Properties

Label 512.2.g.d.193.1
Level $512$
Weight $2$
Character 512.193
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 193.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 512.193
Dual form 512.2.g.d.321.1

$q$-expansion

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

Character values

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

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

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 0.169102 0.985599i \(-0.445913\pi\)
0.816497 + 0.577350i \(0.195913\pi\)
\(4\) 0 0
\(5\) 1.29289 3.12132i 0.578199 1.39590i −0.316228 0.948683i \(-0.602416\pi\)
0.894427 0.447214i \(-0.147584\pi\)
\(6\) 0 0
\(7\) −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i \(-0.336119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 0 0
\(9\) 0.292893 0.292893i 0.0976311 0.0976311i
\(10\) 0 0
\(11\) 0.292893 + 0.121320i 0.0883106 + 0.0365795i 0.426401 0.904534i \(-0.359781\pi\)
−0.338091 + 0.941113i \(0.609781\pi\)
\(12\) 0 0
\(13\) −0.707107 1.70711i −0.196116 0.473466i 0.794977 0.606640i \(-0.207483\pi\)
−0.991093 + 0.133174i \(0.957483\pi\)
\(14\) 0 0
\(15\) 6.24264i 1.61184i
\(16\) 0 0
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) 0 0
\(19\) 2.29289 + 5.53553i 0.526026 + 1.26994i 0.934107 + 0.356993i \(0.116198\pi\)
−0.408081 + 0.912946i \(0.633802\pi\)
\(20\) 0 0
\(21\) −2.41421 1.00000i −0.526825 0.218218i
\(22\) 0 0
\(23\) −0.171573 + 0.171573i −0.0357754 + 0.0357754i −0.724768 0.688993i \(-0.758053\pi\)
0.688993 + 0.724768i \(0.258053\pi\)
\(24\) 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 −0.116900 0.993144i \(-0.537296\pi\)
0.619598 + 0.784920i \(0.287296\pi\)
\(30\) 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 −0.971285 0.237920i \(-0.923534\pi\)
0.855037 + 0.518567i \(0.173534\pi\)
\(38\) 0 0
\(39\) −2.41421 2.41421i −0.386584 0.386584i
\(40\) 0 0
\(41\) 5.82843 5.82843i 0.910247 0.910247i −0.0860440 0.996291i \(-0.527423\pi\)
0.996291 + 0.0860440i \(0.0274225\pi\)
\(42\) 0 0
\(43\) 7.94975 + 3.29289i 1.21233 + 0.502162i 0.894962 0.446143i \(-0.147203\pi\)
0.317363 + 0.948304i \(0.397203\pi\)
\(44\) 0 0
\(45\) −0.535534 1.29289i −0.0798327 0.192733i
\(46\) 0 0
\(47\) 11.6569i 1.70033i 0.526519 + 0.850163i \(0.323497\pi\)
−0.526519 + 0.850163i \(0.676503\pi\)
\(48\) 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 0.834545 0.550939i \(-0.185730\pi\)
0.200540 + 0.979686i \(0.435730\pi\)
\(54\) 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 −0.668485 0.743725i \(-0.733057\pi\)
0.998584 0.0532027i \(-0.0169429\pi\)
\(60\) 0 0
\(61\) 0.707107 0.292893i 0.0905357 0.0375011i −0.336956 0.941520i \(-0.609397\pi\)
0.427492 + 0.904019i \(0.359397\pi\)
\(62\) 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 −0.144563 0.989496i \(-0.546178\pi\)
0.597458 + 0.801900i \(0.296178\pi\)
\(68\) 0 0
\(69\) −0.171573 + 0.414214i −0.0206549 + 0.0498655i
\(70\) 0 0
\(71\) 0.171573 + 0.171573i 0.0203620 + 0.0203620i 0.717214 0.696853i \(-0.245417\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(72\) 0 0
\(73\) −7.00000 + 7.00000i −0.819288 + 0.819288i −0.986005 0.166717i \(-0.946683\pi\)
0.166717 + 0.986005i \(0.446683\pi\)
\(74\) 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 \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 0 0
\(81\) 10.0711i 1.11901i
\(82\) 0 0
\(83\) −2.53553 6.12132i −0.278311 0.671902i 0.721478 0.692437i \(-0.243463\pi\)
−0.999789 + 0.0205350i \(0.993463\pi\)
\(84\) 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 0.833757 0.552131i \(-0.186185\pi\)
