
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 14.9282 2.15470
\(49\) 0 0
\(50\) −2.73205 −0.386370
\(51\) 1.63397 + 2.83013i 0.228802 + 0.396297i
\(52\) 6.19615 10.7321i 0.859252 1.48827i
\(53\) −6.19615 + 10.7321i −0.851107 + 1.47416i 0.0291032 + 0.999576i \(0.490735\pi\)
−0.880210 + 0.474584i \(0.842598\pi\)
\(54\) 1.36603 + 2.36603i 0.185893 + 0.321975i
\(55\) −0.732051 −0.0987097
\(56\) 0 0
\(57\) −4.46410 −0.591285
\(58\) −5.73205 9.92820i −0.752655 1.30364i
\(59\) −0.0980762 + 0.169873i −0.0127684 + 0.0221156i −0.872339 0.488901i \(-0.837398\pi\)
0.859571 + 0.511017i \(0.170731\pi\)
\(60\) 2.73205 4.73205i 0.352706 0.610905i
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) −1.26795 −0.161030
\(63\) 0 0
\(64\) 29.8564 3.73205
\(65\) −1.13397 1.96410i −0.140652 0.243617i
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) 7.33013 12.6962i 0.895518 1.55108i 0.0623548 0.998054i \(-0.480139\pi\)
0.833163 0.553028i \(-0.186528\pi\)
\(68\) 8.92820 + 15.4641i 1.08270 + 1.87530i
\(69\) −4.73205 −0.569672
\(70\) 0 0
\(71\) 6.19615 0.735348 0.367674 0.929955i \(-0.380154\pi\)
0.367674 + 0.929955i \(0.380154\pi\)
\(72\) 4.73205 + 8.19615i 0.557678 + 0.965926i
\(73\) 6.33013 10.9641i 0.740885 1.28325i −0.211207 0.977441i \(-0.567740\pi\)
0.952093 0.305810i \(-0.0989271\pi\)
\(74\) −4.36603 + 7.56218i −0.507540 + 0.879085i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −24.3923 −2.79799
\(77\) 0 0
\(78\) 6.19615 0.701576
\(79\) 3.69615 + 6.40192i 0.415850 + 0.720273i 0.995517 0.0945803i \(-0.0301509\pi\)
−0.579668 + 0.814853i \(0.696818\pi\)
\(80\) 7.46410 12.9282i 0.834512 1.44542i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00000 + 1.73205i 0.110432 + 0.191273i
\(83\) −15.1244 −1.66011 −0.830057 0.557679i \(-0.811692\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(84\) 0 0
\(85\) 3.26795 0.354459
\(86\) 4.36603 + 7.56218i 0.470801 + 0.815451i
\(87\) 2.09808 3.63397i 0.224937 0.389603i
\(88\) 3.46410 6.00000i 0.369274 0.639602i
\(89\) 7.56218 + 13.0981i 0.801589 + 1.38839i 0.918570 + 0.395259i \(0.129345\pi\)
−0.116980 + 0.993134i \(0.537321\pi\)
\(90\) 2.73205 0.287983
\(91\) 0 0
\(92\) −25.8564 −2.69572
\(93\) −0.232051 0.401924i −0.0240625 0.0416776i
\(94\) −2.73205 + 4.73205i −0.281790 + 0.488074i
\(95\) −2.23205 + 3.86603i −0.229004 + 0.396646i
\(96\) 10.9282 + 18.9282i 1.11536 + 1.93185i
\(97\) −14.9282 −1.51573 −0.757865 0.652412i \(-0.773757\pi\)
−0.757865 + 0.652412i \(0.773757\pi\)
\(98\) 0 0
\(99\) 0.732051 0.0735739
\(100\) −2.73205 4.73205i −0.273205 0.473205i
\(101\) −3.63397 + 6.29423i −0.361594 + 0.626299i −0.988223 0.153018i \(-0.951101\pi\)
0.626629 + 0.779317i \(0.284434\pi\)
\(102\) −4.46410 + 7.73205i −0.442012 + 0.765587i
\(103\) −4.59808 7.96410i −0.453062 0.784726i 0.545513 0.838103i \(-0.316335\pi\)
−0.998574 + 0.0533764i \(0.983002\pi\)
\(104\) 21.4641 2.10473
\(105\) 0 0
\(106\) −33.8564 −3.28842
\(107\) −1.09808 1.90192i −0.106155 0.183866i 0.808054 0.589108i \(-0.200521\pi\)
−0.914210 + 0.405242i \(0.867187\pi\)
\(108\) −2.73205 + 4.73205i −0.262892 + 0.455342i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) −3.19615 −0.303365
\(112\) 0 0
\(113\) 8.92820 0.839895 0.419947 0.907548i \(-0.362049\pi\)
0.419947 + 0.907548i \(0.362049\pi\)
\(114\) −6.09808 10.5622i −0.571137 0.989239i
\(115\) −2.36603 + 4.09808i −0.220633 + 0.382148i
\(116\) 11.4641 19.8564i 1.06442 1.84362i
\(117\) 1.13397 + 1.96410i 0.104836 + 0.181581i
\(118\) −0.535898 −0.0493334
\(119\) 0 0
\(120\) 9.46410 0.863950
\(121\) 5.23205 + 9.06218i 0.475641 + 0.823834i
\(122\) −5.46410 + 9.46410i −0.494697 + 0.856840i
\(123\) −0.366025 + 0.633975i −0.0330034 + 0.0571636i
\(124\) −1.26795 2.19615i −0.113865 0.197220i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.80385 0.426273 0.213136 0.977022i \(-0.431632\pi\)
0.213136 + 0.977022i \(0.431632\pi\)
\(128\) 18.9282 + 32.7846i 1.67303 + 2.89778i
\(129\) −1.59808 + 2.76795i −0.140703 + 0.243704i
\(130\) 3.09808 5.36603i 0.271719 0.470632i
\(131\) 7.73205 + 13.3923i 0.675552 + 1.17009i 0.976307 + 0.216390i \(0.0694281\pi\)
−0.300755 + 0.953702i \(0.597239\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) 40.0526 3.46001
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −15.4641 + 26.7846i −1.32604 + 2.29676i
\(137\) −1.09808 + 1.90192i −0.0938150 + 0.162492i −0.909113 0.416549i \(-0.863240\pi\)
0.815298 + 0.579041i \(0.196573\pi\)
