Properties

Label 256.2.g.a.33.1
Level $256$
Weight $2$
Character 256.33
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04417029174\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 33.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 256.33
Dual form 256.2.g.a.225.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 0.707107 1.70711i 0.408248 0.985599i −0.577350 0.816497i \(-0.695913\pi\)
0.985599 0.169102i \(-0.0540867\pi\)
\(4\) 0 0
\(5\) 3.12132 1.29289i 1.39590 0.578199i 0.447214 0.894427i \(-0.352416\pi\)
0.948683 + 0.316228i \(0.102416\pi\)
\(6\) 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
\(11\) 0.121320 + 0.292893i 0.0365795 + 0.0883106i 0.941113 0.338091i \(-0.109781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) −1.70711 0.707107i −0.473466 0.196116i 0.133174 0.991093i \(-0.457483\pi\)
−0.606640 + 0.794977i \(0.707483\pi\)
\(14\) 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
\(19\) −5.53553 2.29289i −1.26994 0.526026i −0.356993 0.934107i \(-0.616198\pi\)
−0.912946 + 0.408081i \(0.866198\pi\)
\(20\) 0 0
\(21\) 1.00000 + 2.41421i 0.218218 + 0.526825i
\(22\) 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
\(27\) 4.41421 1.82843i 0.849516 0.351881i
\(28\) 0 0
\(29\) −1.12132 + 2.70711i −0.208224 + 0.502697i −0.993144 0.116900i \(-0.962704\pi\)
0.784920 + 0.619598i \(0.212704\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0.585786 0.101972
\(34\) 0 0
\(35\) −1.82843 + 4.41421i −0.309061 + 0.746138i
\(36\) 0 0
\(37\) −1.70711 + 0.707107i −0.280647 + 0.116248i −0.518567 0.855037i \(-0.673534\pi\)
0.237920 + 0.971285i \(0.423534\pi\)
\(38\) 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 \(-0.472577\pi\)
−0.996291 + 0.0860440i \(0.972577\pi\)
\(42\) 0 0
\(43\) 3.29289 + 7.94975i 0.502162 + 1.21233i 0.948304 + 0.317363i \(0.102797\pi\)
−0.446143 + 0.894962i \(0.647203\pi\)
\(44\) 0 0
\(45\) −1.29289 0.535534i −0.192733 0.0798327i
\(46\) 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
\(51\) 4.82843 + 2.00000i 0.676115 + 0.280056i
\(52\) 0 0
\(53\) −3.12132 7.53553i −0.428746 1.03509i −0.979686 0.200540i \(-0.935730\pi\)
0.550939 0.834545i \(-0.314270\pi\)
\(54\) 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
\(59\) −6.12132 + 2.53553i −0.796928 + 0.330098i −0.743725 0.668485i \(-0.766943\pi\)
−0.0532027 + 0.998584i \(0.516943\pi\)
\(60\) 0 0
\(61\) −0.292893 + 0.707107i −0.0375011 + 0.0905357i −0.941520 0.336956i \(-0.890603\pi\)
0.904019 + 0.427492i \(0.140603\pi\)
\(62\) 0 0
\(63\) 0.585786 0.0738022
\(64\) 0 0
\(65\) −6.24264 −0.774304
\(66\) 0 0
\(67\) 1.53553 3.70711i 0.187595 0.452895i −0.801900 0.597458i \(-0.796178\pi\)
0.989496 + 0.144563i \(0.0461775\pi\)
\(68\) 0 0
\(69\) −0.414214 + 0.171573i −0.0498655 + 0.0206549i
\(70\) 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 0.986005 0.166717i \(-0.0533166\pi\)
−0.166717 + 0.986005i \(0.553317\pi\)
\(74\) 0 0
\(75\) −4.53553 10.9497i −0.523718 1.26437i
\(76\) 0 0
\(77\) −0.414214 0.171573i −0.0472040 0.0195525i
\(78\) 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
