Properties

Label 800.2.y.a.701.1
Level $800$
Weight $2$
Character 800.701
Analytic conductor $6.388$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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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 701.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 800.701
Dual form 800.2.y.a.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(0.707107 + 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(0.707107 + 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +(-4.12132 + 1.70711i) q^{11} +(-1.41421 - 0.585786i) q^{12} +(-0.292893 + 0.707107i) q^{13} +(-1.41421 - 1.41421i) q^{14} +4.00000 q^{16} +2.82843i q^{17} +(2.41421 - 2.41421i) q^{18} +(1.53553 - 3.70711i) q^{19} +(-1.00000 + 0.414214i) q^{21} +(-2.41421 - 5.82843i) q^{22} +(-5.82843 - 5.82843i) q^{23} +(0.828427 - 2.00000i) q^{24} +(-1.00000 - 0.414214i) q^{26} +(-1.58579 - 3.82843i) q^{27} +(2.00000 - 2.00000i) q^{28} +(-3.12132 - 1.29289i) q^{29} -4.00000 q^{31} +5.65685i q^{32} -3.41421 q^{33} -4.00000 q^{34} +(3.41421 + 3.41421i) q^{36} +(-0.292893 - 0.707107i) q^{37} +(5.24264 + 2.17157i) q^{38} +(-0.414214 + 0.414214i) q^{39} +(-0.171573 - 0.171573i) q^{41} +(-0.585786 - 1.41421i) q^{42} +(-4.70711 + 1.94975i) q^{43} +(8.24264 - 3.41421i) q^{44} +(8.24264 - 8.24264i) q^{46} +0.343146i q^{47} +(2.82843 + 1.17157i) q^{48} +5.00000i q^{49} +(-0.828427 + 2.00000i) q^{51} +(0.585786 - 1.41421i) q^{52} +(1.12132 - 0.464466i) q^{53} +(5.41421 - 2.24264i) q^{54} +(2.82843 + 2.82843i) q^{56} +(2.17157 - 2.17157i) q^{57} +(1.82843 - 4.41421i) q^{58} +(-1.87868 - 4.53553i) q^{59} +(1.70711 + 0.707107i) q^{61} -5.65685i q^{62} +3.41421 q^{63} -8.00000 q^{64} -4.82843i q^{66} +(5.53553 + 2.29289i) q^{67} -5.65685i q^{68} +(-2.41421 - 5.82843i) q^{69} +(-5.82843 + 5.82843i) q^{71} +(-4.82843 + 4.82843i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(1.00000 - 0.414214i) q^{74} +(-3.07107 + 7.41421i) q^{76} +(2.41421 - 5.82843i) q^{77} +(-0.585786 - 0.585786i) q^{78} +6.00000i q^{79} +4.07107i q^{81} +(0.242641 - 0.242641i) q^{82} +(-1.87868 + 4.53553i) q^{83} +(2.00000 - 0.828427i) q^{84} +(-2.75736 - 6.65685i) q^{86} +(-1.82843 - 1.82843i) q^{87} +(4.82843 + 11.6569i) q^{88} +(8.65685 - 8.65685i) q^{89} +(-0.414214 - 1.00000i) q^{91} +(11.6569 + 11.6569i) q^{92} +(-2.82843 - 1.17157i) q^{93} -0.485281 q^{94} +(-1.65685 + 4.00000i) q^{96} +18.4853 q^{97} -7.07107 q^{98} +(9.94975 + 4.12132i) 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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(577\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(1\)

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 + 0.292893i 0.408248 + 0.169102i 0.577350 0.816497i \(-0.304087\pi\)
−0.169102 + 0.985599i \(0.554087\pi\)
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) −0.414214 + 1.00000i −0.169102 + 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
\(9\) −1.70711 1.70711i −0.569036 0.569036i
\(10\) 0 0
\(11\) −4.12132 + 1.70711i −1.24262 + 0.514712i −0.904534 0.426401i \(-0.859781\pi\)
−0.338091 + 0.941113i \(0.609781\pi\)
\(12\) −1.41421 0.585786i −0.408248 0.169102i
\(13\) −0.292893 + 0.707107i −0.0812340 + 0.196116i −0.959278 0.282464i \(-0.908848\pi\)
0.878044 + 0.478580i \(0.158848\pi\)
\(14\) −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 \(0.111442\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) 2.41421 2.41421i 0.569036 0.569036i
\(19\) 1.53553 3.70711i 0.352276 0.850469i −0.644063 0.764973i \(-0.722752\pi\)
0.996339 0.0854961i \(-0.0272475\pi\)
\(20\) 0 0
\(21\) −1.00000 + 0.414214i −0.218218 + 0.0903888i
\(22\) −2.41421 5.82843i −0.514712 1.24262i
\(23\) −5.82843 5.82843i −1.21531 1.21531i −0.969256 0.246055i \(-0.920866\pi\)
−0.246055 0.969256i \(-0.579134\pi\)
\(24\) 0.828427 2.00000i 0.169102 0.408248i
\(25\) 0 0
\(26\) −1.00000 0.414214i −0.196116 0.0812340i
\(27\) −1.58579 3.82843i −0.305185 0.736781i
\(28\) 2.00000 2.00000i 0.377964 0.377964i
\(29\) −3.12132 1.29289i −0.579615 0.240084i 0.0735609 0.997291i \(-0.476564\pi\)
−0.653176 + 0.757206i \(0.726564\pi\)
\(30\) 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
\(33\) −3.41421 −0.594338
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 3.41421 + 3.41421i 0.569036 + 0.569036i
\(37\) −0.292893 0.707107i −0.0481513 0.116248i 0.897974 0.440049i \(-0.145039\pi\)
−0.946125 + 0.323802i \(0.895039\pi\)
\(38\) 5.24264 + 2.17157i 0.850469 + 0.352276i
\(39\) −0.414214 + 0.414214i −0.0663273 + 0.0663273i
\(40\) 0 0
\(41\) −0.171573 0.171573i −0.0267952 0.0267952i 0.693582 0.720377i \(-0.256031\pi\)
−0.720377 + 0.693582i \(0.756031\pi\)
\(42\) −0.585786 1.41421i −0.0903888 0.218218i
\(43\) −4.70711 + 1.94975i −0.717827 + 0.297334i −0.711539 0.702647i \(-0.752002\pi\)
−0.00628798 + 0.999980i \(0.502002\pi\)
\(44\) 8.24264 3.41421i 1.24262 0.514712i
\(45\) 0 0
\(46\) 8.24264 8.24264i 1.21531 1.21531i
\(47\) 0.343146i 0.0500530i 0.999687 + 0.0250265i \(0.00796701\pi\)
−0.999687 + 0.0250265i \(0.992033\pi\)
