Properties

Label 784.2.x.c.165.1
Level $784$
Weight $2$
Character 784.165
Analytic conductor $6.260$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 165.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.165
Dual form 784.2.x.c.765.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +(0.366025 + 1.36603i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.366025 - 1.36603i) q^{5} -2.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +(0.366025 + 1.36603i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.366025 - 1.36603i) q^{5} -2.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.73205 + 1.00000i) q^{10} +(-1.36603 + 0.366025i) q^{11} +(0.732051 - 2.73205i) q^{12} +(1.00000 - 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.366025 + 1.36603i) q^{18} +(4.09808 + 1.09808i) q^{19} +(-2.00000 + 2.00000i) q^{20} -2.00000i q^{22} +(5.19615 - 3.00000i) q^{23} +(3.46410 + 2.00000i) q^{24} +(2.59808 + 1.50000i) q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 + 4.00000i) q^{27} +(3.00000 - 3.00000i) q^{29} +(-0.732051 + 2.73205i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-2.00000 - 2.00000i) q^{34} -2.00000 q^{36} +(1.09808 - 4.09808i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(1.73205 + 1.00000i) q^{39} +(-2.00000 - 3.46410i) q^{40} +(5.00000 + 5.00000i) q^{43} +(2.73205 + 0.732051i) q^{44} +(-0.366025 - 1.36603i) q^{45} +(2.19615 + 8.19615i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-4.00000 + 4.00000i) q^{48} +(-3.00000 + 3.00000i) q^{50} +(-2.73205 - 0.732051i) q^{51} +(-2.73205 + 0.732051i) q^{52} +(6.83013 - 1.83013i) q^{53} +(-6.92820 + 4.00000i) q^{54} +2.00000i q^{55} +6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(-4.09808 + 1.09808i) q^{59} +(-3.46410 - 2.00000i) q^{60} +(-12.2942 - 3.29423i) q^{61} +(-8.00000 - 8.00000i) q^{62} -8.00000i q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.73205 - 0.732051i) q^{66} +(-1.83013 - 6.83013i) q^{67} +(3.46410 - 2.00000i) q^{68} +(6.00000 + 6.00000i) q^{69} -10.0000i q^{71} +(0.732051 - 2.73205i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(5.19615 + 3.00000i) q^{74} +(-1.09808 + 4.09808i) q^{75} +(-6.00000 - 6.00000i) q^{76} +(-2.00000 + 2.00000i) q^{78} +(5.46410 - 1.46410i) q^{80} +(-2.50000 + 4.33013i) q^{81} +(1.00000 - 1.00000i) q^{83} +(2.00000 + 2.00000i) q^{85} +(-8.66025 + 5.00000i) q^{86} +(5.19615 + 3.00000i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(-3.46410 + 2.00000i) q^{89} +2.00000 q^{90} -12.0000 q^{92} +(-10.9282 - 2.92820i) q^{93} +(-10.9282 + 2.92820i) q^{94} +(3.00000 - 5.19615i) q^{95} +(-4.00000 - 6.92820i) q^{96} +2.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} + 8 q^{8} - 2 q^{11} - 4 q^{12} + 4 q^{13} + 8 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} + 4 q^{26} + 16 q^{27} + 12 q^{29} + 4 q^{30} - 16 q^{31} - 8 q^{32} - 4 q^{33} - 8 q^{34} - 8 q^{36} - 6 q^{37} - 12 q^{38} - 8 q^{40} + 20 q^{43} + 4 q^{44} + 2 q^{45} - 12 q^{46} + 16 q^{47} - 16 q^{48} - 12 q^{50} - 4 q^{51} - 4 q^{52} + 10 q^{53} + 12 q^{58} - 6 q^{59} - 18 q^{61} - 32 q^{62} - 4 q^{65} + 4 q^{66} + 10 q^{67} + 24 q^{69} - 4 q^{72} + 6 q^{75} - 24 q^{76} - 8 q^{78} + 8 q^{80} - 10 q^{81} + 4 q^{83} + 8 q^{85} - 8 q^{88} + 8 q^{90} - 48 q^{92} - 16 q^{93} - 16 q^{94} + 12 q^{95} - 16 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 0.366025 + 1.36603i 0.211325 + 0.788675i 0.987428 + 0.158069i \(0.0505269\pi\)
−0.776103 + 0.630606i \(0.782806\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 0.366025 1.36603i 0.163692 0.610905i −0.834512 0.550990i \(-0.814250\pi\)
0.998203 0.0599153i \(-0.0190830\pi\)
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0.866025 0.500000i 0.288675 0.166667i
\(10\) 1.73205 + 1.00000i 0.547723 + 0.316228i
\(11\) −1.36603 + 0.366025i −0.411872 + 0.110361i −0.458804 0.888537i \(-0.651722\pi\)
0.0469323 + 0.998898i \(0.485055\pi\)
\(12\) 0.732051 2.73205i 0.211325 0.788675i
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0.366025 + 1.36603i 0.0862730 + 0.321975i
\(19\) 4.09808 + 1.09808i 0.940163 + 0.251916i 0.696183 0.717864i \(-0.254880\pi\)
0.243980 + 0.969780i \(0.421547\pi\)
\(20\) −2.00000 + 2.00000i −0.447214 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 3.46410 + 2.00000i 0.707107 + 0.408248i
\(25\) 2.59808 + 1.50000i 0.519615 + 0.300000i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) 3.00000 3.00000i 0.557086 0.557086i −0.371391 0.928477i \(-0.621119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) −0.732051 + 2.73205i −0.133654 + 0.498802i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) −2.00000 2.00000i −0.342997 0.342997i
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 1.09808 4.09808i 0.180523 0.673720i −0.815022 0.579430i \(-0.803275\pi\)
0.995545 0.0942898i \(-0.0300580\pi\)
\(38\) −3.00000 + 5.19615i −0.486664 + 0.842927i
\(39\) 1.73205 + 1.00000i 0.277350 + 0.160128i
