Properties

Label 512.2.g.d.321.1
Level $512$
Weight $2$
Character 512.321
Analytic conductor $4.088$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.08834058349\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 321.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 512.321
Dual form 512.2.g.d.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70711 + 0.707107i) q^{3} +(1.29289 + 3.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(0.292893 + 0.292893i) q^{9} +O(q^{10})\) \(q+(1.70711 + 0.707107i) q^{3} +(1.29289 + 3.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(0.292893 + 0.292893i) q^{9} +(0.292893 - 0.121320i) q^{11} +(-0.707107 + 1.70711i) q^{13} +6.24264i q^{15} +2.82843i q^{17} +(2.29289 - 5.53553i) q^{19} +(-2.41421 + 1.00000i) q^{21} +(-0.171573 - 0.171573i) q^{23} +(-4.53553 + 4.53553i) q^{25} +(-1.82843 - 4.41421i) q^{27} +(2.70711 + 1.12132i) q^{29} -4.00000 q^{31} +0.585786 q^{33} +(-4.41421 - 1.82843i) q^{35} +(-0.707107 - 1.70711i) q^{37} +(-2.41421 + 2.41421i) q^{39} +(5.82843 + 5.82843i) q^{41} +(7.94975 - 3.29289i) q^{43} +(-0.535534 + 1.29289i) q^{45} -11.6569i q^{47} +5.00000i q^{49} +(-2.00000 + 4.82843i) q^{51} +(7.53553 - 3.12132i) q^{53} +(0.757359 + 0.757359i) q^{55} +(7.82843 - 7.82843i) q^{57} +(2.53553 + 6.12132i) q^{59} +(0.707107 + 0.292893i) q^{61} -0.585786 q^{63} -6.24264 q^{65} +(3.70711 + 1.53553i) q^{67} +(-0.171573 - 0.414214i) q^{69} +(0.171573 - 0.171573i) q^{71} +(-7.00000 - 7.00000i) q^{73} +(-10.9497 + 4.53553i) q^{75} +(-0.171573 + 0.414214i) q^{77} +6.00000i q^{79} -10.0711i q^{81} +(-2.53553 + 6.12132i) q^{83} +(-8.82843 + 3.65685i) q^{85} +(3.82843 + 3.82843i) q^{87} +(2.65685 - 2.65685i) q^{89} +(-1.00000 - 2.41421i) q^{91} +(-6.82843 - 2.82843i) q^{93} +20.2426 q^{95} -1.51472 q^{97} +(0.121320 + 0.0502525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + 8q^{5} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} + 8q^{5} - 4q^{7} + 4q^{9} + 4q^{11} + 12q^{19} - 4q^{21} - 12q^{23} - 4q^{25} + 4q^{27} + 8q^{29} - 16q^{31} + 8q^{33} - 12q^{35} - 4q^{39} + 12q^{41} + 12q^{43} + 12q^{45} - 8q^{51} + 16q^{53} + 20q^{55} + 20q^{57} - 4q^{59} - 8q^{63} - 8q^{65} + 12q^{67} - 12q^{69} + 12q^{71} - 28q^{73} - 24q^{75} - 12q^{77} + 4q^{83} - 24q^{85} + 4q^{87} - 12q^{89} - 4q^{91} - 16q^{93} + 64q^{95} - 40q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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 0
\(3\) 1.70711 + 0.707107i 0.985599 + 0.408248i 0.816497 0.577350i \(-0.195913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 0 0
\(5\) 1.29289 + 3.12132i 0.578199 + 1.39590i 0.894427 + 0.447214i \(0.147584\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) 0.292893 + 0.292893i 0.0976311 + 0.0976311i
\(10\) 0 0
\(11\) 0.292893 0.121320i 0.0883106 0.0365795i −0.338091 0.941113i \(-0.609781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(12\) 0 0
\(13\) −0.707107 + 1.70711i −0.196116 + 0.473466i −0.991093 0.133174i \(-0.957483\pi\)
0.794977 + 0.606640i \(0.207483\pi\)
\(14\) 0 0
\(15\) 6.24264i 1.61184i
\(16\) 0 0
\(17\) 2.82843i 0.685994i 0.939336 + 0.342997i \(0.111442\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) 0 0
\(19\) 2.29289 5.53553i 0.526026 1.26994i −0.408081 0.912946i \(-0.633802\pi\)
0.934107 0.356993i \(-0.116198\pi\)
\(20\) 0 0
\(21\) −2.41421 + 1.00000i −0.526825 + 0.218218i
\(22\) 0 0
\(23\) −0.171573 0.171573i −0.0357754 0.0357754i 0.688993 0.724768i \(-0.258053\pi\)
−0.724768 + 0.688993i \(0.758053\pi\)
\(24\) 0 0
\(25\) −4.53553 + 4.53553i −0.907107 + 0.907107i
\(26\) 0 0
\(27\) −1.82843 4.41421i −0.351881 0.849516i
\(28\) 0 0
\(29\) 2.70711 + 1.12132i 0.502697 + 0.208224i 0.619598 0.784920i \(-0.287296\pi\)
−0.116900 + 0.993144i \(0.537296\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0.585786 0.101972
\(34\) 0 0
\(35\) −4.41421 1.82843i −0.746138 0.309061i
\(36\) 0 0
\(37\) −0.707107 1.70711i −0.116248 0.280647i 0.855037 0.518567i \(-0.173534\pi\)
−0.971285 + 0.237920i \(0.923534\pi\)
\(38\) 0 0
\(39\) −2.41421 + 2.41421i −0.386584 + 0.386584i
\(40\) 0 0
\(41\) 5.82843 + 5.82843i 0.910247 + 0.910247i 0.996291 0.0860440i \(-0.0274225\pi\)
−0.0860440 + 0.996291i \(0.527423\pi\)
\(42\) 0 0