\(48\) 2.82843 + 1.17157i 0.408248 + 0.169102i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −0.828427 + 2.00000i −0.116003 + 0.280056i
\(52\) 0.585786 1.41421i 0.0812340 0.196116i
\(53\) 1.12132 0.464466i 0.154025 0.0637993i −0.304339 0.952564i \(-0.598436\pi\)
0.458364 + 0.888764i \(0.348436\pi\)
\(54\) 5.41421 2.24264i 0.736781 0.305185i
\(55\) 0 0
\(56\) 2.82843 + 2.82843i 0.377964 + 0.377964i
\(57\) 2.17157 2.17157i 0.287632 0.287632i
\(58\) 1.82843 4.41421i 0.240084 0.579615i
\(59\) −1.87868 4.53553i −0.244583 0.590476i 0.753144 0.657855i \(-0.228536\pi\)
−0.997727 + 0.0673793i \(0.978536\pi\)
\(60\) 0 0
\(61\) 1.70711 + 0.707107i 0.218573 + 0.0905357i 0.489283 0.872125i \(-0.337259\pi\)
−0.270710 + 0.962661i \(0.587259\pi\)
\(62\) 5.65685i 0.718421i
\(63\) 3.41421 0.430150
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 4.82843i 0.594338i
\(67\) 5.53553 + 2.29289i 0.676273 + 0.280121i 0.694268 0.719717i \(-0.255728\pi\)
−0.0179949 + 0.999838i \(0.505728\pi\)
\(68\) 5.65685i 0.685994i
\(69\) −2.41421 5.82843i −0.290637 0.701660i
\(70\) 0 0
\(71\) −5.82843 + 5.82843i −0.691707 + 0.691707i −0.962607 0.270900i \(-0.912679\pi\)
0.270900 + 0.962607i \(0.412679\pi\)
\(72\) −4.82843 + 4.82843i −0.569036 + 0.569036i
\(73\) −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 0.414214i 0.116248 0.0481513i
\(75\) 0 0
\(76\) −3.07107 + 7.41421i −0.352276 + 0.850469i
\(77\) 2.41421 5.82843i 0.275125 0.664211i
\(78\) −0.585786 0.585786i −0.0663273 0.0663273i
\(79\) 6.00000i 0.675053i 0.941316 + 0.337526i \(0.109590\pi\)
−0.941316 + 0.337526i \(0.890410\pi\)
\(80\) 0 0
\(81\) 4.07107i 0.452341i
\(82\) 0.242641 0.242641i 0.0267952 0.0267952i
\(83\) −1.87868 + 4.53553i −0.206212 + 0.497840i −0.992821 0.119612i \(-0.961835\pi\)
0.786609 + 0.617452i \(0.211835\pi\)
\(84\) 2.00000 0.828427i 0.218218 0.0903888i
\(85\) 0 0
\(86\) −2.75736 6.65685i −0.297334 0.717827i
\(87\) −1.82843 1.82843i −0.196028 0.196028i
\(88\) 4.82843 + 11.6569i 0.514712 + 1.24262i
\(89\) 8.65685 8.65685i 0.917625 0.917625i −0.0792315 0.996856i \(-0.525247\pi\)
0.996856 + 0.0792315i \(0.0252466\pi\)
\(90\) 0 0
\(91\) −0.414214 1.00000i −0.0434214 0.104828i
\(92\) 11.6569 + 11.6569i 1.21531 + 1.21531i
\(93\) −2.82843 1.17157i −0.293294 0.121486i
\(94\) −0.485281 −0.0500530
\(95\) 0 0
\(96\) −1.65685 + 4.00000i −0.169102 + 0.408248i
\(97\) 18.4853 1.87690 0.938448 0.345421i \(-0.112264\pi\)
0.938448 + 0.345421i \(0.112264\pi\)
\(98\) −7.07107 −0.714286
\(99\) 9.94975 + 4.12132i 0.999987 + 0.414208i
\(100\) 0 0
\(101\) −1.36396 3.29289i −0.135719 0.327655i 0.841379 0.540446i \(-0.181745\pi\)
−0.977098 + 0.212791i \(0.931745\pi\)
\(102\) −2.82843 1.17157i −0.280056 0.116003i
\(103\) −9.48528 + 9.48528i −0.934613 + 0.934613i −0.997990 0.0633771i \(-0.979813\pi\)
0.0633771 + 0.997990i \(0.479813\pi\)
\(104\) 2.00000 + 0.828427i 0.196116 + 0.0812340i
\(105\) 0 0
\(106\) 0.656854 + 1.58579i 0.0637993 + 0.154025i
\(107\) 4.12132 1.70711i 0.398423 0.165032i −0.174470 0.984663i \(-0.555821\pi\)
0.572893 + 0.819630i \(0.305821\pi\)
\(108\) 3.17157 + 7.65685i 0.305185 + 0.736781i
\(109\) −5.70711 + 13.7782i −0.546642 + 1.31971i 0.373320 + 0.927702i \(0.378219\pi\)
−0.919962 + 0.392007i \(0.871781\pi\)
\(110\) 0 0
\(111\) 0.585786i 0.0556004i
\(112\) −4.00000 + 4.00000i −0.377964 + 0.377964i
\(113\) 6.34315i 0.596713i 0.954455 + 0.298356i \(0.0964384\pi\)
−0.954455 + 0.298356i \(0.903562\pi\)
\(114\) 3.07107 + 3.07107i 0.287632 + 0.287632i
\(115\) 0 0
\(116\) 6.24264 + 2.58579i 0.579615 + 0.240084i
\(117\) 1.70711 0.707107i 0.157822 0.0653720i
\(118\) 6.41421 2.65685i 0.590476 0.244583i
\(119\) −2.82843 2.82843i −0.259281 0.259281i
\(120\) 0 0
\(121\) 6.29289 6.29289i 0.572081 0.572081i
\(122\) −1.00000 + 2.41421i −0.0905357 + 0.218573i
\(123\) −0.0710678 0.171573i −0.00640797 0.0154702i
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 4.82843i 0.430150i
\(127\) −12.9706 −1.15095 −0.575476 0.817819i \(-0.695183\pi\)
−0.575476 + 0.817819i \(0.695183\pi\)
\(128\) 11.3137i 1.00000i
\(129\) −3.89949 −0.343331
\(130\) 0 0
\(131\) −16.3640 6.77817i −1.42973 0.592212i −0.472442 0.881362i \(-0.656627\pi\)
−0.957284 + 0.289150i \(0.906627\pi\)
\(132\) 6.82843 0.594338
\(133\) 2.17157 + 5.24264i 0.188299 + 0.454595i
\(134\) −3.24264 + 7.82843i −0.280121 + 0.676273i
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) 8.65685 + 8.65685i 0.739605 + 0.739605i 0.972502 0.232897i \(-0.0748204\pi\)
−0.232897 + 0.972502i \(0.574820\pi\)
\(138\) 8.24264 3.41421i 0.701660 0.290637i
\(139\) 13.1924 5.46447i 1.11896 0.463490i 0.254948 0.966955i \(-0.417942\pi\)
0.864016 + 0.503465i \(0.167942\pi\)
\(140\) 0 0
\(141\) −0.100505 + 0.242641i −0.00846405 + 0.0204340i
\(142\) −8.24264 8.24264i −0.691707 0.691707i
\(143\) 3.41421i 0.285511i
\(144\) −6.82843 6.82843i −0.569036 0.569036i
\(145\) 0 0
\(146\) 9.89949 9.89949i 0.819288 0.819288i
\(147\) −1.46447 + 3.53553i −0.120787 + 0.291606i
\(148\) 0.585786 + 1.41421i 0.0481513 + 0.116248i