\(40\) −2.00000 3.46410i −0.316228 0.547723i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.00000 + 5.00000i 0.762493 + 0.762493i 0.976772 0.214280i \(-0.0687403\pi\)
−0.214280 + 0.976772i \(0.568740\pi\)
\(44\) 2.73205 + 0.732051i 0.411872 + 0.110361i
\(45\) −0.366025 1.36603i −0.0545638 0.203635i
\(46\) 2.19615 + 8.19615i 0.323805 + 1.20846i
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) −4.00000 + 4.00000i −0.577350 + 0.577350i
\(49\) 0 0
\(50\) −3.00000 + 3.00000i −0.424264 + 0.424264i
\(51\) −2.73205 0.732051i −0.382564 0.102508i
\(52\) −2.73205 + 0.732051i −0.378867 + 0.101517i
\(53\) 6.83013 1.83013i 0.938190 0.251387i 0.242846 0.970065i \(-0.421919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) −6.92820 + 4.00000i −0.942809 + 0.544331i
\(55\) 2.00000i 0.269680i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) −4.09808 + 1.09808i −0.533524 + 0.142957i −0.515515 0.856880i \(-0.672399\pi\)
−0.0180090 + 0.999838i \(0.505733\pi\)
\(60\) −3.46410 2.00000i −0.447214 0.258199i
\(61\) −12.2942 3.29423i −1.57411 0.421783i −0.637017 0.770850i \(-0.719832\pi\)
−0.937098 + 0.349067i \(0.886499\pi\)
\(62\) −8.00000 8.00000i −1.01600 1.01600i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 2.73205 0.732051i 0.336292 0.0901092i
\(67\) −1.83013 6.83013i −0.223586 0.834433i −0.982966 0.183786i \(-0.941165\pi\)
0.759381 0.650647i \(-0.225502\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) 6.00000 + 6.00000i 0.722315 + 0.722315i
\(70\) 0 0
\(71\) 10.0000i 1.18678i −0.804914 0.593391i \(-0.797789\pi\)
0.804914 0.593391i \(-0.202211\pi\)
\(72\) 0.732051 2.73205i 0.0862730 0.321975i
\(73\) −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i \(-0.408542\pi\)
−0.688830 + 0.724923i \(0.741875\pi\)
\(74\) 5.19615 + 3.00000i 0.604040 + 0.348743i
\(75\) −1.09808 + 4.09808i −0.126795 + 0.473205i
\(76\) −6.00000 6.00000i −0.688247 0.688247i
\(77\) 0 0
\(78\) −2.00000 + 2.00000i −0.226455 + 0.226455i
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 5.46410 1.46410i 0.610905 0.163692i
\(81\) −2.50000 + 4.33013i −0.277778 + 0.481125i
\(82\) 0 0
\(83\) 1.00000 1.00000i 0.109764 0.109764i −0.650092 0.759856i \(-0.725269\pi\)
0.759856 + 0.650092i \(0.225269\pi\)
\(84\) 0 0
\(85\) 2.00000 + 2.00000i 0.216930 + 0.216930i
\(86\) −8.66025 + 5.00000i −0.933859 + 0.539164i
\(87\) 5.19615 + 3.00000i 0.557086 + 0.321634i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) −3.46410 + 2.00000i −0.367194 + 0.212000i −0.672232 0.740341i \(-0.734664\pi\)
0.305038 + 0.952340i \(0.401331\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −12.0000 −1.25109
\(93\) −10.9282 2.92820i −1.13320 0.303641i
\(94\) −10.9282 + 2.92820i −1.12716 + 0.302021i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) −4.00000 6.92820i −0.408248 0.707107i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −1.00000 + 1.00000i −0.100504 + 0.100504i
\(100\) −3.00000 5.19615i −0.300000 0.519615i
\(101\) 15.0263 4.02628i 1.49517 0.400630i 0.583691 0.811976i \(-0.301608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) −5.19615 + 3.00000i −0.511992 + 0.295599i −0.733652 0.679525i \(-0.762186\pi\)
0.221660 + 0.975124i \(0.428852\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 0 0
\(106\) 10.0000i 0.971286i
\(107\) −2.56218 + 9.56218i −0.247695 + 0.924411i 0.724315 + 0.689470i \(0.242156\pi\)
−0.972010 + 0.234941i \(0.924510\pi\)
\(108\) −2.92820 10.9282i −0.281766 1.05157i
\(109\) 1.09808 + 4.09808i 0.105177 + 0.392525i 0.998365 0.0571579i \(-0.0182038\pi\)
−0.893189 + 0.449682i \(0.851537\pi\)
\(110\) −2.73205 0.732051i −0.260491 0.0697983i
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −8.19615 2.19615i −0.767640 0.205689i
\(115\) −2.19615 8.19615i −0.204792 0.764295i
\(116\) −8.19615 + 2.19615i −0.760994 + 0.203908i
\(117\) 0.366025 1.36603i 0.0338391 0.126289i
\(118\) 6.00000i 0.552345i
\(119\) 0 0
\(120\) 4.00000 4.00000i 0.365148 0.365148i
\(121\) −7.79423 + 4.50000i −0.708566 + 0.409091i
\(122\) 9.00000 15.5885i 0.814822 1.41131i
\(123\) 0 0
\(124\) 13.8564 8.00000i 1.24434 0.718421i
\(125\) 8.00000 8.00000i 0.715542 0.715542i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 2.73205 0.732051i 0.239617 0.0642051i
\(131\) 15.0263 + 4.02628i 1.31285 + 0.351778i 0.846296 0.532714i \(-0.178828\pi\)
0.466557 + 0.884491i \(0.345494\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 0 0
\(134\) 10.0000 0.863868
\(135\) 6.92820 4.00000i 0.596285 0.344265i
\(136\) 1.46410 + 5.46410i 0.125546 + 0.468543i
\(137\) −6.92820 4.00000i −0.591916 0.341743i 0.173939 0.984757i \(-0.444351\pi\)
−0.765855 + 0.643013i \(0.777684\pi\)
\(138\) −10.3923 + 6.00000i −0.884652 + 0.510754i
\(139\) 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i \(-0.192414\pi\)
−0.568338 + 0.822795i \(0.692414\pi\)
\(140\) 0 0
\(141\) −8.00000 + 8.00000i −0.673722 + 0.673722i
\(142\) 13.6603 + 3.66025i 1.14634 + 0.307162i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 3.46410 + 2.00000i 0.288675 + 0.166667i
