Properties

Label 800.2.y.a.301.1
Level $800$
Weight $2$
Character 800.301
Analytic conductor $6.388$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.y (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.38803216170\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 301.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 800.301
Dual form 800.2.y.a.101.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +(0.121320 + 0.292893i) q^{11} +(1.41421 - 3.41421i) q^{12} +(-1.70711 - 0.707107i) q^{13} +(1.41421 + 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(-0.414214 + 0.414214i) q^{18} +(-5.53553 - 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(0.414214 - 0.171573i) q^{22} +(-0.171573 - 0.171573i) q^{23} +(-4.82843 - 2.00000i) q^{24} +(-1.00000 + 2.41421i) q^{26} +(-4.41421 + 1.82843i) q^{27} +(2.00000 - 2.00000i) q^{28} +(1.12132 - 2.70711i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -0.585786 q^{33} -4.00000 q^{34} +(0.585786 + 0.585786i) q^{36} +(-1.70711 + 0.707107i) q^{37} +(-3.24264 + 7.82843i) q^{38} +(2.41421 - 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(-3.41421 + 1.41421i) q^{42} +(-3.29289 - 7.94975i) q^{43} +(-0.242641 - 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569i q^{47} +(-2.82843 + 6.82843i) q^{48} +5.00000i q^{49} +(4.82843 + 2.00000i) q^{51} +(3.41421 + 1.41421i) q^{52} +(-3.12132 - 7.53553i) q^{53} +(2.58579 + 6.24264i) q^{54} +(-2.82843 - 2.82843i) q^{56} +(7.82843 - 7.82843i) q^{57} +(-3.82843 - 1.58579i) q^{58} +(-6.12132 + 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685i q^{62} +0.585786 q^{63} -8.00000 q^{64} +0.828427i q^{66} +(-1.53553 + 3.70711i) q^{67} +5.65685i q^{68} +(0.414214 - 0.171573i) q^{69} +(-0.171573 + 0.171573i) q^{71} +(0.828427 - 0.828427i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(1.00000 + 2.41421i) q^{74} +(11.0711 + 4.58579i) q^{76} +(-0.414214 - 0.171573i) q^{77} +(-3.41421 - 3.41421i) q^{78} +6.00000i q^{79} -10.0711i q^{81} +(-8.24264 + 8.24264i) q^{82} +(-6.12132 - 2.53553i) q^{83} +(2.00000 + 4.82843i) q^{84} +(-11.2426 + 4.65685i) q^{86} +(3.82843 + 3.82843i) q^{87} +(-0.828427 + 0.343146i) q^{88} +(-2.65685 + 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 + 0.343146i) q^{92} +(2.82843 - 6.82843i) q^{93} +16.4853 q^{94} +(9.65685 + 4.00000i) q^{96} +1.51472 q^{97} +7.07107 q^{98} +(0.0502525 - 0.121320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q - 8 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{9} - 8 q^{11} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 8 q^{19} - 4 q^{21} - 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{26} - 12 q^{27} + 8 q^{28} - 4 q^{29} - 16 q^{31} - 8 q^{33} - 16 q^{34} + 8 q^{36} - 4 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} - 8 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{46} + 8 q^{51} + 8 q^{52} - 4 q^{53} + 16 q^{54} + 20 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{61} + 8 q^{63} - 32 q^{64} + 8 q^{67} - 4 q^{69} - 12 q^{71} - 8 q^{72} - 28 q^{73} + 4 q^{74} + 16 q^{76} + 4 q^{77} - 8 q^{78} - 16 q^{82} - 16 q^{83} + 8 q^{84} - 28 q^{86} + 4 q^{87} + 8 q^{88} + 12 q^{89} + 4 q^{91} + 24 q^{92} + 32 q^{94} + 16 q^{96} + 40 q^{97} + 20 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(577\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) −0.707107 + 1.70711i −0.408248 + 0.985599i 0.577350 + 0.816497i \(0.304087\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) 2.41421 + 1.00000i 0.985599 + 0.408248i
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 2.82843i 1.00000i
\(9\) −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 \(0.859781\pi\)
\(12\) 1.41421 3.41421i 0.408248 0.985599i
\(13\) −1.70711 0.707107i −0.473466 0.196116i 0.133174 0.991093i \(-0.457483\pi\)
−0.606640 + 0.794977i \(0.707483\pi\)
\(14\) 1.41421 + 1.41421i 0.377964 + 0.377964i
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) −0.414214 + 0.414214i −0.0976311 + 0.0976311i
\(19\) −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
\(22\) 0.414214 0.171573i 0.0883106 0.0365795i
\(23\) −0.171573 0.171573i −0.0357754 0.0357754i 0.688993 0.724768i \(-0.258053\pi\)
−0.724768 + 0.688993i \(0.758053\pi\)
\(24\) −4.82843 2.00000i −0.985599 0.408248i
\(25\) 0 0
\(26\) −1.00000 + 2.41421i −0.196116 + 0.473466i
\(27\) −4.41421 + 1.82843i −0.849516 + 0.351881i
\(28\) 2.00000 2.00000i 0.377964 0.377964i
\(29\) 1.12132 2.70711i 0.208224 0.502697i −0.784920 0.619598i \(-0.787296\pi\)
0.993144 + 0.116900i \(0.0372958\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 5.65685i 1.00000i
\(33\) −0.585786 −0.101972
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 0.585786 + 0.585786i 0.0976311 + 0.0976311i