\(149\) −15.6066 + 6.46447i −1.27854 + 0.529590i −0.915551 0.402203i \(-0.868245\pi\)
−0.362992 + 0.931792i \(0.618245\pi\)
\(150\) 0 0
\(151\) −1.48528 1.48528i −0.120870 0.120870i 0.644084 0.764955i \(-0.277239\pi\)
−0.764955 + 0.644084i \(0.777239\pi\)
\(152\) −10.4853 4.34315i −0.850469 0.352276i
\(153\) 4.82843 4.82843i 0.390355 0.390355i
\(154\) 8.24264 + 3.41421i 0.664211 + 0.275125i
\(155\) 0 0
\(156\) 0.828427 0.828427i 0.0663273 0.0663273i
\(157\) −1.70711 0.707107i −0.136242 0.0564333i 0.313521 0.949581i \(-0.398491\pi\)
−0.449763 + 0.893148i \(0.648491\pi\)
\(158\) −8.48528 −0.675053
\(159\) 0.928932 0.0736691
\(160\) 0 0
\(161\) 11.6569 0.918689
\(162\) −5.75736 −0.452341
\(163\) −0.464466 0.192388i −0.0363798 0.0150690i 0.364419 0.931235i \(-0.381267\pi\)
−0.400799 + 0.916166i \(0.631267\pi\)
\(164\) 0.343146 + 0.343146i 0.0267952 + 0.0267952i
\(165\) 0 0
\(166\) −6.41421 2.65685i −0.497840 0.206212i
\(167\) −14.6569 + 14.6569i −1.13418 + 1.13418i −0.144707 + 0.989475i \(0.546224\pi\)
−0.989475 + 0.144707i \(0.953776\pi\)
\(168\) 1.17157 + 2.82843i 0.0903888 + 0.218218i
\(169\) 8.77817 + 8.77817i 0.675244 + 0.675244i
\(170\) 0 0
\(171\) −8.94975 + 3.70711i −0.684404 + 0.283490i
\(172\) 9.41421 3.89949i 0.717827 0.297334i
\(173\) −3.12132 + 7.53553i −0.237310 + 0.572916i −0.997003 0.0773656i \(-0.975349\pi\)
0.759693 + 0.650282i \(0.225349\pi\)
\(174\) 2.58579 2.58579i 0.196028 0.196028i
\(175\) 0 0
\(176\) −16.4853 + 6.82843i −1.24262 + 0.514712i
\(177\) 3.75736i 0.282420i
\(178\) 12.2426 + 12.2426i 0.917625 + 0.917625i
\(179\) −1.63604 + 3.94975i −0.122283 + 0.295218i −0.973153 0.230159i \(-0.926076\pi\)
0.850870 + 0.525377i \(0.176076\pi\)
\(180\) 0 0
\(181\) 16.1924 6.70711i 1.20357 0.498535i 0.311420 0.950272i \(-0.399196\pi\)
0.892151 + 0.451737i \(0.149196\pi\)
\(182\) 1.41421 0.585786i 0.104828 0.0434214i
\(183\) 1.00000 + 1.00000i 0.0739221 + 0.0739221i
\(184\) −16.4853 + 16.4853i −1.21531 + 1.21531i
\(185\) 0 0
\(186\) 1.65685 4.00000i 0.121486 0.293294i
\(187\) −4.82843 11.6569i −0.353090 0.852434i
\(188\) 0.686292i 0.0500530i
\(189\) 5.41421 + 2.24264i 0.393826 + 0.163128i
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) −5.65685 2.34315i −0.408248 0.169102i
\(193\) 1.51472 0.109032 0.0545159 0.998513i \(-0.482638\pi\)
0.0545159 + 0.998513i \(0.482638\pi\)
\(194\) 26.1421i 1.87690i
\(195\) 0 0
\(196\) 10.0000i 0.714286i
\(197\) −4.63604 11.1924i −0.330304 0.797425i −0.998568 0.0535002i \(-0.982962\pi\)
0.668264 0.743924i \(-0.267038\pi\)
\(198\) −5.82843 + 14.0711i −0.414208 + 0.999987i
\(199\) −15.9706 + 15.9706i −1.13212 + 1.13212i −0.142300 + 0.989824i \(0.545450\pi\)
−0.989824 + 0.142300i \(0.954550\pi\)
\(200\) 0 0
\(201\) 3.24264 + 3.24264i 0.228718 + 0.228718i
\(202\) 4.65685 1.92893i 0.327655 0.135719i
\(203\) 4.41421 1.82843i 0.309817 0.128330i
\(204\) 1.65685 4.00000i 0.116003 0.280056i
\(205\) 0 0
\(206\) −13.4142 13.4142i −0.934613 0.934613i
\(207\) 19.8995i 1.38311i
\(208\) −1.17157 + 2.82843i −0.0812340 + 0.196116i
\(209\) 17.8995i 1.23813i
\(210\) 0 0
\(211\) 7.53553 18.1924i 0.518768 1.25242i −0.419893 0.907574i \(-0.637932\pi\)
0.938661 0.344842i \(-0.112068\pi\)
\(212\) −2.24264 + 0.928932i −0.154025 + 0.0637993i
\(213\) −5.82843 + 2.41421i −0.399357 + 0.165419i
\(214\) 2.41421 + 5.82843i 0.165032 + 0.398423i
\(215\) 0 0
\(216\) −10.8284 + 4.48528i −0.736781 + 0.305185i
\(217\) 4.00000 4.00000i 0.271538 0.271538i
\(218\) −19.4853 8.07107i −1.31971 0.546642i
\(219\) −2.89949 7.00000i −0.195930 0.473016i
\(220\) 0 0
\(221\) −2.00000 0.828427i −0.134535 0.0557260i
\(222\) 0.828427 0.0556004
\(223\) 20.9706 1.40429 0.702146 0.712033i \(-0.252225\pi\)
0.702146 + 0.712033i \(0.252225\pi\)
\(224\) −5.65685 5.65685i −0.377964 0.377964i
\(225\) 0 0
\(226\) −8.97056 −0.596713
\(227\) −18.6066 7.70711i −1.23496 0.511539i −0.332826 0.942988i \(-0.608002\pi\)
−0.902137 + 0.431449i \(0.858002\pi\)
\(228\) −4.34315 + 4.34315i −0.287632 + 0.287632i
\(229\) −9.22183 22.2635i −0.609395 1.47121i −0.863659 0.504076i \(-0.831833\pi\)
0.254264 0.967135i \(-0.418167\pi\)
\(230\) 0 0
\(231\) 3.41421 3.41421i 0.224639 0.224639i
\(232\) −3.65685 + 8.82843i −0.240084 + 0.579615i
\(233\) 2.65685 + 2.65685i 0.174056 + 0.174056i 0.788759 0.614703i \(-0.210724\pi\)
−0.614703 + 0.788759i \(0.710724\pi\)
\(234\) 1.00000 + 2.41421i 0.0653720 + 0.157822i
\(235\) 0 0
\(236\) 3.75736 + 9.07107i 0.244583 + 0.590476i
\(237\) −1.75736 + 4.24264i −0.114153 + 0.275589i
\(238\) 4.00000 4.00000i 0.259281 0.259281i
\(239\) 5.31371i 0.343715i −0.985122 0.171858i \(-0.945023\pi\)
0.985122 0.171858i \(-0.0549769\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 8.89949 + 8.89949i 0.572081 + 0.572081i
\(243\) −5.94975 + 14.3640i −0.381676 + 0.921449i
\(244\) −3.41421 1.41421i −0.218573 0.0905357i
\(245\) 0 0
\(246\) 0.242641 0.100505i 0.0154702 0.00640797i
\(247\) 2.17157 + 2.17157i 0.138174 + 0.138174i
\(248\) 11.3137i 0.718421i
\(249\) −2.65685 + 2.65685i −0.168371 + 0.168371i