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 4.00000 4.00000i 0.331042 0.331042i
\(147\) 0 0
\(148\) −6.00000 + 6.00000i −0.493197 + 0.493197i
\(149\) 2.56218 9.56218i 0.209902 0.783364i −0.777997 0.628267i \(-0.783764\pi\)
0.987899 0.155097i \(-0.0495689\pi\)
\(150\) −5.19615 3.00000i −0.424264 0.244949i
\(151\) 8.66025 + 5.00000i 0.704761 + 0.406894i 0.809118 0.587646i \(-0.199945\pi\)
−0.104357 + 0.994540i \(0.533278\pi\)
\(152\) 10.3923 6.00000i 0.842927 0.486664i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 8.00000 + 8.00000i 0.642575 + 0.642575i
\(156\) −2.00000 3.46410i −0.160128 0.277350i
\(157\) −5.49038 20.4904i −0.438180 1.63531i −0.733340 0.679862i \(-0.762039\pi\)
0.295160 0.955448i \(-0.404627\pi\)
\(158\) 0 0
\(159\) 5.00000 + 8.66025i 0.396526 + 0.686803i
\(160\) 8.00000i 0.632456i
\(161\) 0 0
\(162\) −5.00000 5.00000i −0.392837 0.392837i
\(163\) 1.36603 + 0.366025i 0.106995 + 0.0286693i 0.311919 0.950109i \(-0.399028\pi\)
−0.204924 + 0.978778i \(0.565695\pi\)
\(164\) 0 0
\(165\) −2.73205 + 0.732051i −0.212690 + 0.0569901i
\(166\) 1.00000 + 1.73205i 0.0776151 + 0.134433i
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) −3.46410 + 2.00000i −0.265684 + 0.153393i
\(171\) 4.09808 1.09808i 0.313388 0.0839720i
\(172\) −3.66025 13.6603i −0.279092 1.04158i
\(173\) −1.36603 0.366025i −0.103857 0.0278284i 0.206516 0.978443i \(-0.433787\pi\)
−0.310373 + 0.950615i \(0.600454\pi\)
\(174\) −6.00000 + 6.00000i −0.454859 + 0.454859i
\(175\) 0 0
\(176\) −4.00000 4.00000i −0.301511 0.301511i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −1.46410 5.46410i −0.109739 0.409552i
\(179\) −6.22243 23.2224i −0.465086 1.73573i −0.656603 0.754237i \(-0.728007\pi\)
0.191516 0.981489i \(-0.438660\pi\)
\(180\) −0.732051 + 2.73205i −0.0545638 + 0.203635i
\(181\) 9.00000 + 9.00000i 0.668965 + 0.668965i 0.957476 0.288512i \(-0.0931604\pi\)
−0.288512 + 0.957476i \(0.593160\pi\)
\(182\) 0 0
\(183\) 18.0000i 1.33060i
\(184\) 4.39230 16.3923i 0.323805 1.20846i
\(185\) −5.19615 3.00000i −0.382029 0.220564i
\(186\) 8.00000 13.8564i 0.586588 1.01600i
\(187\) 0.732051 2.73205i 0.0535329 0.199787i
\(188\) 16.0000i 1.16692i
\(189\) 0 0
\(190\) 6.00000 + 6.00000i 0.435286 + 0.435286i
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 10.9282 2.92820i 0.788675 0.211325i
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) −0.732051 + 2.73205i −0.0525582 + 0.196150i
\(195\) 2.00000 2.00000i 0.143223 0.143223i
\(196\) 0 0
\(197\) −17.0000 17.0000i −1.21120 1.21120i −0.970632 0.240567i \(-0.922666\pi\)
−0.240567 0.970632i \(-0.577334\pi\)
\(198\) −1.00000 1.73205i −0.0710669 0.123091i
\(199\) 12.1244 + 7.00000i 0.859473 + 0.496217i 0.863836 0.503774i \(-0.168055\pi\)
−0.00436292 + 0.999990i \(0.501389\pi\)
\(200\) 8.19615 2.19615i 0.579555 0.155291i
\(201\) 8.66025 5.00000i 0.610847 0.352673i
\(202\) 22.0000i 1.54791i
\(203\) 0 0
\(204\) 4.00000 + 4.00000i 0.280056 + 0.280056i
\(205\) 0 0
\(206\) −2.19615 8.19615i −0.153013 0.571053i
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) 5.46410 + 1.46410i 0.378867 + 0.101517i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 + 9.00000i −0.619586 + 0.619586i −0.945425 0.325840i \(-0.894353\pi\)
0.325840 + 0.945425i \(0.394353\pi\)
\(212\) −13.6603 3.66025i −0.938190 0.251387i
\(213\) 13.6603 3.66025i 0.935985 0.250796i
\(214\) −12.1244 7.00000i −0.828804 0.478510i
\(215\) 8.66025 5.00000i 0.590624 0.340997i
\(216\) 16.0000 1.08866
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 1.46410 5.46410i 0.0989348 0.369230i
\(220\) 2.00000 3.46410i 0.134840 0.233550i
\(221\) 0.732051 + 2.73205i 0.0492431 + 0.183778i
\(222\) −2.19615 + 8.19615i −0.147396 + 0.550090i
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 2.19615 8.19615i 0.146086 0.545200i
\(227\) −5.49038 20.4904i −0.364409 1.35999i −0.868220 0.496180i \(-0.834736\pi\)
0.503810 0.863814i \(-0.331931\pi\)
\(228\) 6.00000 10.3923i 0.397360 0.688247i
\(229\) −2.56218 + 9.56218i −0.169313 + 0.631886i 0.828137 + 0.560526i \(0.189401\pi\)
−0.997451 + 0.0713609i \(0.977266\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) −3.46410 + 2.00000i −0.226941 + 0.131024i −0.609160 0.793047i \(-0.708493\pi\)
0.382219 + 0.924072i \(0.375160\pi\)
\(234\) 1.73205 + 1.00000i 0.113228 + 0.0653720i
\(235\) 10.9282 2.92820i 0.712877 0.191015i
\(236\) 8.19615 + 2.19615i 0.533524 + 0.142957i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 4.00000 + 6.92820i 0.258199 + 0.447214i
\(241\) −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) −3.29423 12.2942i −0.211761 0.790303i
\(243\) 9.56218 + 2.56218i 0.613414 + 0.164364i
\(244\) 18.0000 + 18.0000i 1.15233 + 1.15233i
\(245\) 0 0
\(246\) 0 0
\(247\) 5.19615 3.00000i 0.330623 0.190885i
\(248\) 5.85641 + 21.8564i 0.371882 + 1.38788i
\(249\) 1.73205 + 1.00000i 0.109764 + 0.0633724i
\(250\) 8.00000 + 13.8564i 0.505964 + 0.876356i