\(37\) −1.70711 + 0.707107i −0.280647 + 0.116248i −0.518567 0.855037i \(-0.673534\pi\)
0.237920 + 0.971285i \(0.423534\pi\)
\(38\) −3.24264 + 7.82843i −0.526026 + 1.26994i
\(39\) 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 \(0.972577\pi\)
\(42\) −3.41421 + 1.41421i −0.526825 + 0.218218i
\(43\) −3.29289 7.94975i −0.502162 1.21233i −0.948304 0.317363i \(-0.897203\pi\)
0.446143 0.894962i \(-0.352797\pi\)
\(44\) −0.242641 0.585786i −0.0365795 0.0883106i
\(45\) 0 0
\(46\) −0.242641 + 0.242641i −0.0357754 + 0.0357754i
\(47\) 11.6569i 1.70033i 0.526519 + 0.850163i \(0.323497\pi\)
−0.526519 + 0.850163i \(0.676503\pi\)
\(48\) −2.82843 + 6.82843i −0.408248 + 0.985599i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 4.82843 + 2.00000i 0.676115 + 0.280056i
\(52\) 3.41421 + 1.41421i 0.473466 + 0.196116i
\(53\) −3.12132 7.53553i −0.428746 1.03509i −0.979686 0.200540i \(-0.935730\pi\)
0.550939 0.834545i \(-0.314270\pi\)
\(54\) 2.58579 + 6.24264i 0.351881 + 0.849516i
\(55\) 0 0
\(56\) −2.82843 2.82843i −0.377964 0.377964i
\(57\) 7.82843 7.82843i 1.03690 1.03690i
\(58\) −3.82843 1.58579i −0.502697 0.208224i
\(59\) −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 −0.904019 0.427492i \(-0.859397\pi\)
0.941520 + 0.336956i \(0.109397\pi\)
\(62\) 5.65685i 0.718421i
\(63\) 0.585786 0.0738022
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0.828427i 0.101972i
\(67\) −1.53553 + 3.70711i −0.187595 + 0.452895i −0.989496 0.144563i \(-0.953822\pi\)
0.801900 + 0.597458i \(0.203822\pi\)
\(68\) 5.65685i 0.685994i
\(69\) 0.414214 0.171573i 0.0498655 0.0206549i
\(70\) 0 0
\(71\) −0.171573 + 0.171573i −0.0203620 + 0.0203620i −0.717214 0.696853i \(-0.754583\pi\)
0.696853 + 0.717214i \(0.254583\pi\)
\(72\) 0.828427 0.828427i 0.0976311 0.0976311i
\(73\) −7.00000 7.00000i −0.819288 0.819288i 0.166717 0.986005i \(-0.446683\pi\)
−0.986005 + 0.166717i \(0.946683\pi\)
\(74\) 1.00000 + 2.41421i 0.116248 + 0.280647i
\(75\) 0 0
\(76\) 11.0711 + 4.58579i 1.26994 + 0.526026i
\(77\) −0.414214 0.171573i −0.0472040 0.0195525i
\(78\) −3.41421 3.41421i −0.386584 0.386584i
\(79\) 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
\(82\) −8.24264 + 8.24264i −0.910247 + 0.910247i
\(83\) −6.12132 2.53553i −0.671902 0.278311i 0.0205350 0.999789i \(-0.493463\pi\)
−0.692437 + 0.721478i \(0.743463\pi\)
\(84\) 2.00000 + 4.82843i 0.218218 + 0.526825i
\(85\) 0 0
\(86\) −11.2426 + 4.65685i −1.21233 + 0.502162i
\(87\) 3.82843 + 3.82843i 0.410450 + 0.410450i
\(88\) −0.828427 + 0.343146i −0.0883106 + 0.0365795i
\(89\) −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
\(92\) 0.343146 + 0.343146i 0.0357754 + 0.0357754i
\(93\) 2.82843 6.82843i 0.293294 0.708075i
\(94\) 16.4853 1.70033
\(95\) 0 0
\(96\) 9.65685 + 4.00000i 0.985599 + 0.408248i
\(97\) 1.51472 0.153796 0.0768982 0.997039i \(-0.475498\pi\)
0.0768982 + 0.997039i \(0.475498\pi\)
\(98\) 7.07107 0.714286
\(99\) 0.0502525 0.121320i 0.00505057 0.0121932i
\(100\) 0 0
\(101\) 11.3640 4.70711i 1.13076 0.468375i 0.262718 0.964873i \(-0.415381\pi\)
0.868038 + 0.496498i \(0.165381\pi\)
\(102\) 2.82843 6.82843i 0.280056 0.676115i
\(103\) 7.48528 7.48528i 0.737547 0.737547i −0.234556 0.972103i \(-0.575364\pi\)
0.972103 + 0.234556i \(0.0753636\pi\)
\(104\) 2.00000 4.82843i 0.196116 0.473466i
\(105\) 0 0
\(106\) −10.6569 + 4.41421i −1.03509 + 0.428746i
\(107\) −0.121320 0.292893i −0.0117285 0.0283151i 0.917907 0.396796i \(-0.129878\pi\)
−0.929635 + 0.368481i \(0.879878\pi\)
\(108\) 8.82843 3.65685i 0.849516 0.351881i
\(109\) −4.29289 1.77817i −0.411185 0.170318i 0.167496 0.985873i \(-0.446432\pi\)
−0.578680 + 0.815555i \(0.696432\pi\)
\(110\) 0 0
\(111\) 3.41421i 0.324063i
\(112\) −4.00000 + 4.00000i −0.377964 + 0.377964i
\(113\) 17.6569i 1.66102i 0.557006 + 0.830509i \(0.311950\pi\)
−0.557006 + 0.830509i \(0.688050\pi\)
\(114\) −11.0711 11.0711i −1.03690 1.03690i
\(115\) 0 0
\(116\) −2.24264 + 5.41421i −0.208224 + 0.502697i
\(117\) 0.292893 + 0.707107i 0.0270780 + 0.0653720i
\(118\) 3.58579 + 8.65685i 0.330098 + 0.796928i
\(119\) 2.82843 + 2.82843i 0.259281 + 0.259281i
\(120\) 0 0
\(121\) 7.70711 7.70711i 0.700646 0.700646i
\(122\) −1.00000 0.414214i −0.0905357 0.0375011i
\(123\) 14.0711 5.82843i 1.26875 0.525532i
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 0.828427i 0.0738022i
\(127\) 20.9706 1.86084 0.930418 0.366499i \(-0.119444\pi\)
0.930418 + 0.366499i \(0.119444\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 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 \(0.988756\pi\)
\(132\) 1.17157 0.101972
\(133\) 7.82843 3.24264i 0.678811 0.281173i
\(134\) 5.24264 + 2.17157i 0.452895 + 0.187595i
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) −2.65685 2.65685i −0.226990 0.226990i 0.584444 0.811434i \(-0.301313\pi\)
