Properties

Label 784.2.x.c.557.1
Level $784$
Weight $2$
Character 784.557
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 557.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.557
Dual form 784.2.x.c.373.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.36603 + 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.36603 - 0.366025i) q^{5} -2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.36603 + 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.36603 - 0.366025i) q^{5} -2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.73205 - 1.00000i) q^{10} +(0.366025 + 1.36603i) q^{11} +(-2.73205 - 0.732051i) q^{12} +(1.00000 + 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.36603 + 0.366025i) q^{18} +(-1.09808 + 4.09808i) 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} +(2.73205 + 0.732051i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-2.00000 + 2.00000i) q^{34} -2.00000 q^{36} +(-4.09808 - 1.09808i) 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} +(-0.732051 + 2.73205i) q^{44} +(1.36603 - 0.366025i) q^{45} +(-8.19615 + 2.19615i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-4.00000 - 4.00000i) q^{48} +(-3.00000 - 3.00000i) q^{50} +(0.732051 - 2.73205i) q^{51} +(0.732051 + 2.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(6.92820 - 4.00000i) q^{54} -2.00000i q^{55} -6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(1.09808 + 4.09808i) q^{59} +(3.46410 + 2.00000i) q^{60} +(3.29423 - 12.2942i) q^{61} +(-8.00000 + 8.00000i) q^{62} +8.00000i q^{64} +(-1.00000 - 1.73205i) q^{65} +(-0.732051 - 2.73205i) q^{66} +(6.83013 - 1.83013i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(6.00000 - 6.00000i) q^{69} +10.0000i q^{71} +(-2.73205 - 0.732051i) q^{72} +(3.46410 + 2.00000i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(4.09808 + 1.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{78} +(-1.46410 - 5.46410i) 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} +(2.92820 - 10.9282i) q^{93} +(2.92820 + 10.9282i) 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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) −1.36603 + 0.366025i −0.788675 + 0.211325i −0.630606 0.776103i \(-0.717194\pi\)
−0.158069 + 0.987428i \(0.550527\pi\)
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) −1.36603 0.366025i −0.610905 0.163692i −0.0599153 0.998203i \(-0.519083\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) −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
\(11\) 0.366025 + 1.36603i 0.110361 + 0.411872i 0.998898 0.0469323i \(-0.0149445\pi\)
−0.888537 + 0.458804i \(0.848278\pi\)
\(12\) −2.73205 0.732051i −0.788675 0.211325i
\(13\) 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i \(-0.187167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 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 \(0.244646\pi\)
\(18\) −1.36603 + 0.366025i −0.321975 + 0.0862730i
\(19\) −1.09808 + 4.09808i −0.251916 + 0.940163i 0.717864 + 0.696183i \(0.245120\pi\)
−0.969780 + 0.243980i \(0.921547\pi\)
\(20\) −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 −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) −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 0.928477 0.371391i \(-0.121119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 2.73205 + 0.732051i 0.498802 + 0.133654i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) −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
\(37\) −4.09808 1.09808i −0.673720 0.180523i −0.0942898 0.995545i \(-0.530058\pi\)
−0.579430 + 0.815022i \(0.696725\pi\)
\(38\) −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 −0.214280 0.976772i \(-0.568740\pi\)
0.976772 + 0.214280i \(0.0687403\pi\)
\(44\) −0.732051 + 2.73205i −0.110361 + 0.411872i
\(45\) 1.36603 0.366025i 0.203635 0.0545638i
\(46\) −8.19615 + 2.19615i −1.20846 + 0.323805i