\(250\) 0 0
\(251\) 6.60660 + 15.9497i 0.417005 + 1.00674i 0.983210 + 0.182475i \(0.0584109\pi\)
−0.566205 + 0.824264i \(0.691589\pi\)
\(252\) −6.82843 −0.430150
\(253\) 33.9706 + 14.0711i 2.13571 + 0.884640i
\(254\) 18.3431i 1.15095i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 5.51472i 0.343331i
\(259\) 1.00000 + 0.414214i 0.0621370 + 0.0257380i
\(260\) 0 0
\(261\) 3.12132 + 7.53553i 0.193205 + 0.466438i
\(262\) 9.58579 23.1421i 0.592212 1.42973i
\(263\) 5.82843 5.82843i 0.359396 0.359396i −0.504194 0.863590i \(-0.668210\pi\)
0.863590 + 0.504194i \(0.168210\pi\)
\(264\) 9.65685i 0.594338i
\(265\) 0 0
\(266\) −7.41421 + 3.07107i −0.454595 + 0.188299i
\(267\) 8.65685 3.58579i 0.529791 0.219447i
\(268\) −11.0711 4.58579i −0.676273 0.280121i
\(269\) 9.12132 22.0208i 0.556137 1.34263i −0.356666 0.934232i \(-0.616087\pi\)
0.912803 0.408401i \(-0.133913\pi\)
\(270\) 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
\(273\) 0.828427i 0.0501387i
\(274\) −12.2426 + 12.2426i −0.739605 + 0.739605i
\(275\) 0 0
\(276\) 4.82843 + 11.6569i 0.290637 + 0.701660i
\(277\) −1.70711 + 0.707107i −0.102570 + 0.0424859i −0.433378 0.901212i \(-0.642679\pi\)
0.330808 + 0.943698i \(0.392679\pi\)
\(278\) 7.72792 + 18.6569i 0.463490 + 1.11896i
\(279\) 6.82843 + 6.82843i 0.408807 + 0.408807i
\(280\) 0 0
\(281\) −11.8284 + 11.8284i −0.705625 + 0.705625i −0.965612 0.259987i \(-0.916282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(282\) −0.343146 0.142136i −0.0204340 0.00846405i
\(283\) −5.77817 13.9497i −0.343477 0.829226i −0.997359 0.0726300i \(-0.976861\pi\)
0.653882 0.756596i \(-0.273139\pi\)
\(284\) 11.6569 11.6569i 0.691707 0.691707i
\(285\) 0 0
\(286\) 4.82843 0.285511
\(287\) 0.343146 0.0202553
\(288\) 9.65685 9.65685i 0.569036 0.569036i
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) 13.0711 + 5.41421i 0.766240 + 0.317387i
\(292\) 14.0000 + 14.0000i 0.819288 + 0.819288i
\(293\) −9.60660 23.1924i −0.561224 1.35491i −0.908788 0.417258i \(-0.862991\pi\)
0.347565 0.937656i \(-0.387009\pi\)
\(294\) −5.00000 2.07107i −0.291606 0.120787i
\(295\) 0 0
\(296\) −2.00000 + 0.828427i −0.116248 + 0.0481513i
\(297\) 13.0711 + 13.0711i 0.758460 + 0.758460i
\(298\) −9.14214 22.0711i −0.529590 1.27854i
\(299\) 5.82843 2.41421i 0.337067 0.139618i
\(300\) 0 0
\(301\) 2.75736 6.65685i 0.158932 0.383695i
\(302\) 2.10051 2.10051i 0.120870 0.120870i
\(303\) 2.72792i 0.156715i
\(304\) 6.14214 14.8284i 0.352276 0.850469i
\(305\) 0 0
\(306\) 6.82843 + 6.82843i 0.390355 + 0.390355i
\(307\) 6.94975 16.7782i 0.396643 0.957581i −0.591813 0.806075i \(-0.701588\pi\)
0.988456 0.151506i \(-0.0484123\pi\)
\(308\) −4.82843 + 11.6569i −0.275125 + 0.664211i
\(309\) −9.48528 + 3.92893i −0.539599 + 0.223509i
\(310\) 0 0
\(311\) −2.65685 2.65685i −0.150656 0.150656i 0.627755 0.778411i \(-0.283974\pi\)
−0.778411 + 0.627755i \(0.783974\pi\)
\(312\) 1.17157 + 1.17157i 0.0663273 + 0.0663273i
\(313\) 7.48528 7.48528i 0.423093 0.423093i −0.463174 0.886267i \(-0.653290\pi\)
0.886267 + 0.463174i \(0.153290\pi\)
\(314\) 1.00000 2.41421i 0.0564333 0.136242i
\(315\) 0 0
\(316\) 12.0000i 0.675053i
\(317\) −17.3640 7.19239i −0.975257 0.403965i −0.162591 0.986694i \(-0.551985\pi\)
−0.812667 + 0.582729i \(0.801985\pi\)
\(318\) 1.31371i 0.0736691i
\(319\) 15.0711 0.843818
\(320\) 0 0
\(321\) 3.41421 0.190563
\(322\) 16.4853i 0.918689i
\(323\) 10.4853 + 4.34315i 0.583417 + 0.241659i
\(324\) 8.14214i 0.452341i
\(325\) 0 0
\(326\) 0.272078 0.656854i 0.0150690 0.0363798i
\(327\) −8.07107 + 8.07107i −0.446331 + 0.446331i
\(328\) −0.485281 + 0.485281i −0.0267952 + 0.0267952i
\(329\) −0.343146 0.343146i −0.0189182 0.0189182i
\(330\) 0 0
\(331\) −1.29289 + 0.535534i −0.0710638 + 0.0294356i −0.417932 0.908478i \(-0.637245\pi\)
0.346868 + 0.937914i \(0.387245\pi\)
\(332\) 3.75736 9.07107i 0.206212 0.497840i
\(333\) −0.707107 + 1.70711i −0.0387492 + 0.0935489i
\(334\) −20.7279 20.7279i −1.13418 1.13418i
\(335\) 0 0
\(336\) −4.00000 + 1.65685i −0.218218 + 0.0903888i
\(337\) 16.9706i 0.924445i 0.886764 + 0.462223i \(0.152948\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(338\) −12.4142 + 12.4142i −0.675244 + 0.675244i
\(339\) −1.85786 + 4.48528i −0.100905 + 0.243607i
\(340\) 0 0
\(341\) 16.4853 6.82843i 0.892728 0.369780i
\(342\) −5.24264 12.6569i −0.283490 0.684404i
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 5.51472 + 13.3137i 0.297334 + 0.717827i
\(345\) 0 0
\(346\) −10.6569 4.41421i −0.572916 0.237310i
\(347\) −1.63604 3.94975i −0.0878272 0.212034i 0.873863 0.486172i \(-0.161607\pi\)
−0.961690 + 0.274139i \(0.911607\pi\)
\(348\) 3.65685 + 3.65685i 0.196028 + 0.196028i
\(349\) 24.6777 + 10.2218i 1.32097 + 0.547162i 0.928065 0.372419i \(-0.121472\pi\)
0.392901 + 0.919581i \(0.371472\pi\)
\(350\) 0 0
\(351\) 3.17157 0.169286
\(352\) −9.65685 23.3137i −0.514712 1.24262i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 5.31371 0.282420
\(355\) 0 0
\(356\) −17.3137 + 17.3137i −0.917625 + 0.917625i
\(357\) −1.17157 2.82843i −0.0620062 0.149696i