−0.811434 + 0.584444i \(0.801313\pi\)
\(138\) −0.242641 0.585786i −0.0206549 0.0498655i
\(139\) −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
\(142\) 0.242641 + 0.242641i 0.0203620 + 0.0203620i
\(143\) 0.585786i 0.0489859i
\(144\) −1.17157 1.17157i −0.0976311 0.0976311i
\(145\) 0 0
\(146\) −9.89949 + 9.89949i −0.819288 + 0.819288i
\(147\) −8.53553 3.53553i −0.703999 0.291606i
\(148\) 3.41421 1.41421i 0.280647 0.116248i
\(149\) 5.60660 + 13.5355i 0.459311 + 1.10887i 0.968677 + 0.248324i \(0.0798799\pi\)
−0.509366 + 0.860550i \(0.670120\pi\)
\(150\) 0 0
\(151\) 15.4853 + 15.4853i 1.26017 + 1.26017i 0.951008 + 0.309166i \(0.100050\pi\)
0.309166 + 0.951008i \(0.399950\pi\)
\(152\) 6.48528 15.6569i 0.526026 1.26994i
\(153\) −0.828427 + 0.828427i −0.0669744 + 0.0669744i
\(154\) −0.242641 + 0.585786i −0.0195525 + 0.0472040i
\(155\) 0 0
\(156\) −4.82843 + 4.82843i −0.386584 + 0.386584i
\(157\) −0.292893 + 0.707107i −0.0233754 + 0.0564333i −0.935136 0.354288i \(-0.884723\pi\)
0.911761 + 0.410722i \(0.134723\pi\)
\(158\) 8.48528 0.675053
\(159\) 15.0711 1.19521
\(160\) 0 0
\(161\) 0.343146 0.0270437
\(162\) −14.2426 −1.11901
\(163\) −7.53553 + 18.1924i −0.590229 + 1.42494i 0.293054 + 0.956096i \(0.405329\pi\)
−0.883282 + 0.468842i \(0.844671\pi\)
\(164\) 11.6569 + 11.6569i 0.910247 + 0.910247i
\(165\) 0 0
\(166\) −3.58579 + 8.65685i −0.278311 + 0.671902i
\(167\) −3.34315 + 3.34315i −0.258700 + 0.258700i −0.824525 0.565825i \(-0.808558\pi\)
0.565825 + 0.824525i \(0.308558\pi\)
\(168\) 6.82843 2.82843i 0.526825 0.218218i
\(169\) −6.77817 6.77817i −0.521398 0.521398i
\(170\) 0 0
\(171\) 0.949747 + 2.29289i 0.0726290 + 0.175342i
\(172\) 6.58579 + 15.8995i 0.502162 + 1.21233i
\(173\) 1.12132 + 0.464466i 0.0852524 + 0.0353127i 0.424902 0.905239i \(-0.360309\pi\)
−0.339650 + 0.940552i \(0.610309\pi\)
\(174\) 5.41421 5.41421i 0.410450 0.410450i
\(175\) 0 0
\(176\) 0.485281 + 1.17157i 0.0365795 + 0.0883106i
\(177\) 12.2426i 0.920213i
\(178\) 3.75736 + 3.75736i 0.281626 + 0.281626i
\(179\) −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 0.821216 0.570618i \(-0.193296\pi\)
−0.984175 + 0.177200i \(0.943296\pi\)
\(182\) −1.41421 3.41421i −0.104828 0.253078i
\(183\) 1.00000 + 1.00000i 0.0739221 + 0.0739221i
\(184\) 0.485281 0.485281i 0.0357754 0.0357754i
\(185\) 0 0
\(186\) −9.65685 4.00000i −0.708075 0.293294i
\(187\) 0.828427 0.343146i 0.0605806 0.0250933i
\(188\) 23.3137i 1.70033i
\(189\) 2.58579 6.24264i 0.188088 0.454085i
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 5.65685 13.6569i 0.408248 0.985599i
\(193\) 18.4853 1.33060 0.665300 0.746576i \(-0.268304\pi\)
0.665300 + 0.746576i \(0.268304\pi\)
\(194\) 2.14214i 0.153796i
\(195\) 0 0
\(196\) 10.0000i 0.714286i
\(197\) −17.3640 + 7.19239i −1.23713 + 0.512436i −0.902817 0.430025i \(-0.858505\pi\)
−0.334314 + 0.942462i \(0.608505\pi\)
\(198\) −0.171573 0.0710678i −0.0121932 0.00505057i
\(199\) 17.9706 17.9706i 1.27390 1.27390i 0.329875 0.944025i \(-0.392994\pi\)
0.944025 0.329875i \(-0.107006\pi\)
\(200\) 0 0
\(201\) −5.24264 5.24264i −0.369787 0.369787i
\(202\) −6.65685 16.0711i −0.468375 1.13076i
\(203\) 1.58579 + 3.82843i 0.111300 + 0.268703i
\(204\) −9.65685 4.00000i −0.676115 0.280056i
\(205\) 0 0
\(206\) −10.5858 10.5858i −0.737547 0.737547i
\(207\) 0.100505i 0.00698558i
\(208\) −6.82843 2.82843i −0.473466 0.196116i
\(209\) 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 \(0.619491\pi\)
\(212\) 6.24264 + 15.0711i 0.428746 + 1.03509i
\(213\) −0.171573 0.414214i −0.0117560 0.0283814i
\(214\) −0.414214 + 0.171573i −0.0283151 + 0.0117285i
\(215\) 0 0
\(216\) −5.17157 12.4853i −0.351881 0.849516i
\(217\) 4.00000 4.00000i 0.271538 0.271538i
\(218\) −2.51472 + 6.07107i −0.170318 + 0.411185i
\(219\) 16.8995 7.00000i 1.14196 0.473016i
\(220\) 0 0
\(221\) −2.00000 + 4.82843i −0.134535 + 0.324795i
\(222\) −4.82843 −0.324063
\(223\) −12.9706 −0.868573 −0.434287 0.900775i \(-0.642999\pi\)
−0.434287 + 0.900775i \(0.642999\pi\)
\(224\) 5.65685 + 5.65685i 0.377964 + 0.377964i
\(225\) 0 0
\(226\) 24.9706 1.66102
\(227\) 2.60660 6.29289i 0.173006 0.417674i −0.813464 0.581616i \(-0.802421\pi\)
0.986470 + 0.163942i \(0.0524208\pi\)
\(228\) −15.6569 + 15.6569i −1.03690 + 1.03690i
\(229\) −24.7782 + 10.2635i −1.63739 + 0.678228i −0.996030 0.0890139i \(-0.971628\pi\)
−0.641357 + 0.767242i \(0.721628\pi\)
\(230\) 0 0
\(231\) 0.585786 0.585786i 0.0385419 0.0385419i
\(232\) 7.65685 + 3.17157i 0.502697 + 0.208224i
\(233\) −8.65685 8.65685i −0.567129 0.567129i 0.364194 0.931323i \(-0.381345\pi\)
−0.931323 + 0.364194i \(0.881345\pi\)
\(234\) 1.00000 0.414214i 0.0653720 0.0270780i
\(235\) 0 0
\(236\) 12.2426 5.07107i 0.796928 0.330098i
\(237\) −10.2426 4.24264i −0.665331 0.275589i
\(238\) 4.00000 4.00000i 0.259281 0.259281i