\(251\) −21.0000 21.0000i −1.32551 1.32551i −0.909243 0.416265i \(-0.863339\pi\)
−0.416265 0.909243i \(-0.636661\pi\)
\(252\) 0 0
\(253\) −6.00000 + 6.00000i −0.377217 + 0.377217i
\(254\) −2.92820 + 10.9282i −0.183732 + 0.685696i
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −11.0000 19.0526i −0.686161 1.18847i −0.973070 0.230508i \(-0.925961\pi\)
0.286909 0.957958i \(-0.407372\pi\)
\(258\) −10.0000 10.0000i −0.622573 0.622573i
\(259\) 0 0
\(260\) 4.00000i 0.248069i
\(261\) 1.09808 4.09808i 0.0679692 0.253665i
\(262\) −11.0000 + 19.0526i −0.679582 + 1.17707i
\(263\) −5.19615 3.00000i −0.320408 0.184988i 0.331166 0.943572i \(-0.392558\pi\)
−0.651575 + 0.758585i \(0.725891\pi\)
\(264\) −5.46410 1.46410i −0.336292 0.0901092i
\(265\) 10.0000i 0.614295i
\(266\) 0 0
\(267\) −4.00000 4.00000i −0.244796 0.244796i
\(268\) −3.66025 + 13.6603i −0.223586 + 0.834433i
\(269\) −1.09808 4.09808i −0.0669509 0.249864i 0.924337 0.381577i \(-0.124619\pi\)
−0.991288 + 0.131713i \(0.957952\pi\)
\(270\) 2.92820 + 10.9282i 0.178205 + 0.665069i
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 8.00000 8.00000i 0.483298 0.483298i
\(275\) −4.09808 1.09808i −0.247123 0.0662165i
\(276\) −4.39230 16.3923i −0.264386 0.986701i
\(277\) −4.09808 + 1.09808i −0.246230 + 0.0659770i −0.379823 0.925059i \(-0.624015\pi\)
0.133593 + 0.991036i \(0.457348\pi\)
\(278\) −5.19615 + 3.00000i −0.311645 + 0.179928i
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) −8.00000 13.8564i −0.476393 0.825137i
\(283\) −20.4904 + 5.49038i −1.21803 + 0.326369i −0.809907 0.586559i \(-0.800482\pi\)
−0.408120 + 0.912928i \(0.633816\pi\)
\(284\) −10.0000 + 17.3205i −0.593391 + 1.02778i
\(285\) 8.19615 + 2.19615i 0.485498 + 0.130089i
\(286\) −2.00000 2.00000i −0.118262 0.118262i
\(287\) 0 0
\(288\) −4.00000 + 4.00000i −0.235702 + 0.235702i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 8.19615 2.19615i 0.481295 0.128963i
\(291\) 0.732051 + 2.73205i 0.0429136 + 0.160156i
\(292\) 4.00000 + 6.92820i 0.234082 + 0.405442i
\(293\) −15.0000 15.0000i −0.876309 0.876309i 0.116841 0.993151i \(-0.462723\pi\)
−0.993151 + 0.116841i \(0.962723\pi\)
\(294\) 0 0
\(295\) 6.00000i 0.349334i
\(296\) −6.00000 10.3923i −0.348743 0.604040i
\(297\) −6.92820 4.00000i −0.402015 0.232104i
\(298\) 12.1244 + 7.00000i 0.702345 + 0.405499i
\(299\) 2.19615 8.19615i 0.127007 0.473996i
\(300\) 6.00000 6.00000i 0.346410 0.346410i
\(301\) 0 0
\(302\) −10.0000 + 10.0000i −0.575435 + 0.575435i
\(303\) 11.0000 + 19.0526i 0.631933 + 1.09454i
\(304\) 4.39230 + 16.3923i 0.251916 + 0.940163i
\(305\) −9.00000 + 15.5885i −0.515339 + 0.892592i
\(306\) −2.73205 0.732051i −0.156181 0.0418486i
\(307\) 5.00000 5.00000i 0.285365 0.285365i −0.549879 0.835244i \(-0.685326\pi\)
0.835244 + 0.549879i \(0.185326\pi\)
\(308\) 0 0
\(309\) −6.00000 6.00000i −0.341328 0.341328i
\(310\) −13.8564 + 8.00000i −0.786991 + 0.454369i
\(311\) 25.9808 + 15.0000i 1.47323 + 0.850572i 0.999546 0.0301210i \(-0.00958925\pi\)
0.473688 + 0.880693i \(0.342923\pi\)
\(312\) 5.46410 1.46410i 0.309344 0.0828884i
\(313\) −13.8564 + 8.00000i −0.783210 + 0.452187i −0.837567 0.546335i \(-0.816023\pi\)
0.0543564 + 0.998522i \(0.482689\pi\)
\(314\) 30.0000 1.69300
\(315\) 0 0
\(316\) 0 0
\(317\) 6.83013 + 1.83013i 0.383618 + 0.102790i 0.445474 0.895295i \(-0.353035\pi\)
−0.0618557 + 0.998085i \(0.519702\pi\)
\(318\) −13.6603 + 3.66025i −0.766029 + 0.205257i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −10.9282 2.92820i −0.610905 0.163692i
\(321\) −14.0000 −0.781404
\(322\) 0 0
\(323\) −6.00000 + 6.00000i −0.333849 + 0.333849i
\(324\) 8.66025 5.00000i 0.481125 0.277778i
\(325\) 4.09808 1.09808i 0.227320 0.0609103i
\(326\) −1.00000 + 1.73205i −0.0553849 + 0.0959294i
\(327\) −5.19615 + 3.00000i −0.287348 + 0.165900i
\(328\) 0 0
\(329\) 0 0
\(330\) 4.00000i 0.220193i
\(331\) 0.366025 1.36603i 0.0201186 0.0750835i −0.955137 0.296165i \(-0.904292\pi\)
0.975255 + 0.221082i \(0.0709588\pi\)
\(332\) −2.73205 + 0.732051i −0.149941 + 0.0401765i
\(333\) −1.09808 4.09808i −0.0601742 0.224573i
\(334\) −2.73205 0.732051i −0.149491 0.0400560i
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −15.0263 4.02628i −0.817322 0.219001i
\(339\) −2.19615 8.19615i −0.119279 0.445154i
\(340\) −1.46410 5.46410i −0.0794021 0.296333i
\(341\) 2.92820 10.9282i 0.158571 0.591795i
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) 20.0000 1.07833
\(345\) 10.3923 6.00000i 0.559503 0.323029i
\(346\) 1.00000 1.73205i 0.0537603 0.0931156i
\(347\) −17.7583 + 4.75833i −0.953317 + 0.255441i −0.701769 0.712404i \(-0.747606\pi\)
−0.251548 + 0.967845i \(0.580940\pi\)
\(348\) −6.00000 10.3923i −0.321634 0.557086i
\(349\) −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i \(-0.786223\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 6.92820 4.00000i 0.369274 0.213201i
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 8.19615 2.19615i 0.435621 0.116724i
\(355\) −13.6603 3.66025i −0.725011 0.194266i
