Properties

Label 256.2.g.a.225.1
Level $256$
Weight $2$
Character 256.225
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 225.1
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 256.225
Dual form 256.2.g.a.33.1

$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

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

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 0.985599 + 0.169102i \(0.0540867\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) 3.12132 + 1.29289i 1.39590 + 0.578199i 0.948683 0.316228i \(-0.102416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 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
\(11\) 0.121320 0.292893i 0.0365795 0.0883106i −0.904534 0.426401i \(-0.859781\pi\)
0.941113 + 0.338091i \(0.109781\pi\)
\(12\) 0 0
\(13\) −1.70711 + 0.707107i −0.473466 + 0.196116i −0.606640 0.794977i \(-0.707483\pi\)
0.133174 + 0.991093i \(0.457483\pi\)
\(14\) 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
\(19\) −5.53553 + 2.29289i −1.26994 + 0.526026i −0.912946 0.408081i \(-0.866198\pi\)
−0.356993 + 0.934107i \(0.616198\pi\)
\(20\) 0 0
\(21\) 1.00000 2.41421i 0.218218 0.526825i
\(22\) 0 0
\(23\) −0.171573 + 0.171573i −0.0357754 + 0.0357754i −0.724768 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
\(27\) 4.41421 + 1.82843i 0.849516 + 0.351881i
\(28\) 0 0
\(29\) −1.12132 2.70711i −0.208224 0.502697i 0.784920 0.619598i \(-0.212704\pi\)
−0.993144 + 0.116900i \(0.962704\pi\)
\(30\) 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 0.237920 0.971285i \(-0.423534\pi\)
−0.518567 + 0.855037i \(0.673534\pi\)
\(38\) 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 \(-0.972577\pi\)
0.0860440 + 0.996291i \(0.472577\pi\)
\(42\) 0 0
\(43\) 3.29289 7.94975i 0.502162 1.21233i −0.446143 0.894962i \(-0.647203\pi\)
0.948304 0.317363i \(-0.102797\pi\)
\(44\) 0 0
\(45\) −1.29289 + 0.535534i −0.192733 + 0.0798327i
\(46\) 0 0
\(47\) 11.6569i 1.70033i −0.526519 0.850163i \(-0.676503\pi\)
0.526519 0.850163i \(-0.323497\pi\)
\(48\) 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 0.550939 + 0.834545i \(0.314270\pi\)
−0.979686 + 0.200540i \(0.935730\pi\)
\(54\) 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 −0.0532027 0.998584i \(-0.516943\pi\)
−0.743725 + 0.668485i \(0.766943\pi\)
\(60\) 0 0
\(61\) −0.292893 0.707107i −0.0375011 0.0905357i 0.904019 0.427492i \(-0.140603\pi\)
−0.941520 + 0.336956i \(0.890603\pi\)
\(62\) 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 0.989496 0.144563i \(-0.0461775\pi\)
−0.801900 + 0.597458i \(0.796178\pi\)
\(68\) 0 0
\(69\) −0.414214 0.171573i −0.0498655 0.0206549i
\(70\) 0 0
\(71\) 0.171573 + 0.171573i 0.0203620 + 0.0203620i 0.717214 0.696853i \(-0.245417\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(72\) 0 0
\(73\) 7.00000 7.00000i 0.819288 0.819288i −0.166717 0.986005i \(-0.553317\pi\)
0.986005 + 0.166717i \(0.0533166\pi\)
\(74\) 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 \(0.109590\pi\)
−0.941316 + 0.337526i \(0.890410\pi\)
\(80\) 0 0
\(81\) 10.0711i 1.11901i
\(82\) 0 0
\(83\) 6.12132 2.53553i 0.671902 0.278311i −0.0205350 0.999789i \(-0.506537\pi\)
0.692437 + 0.721478i \(0.256537\pi\)
\(84\) 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 0.552131 0.833757i \(-0.313815\pi\)
−0.833757 + 0.552131i \(0.813815\pi\)
\(90\) 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 −0.262718 0.964873i \(-0.584619\pi\)
−0.868038 + 0.496498i \(0.834619\pi\)
\(102\) 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
\(107\) 0.121320 0.292893i 0.0117285 0.0283151i −0.917907 0.396796i \(-0.870122\pi\)
0.929635 + 0.368481i \(0.120122\pi\)
\(108\) 0 0
\(109\) 4.29289 1.77817i 0.411185 0.170318i −0.167496 0.985873i \(-0.553568\pi\)
0.578680 + 0.815555i \(0.303568\pi\)
\(110\) 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
\(115\) −0.757359 + 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 −0.999376 0.0353153i \(-0.988756\pi\)
0.681694 0.731637i \(-0.261244\pi\)
\(132\) 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 −0.584444 0.811434i \(-0.698687\pi\)
0.811434 + 0.584444i \(0.198687\pi\)
\(138\) 0 0