\(239\) 17.3137i 1.11993i 0.828516 + 0.559965i \(0.189186\pi\)
−0.828516 + 0.559965i \(0.810814\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) −10.8995 10.8995i −0.700646 0.700646i
\(243\) 3.94975 + 1.63604i 0.253376 + 0.104952i
\(244\) −0.585786 + 1.41421i −0.0375011 + 0.0905357i
\(245\) 0 0
\(246\) −8.24264 19.8995i −0.525532 1.26875i
\(247\) 7.82843 + 7.82843i 0.498111 + 0.498111i
\(248\) 11.3137i 0.718421i
\(249\) 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 \(0.541285\pi\)
\(252\) −1.17157 −0.0738022
\(253\) 0.0294373 0.0710678i 0.00185070 0.00446800i
\(254\) 29.6569i 1.86084i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 22.4853i 1.39987i
\(259\) 1.00000 2.41421i 0.0621370 0.150012i
\(260\) 0 0
\(261\) −1.12132 + 0.464466i −0.0694080 + 0.0287497i
\(262\) 12.4142 + 5.14214i 0.766953 + 0.317682i
\(263\) 0.171573 0.171573i 0.0105796 0.0105796i −0.701797 0.712377i \(-0.747619\pi\)
0.712377 + 0.701797i \(0.247619\pi\)
\(264\) 1.65685i 0.101972i
\(265\) 0 0
\(266\) −4.58579 11.0711i −0.281173 0.678811i
\(267\) −2.65685 6.41421i −0.162597 0.392543i
\(268\) 3.07107 7.41421i 0.187595 0.452895i
\(269\) 4.87868 + 2.02082i 0.297458 + 0.123211i 0.526421 0.850224i \(-0.323533\pi\)
−0.228963 + 0.973435i \(0.573533\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i 0.837321 + 0.546711i \(0.184120\pi\)
−0.837321 + 0.546711i \(0.815880\pi\)
\(272\) 11.3137i 0.685994i
\(273\) 4.82843i 0.292230i
\(274\) −3.75736 + 3.75736i −0.226990 + 0.226990i
\(275\) 0 0
\(276\) −0.828427 + 0.343146i −0.0498655 + 0.0206549i
\(277\) −0.292893 0.707107i −0.0175982 0.0424859i 0.914836 0.403825i \(-0.132320\pi\)
−0.932434 + 0.361339i \(0.882320\pi\)
\(278\) −17.7279 + 7.34315i −1.06325 + 0.440413i
\(279\) 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 \(0.333832\pi\)
\(282\) −11.6569 + 28.1421i −0.694156 + 1.67584i
\(283\) 9.77817 4.05025i 0.581252 0.240763i −0.0726300 0.997359i \(-0.523139\pi\)
0.653882 + 0.756596i \(0.273139\pi\)
\(284\) 0.343146 0.343146i 0.0203620 0.0203620i
\(285\) 0 0
\(286\) −0.828427 −0.0489859
\(287\) 11.6569 0.688082
\(288\) −1.65685 + 1.65685i −0.0976311 + 0.0976311i
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) −1.07107 + 2.58579i −0.0627871 + 0.151581i
\(292\) 14.0000 + 14.0000i 0.819288 + 0.819288i
\(293\) 11.6066 4.80761i 0.678065 0.280864i −0.0169528 0.999856i \(-0.505397\pi\)
0.695018 + 0.718993i \(0.255397\pi\)
\(294\) −5.00000 + 12.0711i −0.291606 + 0.703999i
\(295\) 0 0
\(296\) −2.00000 4.82843i −0.116248 0.280647i
\(297\) −1.07107 1.07107i −0.0621497 0.0621497i
\(298\) 19.1421 7.92893i 1.10887 0.459311i
\(299\) 0.171573 + 0.414214i 0.00992232 + 0.0239546i
\(300\) 0 0
\(301\) 11.2426 + 4.65685i 0.648015 + 0.268417i
\(302\) 21.8995 21.8995i 1.26017 1.26017i
\(303\) 22.7279i 1.30569i
\(304\) −22.1421 9.17157i −1.26994 0.526026i
\(305\) 0 0
\(306\) 1.17157 + 1.17157i 0.0669744 + 0.0669744i
\(307\) −2.94975 1.22183i −0.168351 0.0697333i 0.296916 0.954904i \(-0.404042\pi\)
−0.465267 + 0.885170i \(0.654042\pi\)
\(308\) 0.828427 + 0.343146i 0.0472040 + 0.0195525i
\(309\) 7.48528 + 18.0711i 0.425823 + 1.02803i
\(310\) 0 0
\(311\) 8.65685 + 8.65685i 0.490885 + 0.490885i 0.908585 0.417700i \(-0.137164\pi\)
−0.417700 + 0.908585i \(0.637164\pi\)
\(312\) 6.82843 + 6.82843i 0.386584 + 0.386584i
\(313\) −9.48528 + 9.48528i −0.536140 + 0.536140i −0.922393 0.386253i \(-0.873769\pi\)
0.386253 + 0.922393i \(0.373769\pi\)
\(314\) 1.00000 + 0.414214i 0.0564333 + 0.0233754i
\(315\) 0 0
\(316\) 12.0000i 0.675053i
\(317\) −4.63604 + 11.1924i −0.260386 + 0.628627i −0.998962 0.0455425i \(-0.985498\pi\)
0.738577 + 0.674170i \(0.235498\pi\)
\(318\) 21.3137i 1.19521i
\(319\) 0.928932 0.0520102
\(320\) 0 0
\(321\) 0.585786 0.0326954
\(322\) 0.485281i 0.0270437i
\(323\) −6.48528 + 15.6569i −0.360851 + 0.871171i
\(324\) 20.1421i 1.11901i
\(325\) 0 0
\(326\) 25.7279 + 10.6569i 1.42494 + 0.590229i
\(327\) 6.07107 6.07107i 0.335731 0.335731i
\(328\) 16.4853 16.4853i 0.910247 0.910247i
\(329\) −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 \(0.937280\pi\)
\(332\) 12.2426 + 5.07107i 0.671902 + 0.278311i
\(333\) 0.707107 + 0.292893i 0.0387492 + 0.0160504i
\(334\) 4.72792 + 4.72792i 0.258700 + 0.258700i
\(335\) 0 0
\(336\) −4.00000 9.65685i −0.218218 0.526825i
\(337\) 16.9706i 0.924445i −0.886764 0.462223i \(-0.847052\pi\)
0.886764 0.462223i \(-0.152948\pi\)
\(338\) −9.58579 + 9.58579i −0.521398 + 0.521398i
\(339\) −30.1421 12.4853i −1.63710 0.678107i
\(340\) 0 0
\(341\) −0.485281 1.17157i −0.0262795 0.0634442i
\(342\) 3.24264 1.34315i 0.175342 0.0726290i
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 22.4853 9.31371i 1.21233 0.502162i
\(345\) 0 0
\(346\) 0.656854 1.58579i 0.0353127 0.0852524i