\(83\) 6.12132 + 2.53553i 0.671902 + 0.278311i 0.692437 0.721478i \(-0.256537\pi\)
−0.0205350 + 0.999789i \(0.506537\pi\)
\(84\) 0 0
\(85\) 3.65685 + 8.82843i 0.396642 + 0.957577i
\(86\) 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 \(-0.813815\pi\)
0.552131 + 0.833757i \(0.313815\pi\)
\(90\) 0 0
\(91\) 2.41421 1.00000i 0.253078 0.104828i
\(92\) 0 0
\(93\) 2.82843 6.82843i 0.293294 0.708075i
\(94\) 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
\(99\) 0.0502525 0.121320i 0.00505057 0.0121932i
\(100\) 0 0
\(101\) −11.3640 + 4.70711i −1.13076 + 0.468375i −0.868038 0.496498i \(-0.834619\pi\)
−0.262718 + 0.964873i \(0.584619\pi\)
\(102\) 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
\(107\) 0.121320 + 0.292893i 0.0117285 + 0.0283151i 0.929635 0.368481i \(-0.120122\pi\)
−0.917907 + 0.396796i \(0.870122\pi\)
\(108\) 0 0
\(109\) 4.29289 + 1.77817i 0.411185 + 0.170318i 0.578680 0.815555i \(-0.303568\pi\)
−0.167496 + 0.985873i \(0.553568\pi\)
\(110\) 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
\(115\) −0.757359 0.313708i −0.0706241 0.0292535i
\(116\) 0 0
\(117\) 0.292893 + 0.707107i 0.0270780 + 0.0653720i
\(118\) 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
\(123\) −14.0711 + 5.82843i −1.26875 + 0.525532i
\(124\) 0 0
\(125\) 1.82843 4.41421i 0.163539 0.394819i
\(126\) 0 0
\(127\) 20.9706 1.86084 0.930418 0.366499i \(-0.119444\pi\)
0.930418 + 0.366499i \(0.119444\pi\)
\(128\) 0 0
\(129\) 15.8995 1.39987
\(130\) 0 0
\(131\) −3.63604 + 8.77817i −0.317682 + 0.766953i 0.681694 + 0.731637i \(0.261244\pi\)
−0.999376 + 0.0353153i \(0.988756\pi\)
\(132\) 0 0
\(133\) 7.82843 3.24264i 0.678811 0.281173i
\(134\) 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 \(-0.198687\pi\)
−0.584444 + 0.811434i \(0.698687\pi\)
\(138\) 0 0
\(139\) −5.19239 12.5355i −0.440413 1.06325i −0.975804 0.218646i \(-0.929836\pi\)
0.535392 0.844604i \(-0.320164\pi\)
\(140\) 0 0
\(141\) 19.8995 + 8.24264i 1.67584 + 0.694156i
\(142\) 0 0
\(143\) 0.585786i 0.0489859i
\(144\) 0 0
\(145\) 9.89949i 0.822108i
\(146\) 0 0
\(147\) 8.53553 + 3.53553i 0.703999 + 0.291606i
\(148\) 0 0
\(149\) −5.60660 13.5355i −0.459311 1.10887i −0.968677 0.248324i \(-0.920120\pi\)
0.509366 0.860550i \(-0.329880\pi\)
\(150\) 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
\(155\) 12.4853 5.17157i 1.00284 0.415391i
\(156\) 0 0
\(157\) −0.292893 + 0.707107i −0.0233754 + 0.0564333i −0.935136 0.354288i \(-0.884723\pi\)
0.911761 + 0.410722i \(0.134723\pi\)
\(158\) 0 0
\(159\) −15.0711 −1.19521
\(160\) 0 0
\(161\) 0.343146 0.0270437
\(162\) 0 0
\(163\) 7.53553 18.1924i 0.590229 1.42494i −0.293054 0.956096i \(-0.594671\pi\)
0.883282 0.468842i \(-0.155329\pi\)
\(164\) 0 0
\(165\) 1.82843 0.757359i 0.142343 0.0589603i
\(166\) 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
\(171\) 0.949747 + 2.29289i 0.0726290 + 0.175342i
\(172\) 0 0
\(173\) 1.12132 + 0.464466i 0.0852524 + 0.0353127i 0.424902 0.905239i \(-0.360309\pi\)
−0.339650 + 0.940552i \(0.610309\pi\)
\(174\) 0 0
\(175\) 9.07107i 0.685708i
\(176\) 0 0
\(177\) 12.2426i 0.920213i
\(178\) 0 0
\(179\) −14.3640 5.94975i −1.07361 0.444705i −0.225349 0.974278i \(-0.572352\pi\)