\(43\) 7.94975 3.29289i 1.21233 0.502162i 0.317363 0.948304i \(-0.397203\pi\)
0.894962 + 0.446143i \(0.147203\pi\)
\(44\) 0 0
\(45\) −0.535534 + 1.29289i −0.0798327 + 0.192733i
\(46\) 0 0
\(47\) 11.6569i 1.70033i −0.526519 0.850163i \(-0.676503\pi\)
0.526519 0.850163i \(-0.323497\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −2.00000 + 4.82843i −0.280056 + 0.676115i
\(52\) 0 0
\(53\) 7.53553 3.12132i 1.03509 0.428746i 0.200540 0.979686i \(-0.435730\pi\)
0.834545 + 0.550939i \(0.185730\pi\)
\(54\) 0 0
\(55\) 0.757359 + 0.757359i 0.102122 + 0.102122i
\(56\) 0 0
\(57\) 7.82843 7.82843i 1.03690 1.03690i
\(58\) 0 0
\(59\) 2.53553 + 6.12132i 0.330098 + 0.796928i 0.998584 + 0.0532027i \(0.0169429\pi\)
−0.668485 + 0.743725i \(0.733057\pi\)
\(60\) 0 0
\(61\) 0.707107 + 0.292893i 0.0905357 + 0.0375011i 0.427492 0.904019i \(-0.359397\pi\)
−0.336956 + 0.941520i \(0.609397\pi\)
\(62\) 0 0
\(63\) −0.585786 −0.0738022
\(64\) 0 0
\(65\) −6.24264 −0.774304
\(66\) 0 0
\(67\) 3.70711 + 1.53553i 0.452895 + 0.187595i 0.597458 0.801900i \(-0.296178\pi\)
−0.144563 + 0.989496i \(0.546178\pi\)
\(68\) 0 0
\(69\) −0.171573 0.414214i −0.0206549 0.0498655i
\(70\) 0 0
\(71\) 0.171573 0.171573i 0.0203620 0.0203620i −0.696853 0.717214i \(-0.745417\pi\)
0.717214 + 0.696853i \(0.245417\pi\)
\(72\) 0 0
\(73\) −7.00000 7.00000i −0.819288 0.819288i 0.166717 0.986005i \(-0.446683\pi\)
−0.986005 + 0.166717i \(0.946683\pi\)
\(74\) 0 0
\(75\) −10.9497 + 4.53553i −1.26437 + 0.523718i
\(76\) 0 0
\(77\) −0.171573 + 0.414214i −0.0195525 + 0.0472040i
\(78\) 0 0
\(79\) 6.00000i 0.675053i 0.941316 + 0.337526i \(0.109590\pi\)
−0.941316 + 0.337526i \(0.890410\pi\)
\(80\) 0 0
\(81\) 10.0711i 1.11901i
\(82\) 0 0
\(83\) −2.53553 + 6.12132i −0.278311 + 0.671902i −0.999789 0.0205350i \(-0.993463\pi\)
0.721478 + 0.692437i \(0.243463\pi\)
\(84\) 0 0
\(85\) −8.82843 + 3.65685i −0.957577 + 0.396642i
\(86\) 0 0
\(87\) 3.82843 + 3.82843i 0.410450 + 0.410450i
\(88\) 0 0
\(89\) 2.65685 2.65685i 0.281626 0.281626i −0.552131 0.833757i \(-0.686185\pi\)
0.833757 + 0.552131i \(0.186185\pi\)
\(90\) 0 0
\(91\) −1.00000 2.41421i −0.104828 0.253078i
\(92\) 0 0
\(93\) −6.82843 2.82843i −0.708075 0.293294i
\(94\) 0 0
\(95\) 20.2426 2.07685
\(96\) 0 0
\(97\) −1.51472 −0.153796 −0.0768982 0.997039i \(-0.524502\pi\)
−0.0768982 + 0.997039i \(0.524502\pi\)
\(98\) 0 0
\(99\) 0.121320 + 0.0502525i 0.0121932 + 0.00505057i
\(100\) 0 0
\(101\) −4.70711 11.3640i −0.468375 1.13076i −0.964873 0.262718i \(-0.915381\pi\)
0.496498 0.868038i \(-0.334619\pi\)
\(102\) 0 0
\(103\) 7.48528 7.48528i 0.737547 0.737547i −0.234556 0.972103i \(-0.575364\pi\)
0.972103 + 0.234556i \(0.0753636\pi\)
\(104\) 0 0
\(105\) −6.24264 6.24264i −0.609219 0.609219i
\(106\) 0 0
\(107\) 0.292893 0.121320i 0.0283151 0.0117285i −0.368481 0.929635i \(-0.620122\pi\)
0.396796 + 0.917907i \(0.370122\pi\)
\(108\) 0 0
\(109\) 1.77817 4.29289i 0.170318 0.411185i −0.815555 0.578680i \(-0.803568\pi\)
0.985873 + 0.167496i \(0.0535680\pi\)
\(110\) 0 0
\(111\) 3.41421i 0.324063i
\(112\) 0 0
\(113\) 17.6569i 1.66102i −0.557006 0.830509i \(-0.688050\pi\)
0.557006 0.830509i \(-0.311950\pi\)
\(114\) 0 0
\(115\) 0.313708 0.757359i 0.0292535 0.0706241i
\(116\) 0 0
\(117\) −0.707107 + 0.292893i −0.0653720 + 0.0270780i
\(118\) 0 0
\(119\) −2.82843 2.82843i −0.259281 0.259281i
\(120\) 0 0
\(121\) −7.70711 + 7.70711i −0.700646 + 0.700646i
\(122\) 0 0
\(123\) 5.82843 + 14.0711i 0.525532 + 1.26875i
\(124\) 0 0
\(125\) −4.41421 1.82843i −0.394819 0.163539i
\(126\) 0 0
\(127\) −20.9706 −1.86084 −0.930418 0.366499i \(-0.880556\pi\)
−0.930418 + 0.366499i \(0.880556\pi\)
\(128\) 0 0
\(129\) 15.8995 1.39987
\(130\) 0 0
\(131\) −8.77817 3.63604i −0.766953 0.317682i −0.0353153 0.999376i \(-0.511244\pi\)
−0.731637 + 0.681694i \(0.761244\pi\)
\(132\) 0 0
\(133\) 3.24264 + 7.82843i 0.281173 + 0.678811i
\(134\) 0 0
\(135\) 11.4142 11.4142i 0.982379 0.982379i
\(136\) 0 0
\(137\) −2.65685 2.65685i −0.226990 0.226990i 0.584444 0.811434i \(-0.301313\pi\)
−0.811434 + 0.584444i \(0.801313\pi\)
\(138\) 0 0
\(139\) −12.5355 + 5.19239i −1.06325 + 0.440413i −0.844604 0.535392i \(-0.820164\pi\)
−0.218646 + 0.975804i \(0.570164\pi\)
\(140\) 0 0
\(141\) 8.24264 19.8995i 0.694156 1.67584i