\(138\) −6.46410 11.1962i −0.550261 0.953080i
\(139\) −5.92820 −0.502824 −0.251412 0.967880i \(-0.580895\pi\)
−0.251412 + 0.967880i \(0.580895\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 8.46410 + 14.6603i 0.710292 + 1.23026i
\(143\) 0.830127 1.43782i 0.0694187 0.120237i
\(144\) −7.46410 + 12.9282i −0.622008 + 1.07735i
\(145\) −2.09808 3.63397i −0.174236 0.301785i
\(146\) 34.5885 2.86256
\(147\) 0 0
\(148\) −17.4641 −1.43554
\(149\) −2.92820 5.07180i −0.239888 0.415498i 0.720794 0.693149i \(-0.243777\pi\)
−0.960682 + 0.277651i \(0.910444\pi\)
\(150\) 1.36603 2.36603i 0.111536 0.193185i
\(151\) 4.46410 7.73205i 0.363283 0.629225i −0.625216 0.780452i \(-0.714989\pi\)
0.988499 + 0.151227i \(0.0483223\pi\)
\(152\) −21.1244 36.5885i −1.71341 2.96772i
\(153\) −3.26795 −0.264198
\(154\) 0 0
\(155\) −0.464102 −0.0372775
\(156\) 6.19615 + 10.7321i 0.496089 + 0.859252i
\(157\) 3.19615 5.53590i 0.255081 0.441813i −0.709837 0.704366i \(-0.751231\pi\)
0.964917 + 0.262553i \(0.0845646\pi\)
\(158\) −10.0981 + 17.4904i −0.803360 + 1.39146i
\(159\) −6.19615 10.7321i −0.491387 0.851107i
\(160\) 21.8564 1.72790
\(161\) 0 0
\(162\) −2.73205 −0.214650
\(163\) −10.9282 18.9282i −0.855963 1.48257i −0.875749 0.482767i \(-0.839632\pi\)
0.0197859 0.999804i \(-0.493702\pi\)
\(164\) −2.00000 + 3.46410i −0.156174 + 0.270501i
\(165\) 0.366025 0.633975i 0.0284950 0.0493549i
\(166\) −20.6603 35.7846i −1.60355 2.77742i
\(167\) 17.6603 1.36659 0.683296 0.730142i \(-0.260546\pi\)
0.683296 + 0.730142i \(0.260546\pi\)
\(168\) 0 0
\(169\) −7.85641 −0.604339
\(170\) 4.46410 + 7.73205i 0.342381 + 0.593021i
\(171\) 2.23205 3.86603i 0.170689 0.295642i
\(172\) −8.73205 + 15.1244i −0.665813 + 1.15322i
\(173\) 7.26795 + 12.5885i 0.552572 + 0.957083i 0.998088 + 0.0618087i \(0.0196869\pi\)
−0.445516 + 0.895274i \(0.646980\pi\)
\(174\) 11.4641 0.869091
\(175\) 0 0
\(176\) 10.9282 0.823744
\(177\) −0.0980762 0.169873i −0.00737186 0.0127684i
\(178\) −20.6603 + 35.7846i −1.54855 + 2.68217i
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) 2.73205 + 4.73205i 0.203635 + 0.352706i
\(181\) 24.3205 1.80773 0.903865 0.427819i \(-0.140718\pi\)
0.903865 + 0.427819i \(0.140718\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) −22.3923 38.7846i −1.65078 2.85924i
\(185\) −1.59808 + 2.76795i −0.117493 + 0.203504i
\(186\) 0.633975 1.09808i 0.0464853 0.0805149i
\(187\) 1.19615 + 2.07180i 0.0874713 + 0.151505i
\(188\) −10.9282 −0.797021
\(189\) 0 0
\(190\) −12.1962 −0.884802
\(191\) 4.46410 + 7.73205i 0.323011 + 0.559472i 0.981108 0.193462i \(-0.0619716\pi\)
−0.658097 + 0.752933i \(0.728638\pi\)
\(192\) −14.9282 + 25.8564i −1.07735 + 1.86603i
\(193\) −0.598076 + 1.03590i −0.0430505 + 0.0745656i −0.886748 0.462254i \(-0.847041\pi\)
0.843697 + 0.536819i \(0.180374\pi\)
\(194\) −20.3923 35.3205i −1.46408 2.53586i
\(195\) 2.26795 0.162411
\(196\) 0 0
\(197\) −0.339746 −0.0242059 −0.0121029 0.999927i \(-0.503853\pi\)
−0.0121029 + 0.999927i \(0.503853\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i \(-0.548670\pi\)
0.932075 0.362267i \(-0.117997\pi\)
\(200\) 4.73205 8.19615i 0.334607 0.579555i
\(201\) 7.33013 + 12.6962i 0.517027 + 0.895518i
\(202\) −19.8564 −1.39709
\(203\) 0 0
\(204\) −17.8564 −1.25020
\(205\) 0.366025 + 0.633975i 0.0255643 + 0.0442787i
\(206\) 12.5622 21.7583i 0.875248 1.51597i
\(207\) 2.36603 4.09808i 0.164450 0.284836i
\(208\) 16.9282 + 29.3205i 1.17376 + 2.03301i
\(209\) −3.26795 −0.226049
\(210\) 0 0
\(211\) 7.07180 0.486843 0.243421 0.969921i \(-0.421730\pi\)
0.243421 + 0.969921i \(0.421730\pi\)
\(212\) −33.8564 58.6410i −2.32527 4.02748i
\(213\) −3.09808 + 5.36603i −0.212277 + 0.367674i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 1.59808 + 2.76795i 0.108988 + 0.188773i
\(216\) −9.46410 −0.643951
\(217\) 0 0
\(218\) −30.0526 −2.03542
\(219\) 6.33013 + 10.9641i 0.427750 + 0.740885i
\(220\) 2.00000 3.46410i 0.134840 0.233550i
\(221\) −3.70577 + 6.41858i −0.249277 + 0.431761i
\(222\) −4.36603 7.56218i −0.293028 0.507540i
\(223\) 20.3923 1.36557 0.682785 0.730619i \(-0.260769\pi\)
0.682785 + 0.730619i \(0.260769\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 12.1962 + 21.1244i 0.811276 + 1.40517i
\(227\) −0.830127 + 1.43782i −0.0550975 + 0.0954316i −0.892259 0.451525i \(-0.850880\pi\)
0.837161 + 0.546956i \(0.184214\pi\)
\(228\) 12.1962 21.1244i 0.807710 1.39899i