\(139\) −5.19239 + 12.5355i −0.440413 + 1.06325i 0.535392 + 0.844604i \(0.320164\pi\)
−0.975804 + 0.218646i \(0.929836\pi\)
\(140\) 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 0.509366 + 0.860550i \(0.329880\pi\)
−0.968677 + 0.248324i \(0.920120\pi\)
\(150\) 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
\(155\) 12.4853 + 5.17157i 1.00284 + 0.415391i
\(156\) 0 0
\(157\) −0.292893 0.707107i −0.0233754 0.0564333i 0.911761 0.410722i \(-0.134723\pi\)
−0.935136 + 0.354288i \(0.884723\pi\)
\(158\) 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 0.883282 + 0.468842i \(0.155329\pi\)
−0.293054 + 0.956096i \(0.594671\pi\)
\(164\) 0 0
\(165\) 1.82843 + 0.757359i 0.142343 + 0.0589603i
\(166\) 0 0
\(167\) −3.34315 3.34315i −0.258700 0.258700i 0.565825 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
\(171\) 0.949747 2.29289i 0.0726290 0.175342i
\(172\) 0 0
\(173\) 1.12132 0.464466i 0.0852524 0.0353127i −0.339650 0.940552i \(-0.610309\pi\)
0.424902 + 0.905239i \(0.360309\pi\)
\(174\) 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 −0.848264 0.529573i \(-0.822352\pi\)
−0.225349 + 0.974278i \(0.572352\pi\)
\(180\) 0 0
\(181\) 2.19239 5.29289i 0.162959 0.393418i −0.821216 0.570618i \(-0.806704\pi\)
0.984175 + 0.177200i \(0.0567039\pi\)
\(182\) 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 −0.334314 0.942462i \(-0.608505\pi\)
−0.902817 + 0.430025i \(0.858505\pi\)
\(198\) 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
\(203\) −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 −0.366639 0.930363i \(-0.619491\pi\)
0.398614 + 0.917119i \(0.369491\pi\)
\(212\) 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 0.813464 0.581616i \(-0.197579\pi\)
−0.986470 + 0.163942i \(0.947579\pi\)
\(228\) 0 0
\(229\) 24.7782 + 10.2635i 1.63739 + 0.678228i 0.996030 0.0890139i \(-0.0283716\pi\)
0.641357 + 0.767242i \(0.278372\pi\)
\(230\) 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 \(-0.618655\pi\)
0.931323 + 0.364194i \(0.118655\pi\)
\(234\) 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 \(0.189186\pi\)
−0.828516 + 0.559965i \(0.810814\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 0 0
\(243\) −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 −0.129338 0.991601i \(-0.541285\pi\)
−0.792623 + 0.609712i \(0.791285\pi\)
\(252\) 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 0.712377 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
\(267\) 2.65685 6.41421i 0.162597 0.392543i
\(268\) 0 0
\(269\) −4.87868 + 2.02082i −0.297458 + 0.123211i −0.526421 0.850224i \(-0.676467\pi\)
0.228963 + 0.973435i \(0.426467\pi\)
\(270\) 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
\(275\) 1.87868 0.778175i 0.113289 0.0469257i
\(276\) 0 0
\(277\) −0.292893 + 0.707107i −0.0175982 + 0.0424859i −0.932434 0.361339i \(-0.882320\pi\)
0.914836 + 0.403825i \(0.132320\pi\)
\(278\) 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 \(-0.333832\pi\)
−0.866808 + 0.498643i \(0.833832\pi\)
\(282\) 0 0
\(283\) −9.77817 4.05025i −0.581252 0.240763i 0.0726300 0.997359i \(-0.476861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 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 0.695018 0.718993i \(-0.255397\pi\)
−0.0169528 + 0.999856i \(0.505397\pi\)
\(294\) 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 −0.296916 0.954904i \(-0.595958\pi\)
0.465267 + 0.885170i \(0.345958\pi\)
\(308\) 0 0
\(309\) −7.48528 + 18.0711i −0.425823 + 1.02803i
\(310\) 0 0
\(311\) −8.65685 + 8.65685i −0.490885 + 0.490885i −0.908585 0.417700i \(-0.862836\pi\)
0.417700 + 0.908585i \(0.362836\pi\)
\(312\) 0 0
\(313\) 9.48528 + 9.48528i 0.536140 + 0.536140i 0.922393 0.386253i \(-0.126231\pi\)
−0.386253 + 0.922393i \(0.626231\pi\)
\(314\) 0 0
\(315\) 1.82843 + 0.757359i 0.103020 + 0.0426724i
\(316\) 0 0
\(317\) −4.63604 11.1924i −0.260386 0.628627i 0.738577 0.674170i \(-0.235498\pi\)
−0.998962 + 0.0455425i \(0.985498\pi\)
\(318\) 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 −0.980650 0.195769i \(-0.937280\pi\)
0.831854 + 0.554995i \(0.187280\pi\)
\(332\) 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 \(-0.847052\pi\)
0.886764 0.462223i \(-0.152948\pi\)