\(47\) 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
\(51\) 0.732051 2.73205i 0.102508 0.382564i
\(52\) 0.732051 + 2.73205i 0.101517 + 0.378867i
\(53\) −1.83013 6.83013i −0.251387 0.938190i −0.970065 0.242846i \(-0.921919\pi\)
0.718677 0.695344i \(-0.244748\pi\)
\(54\) 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
\(59\) 1.09808 + 4.09808i 0.142957 + 0.533524i 0.999838 + 0.0180090i \(0.00573274\pi\)
−0.856880 + 0.515515i \(0.827601\pi\)
\(60\) 3.46410 + 2.00000i 0.447214 + 0.258199i
\(61\) 3.29423 12.2942i 0.421783 1.57411i −0.349067 0.937098i \(-0.613501\pi\)
0.770850 0.637017i \(-0.219832\pi\)
\(62\) −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
\(66\) −0.732051 2.73205i −0.0901092 0.336292i
\(67\) 6.83013 1.83013i 0.834433 0.223586i 0.183786 0.982966i \(-0.441165\pi\)
0.650647 + 0.759381i \(0.274498\pi\)
\(68\) −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 \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) −2.73205 0.732051i −0.321975 0.0862730i
\(73\) 3.46410 + 2.00000i 0.405442 + 0.234082i 0.688830 0.724923i \(-0.258125\pi\)
−0.283387 + 0.959006i \(0.591458\pi\)
\(74\) −5.19615 3.00000i −0.604040 0.348743i
\(75\) 4.09808 + 1.09808i 0.473205 + 0.126795i
\(76\) −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 \(0.833333\pi\)
\(80\) −1.46410 5.46410i −0.163692 0.610905i
\(81\) −2.50000 + 4.33013i −0.277778 + 0.481125i
\(82\) 0 0
\(83\) 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i \(-0.225269\pi\)
−0.650092 + 0.759856i \(0.725269\pi\)
\(84\) 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 −0.305038 0.952340i \(-0.598669\pi\)
0.672232 + 0.740341i \(0.265336\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −12.0000 −1.25109
\(93\) 2.92820 10.9282i 0.303641 1.13320i
\(94\) 2.92820 + 10.9282i 0.302021 + 1.12716i
\(95\) 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
\(101\) −4.02628 15.0263i −0.400630 1.49517i −0.811976 0.583691i \(-0.801608\pi\)
0.411346 0.911479i \(-0.365059\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) 5.19615 3.00000i 0.511992 0.295599i −0.221660 0.975124i \(-0.571148\pi\)
0.733652 + 0.679525i \(0.237814\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 0 0
\(106\) 10.0000i 0.971286i
\(107\) 9.56218 + 2.56218i 0.924411 + 0.247695i 0.689470 0.724315i \(-0.257844\pi\)
0.234941 + 0.972010i \(0.424510\pi\)
\(108\) 10.9282 2.92820i 1.05157 0.281766i
\(109\) −4.09808 + 1.09808i −0.392525 + 0.105177i −0.449682 0.893189i \(-0.648463\pi\)
0.0571579 + 0.998365i \(0.481796\pi\)
\(110\) 0.732051 2.73205i 0.0697983 0.260491i
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 2.19615 8.19615i 0.205689 0.767640i
\(115\) 8.19615 2.19615i 0.764295 0.204792i
\(116\) 2.19615 + 8.19615i 0.203908 + 0.760994i
\(117\) −1.36603 0.366025i −0.126289 0.0338391i
\(118\) 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 \(0.384500\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) −0.732051 2.73205i −0.0642051 0.239617i
\(131\) −4.02628 + 15.0263i −0.351778 + 1.31285i 0.532714 + 0.846296i \(0.321172\pi\)
−0.884491 + 0.466557i \(0.845494\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 0 0
\(134\) 10.0000 0.863868
\(135\) −6.92820 + 4.00000i −0.596285 + 0.344265i
\(136\) −5.46410 + 1.46410i −0.468543 + 0.125546i
\(137\) 6.92820 + 4.00000i 0.591916 + 0.341743i 0.765855 0.643013i \(-0.222316\pi\)
−0.173939 + 0.984757i \(0.555649\pi\)
\(138\) 10.3923 6.00000i 0.884652 0.510754i
\(139\) 3.00000 3.00000i 0.254457 0.254457i −0.568338 0.822795i \(-0.692414\pi\)
0.822795 + 0.568338i \(0.192414\pi\)
\(140\) 0 0
\(141\) −8.00000 8.00000i −0.673722 0.673722i
\(142\) −3.66025 + 13.6603i −0.307162 + 1.14634i
\(143\) −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
\(149\) −9.56218 2.56218i −0.783364 0.209902i −0.155097 0.987899i \(-0.549569\pi\)
−0.628267 + 0.777997i \(0.716236\pi\)
\(150\) 5.19615 + 3.00000i 0.424264 + 0.244949i