\(142\) 0 0
\(143\) 0.585786i 0.0489859i
\(144\) 0 0
\(145\) 9.89949i 0.822108i
\(146\) 0 0
\(147\) −3.53553 + 8.53553i −0.291606 + 0.703999i
\(148\) 0 0
\(149\) 13.5355 5.60660i 1.10887 0.459311i 0.248324 0.968677i \(-0.420120\pi\)
0.860550 + 0.509366i \(0.170120\pi\)
\(150\) 0 0
\(151\) −15.4853 15.4853i −1.26017 1.26017i −0.951008 0.309166i \(-0.899950\pi\)
−0.309166 0.951008i \(-0.600050\pi\)
\(152\) 0 0
\(153\) −0.828427 + 0.828427i −0.0669744 + 0.0669744i
\(154\) 0 0
\(155\) −5.17157 12.4853i −0.415391 1.00284i
\(156\) 0 0
\(157\) 0.707107 + 0.292893i 0.0564333 + 0.0233754i 0.410722 0.911761i \(-0.365277\pi\)
−0.354288 + 0.935136i \(0.615277\pi\)
\(158\) 0 0
\(159\) 15.0711 1.19521
\(160\) 0 0
\(161\) 0.343146 0.0270437
\(162\) 0 0
\(163\) 18.1924 + 7.53553i 1.42494 + 0.590229i 0.956096 0.293054i \(-0.0946714\pi\)
0.468842 + 0.883282i \(0.344671\pi\)
\(164\) 0 0
\(165\) 0.757359 + 1.82843i 0.0589603 + 0.142343i
\(166\) 0 0
\(167\) −3.34315 + 3.34315i −0.258700 + 0.258700i −0.824525 0.565825i \(-0.808558\pi\)
0.565825 + 0.824525i \(0.308558\pi\)
\(168\) 0 0
\(169\) 6.77817 + 6.77817i 0.521398 + 0.521398i
\(170\) 0 0
\(171\) 2.29289 0.949747i 0.175342 0.0726290i
\(172\) 0 0
\(173\) 0.464466 1.12132i 0.0353127 0.0852524i −0.905239 0.424902i \(-0.860309\pi\)
0.940552 + 0.339650i \(0.110309\pi\)
\(174\) 0 0
\(175\) 9.07107i 0.685708i
\(176\) 0 0
\(177\) 12.2426i 0.920213i
\(178\) 0 0
\(179\) 5.94975 14.3640i 0.444705 1.07361i −0.529573 0.848264i \(-0.677648\pi\)
0.974278 0.225349i \(-0.0723521\pi\)
\(180\) 0 0
\(181\) −5.29289 + 2.19239i −0.393418 + 0.162959i −0.570618 0.821216i \(-0.693296\pi\)
0.177200 + 0.984175i \(0.443296\pi\)
\(182\) 0 0
\(183\) 1.00000 + 1.00000i 0.0739221 + 0.0739221i
\(184\) 0 0
\(185\) 4.41421 4.41421i 0.324539 0.324539i
\(186\) 0 0
\(187\) 0.343146 + 0.828427i 0.0250933 + 0.0605806i
\(188\) 0 0
\(189\) 6.24264 + 2.58579i 0.454085 + 0.188088i
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −18.4853 −1.33060 −0.665300 0.746576i \(-0.731696\pi\)
−0.665300 + 0.746576i \(0.731696\pi\)
\(194\) 0 0
\(195\) −10.6569 4.41421i −0.763153 0.316108i
\(196\) 0 0
\(197\) −7.19239 17.3640i −0.512436 1.23713i −0.942462 0.334314i \(-0.891495\pi\)
0.430025 0.902817i \(-0.358505\pi\)
\(198\) 0 0
\(199\) −17.9706 + 17.9706i −1.27390 + 1.27390i −0.329875 + 0.944025i \(0.607006\pi\)
−0.944025 + 0.329875i \(0.892994\pi\)
\(200\) 0 0
\(201\) 5.24264 + 5.24264i 0.369787 + 0.369787i
\(202\) 0 0
\(203\) −3.82843 + 1.58579i −0.268703 + 0.111300i
\(204\) 0 0
\(205\) −10.6569 + 25.7279i −0.744307 + 1.79692i
\(206\) 0 0
\(207\) 0.100505i 0.00698558i
\(208\) 0 0
\(209\) 1.89949i 0.131391i
\(210\) 0 0
\(211\) −0.192388 + 0.464466i −0.0132445 + 0.0319752i −0.930363 0.366639i \(-0.880509\pi\)
0.917119 + 0.398614i \(0.130509\pi\)
\(212\) 0 0
\(213\) 0.414214 0.171573i 0.0283814 0.0117560i
\(214\) 0 0
\(215\) 20.5563 + 20.5563i 1.40193 + 1.40193i
\(216\) 0 0
\(217\) 4.00000 4.00000i 0.271538 0.271538i
\(218\) 0 0
\(219\) −7.00000 16.8995i −0.473016 1.14196i
\(220\) 0 0
\(221\) −4.82843 2.00000i −0.324795 0.134535i
\(222\) 0 0
\(223\) 12.9706 0.868573 0.434287 0.900775i \(-0.357001\pi\)
0.434287 + 0.900775i \(0.357001\pi\)
\(224\) 0 0
\(225\) −2.65685 −0.177124
\(226\) 0 0
\(227\) −6.29289 2.60660i −0.417674 0.173006i 0.163942 0.986470i \(-0.447579\pi\)
−0.581616 + 0.813464i \(0.697579\pi\)
\(228\) 0 0
\(229\) 10.2635 + 24.7782i 0.678228 + 1.63739i 0.767242 + 0.641357i \(0.221628\pi\)
−0.0890139 + 0.996030i \(0.528372\pi\)
\(230\) 0 0
\(231\) −0.585786 + 0.585786i −0.0385419 + 0.0385419i
\(232\) 0 0
\(233\) −8.65685 8.65685i −0.567129 0.567129i 0.364194 0.931323i \(-0.381345\pi\)
−0.931323 + 0.364194i \(0.881345\pi\)
\(234\) 0 0
\(235\) 36.3848 15.0711i 2.37348 0.983128i
\(236\) 0 0
\(237\) −4.24264 + 10.2426i −0.275589 + 0.665331i
\(238\) 0 0
\(239\) 17.3137i 1.11993i 0.828516 + 0.559965i \(0.189186\pi\)
−0.828516 + 0.559965i \(0.810814\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) 0 0
\(243\) 1.63604 3.94975i 0.104952 0.253376i
\(244\) 0 0
\(245\) −15.6066 + 6.46447i −0.997069 + 0.413000i
\(246\) 0 0
\(247\) 7.82843 + 7.82843i 0.498111 + 0.498111i
\(248\) 0 0
\(249\) −8.65685 + 8.65685i −0.548606 + 0.548606i