\(229\) −1.50000 2.59808i −0.0991228 0.171686i 0.812199 0.583380i \(-0.198270\pi\)
−0.911322 + 0.411695i \(0.864937\pi\)
\(230\) −12.9282 −0.852460
\(231\) 0 0
\(232\) 39.7128 2.60727
\(233\) −8.66025 15.0000i −0.567352 0.982683i −0.996827 0.0796037i \(-0.974635\pi\)
0.429474 0.903079i \(-0.358699\pi\)
\(234\) −3.09808 + 5.36603i −0.202528 + 0.350788i
\(235\) −1.00000 + 1.73205i −0.0652328 + 0.112987i
\(236\) −0.535898 0.928203i −0.0348840 0.0604209i
\(237\) −7.39230 −0.480182
\(238\) 0 0
\(239\) 7.07180 0.457437 0.228718 0.973493i \(-0.426547\pi\)
0.228718 + 0.973493i \(0.426547\pi\)
\(240\) 7.46410 + 12.9282i 0.481806 + 0.834512i
\(241\) 6.73205 11.6603i 0.433650 0.751103i −0.563535 0.826092i \(-0.690559\pi\)
0.997184 + 0.0749893i \(0.0238923\pi\)
\(242\) −14.2942 + 24.7583i −0.918868 + 1.59153i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −21.8564 −1.39921
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −5.06218 8.76795i −0.322099 0.557891i
\(248\) 2.19615 3.80385i 0.139456 0.241545i
\(249\) 7.56218 13.0981i 0.479234 0.830057i
\(250\) −1.36603 2.36603i −0.0863950 0.149641i
\(251\) 24.5885 1.55201 0.776005 0.630727i \(-0.217243\pi\)
0.776005 + 0.630727i \(0.217243\pi\)
\(252\) 0 0
\(253\) −3.46410 −0.217786
\(254\) 6.56218 + 11.3660i 0.411748 + 0.713168i
\(255\) −1.63397 + 2.83013i −0.102323 + 0.177229i
\(256\) −21.8564 + 37.8564i −1.36603 + 2.36603i
\(257\) −2.83013 4.90192i −0.176538 0.305774i 0.764154 0.645034i \(-0.223157\pi\)
−0.940693 + 0.339260i \(0.889823\pi\)
\(258\) −8.73205 −0.543634
\(259\) 0 0
\(260\) 12.3923 0.768538
\(261\) 2.09808 + 3.63397i 0.129868 + 0.224937i
\(262\) −21.1244 + 36.5885i −1.30507 + 2.26044i
\(263\) −4.19615 + 7.26795i −0.258746 + 0.448161i −0.965906 0.258892i \(-0.916643\pi\)
0.707160 + 0.707053i \(0.249976\pi\)
\(264\) 3.46410 + 6.00000i 0.213201 + 0.369274i
\(265\) −12.3923 −0.761253
\(266\) 0 0
\(267\) −15.1244 −0.925596
\(268\) 40.0526 + 69.3731i 2.44660 + 4.23763i
\(269\) −6.26795 + 10.8564i −0.382164 + 0.661927i −0.991371 0.131084i \(-0.958154\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(270\) −1.36603 + 2.36603i −0.0831337 + 0.143992i
\(271\) 1.53590 + 2.66025i 0.0932992 + 0.161599i 0.908897 0.417020i \(-0.136925\pi\)
−0.815598 + 0.578619i \(0.803592\pi\)
\(272\) −48.7846 −2.95800
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −0.366025 0.633975i −0.0220722 0.0382301i
\(276\) 12.9282 22.3923i 0.778186 1.34786i
\(277\) 7.33013 12.6962i 0.440425 0.762838i −0.557296 0.830314i \(-0.688161\pi\)
0.997721 + 0.0674759i \(0.0214946\pi\)
\(278\) −8.09808 14.0263i −0.485690 0.841240i
\(279\) 0.464102 0.0277850
\(280\) 0 0
\(281\) 13.8564 0.826604 0.413302 0.910594i \(-0.364375\pi\)
0.413302 + 0.910594i \(0.364375\pi\)
\(282\) −2.73205 4.73205i −0.162691 0.281790i
\(283\) −12.0622 + 20.8923i −0.717022 + 1.24192i 0.245152 + 0.969485i \(0.421162\pi\)
−0.962174 + 0.272434i \(0.912171\pi\)
\(284\) −16.9282 + 29.3205i −1.00450 + 1.73985i
\(285\) −2.23205 3.86603i −0.132215 0.229004i
\(286\) 4.53590 0.268213
\(287\) 0 0
\(288\) −21.8564 −1.28790
\(289\) 3.16025 + 5.47372i 0.185897 + 0.321984i
\(290\) 5.73205 9.92820i 0.336598 0.583004i
\(291\) 7.46410 12.9282i 0.437553 0.757865i
\(292\) 34.5885 + 59.9090i 2.02414 + 3.50591i
\(293\) −18.9282 −1.10580 −0.552899 0.833248i \(-0.686478\pi\)
−0.552899 + 0.833248i \(0.686478\pi\)
\(294\) 0 0
\(295\) −0.196152 −0.0114204
\(296\) −15.1244 26.1962i −0.879085 1.52262i
\(297\) −0.366025 + 0.633975i −0.0212389 + 0.0367869i
\(298\) 8.00000 13.8564i 0.463428 0.802680i
\(299\) −5.36603 9.29423i −0.310325 0.537499i
\(300\) 5.46410 0.315470
\(301\) 0 0
\(302\) 24.3923 1.40362
\(303\) −3.63397 6.29423i −0.208766 0.361594i
\(304\) 33.3205 57.7128i 1.91106 3.31006i
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) −4.46410 7.73205i −0.255196 0.442012i
\(307\) 32.1244 1.83343 0.916717 0.399537i \(-0.130829\pi\)
0.916717 + 0.399537i \(0.130829\pi\)
\(308\) 0 0
\(309\) 9.19615 0.523151
\(310\) −0.633975 1.09808i −0.0360073 0.0623665i
\(311\) 4.56218 7.90192i 0.258697 0.448077i −0.707196 0.707018i \(-0.750040\pi\)
0.965893 + 0.258941i \(0.0833734\pi\)
\(312\) −10.7321 + 18.5885i −0.607583 + 1.05236i
\(313\) −6.33013 10.9641i −0.357800 0.619728i 0.629793 0.776763i \(-0.283140\pi\)
−0.987593 + 0.157035i \(0.949806\pi\)
\(314\) 17.4641 0.985556
\(315\) 0 0
\(316\) −40.3923 −2.27224
\(317\) 14.2224 + 24.6340i 0.798811 + 1.38358i 0.920391 + 0.391000i \(0.127871\pi\)