\(151\) −8.66025 5.00000i −0.704761 0.406894i 0.104357 0.994540i \(-0.466722\pi\)
−0.809118 + 0.587646i \(0.800055\pi\)
\(152\) −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
\(157\) 20.4904 5.49038i 1.63531 0.438180i 0.679862 0.733340i \(-0.262039\pi\)
0.955448 + 0.295160i \(0.0953728\pi\)
\(158\) 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
\(163\) −0.366025 + 1.36603i −0.0286693 + 0.106995i −0.978778 0.204924i \(-0.934305\pi\)
0.950109 + 0.311919i \(0.100972\pi\)
\(164\) 0 0
\(165\) 0.732051 + 2.73205i 0.0569901 + 0.212690i
\(166\) 1.00000 + 1.73205i 0.0776151 + 0.134433i
\(167\) 2.00000i 0.154765i −0.997001 0.0773823i \(-0.975344\pi\)
0.997001 0.0773823i \(-0.0246562\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 3.46410 2.00000i 0.265684 0.153393i
\(171\) −1.09808 4.09808i −0.0839720 0.313388i
\(172\) 13.6603 3.66025i 1.04158 0.279092i
\(173\) 0.366025 1.36603i 0.0278284 0.103857i −0.950615 0.310373i \(-0.899546\pi\)
0.978443 + 0.206516i \(0.0662126\pi\)
\(174\) −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
\(178\) 5.46410 1.46410i 0.409552 0.109739i
\(179\) 23.2224 6.22243i 1.73573 0.465086i 0.754237 0.656603i \(-0.228007\pi\)
0.981489 + 0.191516i \(0.0613405\pi\)
\(180\) 2.73205 + 0.732051i 0.203635 + 0.0545638i
\(181\) 9.00000 9.00000i 0.668965 0.668965i −0.288512 0.957476i \(-0.593160\pi\)
0.957476 + 0.288512i \(0.0931604\pi\)
\(182\) 0 0
\(183\) 18.0000i 1.33060i
\(184\) −16.3923 4.39230i −1.20846 0.323805i
\(185\) 5.19615 + 3.00000i 0.382029 + 0.220564i
\(186\) 8.00000 13.8564i 0.586588 1.01600i
\(187\) −2.73205 0.732051i −0.199787 0.0535329i
\(188\) 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 \(0.739868\pi\)
\(192\) −2.92820 10.9282i −0.211325 0.788675i
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 2.73205 + 0.732051i 0.196150 + 0.0525582i
\(195\) 2.00000 + 2.00000i 0.143223 + 0.143223i
\(196\) 0 0
\(197\) −17.0000 + 17.0000i −1.21120 + 1.21120i −0.240567 + 0.970632i \(0.577334\pi\)
−0.970632 + 0.240567i \(0.922666\pi\)
\(198\) −1.00000 1.73205i −0.0710669 0.123091i
\(199\) −12.1244 7.00000i −0.859473 0.496217i 0.00436292 0.999990i \(-0.498611\pi\)
−0.863836 + 0.503774i \(0.831945\pi\)
\(200\) −2.19615 8.19615i −0.155291 0.579555i
\(201\) −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
\(206\) 8.19615 2.19615i 0.571053 0.153013i
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) −1.46410 + 5.46410i −0.101517 + 0.378867i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 9.00000i −0.619586 0.619586i 0.325840 0.945425i \(-0.394353\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(212\) 3.66025 13.6603i 0.251387 0.938190i
\(213\) −3.66025 13.6603i −0.250796 0.935985i
\(214\) 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
\(219\) −5.46410 1.46410i −0.369230 0.0989348i
\(220\) 2.00000 3.46410i 0.134840 0.233550i
\(221\) −2.73205 + 0.732051i −0.183778 + 0.0492431i
\(222\) 8.19615 + 2.19615i 0.550090 + 0.147396i
\(223\) −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
\(226\) −8.19615 2.19615i −0.545200 0.146086i
\(227\) 20.4904 5.49038i 1.35999 0.364409i 0.496180 0.868220i \(-0.334736\pi\)
0.863814 + 0.503810i \(0.168069\pi\)
\(228\) 6.00000 10.3923i 0.397360 0.688247i
\(229\) 9.56218 + 2.56218i 0.631886 + 0.169313i 0.560526 0.828137i \(-0.310599\pi\)
0.0713609 + 0.997451i \(0.477266\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 3.46410 2.00000i 0.226941 0.131024i −0.382219 0.924072i \(-0.624840\pi\)
0.609160 + 0.793047i \(0.291507\pi\)
\(234\) −1.73205 1.00000i −0.113228 0.0653720i
\(235\) −2.92820 10.9282i −0.191015 0.712877i
\(236\) −2.19615 + 8.19615i −0.142957 + 0.533524i
\(237\) 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 \(0.969820\pi\)
\(242\) 12.2942 3.29423i 0.790303 0.211761i
\(243\) −2.56218 + 9.56218i −0.164364 + 0.613414i