\(250\) 0 0
\(251\) 6.05025 + 14.6066i 0.381889 + 0.921961i 0.991601 + 0.129338i \(0.0412851\pi\)
−0.609712 + 0.792623i \(0.708715\pi\)
\(252\) 0 0
\(253\) −0.0710678 0.0294373i −0.00446800 0.00185070i
\(254\) 0 0
\(255\) −17.6569 −1.10572
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 2.41421 + 1.00000i 0.150012 + 0.0621370i
\(260\) 0 0
\(261\) 0.464466 + 1.12132i 0.0287497 + 0.0694080i
\(262\) 0 0
\(263\) 0.171573 0.171573i 0.0105796 0.0105796i −0.701797 0.712377i \(-0.747619\pi\)
0.712377 + 0.701797i \(0.247619\pi\)
\(264\) 0 0
\(265\) 19.4853 + 19.4853i 1.19697 + 1.19697i
\(266\) 0 0
\(267\) 6.41421 2.65685i 0.392543 0.162597i
\(268\) 0 0
\(269\) −2.02082 + 4.87868i −0.123211 + 0.297458i −0.973435 0.228963i \(-0.926467\pi\)
0.850224 + 0.526421i \(0.176467\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i 0.837321 + 0.546711i \(0.184120\pi\)
−0.837321 + 0.546711i \(0.815880\pi\)
\(272\) 0 0
\(273\) 4.82843i 0.292230i
\(274\) 0 0
\(275\) −0.778175 + 1.87868i −0.0469257 + 0.113289i
\(276\) 0 0
\(277\) 0.707107 0.292893i 0.0424859 0.0175982i −0.361339 0.932434i \(-0.617680\pi\)
0.403825 + 0.914836i \(0.367680\pi\)
\(278\) 0 0
\(279\) −1.17157 1.17157i −0.0701402 0.0701402i
\(280\) 0 0
\(281\) 6.17157 6.17157i 0.368165 0.368165i −0.498643 0.866808i \(-0.666168\pi\)
0.866808 + 0.498643i \(0.166168\pi\)
\(282\) 0 0
\(283\) 4.05025 + 9.77817i 0.240763 + 0.581252i 0.997359 0.0726300i \(-0.0231392\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) 0 0
\(285\) 34.5563 + 14.3137i 2.04694 + 0.847871i
\(286\) 0 0
\(287\) −11.6569 −0.688082
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) −2.58579 1.07107i −0.151581 0.0627871i
\(292\) 0 0
\(293\) 4.80761 + 11.6066i 0.280864 + 0.678065i 0.999856 0.0169528i \(-0.00539650\pi\)
−0.718993 + 0.695018i \(0.755397\pi\)
\(294\) 0 0
\(295\) −15.8284 + 15.8284i −0.921567 + 0.921567i
\(296\) 0 0
\(297\) −1.07107 1.07107i −0.0621497 0.0621497i
\(298\) 0 0
\(299\) 0.414214 0.171573i 0.0239546 0.00992232i
\(300\) 0 0
\(301\) −4.65685 + 11.2426i −0.268417 + 0.648015i
\(302\) 0 0
\(303\) 22.7279i 1.30569i
\(304\) 0 0
\(305\) 2.58579i 0.148062i
\(306\) 0 0
\(307\) −1.22183 + 2.94975i −0.0697333 + 0.168351i −0.954904 0.296916i \(-0.904042\pi\)
0.885170 + 0.465267i \(0.154042\pi\)
\(308\) 0 0
\(309\) 18.0711 7.48528i 1.02803 0.425823i
\(310\) 0 0
\(311\) −8.65685 8.65685i −0.490885 0.490885i 0.417700 0.908585i \(-0.362836\pi\)
−0.908585 + 0.417700i \(0.862836\pi\)
\(312\) 0 0
\(313\) −9.48528 + 9.48528i −0.536140 + 0.536140i −0.922393 0.386253i \(-0.873769\pi\)
0.386253 + 0.922393i \(0.373769\pi\)
\(314\) 0 0
\(315\) −0.757359 1.82843i −0.0426724 0.103020i
\(316\) 0 0
\(317\) 11.1924 + 4.63604i 0.628627 + 0.260386i 0.674170 0.738577i \(-0.264502\pi\)
−0.0455425 + 0.998962i \(0.514502\pi\)
\(318\) 0 0
\(319\) 0.928932 0.0520102
\(320\) 0 0
\(321\) 0.585786 0.0326954
\(322\) 0 0
\(323\) 15.6569 + 6.48528i 0.871171 + 0.360851i
\(324\) 0 0
\(325\) −4.53553 10.9497i −0.251586 0.607383i
\(326\) 0 0
\(327\) 6.07107 6.07107i 0.335731 0.335731i
\(328\) 0 0
\(329\) 11.6569 + 11.6569i 0.642663 + 0.642663i
\(330\) 0 0
\(331\) −6.53553 + 2.70711i −0.359225 + 0.148796i −0.554995 0.831854i \(-0.687280\pi\)
0.195769 + 0.980650i \(0.437280\pi\)
\(332\) 0 0
\(333\) 0.292893 0.707107i 0.0160504 0.0387492i
\(334\) 0 0
\(335\) 13.5563i 0.740662i
\(336\) 0 0
\(337\) 16.9706i 0.924445i 0.886764 + 0.462223i \(0.152948\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(338\) 0 0
\(339\) 12.4853 30.1421i 0.678107 1.63710i
\(340\) 0 0
\(341\) −1.17157 + 0.485281i −0.0634442 + 0.0262795i
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) 1.07107 1.07107i 0.0576644 0.0576644i
\(346\) 0 0
\(347\) −5.94975 14.3640i −0.319399 0.771098i −0.999286 0.0377808i \(-0.987971\pi\)
0.679887 0.733317i \(-0.262029\pi\)
\(348\) 0 0
\(349\) −25.7782 10.6777i −1.37987 0.571563i −0.435426 0.900224i \(-0.643402\pi\)
−0.944448 + 0.328662i \(0.893402\pi\)
\(350\) 0 0
\(351\) 8.82843 0.471227
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0.757359 + 0.313708i 0.0401965 + 0.0166499i
\(356\) 0 0
\(357\) −2.82843 6.82843i −0.149696 0.361399i
\(358\) 0 0
\(359\) 12.1716 12.1716i 0.642391 0.642391i −0.308752 0.951143i \(-0.599911\pi\)