−0.121579 + 0.992582i \(0.538796\pi\)
\(318\) 16.9282 29.3205i 0.949286 1.64421i
\(319\) 1.53590 2.66025i 0.0859938 0.148946i
\(320\) 14.9282 + 25.8564i 0.834512 + 1.44542i
\(321\) 2.19615 0.122577
\(322\) 0 0
\(323\) 14.5885 0.811723
\(324\) −2.73205 4.73205i −0.151781 0.262892i
\(325\) 1.13397 1.96410i 0.0629016 0.108949i
\(326\) 29.8564 51.7128i 1.65359 2.86411i
\(327\) −5.50000 9.52628i −0.304151 0.526804i
\(328\) −6.92820 −0.382546
\(329\) 0 0
\(330\) 2.00000 0.110096
\(331\) −4.03590 6.99038i −0.221833 0.384226i 0.733532 0.679655i \(-0.237871\pi\)
−0.955365 + 0.295429i \(0.904537\pi\)
\(332\) 41.3205 71.5692i 2.26776 3.92787i
\(333\) 1.59808 2.76795i 0.0875740 0.151683i
\(334\) 24.1244 + 41.7846i 1.32003 + 2.28635i
\(335\) 14.6603 0.800975
\(336\) 0 0
\(337\) 17.9808 0.979475 0.489737 0.871870i \(-0.337093\pi\)
0.489737 + 0.871870i \(0.337093\pi\)
\(338\) −10.7321 18.5885i −0.583747 1.01108i
\(339\) −4.46410 + 7.73205i −0.242457 + 0.419947i
\(340\) −8.92820 + 15.4641i −0.484200 + 0.838659i
\(341\) −0.169873 0.294229i −0.00919914 0.0159334i
\(342\) 12.1962 0.659492
\(343\) 0 0
\(344\) −30.2487 −1.63090
\(345\) −2.36603 4.09808i −0.127383 0.220633i
\(346\) −19.8564 + 34.3923i −1.06749 + 1.84894i
\(347\) 10.5359 18.2487i 0.565597 0.979642i −0.431397 0.902162i \(-0.641979\pi\)
0.996994 0.0774801i \(-0.0246874\pi\)
\(348\) 11.4641 + 19.8564i 0.614540 + 1.06442i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −2.26795 −0.121054
\(352\) 8.00000 + 13.8564i 0.426401 + 0.738549i
\(353\) −1.56218 + 2.70577i −0.0831463 + 0.144014i −0.904600 0.426262i \(-0.859830\pi\)
0.821453 + 0.570276i \(0.193164\pi\)
\(354\) 0.267949 0.464102i 0.0142413 0.0246667i
\(355\) 3.09808 + 5.36603i 0.164429 + 0.284799i
\(356\) −82.6410 −4.37997
\(357\) 0 0
\(358\) 27.3205 1.44393
\(359\) 0.633975 + 1.09808i 0.0334599 + 0.0579542i 0.882270 0.470743i \(-0.156014\pi\)
−0.848811 + 0.528697i \(0.822681\pi\)
\(360\) −4.73205 + 8.19615i −0.249401 + 0.431975i
\(361\) −0.464102 + 0.803848i −0.0244264 + 0.0423078i
\(362\) 33.2224 + 57.5429i 1.74613 + 3.02439i
\(363\) −10.4641 −0.549223
\(364\) 0 0
\(365\) 12.6603 0.662668
\(366\) −5.46410 9.46410i −0.285613 0.494697i
\(367\) 5.59808 9.69615i 0.292217 0.506135i −0.682117 0.731244i \(-0.738940\pi\)
0.974334 + 0.225108i \(0.0722736\pi\)
\(368\) 35.3205 61.1769i 1.84121 3.18907i
\(369\) −0.366025 0.633975i −0.0190545 0.0330034i
\(370\) −8.73205 −0.453958
\(371\) 0 0
\(372\) 2.53590 0.131480
\(373\) −13.2583 22.9641i −0.686490 1.18904i −0.972966 0.230949i \(-0.925817\pi\)
0.286476 0.958088i \(-0.407516\pi\)
\(374\) −3.26795 + 5.66025i −0.168982 + 0.292685i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) −9.46410 16.3923i −0.488074 0.845369i
\(377\) 9.51666 0.490133
\(378\) 0 0
\(379\) 6.32051 0.324663 0.162331 0.986736i \(-0.448099\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(380\) −12.1962 21.1244i −0.625649 1.08366i
\(381\) −2.40192 + 4.16025i −0.123054 + 0.213136i
\(382\) −12.1962 + 21.1244i −0.624009 + 1.08082i
\(383\) −11.6603 20.1962i −0.595811 1.03198i −0.993432 0.114425i \(-0.963497\pi\)
0.397621 0.917550i \(-0.369836\pi\)
\(384\) −37.8564 −1.93185
\(385\) 0 0
\(386\) −3.26795 −0.166334
\(387\) −1.59808 2.76795i −0.0812348 0.140703i
\(388\) 40.7846 70.6410i 2.07052 3.58625i
\(389\) −2.70577 + 4.68653i −0.137188 + 0.237617i −0.926431 0.376464i \(-0.877140\pi\)
0.789243 + 0.614081i \(0.210473\pi\)
\(390\) 3.09808 + 5.36603i 0.156877 + 0.271719i
\(391\) 15.4641 0.782053
\(392\) 0 0
\(393\) −15.4641 −0.780061
\(394\) −0.464102 0.803848i −0.0233811 0.0404973i
\(395\) −3.69615 + 6.40192i −0.185974 + 0.322116i
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) −15.5981 27.0167i −0.782845 1.35593i −0.930278 0.366855i \(-0.880434\pi\)
0.147433 0.989072i \(-0.452899\pi\)
\(398\) 60.1051 3.01280
\(399\) 0 0
\(400\) 14.9282 0.746410
\(401\) 8.19615 + 14.1962i 0.409296 + 0.708922i 0.994811 0.101740i \(-0.0324409\pi\)
−0.585515 + 0.810662i \(0.699108\pi\)
\(402\) −20.0263 + 34.6865i −0.998820 + 1.73001i
\(403\) 0.526279 0.911543i 0.0262158 0.0454072i
\(404\) −19.8564 34.3923i −0.987893 1.71108i
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −2.33975 −0.115977
\(408\) −15.4641 26.7846i −0.765587 1.32604i
\(409\) 1.57180 2.72243i 0.0777203 0.134616i −0.824546 0.565795i \(-0.808569\pi\)
0.902266 + 0.431180i \(0.141903\pi\)
\(410\) −1.00000 + 1.73205i −0.0493865 + 0.0855399i