−0.848264 + 0.529573i \(0.822352\pi\)
\(180\) 0 0
\(181\) 2.19239 + 5.29289i 0.162959 + 0.393418i 0.984175 0.177200i \(-0.0567039\pi\)
−0.821216 + 0.570618i \(0.806704\pi\)
\(182\) 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
\(187\) −0.828427 + 0.343146i −0.0605806 + 0.0250933i
\(188\) 0 0
\(189\) −2.58579 + 6.24264i −0.188088 + 0.454085i
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −18.4853 −1.33060 −0.665300 0.746576i \(-0.731696\pi\)
−0.665300 + 0.746576i \(0.731696\pi\)
\(194\) 0 0
\(195\) −4.41421 + 10.6569i −0.316108 + 0.763153i
\(196\) 0 0
\(197\) −17.3640 + 7.19239i −1.23713 + 0.512436i −0.902817 0.430025i \(-0.858505\pi\)
−0.334314 + 0.942462i \(0.608505\pi\)
\(198\) 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
\(203\) −1.58579 3.82843i −0.111300 0.268703i
\(204\) 0 0
\(205\) −25.7279 10.6569i −1.79692 0.744307i
\(206\) 0 0
\(207\) 0.100505i 0.00698558i
\(208\) 0 0
\(209\) 1.89949i 0.131391i
\(210\) 0 0
\(211\) 0.464466 + 0.192388i 0.0319752 + 0.0132445i 0.398614 0.917119i \(-0.369491\pi\)
−0.366639 + 0.930363i \(0.619491\pi\)
\(212\) 0 0
\(213\) −0.171573 0.414214i −0.0117560 0.0283814i
\(214\) 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
\(219\) 16.8995 7.00000i 1.14196 0.473016i
\(220\) 0 0
\(221\) 2.00000 4.82843i 0.134535 0.324795i
\(222\) 0 0
\(223\) −12.9706 −0.868573 −0.434287 0.900775i \(-0.642999\pi\)
−0.434287 + 0.900775i \(0.642999\pi\)
\(224\) 0 0
\(225\) −2.65685 −0.177124
\(226\) 0 0
\(227\) −2.60660 + 6.29289i −0.173006 + 0.417674i −0.986470 0.163942i \(-0.947579\pi\)
0.813464 + 0.581616i \(0.197579\pi\)
\(228\) 0 0
\(229\) 24.7782 10.2635i 1.63739 0.678228i 0.641357 0.767242i \(-0.278372\pi\)
0.996030 + 0.0890139i \(0.0283716\pi\)
\(230\) 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 \(-0.118655\pi\)
−0.364194 + 0.931323i \(0.618655\pi\)
\(234\) 0 0
\(235\) 15.0711 + 36.3848i 0.983128 + 2.37348i
\(236\) 0 0
\(237\) −10.2426 4.24264i −0.665331 0.275589i
\(238\) 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 \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) 0 0
\(243\) −3.94975 1.63604i −0.253376 0.104952i
\(244\) 0 0
\(245\) 6.46447 + 15.6066i 0.413000 + 0.997069i
\(246\) 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
\(251\) −14.6066 + 6.05025i −0.921961 + 0.381889i −0.792623 0.609712i \(-0.791285\pi\)
−0.129338 + 0.991601i \(0.541285\pi\)
\(252\) 0 0
\(253\) 0.0294373 0.0710678i 0.00185070 0.00446800i
\(254\) 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
\(259\) 1.00000 2.41421i 0.0621370 0.150012i
\(260\) 0 0
\(261\) 1.12132 0.464466i 0.0694080 0.0287497i
\(262\) 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
\(267\) 2.65685 + 6.41421i 0.162597 + 0.392543i
\(268\) 0 0
\(269\) −4.87868 2.02082i −0.297458 0.123211i 0.228963 0.973435i \(-0.426467\pi\)
−0.526421 + 0.850224i \(0.676467\pi\)
\(270\) 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
\(275\) 1.87868 + 0.778175i 0.113289 + 0.0469257i
\(276\) 0 0
\(277\) −0.292893 0.707107i −0.0175982 0.0424859i 0.914836 0.403825i \(-0.132320\pi\)