0.951143 + 0.308752i \(0.0999112\pi\)
\(360\) 0 0
\(361\) −11.9497 11.9497i −0.628934 0.628934i
\(362\) 0 0
\(363\) −18.6066 + 7.70711i −0.976593 + 0.404518i
\(364\) 0 0
\(365\) 12.7990 30.8995i 0.669930 1.61735i
\(366\) 0 0
\(367\) 6.00000i 0.313197i −0.987662 0.156599i \(-0.949947\pi\)
0.987662 0.156599i \(-0.0500529\pi\)
\(368\) 0 0
\(369\) 3.41421i 0.177737i
\(370\) 0 0
\(371\) −4.41421 + 10.6569i −0.229175 + 0.553276i
\(372\) 0 0
\(373\) −28.2635 + 11.7071i −1.46343 + 0.606171i −0.965349 0.260962i \(-0.915960\pi\)
−0.498077 + 0.867133i \(0.665960\pi\)
\(374\) 0 0
\(375\) −6.24264 6.24264i −0.322369 0.322369i
\(376\) 0 0
\(377\) −3.82843 + 3.82843i −0.197174 + 0.197174i
\(378\) 0 0
\(379\) −8.97918 21.6777i −0.461230 1.11351i −0.967893 0.251363i \(-0.919121\pi\)
0.506663 0.862144i \(-0.330879\pi\)
\(380\) 0 0
\(381\) −35.7990 14.8284i −1.83404 0.759683i
\(382\) 0 0
\(383\) 16.9706 0.867155 0.433578 0.901116i \(-0.357251\pi\)
0.433578 + 0.901116i \(0.357251\pi\)
\(384\) 0 0
\(385\) −1.51472 −0.0771972
\(386\) 0 0
\(387\) 3.29289 + 1.36396i 0.167387 + 0.0693340i
\(388\) 0 0
\(389\) 12.2635 + 29.6066i 0.621782 + 1.50111i 0.849609 + 0.527413i \(0.176838\pi\)
−0.227827 + 0.973702i \(0.573162\pi\)
\(390\) 0 0
\(391\) 0.485281 0.485281i 0.0245417 0.0245417i
\(392\) 0 0
\(393\) −12.4142 12.4142i −0.626214 0.626214i
\(394\) 0 0
\(395\) −18.7279 + 7.75736i −0.942304 + 0.390315i
\(396\) 0 0
\(397\) 10.2635 24.7782i 0.515108 1.24358i −0.425769 0.904832i \(-0.639996\pi\)
0.940877 0.338749i \(-0.110004\pi\)
\(398\) 0 0
\(399\) 15.6569i 0.783823i
\(400\) 0 0
\(401\) 2.82843i 0.141245i 0.997503 + 0.0706225i \(0.0224986\pi\)
−0.997503 + 0.0706225i \(0.977501\pi\)
\(402\) 0 0
\(403\) 2.82843 6.82843i 0.140894 0.340148i
\(404\) 0 0
\(405\) 31.4350 13.0208i 1.56202 0.647010i
\(406\) 0 0
\(407\) −0.414214 0.414214i −0.0205318 0.0205318i
\(408\) 0 0
\(409\) −4.51472 + 4.51472i −0.223238 + 0.223238i −0.809861 0.586622i \(-0.800457\pi\)
0.586622 + 0.809861i \(0.300457\pi\)
\(410\) 0 0
\(411\) −2.65685 6.41421i −0.131053 0.316390i
\(412\) 0 0
\(413\) −8.65685 3.58579i −0.425976 0.176445i
\(414\) 0 0
\(415\) −22.3848 −1.09883
\(416\) 0 0
\(417\) −25.0711 −1.22774
\(418\) 0 0
\(419\) −20.7782 8.60660i −1.01508 0.420460i −0.187775 0.982212i \(-0.560127\pi\)
−0.827306 + 0.561752i \(0.810127\pi\)
\(420\) 0 0
\(421\) −3.19239 7.70711i −0.155587 0.375621i 0.826795 0.562504i \(-0.190162\pi\)
−0.982382 + 0.186882i \(0.940162\pi\)
\(422\) 0 0
\(423\) 3.41421 3.41421i 0.166005 0.166005i
\(424\) 0 0
\(425\) −12.8284 12.8284i −0.622270 0.622270i
\(426\) 0 0
\(427\) −1.00000 + 0.414214i −0.0483934 + 0.0200452i
\(428\) 0 0
\(429\) −0.414214 + 1.00000i −0.0199984 + 0.0482805i
\(430\) 0 0
\(431\) 23.6569i 1.13951i −0.821814 0.569755i \(-0.807038\pi\)
0.821814 0.569755i \(-0.192962\pi\)
\(432\) 0 0
\(433\) 32.4853i 1.56114i −0.625067 0.780571i \(-0.714928\pi\)
0.625067 0.780571i \(-0.285072\pi\)
\(434\) 0 0
\(435\) −7.00000 + 16.8995i −0.335624 + 0.810269i
\(436\) 0 0
\(437\) −1.34315 + 0.556349i −0.0642514 + 0.0266138i
\(438\) 0 0
\(439\) 17.0000 + 17.0000i 0.811366 + 0.811366i 0.984839 0.173473i \(-0.0554989\pi\)
−0.173473 + 0.984839i \(0.555499\pi\)
\(440\) 0 0
\(441\) −1.46447 + 1.46447i −0.0697365 + 0.0697365i
\(442\) 0 0
\(443\) 8.53553 + 20.6066i 0.405535 + 0.979049i 0.986298 + 0.164976i \(0.0527546\pi\)
−0.580762 + 0.814073i \(0.697245\pi\)
\(444\) 0 0
\(445\) 11.7279 + 4.85786i 0.555957 + 0.230285i
\(446\) 0 0
\(447\) 27.0711 1.28042
\(448\) 0 0
\(449\) 31.4558 1.48449 0.742247 0.670127i \(-0.233760\pi\)
0.742247 + 0.670127i \(0.233760\pi\)
\(450\) 0 0
\(451\) 2.41421 + 1.00000i 0.113681 + 0.0470882i
\(452\) 0 0
\(453\) −15.4853 37.3848i −0.727562 1.75649i
\(454\) 0 0
\(455\) 6.24264 6.24264i 0.292660 0.292660i
\(456\) 0 0
\(457\) −9.48528 9.48528i −0.443703 0.443703i 0.449552 0.893254i \(-0.351584\pi\)
−0.893254 + 0.449552i \(0.851584\pi\)
\(458\) 0 0
\(459\) 12.4853 5.17157i 0.582763 0.241388i
\(460\) 0 0
\(461\) −5.53553 + 13.3640i −0.257816 + 0.622422i −0.998793 0.0491076i \(-0.984362\pi\)
0.740978 + 0.671529i \(0.234362\pi\)
\(462\) 0 0
\(463\) 10.9706i 0.509845i −0.966961 0.254923i \(-0.917950\pi\)
0.966961 0.254923i \(-0.0820500\pi\)