\(411\) −1.09808 1.90192i −0.0541641 0.0938150i
\(412\) 50.2487 2.47558
\(413\) 0 0
\(414\) 12.9282 0.635387
\(415\) −7.56218 13.0981i −0.371213 0.642959i
\(416\) −24.7846 + 42.9282i −1.21517 + 2.10473i
\(417\) 2.96410 5.13397i 0.145153 0.251412i
\(418\) −4.46410 7.73205i −0.218346 0.378187i
\(419\) 35.4641 1.73253 0.866267 0.499581i \(-0.166513\pi\)
0.866267 + 0.499581i \(0.166513\pi\)
\(420\) 0 0
\(421\) 0.0717968 0.00349916 0.00174958 0.999998i \(-0.499443\pi\)
0.00174958 + 0.999998i \(0.499443\pi\)
\(422\) 9.66025 + 16.7321i 0.470254 + 0.814503i
\(423\) 1.00000 1.73205i 0.0486217 0.0842152i
\(424\) 58.6410 101.569i 2.84786 4.93264i
\(425\) 1.63397 + 2.83013i 0.0792594 + 0.137281i
\(426\) −16.9282 −0.820174
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 0.830127 + 1.43782i 0.0400789 + 0.0694187i
\(430\) −4.36603 + 7.56218i −0.210548 + 0.364681i
\(431\) −8.66025 + 15.0000i −0.417150 + 0.722525i −0.995651 0.0931566i \(-0.970304\pi\)
0.578502 + 0.815681i \(0.303638\pi\)
\(432\) −7.46410 12.9282i −0.359117 0.622008i
\(433\) −15.1962 −0.730280 −0.365140 0.930953i \(-0.618979\pi\)
−0.365140 + 0.930953i \(0.618979\pi\)
\(434\) 0 0
\(435\) 4.19615 0.201190
\(436\) −30.0526 52.0526i −1.43926 2.49287i
\(437\) −10.5622 + 18.2942i −0.505257 + 0.875132i
\(438\) −17.2942 + 29.9545i −0.826350 + 1.43128i
\(439\) 0.267949 + 0.464102i 0.0127885 + 0.0221504i 0.872349 0.488884i \(-0.162596\pi\)
−0.859560 + 0.511034i \(0.829263\pi\)
\(440\) 6.92820 0.330289
\(441\) 0 0
\(442\) −20.2487 −0.963133
\(443\) −4.73205 8.19615i −0.224827 0.389411i 0.731441 0.681905i \(-0.238848\pi\)
−0.956267 + 0.292494i \(0.905515\pi\)
\(444\) 8.73205 15.1244i 0.414405 0.717770i
\(445\) −7.56218 + 13.0981i −0.358482 + 0.620908i
\(446\) 27.8564 + 48.2487i 1.31904 + 2.28464i
\(447\) 5.85641 0.276999
\(448\) 0 0
\(449\) −35.8564 −1.69217 −0.846084 0.533049i \(-0.821046\pi\)
−0.846084 + 0.533049i \(0.821046\pi\)
\(450\) 1.36603 + 2.36603i 0.0643951 + 0.111536i
\(451\) −0.267949 + 0.464102i −0.0126172 + 0.0218537i
\(452\) −24.3923 + 42.2487i −1.14732 + 1.98721i
\(453\) 4.46410 + 7.73205i 0.209742 + 0.363283i
\(454\) −4.53590 −0.212880
\(455\) 0 0
\(456\) 42.2487 1.97848
\(457\) 8.33013 + 14.4282i 0.389667 + 0.674923i 0.992405 0.123016i \(-0.0392568\pi\)
−0.602738 + 0.797939i \(0.705923\pi\)
\(458\) 4.09808 7.09808i 0.191491 0.331671i
\(459\) 1.63397 2.83013i 0.0762674 0.132099i
\(460\) −12.9282 22.3923i −0.602781 1.04405i
\(461\) −16.9808 −0.790873 −0.395436 0.918493i \(-0.629407\pi\)
−0.395436 + 0.918493i \(0.629407\pi\)
\(462\) 0 0
\(463\) 25.7321 1.19587 0.597935 0.801545i \(-0.295988\pi\)
0.597935 + 0.801545i \(0.295988\pi\)
\(464\) 31.3205 + 54.2487i 1.45402 + 2.51843i
\(465\) 0.232051 0.401924i 0.0107611 0.0186388i
\(466\) 23.6603 40.9808i 1.09604 1.89840i
\(467\) −0.0717968 0.124356i −0.00332236 0.00575449i 0.864359 0.502874i \(-0.167724\pi\)
−0.867682 + 0.497120i \(0.834391\pi\)
\(468\) −12.3923 −0.572834
\(469\) 0 0
\(470\) −5.46410 −0.252040
\(471\) 3.19615 + 5.53590i 0.147271 + 0.255081i
\(472\) 0.928203 1.60770i 0.0427240 0.0740002i
\(473\) −1.16987 + 2.02628i −0.0537908 + 0.0931684i
\(474\) −10.0981 17.4904i −0.463820 0.803360i
\(475\) −4.46410 −0.204827
\(476\) 0 0
\(477\) 12.3923 0.567405
\(478\) 9.66025 + 16.7321i 0.441850 + 0.765306i
\(479\) 4.39230 7.60770i 0.200690 0.347604i −0.748061 0.663630i \(-0.769015\pi\)
0.948751 + 0.316025i \(0.102348\pi\)
\(480\) −10.9282 + 18.9282i −0.498802 + 0.863950i
\(481\) −3.62436 6.27757i −0.165256 0.286232i
\(482\) 36.7846 1.67549
\(483\) 0 0
\(484\) −57.1769 −2.59895
\(485\) −7.46410 12.9282i −0.338927 0.587039i
\(486\) 1.36603 2.36603i 0.0619642 0.107325i
\(487\) 0.205771 0.356406i 0.00932439 0.0161503i −0.861326 0.508053i \(-0.830365\pi\)
0.870650 + 0.491903i \(0.163699\pi\)
\(488\) −18.9282 32.7846i −0.856840 1.48409i
\(489\) 21.8564 0.988381
\(490\) 0 0
\(491\) −38.2487 −1.72614 −0.863070 0.505084i \(-0.831461\pi\)
−0.863070 + 0.505084i \(0.831461\pi\)
\(492\) −2.00000 3.46410i −0.0901670 0.156174i
\(493\) −6.85641 + 11.8756i −0.308797 + 0.534852i
\(494\) 13.8301 23.9545i 0.622247 1.07776i
\(495\) 0.366025 + 0.633975i 0.0164516 + 0.0284950i
\(496\) 6.92820 0.311086
\(497\) 0 0
\(498\) 41.3205 1.85162
\(499\) 6.76795 + 11.7224i 0.302975 + 0.524768i 0.976808 0.214115i \(-0.0686868\pi\)
−0.673833 + 0.738883i \(0.735353\pi\)
\(500\) 2.73205 4.73205i 0.122181 0.211624i