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) 34.0000 1.79696
\(359\) −22.5167 + 13.0000i −1.18838 + 0.686114i −0.957939 0.286972i \(-0.907351\pi\)
−0.230445 + 0.973085i \(0.574018\pi\)
\(360\) −3.46410 2.00000i −0.182574 0.105409i
\(361\) −0.866025 0.500000i −0.0455803 0.0263158i
\(362\) −15.5885 + 9.00000i −0.819311 + 0.473029i
\(363\) −9.00000 9.00000i −0.472377 0.472377i
\(364\) 0 0
\(365\) −4.00000 + 4.00000i −0.209370 + 0.209370i
\(366\) 24.5885 + 6.58846i 1.28526 + 0.344384i
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 20.7846 + 12.0000i 1.08347 + 0.625543i
\(369\) 0 0
\(370\) 6.00000 6.00000i 0.311925 0.311925i
\(371\) 0 0
\(372\) 16.0000 + 16.0000i 0.829561 + 0.829561i
\(373\) −1.83013 + 6.83013i −0.0947604 + 0.353651i −0.996983 0.0776200i \(-0.975268\pi\)
0.902223 + 0.431271i \(0.141935\pi\)
\(374\) 3.46410 + 2.00000i 0.179124 + 0.103418i
\(375\) 13.8564 + 8.00000i 0.715542 + 0.413118i
\(376\) 21.8564 + 5.85641i 1.12716 + 0.302021i
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −3.00000 3.00000i −0.154100 0.154100i 0.625847 0.779946i \(-0.284754\pi\)
−0.779946 + 0.625847i \(0.784754\pi\)
\(380\) −10.3923 + 6.00000i −0.533114 + 0.307794i
\(381\) 2.92820 + 10.9282i 0.150016 + 0.559869i
\(382\) −10.9282 + 2.92820i −0.559136 + 0.149820i
\(383\) −8.00000 13.8564i −0.408781 0.708029i 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) 16.0000i 0.816497i
\(385\) 0 0
\(386\) −14.0000 14.0000i −0.712581 0.712581i
\(387\) 6.83013 + 1.83013i 0.347195 + 0.0930306i
\(388\) −3.46410 2.00000i −0.175863 0.101535i
\(389\) 17.7583 4.75833i 0.900383 0.241257i 0.221202 0.975228i \(-0.429002\pi\)
0.679181 + 0.733971i \(0.262335\pi\)
\(390\) 2.00000 + 3.46410i 0.101274 + 0.175412i
\(391\) 12.0000i 0.606866i
\(392\) 0 0
\(393\) 22.0000i 1.10975i
\(394\) 29.4449 17.0000i 1.48341 0.856448i
\(395\) 0 0
\(396\) 2.73205 0.732051i 0.137291 0.0367869i
\(397\) −6.83013 1.83013i −0.342794 0.0918514i 0.0833147 0.996523i \(-0.473449\pi\)
−0.426109 + 0.904672i \(0.640116\pi\)
\(398\) −14.0000 + 14.0000i −0.701757 + 0.701757i
\(399\) 0 0
\(400\) 12.0000i 0.600000i
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 3.66025 + 13.6603i 0.182557 + 0.681312i
\(403\) 2.92820 + 10.9282i 0.145864 + 0.544373i
\(404\) −30.0526 8.05256i −1.49517 0.400630i
\(405\) 5.00000 + 5.00000i 0.248452 + 0.248452i
\(406\) 0 0
\(407\) 6.00000i 0.297409i
\(408\) −6.92820 + 4.00000i −0.342997 + 0.198030i
\(409\) −13.8564 8.00000i −0.685155 0.395575i 0.116639 0.993174i \(-0.462788\pi\)
−0.801795 + 0.597600i \(0.796121\pi\)
\(410\) 0 0
\(411\) 2.92820 10.9282i 0.144438 0.539049i
\(412\) 12.0000 0.591198
\(413\) 0 0
\(414\) 6.00000 + 6.00000i 0.294884 + 0.294884i
\(415\) −1.00000 1.73205i −0.0490881 0.0850230i
\(416\) −4.00000 + 6.92820i −0.196116 + 0.339683i
\(417\) −3.00000 + 5.19615i −0.146911 + 0.254457i
\(418\) 2.19615 8.19615i 0.107417 0.400887i
\(419\) −3.00000 + 3.00000i −0.146560 + 0.146560i −0.776579 0.630020i \(-0.783047\pi\)
0.630020 + 0.776579i \(0.283047\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) −9.00000 15.5885i −0.438113 0.758834i
\(423\) 6.92820 + 4.00000i 0.336861 + 0.194487i
\(424\) 10.0000 17.3205i 0.485643 0.841158i
\(425\) −5.19615 + 3.00000i −0.252050 + 0.145521i
\(426\) 20.0000i 0.969003i
\(427\) 0 0
\(428\) 14.0000 14.0000i 0.676716 0.676716i
\(429\) −2.73205 0.732051i −0.131905 0.0353437i
\(430\) 3.66025 + 13.6603i 0.176513 + 0.658756i
\(431\) −16.0000 + 27.7128i −0.770693 + 1.33488i 0.166491 + 0.986043i \(0.446756\pi\)
−0.937184 + 0.348836i \(0.886577\pi\)
\(432\) −5.85641 + 21.8564i −0.281766 + 1.05157i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 6.00000 6.00000i 0.287678 0.287678i
\(436\) 2.19615 8.19615i 0.105177 0.392525i
\(437\) 24.5885 6.58846i 1.17623 0.315169i
\(438\) 6.92820 + 4.00000i 0.331042 + 0.191127i
\(439\) −12.1244 + 7.00000i −0.578664 + 0.334092i −0.760602 0.649218i \(-0.775096\pi\)
0.181938 + 0.983310i \(0.441763\pi\)
\(440\) 4.00000 + 4.00000i 0.190693 + 0.190693i
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) −5.49038 + 20.4904i −0.260856 + 0.973527i 0.703882 + 0.710316i \(0.251448\pi\)
−0.964738 + 0.263211i \(0.915218\pi\)
\(444\) −10.3923 6.00000i −0.493197 0.284747i
\(445\) 1.46410 + 5.46410i 0.0694051 + 0.259023i
\(446\) 8.78461 32.7846i 0.415963 1.55240i
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −1.09808 + 4.09808i −0.0517638 + 0.193185i
\(451\) 0 0
\(452\) 10.3923 + 6.00000i 0.488813 + 0.282216i
\(453\) −3.66025 + 13.6603i −0.171974 + 0.641815i
\(454\) 30.0000 1.40797
\(455\) 0 0
\(456\) 12.0000 + 12.0000i 0.561951 + 0.561951i
\(457\) −27.7128 + 16.0000i −1.29635 + 0.748448i −0.979772 0.200118i \(-0.935868\pi\)
−0.316579 + 0.948566i \(0.602534\pi\)
\(458\) −12.1244 7.00000i −0.566534 0.327089i
\(459\) −10.9282 + 2.92820i −0.510085 + 0.136677i
\(460\) −4.39230 + 16.3923i −0.204792 + 0.764295i
\(461\) −11.0000 + 11.0000i −0.512321 + 0.512321i −0.915237 0.402916i \(-0.867997\pi\)