\(464\) 0 0
\(465\) 24.9706i 1.15798i
\(466\) 0 0
\(467\) −12.0503 + 29.0919i −0.557619 + 1.34621i 0.354027 + 0.935235i \(0.384812\pi\)
−0.911646 + 0.410977i \(0.865188\pi\)
\(468\) 0 0
\(469\) −5.24264 + 2.17157i −0.242083 + 0.100274i
\(470\) 0 0
\(471\) 1.00000 + 1.00000i 0.0460776 + 0.0460776i
\(472\) 0 0
\(473\) 1.92893 1.92893i 0.0886924 0.0886924i
\(474\) 0 0
\(475\) 14.7071 + 35.5061i 0.674808 + 1.62913i
\(476\) 0 0
\(477\) 3.12132 + 1.29289i 0.142915 + 0.0591975i
\(478\) 0 0
\(479\) −4.97056 −0.227111 −0.113555 0.993532i \(-0.536224\pi\)
−0.113555 + 0.993532i \(0.536224\pi\)
\(480\) 0 0
\(481\) 3.41421 0.155675
\(482\) 0 0
\(483\) 0.585786 + 0.242641i 0.0266542 + 0.0110405i
\(484\) 0 0
\(485\) −1.95837 4.72792i −0.0889250 0.214684i
\(486\) 0 0
\(487\) 11.0000 11.0000i 0.498458 0.498458i −0.412500 0.910958i \(-0.635344\pi\)
0.910958 + 0.412500i \(0.135344\pi\)
\(488\) 0 0
\(489\) 25.7279 + 25.7279i 1.16346 + 1.16346i
\(490\) 0 0
\(491\) −17.7071 + 7.33452i −0.799111 + 0.331002i −0.744600 0.667511i \(-0.767360\pi\)
−0.0545104 + 0.998513i \(0.517360\pi\)
\(492\) 0 0
\(493\) −3.17157 + 7.65685i −0.142840 + 0.344847i
\(494\) 0 0
\(495\) 0.443651i 0.0199406i
\(496\) 0 0
\(497\) 0.343146i 0.0153922i
\(498\) 0 0
\(499\) −3.70711 + 8.94975i −0.165953 + 0.400646i −0.984877 0.173256i \(-0.944571\pi\)
0.818924 + 0.573902i \(0.194571\pi\)
\(500\) 0 0
\(501\) −8.07107 + 3.34315i −0.360589 + 0.149361i
\(502\) 0 0
\(503\) −17.1421 17.1421i −0.764330 0.764330i 0.212772 0.977102i \(-0.431751\pi\)
−0.977102 + 0.212772i \(0.931751\pi\)
\(504\) 0 0
\(505\) 29.3848 29.3848i 1.30761 1.30761i
\(506\) 0 0
\(507\) 6.77817 + 16.3640i 0.301029 + 0.726749i
\(508\) 0 0
\(509\) 29.1924 + 12.0919i 1.29393 + 0.535963i 0.920154 0.391556i \(-0.128063\pi\)
0.373776 + 0.927519i \(0.378063\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 0 0
\(513\) −28.6274 −1.26393
\(514\) 0 0
\(515\) 33.0416 + 13.6863i 1.45599 + 0.603090i
\(516\) 0 0
\(517\) −1.41421 3.41421i −0.0621970 0.150157i
\(518\) 0 0
\(519\) 1.58579 1.58579i 0.0696083 0.0696083i
\(520\) 0 0
\(521\) −14.6569 14.6569i −0.642128 0.642128i 0.308950 0.951078i \(-0.400022\pi\)
−0.951078 + 0.308950i \(0.900022\pi\)
\(522\) 0 0
\(523\) 1.94975 0.807612i 0.0852565 0.0353144i −0.339648 0.940553i \(-0.610308\pi\)
0.424904 + 0.905238i \(0.360308\pi\)
\(524\) 0 0
\(525\) 6.41421 15.4853i 0.279939 0.675833i
\(526\) 0 0
\(527\) 11.3137i 0.492833i
\(528\) 0 0
\(529\) 22.9411i 0.997440i
\(530\) 0 0
\(531\) −1.05025 + 2.53553i −0.0455771 + 0.110033i
\(532\) 0 0
\(533\) −14.0711 + 5.82843i −0.609486 + 0.252457i
\(534\) 0 0
\(535\) 0.757359 + 0.757359i 0.0327435 + 0.0327435i
\(536\) 0 0
\(537\) 20.3137 20.3137i 0.876601 0.876601i
\(538\) 0 0
\(539\) 0.606602 + 1.46447i 0.0261282 + 0.0630790i
\(540\) 0 0
\(541\) 12.7071 + 5.26346i 0.546321 + 0.226294i 0.638735 0.769427i \(-0.279458\pi\)
−0.0924135 + 0.995721i \(0.529458\pi\)
\(542\) 0 0
\(543\) −10.5858 −0.454280
\(544\) 0 0
\(545\) 15.6985 0.672449
\(546\) 0 0
\(547\) −25.2635 10.4645i −1.08019 0.447428i −0.229612 0.973282i \(-0.573746\pi\)
−0.850575 + 0.525854i \(0.823746\pi\)
\(548\) 0 0
\(549\) 0.121320 + 0.292893i 0.00517783 + 0.0125004i
\(550\) 0 0
\(551\) 12.4142 12.4142i 0.528863 0.528863i
\(552\) 0 0
\(553\) −6.00000 6.00000i −0.255146 0.255146i
\(554\) 0 0
\(555\) 10.6569 4.41421i 0.452358 0.187373i
\(556\) 0 0
\(557\) −4.50610 + 10.8787i −0.190929 + 0.460944i −0.990136 0.140113i \(-0.955254\pi\)
0.799206 + 0.601057i \(0.205254\pi\)
\(558\) 0 0
\(559\) 15.8995i 0.672477i
\(560\) 0 0
\(561\) 1.65685i 0.0699524i
\(562\) 0 0
\(563\) −5.02082 + 12.1213i −0.211602 + 0.510853i −0.993670 0.112341i \(-0.964165\pi\)
0.782068 + 0.623194i \(0.214165\pi\)
\(564\) 0 0
\(565\) 55.1127 22.8284i 2.31861 0.960399i
\(566\) 0 0
\(567\) 10.0711 + 10.0711i 0.422945 + 0.422945i
\(568\) 0 0
\(569\) −3.34315 + 3.34315i −0.140152 + 0.140152i −0.773702 0.633550i \(-0.781597\pi\)
0.633550 + 0.773702i \(0.281597\pi\)
\(570\) 0 0
\(571\) 0.535534 + 1.29289i 0.0224114 + 0.0541059i 0.934689 0.355466i \(-0.115678\pi\)
−0.912278 + 0.409572i \(0.865678\pi\)
\(572\) 0 0
\(573\) −20.4853 8.48528i −0.855785 0.354478i
\(574\) 0 0
\(575\) 1.55635 0.0649042
\(576\) 0 0