\(347\) −14.3640 + 5.94975i −0.771098 + 0.319399i −0.733317 0.679887i \(-0.762029\pi\)
−0.0377808 + 0.999286i \(0.512029\pi\)
\(348\) −7.65685 7.65685i −0.410450 0.410450i
\(349\) −10.6777 + 25.7782i −0.571563 + 1.37987i 0.328662 + 0.944448i \(0.393402\pi\)
−0.900224 + 0.435426i \(0.856598\pi\)
\(350\) 0 0
\(351\) 8.82843 0.471227
\(352\) 1.65685 0.686292i 0.0883106 0.0365795i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −17.3137 −0.920213
\(355\) 0 0
\(356\) 5.31371 5.31371i 0.281626 0.281626i
\(357\) −6.82843 + 2.82843i −0.361399 + 0.149696i
\(358\) −8.41421 + 20.3137i −0.444705 + 1.07361i
\(359\) −12.1716 + 12.1716i −0.642391 + 0.642391i −0.951143 0.308752i \(-0.900089\pi\)
0.308752 + 0.951143i \(0.400089\pi\)
\(360\) 0 0
\(361\) 11.9497 + 11.9497i 0.628934 + 0.628934i
\(362\) −7.48528 + 3.10051i −0.393418 + 0.162959i
\(363\) 7.70711 + 18.6066i 0.404518 + 0.976593i
\(364\) −4.82843 + 2.00000i −0.253078 + 0.104828i
\(365\) 0 0
\(366\) 1.41421 1.41421i 0.0739221 0.0739221i
\(367\) 6.00000i 0.313197i 0.987662 + 0.156599i \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) −0.686292 0.686292i −0.0357754 0.0357754i
\(369\) 3.41421i 0.177737i
\(370\) 0 0
\(371\) 10.6569 + 4.41421i 0.553276 + 0.229175i
\(372\) −5.65685 + 13.6569i −0.293294 + 0.708075i
\(373\) 11.7071 + 28.2635i 0.606171 + 1.46343i 0.867133 + 0.498077i \(0.165960\pi\)
−0.260962 + 0.965349i \(0.584040\pi\)
\(374\) −0.485281 1.17157i −0.0250933 0.0605806i
\(375\) 0 0
\(376\) −32.9706 −1.70033
\(377\) −3.82843 + 3.82843i −0.197174 + 0.197174i
\(378\) −8.82843 3.65685i −0.454085 0.188088i
\(379\) 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
\(382\) 16.9706i 0.868290i
\(383\) −16.9706 −0.867155 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(384\) −19.3137 8.00000i −0.985599 0.408248i
\(385\) 0 0
\(386\) 26.1421i 1.33060i
\(387\) −1.36396 + 3.29289i −0.0693340 + 0.167387i
\(388\) −3.02944 −0.153796
\(389\) −29.6066 + 12.2635i −1.50111 + 0.621782i −0.973702 0.227827i \(-0.926838\pi\)
−0.527413 + 0.849609i \(0.676838\pi\)
\(390\) 0 0
\(391\) −0.485281 + 0.485281i −0.0245417 + 0.0245417i
\(392\) −14.1421 −0.714286
\(393\) −12.4142 12.4142i −0.626214 0.626214i
\(394\) 10.1716 + 24.5563i 0.512436 + 1.23713i
\(395\) 0 0
\(396\) −0.100505 + 0.242641i −0.00505057 + 0.0121932i
\(397\) 24.7782 + 10.2635i 1.24358 + 0.515108i 0.904832 0.425769i \(-0.139996\pi\)
0.338749 + 0.940877i \(0.389996\pi\)
\(398\) −25.4142 25.4142i −1.27390 1.27390i
\(399\) 15.6569i 0.783823i
\(400\) 0 0
\(401\) 2.82843i 0.141245i 0.997503 + 0.0706225i \(0.0224986\pi\)
−0.997503 + 0.0706225i \(0.977501\pi\)
\(402\) −7.41421 + 7.41421i −0.369787 + 0.369787i
\(403\) 6.82843 + 2.82843i 0.340148 + 0.140894i
\(404\) −22.7279 + 9.41421i −1.13076 + 0.468375i
\(405\) 0 0
\(406\) 5.41421 2.24264i 0.268703 0.111300i
\(407\) −0.414214 0.414214i −0.0205318 0.0205318i
\(408\) −5.65685 + 13.6569i −0.280056 + 0.676115i
\(409\) 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
\(412\) −14.9706 + 14.9706i −0.737547 + 0.737547i
\(413\) 3.58579 8.65685i 0.176445 0.425976i
\(414\) 0.142136 0.00698558
\(415\) 0 0
\(416\) −4.00000 + 9.65685i −0.196116 + 0.473466i
\(417\) 25.0711 1.22774
\(418\) −2.68629 −0.131391
\(419\) −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 −0.186882 0.982382i \(-0.559838\pi\)
0.562504 + 0.826795i \(0.309838\pi\)
\(422\) 0.272078 0.656854i 0.0132445 0.0319752i
\(423\) 3.41421 3.41421i 0.166005 0.166005i
\(424\) 21.3137 8.82843i 1.03509 0.428746i
\(425\) 0 0
\(426\) −0.585786 + 0.242641i −0.0283814 + 0.0117560i
\(427\) 0.414214 + 1.00000i 0.0200452 + 0.0483934i
\(428\) 0.242641 + 0.585786i 0.0117285 + 0.0283151i
\(429\) 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 \(-0.192962\pi\)
\(432\) −17.6569 + 7.31371i −0.849516 + 0.351881i
\(433\) 32.4853i 1.56114i 0.625067 + 0.780571i \(0.285072\pi\)
−0.625067 + 0.780571i \(0.714928\pi\)
\(434\) −5.65685 5.65685i −0.271538 0.271538i
\(435\) 0 0
\(436\) 8.58579 + 3.55635i 0.411185 + 0.170318i
\(437\) 0.556349 + 1.34315i 0.0266138 + 0.0642514i
\(438\) −9.89949 23.8995i −0.473016 1.14196i
\(439\) −17.0000 17.0000i −0.811366 0.811366i 0.173473 0.984839i \(-0.444501\pi\)
−0.984839 + 0.173473i \(0.944501\pi\)
\(440\) 0 0
\(441\) 1.46447 1.46447i 0.0697365 0.0697365i
\(442\) 6.82843 + 2.82843i 0.324795 + 0.134535i
\(443\) 20.6066 8.53553i 0.979049 0.405535i 0.164976 0.986298i \(-0.447245\pi\)
0.814073 + 0.580762i \(0.197245\pi\)
\(444\) 6.82843i 0.324063i
\(445\) 0 0
\(446\) 18.3431i 0.868573i
\(447\) −27.0711 −1.28042
\(448\) 8.00000 8.00000i 0.377964 0.377964i
\(449\) 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
\(452\) 35.3137i 1.66102i
\(453\) −37.3848 + 15.4853i −1.75649 + 0.727562i
\(454\) −8.89949 3.68629i −0.417674 0.173006i