−0.932434 + 0.361339i \(0.882320\pi\)
\(278\) 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 \(-0.833832\pi\)
0.498643 + 0.866808i \(0.333832\pi\)
\(282\) 0 0
\(283\) −9.77817 + 4.05025i −0.581252 + 0.240763i −0.653882 0.756596i \(-0.726861\pi\)
0.0726300 + 0.997359i \(0.476861\pi\)
\(284\) 0 0
\(285\) −14.3137 + 34.5563i −0.847871 + 2.04694i
\(286\) 0 0
\(287\) 11.6569 0.688082
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) −1.07107 + 2.58579i −0.0627871 + 0.151581i
\(292\) 0 0
\(293\) 11.6066 4.80761i 0.678065 0.280864i −0.0169528 0.999856i \(-0.505397\pi\)
0.695018 + 0.718993i \(0.255397\pi\)
\(294\) 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
\(299\) 0.171573 + 0.414214i 0.00992232 + 0.0239546i
\(300\) 0 0
\(301\) −11.2426 4.65685i −0.648015 0.268417i
\(302\) 0 0
\(303\) 22.7279i 1.30569i
\(304\) 0 0
\(305\) 2.58579i 0.148062i
\(306\) 0 0
\(307\) 2.94975 + 1.22183i 0.168351 + 0.0697333i 0.465267 0.885170i \(-0.345958\pi\)
−0.296916 + 0.954904i \(0.595958\pi\)
\(308\) 0 0
\(309\) −7.48528 18.0711i −0.425823 1.02803i
\(310\) 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 −0.386253 0.922393i \(-0.626231\pi\)
0.922393 + 0.386253i \(0.126231\pi\)
\(314\) 0 0
\(315\) 1.82843 0.757359i 0.103020 0.0426724i
\(316\) 0 0
\(317\) −4.63604 + 11.1924i −0.260386 + 0.628627i −0.998962 0.0455425i \(-0.985498\pi\)
0.738577 + 0.674170i \(0.235498\pi\)
\(318\) 0 0
\(319\) −0.928932 −0.0520102
\(320\) 0 0
\(321\) 0.585786 0.0326954
\(322\) 0 0
\(323\) 6.48528 15.6569i 0.360851 0.871171i
\(324\) 0 0
\(325\) −10.9497 + 4.53553i −0.607383 + 0.251586i
\(326\) 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
\(331\) −2.70711 6.53553i −0.148796 0.359225i 0.831854 0.554995i \(-0.187280\pi\)
−0.980650 + 0.195769i \(0.937280\pi\)
\(332\) 0 0
\(333\) 0.707107 + 0.292893i 0.0387492 + 0.0160504i
\(334\) 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
\(339\) −30.1421 12.4853i −1.63710 0.678107i
\(340\) 0 0
\(341\) 0.485281 + 1.17157i 0.0262795 + 0.0634442i
\(342\) 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
\(347\) 14.3640 5.94975i 0.771098 0.319399i 0.0377808 0.999286i \(-0.487971\pi\)
0.733317 + 0.679887i \(0.237971\pi\)
\(348\) 0 0
\(349\) 10.6777 25.7782i 0.571563 1.37987i −0.328662 0.944448i \(-0.606598\pi\)
0.900224 0.435426i \(-0.143402\pi\)
\(350\) 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
\(355\) 0.313708 0.757359i 0.0166499 0.0401965i
\(356\) 0 0
\(357\) −6.82843 + 2.82843i −0.361399 + 0.149696i
\(358\) 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
\(363\) −7.70711 18.6066i −0.404518 0.976593i
\(364\) 0 0
\(365\) 30.8995 + 12.7990i 1.61735 + 0.669930i
\(366\) 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
\(371\) 10.6569 + 4.41421i 0.553276 + 0.229175i
\(372\) 0 0
\(373\) 11.7071 + 28.2635i 0.606171 + 1.46343i 0.867133 + 0.498077i \(0.165960\pi\)
−0.260962 + 0.965349i \(0.584040\pi\)
\(374\) 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
\(379\) 21.6777 8.97918i 1.11351 0.461230i 0.251363 0.967893i \(-0.419121\pi\)
0.862144 + 0.506663i \(0.169121\pi\)
\(380\) 0 0