−0.552131 + 0.833757i \(0.686185\pi\)
\(90\) 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 0.496498 + 0.868038i \(0.334619\pi\)
−0.964873 + 0.262718i \(0.915381\pi\)
\(102\) 0 0
\(103\) 7.48528 + 7.48528i 0.737547 + 0.737547i 0.972103 0.234556i \(-0.0753636\pi\)
−0.234556 + 0.972103i \(0.575364\pi\)
\(104\) 0 0
\(105\) −6.24264 + 6.24264i −0.609219 + 0.609219i
\(106\) 0 0
\(107\) 0.292893 + 0.121320i 0.0283151 + 0.0117285i 0.396796 0.917907i \(-0.370122\pi\)
−0.368481 + 0.929635i \(0.620122\pi\)
\(108\) 0 0
\(109\) 1.77817 + 4.29289i 0.170318 + 0.411185i 0.985873 0.167496i \(-0.0535680\pi\)
−0.815555 + 0.578680i \(0.803568\pi\)
\(110\) 0 0
\(111\) 3.41421i 0.324063i
\(112\) 0 0
\(113\) 17.6569i 1.66102i 0.557006 + 0.830509i \(0.311950\pi\)
−0.557006 + 0.830509i \(0.688050\pi\)
\(114\) 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 −0.731637 0.681694i \(-0.761244\pi\)
−0.0353153 + 0.999376i \(0.511244\pi\)
\(132\) 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 −0.811434 0.584444i \(-0.801313\pi\)
0.584444 + 0.811434i \(0.301313\pi\)
\(138\) 0 0
\(139\) −12.5355 5.19239i −1.06325 0.440413i −0.218646 0.975804i \(-0.570164\pi\)
−0.844604 + 0.535392i \(0.820164\pi\)
\(140\) 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 0.860550 0.509366i \(-0.170120\pi\)
0.248324 + 0.968677i \(0.420120\pi\)
\(150\) 0 0
\(151\) −15.4853 + 15.4853i −1.26017 + 1.26017i −0.309166 + 0.951008i \(0.600050\pi\)
−0.951008 + 0.309166i \(0.899950\pi\)
\(152\) 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 −0.354288 0.935136i \(-0.615277\pi\)
0.410722 + 0.911761i \(0.365277\pi\)
\(158\) 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 0.468842 0.883282i \(-0.344671\pi\)
0.956096 + 0.293054i \(0.0946714\pi\)
\(164\) 0 0
\(165\) 0.757359 1.82843i 0.0589603 0.142343i
\(166\) 0 0
\(167\) −3.34315 3.34315i −0.258700 0.258700i 0.565825 0.824525i \(-0.308558\pi\)
−0.824525 + 0.565825i \(0.808558\pi\)
\(168\) 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 0.940552 0.339650i \(-0.110309\pi\)
−0.905239 + 0.424902i \(0.860309\pi\)
\(174\) 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 0.974278 + 0.225349i \(0.0723521\pi\)
−0.529573 + 0.848264i \(0.677648\pi\)
\(180\) 0 0
\(181\) −5.29289 2.19239i −0.393418 0.162959i 0.177200 0.984175i \(-0.443296\pi\)
−0.570618 + 0.821216i \(0.693296\pi\)
\(182\) 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 0.430025 + 0.902817i \(0.358505\pi\)
−0.942462 + 0.334314i \(0.891495\pi\)
\(198\) 0 0
\(199\) −17.9706 17.9706i −1.27390 1.27390i −0.944025 0.329875i \(-0.892994\pi\)
−0.329875 0.944025i \(-0.607006\pi\)
\(200\) 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 0.917119 0.398614i \(-0.130509\pi\)
−0.930363 + 0.366639i \(0.880509\pi\)
\(212\) 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 −0.581616 0.813464i \(-0.697579\pi\)
0.163942 + 0.986470i \(0.447579\pi\)
\(228\) 0 0
\(229\) 10.2635 24.7782i 0.678228 1.63739i −0.0890139 0.996030i \(-0.528372\pi\)
0.767242 0.641357i \(-0.221628\pi\)
\(230\) 0 0
\(231\) −0.585786 0.585786i −0.0385419 0.0385419i
\(232\) 0 0
\(233\) −8.65685 + 8.65685i −0.567129 + 0.567129i −0.931323 0.364194i \(-0.881345\pi\)
0.364194 + 0.931323i \(0.381345\pi\)
\(234\) 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 \(-0.810814\pi\)
0.828516 0.559965i \(-0.189186\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 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 −0.609712 0.792623i \(-0.708715\pi\)
0.991601 0.129338i \(-0.0412851\pi\)