\(577\) −14.9706 −0.623233 −0.311616 0.950208i \(-0.600870\pi\)
−0.311616 + 0.950208i \(0.600870\pi\)
\(578\) 0 0
\(579\) −31.5563 13.0711i −1.31144 0.543215i
\(580\) 0 0
\(581\) −3.58579 8.65685i −0.148763 0.359147i
\(582\) 0 0
\(583\) 1.82843 1.82843i 0.0757257 0.0757257i
\(584\) 0 0
\(585\) −1.82843 1.82843i −0.0755962 0.0755962i
\(586\) 0 0
\(587\) 20.7782 8.60660i 0.857607 0.355232i 0.0898359 0.995957i \(-0.471366\pi\)
0.767771 + 0.640724i \(0.221366\pi\)
\(588\) 0 0
\(589\) −9.17157 + 22.1421i −0.377908 + 0.912351i
\(590\) 0 0
\(591\) 34.7279i 1.42852i
\(592\) 0 0
\(593\) 28.2843i 1.16150i 0.814083 + 0.580748i \(0.197240\pi\)
−0.814083 + 0.580748i \(0.802760\pi\)
\(594\) 0 0
\(595\) 5.17157 12.4853i 0.212014 0.511847i
\(596\) 0 0
\(597\) −43.3848 + 17.9706i −1.77562 + 0.735486i
\(598\) 0 0
\(599\) 15.3431 + 15.3431i 0.626904 + 0.626904i 0.947288 0.320384i \(-0.103812\pi\)
−0.320384 + 0.947288i \(0.603812\pi\)
\(600\) 0 0
\(601\) −11.9706 + 11.9706i −0.488289 + 0.488289i −0.907766 0.419477i \(-0.862214\pi\)
0.419477 + 0.907766i \(0.362214\pi\)
\(602\) 0 0
\(603\) 0.636039 + 1.53553i 0.0259015 + 0.0625318i
\(604\) 0 0
\(605\) −34.0208 14.0919i −1.38314 0.572917i
\(606\) 0 0
\(607\) 0.970563 0.0393939 0.0196970 0.999806i \(-0.493730\pi\)
0.0196970 + 0.999806i \(0.493730\pi\)
\(608\) 0 0
\(609\) −7.65685 −0.310271
\(610\) 0 0
\(611\) 19.8995 + 8.24264i 0.805047 + 0.333462i
\(612\) 0 0
\(613\) −15.1924 36.6777i −0.613615 1.48140i −0.859002 0.511972i \(-0.828915\pi\)
0.245387 0.969425i \(-0.421085\pi\)
\(614\) 0 0
\(615\) −36.3848 + 36.3848i −1.46718 + 1.46718i
\(616\) 0 0
\(617\) 16.7990 + 16.7990i 0.676302 + 0.676302i 0.959161 0.282859i \(-0.0912830\pi\)
−0.282859 + 0.959161i \(0.591283\pi\)
\(618\) 0 0
\(619\) −15.0208 + 6.22183i −0.603738 + 0.250076i −0.663548 0.748133i \(-0.730950\pi\)
0.0598107 + 0.998210i \(0.480950\pi\)
\(620\) 0 0
\(621\) −0.443651 + 1.07107i −0.0178031 + 0.0429805i
\(622\) 0 0
\(623\) 5.31371i 0.212889i
\(624\) 0 0
\(625\) 15.9289i 0.637157i
\(626\) 0 0
\(627\) 1.34315 3.24264i 0.0536401 0.129499i
\(628\) 0 0
\(629\) 4.82843 2.00000i 0.192522 0.0797452i
\(630\) 0 0
\(631\) 18.4558 + 18.4558i 0.734716 + 0.734716i 0.971550 0.236834i \(-0.0761099\pi\)
−0.236834 + 0.971550i \(0.576110\pi\)
\(632\) 0 0
\(633\) −0.656854 + 0.656854i −0.0261076 + 0.0261076i
\(634\) 0 0
\(635\) −27.1127 65.4558i −1.07593 2.59754i
\(636\) 0 0
\(637\) −8.53553 3.53553i −0.338190 0.140083i
\(638\) 0 0
\(639\) 0.100505 0.00397592
\(640\) 0 0
\(641\) −43.4558 −1.71640 −0.858201 0.513313i \(-0.828418\pi\)
−0.858201 + 0.513313i \(0.828418\pi\)
\(642\) 0 0
\(643\) −37.2635 15.4350i −1.46953 0.608698i −0.502776 0.864417i \(-0.667688\pi\)
−0.966751 + 0.255719i \(0.917688\pi\)
\(644\) 0 0
\(645\) 20.5563 + 49.6274i 0.809405 + 1.95408i
\(646\) 0 0
\(647\) −11.8284 + 11.8284i −0.465023 + 0.465023i −0.900298 0.435274i \(-0.856651\pi\)
0.435274 + 0.900298i \(0.356651\pi\)
\(648\) 0 0
\(649\) 1.48528 + 1.48528i 0.0583024 + 0.0583024i
\(650\) 0 0
\(651\) 9.65685 4.00000i 0.378482 0.156772i
\(652\) 0 0
\(653\) 14.9497 36.0919i 0.585029 1.41238i −0.303175 0.952935i \(-0.598047\pi\)
0.888204 0.459450i \(-0.151953\pi\)
\(654\) 0 0
\(655\) 32.1005i 1.25427i
\(656\) 0 0
\(657\) 4.10051i 0.159976i
\(658\) 0 0
\(659\) 2.43503 5.87868i 0.0948553 0.229001i −0.869329 0.494234i \(-0.835449\pi\)
0.964184 + 0.265233i \(0.0854488\pi\)
\(660\) 0 0
\(661\) 18.7071 7.74874i 0.727622 0.301391i 0.0120477 0.999927i \(-0.496165\pi\)
0.715574 + 0.698536i \(0.246165\pi\)
\(662\) 0 0
\(663\) −6.82843 6.82843i −0.265194 0.265194i
\(664\) 0 0
\(665\) −20.2426 + 20.2426i −0.784976 + 0.784976i
\(666\) 0 0
\(667\) −0.272078 0.656854i −0.0105349 0.0254335i
\(668\) 0 0
\(669\) 22.1421 + 9.17157i 0.856064 + 0.354593i
\(670\) 0 0
\(671\) 0.242641 0.00936704
\(672\) 0 0
\(673\) 5.51472 0.212577 0.106288 0.994335i \(-0.466103\pi\)
0.106288 + 0.994335i \(0.466103\pi\)
\(674\) 0 0
\(675\) 28.3137 + 11.7279i 1.08980 + 0.451408i
\(676\) 0 0
\(677\) 2.32233 + 5.60660i 0.0892544 + 0.215479i 0.962203 0.272333i \(-0.0877952\pi\)
−0.872949 + 0.487812i \(0.837795\pi\)
\(678\) 0 0
\(679\) 1.51472 1.51472i 0.0581296 0.0581296i
\(680\) 0 0
\(681\) −8.89949 8.89949i −0.341029 0.341029i
\(682\) 0 0