\(455\) 0 0
\(456\) 22.1421 + 22.1421i 1.03690 + 1.03690i
\(457\) −9.48528 9.48528i −0.443703 0.443703i 0.449552 0.893254i \(-0.351584\pi\)
−0.893254 + 0.449552i \(0.851584\pi\)
\(458\) 14.5147 + 35.0416i 0.678228 + 1.63739i
\(459\) 5.17157 + 12.4853i 0.241388 + 0.582763i
\(460\) 0 0
\(461\) 13.3640 + 5.53553i 0.622422 + 0.257816i 0.671529 0.740978i \(-0.265638\pi\)
−0.0491076 + 0.998793i \(0.515638\pi\)
\(462\) −0.828427 0.828427i −0.0385419 0.0385419i
\(463\) 10.9706i 0.509845i 0.966961 + 0.254923i \(0.0820500\pi\)
−0.966961 + 0.254923i \(0.917950\pi\)
\(464\) 4.48528 10.8284i 0.208224 0.502697i
\(465\) 0 0
\(466\) −12.2426 + 12.2426i −0.567129 + 0.567129i
\(467\) −29.0919 12.0503i −1.34621 0.557619i −0.410977 0.911646i \(-0.634812\pi\)
−0.935235 + 0.354027i \(0.884812\pi\)
\(468\) −0.585786 1.41421i −0.0270780 0.0653720i
\(469\) −2.17157 5.24264i −0.100274 0.242083i
\(470\) 0 0
\(471\) −1.00000 1.00000i −0.0460776 0.0460776i
\(472\) −7.17157 17.3137i −0.330098 0.796928i
\(473\) 1.92893 1.92893i 0.0886924 0.0886924i
\(474\) −6.00000 + 14.4853i −0.275589 + 0.665331i
\(475\) 0 0
\(476\) −5.65685 5.65685i −0.259281 0.259281i
\(477\) −1.29289 + 3.12132i −0.0591975 + 0.142915i
\(478\) 24.4853 1.11993
\(479\) −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
\(482\) 12.0000 0.546585
\(483\) −0.242641 + 0.585786i −0.0110405 + 0.0266542i
\(484\) −15.4142 + 15.4142i −0.700646 + 0.700646i
\(485\) 0 0
\(486\) 2.31371 5.58579i 0.104952 0.253376i
\(487\) 11.0000 11.0000i 0.498458 0.498458i −0.412500 0.910958i \(-0.635344\pi\)
0.910958 + 0.412500i \(0.135344\pi\)
\(488\) 2.00000 + 0.828427i 0.0905357 + 0.0375011i
\(489\) −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 \(-0.267360\pi\)
\(492\) −28.1421 + 11.6569i −1.26875 + 0.525532i
\(493\) −7.65685 3.17157i −0.344847 0.142840i
\(494\) 11.0711 11.0711i 0.498111 0.498111i
\(495\) 0 0
\(496\) −16.0000 −0.718421
\(497\) 0.343146i 0.0153922i
\(498\) −12.2426 12.2426i −0.548606 0.548606i
\(499\) 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
\(502\) 8.55635 + 20.6569i 0.381889 + 0.921961i
\(503\) −17.1421 17.1421i −0.764330 0.764330i 0.212772 0.977102i \(-0.431751\pi\)
−0.977102 + 0.212772i \(0.931751\pi\)
\(504\) 1.65685i 0.0738022i
\(505\) 0 0
\(506\) −0.100505 0.0416306i −0.00446800 0.00185070i
\(507\) 16.3640 6.77817i 0.726749 0.301029i
\(508\) −41.9411 −1.86084
\(509\) 12.0919 29.1924i 0.535963 1.29393i −0.391556 0.920154i \(-0.628063\pi\)
0.927519 0.373776i \(-0.121937\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 22.6274i 1.00000i
\(513\) 28.6274 1.26393
\(514\) 8.48528i 0.374270i
\(515\) 0 0
\(516\) −31.7990 −1.39987
\(517\) −3.41421 + 1.41421i −0.150157 + 0.0621970i
\(518\) −3.41421 1.41421i −0.150012 0.0621370i
\(519\) −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 \(0.599978\pi\)
\(522\) 0.656854 + 1.58579i 0.0287497 + 0.0694080i
\(523\) −0.807612 1.94975i −0.0353144 0.0852565i 0.905238 0.424904i \(-0.139692\pi\)
−0.940553 + 0.339648i \(0.889692\pi\)
\(524\) 7.27208 17.5563i 0.317682 0.766953i
\(525\) 0 0
\(526\) −0.242641 0.242641i −0.0105796 0.0105796i
\(527\) 11.3137i 0.492833i
\(528\) −2.34315 −0.101972
\(529\) 22.9411i 0.997440i
\(530\) 0 0
\(531\) 2.53553 + 1.05025i 0.110033 + 0.0455771i
\(532\) −15.6569 + 6.48528i −0.678811 + 0.281173i
\(533\) 5.82843 + 14.0711i 0.252457 + 0.609486i
\(534\) −9.07107 + 3.75736i −0.392543 + 0.162597i
\(535\) 0 0
\(536\) −10.4853 4.34315i −0.452895 0.187595i
\(537\) 20.3137 20.3137i 0.876601 0.876601i
\(538\) 2.85786 6.89949i 0.123211 0.297458i
\(539\) −1.46447 + 0.606602i −0.0630790 + 0.0261282i
\(540\) 0 0
\(541\) 5.26346 12.7071i 0.226294 0.546321i −0.769427 0.638735i \(-0.779458\pi\)
0.995721 + 0.0924135i \(0.0294582\pi\)
\(542\) 25.4558 1.09342
\(543\) 10.5858 0.454280
\(544\) −16.0000 −0.685994
\(545\) 0 0
\(546\) 6.82843 0.292230
\(547\) 10.4645 25.2635i 0.447428 1.08019i −0.525854 0.850575i \(-0.676254\pi\)
0.973282 0.229612i \(-0.0737459\pi\)
\(548\) 5.31371 + 5.31371i 0.226990 + 0.226990i
\(549\) −0.292893 + 0.121320i −0.0125004 + 0.00517783i
\(550\) 0 0
\(551\) −12.4142 + 12.4142i −0.528863 + 0.528863i
\(552\) 0.485281 + 1.17157i 0.0206549 + 0.0498655i
\(553\) −6.00000 6.00000i −0.255146 0.255146i
\(554\) −1.00000 + 0.414214i −0.0424859 + 0.0175982i
\(555\) 0 0
\(556\) 10.3848 + 25.0711i 0.440413 + 1.06325i
\(557\) −10.8787 4.50610i −0.460944 0.190929i 0.140113 0.990136i \(-0.455254\pi\)
−0.601057 + 0.799206i \(0.705254\pi\)
\(558\) 1.65685 1.65685i 0.0701402 0.0701402i
\(559\) 15.8995i 0.672477i
\(560\) 0 0
\(561\) 1.65685i 0.0699524i
\(562\) 8.72792 + 8.72792i 0.368165 + 0.368165i
\(563\) −12.1213 5.02082i −0.510853 0.211602i 0.112341 0.993670i \(-0.464165\pi\)
−0.623194 + 0.782068i \(0.714165\pi\)