\(381\) 14.8284 35.7990i 0.759683 1.83404i
\(382\) 0 0
\(383\) −16.9706 −0.867155 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(384\) 0 0
\(385\) −1.51472 −0.0771972
\(386\) 0 0
\(387\) 1.36396 3.29289i 0.0693340 0.167387i
\(388\) 0 0
\(389\) 29.6066 12.2635i 1.50111 0.621782i 0.527413 0.849609i \(-0.323162\pi\)
0.973702 + 0.227827i \(0.0731622\pi\)
\(390\) 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
\(395\) −7.75736 18.7279i −0.390315 0.942304i
\(396\) 0 0
\(397\) 24.7782 + 10.2635i 1.24358 + 0.515108i 0.904832 0.425769i \(-0.139996\pi\)
0.338749 + 0.940877i \(0.389996\pi\)
\(398\) 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
\(403\) −6.82843 2.82843i −0.340148 0.140894i
\(404\) 0 0
\(405\) −13.0208 31.4350i −0.647010 1.56202i
\(406\) 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 \(-0.699543\pi\)
0.809861 + 0.586622i \(0.199543\pi\)
\(410\) 0 0
\(411\) 6.41421 2.65685i 0.316390 0.131053i
\(412\) 0 0
\(413\) 3.58579 8.65685i 0.176445 0.425976i
\(414\) 0 0
\(415\) 22.3848 1.09883
\(416\) 0 0
\(417\) −25.0711 −1.22774
\(418\) 0 0
\(419\) −8.60660 + 20.7782i −0.420460 + 1.01508i 0.561752 + 0.827306i \(0.310127\pi\)
−0.982212 + 0.187775i \(0.939873\pi\)
\(420\) 0 0
\(421\) −7.70711 + 3.19239i −0.375621 + 0.155587i −0.562504 0.826795i \(-0.690162\pi\)
0.186882 + 0.982382i \(0.440162\pi\)
\(422\) 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
\(427\) −0.414214 1.00000i −0.0200452 0.0483934i
\(428\) 0 0
\(429\) −1.00000 0.414214i −0.0482805 0.0199984i
\(430\) 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 \(-0.714928\pi\)
0.625067 0.780571i \(-0.285072\pi\)
\(434\) 0 0
\(435\) 16.8995 + 7.00000i 0.810269 + 0.335624i
\(436\) 0 0
\(437\) 0.556349 + 1.34315i 0.0266138 + 0.0642514i
\(438\) 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
\(443\) −20.6066 + 8.53553i −0.979049 + 0.405535i −0.814073 0.580762i \(-0.802755\pi\)
−0.164976 + 0.986298i \(0.552755\pi\)
\(444\) 0 0
\(445\) −4.85786 + 11.7279i −0.230285 + 0.555957i
\(446\) 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
\(451\) 1.00000 2.41421i 0.0470882 0.113681i
\(452\) 0 0
\(453\) −37.3848 + 15.4853i −1.75649 + 0.727562i
\(454\) 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 \(-0.148416\pi\)
−0.449552 + 0.893254i \(0.648416\pi\)
\(458\) 0 0
\(459\) 5.17157 + 12.4853i 0.241388 + 0.582763i
\(460\) 0 0
\(461\) −13.3640 5.53553i −0.622422 0.257816i 0.0491076 0.998793i \(-0.484362\pi\)
−0.671529 + 0.740978i \(0.734362\pi\)
\(462\) 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
\(467\) 29.0919 + 12.0503i 1.34621 + 0.557619i 0.935235 0.354027i \(-0.115188\pi\)
0.410977 + 0.911646i \(0.365188\pi\)
\(468\) 0 0
\(469\) 2.17157 + 5.24264i 0.100274 + 0.242083i
\(470\) 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
\(475\) −35.5061 + 14.7071i −1.62913 + 0.674808i
\(476\) 0 0
\(477\) −1.29289 + 3.12132i −0.0591975 + 0.142915i
\(478\) 0 0
\(479\) 4.97056 0.227111 0.113555 0.993532i \(-0.463776\pi\)
0.113555 + 0.993532i \(0.463776\pi\)
\(480\) 0 0
\(481\) 3.41421 0.155675
\(482\) 0 0
\(483\) 0.242641 0.585786i 0.0110405 0.0266542i
\(484\) 0 0