\(683\) −14.1924 + 5.87868i −0.543057 + 0.224941i −0.637311 0.770607i \(-0.719953\pi\)
0.0942543 + 0.995548i \(0.469953\pi\)
\(684\) 0 0
\(685\) 4.85786 11.7279i 0.185609 0.448101i
\(686\) 0 0
\(687\) 49.5563i 1.89069i
\(688\) 0 0
\(689\) 15.0711i 0.574162i
\(690\) 0 0
\(691\) 11.8076 28.5061i 0.449183 1.08442i −0.523446 0.852059i \(-0.675354\pi\)
0.972629 0.232364i \(-0.0746461\pi\)
\(692\) 0 0
\(693\) −0.171573 + 0.0710678i −0.00651751 + 0.00269964i
\(694\) 0 0
\(695\) −32.4142 32.4142i −1.22954 1.22954i
\(696\) 0 0
\(697\) −16.4853 + 16.4853i −0.624425 + 0.624425i
\(698\) 0 0
\(699\) −8.65685 20.8995i −0.327432 0.790491i
\(700\) 0 0
\(701\) 17.1924 + 7.12132i 0.649348 + 0.268969i 0.682948 0.730467i \(-0.260697\pi\)
−0.0336007 + 0.999435i \(0.510697\pi\)
\(702\) 0 0
\(703\) −11.0711 −0.417553
\(704\) 0 0
\(705\) 72.7696 2.74066
\(706\) 0 0
\(707\) 16.0711 + 6.65685i 0.604415 + 0.250357i
\(708\) 0 0
\(709\) 2.80761 + 6.77817i 0.105442 + 0.254560i 0.967791 0.251755i \(-0.0810076\pi\)
−0.862349 + 0.506314i \(0.831008\pi\)
\(710\) 0 0
\(711\) −1.75736 + 1.75736i −0.0659061 + 0.0659061i
\(712\) 0 0
\(713\) 0.686292 + 0.686292i 0.0257018 + 0.0257018i
\(714\) 0 0
\(715\) −1.82843 + 0.757359i −0.0683793 + 0.0283236i
\(716\) 0 0
\(717\) −12.2426 + 29.5563i −0.457210 + 1.10380i
\(718\) 0 0
\(719\) 24.3431i 0.907846i 0.891041 + 0.453923i \(0.149976\pi\)
−0.891041 + 0.453923i \(0.850024\pi\)
\(720\) 0 0
\(721\) 14.9706i 0.557533i
\(722\) 0 0
\(723\) −6.00000 + 14.4853i −0.223142 + 0.538713i
\(724\) 0 0
\(725\) −17.3640 + 7.19239i −0.644881 + 0.267119i
\(726\) 0 0
\(727\) −23.9706 23.9706i −0.889019 0.889019i 0.105410 0.994429i \(-0.466385\pi\)
−0.994429 + 0.105410i \(0.966385\pi\)
\(728\) 0 0
\(729\) −15.7782 + 15.7782i −0.584377 + 0.584377i
\(730\) 0 0
\(731\) 9.31371 + 22.4853i 0.344480 + 0.831648i
\(732\) 0 0
\(733\) −1.77817 0.736544i −0.0656784 0.0272049i 0.349602 0.936898i \(-0.386317\pi\)
−0.415281 + 0.909693i \(0.636317\pi\)
\(734\) 0 0
\(735\) −31.2132 −1.15132
\(736\) 0 0
\(737\) 1.27208 0.0468576
\(738\) 0 0
\(739\) 18.1924 + 7.53553i 0.669218 + 0.277199i 0.691312 0.722557i \(-0.257033\pi\)
−0.0220937 + 0.999756i \(0.507033\pi\)
\(740\) 0 0
\(741\) 7.82843 + 18.8995i 0.287584 + 0.694290i
\(742\) 0 0
\(743\) 13.6274 13.6274i 0.499941 0.499941i −0.411478 0.911420i \(-0.634987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(744\) 0 0
\(745\) 35.0000 + 35.0000i 1.28230 + 1.28230i
\(746\) 0 0
\(747\) −2.53553 + 1.05025i −0.0927703 + 0.0384267i
\(748\) 0 0
\(749\) −0.171573 + 0.414214i −0.00626914 + 0.0151350i
\(750\) 0 0
\(751\) 22.9706i 0.838208i 0.907938 + 0.419104i \(0.137656\pi\)
−0.907938 + 0.419104i \(0.862344\pi\)
\(752\) 0 0
\(753\) 29.2132i 1.06459i
\(754\) 0 0
\(755\) 28.3137 68.3553i 1.03044 2.48771i
\(756\) 0 0
\(757\) −1.77817 + 0.736544i −0.0646289 + 0.0267701i −0.414764 0.909929i \(-0.636136\pi\)
0.350135 + 0.936699i \(0.386136\pi\)
\(758\) 0 0
\(759\) −0.100505 0.100505i −0.00364810 0.00364810i
\(760\) 0 0
\(761\) 24.1716 24.1716i 0.876219 0.876219i −0.116922 0.993141i \(-0.537303\pi\)
0.993141 + 0.116922i \(0.0373028\pi\)
\(762\) 0 0
\(763\) 2.51472 + 6.07107i 0.0910389 + 0.219787i
\(764\) 0 0
\(765\) −3.65685 1.51472i −0.132214 0.0547648i
\(766\) 0 0
\(767\) −12.2426 −0.442056
\(768\) 0 0
\(769\) 22.4853 0.810840 0.405420 0.914131i \(-0.367125\pi\)
0.405420 + 0.914131i \(0.367125\pi\)
\(770\) 0 0
\(771\) 10.2426 + 4.24264i 0.368880 + 0.152795i
\(772\) 0 0
\(773\) 10.8076 + 26.0919i 0.388723 + 0.938460i 0.990211 + 0.139578i \(0.0445747\pi\)
−0.601488 + 0.798882i \(0.705425\pi\)
\(774\) 0 0
\(775\) 18.1421 18.1421i 0.651685 0.651685i
\(776\) 0 0
\(777\) 3.41421 + 3.41421i 0.122484 + 0.122484i
\(778\) 0 0
\(779\) 45.6274 18.8995i 1.63477 0.677145i
\(780\) 0 0
\(781\) 0.0294373 0.0710678i 0.00105335 0.00254301i
\(782\) 0 0
\(783\) 14.0000i 0.500319i
\(784\) 0 0
\(785\) 2.58579i 0.0922907i
\(786\) 0 0
\(787\) −3.70711 + 8.94975i −0.132144 + 0.319024i −0.976077 0.217424i \(-0.930234\pi\)
0.843933 + 0.536448i \(0.180234\pi\)
\(788\) 0 0
\(789\) 0.414214 0.171573i 0.0147464 0.00610816i
\(790\) 0 0
\(791\) 17.6569 + 17.6569i 0.627805 + 0.627805i
\(792\) 0 0
\(793\) −1.00000 + 1.00000i −0.0355110 + 0.0355110i
\(794\) 0 0