\(564\) 39.7990 + 16.4853i 1.67584 + 0.694156i
\(565\) 0 0
\(566\) −5.72792 13.8284i −0.240763 0.581252i
\(567\) 10.0711 + 10.0711i 0.422945 + 0.422945i
\(568\) −0.485281 0.485281i −0.0203620 0.0203620i
\(569\) 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 \(0.384322\pi\)
\(572\) 1.17157i 0.0489859i
\(573\) 8.48528 20.4853i 0.354478 0.855785i
\(574\) 16.4853i 0.688082i
\(575\) 0 0
\(576\) 2.34315 + 2.34315i 0.0976311 + 0.0976311i
\(577\) 14.9706 0.623233 0.311616 0.950208i \(-0.399130\pi\)
0.311616 + 0.950208i \(0.399130\pi\)
\(578\) 12.7279i 0.529412i
\(579\) −13.0711 + 31.5563i −0.543215 + 1.31144i
\(580\) 0 0
\(581\) 8.65685 3.58579i 0.359147 0.148763i
\(582\) 3.65685 + 1.51472i 0.151581 + 0.0627871i
\(583\) 1.82843 1.82843i 0.0757257 0.0757257i
\(584\) 19.7990 19.7990i 0.819288 0.819288i
\(585\) 0 0
\(586\) −6.79899 16.4142i −0.280864 0.678065i
\(587\) −8.60660 20.7782i −0.355232 0.857607i −0.995957 0.0898359i \(-0.971366\pi\)
0.640724 0.767771i \(-0.278634\pi\)
\(588\) 17.0711 + 7.07107i 0.703999 + 0.291606i
\(589\) 22.1421 + 9.17157i 0.912351 + 0.377908i
\(590\) 0 0
\(591\) 34.7279i 1.42852i
\(592\) −6.82843 + 2.82843i −0.280647 + 0.116248i
\(593\) 28.2843i 1.16150i −0.814083 0.580748i \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) −1.51472 + 1.51472i −0.0621497 + 0.0621497i
\(595\) 0 0
\(596\) −11.2132 27.0711i −0.459311 1.10887i
\(597\) 17.9706 + 43.3848i 0.735486 + 1.77562i
\(598\) 0.585786 0.242641i 0.0239546 0.00992232i
\(599\) −15.3431 15.3431i −0.626904 0.626904i 0.320384 0.947288i \(-0.396188\pi\)
−0.947288 + 0.320384i \(0.896188\pi\)
\(600\) 0 0
\(601\) 11.9706 11.9706i 0.488289 0.488289i −0.419477 0.907766i \(-0.637786\pi\)
0.907766 + 0.419477i \(0.137786\pi\)
\(602\) 6.58579 15.8995i 0.268417 0.648015i
\(603\) 1.53553 0.636039i 0.0625318 0.0259015i
\(604\) −30.9706 30.9706i −1.26017 1.26017i
\(605\) 0 0
\(606\) 32.1421 1.30569
\(607\) −0.970563 −0.0393939 −0.0196970 0.999806i \(-0.506270\pi\)
−0.0196970 + 0.999806i \(0.506270\pi\)
\(608\) −12.9706 + 31.3137i −0.526026 + 1.26994i
\(609\) −7.65685 −0.310271
\(610\) 0 0
\(611\) 8.24264 19.8995i 0.333462 0.805047i
\(612\) 1.65685 1.65685i 0.0669744 0.0669744i
\(613\) −36.6777 + 15.1924i −1.48140 + 0.613615i −0.969425 0.245387i \(-0.921085\pi\)
−0.511972 + 0.859002i \(0.671085\pi\)
\(614\) −1.72792 + 4.17157i −0.0697333 + 0.168351i
\(615\) 0 0
\(616\) 0.485281 1.17157i 0.0195525 0.0472040i
\(617\) 16.7990 + 16.7990i 0.676302 + 0.676302i 0.959161 0.282859i \(-0.0912830\pi\)
−0.282859 + 0.959161i \(0.591283\pi\)
\(618\) 25.5563 10.5858i 1.02803 0.425823i
\(619\) −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
\(622\) 12.2426 12.2426i 0.490885 0.490885i
\(623\) 5.31371i 0.212889i
\(624\) 9.65685 9.65685i 0.386584 0.386584i
\(625\) 0 0
\(626\) 13.4142 + 13.4142i 0.536140 + 0.536140i
\(627\) 3.24264 + 1.34315i 0.129499 + 0.0536401i
\(628\) 0.585786 1.41421i 0.0233754 0.0564333i
\(629\) 2.00000 + 4.82843i 0.0797452 + 0.192522i
\(630\) 0 0
\(631\) −18.4558 18.4558i −0.734716 0.734716i 0.236834 0.971550i \(-0.423890\pi\)
−0.971550 + 0.236834i \(0.923890\pi\)
\(632\) −16.9706 −0.675053
\(633\) −0.656854 + 0.656854i −0.0261076 + 0.0261076i
\(634\) 15.8284 + 6.55635i 0.628627 + 0.260386i
\(635\) 0 0
\(636\) −30.1421 −1.19521
\(637\) 3.53553 8.53553i 0.140083 0.338190i
\(638\) 1.31371i 0.0520102i
\(639\) 0.100505 0.00397592
\(640\) 0 0
\(641\) −43.4558 −1.71640 −0.858201 0.513313i \(-0.828418\pi\)
−0.858201 + 0.513313i \(0.828418\pi\)
\(642\) 0.828427i 0.0326954i
\(643\) 15.4350 37.2635i 0.608698 1.46953i −0.255719 0.966751i \(-0.582312\pi\)
0.864417 0.502776i \(-0.167688\pi\)
\(644\) −0.686292 −0.0270437
\(645\) 0 0
\(646\) 22.1421 + 9.17157i 0.871171 + 0.360851i
\(647\) −11.8284 + 11.8284i −0.465023 + 0.465023i −0.900298 0.435274i \(-0.856651\pi\)
0.435274 + 0.900298i \(0.356651\pi\)
\(648\) 28.4853 1.11901
\(649\) −1.48528 1.48528i −0.0583024 0.0583024i
\(650\) 0 0
\(651\) 4.00000 + 9.65685i 0.156772 + 0.378482i
\(652\) 15.0711 36.3848i 0.590229 1.42494i
\(653\) 36.0919 + 14.9497i 1.41238 + 0.585029i 0.952935 0.303175i \(-0.0980467\pi\)
0.459450 + 0.888204i \(0.348047\pi\)
\(654\) −8.58579 8.58579i −0.335731 0.335731i
\(655\) 0 0
\(656\) −23.3137 23.3137i −0.910247 0.910247i
\(657\) 4.10051i 0.159976i
\(658\) −16.4853 + 16.4853i −0.642663 + 0.642663i
\(659\) −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 \(0.00383499\pi\)
−0.698536 + 0.715574i \(0.746165\pi\)
\(662\) −9.24264 + 3.82843i −0.359225 + 0.148796i
\(663\) −6.82843 6.82843i −0.265194 0.265194i
\(664\) 7.17157 17.3137i 0.278311 0.671902i
\(665\) 0 0
\(666\) 0.414214 1.00000i 0.0160504 0.0387492i
\(667\) −0.656854 + 0.272078i −0.0254335 + 0.0105349i
\(668\) 6.68629 6.68629i 0.258700 0.258700i