\(358\) −5.58579 2.31371i −0.295218 0.122283i
\(359\) −17.8284 + 17.8284i −0.940948 + 0.940948i −0.998351 0.0574027i \(-0.981718\pi\)
0.0574027 + 0.998351i \(0.481718\pi\)
\(360\) 0 0
\(361\) 2.05025 + 2.05025i 0.107908 + 0.107908i
\(362\) 9.48528 + 22.8995i 0.498535 + 1.20357i
\(363\) 6.29289 2.60660i 0.330291 0.136811i
\(364\) 0.828427 + 2.00000i 0.0434214 + 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 \(0.949947\pi\)
\(368\) −23.3137 23.3137i −1.21531 1.21531i
\(369\) 0.585786i 0.0304948i
\(370\) 0 0
\(371\) −0.656854 + 1.58579i −0.0341022 + 0.0823299i
\(372\) 5.65685 + 2.34315i 0.293294 + 0.121486i
\(373\) 10.2929 4.26346i 0.532946 0.220753i −0.0999471 0.994993i \(-0.531867\pi\)
0.632893 + 0.774239i \(0.281867\pi\)
\(374\) 16.4853 6.82843i 0.852434 0.353090i
\(375\) 0 0
\(376\) 0.970563 0.0500530
\(377\) 1.82843 1.82843i 0.0941688 0.0941688i
\(378\) −3.17157 + 7.65685i −0.163128 + 0.393826i
\(379\) −13.6777 33.0208i −0.702575 1.69617i −0.717769 0.696281i \(-0.754837\pi\)
0.0151948 0.999885i \(-0.495163\pi\)
\(380\) 0 0
\(381\) −9.17157 3.79899i −0.469874 0.194628i
\(382\) 16.9706i 0.868290i
\(383\) 16.9706 0.867155 0.433578 0.901116i \(-0.357251\pi\)
0.433578 + 0.901116i \(0.357251\pi\)
\(384\) 3.31371 8.00000i 0.169102 0.408248i
\(385\) 0 0
\(386\) 2.14214i 0.109032i
\(387\) 11.3640 + 4.70711i 0.577663 + 0.239276i
\(388\) −36.9706 −1.87690
\(389\) −8.39340 20.2635i −0.425562 1.02740i −0.980679 0.195625i \(-0.937326\pi\)
0.555117 0.831773i \(-0.312674\pi\)
\(390\) 0 0
\(391\) 16.4853 16.4853i 0.833697 0.833697i
\(392\) 14.1421 0.714286
\(393\) −9.58579 9.58579i −0.483539 0.483539i
\(394\) 15.8284 6.55635i 0.797425 0.330304i
\(395\) 0 0
\(396\) −19.8995 8.24264i −0.999987 0.414208i
\(397\) 9.22183 22.2635i 0.462830 1.11737i −0.504400 0.863470i \(-0.668286\pi\)
0.967230 0.253901i \(-0.0817137\pi\)
\(398\) −22.5858 22.5858i −1.13212 1.13212i
\(399\) 4.34315i 0.217429i
\(400\) 0 0
\(401\) 2.82843i 0.141245i −0.997503 0.0706225i \(-0.977501\pi\)
0.997503 0.0706225i \(-0.0224986\pi\)
\(402\) −4.58579 + 4.58579i −0.228718 + 0.228718i
\(403\) 1.17157 2.82843i 0.0583602 0.140894i
\(404\) 2.72792 + 6.58579i 0.135719 + 0.327655i
\(405\) 0 0
\(406\) 2.58579 + 6.24264i 0.128330 + 0.309817i
\(407\) 2.41421 + 2.41421i 0.119668 + 0.119668i
\(408\) 5.65685 + 2.34315i 0.280056 + 0.116003i
\(409\) 21.4853 21.4853i 1.06238 1.06238i 0.0644584 0.997920i \(-0.479468\pi\)
0.997920 0.0644584i \(-0.0205320\pi\)
\(410\) 0 0
\(411\) 3.58579 + 8.65685i 0.176874 + 0.427011i
\(412\) 18.9706 18.9706i 0.934613 0.934613i
\(413\) 6.41421 + 2.65685i 0.315623 + 0.130735i
\(414\) −28.1421 −1.38311
\(415\) 0 0
\(416\) −4.00000 1.65685i −0.196116 0.0812340i
\(417\) 10.9289 0.535192
\(418\) −25.3137 −1.23813
\(419\) 12.6066 + 5.22183i 0.615873 + 0.255103i 0.668737 0.743499i \(-0.266835\pi\)
−0.0528644 + 0.998602i \(0.516835\pi\)
\(420\) 0 0
\(421\) 6.29289 + 15.1924i 0.306697 + 0.740432i 0.999808 + 0.0196009i \(0.00623955\pi\)
−0.693111 + 0.720831i \(0.743760\pi\)
\(422\) 25.7279 + 10.6569i 1.25242 + 0.518768i
\(423\) 0.585786 0.585786i 0.0284819 0.0284819i
\(424\) −1.31371 3.17157i −0.0637993 0.154025i
\(425\) 0 0
\(426\) −3.41421 8.24264i −0.165419 0.399357i
\(427\) −2.41421 + 1.00000i −0.116832 + 0.0483934i
\(428\) −8.24264 + 3.41421i −0.398423 + 0.165032i
\(429\) 1.00000 2.41421i 0.0482805 0.116559i
\(430\) 0 0
\(431\) 12.3431i 0.594548i −0.954792 0.297274i \(-0.903922\pi\)
0.954792 0.297274i \(-0.0960775\pi\)
\(432\) −6.34315 15.3137i −0.305185 0.736781i
\(433\) 15.5147i 0.745590i 0.927914 + 0.372795i \(0.121600\pi\)
−0.927914 + 0.372795i \(0.878400\pi\)
\(434\) 5.65685 + 5.65685i 0.271538 + 0.271538i
\(435\) 0 0
\(436\) 11.4142 27.5563i 0.546642 1.31971i
\(437\) −30.5563 + 12.6569i −1.46171 + 0.605459i
\(438\) 9.89949 4.10051i 0.473016 0.195930i
\(439\) −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
\(441\) 8.53553 8.53553i 0.406454 0.406454i
\(442\) 1.17157 2.82843i 0.0557260 0.134535i
\(443\) −0.606602 1.46447i −0.0288205 0.0695789i 0.908814 0.417201i \(-0.136989\pi\)
−0.937635 + 0.347623i \(0.886989\pi\)
\(444\) 1.17157i 0.0556004i
\(445\) 0 0
\(446\) 29.6569i 1.40429i
\(447\) −12.9289 −0.611518
\(448\) 8.00000 8.00000i 0.377964 0.377964i
\(449\) −19.4558 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(450\) 0 0
\(451\) 1.00000 + 0.414214i 0.0470882 + 0.0195046i
\(452\) 12.6863i 0.596713i
\(453\) −0.615224 1.48528i −0.0289057 0.0697846i
\(454\) 10.8995 26.3137i 0.511539 1.23496i
\(455\) 0 0
\(456\) −6.14214 6.14214i −0.287632 0.287632i
\(457\) 7.48528 + 7.48528i 0.350147 + 0.350147i 0.860164 0.510017i \(-0.170361\pi\)
−0.510017 + 0.860164i \(0.670361\pi\)
\(458\) 31.4853 13.0416i 1.47121 0.609395i
\(459\) 10.8284 4.48528i 0.505428 0.209355i
\(460\) 0 0
\(461\) 0.636039 1.53553i 0.0296233 0.0715169i −0.908376 0.418155i \(-0.862677\pi\)
0.937999 + 0.346638i \(0.112677\pi\)
\(462\) 4.82843 + 4.82843i 0.224639 + 0.224639i
\(463\) 22.9706i 1.06753i −0.845632 0.533766i \(-0.820776\pi\)