\(338\) 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 0.733317 0.679887i \(-0.237971\pi\)
0.0377808 + 0.999286i \(0.487971\pi\)
\(348\) 0 0
\(349\) 10.6777 + 25.7782i 0.571563 + 1.37987i 0.900224 + 0.435426i \(0.143402\pi\)
−0.328662 + 0.944448i \(0.606598\pi\)
\(350\) 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 0.951143 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
\(363\) −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 \(-0.949947\pi\)
0.987662 0.156599i \(-0.0500529\pi\)
\(368\) 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 −0.260962 0.965349i \(-0.584040\pi\)
0.867133 0.498077i \(-0.165960\pi\)
\(374\) 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 0.862144 0.506663i \(-0.169121\pi\)
0.251363 + 0.967893i \(0.419121\pi\)
\(380\) 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 0.973702 0.227827i \(-0.0731622\pi\)
0.527413 + 0.849609i \(0.323162\pi\)
\(390\) 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 0.338749 0.940877i \(-0.389996\pi\)
0.904832 + 0.425769i \(0.139996\pi\)
\(398\) 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
\(403\) −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 0.809861 0.586622i \(-0.199543\pi\)
−0.586622 + 0.809861i \(0.699543\pi\)
\(410\) 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 −0.982212 0.187775i \(-0.939873\pi\)
0.561752 0.827306i \(-0.310127\pi\)
\(420\) 0 0
\(421\) −7.70711 3.19239i −0.375621 0.155587i 0.186882 0.982382i \(-0.440162\pi\)
−0.562504 + 0.826795i \(0.690162\pi\)
\(422\) 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 \(-0.807038\pi\)
0.821814 0.569755i \(-0.192962\pi\)
\(432\) 0 0
\(433\) 32.4853i 1.56114i 0.625067 + 0.780571i \(0.285072\pi\)
−0.625067 + 0.780571i \(0.714928\pi\)
\(434\) 0 0
\(435\) 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 −0.173473 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
\(443\) −20.6066 8.53553i −0.979049 0.405535i −0.164976 0.986298i \(-0.552755\pi\)
−0.814073 + 0.580762i \(0.802755\pi\)
\(444\) 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 −0.449552 0.893254i \(-0.648416\pi\)
0.893254 + 0.449552i \(0.148416\pi\)
\(458\) 0 0
\(459\) 5.17157 12.4853i 0.241388 0.582763i
\(460\) 0 0
\(461\) −13.3640 + 5.53553i −0.622422 + 0.257816i −0.671529 0.740978i \(-0.734362\pi\)
0.0491076 + 0.998793i \(0.484362\pi\)
\(462\) 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
\(467\) 29.0919 12.0503i 1.34621 0.557619i 0.410977 0.911646i \(-0.365188\pi\)
0.935235 + 0.354027i \(0.115188\pi\)
\(468\) 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 0.910958 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
\(491\) −7.33452 + 17.7071i −0.331002 + 0.799111i 0.667511 + 0.744600i \(0.267360\pi\)
−0.998513 + 0.0545104i \(0.982640\pi\)
\(492\) 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 −0.173256 0.984877i \(-0.555429\pi\)
0.573902 + 0.818924i \(0.305429\pi\)
\(500\) 0 0
\(501\) 3.34315 8.07107i 0.149361 0.360589i
\(502\) 0 0
\(503\) −17.1421 + 17.1421i −0.764330 + 0.764330i −0.977102 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
\(507\) −16.3640 6.77817i −0.726749 0.301029i
\(508\) 0 0
\(509\) −12.0919 29.1924i −0.535963 1.29393i −0.927519 0.373776i \(-0.878063\pi\)
0.391556 0.920154i \(-0.371937\pi\)
\(510\) 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 −0.308950 0.951078i \(-0.599978\pi\)
0.951078 + 0.308950i \(0.0999775\pi\)
\(522\) 0 0
\(523\) 0.807612 1.94975i 0.0353144 0.0852565i −0.905238 0.424904i \(-0.860308\pi\)
0.940553 + 0.339648i \(0.110308\pi\)
\(524\) 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 0.769427 0.638735i \(-0.220542\pi\)
−0.995721 + 0.0924135i \(0.970542\pi\)
\(542\) 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 −0.973282 0.229612i \(-0.926254\pi\)
0.525854 0.850575i \(-0.323746\pi\)
\(548\) 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 −0.601057 0.799206i \(-0.705254\pi\)
0.140113 + 0.990136i \(0.455254\pi\)
\(558\) 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 −0.112341 0.993670i \(-0.535835\pi\)
0.623194 + 0.782068i \(0.285835\pi\)
\(564\) 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 0.773702 0.633550i \(-0.218403\pi\)