\(252\) 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 0.712377 0.701797i \(-0.247619\pi\)
−0.701797 + 0.712377i \(0.747619\pi\)
\(264\) 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 0.850224 0.526421i \(-0.176467\pi\)
−0.973435 + 0.228963i \(0.926467\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i −0.837321 0.546711i \(-0.815880\pi\)
0.837321 0.546711i \(-0.184120\pi\)
\(272\) 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 0.403825 0.914836i \(-0.367680\pi\)
−0.361339 + 0.932434i \(0.617680\pi\)
\(278\) 0 0
\(279\) −1.17157 + 1.17157i −0.0701402 + 0.0701402i
\(280\) 0 0
\(281\) 6.17157 + 6.17157i 0.368165 + 0.368165i 0.866808 0.498643i \(-0.166168\pi\)
−0.498643 + 0.866808i \(0.666168\pi\)
\(282\) 0 0
\(283\) 4.05025 9.77817i 0.240763 0.581252i −0.756596 0.653882i \(-0.773139\pi\)
0.997359 + 0.0726300i \(0.0231392\pi\)
\(284\) 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 −0.718993 0.695018i \(-0.755397\pi\)
0.999856 + 0.0169528i \(0.00539650\pi\)
\(294\) 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 0.885170 0.465267i \(-0.154042\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(308\) 0 0
\(309\) 18.0711 + 7.48528i 1.02803 + 0.425823i
\(310\) 0 0
\(311\) −8.65685 + 8.65685i −0.490885 + 0.490885i −0.908585 0.417700i \(-0.862836\pi\)
0.417700 + 0.908585i \(0.362836\pi\)
\(312\) 0 0
\(313\) −9.48528 9.48528i −0.536140 0.536140i 0.386253 0.922393i \(-0.373769\pi\)
−0.922393 + 0.386253i \(0.873769\pi\)
\(314\) 0 0
\(315\) −0.757359 + 1.82843i −0.0426724 + 0.103020i
\(316\) 0 0
\(317\) 11.1924 4.63604i 0.628627 0.260386i −0.0455425 0.998962i \(-0.514502\pi\)
0.674170 + 0.738577i \(0.264502\pi\)
\(318\) 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 0.195769 0.980650i \(-0.437280\pi\)
−0.554995 + 0.831854i \(0.687280\pi\)
\(332\) 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 \(-0.847052\pi\)
0.886764 0.462223i \(-0.152948\pi\)
\(338\) 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 0.679887 + 0.733317i \(0.262029\pi\)
−0.999286 + 0.0377808i \(0.987971\pi\)
\(348\) 0 0
\(349\) −25.7782 + 10.6777i −1.37987 + 0.571563i −0.944448 0.328662i \(-0.893402\pi\)
−0.435426 + 0.900224i \(0.643402\pi\)
\(350\) 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 0.951143 0.308752i \(-0.0999112\pi\)
−0.308752 + 0.951143i \(0.599911\pi\)
\(360\) 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 \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) 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 −0.498077 0.867133i \(-0.665960\pi\)
−0.965349 + 0.260962i \(0.915960\pi\)
\(374\) 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 0.506663 + 0.862144i \(0.330879\pi\)
−0.967893 + 0.251363i \(0.919121\pi\)
\(380\) 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 −0.227827 0.973702i \(-0.573162\pi\)
0.849609 0.527413i \(-0.176838\pi\)
\(390\) 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 0.940877 + 0.338749i \(0.110004\pi\)
−0.425769 + 0.904832i \(0.639996\pi\)
\(398\) 0 0
\(399\) 15.6569i 0.783823i
\(400\) 0 0
\(401\) 2.82843i 0.141245i −0.997503 0.0706225i \(-0.977501\pi\)
0.997503 0.0706225i \(-0.0224986\pi\)
\(402\) 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 0.586622 0.809861i \(-0.300457\pi\)
−0.809861 + 0.586622i \(0.800457\pi\)
\(410\) 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 −0.827306 0.561752i \(-0.810127\pi\)
−0.187775 + 0.982212i \(0.560127\pi\)
\(420\) 0 0
\(421\) −3.19239 + 7.70711i −0.155587 + 0.375621i −0.982382 0.186882i \(-0.940162\pi\)
0.826795 + 0.562504i \(0.190162\pi\)