\(501\) −8.83013 + 15.2942i −0.394501 + 0.683296i
\(502\) 33.5885 + 58.1769i 1.49913 + 2.59656i
\(503\) −14.3923 −0.641721 −0.320861 0.947126i \(-0.603972\pi\)
−0.320861 + 0.947126i \(0.603972\pi\)
\(504\) 0 0
\(505\) −7.26795 −0.323419
\(506\) −4.73205 8.19615i −0.210365 0.364363i
\(507\) 3.92820 6.80385i 0.174458 0.302169i
\(508\) −13.1244 + 22.7321i −0.582299 + 1.00857i
\(509\) 2.26795 + 3.92820i 0.100525 + 0.174115i 0.911901 0.410410i \(-0.134614\pi\)
−0.811376 + 0.584525i \(0.801281\pi\)
\(510\) −8.92820 −0.395347
\(511\) 0 0
\(512\) −43.7128 −1.93185
\(513\) 2.23205 + 3.86603i 0.0985475 + 0.170689i
\(514\) 7.73205 13.3923i 0.341046 0.590709i
\(515\) 4.59808 7.96410i 0.202615 0.350940i
\(516\) −8.73205 15.1244i −0.384407 0.665813i
\(517\) −1.46410 −0.0643911
\(518\) 0 0
\(519\) −14.5359 −0.638055
\(520\) 10.7321 + 18.5885i 0.470632 + 0.815158i
\(521\) −2.73205 + 4.73205i −0.119693 + 0.207315i −0.919646 0.392748i \(-0.871524\pi\)
0.799953 + 0.600063i \(0.204858\pi\)
\(522\) −5.73205 + 9.92820i −0.250885 + 0.434546i
\(523\) −13.8660 24.0167i −0.606319 1.05018i −0.991842 0.127477i \(-0.959312\pi\)
0.385523 0.922698i \(-0.374021\pi\)
\(524\) −84.4974 −3.69129
\(525\) 0 0
\(526\) −22.9282 −0.999717
\(527\) 0.758330 + 1.31347i 0.0330334 + 0.0572155i
\(528\) −5.46410 + 9.46410i −0.237795 + 0.411872i
\(529\) 0.303848 0.526279i 0.0132108 0.0228817i
\(530\) −16.9282 29.3205i −0.735314 1.27360i
\(531\) 0.196152 0.00851229
\(532\) 0 0
\(533\) −1.66025 −0.0719136
\(534\) −20.6603 35.7846i −0.894057 1.54855i
\(535\) 1.09808 1.90192i 0.0474740 0.0822273i
\(536\) −69.3731 + 120.158i −2.99646 + 5.19002i
\(537\) 5.00000 + 8.66025i 0.215766 + 0.373718i
\(538\) −34.2487 −1.47657
\(539\) 0 0
\(540\) −5.46410 −0.235137
\(541\) −2.89230 5.00962i −0.124350 0.215380i 0.797129 0.603809i \(-0.206351\pi\)
−0.921479 + 0.388429i \(0.873018\pi\)
\(542\) −4.19615 + 7.26795i −0.180240 + 0.312185i
\(543\) −12.1603 + 21.0622i −0.521846 + 0.903865i
\(544\) −35.7128 61.8564i −1.53117 2.65207i
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) −26.2487 −1.12231 −0.561157 0.827709i \(-0.689644\pi\)
−0.561157 + 0.827709i \(0.689644\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) −9.36603 16.2224i −0.399006 0.691099i
\(552\) 44.7846 1.90616
\(553\) 0 0
\(554\) 40.0526 1.70167
\(555\) −1.59808 2.76795i −0.0678346 0.117493i
\(556\) 16.1962 28.0526i 0.686870 1.18969i
\(557\) −7.39230 + 12.8038i −0.313222 + 0.542516i −0.979058 0.203582i \(-0.934742\pi\)
0.665836 + 0.746098i \(0.268075\pi\)
\(558\) 0.633975 + 1.09808i 0.0268383 + 0.0464853i
\(559\) −7.24871 −0.306588
\(560\) 0 0
\(561\) −2.39230 −0.101003
\(562\) 18.9282 + 32.7846i 0.798438 + 1.38294i
\(563\) −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i \(-0.957170\pi\)
0.611656 + 0.791123i \(0.290503\pi\)
\(564\) 5.46410 9.46410i 0.230080 0.398511i
\(565\) 4.46410 + 7.73205i 0.187806 + 0.325290i
\(566\) −65.9090 −2.77036
\(567\) 0 0
\(568\) −58.6410 −2.46052
\(569\) −16.2224 28.0981i −0.680080 1.17793i −0.974956 0.222397i \(-0.928612\pi\)
0.294876 0.955535i \(-0.404722\pi\)
\(570\) 6.09808 10.5622i 0.255420 0.442401i
\(571\) −9.30385 + 16.1147i −0.389354 + 0.674381i −0.992363 0.123354i \(-0.960635\pi\)
0.603009 + 0.797734i \(0.293968\pi\)
\(572\) 4.53590 + 7.85641i 0.189655 + 0.328493i
\(573\) −8.92820 −0.372981
\(574\) 0 0
\(575\) −4.73205 −0.197340
\(576\) −14.9282 25.8564i −0.622008 1.07735i
\(577\) 14.3301 24.8205i 0.596571 1.03329i −0.396752 0.917926i \(-0.629863\pi\)
0.993323 0.115365i \(-0.0368039\pi\)
\(578\) −8.63397 + 14.9545i −0.359126 + 0.622024i
\(579\) −0.598076 1.03590i −0.0248552 0.0430505i
\(580\) 22.9282 0.952042
\(581\) 0 0
\(582\) 40.7846 1.69058
\(583\) −4.53590 7.85641i −0.187858 0.325379i
\(584\) −59.9090 + 103.765i −2.47905 + 4.29384i
\(585\) −1.13397 + 1.96410i −0.0468841 + 0.0812056i
\(586\) −25.8564 44.7846i −1.06812 1.85004i
\(587\) −40.7321 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(588\) 0 0
\(589\) −2.07180 −0.0853669
\(590\) −0.267949 0.464102i −0.0110313 0.0191068i
\(591\) 0.169873 0.294229i 0.00698764 0.0121029i
\(592\) 23.8564 41.3205i 0.980492 1.69826i
\(593\) 13.9545 + 24.1699i 0.573042 + 0.992538i 0.996251 + 0.0865058i \(0.0275701\pi\)
−0.423209 + 0.906032i \(0.639097\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 32.0000 1.31077
\(597\) 11.0000 + 19.0526i 0.450200 + 0.779769i
\(598\) 14.6603 25.3923i 0.599502 1.03837i