\(485\) −4.72792 + 1.95837i −0.214684 + 0.0889250i
\(486\) 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
\(491\) −7.33452 17.7071i −0.331002 0.799111i −0.998513 0.0545104i \(-0.982640\pi\)
0.667511 0.744600i \(-0.267360\pi\)
\(492\) 0 0
\(493\) −7.65685 3.17157i −0.344847 0.142840i
\(494\) 0 0
\(495\) 0.443651i 0.0199406i
\(496\) 0 0
\(497\) 0.343146i 0.0153922i
\(498\) 0 0
\(499\) 8.94975 + 3.70711i 0.400646 + 0.165953i 0.573902 0.818924i \(-0.305429\pi\)
−0.173256 + 0.984877i \(0.555429\pi\)
\(500\) 0 0
\(501\) 3.34315 + 8.07107i 0.149361 + 0.360589i
\(502\) 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
\(507\) −16.3640 + 6.77817i −0.726749 + 0.301029i
\(508\) 0 0
\(509\) −12.0919 + 29.1924i −0.535963 + 1.29393i 0.391556 + 0.920154i \(0.371937\pi\)
−0.927519 + 0.373776i \(0.878063\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) −28.6274 −1.26393
\(514\) 0 0
\(515\) 13.6863 33.0416i 0.603090 1.45599i
\(516\) 0 0
\(517\) −3.41421 + 1.41421i −0.150157 + 0.0621970i
\(518\) 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 \(-0.0999775\pi\)
−0.308950 + 0.951078i \(0.599978\pi\)
\(522\) 0 0
\(523\) 0.807612 + 1.94975i 0.0353144 + 0.0852565i 0.940553 0.339648i \(-0.110308\pi\)
−0.905238 + 0.424904i \(0.860308\pi\)
\(524\) 0 0
\(525\) 15.4853 + 6.41421i 0.675833 + 0.279939i
\(526\) 0 0
\(527\) 11.3137i 0.492833i
\(528\) 0 0
\(529\) 22.9411i 0.997440i
\(530\) 0 0
\(531\) 2.53553 + 1.05025i 0.110033 + 0.0455771i
\(532\) 0 0
\(533\) 5.82843 + 14.0711i 0.252457 + 0.609486i
\(534\) 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
\(539\) −1.46447 + 0.606602i −0.0630790 + 0.0261282i
\(540\) 0 0
\(541\) −5.26346 + 12.7071i −0.226294 + 0.546321i −0.995721 0.0924135i \(-0.970542\pi\)
0.769427 + 0.638735i \(0.220542\pi\)
\(542\) 0 0
\(543\) 10.5858 0.454280
\(544\) 0 0
\(545\) 15.6985 0.672449
\(546\) 0 0
\(547\) −10.4645 + 25.2635i −0.447428 + 1.08019i 0.525854 + 0.850575i \(0.323746\pi\)
−0.973282 + 0.229612i \(0.926254\pi\)
\(548\) 0 0
\(549\) 0.292893 0.121320i 0.0125004 0.00517783i
\(550\) 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
\(555\) 4.41421 + 10.6569i 0.187373 + 0.452358i
\(556\) 0 0
\(557\) −10.8787 4.50610i −0.460944 0.190929i 0.140113 0.990136i \(-0.455254\pi\)
−0.601057 + 0.799206i \(0.705254\pi\)
\(558\) 0 0
\(559\) 15.8995i 0.672477i
\(560\) 0 0
\(561\) 1.65685i 0.0699524i
\(562\) 0 0
\(563\) 12.1213 + 5.02082i 0.510853 + 0.211602i 0.623194 0.782068i \(-0.285835\pi\)
−0.112341 + 0.993670i \(0.535835\pi\)
\(564\) 0 0
\(565\) −22.8284 55.1127i −0.960399 2.31861i
\(566\) 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 \(-0.718403\pi\)
0.773702 + 0.633550i \(0.218403\pi\)
\(570\) 0 0
\(571\) −1.29289 + 0.535534i −0.0541059 + 0.0224114i −0.409572 0.912278i \(-0.634322\pi\)
0.355466 + 0.934689i \(0.384322\pi\)
\(572\) 0 0
\(573\) 8.48528 20.4853i 0.354478 0.855785i
\(574\) 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
\(579\) −13.0711 + 31.5563i −0.543215 + 1.31144i
\(580\) 0 0
\(581\) −8.65685 + 3.58579i −0.359147 + 0.148763i
\(582\) 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