\(422\) 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 \(0.192962\pi\)
−0.821814 + 0.569755i \(0.807038\pi\)
\(432\) 0 0
\(433\) 32.4853i 1.56114i 0.625067 + 0.780571i \(0.285072\pi\)
−0.625067 + 0.780571i \(0.714928\pi\)
\(434\) 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 −0.173473 0.984839i \(-0.555499\pi\)
0.984839 + 0.173473i \(0.0554989\pi\)
\(440\) 0 0
\(441\) −1.46447 1.46447i −0.0697365 0.0697365i
\(442\) 0 0
\(443\) 8.53553 20.6066i 0.405535 0.979049i −0.580762 0.814073i \(-0.697245\pi\)
0.986298 0.164976i \(-0.0527546\pi\)
\(444\) 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 −0.893254 0.449552i \(-0.851584\pi\)
0.449552 + 0.893254i \(0.351584\pi\)
\(458\) 0 0
\(459\) 12.4853 + 5.17157i 0.582763 + 0.241388i
\(460\) 0 0
\(461\) −5.53553 13.3640i −0.257816 0.622422i 0.740978 0.671529i \(-0.234362\pi\)
−0.998793 + 0.0491076i \(0.984362\pi\)
\(462\) 0 0
\(463\) 10.9706i 0.509845i 0.966961 + 0.254923i \(0.0820500\pi\)
−0.966961 + 0.254923i \(0.917950\pi\)
\(464\) 0 0
\(465\) 24.9706i 1.15798i
\(466\) 0 0
\(467\) −12.0503 29.0919i −0.557619 1.34621i −0.911646 0.410977i \(-0.865188\pi\)
0.354027 0.935235i \(-0.384812\pi\)
\(468\) 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 0.910958 0.412500i \(-0.135344\pi\)
−0.412500 + 0.910958i \(0.635344\pi\)
\(488\) 0 0
\(489\) 25.7279 25.7279i 1.16346 1.16346i
\(490\) 0 0
\(491\) −17.7071 7.33452i −0.799111 0.331002i −0.0545104 0.998513i \(-0.517360\pi\)
−0.744600 + 0.667511i \(0.767360\pi\)
\(492\) 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 0.818924 0.573902i \(-0.194571\pi\)
−0.984877 + 0.173256i \(0.944571\pi\)
\(500\) 0 0
\(501\) −8.07107 3.34315i −0.360589 0.149361i
\(502\) 0 0
\(503\) −17.1421 + 17.1421i −0.764330 + 0.764330i −0.977102 0.212772i \(-0.931751\pi\)
0.212772 + 0.977102i \(0.431751\pi\)
\(504\) 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 0.373776 0.927519i \(-0.378063\pi\)
0.920154 + 0.391556i \(0.128063\pi\)
\(510\) 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 −0.951078 0.308950i \(-0.900022\pi\)
0.308950 + 0.951078i \(0.400022\pi\)
\(522\) 0 0
\(523\) 1.94975 + 0.807612i 0.0852565 + 0.0353144i 0.424904 0.905238i \(-0.360308\pi\)
−0.339648 + 0.940553i \(0.610308\pi\)
\(524\) 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 −0.0924135 0.995721i \(-0.529458\pi\)
0.638735 + 0.769427i \(0.279458\pi\)
\(542\) 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 −0.850575 0.525854i \(-0.823746\pi\)
−0.229612 + 0.973282i \(0.573746\pi\)
\(548\) 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 0.799206 0.601057i \(-0.205254\pi\)
−0.990136 + 0.140113i \(0.955254\pi\)
\(558\) 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 0.782068 0.623194i \(-0.214165\pi\)
−0.993670 + 0.112341i \(0.964165\pi\)
\(564\) 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 0.633550 0.773702i \(-0.281597\pi\)
−0.773702 + 0.633550i \(0.781597\pi\)
\(570\) 0 0
\(571\) 0.535534 1.29289i 0.0224114 0.0541059i −0.912278 0.409572i \(-0.865678\pi\)
0.934689 + 0.355466i \(0.115678\pi\)
\(572\) 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 0.767771 0.640724i \(-0.221366\pi\)
0.0898359 + 0.995957i \(0.471366\pi\)
\(588\) 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 \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) 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 −0.320384 0.947288i \(-0.603812\pi\)
0.947288 + 0.320384i \(0.103812\pi\)
\(600\) 0 0
\(601\) −11.9706 11.9706i −0.488289 0.488289i 0.419477 0.907766i \(-0.362214\pi\)