\(599\) 19.1244 33.1244i 0.781400 1.35342i −0.149726 0.988727i \(-0.547839\pi\)
0.931126 0.364697i \(-0.118827\pi\)
\(600\) 4.73205 + 8.19615i 0.193185 + 0.334607i
\(601\) 0.0717968 0.00292865 0.00146433 0.999999i \(-0.499534\pi\)
0.00146433 + 0.999999i \(0.499534\pi\)
\(602\) 0 0
\(603\) −14.6603 −0.597012
\(604\) 24.3923 + 42.2487i 0.992509 + 1.71908i
\(605\) −5.23205 + 9.06218i −0.212713 + 0.368430i
\(606\) 9.92820 17.1962i 0.403306 0.698546i
\(607\) 1.59808 + 2.76795i 0.0648639 + 0.112348i 0.896634 0.442773i \(-0.146005\pi\)
−0.831770 + 0.555121i \(0.812672\pi\)
\(608\) 97.5692 3.95695
\(609\) 0 0
\(610\) −10.9282 −0.442470
\(611\) −2.26795 3.92820i −0.0917514 0.158918i
\(612\) 8.92820 15.4641i 0.360901 0.625099i
\(613\) 13.4641 23.3205i 0.543810 0.941906i −0.454871 0.890557i \(-0.650315\pi\)
0.998681 0.0513490i \(-0.0163521\pi\)
\(614\) 43.8827 + 76.0070i 1.77096 + 3.06739i
\(615\) −0.732051 −0.0295191
\(616\) 0 0
\(617\) −36.2487 −1.45932 −0.729659 0.683811i \(-0.760321\pi\)
−0.729659 + 0.683811i \(0.760321\pi\)
\(618\) 12.5622 + 21.7583i 0.505325 + 0.875248i
\(619\) −15.0359 + 26.0429i −0.604344 + 1.04675i 0.387811 + 0.921739i \(0.373231\pi\)
−0.992155 + 0.125015i \(0.960102\pi\)
\(620\) 1.26795 2.19615i 0.0509221 0.0881996i
\(621\) 2.36603 + 4.09808i 0.0949453 + 0.164450i
\(622\) 24.9282 0.999530
\(623\) 0 0
\(624\) −33.8564 −1.35534
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 17.2942 29.9545i 0.691216 1.19722i
\(627\) 1.63397 2.83013i 0.0652547 0.113024i
\(628\) 17.4641 + 30.2487i 0.696894 + 1.20705i
\(629\) 10.4449 0.416464
\(630\) 0 0
\(631\) 48.7846 1.94208 0.971042 0.238908i \(-0.0767893\pi\)
0.971042 + 0.238908i \(0.0767893\pi\)
\(632\) −34.9808 60.5885i −1.39146 2.41008i
\(633\) −3.53590 + 6.12436i −0.140539 + 0.243421i
\(634\) −38.8564 + 67.3013i −1.54319 + 2.67287i
\(635\) 2.40192 + 4.16025i 0.0953174 + 0.165095i
\(636\) 67.7128 2.68499
\(637\) 0 0
\(638\) 8.39230 0.332255
\(639\) −3.09808 5.36603i −0.122558 0.212277i
\(640\) −18.9282 + 32.7846i −0.748203 + 1.29593i
\(641\) −1.90192 + 3.29423i −0.0751215 + 0.130114i −0.901139 0.433530i \(-0.857268\pi\)
0.826018 + 0.563644i \(0.190601\pi\)
\(642\) 3.00000 + 5.19615i 0.118401 + 0.205076i
\(643\) −4.51666 −0.178120 −0.0890599 0.996026i \(-0.528386\pi\)
−0.0890599 + 0.996026i \(0.528386\pi\)
\(644\) 0 0
\(645\) −3.19615 −0.125848
\(646\) 19.9282 + 34.5167i 0.784065 + 1.35804i
\(647\) −13.9545 + 24.1699i −0.548607 + 0.950216i 0.449763 + 0.893148i \(0.351508\pi\)
−0.998370 + 0.0570678i \(0.981825\pi\)
\(648\) 4.73205 8.19615i 0.185893 0.321975i
\(649\) −0.0717968 0.124356i −0.00281827 0.00488139i
\(650\) 6.19615 0.243033
\(651\) 0 0
\(652\) 119.426 4.67707
\(653\) 22.2942 + 38.6147i 0.872441 + 1.51111i 0.859464 + 0.511196i \(0.170797\pi\)
0.0129762 + 0.999916i \(0.495869\pi\)
\(654\) 15.0263 26.0263i 0.587574 1.01771i
\(655\) −7.73205 + 13.3923i −0.302116 + 0.523281i
\(656\) −5.46410 9.46410i −0.213337 0.369511i
\(657\) −12.6603 −0.493924
\(658\) 0 0
\(659\) 2.92820 0.114067 0.0570333 0.998372i \(-0.481836\pi\)
0.0570333 + 0.998372i \(0.481836\pi\)
\(660\) 2.00000 + 3.46410i 0.0778499 + 0.134840i
\(661\) 5.23205 9.06218i 0.203503 0.352478i −0.746152 0.665776i \(-0.768101\pi\)
0.949655 + 0.313298i \(0.101434\pi\)
\(662\) 11.0263 19.0981i 0.428549 0.742268i
\(663\) −3.70577 6.41858i −0.143920 0.249277i
\(664\) 143.138 5.55485
\(665\) 0 0
\(666\) 8.73205 0.338360
\(667\) −9.92820 17.1962i −0.384422 0.665838i
\(668\) −48.2487 + 83.5692i −1.86680 + 3.23339i
\(669\) −10.1962 + 17.6603i −0.394206 + 0.682785i
\(670\) 20.0263 + 34.6865i 0.773683 + 1.34006i
\(671\) −2.92820 −0.113042
\(672\) 0 0
\(673\) −27.3397 −1.05387 −0.526935 0.849906i \(-0.676659\pi\)
−0.526935 + 0.849906i \(0.676659\pi\)
\(674\) 24.5622 + 42.5429i 0.946100 + 1.63869i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 21.4641 37.1769i 0.825542 1.42988i
\(677\) −16.5622 28.6865i −0.636536 1.10251i −0.986187 0.165633i \(-0.947033\pi\)
0.349651 0.936880i \(-0.386300\pi\)
\(678\) −24.3923 −0.936781
\(679\) 0 0
\(680\) −30.9282 −1.18604
\(681\) −0.830127 1.43782i −0.0318105 0.0550975i
\(682\) 0.464102 0.803848i 0.0177714 0.0307809i
\(683\) 14.0263 24.2942i 0.536701 0.929593i −0.462378 0.886683i \(-0.653004\pi\)
0.999079 0.0429101i \(-0.0136629\pi\)
\(684\) 12.1962 + 21.1244i 0.466332 + 0.807710i
\(685\) −2.19615 −0.0839107
\(686\) 0 0
\(687\) 3.00000 0.114457