\(244\) 18.0000 18.0000i 1.15233 1.15233i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.19615 + 3.00000i −0.330623 + 0.190885i
\(248\) −21.8564 + 5.85641i −1.38788 + 0.371882i
\(249\) −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 −0.416265 + 0.909243i \(0.636661\pi\)
−0.909243 + 0.416265i \(0.863339\pi\)
\(252\) 0 0
\(253\) −6.00000 6.00000i −0.377217 0.377217i
\(254\) 10.9282 + 2.92820i 0.685696 + 0.183732i
\(255\) −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
\(261\) −4.09808 1.09808i −0.253665 0.0679692i
\(262\) −11.0000 + 19.0526i −0.679582 + 1.17707i
\(263\) 5.19615 + 3.00000i 0.320408 + 0.184988i 0.651575 0.758585i \(-0.274109\pi\)
−0.331166 + 0.943572i \(0.607442\pi\)
\(264\) 1.46410 5.46410i 0.0901092 0.336292i
\(265\) 10.0000i 0.614295i
\(266\) 0 0
\(267\) −4.00000 + 4.00000i −0.244796 + 0.244796i
\(268\) 13.6603 + 3.66025i 0.834433 + 0.223586i
\(269\) 4.09808 1.09808i 0.249864 0.0669509i −0.131713 0.991288i \(-0.542048\pi\)
0.381577 + 0.924337i \(0.375381\pi\)
\(270\) −10.9282 + 2.92820i −0.665069 + 0.178205i
\(271\) −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
\(275\) 1.09808 4.09808i 0.0662165 0.247123i
\(276\) 16.3923 4.39230i 0.986701 0.264386i
\(277\) 1.09808 + 4.09808i 0.0659770 + 0.246230i 0.991036 0.133593i \(-0.0426516\pi\)
−0.925059 + 0.379823i \(0.875985\pi\)
\(278\) 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 \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) −8.00000 13.8564i −0.476393 0.825137i
\(283\) 5.49038 + 20.4904i 0.326369 + 1.21803i 0.912928 + 0.408120i \(0.133816\pi\)
−0.586559 + 0.809907i \(0.699518\pi\)
\(284\) −10.0000 + 17.3205i −0.593391 + 1.02778i
\(285\) −2.19615 + 8.19615i −0.130089 + 0.485498i
\(286\) −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
\(290\) −2.19615 8.19615i −0.128963 0.481295i
\(291\) −2.73205 + 0.732051i −0.160156 + 0.0429136i
\(292\) 4.00000 + 6.92820i 0.234082 + 0.405442i
\(293\) −15.0000 + 15.0000i −0.876309 + 0.876309i −0.993151 0.116841i \(-0.962723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 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
\(299\) −8.19615 2.19615i −0.473996 0.127007i
\(300\) 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
\(304\) −16.3923 + 4.39230i −0.940163 + 0.251916i
\(305\) −9.00000 + 15.5885i −0.515339 + 0.892592i
\(306\) 0.732051 2.73205i 0.0418486 0.156181i
\(307\) 5.00000 + 5.00000i 0.285365 + 0.285365i 0.835244 0.549879i \(-0.185326\pi\)
−0.549879 + 0.835244i \(0.685326\pi\)
\(308\) 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 −0.473688 0.880693i \(-0.657077\pi\)
−0.999546 + 0.0301210i \(0.990411\pi\)
\(312\) −1.46410 5.46410i −0.0828884 0.309344i
\(313\) 13.8564 8.00000i 0.783210 0.452187i −0.0543564 0.998522i \(-0.517311\pi\)
0.837567 + 0.546335i \(0.183977\pi\)
\(314\) 30.0000 1.69300
\(315\) 0 0
\(316\) 0 0
\(317\) −1.83013 + 6.83013i −0.102790 + 0.383618i −0.998085 0.0618557i \(-0.980298\pi\)
0.895295 + 0.445474i \(0.146965\pi\)
\(318\) 3.66025 + 13.6603i 0.205257 + 0.766029i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 2.92820 10.9282i 0.163692 0.610905i
\(321\) −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
\(325\) −1.09808 4.09808i −0.0609103 0.227320i
\(326\) −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
\(331\) −1.36603 0.366025i −0.0750835 0.0201186i 0.221082 0.975255i \(-0.429041\pi\)
−0.296165 + 0.955137i \(0.595708\pi\)
\(332\) 0.732051 + 2.73205i 0.0401765 + 0.149941i
\(333\) 4.09808 1.09808i 0.224573 0.0601742i
\(334\) 0.732051 2.73205i 0.0400560 0.149491i
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 4.02628 15.0263i 0.219001 0.817322i
\(339\) 8.19615 2.19615i 0.445154 0.119279i
\(340\) 5.46410 1.46410i 0.296333 0.0794021i
\(341\) −10.9282 2.92820i −0.591795 0.158571i
\(342\) 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