0.402916 + 0.915237i \(0.367997\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 16.3923 + 4.39230i 0.760994 + 0.203908i
\(465\) −8.00000 + 13.8564i −0.370991 + 0.642575i
\(466\) −1.46410 5.46410i −0.0678232 0.253120i
\(467\) −6.83013 1.83013i −0.316061 0.0846882i 0.0973014 0.995255i \(-0.468979\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(468\) −2.00000 + 2.00000i −0.0924500 + 0.0924500i
\(469\) 0 0
\(470\) 16.0000i 0.738025i
\(471\) 25.9808 15.0000i 1.19713 0.691164i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −8.66025 5.00000i −0.398199 0.229900i
\(474\) 0 0
\(475\) 9.00000 + 9.00000i 0.412948 + 0.412948i
\(476\) 0 0
\(477\) 5.00000 5.00000i 0.228934 0.228934i
\(478\) 0 0
\(479\) −20.0000 + 34.6410i −0.913823 + 1.58279i −0.105208 + 0.994450i \(0.533551\pi\)
−0.808615 + 0.588338i \(0.799782\pi\)
\(480\) −10.9282 + 2.92820i −0.498802 + 0.133654i
\(481\) −3.00000 5.19615i −0.136788 0.236924i
\(482\) −18.0000 18.0000i −0.819878 0.819878i
\(483\) 0 0
\(484\) 18.0000 0.818182
\(485\) 0.732051 2.73205i 0.0332407 0.124056i
\(486\) −7.00000 + 12.1244i −0.317526 + 0.549972i
\(487\) 1.73205 + 1.00000i 0.0784867 + 0.0453143i 0.538730 0.842479i \(-0.318904\pi\)
−0.460243 + 0.887793i \(0.652238\pi\)
\(488\) −31.1769 + 18.0000i −1.41131 + 0.814822i
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) −19.0000 19.0000i −0.857458 0.857458i 0.133580 0.991038i \(-0.457353\pi\)
−0.991038 + 0.133580i \(0.957353\pi\)
\(492\) 0 0
\(493\) 2.19615 + 8.19615i 0.0989097 + 0.369136i
\(494\) 2.19615 + 8.19615i 0.0988096 + 0.368762i
\(495\) 1.00000 + 1.73205i 0.0449467 + 0.0778499i
\(496\) −32.0000 −1.43684
\(497\) 0 0
\(498\) −2.00000 + 2.00000i −0.0896221 + 0.0896221i
\(499\) −31.4186 8.41858i −1.40649 0.376868i −0.525818 0.850597i \(-0.676241\pi\)
−0.880671 + 0.473729i \(0.842908\pi\)
\(500\) −21.8564 + 5.85641i −0.977448 + 0.261906i
\(501\) −2.73205 + 0.732051i −0.122059 + 0.0327056i
\(502\) 36.3731 21.0000i 1.62341 0.937276i
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 0 0
\(505\) 22.0000i 0.978987i
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) −15.0263 + 4.02628i −0.667340 + 0.178813i
\(508\) −13.8564 8.00000i −0.614779 0.354943i
\(509\) 31.4186 + 8.41858i 1.39260 + 0.373147i 0.875683 0.482886i \(-0.160411\pi\)
0.516921 + 0.856033i \(0.327078\pi\)
\(510\) −4.00000 4.00000i −0.177123 0.177123i
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 12.0000 + 20.7846i 0.529813 + 0.917663i
\(514\) 30.0526 8.05256i 1.32556 0.355183i
\(515\) 2.19615 + 8.19615i 0.0967740 + 0.361166i
\(516\) 17.3205 10.0000i 0.762493 0.440225i
\(517\) −8.00000 8.00000i −0.351840 0.351840i
\(518\) 0 0
\(519\) 2.00000i 0.0877903i
\(520\) −5.46410 1.46410i −0.239617 0.0642051i
\(521\) 34.6410 + 20.0000i 1.51765 + 0.876216i 0.999785 + 0.0207541i \(0.00660670\pi\)
0.517866 + 0.855462i \(0.326727\pi\)
\(522\) 5.19615 + 3.00000i 0.227429 + 0.131306i
\(523\) −9.15064 + 34.1506i −0.400129 + 1.49330i 0.412736 + 0.910851i \(0.364573\pi\)
−0.812865 + 0.582452i \(0.802093\pi\)
\(524\) −22.0000 22.0000i −0.961074 0.961074i
\(525\) 0 0
\(526\) 6.00000 6.00000i 0.261612 0.261612i
\(527\) −8.00000 13.8564i −0.348485 0.603595i
\(528\) 4.00000 6.92820i 0.174078 0.301511i
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 13.6603 + 3.66025i 0.593364 + 0.158991i
\(531\) −3.00000 + 3.00000i −0.130189 + 0.130189i
\(532\) 0 0
\(533\) 0 0
\(534\) 6.92820 4.00000i 0.299813 0.173097i
\(535\) 12.1244 + 7.00000i 0.524182 + 0.302636i
\(536\) −17.3205 10.0000i −0.748132 0.431934i
\(537\) 29.4449 17.0000i 1.27064 0.733604i
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) −16.0000 −0.688530
\(541\) 12.2942 + 3.29423i 0.528570 + 0.141630i 0.513228 0.858252i \(-0.328450\pi\)
0.0153422 + 0.999882i \(0.495116\pi\)
\(542\) 10.9282 2.92820i 0.469407 0.125777i
\(543\) −9.00000 + 15.5885i −0.386227 + 0.668965i
\(544\) 2.92820 10.9282i 0.125546 0.468543i
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) −5.00000 + 5.00000i −0.213785 + 0.213785i −0.805873 0.592088i \(-0.798304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) −12.2942 + 3.29423i −0.524705 + 0.140594i
\(550\) 3.00000 5.19615i 0.127920 0.221565i
\(551\) 15.5885 9.00000i 0.664091 0.383413i
\(552\) 24.0000 1.02151
\(553\) 0 0
\(554\) 6.00000i 0.254916i
\(555\) 2.19615 8.19615i 0.0932215 0.347907i
\(556\) −2.19615 8.19615i −0.0931376 0.347594i
\(557\) −9.15064 34.1506i −0.387725 1.44701i −0.833827 0.552027i \(-0.813855\pi\)
0.446102 0.894982i \(-0.352812\pi\)
\(558\) −10.9282 2.92820i −0.462628 0.123961i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 27.3205 + 7.32051i 1.15245 + 0.308797i
\(563\) −6.95448 25.9545i −0.293096 1.09385i −0.942717 0.333593i \(-0.891739\pi\)
0.649621 0.760258i \(-0.274928\pi\)
\(564\) 21.8564 5.85641i 0.920321 0.246599i
\(565\) −2.19615 + 8.19615i −0.0923928 + 0.344815i
\(566\) 30.0000i 1.26099i
\(567\) 0 0