−0.633550 + 0.773702i \(0.718403\pi\)
\(570\) 0 0
\(571\) −1.29289 0.535534i −0.0541059 0.0224114i 0.355466 0.934689i \(-0.384322\pi\)
−0.409572 + 0.912278i \(0.634322\pi\)
\(572\) 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 −0.640724 0.767771i \(-0.721366\pi\)
0.995957 0.0898359i \(-0.0286342\pi\)
\(588\) 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 \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) 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 −0.320384 0.947288i \(-0.603812\pi\)
0.947288 + 0.320384i \(0.103812\pi\)
\(600\) 0 0
\(601\) 11.9706 + 11.9706i 0.488289 + 0.488289i 0.907766 0.419477i \(-0.137786\pi\)
−0.419477 + 0.907766i \(0.637786\pi\)
\(602\) 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 −0.511972 0.859002i \(-0.671085\pi\)
−0.969425 + 0.245387i \(0.921085\pi\)
\(614\) 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 \(-0.908717\pi\)
0.282859 + 0.959161i \(0.408717\pi\)
\(618\) 0 0
\(619\) −6.22183 + 15.0208i −0.250076 + 0.603738i −0.998210 0.0598107i \(-0.980950\pi\)
0.748133 + 0.663548i \(0.230950\pi\)
\(620\) 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 −0.236834 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
\(635\) 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 −0.864417 0.502776i \(-0.832312\pi\)
0.255719 0.966751i \(-0.417688\pi\)
\(644\) 0 0
\(645\) 49.6274 + 20.5563i 1.95408 + 0.809405i
\(646\) 0 0
\(647\) −11.8284 11.8284i −0.465023 0.465023i 0.435274 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
\(651\) 4.00000 9.65685i 0.156772 0.378482i
\(652\) 0 0
\(653\) 36.0919 14.9497i 1.41238 0.585029i 0.459450 0.888204i \(-0.348047\pi\)
0.952935 + 0.303175i \(0.0980467\pi\)
\(654\) 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 −0.494234 0.869329i \(-0.664551\pi\)
0.265233 + 0.964184i \(0.414551\pi\)
\(660\) 0 0
\(661\) −7.74874 + 18.7071i −0.301391 + 0.727622i 0.698536 + 0.715574i \(0.253835\pi\)
−0.999927 + 0.0120477i \(0.996165\pi\)
\(662\) 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 0.487812 0.872949i \(-0.337795\pi\)
−0.272333 + 0.962203i \(0.587795\pi\)
\(678\) 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 −0.995548 0.0942543i \(-0.969953\pi\)
0.770607 + 0.637311i \(0.219953\pi\)
\(684\) 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 −0.852059 0.523446i \(-0.824646\pi\)
−0.232364 + 0.972629i \(0.574646\pi\)
\(692\) 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 0.730467 0.682948i \(-0.239303\pi\)
−0.999435 + 0.0336007i \(0.989303\pi\)
\(702\) 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 0.506314 0.862349i \(-0.331008\pi\)
−0.251755 + 0.967791i \(0.581008\pi\)
\(710\) 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 \(0.149976\pi\)
−0.891041 + 0.453923i \(0.850024\pi\)
\(720\) 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 −0.994429 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
\(731\) −22.4853 9.31371i −0.831648 0.344480i
\(732\) 0 0
\(733\) 0.736544 + 1.77817i 0.0272049 + 0.0656784i 0.936898 0.349602i \(-0.113683\pi\)
−0.909693 + 0.415281i \(0.863683\pi\)
\(734\) 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 0.999756 0.0220937i \(-0.00703323\pi\)
−0.722557 + 0.691312i \(0.757033\pi\)
\(740\) 0 0
\(741\) 18.8995 + 7.82843i 0.694290 + 0.287584i
\(742\) 0 0
\(743\) 13.6274 + 13.6274i 0.499941 + 0.499941i 0.911420 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
\(747\) −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 \(0.137656\pi\)
−0.907938 + 0.419104i \(0.862344\pi\)
\(752\) 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 −0.909929 0.414764i \(-0.863864\pi\)
0.936699 + 0.350135i \(0.113864\pi\)
\(758\) 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 \(-0.462697\pi\)
−0.993141 + 0.116922i \(0.962697\pi\)
\(762\) 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 0.798882 0.601488i \(-0.205425\pi\)
0.139578 + 0.990211i \(0.455425\pi\)
\(774\) 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 −0.217424 0.976077i \(-0.569766\pi\)
0.536448 + 0.843933i \(0.319766\pi\)
\(788\) 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