−0.907766 + 0.419477i \(0.862214\pi\)
\(602\) 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 0.245387 + 0.969425i \(0.421085\pi\)
−0.859002 + 0.511972i \(0.828915\pi\)
\(614\) 0 0
\(615\) −36.3848 36.3848i −1.46718 1.46718i
\(616\) 0 0
\(617\) 16.7990 16.7990i 0.676302 0.676302i −0.282859 0.959161i \(-0.591283\pi\)
0.959161 + 0.282859i \(0.0912830\pi\)
\(618\) 0 0
\(619\) −15.0208 6.22183i −0.603738 0.250076i 0.0598107 0.998210i \(-0.480950\pi\)
−0.663548 + 0.748133i \(0.730950\pi\)
\(620\) 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 −0.236834 0.971550i \(-0.576110\pi\)
0.971550 + 0.236834i \(0.0761099\pi\)
\(632\) 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 −0.966751 0.255719i \(-0.917688\pi\)
−0.502776 + 0.864417i \(0.667688\pi\)
\(644\) 0 0
\(645\) 20.5563 49.6274i 0.809405 1.95408i
\(646\) 0 0
\(647\) −11.8284 11.8284i −0.465023 0.465023i 0.435274 0.900298i \(-0.356651\pi\)
−0.900298 + 0.435274i \(0.856651\pi\)
\(648\) 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 0.888204 + 0.459450i \(0.151953\pi\)
−0.303175 + 0.952935i \(0.598047\pi\)
\(654\) 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 0.964184 0.265233i \(-0.0854488\pi\)
−0.869329 + 0.494234i \(0.835449\pi\)
\(660\) 0 0
\(661\) 18.7071 + 7.74874i 0.727622 + 0.301391i 0.715574 0.698536i \(-0.246165\pi\)
0.0120477 + 0.999927i \(0.496165\pi\)
\(662\) 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 −0.872949 0.487812i \(-0.837795\pi\)
0.962203 + 0.272333i \(0.0877952\pi\)
\(678\) 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 0.0942543 0.995548i \(-0.469953\pi\)
−0.637311 + 0.770607i \(0.719953\pi\)
\(684\) 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 0.972629 + 0.232364i \(0.0746461\pi\)
−0.523446 + 0.852059i \(0.675354\pi\)
\(692\) 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 −0.0336007 0.999435i \(-0.510697\pi\)
0.682948 + 0.730467i \(0.260697\pi\)
\(702\) 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 −0.862349 0.506314i \(-0.831008\pi\)
0.967791 + 0.251755i \(0.0810076\pi\)
\(710\) 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 \(-0.850024\pi\)
0.891041 0.453923i \(-0.149976\pi\)
\(720\) 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 −0.994429 0.105410i \(-0.966385\pi\)
0.105410 + 0.994429i \(0.466385\pi\)
\(728\) 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 −0.415281 0.909693i \(-0.636317\pi\)
0.349602 + 0.936898i \(0.386317\pi\)
\(734\) 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 −0.0220937 0.999756i \(-0.507033\pi\)
0.691312 + 0.722557i \(0.257033\pi\)
\(740\) 0 0
\(741\) 7.82843 18.8995i 0.287584 0.694290i
\(742\) 0 0
\(743\) 13.6274 + 13.6274i 0.499941 + 0.499941i 0.911420 0.411478i \(-0.134987\pi\)
−0.411478 + 0.911420i \(0.634987\pi\)
\(744\) 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 \(-0.862344\pi\)
0.907938 0.419104i \(-0.137656\pi\)
\(752\) 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 0.350135 0.936699i \(-0.386136\pi\)
−0.414764 + 0.909929i \(0.636136\pi\)
\(758\) 0 0
\(759\) −0.100505 + 0.100505i −0.00364810 + 0.00364810i
\(760\) 0 0
\(761\) 24.1716 + 24.1716i 0.876219 + 0.876219i 0.993141 0.116922i \(-0.0373028\pi\)
−0.116922 + 0.993141i \(0.537303\pi\)
\(762\) 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 −0.601488 0.798882i \(-0.705425\pi\)
0.990211 0.139578i \(-0.0445747\pi\)
\(774\) 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 0.843933 0.536448i \(-0.180234\pi\)
−0.976077 + 0.217424i \(0.930234\pi\)
\(788\) 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