\(347\) 4.75833 + 17.7583i 0.255441 + 0.953317i 0.967845 + 0.251548i \(0.0809396\pi\)
−0.712404 + 0.701769i \(0.752394\pi\)
\(348\) −6.00000 10.3923i −0.321634 0.557086i
\(349\) −3.00000 3.00000i −0.160586 0.160586i 0.622240 0.782826i \(-0.286223\pi\)
−0.782826 + 0.622240i \(0.786223\pi\)
\(350\) 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 \(0.217711\pi\)
\(354\) −2.19615 8.19615i −0.116724 0.435621i
\(355\) 3.66025 13.6603i 0.194266 0.725011i
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) 34.0000 1.79696
\(359\) 22.5167 13.0000i 1.18838 0.686114i 0.230445 0.973085i \(-0.425982\pi\)
0.957939 + 0.286972i \(0.0926486\pi\)
\(360\) 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
\(366\) −6.58846 + 24.5885i −0.344384 + 1.28526i
\(367\) 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
\(373\) 6.83013 + 1.83013i 0.353651 + 0.0947604i 0.431271 0.902223i \(-0.358065\pi\)
−0.0776200 + 0.996983i \(0.524732\pi\)
\(374\) −3.46410 2.00000i −0.179124 0.103418i
\(375\) −13.8564 8.00000i −0.715542 0.413118i
\(376\) −5.85641 + 21.8564i −0.302021 + 1.12716i
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −3.00000 + 3.00000i −0.154100 + 0.154100i −0.779946 0.625847i \(-0.784754\pi\)
0.625847 + 0.779946i \(0.284754\pi\)
\(380\) 10.3923 6.00000i 0.533114 0.307794i
\(381\) −10.9282 + 2.92820i −0.559869 + 0.150016i
\(382\) 2.92820 + 10.9282i 0.149820 + 0.559136i
\(383\) −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
\(387\) −1.83013 + 6.83013i −0.0930306 + 0.347195i
\(388\) 3.46410 + 2.00000i 0.175863 + 0.101535i
\(389\) −4.75833 17.7583i −0.241257 0.900383i −0.975228 0.221202i \(-0.929002\pi\)
0.733971 0.679181i \(-0.237665\pi\)
\(390\) 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
\(396\) −0.732051 2.73205i −0.0367869 0.137291i
\(397\) 1.83013 6.83013i 0.0918514 0.342794i −0.904672 0.426109i \(-0.859884\pi\)
0.996523 + 0.0833147i \(0.0265507\pi\)
\(398\) −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 \(0.684957\pi\)
\(402\) −13.6603 + 3.66025i −0.681312 + 0.182557i
\(403\) −10.9282 + 2.92820i −0.544373 + 0.145864i
\(404\) 8.05256 30.0526i 0.400630 1.49517i
\(405\) 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 0.801795 0.597600i \(-0.203879\pi\)
−0.116639 + 0.993174i \(0.537212\pi\)
\(410\) 0 0
\(411\) −10.9282 2.92820i −0.539049 0.144438i
\(412\) 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
\(418\) −8.19615 2.19615i −0.400887 0.107417i
\(419\) −3.00000 3.00000i −0.146560 0.146560i 0.630020 0.776579i \(-0.283047\pi\)
−0.776579 + 0.630020i \(0.783047\pi\)
\(420\) 0 0
\(421\) −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i \(-0.850383\pi\)
0.452919 + 0.891552i \(0.350383\pi\)
\(422\) −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
\(429\) 0.732051 2.73205i 0.0353437 0.131905i
\(430\) −13.6603 + 3.66025i −0.658756 + 0.176513i
\(431\) −16.0000 + 27.7128i −0.770693 + 1.33488i 0.166491 + 0.986043i \(0.446756\pi\)
−0.937184 + 0.348836i \(0.886577\pi\)
\(432\) 21.8564 + 5.85641i 1.05157 + 0.281766i
\(433\) −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
\(436\) −8.19615 2.19615i −0.392525 0.105177i
\(437\) −6.58846 24.5885i −0.315169 1.17623i
\(438\) −6.92820 4.00000i −0.331042 0.191127i
\(439\) 12.1244 7.00000i 0.578664 0.334092i −0.181938 0.983310i \(-0.558237\pi\)
0.760602 + 0.649218i \(0.224904\pi\)
\(440\) 4.00000 4.00000i 0.190693 0.190693i
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) 20.4904 + 5.49038i 0.973527 + 0.260856i 0.710316 0.703882i \(-0.248552\pi\)
0.263211 + 0.964738i \(0.415218\pi\)
\(444\) 10.3923 + 6.00000i 0.493197 + 0.284747i
\(445\) −5.46410 + 1.46410i −0.259023 + 0.0694051i
\(446\) −32.7846 8.78461i −1.55240 0.415963i
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 4.09808 + 1.09808i 0.193185 + 0.0517638i
\(451\) 0 0
\(452\) −10.3923 6.00000i −0.488813 0.282216i
\(453\) 13.6603 + 3.66025i 0.641815 + 0.171974i