0.845632 0.533766i \(-0.179224\pi\)
\(464\) −12.4853 5.17157i −0.579615 0.240084i
\(465\) 0 0
\(466\) −3.75736 + 3.75736i −0.174056 + 0.174056i
\(467\) 9.09188 21.9497i 0.420722 1.01571i −0.561413 0.827536i \(-0.689742\pi\)
0.982135 0.188177i \(-0.0602580\pi\)
\(468\) −3.41421 + 1.41421i −0.157822 + 0.0653720i
\(469\) −7.82843 + 3.24264i −0.361483 + 0.149731i
\(470\) 0 0
\(471\) −1.00000 1.00000i −0.0460776 0.0460776i
\(472\) −12.8284 + 5.31371i −0.590476 + 0.244583i
\(473\) 16.0711 16.0711i 0.738948 0.738948i
\(474\) −6.00000 2.48528i −0.275589 0.114153i
\(475\) 0 0
\(476\) 5.65685 + 5.65685i 0.259281 + 0.259281i
\(477\) −2.70711 1.12132i −0.123950 0.0513417i
\(478\) 7.51472 0.343715
\(479\) 28.9706 1.32370 0.661849 0.749637i \(-0.269772\pi\)
0.661849 + 0.749637i \(0.269772\pi\)
\(480\) 0 0
\(481\) 0.585786 0.0267096
\(482\) 12.0000 0.546585
\(483\) 8.24264 + 3.41421i 0.375053 + 0.155352i
\(484\) −12.5858 + 12.5858i −0.572081 + 0.572081i
\(485\) 0 0
\(486\) −20.3137 8.41421i −0.921449 0.381676i
\(487\) 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 4.82843i 0.0905357 0.218573i
\(489\) −0.272078 0.272078i −0.0123038 0.0123038i
\(490\) 0 0
\(491\) 39.3345 16.2929i 1.77514 0.735288i 0.781343 0.624102i \(-0.214535\pi\)
0.993800 0.111186i \(-0.0354648\pi\)
\(492\) 0.142136 + 0.343146i 0.00640797 + 0.0154702i
\(493\) 3.65685 8.82843i 0.164696 0.397612i
\(494\) −3.07107 + 3.07107i −0.138174 + 0.138174i
\(495\) 0 0
\(496\) −16.0000 −0.718421
\(497\) 11.6569i 0.522881i
\(498\) −3.75736 3.75736i −0.168371 0.168371i
\(499\) −0.949747 + 2.29289i −0.0425165 + 0.102644i −0.943711 0.330771i \(-0.892691\pi\)
0.901195 + 0.433415i \(0.142691\pi\)
\(500\) 0 0
\(501\) −14.6569 + 6.07107i −0.654820 + 0.271235i
\(502\) −22.5563 + 9.34315i −1.00674 + 0.417005i
\(503\) 11.1421 + 11.1421i 0.496803 + 0.496803i 0.910441 0.413638i \(-0.135742\pi\)
−0.413638 + 0.910441i \(0.635742\pi\)
\(504\) 9.65685i 0.430150i
\(505\) 0 0
\(506\) −19.8995 + 48.0416i −0.884640 + 2.13571i
\(507\) 3.63604 + 8.77817i 0.161482 + 0.389852i
\(508\) 25.9411 1.15095
\(509\) −26.0919 10.8076i −1.15650 0.479039i −0.279793 0.960060i \(-0.590266\pi\)
−0.876709 + 0.481021i \(0.840266\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 22.6274i 1.00000i
\(513\) −16.6274 −0.734118
\(514\) 8.48528i 0.374270i
\(515\) 0 0
\(516\) 7.79899 0.343331
\(517\) −0.585786 1.41421i −0.0257629 0.0621970i
\(518\) −0.585786 + 1.41421i −0.0257380 + 0.0621370i
\(519\) −4.41421 + 4.41421i −0.193762 + 0.193762i
\(520\) 0 0
\(521\) 3.34315 + 3.34315i 0.146466 + 0.146466i 0.776537 0.630071i \(-0.216974\pi\)
−0.630071 + 0.776537i \(0.716974\pi\)
\(522\) −10.6569 + 4.41421i −0.466438 + 0.193205i
\(523\) −19.1924 + 7.94975i −0.839225 + 0.347618i −0.760548 0.649282i \(-0.775070\pi\)
−0.0786768 + 0.996900i \(0.525070\pi\)
\(524\) 32.7279 + 13.5563i 1.42973 + 0.592212i
\(525\) 0 0
\(526\) 8.24264 + 8.24264i 0.359396 + 0.359396i
\(527\) 11.3137i 0.492833i
\(528\) −13.6569 −0.594338
\(529\) 44.9411i 1.95396i
\(530\) 0 0
\(531\) −4.53553 + 10.9497i −0.196825 + 0.475179i
\(532\) −4.34315 10.4853i −0.188299 0.454595i
\(533\) 0.171573 0.0710678i 0.00743165 0.00307829i
\(534\) 5.07107 + 12.2426i 0.219447 + 0.529791i
\(535\) 0 0
\(536\) 6.48528 15.6569i 0.280121 0.676273i
\(537\) −2.31371 + 2.31371i −0.0998439 + 0.0998439i
\(538\) 31.1421 + 12.8995i 1.34263 + 0.556137i
\(539\) −8.53553 20.6066i −0.367651 0.887589i
\(540\) 0 0
\(541\) −27.2635 11.2929i −1.17215 0.485519i −0.290246 0.956952i \(-0.593737\pi\)
−0.881902 + 0.471433i \(0.843737\pi\)
\(542\) −25.4558 −1.09342
\(543\) 13.4142 0.575659
\(544\) −16.0000 −0.685994
\(545\) 0 0
\(546\) 1.17157 0.0501387
\(547\) 17.5355 + 7.26346i 0.749765 + 0.310563i 0.724646 0.689122i \(-0.242003\pi\)
0.0251195 + 0.999684i \(0.492003\pi\)
\(548\) −17.3137 17.3137i −0.739605 0.739605i
\(549\) −1.70711 4.12132i −0.0728575 0.175894i
\(550\) 0 0
\(551\) −9.58579 + 9.58579i −0.408368 + 0.408368i
\(552\) −16.4853 + 6.82843i −0.701660 + 0.290637i
\(553\) −6.00000 6.00000i −0.255146 0.255146i
\(554\) −1.00000 2.41421i −0.0424859 0.102570i
\(555\) 0 0
\(556\) −26.3848 + 10.9289i −1.11896 + 0.463490i
\(557\) −15.1213 + 36.5061i −0.640711 + 1.54681i 0.185012 + 0.982736i \(0.440768\pi\)
−0.825722 + 0.564077i \(0.809232\pi\)
\(558\) −9.65685 + 9.65685i −0.408807 + 0.408807i
\(559\) 3.89949i 0.164931i
\(560\) 0 0
\(561\) 9.65685i 0.407713i
\(562\) −16.7279 16.7279i −0.705625 0.705625i
\(563\) −7.87868 + 19.0208i −0.332047 + 0.801632i 0.666383 + 0.745610i \(0.267842\pi\)
−0.998430 + 0.0560220i \(0.982158\pi\)
\(564\) 0.201010 0.485281i 0.00846405 0.0204340i
\(565\) 0 0
\(566\) 19.7279 8.17157i 0.829226 0.343477i
\(567\) −4.07107 4.07107i −0.170969 0.170969i
\(568\) 16.4853 + 16.4853i 0.691707 + 0.691707i
\(569\) 14.6569 14.6569i 0.614447 0.614447i −0.329654 0.944102i \(-0.606932\pi\)
0.944102 + 0.329654i \(0.106932\pi\)
\(570\) 0 0
\(571\) −2.70711 6.53553i −0.113289 0.273504i 0.857058 0.515220i \(-0.172290\pi\)
−0.970347 + 0.241716i \(0.922290\pi\)
\(572\) 6.82843i 0.285511i