\(568\) −20.0000 20.0000i −0.839181 0.839181i
\(569\) 20.7846 12.0000i 0.871336 0.503066i 0.00354413 0.999994i \(-0.498872\pi\)
0.867792 + 0.496928i \(0.165539\pi\)
\(570\) −6.00000 + 10.3923i −0.251312 + 0.435286i
\(571\) −1.36603 + 0.366025i −0.0571664 + 0.0153177i −0.287289 0.957844i \(-0.592754\pi\)
0.230123 + 0.973162i \(0.426087\pi\)
\(572\) 3.46410 2.00000i 0.144841 0.0836242i
\(573\) −8.00000 + 8.00000i −0.334205 + 0.334205i
\(574\) 0 0
\(575\) 18.0000 0.750652
\(576\) −4.00000 6.92820i −0.166667 0.288675i
\(577\) 9.00000 15.5885i 0.374675 0.648956i −0.615603 0.788056i \(-0.711088\pi\)
0.990278 + 0.139100i \(0.0444210\pi\)
\(578\) −17.7583 + 4.75833i −0.738649 + 0.197920i
\(579\) −19.1244 5.12436i −0.794781 0.212961i
\(580\) 12.0000i 0.498273i
\(581\) 0 0
\(582\) −4.00000 −0.165805
\(583\) −8.66025 + 5.00000i −0.358671 + 0.207079i
\(584\) −10.9282 + 2.92820i −0.452212 + 0.121170i
\(585\) −1.73205 1.00000i −0.0716115 0.0413449i
\(586\) 25.9808 15.0000i 1.07326 0.619644i
\(587\) 7.00000 + 7.00000i 0.288921 + 0.288921i 0.836653 0.547733i \(-0.184509\pi\)
−0.547733 + 0.836653i \(0.684509\pi\)
\(588\) 0 0
\(589\) −24.0000 + 24.0000i −0.988903 + 0.988903i
\(590\) −8.19615 2.19615i −0.337430 0.0904142i
\(591\) 17.0000 29.4449i 0.699287 1.21120i
\(592\) 16.3923 4.39230i 0.673720 0.180523i
\(593\) 17.0000 + 29.4449i 0.698106 + 1.20916i 0.969122 + 0.246581i \(0.0793071\pi\)
−0.271016 + 0.962575i \(0.587360\pi\)
\(594\) 8.00000 8.00000i 0.328244 0.328244i
\(595\) 0 0
\(596\) −14.0000 + 14.0000i −0.573462 + 0.573462i
\(597\) −5.12436 + 19.1244i −0.209726 + 0.782708i
\(598\) 10.3923 + 6.00000i 0.424973 + 0.245358i
\(599\) −12.1244 7.00000i −0.495388 0.286012i 0.231419 0.972854i \(-0.425663\pi\)
−0.726807 + 0.686842i \(0.758996\pi\)
\(600\) 6.00000 + 10.3923i 0.244949 + 0.424264i
\(601\) 20.0000i 0.815817i −0.913023 0.407909i \(-0.866258\pi\)
0.913023 0.407909i \(-0.133742\pi\)
\(602\) 0 0
\(603\) −5.00000 5.00000i −0.203616 0.203616i
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) 3.29423 + 12.2942i 0.133929 + 0.499831i
\(606\) −30.0526 + 8.05256i −1.22080 + 0.327113i
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) −24.0000 −0.973329
\(609\) 0 0
\(610\) −18.0000 18.0000i −0.728799 0.728799i
\(611\) 10.9282 + 2.92820i 0.442108 + 0.118462i
\(612\) 2.00000 3.46410i 0.0808452 0.140028i
\(613\) 34.1506 9.15064i 1.37933 0.369591i 0.508453 0.861090i \(-0.330218\pi\)
0.870878 + 0.491499i \(0.163551\pi\)
\(614\) 5.00000 + 8.66025i 0.201784 + 0.349499i
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 10.3923 6.00000i 0.418040 0.241355i
\(619\) 23.2224 6.22243i 0.933388 0.250101i 0.240089 0.970751i \(-0.422823\pi\)
0.693299 + 0.720650i \(0.256157\pi\)
\(620\) −5.85641 21.8564i −0.235199 0.877774i
\(621\) 32.7846 + 8.78461i 1.31560 + 0.352514i
\(622\) −30.0000 + 30.0000i −1.20289 + 1.20289i
\(623\) 0 0
\(624\) 8.00000i 0.320256i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −5.85641 21.8564i −0.234069 0.873558i
\(627\) −2.19615 8.19615i −0.0877059 0.327323i
\(628\) −10.9808 + 40.9808i −0.438180 + 1.63531i
\(629\) 6.00000 + 6.00000i 0.239236 + 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i −0.979990 0.199047i \(-0.936215\pi\)
0.979990 0.199047i \(-0.0637846\pi\)
\(632\) 0 0
\(633\) −15.5885 9.00000i −0.619586 0.357718i
\(634\) −5.00000 + 8.66025i −0.198575 + 0.343943i
\(635\) 2.92820 10.9282i 0.116202 0.433673i
\(636\) 20.0000i 0.793052i
\(637\) 0 0
\(638\) −6.00000 6.00000i −0.237542 0.237542i
\(639\) −5.00000 8.66025i −0.197797 0.342594i
\(640\) 8.00000 13.8564i 0.316228 0.547723i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 5.12436 19.1244i 0.202242 0.754778i
\(643\) 21.0000 21.0000i 0.828159 0.828159i −0.159103 0.987262i \(-0.550860\pi\)
0.987262 + 0.159103i \(0.0508601\pi\)
\(644\) 0 0
\(645\) 10.0000 + 10.0000i 0.393750 + 0.393750i
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) −36.3731 21.0000i −1.42997 0.825595i −0.432855 0.901464i \(-0.642494\pi\)
−0.997118 + 0.0758684i \(0.975827\pi\)
\(648\) 3.66025 + 13.6603i 0.143788 + 0.536625i
\(649\) 5.19615 3.00000i 0.203967 0.117760i
\(650\) 6.00000i 0.235339i
\(651\) 0 0
\(652\) −2.00000 2.00000i −0.0783260 0.0783260i
\(653\) −25.9545 6.95448i −1.01568 0.272150i −0.287678 0.957727i \(-0.592883\pi\)
−0.728000 + 0.685577i \(0.759550\pi\)
\(654\) −2.19615 8.19615i −0.0858764 0.320495i
\(655\) 11.0000 19.0526i 0.429806 0.744445i
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) −17.0000 + 17.0000i −0.662226 + 0.662226i −0.955904 0.293678i \(-0.905121\pi\)
0.293678 + 0.955904i \(0.405121\pi\)
\(660\) 5.46410 + 1.46410i 0.212690 + 0.0569901i
\(661\) −12.2942 + 3.29423i −0.478190 + 0.128131i −0.489860 0.871801i \(-0.662952\pi\)
0.0116697 + 0.999932i \(0.496285\pi\)
\(662\) 1.73205 + 1.00000i 0.0673181 + 0.0388661i
\(663\) −3.46410 + 2.00000i −0.134535 + 0.0776736i
\(664\) 4.00000i 0.155230i
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 6.58846 24.5885i 0.255106 0.952069i