\(454\) 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 0.316579 0.948566i \(-0.397466\pi\)
0.979772 + 0.200118i \(0.0641325\pi\)
\(458\) 12.1244 + 7.00000i 0.566534 + 0.327089i
\(459\) 2.92820 + 10.9282i 0.136677 + 0.510085i
\(460\) 16.3923 + 4.39230i 0.764295 + 0.204792i
\(461\) −11.0000 11.0000i −0.512321 0.512321i 0.402916 0.915237i \(-0.367997\pi\)
−0.915237 + 0.402916i \(0.867997\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −4.39230 + 16.3923i −0.203908 + 0.760994i
\(465\) −8.00000 + 13.8564i −0.370991 + 0.642575i
\(466\) 5.46410 1.46410i 0.253120 0.0678232i
\(467\) 1.83013 6.83013i 0.0846882 0.316061i −0.910567 0.413362i \(-0.864354\pi\)
0.995255 + 0.0973014i \(0.0310211\pi\)
\(468\) −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 \(0.799782\pi\)
\(480\) 2.92820 + 10.9282i 0.133654 + 0.498802i
\(481\) −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
\(485\) −2.73205 0.732051i −0.124056 0.0332407i
\(486\) −7.00000 + 12.1244i −0.317526 + 0.549972i
\(487\) −1.73205 1.00000i −0.0784867 0.0453143i 0.460243 0.887793i \(-0.347762\pi\)
−0.538730 + 0.842479i \(0.681096\pi\)
\(488\) 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 −0.991038 0.133580i \(-0.957353\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(492\) 0 0
\(493\) −8.19615 + 2.19615i −0.369136 + 0.0989097i
\(494\) −8.19615 + 2.19615i −0.368762 + 0.0988096i
\(495\) 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
\(499\) 8.41858 31.4186i 0.376868 1.40649i −0.473729 0.880671i \(-0.657092\pi\)
0.850597 0.525818i \(-0.176241\pi\)
\(500\) 5.85641 + 21.8564i 0.261906 + 0.977448i
\(501\) 0.732051 + 2.73205i 0.0327056 + 0.122059i
\(502\) −36.3731 + 21.0000i −1.62341 + 0.937276i
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) 0 0
\(505\) 22.0000i 0.978987i
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) 4.02628 + 15.0263i 0.178813 + 0.667340i
\(508\) 13.8564 + 8.00000i 0.614779 + 0.354943i
\(509\) −8.41858 + 31.4186i −0.373147 + 1.39260i 0.482886 + 0.875683i \(0.339589\pi\)
−0.856033 + 0.516921i \(0.827078\pi\)
\(510\) −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
\(514\) −8.05256 30.0526i −0.355183 1.32556i
\(515\) −8.19615 + 2.19615i −0.361166 + 0.0967740i
\(516\) −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
\(520\) 1.46410 5.46410i 0.0642051 0.239617i
\(521\) −34.6410 20.0000i −1.51765 0.876216i −0.999785 0.0207541i \(-0.993393\pi\)
−0.517866 0.855462i \(-0.673273\pi\)
\(522\) −5.19615 3.00000i −0.227429 0.131306i
\(523\) 34.1506 + 9.15064i 1.49330 + 0.400129i 0.910851 0.412736i \(-0.135427\pi\)
0.582452 + 0.812865i \(0.302093\pi\)
\(524\) −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
\(530\) −3.66025 + 13.6603i −0.158991 + 0.593364i
\(531\) −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
\(541\) −3.29423 + 12.2942i −0.141630 + 0.528570i 0.858252 + 0.513228i \(0.171550\pi\)
−0.999882 + 0.0153422i \(0.995116\pi\)
\(542\) −2.92820 10.9282i −0.125777 0.469407i
\(543\) −9.00000 + 15.5885i −0.386227 + 0.668965i
\(544\) −10.9282 2.92820i −0.468543 0.125546i
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i \(-0.298304\pi\)
−0.805873 + 0.592088i \(0.798304\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) 3.29423 + 12.2942i 0.140594 + 0.524705i
\(550\) 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
\(555\) −8.19615 2.19615i −0.347907 0.0932215i
\(556\) 8.19615 2.19615i 0.347594 0.0931376i
\(557\) 34.1506 9.15064i 1.44701 0.387725i 0.552027 0.833827i \(-0.313855\pi\)
0.894982 + 0.446102i \(0.147188\pi\)
\(558\) 2.92820 10.9282i 0.123961 0.462628i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) −7.32051 + 27.3205i −0.308797 + 1.15245i
\(563\) 25.9545 6.95448i 1.09385 0.293096i 0.333593 0.942717i \(-0.391739\pi\)
0.760258 + 0.649621i \(0.225072\pi\)
\(564\) −5.85641 21.8564i −0.246599 0.920321i