\(573\) −8.48528 3.51472i −0.354478 0.146829i
\(574\) 0.485281i 0.0202553i
\(575\) 0 0
\(576\) 13.6569 + 13.6569i 0.569036 + 0.569036i
\(577\) −18.9706 −0.789755 −0.394877 0.918734i \(-0.629213\pi\)
−0.394877 + 0.918734i \(0.629213\pi\)
\(578\) 12.7279i 0.529412i
\(579\) 1.07107 + 0.443651i 0.0445121 + 0.0184375i
\(580\) 0 0
\(581\) −2.65685 6.41421i −0.110225 0.266106i
\(582\) −7.65685 + 18.4853i −0.317387 + 0.766240i
\(583\) −3.82843 + 3.82843i −0.158557 + 0.158557i
\(584\) −19.7990 + 19.7990i −0.819288 + 0.819288i
\(585\) 0 0
\(586\) 32.7990 13.5858i 1.35491 0.561224i
\(587\) 12.6066 5.22183i 0.520330 0.215528i −0.107032 0.994256i \(-0.534135\pi\)
0.627362 + 0.778728i \(0.284135\pi\)
\(588\) 2.92893 7.07107i 0.120787 0.291606i
\(589\) −6.14214 + 14.8284i −0.253082 + 0.610995i
\(590\) 0 0
\(591\) 9.27208i 0.381402i
\(592\) −1.17157 2.82843i −0.0481513 0.116248i
\(593\) 28.2843i 1.16150i 0.814083 + 0.580748i \(0.197240\pi\)
−0.814083 + 0.580748i \(0.802760\pi\)
\(594\) −18.4853 + 18.4853i −0.758460 + 0.758460i
\(595\) 0 0
\(596\) 31.2132 12.9289i 1.27854 0.529590i
\(597\) −15.9706 + 6.61522i −0.653632 + 0.270743i
\(598\) 3.41421 + 8.24264i 0.139618 + 0.337067i
\(599\) −26.6569 26.6569i −1.08917 1.08917i −0.995614 0.0935555i \(-0.970177\pi\)
−0.0935555 0.995614i \(-0.529823\pi\)
\(600\) 0 0
\(601\) −21.9706 + 21.9706i −0.896198 + 0.896198i −0.995097 0.0988995i \(-0.968468\pi\)
0.0988995 + 0.995097i \(0.468468\pi\)
\(602\) 9.41421 + 3.89949i 0.383695 + 0.158932i
\(603\) −5.53553 13.3640i −0.225424 0.544223i
\(604\) 2.97056 + 2.97056i 0.120870 + 0.120870i
\(605\) 0 0
\(606\) 3.85786 0.156715
\(607\) 32.9706 1.33823 0.669117 0.743157i \(-0.266673\pi\)
0.669117 + 0.743157i \(0.266673\pi\)
\(608\) 20.9706 + 8.68629i 0.850469 + 0.352276i
\(609\) 3.65685 0.148183
\(610\) 0 0
\(611\) −0.242641 0.100505i −0.00981619 0.00406600i
\(612\) −9.65685 + 9.65685i −0.390355 + 0.390355i
\(613\) −1.32233 3.19239i −0.0534084 0.128939i 0.894923 0.446220i \(-0.147230\pi\)
−0.948332 + 0.317281i \(0.897230\pi\)
\(614\) 23.7279 + 9.82843i 0.957581 + 0.396643i
\(615\) 0 0
\(616\) −16.4853 6.82843i −0.664211 0.275125i
\(617\) −22.7990 22.7990i −0.917853 0.917853i 0.0790202 0.996873i \(-0.474821\pi\)
−0.996873 + 0.0790202i \(0.974821\pi\)
\(618\) −5.55635 13.4142i −0.223509 0.539599i
\(619\) −21.7782 + 9.02082i −0.875339 + 0.362577i −0.774687 0.632345i \(-0.782093\pi\)
−0.100651 + 0.994922i \(0.532093\pi\)
\(620\) 0 0
\(621\) −13.0711 + 31.5563i −0.524524 + 1.26631i
\(622\) 3.75736 3.75736i 0.150656 0.150656i
\(623\) 17.3137i 0.693659i
\(624\) −1.65685 + 1.65685i −0.0663273 + 0.0663273i
\(625\) 0 0
\(626\) 10.5858 + 10.5858i 0.423093 + 0.423093i
\(627\) −5.24264 + 12.6569i −0.209371 + 0.505466i
\(628\) 3.41421 + 1.41421i 0.136242 + 0.0564333i
\(629\) 2.00000 0.828427i 0.0797452 0.0330316i
\(630\) 0 0
\(631\) 32.4558 + 32.4558i 1.29205 + 1.29205i 0.933519 + 0.358528i \(0.116721\pi\)
0.358528 + 0.933519i \(0.383279\pi\)
\(632\) 16.9706 0.675053
\(633\) 10.6569 10.6569i 0.423572 0.423572i
\(634\) 10.1716 24.5563i 0.403965 0.975257i
\(635\) 0 0
\(636\) −1.85786 −0.0736691
\(637\) −3.53553 1.46447i −0.140083 0.0580243i
\(638\) 21.3137i 0.843818i
\(639\) 19.8995 0.787212
\(640\) 0 0
\(641\) 7.45584 0.294488 0.147244 0.989100i \(-0.452960\pi\)
0.147244 + 0.989100i \(0.452960\pi\)
\(642\) 4.82843i 0.190563i
\(643\) −11.4350 4.73654i −0.450954 0.186791i 0.145635 0.989338i \(-0.453478\pi\)
−0.596588 + 0.802547i \(0.703478\pi\)
\(644\) −23.3137 −0.918689
\(645\) 0 0
\(646\) −6.14214 + 14.8284i −0.241659 + 0.583417i
\(647\) −6.17157 + 6.17157i −0.242630 + 0.242630i −0.817937 0.575308i \(-0.804882\pi\)
0.575308 + 0.817937i \(0.304882\pi\)
\(648\) 11.5147 0.452341
\(649\) 15.4853 + 15.4853i 0.607850 + 0.607850i
\(650\) 0 0
\(651\) 4.00000 1.65685i 0.156772 0.0649372i
\(652\) 0.928932 + 0.384776i 0.0363798 + 0.0150690i
\(653\) −2.09188 + 5.05025i −0.0818617 + 0.197632i −0.959511 0.281672i \(-0.909111\pi\)
0.877649 + 0.479304i \(0.159111\pi\)
\(654\) −11.4142 11.4142i −0.446331 0.446331i
\(655\) 0 0
\(656\) −0.686292 0.686292i −0.0267952 0.0267952i
\(657\) 23.8995i 0.932408i
\(658\) 0.485281 0.485281i 0.0189182 0.0189182i
\(659\) −10.1213 + 24.4350i −0.394271 + 0.951854i 0.594728 + 0.803927i \(0.297260\pi\)
−0.988998 + 0.147926i \(0.952740\pi\)
\(660\) 0 0
\(661\) −41.7487 + 17.2929i −1.62384 + 0.672616i −0.994521 0.104534i \(-0.966665\pi\)
−0.629316 + 0.777149i \(0.716665\pi\)
\(662\) −0.757359 1.82843i −0.0294356 0.0710638i
\(663\) −1.17157 1.17157i −0.0455001 0.0455001i
\(664\) 12.8284 + 5.31371i 0.497840 + 0.206212i
\(665\) 0 0
\(666\) −2.41421 1.00000i −0.0935489 0.0387492i
\(667\) 10.6569 + 25.7279i 0.412635 + 0.996189i
\(668\) 29.3137 29.3137i 1.13418 1.13418i
\(669\) 14.8284 + 6.14214i 0.573300 + 0.237469i
\(670\) 0 0
\(671\) −8.24264 −0.318204
\(672\) −2.34315 5.65685i −0.0903888 0.218218i
\(673\) −22.4853 −0.866744 −0.433372 0.901215i \(-0.642676\pi\)
−0.433372 + 0.901215i \(0.642676\pi\)
\(674\) −24.0000 −0.924445