\(587\) 8.60660 + 20.7782i 0.355232 + 0.857607i 0.995957 + 0.0898359i \(0.0286342\pi\)
−0.640724 + 0.767771i \(0.721366\pi\)
\(588\) 0 0
\(589\) −22.1421 9.17157i −0.912351 0.377908i
\(590\) 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
\(595\) −12.4853 5.17157i −0.511847 0.212014i
\(596\) 0 0
\(597\) 17.9706 + 43.3848i 0.735486 + 1.77562i
\(598\) 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 −0.419477 0.907766i \(-0.637786\pi\)
0.907766 + 0.419477i \(0.137786\pi\)
\(602\) 0 0
\(603\) −1.53553 + 0.636039i −0.0625318 + 0.0259015i
\(604\) 0 0
\(605\) 14.0919 34.0208i 0.572917 1.38314i
\(606\) 0 0
\(607\) −0.970563 −0.0393939 −0.0196970 0.999806i \(-0.506270\pi\)
−0.0196970 + 0.999806i \(0.506270\pi\)
\(608\) 0 0
\(609\) −7.65685 −0.310271
\(610\) 0 0
\(611\) 8.24264 19.8995i 0.333462 0.805047i
\(612\) 0 0
\(613\) −36.6777 + 15.1924i −1.48140 + 0.613615i −0.969425 0.245387i \(-0.921085\pi\)
−0.511972 + 0.859002i \(0.671085\pi\)
\(614\) 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 \(-0.408717\pi\)
−0.959161 + 0.282859i \(0.908717\pi\)
\(618\) 0 0
\(619\) −6.22183 15.0208i −0.250076 0.603738i 0.748133 0.663548i \(-0.230950\pi\)
−0.998210 + 0.0598107i \(0.980950\pi\)
\(620\) 0 0
\(621\) −1.07107 0.443651i −0.0429805 0.0178031i
\(622\) 0 0
\(623\) 5.31371i 0.212889i
\(624\) 0 0
\(625\) 15.9289i 0.637157i
\(626\) 0 0
\(627\) −3.24264 1.34315i −0.129499 0.0536401i
\(628\) 0 0
\(629\) −2.00000 4.82843i −0.0797452 0.192522i
\(630\) 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
\(635\) 65.4558 27.1127i 2.59754 1.07593i
\(636\) 0 0
\(637\) 3.53553 8.53553i 0.140083 0.338190i
\(638\) 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
\(643\) −15.4350 + 37.2635i −0.608698 + 1.46953i 0.255719 + 0.966751i \(0.417688\pi\)
−0.864417 + 0.502776i \(0.832312\pi\)
\(644\) 0 0
\(645\) 49.6274 20.5563i 1.95408 0.809405i
\(646\) 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
\(651\) 4.00000 + 9.65685i 0.156772 + 0.378482i
\(652\) 0 0
\(653\) 36.0919 + 14.9497i 1.41238 + 0.585029i 0.952935 0.303175i \(-0.0980467\pi\)
0.459450 + 0.888204i \(0.348047\pi\)
\(654\) 0 0
\(655\) 32.1005i 1.25427i
\(656\) 0 0
\(657\) 4.10051i 0.159976i
\(658\) 0 0
\(659\) −5.87868 2.43503i −0.229001 0.0948553i 0.265233 0.964184i \(-0.414551\pi\)
−0.494234 + 0.869329i \(0.664551\pi\)
\(660\) 0 0
\(661\) −7.74874 18.7071i −0.301391 0.727622i −0.999927 0.0120477i \(-0.996165\pi\)
0.698536 0.715574i \(-0.253835\pi\)
\(662\) 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
\(667\) 0.656854 0.272078i 0.0254335 0.0105349i
\(668\) 0 0
\(669\) −9.17157 + 22.1421i −0.354593 + 0.856064i
\(670\) 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
\(675\) 11.7279 28.3137i 0.451408 1.08980i
\(676\) 0 0
\(677\) 5.60660 2.32233i 0.215479 0.0892544i −0.272333 0.962203i \(-0.587795\pi\)
0.487812 + 0.872949i \(0.337795\pi\)
\(678\) 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
\(683\) −5.87868 14.1924i −0.224941 0.543057i 0.770607 0.637311i \(-0.219953\pi\)
−0.995548 + 0.0942543i \(0.969953\pi\)
\(684\) 0 0
\(685\) 11.7279 + 4.85786i 0.448101 + 0.185609i