\(669\) 9.17157 22.1421i 0.354593 0.856064i
\(670\) 0 0
\(671\) 0.242641 0.00936704
\(672\) −13.6569 + 5.65685i −0.526825 + 0.218218i
\(673\) −5.51472 −0.212577 −0.106288 0.994335i \(-0.533897\pi\)
−0.106288 + 0.994335i \(0.533897\pi\)
\(674\) −24.0000 −0.924445
\(675\) 0 0
\(676\) 13.5563 + 13.5563i 0.521398 + 0.521398i
\(677\) 5.60660 2.32233i 0.215479 0.0892544i −0.272333 0.962203i \(-0.587795\pi\)
0.487812 + 0.872949i \(0.337795\pi\)
\(678\) −17.6569 + 42.6274i −0.678107 + 1.63710i
\(679\) −1.51472 + 1.51472i −0.0581296 + 0.0581296i
\(680\) 0 0
\(681\) 8.89949 + 8.89949i 0.341029 + 0.341029i
\(682\) −1.65685 + 0.686292i −0.0634442 + 0.0262795i
\(683\) 5.87868 + 14.1924i 0.224941 + 0.543057i 0.995548 0.0942543i \(-0.0300467\pi\)
−0.770607 + 0.637311i \(0.780047\pi\)
\(684\) −1.89949 4.58579i −0.0726290 0.175342i
\(685\) 0 0
\(686\) −16.9706 + 16.9706i −0.647939 + 0.647939i
\(687\) 49.5563i 1.89069i
\(688\) −13.1716 31.7990i −0.502162 1.21233i
\(689\) 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 \(0.824646\pi\)
\(692\) −2.24264 0.928932i −0.0852524 0.0353127i
\(693\) 0.0710678 + 0.171573i 0.00269964 + 0.00651751i
\(694\) 8.41421 + 20.3137i 0.319399 + 0.771098i
\(695\) 0 0
\(696\) −10.8284 + 10.8284i −0.410450 + 0.410450i
\(697\) −16.4853 + 16.4853i −0.624425 + 0.624425i
\(698\) 36.4558 + 15.1005i 1.37987 + 0.571563i
\(699\) 20.8995 8.65685i 0.790491 0.327432i
\(700\) 0 0
\(701\) 7.12132 17.1924i 0.268969 0.649348i −0.730467 0.682948i \(-0.760697\pi\)
0.999435 + 0.0336007i \(0.0106974\pi\)
\(702\) 12.4853i 0.471227i
\(703\) 11.0711 0.417553
\(704\) −0.970563 2.34315i −0.0365795 0.0883106i
\(705\) 0 0
\(706\) 8.48528i 0.319348i
\(707\) −6.65685 + 16.0711i −0.250357 + 0.604415i
\(708\) 24.4853i 0.920213i
\(709\) −6.77817 + 2.80761i −0.254560 + 0.105442i −0.506314 0.862349i \(-0.668992\pi\)
0.251755 + 0.967791i \(0.418992\pi\)
\(710\) 0 0
\(711\) 1.75736 1.75736i 0.0659061 0.0659061i
\(712\) −7.51472 7.51472i −0.281626 0.281626i
\(713\) 0.686292 + 0.686292i 0.0257018 + 0.0257018i
\(714\) 4.00000 + 9.65685i 0.149696 + 0.361399i
\(715\) 0 0
\(716\) 28.7279 + 11.8995i 1.07361 + 0.444705i
\(717\) −29.5563 12.2426i −1.10380 0.457210i
\(718\) 17.2132 + 17.2132i 0.642391 + 0.642391i
\(719\) 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
\(722\) 16.8995 16.8995i 0.628934 0.628934i
\(723\) −14.4853 6.00000i −0.538713 0.223142i
\(724\) 4.38478 + 10.5858i 0.162959 + 0.393418i
\(725\) 0 0
\(726\) 26.3137 10.8995i 0.976593 0.404518i
\(727\) −23.9706 23.9706i −0.889019 0.889019i 0.105410 0.994429i \(-0.466385\pi\)
−0.994429 + 0.105410i \(0.966385\pi\)
\(728\) 2.82843 + 6.82843i 0.104828 + 0.253078i
\(729\) 15.7782 15.7782i 0.584377 0.584377i
\(730\) 0 0
\(731\) −22.4853 + 9.31371i −0.831648 + 0.344480i
\(732\) −2.00000 2.00000i −0.0739221 0.0739221i
\(733\) 0.736544 1.77817i 0.0272049 0.0656784i −0.909693 0.415281i \(-0.863683\pi\)
0.936898 + 0.349602i \(0.113683\pi\)
\(734\) 8.48528 0.313197
\(735\) 0 0
\(736\) −0.970563 + 0.970563i −0.0357754 + 0.0357754i
\(737\) −1.27208 −0.0468576
\(738\) 4.82843 0.177737
\(739\) 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
\(742\) 6.24264 15.0711i 0.229175 0.553276i
\(743\) 13.6274 13.6274i 0.499941 0.499941i −0.411478 0.911420i \(-0.634987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(744\) 19.3137 + 8.00000i 0.708075 + 0.293294i
\(745\) 0 0
\(746\) 39.9706 16.5563i 1.46343 0.606171i
\(747\) 1.05025 + 2.53553i 0.0384267 + 0.0927703i
\(748\) −1.65685 + 0.686292i −0.0605806 + 0.0250933i
\(749\) 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 \(0.862344\pi\)
\(752\) 46.6274i 1.70033i
\(753\) 29.2132i 1.06459i
\(754\) 5.41421 + 5.41421i 0.197174 + 0.197174i
\(755\) 0 0
\(756\) −5.17157 + 12.4853i −0.188088 + 0.454085i
\(757\) 0.736544 + 1.77817i 0.0267701 + 0.0646289i 0.936699 0.350135i \(-0.113864\pi\)
−0.909929 + 0.414764i \(0.863864\pi\)
\(758\) −12.6985 30.6569i −0.461230 1.11351i
\(759\) 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 \(0.462697\pi\)
\(762\) 50.6274 + 20.9706i 1.83404 + 0.759683i
\(763\) 6.07107 2.51472i 0.219787 0.0910389i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 24.0000i 0.867155i
\(767\) 12.2426 0.442056
\(768\) −11.3137 + 27.3137i −0.408248 + 0.985599i
\(769\) 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
\(772\) −36.9706 −1.33060
\(773\) 26.0919 10.8076i 0.938460 0.388723i 0.139578 0.990211i \(-0.455425\pi\)
0.798882 + 0.601488i \(0.205425\pi\)
\(774\) 4.65685 + 1.92893i 0.167387 + 0.0693340i
\(775\) 0 0
\(776\) 4.28427i 0.153796i
\(777\) 3.41421 + 3.41421i 0.122484 + 0.122484i
\(778\) 17.3431 + 41.8701i 0.621782 + 1.50111i
\(779\) 18.8995 + 45.6274i 0.677145 + 1.63477i
\(780\) 0 0
\(781\) −0.0710678 0.0294373i −0.00254301 0.00105335i