\(688\) −23.8564 41.3205i −0.909517 1.57533i
\(689\) 14.0526 24.3397i 0.535360 0.927270i
\(690\) 6.46410 11.1962i 0.246084 0.426230i
\(691\) 4.42820 + 7.66987i 0.168457 + 0.291776i 0.937877 0.346967i \(-0.112788\pi\)
−0.769421 + 0.638742i \(0.779455\pi\)
\(692\) −79.4256 −3.01931
\(693\) 0 0
\(694\) 57.5692 2.18530
\(695\) −2.96410 5.13397i −0.112435 0.194743i
\(696\) −19.8564 + 34.3923i −0.752655 + 1.30364i
\(697\) 1.19615 2.07180i 0.0453075 0.0784749i
\(698\) −30.0526 52.0526i −1.13751 1.97022i
\(699\) 17.3205 0.655122
\(700\) 0 0
\(701\) −8.58846 −0.324382 −0.162191 0.986759i \(-0.551856\pi\)
−0.162191 + 0.986759i \(0.551856\pi\)
\(702\) −3.09808 5.36603i −0.116929 0.202528i
\(703\) −7.13397 + 12.3564i −0.269063 + 0.466031i
\(704\) −10.9282 + 18.9282i −0.411872 + 0.713384i
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) −8.53590 −0.321253
\(707\) 0 0
\(708\) 1.07180 0.0402806
\(709\) 0.535898 + 0.928203i 0.0201261 + 0.0348594i 0.875913 0.482469i \(-0.160260\pi\)
−0.855787 + 0.517328i \(0.826927\pi\)
\(710\) −8.46410 + 14.6603i −0.317652 + 0.550190i
\(711\) 3.69615 6.40192i 0.138617 0.240091i
\(712\) −71.5692 123.962i −2.68217 4.64565i
\(713\) −2.19615 −0.0822466
\(714\) 0 0
\(715\) 1.66025 0.0620900
\(716\) 27.3205 + 47.3205i 1.02102 + 1.76845i
\(717\) −3.53590 + 6.12436i −0.132051 + 0.228718i
\(718\) −1.73205 + 3.00000i −0.0646396 + 0.111959i
\(719\) −10.2679 17.7846i −0.382930 0.663254i 0.608550 0.793516i \(-0.291752\pi\)
−0.991480 + 0.130262i \(0.958418\pi\)
\(720\) −14.9282 −0.556341
\(721\) 0 0
\(722\) −2.53590 −0.0943764
\(723\) 6.73205 + 11.6603i 0.250368 + 0.433650i
\(724\) −66.4449 + 115.086i −2.46940 + 4.27713i
\(725\) 2.09808 3.63397i 0.0779206 0.134962i
\(726\) −14.2942 24.7583i −0.530509 0.918868i
\(727\) 13.3397 0.494744 0.247372 0.968921i \(-0.420433\pi\)
0.247372 + 0.968921i \(0.420433\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 17.2942 + 29.9545i 0.640088 + 1.10867i
\(731\) 5.22243 9.04552i 0.193159 0.334561i
\(732\) 10.9282 18.9282i 0.403918 0.699607i
\(733\) −0.669873 1.16025i −0.0247423 0.0428550i 0.853389 0.521274i \(-0.174543\pi\)
−0.878131 + 0.478419i \(0.841210\pi\)
\(734\) 30.5885 1.12904
\(735\) 0 0
\(736\) 103.426 3.81232
\(737\) 5.36603 + 9.29423i 0.197660 + 0.342357i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) −13.8923 + 24.0622i −0.511037 + 0.885142i 0.488881 + 0.872350i \(0.337405\pi\)
−0.999918 + 0.0127913i \(0.995928\pi\)
\(740\) −8.73205 15.1244i −0.320997 0.555982i
\(741\) 10.1244 0.371927
\(742\) 0 0
\(743\) −15.9090 −0.583643 −0.291822 0.956473i \(-0.594261\pi\)
−0.291822 + 0.956473i \(0.594261\pi\)
\(744\) 2.19615 + 3.80385i 0.0805149 + 0.139456i
\(745\) 2.92820 5.07180i 0.107281 0.185816i
\(746\) 36.2224 62.7391i 1.32620 2.29704i
\(747\) 7.56218 + 13.0981i 0.276686 + 0.479234i
\(748\) −13.0718 −0.477952
\(749\) 0 0
\(750\) 2.73205 0.0997604
\(751\) −9.03590 15.6506i −0.329725 0.571100i 0.652732 0.757588i \(-0.273623\pi\)
−0.982457 + 0.186489i \(0.940289\pi\)
\(752\) 14.9282 25.8564i 0.544376 0.942886i
\(753\) −12.2942 + 21.2942i −0.448027 + 0.776005i
\(754\) 13.0000 + 22.5167i 0.473432 + 0.820008i
\(755\) 8.92820 0.324931
\(756\) 0 0
\(757\) −27.8564 −1.01246 −0.506229 0.862399i \(-0.668961\pi\)
−0.506229 + 0.862399i \(0.668961\pi\)
\(758\) 8.63397 + 14.9545i 0.313600 + 0.543171i
\(759\) 1.73205 3.00000i 0.0628695 0.108893i
\(760\) 21.1244 36.5885i 0.766261 1.32720i
\(761\) 23.3660 + 40.4711i 0.847018 + 1.46708i 0.883857 + 0.467757i \(0.154938\pi\)
−0.0368396 + 0.999321i \(0.511729\pi\)
\(762\) −13.1244 −0.475445
\(763\) 0 0
\(764\) −48.7846 −1.76497
\(765\) −1.63397 2.83013i −0.0590765 0.102323i
\(766\) 31.8564 55.1769i 1.15102 1.99362i
\(767\) 0.222432 0.385263i 0.00803155 0.0139111i
\(768\) −21.8564 37.8564i −0.788675 1.36603i
\(769\) −52.3205 −1.88673 −0.943363 0.331763i \(-0.892357\pi\)
−0.943363 + 0.331763i \(0.892357\pi\)
\(770\) 0 0
\(771\) 5.66025 0.203849
\(772\) −3.26795 5.66025i −0.117616 0.203717i
\(773\) 21.7583 37.6865i 0.782593 1.35549i −0.147834 0.989012i \(-0.547230\pi\)
0.930427 0.366478i \(-0.119437\pi\)
\(774\) 4.36603 7.56218i 0.156934 0.271817i
\(775\) −0.232051 0.401924i −0.00833551 0.0144375i
\(776\) 141.282 5.07173
\(777\) 0 0
\(778\) −14.7846 −0.530054
\(779\) 1.63397 + 2.83013i 0.0585432 + 0.101400i
\(780\) −6.19615 + 10.7321i −0.221858 + 0.384269i
\(781\) −2.26795 + 3.92820i −0.0811536 + 0.140562i
\(782\) 21.1244 + 36.5885i 0.75