\(686\) 0 0
\(687\) 49.5563i 1.89069i
\(688\) 0 0
\(689\) 15.0711i 0.574162i
\(690\) 0 0
\(691\) −28.5061 11.8076i −1.08442 0.449183i −0.232364 0.972629i \(-0.574646\pi\)
−0.852059 + 0.523446i \(0.824646\pi\)
\(692\) 0 0
\(693\) 0.0710678 + 0.171573i 0.00269964 + 0.00651751i
\(694\) 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
\(699\) 20.8995 8.65685i 0.790491 0.327432i
\(700\) 0 0
\(701\) −7.12132 + 17.1924i −0.268969 + 0.649348i −0.999435 0.0336007i \(-0.989303\pi\)
0.730467 + 0.682948i \(0.239303\pi\)
\(702\) 0 0
\(703\) 11.0711 0.417553
\(704\) 0 0
\(705\) 72.7696 2.74066
\(706\) 0 0
\(707\) 6.65685 16.0711i 0.250357 0.604415i
\(708\) 0 0
\(709\) 6.77817 2.80761i 0.254560 0.105442i −0.251755 0.967791i \(-0.581008\pi\)
0.506314 + 0.862349i \(0.331008\pi\)
\(710\) 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
\(715\) −0.757359 1.82843i −0.0283236 0.0683793i
\(716\) 0 0
\(717\) −29.5563 12.2426i −1.10380 0.457210i
\(718\) 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
\(723\) 14.4853 + 6.00000i 0.538713 + 0.223142i
\(724\) 0 0
\(725\) 7.19239 + 17.3640i 0.267119 + 0.644881i
\(726\) 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
\(731\) −22.4853 + 9.31371i −0.831648 + 0.344480i
\(732\) 0 0
\(733\) 0.736544 1.77817i 0.0272049 0.0656784i −0.909693 0.415281i \(-0.863683\pi\)
0.936898 + 0.349602i \(0.113683\pi\)
\(734\) 0 0
\(735\) 31.2132 1.15132
\(736\) 0 0
\(737\) 1.27208 0.0468576
\(738\) 0 0
\(739\) 7.53553 18.1924i 0.277199 0.669218i −0.722557 0.691312i \(-0.757033\pi\)
0.999756 + 0.0220937i \(0.00703323\pi\)
\(740\) 0 0
\(741\) 18.8995 7.82843i 0.694290 0.287584i
\(742\) 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
\(747\) −1.05025 2.53553i −0.0384267 0.0927703i
\(748\) 0 0
\(749\) −0.414214 0.171573i −0.0151350 0.00626914i
\(750\) 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
\(755\) −68.3553 28.3137i −2.48771 1.03044i
\(756\) 0 0
\(757\) 0.736544 + 1.77817i 0.0267701 + 0.0646289i 0.936699 0.350135i \(-0.113864\pi\)
−0.909929 + 0.414764i \(0.863864\pi\)
\(758\) 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 \(-0.962697\pi\)
0.116922 + 0.993141i \(0.462697\pi\)
\(762\) 0 0
\(763\) −6.07107 + 2.51472i −0.219787 + 0.0910389i
\(764\) 0 0
\(765\) 1.51472 3.65685i 0.0547648 0.132214i
\(766\) 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
\(771\) 4.24264 10.2426i 0.152795 0.368880i
\(772\) 0 0
\(773\) 26.0919 10.8076i 0.938460 0.388723i 0.139578 0.990211i \(-0.455425\pi\)
0.798882 + 0.601488i \(0.205425\pi\)
\(774\) 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
\(779\) 18.8995 + 45.6274i 0.677145 + 1.63477i
\(780\) 0 0
\(781\) 0.0710678 + 0.0294373i 0.00254301 + 0.00105335i
\(782\) 0 0
\(783\) 14.0000i 0.500319i
\(784\) 0 0
\(785\) 2.58579i 0.0922907i
\(786\) 0 0
\(787\) 8.94975 + 3.70711i 0.319024 + 0.132144i 0.536448 0.843933i \(-0.319766\pi\)
−0.217424 + 0.976077i \(0.569766\pi\)
\(788\) 0 0
\(789\) −0.171573 0.414214i −0.00610816 0.0147464i
\(790\) 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
\(795\) −47.0416 + 19.4853i −1.66839 + 0.691072i
\(796\)