\(675\) 0 0
\(676\) −17.5563 17.5563i −0.675244 0.675244i
\(677\) −15.6066 37.6777i −0.599810 1.44807i −0.873775 0.486331i \(-0.838335\pi\)
0.273964 0.961740i \(-0.411665\pi\)
\(678\) −6.34315 2.62742i −0.243607 0.100905i
\(679\) −18.4853 + 18.4853i −0.709400 + 0.709400i
\(680\) 0 0
\(681\) −10.8995 10.8995i −0.417670 0.417670i
\(682\) 9.65685 + 23.3137i 0.369780 + 0.892728i
\(683\) 10.1213 4.19239i 0.387282 0.160417i −0.180543 0.983567i \(-0.557785\pi\)
0.567824 + 0.823150i \(0.307785\pi\)
\(684\) 17.8995 7.41421i 0.684404 0.283490i
\(685\) 0 0
\(686\) 16.9706 16.9706i 0.647939 0.647939i
\(687\) 18.4437i 0.703669i
\(688\) −18.8284 + 7.79899i −0.717827 + 0.297334i
\(689\) 0.928932i 0.0353895i
\(690\) 0 0
\(691\) 12.5061 30.1924i 0.475754 1.14857i −0.485828 0.874055i \(-0.661482\pi\)
0.961582 0.274518i \(-0.0885183\pi\)
\(692\) 6.24264 15.0711i 0.237310 0.572916i
\(693\) −14.0711 + 5.82843i −0.534516 + 0.221404i
\(694\) 5.58579 2.31371i 0.212034 0.0878272i
\(695\) 0 0
\(696\) −5.17157 + 5.17157i −0.196028 + 0.196028i
\(697\) 0.485281 0.485281i 0.0183813 0.0183813i
\(698\) −14.4558 + 34.8995i −0.547162 + 1.32097i
\(699\) 1.10051 + 2.65685i 0.0416249 + 0.100491i
\(700\) 0 0
\(701\) 2.87868 + 1.19239i 0.108726 + 0.0450359i 0.436383 0.899761i \(-0.356259\pi\)
−0.327657 + 0.944797i \(0.606259\pi\)
\(702\) 4.48528i 0.169286i
\(703\) −3.07107 −0.115828
\(704\) 32.9706 13.6569i 1.24262 0.514712i
\(705\) 0 0
\(706\) 8.48528i 0.319348i
\(707\) 4.65685 + 1.92893i 0.175139 + 0.0725450i
\(708\) 7.51472i 0.282420i
\(709\) 8.77817 + 21.1924i 0.329671 + 0.795897i 0.998616 + 0.0525851i \(0.0167461\pi\)
−0.668945 + 0.743312i \(0.733254\pi\)
\(710\) 0 0
\(711\) 10.2426 10.2426i 0.384129 0.384129i
\(712\) −24.4853 24.4853i −0.917625 0.917625i
\(713\) 23.3137 + 23.3137i 0.873105 + 0.873105i
\(714\) 4.00000 1.65685i 0.149696 0.0620062i
\(715\) 0 0
\(716\) 3.27208 7.89949i 0.122283 0.295218i
\(717\) 1.55635 3.75736i 0.0581229 0.140321i
\(718\) −25.2132 25.2132i −0.940948 0.940948i
\(719\) 35.6569i 1.32978i 0.746943 + 0.664888i \(0.231521\pi\)
−0.746943 + 0.664888i \(0.768479\pi\)
\(720\) 0 0
\(721\) 18.9706i 0.706501i
\(722\) −2.89949 + 2.89949i −0.107908 + 0.107908i
\(723\) 2.48528 6.00000i 0.0924286 0.223142i
\(724\) −32.3848 + 13.4142i −1.20357 + 0.498535i
\(725\) 0 0
\(726\) 3.68629 + 8.89949i 0.136811 + 0.330291i
\(727\) 9.97056 + 9.97056i 0.369788 + 0.369788i 0.867400 0.497612i \(-0.165790\pi\)
−0.497612 + 0.867400i \(0.665790\pi\)
\(728\) −2.82843 + 1.17157i −0.104828 + 0.0434214i
\(729\) 0.221825 0.221825i 0.00821576 0.00821576i
\(730\) 0 0
\(731\) −5.51472 13.3137i −0.203969 0.492425i
\(732\) −2.00000 2.00000i −0.0739221 0.0739221i
\(733\) 33.2635 + 13.7782i 1.22861 + 0.508908i 0.900138 0.435604i \(-0.143465\pi\)
0.328475 + 0.944513i \(0.393465\pi\)
\(734\) −8.48528 −0.313197
\(735\) 0 0
\(736\) 32.9706 32.9706i 1.21531 1.21531i
\(737\) −26.7279 −0.984536
\(738\) −0.828427 −0.0304948
\(739\) 0.464466 + 0.192388i 0.0170857 + 0.00707711i 0.391210 0.920301i \(-0.372057\pi\)
−0.374124 + 0.927379i \(0.622057\pi\)
\(740\) 0 0
\(741\) 0.899495 + 2.17157i 0.0330438 + 0.0797747i
\(742\) −2.24264 0.928932i −0.0823299 0.0341022i
\(743\) −31.6274 + 31.6274i −1.16030 + 1.16030i −0.175887 + 0.984410i \(0.556279\pi\)
−0.984410 + 0.175887i \(0.943721\pi\)
\(744\) −3.31371 + 8.00000i −0.121486 + 0.293294i
\(745\) 0 0
\(746\) 6.02944 + 14.5563i 0.220753 + 0.532946i
\(747\) 10.9497 4.53553i 0.400630 0.165947i
\(748\) 9.65685 + 23.3137i 0.353090 + 0.852434i
\(749\) −2.41421 + 5.82843i −0.0882134 + 0.212966i
\(750\) 0 0
\(751\) 10.9706i 0.400322i −0.979763 0.200161i \(-0.935854\pi\)
0.979763 0.200161i \(-0.0641464\pi\)
\(752\) 1.37258i 0.0500530i
\(753\) 13.2132i 0.481516i
\(754\) 2.58579 + 2.58579i 0.0941688 + 0.0941688i
\(755\) 0 0
\(756\) −10.8284 4.48528i −0.393826 0.163128i
\(757\) 33.2635 13.7782i 1.20898 0.500776i 0.315090 0.949062i \(-0.397965\pi\)
0.893890 + 0.448285i \(0.147965\pi\)
\(758\) 46.6985 19.3431i 1.69617 0.702575i
\(759\) 19.8995 + 19.8995i 0.722306 + 0.722306i
\(760\) 0 0
\(761\) −29.8284 + 29.8284i −1.08128 + 1.08128i −0.0848892 + 0.996390i \(0.527054\pi\)
−0.996390 + 0.0848892i \(0.972946\pi\)
\(762\) 5.37258 12.9706i 0.194628 0.469874i
\(763\) −8.07107 19.4853i −0.292192 0.705415i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 24.0000i 0.867155i
\(767\) 3.75736 0.135670
\(768\) 11.3137 + 4.68629i 0.408248 + 0.169102i
\(769\) 5.51472 0.198866 0.0994329 0.995044i \(-0.468297\pi\)
0.0994329 + 0.995044i \(0.468297\pi\)
\(770\) 0 0
\(771\) −4.24264 1.75736i −0.152795 0.0632897i
\(772\) −3.02944 −0.109032
\(773\) −12.0919 29.1924i −0.434915 1.04998i −0.977681 0.210094i \(-0.932623\pi\)
0.542766 0.839884i \(-0.317377\pi\)
\(774\) −6.65685 + 16.0711i −0.239276 + 0.577663i
\(775\) 0 0
\(776\) 52.2843i 1.87690i
\(777\) 0.585786 + 0.585786i 0.0210150 + 0.0210150i
\(778\) 28.6569 11.8701i 1.02740 0.425562i
\(779\) −0.899495 + 0.372583i −0.0322278 + 0.0133492i
\(780\) 0 0
\(781\) 14.0711 33.9706i 0.503502 1.21556i