\(565\) 8.19615 + 2.19615i 0.344815 + 0.0923928i
\(566\) 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 −0.867792 0.496928i \(-0.834461\pi\)
−0.00354413 + 0.999994i \(0.501128\pi\)
\(570\) −6.00000 + 10.3923i −0.251312 + 0.435286i
\(571\) 0.366025 + 1.36603i 0.0153177 + 0.0571664i 0.973162 0.230123i \(-0.0739127\pi\)
−0.957844 + 0.287289i \(0.907246\pi\)
\(572\) −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 \(0.0444210\pi\)
\(578\) 4.75833 + 17.7583i 0.197920 + 0.738649i
\(579\) 5.12436 19.1244i 0.212961 0.794781i
\(580\) 12.0000i 0.498273i
\(581\) 0 0
\(582\) −4.00000 −0.165805
\(583\) 8.66025 5.00000i 0.358671 0.207079i
\(584\) 2.92820 + 10.9282i 0.121170 + 0.452212i
\(585\) 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 −0.547733 0.836653i \(-0.684509\pi\)
0.836653 + 0.547733i \(0.184509\pi\)
\(588\) 0 0
\(589\) −24.0000 24.0000i −0.988903 0.988903i
\(590\) 2.19615 8.19615i 0.0904142 0.337430i
\(591\) 17.0000 29.4449i 0.699287 1.21120i
\(592\) −4.39230 16.3923i −0.180523 0.673720i
\(593\) 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
\(597\) 19.1244 + 5.12436i 0.782708 + 0.209726i
\(598\) −10.3923 6.00000i −0.424973 0.245358i
\(599\) 12.1244 + 7.00000i 0.495388 + 0.286012i 0.726807 0.686842i \(-0.241004\pi\)
−0.231419 + 0.972854i \(0.574337\pi\)
\(600\) 6.00000 + 10.3923i 0.244949 + 0.424264i
\(601\) 20.0000i 0.815817i 0.913023 + 0.407909i \(0.133742\pi\)
−0.913023 + 0.407909i \(0.866258\pi\)
\(602\) 0 0
\(603\) −5.00000 + 5.00000i −0.203616 + 0.203616i
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) −12.2942 + 3.29423i −0.499831 + 0.133929i
\(606\) 8.05256 + 30.0526i 0.327113 + 1.22080i
\(607\) −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
\(611\) −2.92820 + 10.9282i −0.118462 + 0.442108i
\(612\) 2.00000 3.46410i 0.0808452 0.140028i
\(613\) −9.15064 34.1506i −0.369591 1.37933i −0.861090 0.508453i \(-0.830218\pi\)
0.491499 0.870878i \(-0.336449\pi\)
\(614\) 5.00000 + 8.66025i 0.201784 + 0.349499i
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) −10.3923 + 6.00000i −0.418040 + 0.241355i
\(619\) −6.22243 23.2224i −0.250101 0.933388i −0.970751 0.240089i \(-0.922823\pi\)
0.720650 0.693299i \(-0.243843\pi\)
\(620\) 21.8564 5.85641i 0.877774 0.235199i
\(621\) −8.78461 + 32.7846i −0.352514 + 1.31560i
\(622\) −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
\(626\) 21.8564 5.85641i 0.873558 0.234069i
\(627\) 8.19615 2.19615i 0.327323 0.0877059i
\(628\) 40.9808 + 10.9808i 1.63531 + 0.438180i
\(629\) 6.00000 6.00000i 0.239236 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 15.5885 + 9.00000i 0.619586 + 0.357718i
\(634\) −5.00000 + 8.66025i −0.198575 + 0.343943i
\(635\) −10.9282 2.92820i −0.433673 0.116202i
\(636\) 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 \(0.0509845\pi\)
\(642\) −19.1244 5.12436i −0.754778 0.202242i
\(643\) 21.0000 + 21.0000i 0.828159 + 0.828159i 0.987262 0.159103i \(-0.0508601\pi\)
−0.159103 + 0.987262i \(0.550860\pi\)
\(644\) 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 0.997118 0.0758684i \(-0.0241729\pi\)
0.432855 + 0.901464i \(0.357506\pi\)
\(648\) −13.6603 + 3.66025i −0.536625 + 0.143788i
\(649\) −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
\(653\) 6.95448 25.9545i 0.272150 1.01568i −0.685577 0.728000i \(-0.740450\pi\)
0.957727 0.287678i \(-0.0928832\pi\)
\(654\) 8.19615 2.19615i 0.320495 0.0858764i
\(655\) 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 0.293678 0.955904i \(-0.405121\pi\)
−0.955904 + 0.293678i \(0.905121\pi\)
\(660\) −1.46410 + 5.46410i −0.0569901 + 0.212690i
\(661\) 3.29423 + 12.2942i 0.128131 + 0.478190i 0.999932 0.0116697i \(-0.00371465\pi\)
−0.871801 + 0.489860i \(0.837048\pi\)
\(662\) −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
\(667\) −24.5885 6.58846i −0.952069 0.255106i
\(668\) 2.00000 3.46410i 0.0773823 0.134030i