\(668\) 2.00000 3.46410i 0.0773823 0.134030i
\(669\) −8.78461 32.7846i −0.339633 1.26753i
\(670\) 3.66025 13.6603i 0.141408 0.527742i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −6.58846 + 24.5885i −0.253778 + 0.947112i
\(675\) 4.39230 + 16.3923i 0.169060 + 0.630940i
\(676\) 11.0000 19.0526i 0.423077 0.732791i
\(677\) −1.09808 + 4.09808i −0.0422025 + 0.157502i −0.983811 0.179206i \(-0.942647\pi\)
0.941609 + 0.336708i \(0.109314\pi\)
\(678\) 12.0000 0.460857
\(679\) 0 0
\(680\) 8.00000 0.306786
\(681\) 25.9808 15.0000i 0.995585 0.574801i
\(682\) 13.8564 + 8.00000i 0.530589 + 0.306336i
\(683\) −6.83013 + 1.83013i −0.261348 + 0.0700279i −0.387113 0.922032i \(-0.626528\pi\)
0.125766 + 0.992060i \(0.459861\pi\)
\(684\) −8.19615 2.19615i −0.313388 0.0839720i
\(685\) −8.00000 + 8.00000i −0.305664 + 0.305664i
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) −7.32051 + 27.3205i −0.279092 + 1.04158i
\(689\) 5.00000 8.66025i 0.190485 0.329929i
\(690\) 4.39230 + 16.3923i 0.167212 + 0.624044i
\(691\) −12.2942 3.29423i −0.467694 0.125318i 0.0172725 0.999851i \(-0.494502\pi\)
−0.484967 + 0.874532i \(0.661168\pi\)
\(692\) 2.00000 + 2.00000i 0.0760286 + 0.0760286i
\(693\) 0 0
\(694\) 26.0000i 0.986947i
\(695\) 5.19615 3.00000i 0.197101 0.113796i
\(696\) 16.3923 4.39230i 0.621349 0.166490i
\(697\) 0 0
\(698\) −3.00000 5.19615i −0.113552 0.196677i
\(699\) −4.00000 4.00000i −0.151294 0.151294i
\(700\) 0 0
\(701\) 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i \(-0.439525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) −2.92820 + 10.9282i −0.110518 + 0.412458i
\(703\) 9.00000 15.5885i 0.339441 0.587930i
\(704\) 2.92820 + 10.9282i 0.110361 + 0.411872i
\(705\) 8.00000 + 13.8564i 0.301297 + 0.521862i
\(706\) −6.00000 6.00000i −0.225813 0.225813i
\(707\) 0 0
\(708\) 12.0000i 0.450988i
\(709\) 9.88269 36.8827i 0.371152 1.38516i −0.487734 0.872992i \(-0.662177\pi\)
0.858886 0.512166i \(-0.171157\pi\)
\(710\) 10.0000 17.3205i 0.375293 0.650027i
\(711\) 0 0
\(712\) −2.92820 + 10.9282i −0.109739 + 0.409552i
\(713\) 48.0000i 1.79761i
\(714\) 0 0
\(715\) 2.00000 + 2.00000i 0.0747958 + 0.0747958i
\(716\) −12.4449 + 46.4449i −0.465086 + 1.73573i
\(717\) 0 0
\(718\) −9.51666 35.5167i −0.355159 1.32547i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 4.00000 4.00000i 0.149071 0.149071i
\(721\) 0 0
\(722\) 1.00000 1.00000i 0.0372161 0.0372161i
\(723\) −24.5885 6.58846i −0.914455 0.245027i
\(724\) −6.58846 24.5885i −0.244858 0.913823i
\(725\) 12.2942 3.29423i 0.456596 0.122345i
\(726\) 15.5885 9.00000i 0.578542 0.334021i
\(727\) 2.00000i 0.0741759i 0.999312 + 0.0370879i \(0.0118082\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) −4.00000 6.92820i −0.148047 0.256424i
\(731\) −13.6603 + 3.66025i −0.505243 + 0.135379i
\(732\) −18.0000 + 31.1769i −0.665299 + 1.15233i
\(733\) −28.6865 7.68653i −1.05956 0.283909i −0.313364 0.949633i \(-0.601456\pi\)
−0.746198 + 0.665725i \(0.768123\pi\)
\(734\) 8.00000 + 8.00000i 0.295285 + 0.295285i
\(735\) 0 0
\(736\) −24.0000 + 24.0000i −0.884652 + 0.884652i
\(737\) 5.00000 + 8.66025i 0.184177 + 0.319005i
\(738\) 0 0
\(739\) 8.41858 + 31.4186i 0.309683 + 1.15575i 0.928839 + 0.370484i \(0.120808\pi\)
−0.619156 + 0.785268i \(0.712525\pi\)
\(740\) 6.00000 + 10.3923i 0.220564 + 0.382029i
\(741\) 6.00000 + 6.00000i 0.220416 + 0.220416i
\(742\) 0 0
\(743\) 46.0000i 1.68758i 0.536676 + 0.843788i \(0.319680\pi\)
−0.536676 + 0.843788i \(0.680320\pi\)
\(744\) −27.7128 + 16.0000i −1.01600 + 0.586588i
\(745\) −12.1244 7.00000i −0.444202 0.256460i
\(746\) −8.66025 5.00000i −0.317074 0.183063i
\(747\) 0.366025 1.36603i 0.0133922 0.0499803i
\(748\) −4.00000 + 4.00000i −0.146254 + 0.146254i
\(749\) 0 0
\(750\) −16.0000 + 16.0000i −0.584237 + 0.584237i
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −16.0000 + 27.7128i −0.583460 + 1.01058i
\(753\) 21.0000 36.3731i 0.765283 1.32551i
\(754\) 8.19615 + 2.19615i 0.298486 + 0.0799792i
\(755\) 10.0000 10.0000i 0.363937 0.363937i
\(756\) 0 0
\(757\) 23.0000 + 23.0000i 0.835949 + 0.835949i 0.988323 0.152374i \(-0.0486917\pi\)
−0.152374 + 0.988323i \(0.548692\pi\)
\(758\) 5.19615 3.00000i 0.188733 0.108965i
\(759\) −10.3923 6.00000i −0.377217 0.217786i
\(760\) −4.39230 16.3923i −0.159326 0.594611i
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) 16.0000i 0.578860i
\(765\) 2.73205 + 0.732051i 0.0987775 + 0.0264674i
\(766\) 21.8564 5.85641i 0.789704 0.211601i
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) −21.8564 5.85641i −0.788675 0.211325i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 22.0000 22.0000i 0.792311 0.792311i
\(772\) 24.2487 14.0000i 0.872730 0.503871i
\(773\) −6.83013 + 1.83013i −0.245663 + 0.0658251i −0.379549 0.925172i \(-0.623921\pi\)
0.133887 + 0.990997i \(0.457254\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) −20.7846 + 12.0000i −0.746605 + 0.431053i
\(776\) 4.00000 4.00000i 0.143592 0.143592i