\(669\) 32.7846 8.78461i 1.26753 0.339633i
\(670\) −13.6603 3.66025i −0.527742 0.141408i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 24.5885 + 6.58846i 0.947112 + 0.253778i
\(675\) −16.3923 + 4.39230i −0.630940 + 0.169060i
\(676\) 11.0000 19.0526i 0.423077 0.732791i
\(677\) 4.09808 + 1.09808i 0.157502 + 0.0422025i 0.336708 0.941609i \(-0.390686\pi\)
−0.179206 + 0.983811i \(0.557353\pi\)
\(678\) 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
\(683\) 1.83013 + 6.83013i 0.0700279 + 0.261348i 0.992060 0.125766i \(-0.0401388\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(684\) 2.19615 8.19615i 0.0839720 0.313388i
\(685\) −8.00000 8.00000i −0.305664 0.305664i
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) 27.3205 + 7.32051i 1.04158 + 0.279092i
\(689\) 5.00000 8.66025i 0.190485 0.329929i
\(690\) −16.3923 + 4.39230i −0.624044 + 0.167212i
\(691\) 3.29423 12.2942i 0.125318 0.467694i −0.874532 0.484967i \(-0.838832\pi\)
0.999851 + 0.0172725i \(0.00549828\pi\)
\(692\) 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
\(696\) −4.39230 16.3923i −0.166490 0.621349i
\(697\) 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 0.982006 + 0.188847i \(0.0604752\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 10.9282 + 2.92820i 0.412458 + 0.110518i
\(703\) 9.00000 15.5885i 0.339441 0.587930i
\(704\) −10.9282 + 2.92820i −0.411872 + 0.110361i
\(705\) 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
\(709\) −36.8827 9.88269i −1.38516 0.371152i −0.512166 0.858886i \(-0.671157\pi\)
−0.872992 + 0.487734i \(0.837823\pi\)
\(710\) 10.0000 17.3205i 0.375293 0.650027i
\(711\) 0 0
\(712\) 10.9282 + 2.92820i 0.409552 + 0.109739i
\(713\) 48.0000i 1.79761i
\(714\) 0 0
\(715\) 2.00000 2.00000i 0.0747958 0.0747958i
\(716\) 46.4449 + 12.4449i 1.73573 + 0.465086i
\(717\) 0 0
\(718\) 35.5167 9.51666i 1.32547 0.355159i
\(719\) 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
\(723\) 6.58846 24.5885i 0.245027 0.914455i
\(724\) 24.5885 6.58846i 0.913823 0.244858i
\(725\) −3.29423 12.2942i −0.122345 0.456596i
\(726\) −15.5885 + 9.00000i −0.578542 + 0.334021i
\(727\) 2.00000i 0.0741759i −0.999312 0.0370879i \(-0.988192\pi\)
0.999312 0.0370879i \(-0.0118082\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) −4.00000 6.92820i −0.148047 0.256424i
\(731\) 3.66025 + 13.6603i 0.135379 + 0.505243i
\(732\) −18.0000 + 31.1769i −0.665299 + 1.15233i
\(733\) 7.68653 28.6865i 0.283909 1.05956i −0.665725 0.746198i \(-0.731877\pi\)
0.949633 0.313364i \(-0.101456\pi\)
\(734\) 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
\(739\) −31.4186 + 8.41858i −1.15575 + 0.309683i −0.785268 0.619156i \(-0.787475\pi\)
−0.370484 + 0.928839i \(0.620808\pi\)
\(740\) 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 \(-0.680320\pi\)
0.536676 0.843788i \(-0.319680\pi\)
\(744\) 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
\(747\) −1.36603 0.366025i −0.0499803 0.0133922i
\(748\) −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
\(754\) −2.19615 + 8.19615i −0.0799792 + 0.298486i
\(755\) 10.0000 + 10.0000i 0.363937 + 0.363937i
\(756\) 0 0
\(757\) 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i \(-0.548692\pi\)
0.988323 + 0.152374i \(0.0486917\pi\)
\(758\) −5.19615 + 3.00000i −0.188733 + 0.108965i
\(759\) 10.3923 + 6.00000i 0.377217 + 0.217786i
\(760\) 16.3923 4.39230i 0.594611 0.159326i
\(761\) 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
\(765\) −0.732051 + 2.73205i −0.0264674 + 0.0987775i
\(766\) −5.85641 21.8564i −0.211601 0.789704i
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 5.85641 21.8564i 0.211325 0.788675i
\(769\) 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
\(773\) 1.83013 + 6.83013i 0.0658251 + 0.245663i 0.990997 0.133887i \(-0.0427458\pi\)
−0.925172 + 0.379549i \(0.876079\pi\)
\(774\) −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