Properties

Label 1078.2.e.l.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.l.177.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.00000 + 1.73205i) q^{12} +4.00000 q^{13} +4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -2.00000 q^{20} -1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} +4.00000 q^{27} +2.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +1.00000 q^{36} +(3.00000 + 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(4.00000 - 6.92820i) q^{39} +(-1.00000 - 1.73205i) q^{40} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(2.00000 - 3.46410i) q^{46} +(5.00000 + 8.66025i) q^{47} -2.00000 q^{48} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(7.00000 - 12.1244i) q^{53} +(2.00000 + 3.46410i) q^{54} -2.00000 q^{55} +8.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(-4.00000 - 6.92820i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(-4.00000 + 6.92820i) q^{67} -8.00000 q^{69} -4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(2.00000 - 3.46410i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-1.00000 - 1.73205i) q^{75} -4.00000 q^{76} +8.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(1.00000 - 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} -4.00000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(2.00000 - 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} +(5.00000 + 8.66025i) q^{89} +2.00000 q^{90} +4.00000 q^{92} +(10.0000 + 17.3205i) q^{93} +(-5.00000 + 8.66025i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{96} -6.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{8} - q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 8 q^{15} - q^{16} + q^{18} + 4 q^{19} - 4 q^{20} - 2 q^{22} - 4 q^{23} - 2 q^{24} + q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{29} + 4 q^{30} - 10 q^{31} + q^{32} + 2 q^{33} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 2 q^{40} - 8 q^{43} - q^{44} + 2 q^{45} + 4 q^{46} + 10 q^{47} - 4 q^{48} + 2 q^{50} - 4 q^{52} + 14 q^{53} + 4 q^{54} - 4 q^{55} + 16 q^{57} + 2 q^{58} + 10 q^{59} - 4 q^{60} - 8 q^{61} - 20 q^{62} + 2 q^{64} + 8 q^{65} - 2 q^{66} - 8 q^{67} - 16 q^{69} - 8 q^{71} + q^{72} + 4 q^{73} - 6 q^{74} - 2 q^{75} - 8 q^{76} + 16 q^{78} - 16 q^{79} + 2 q^{80} + 11 q^{81} - 8 q^{83} - 4 q^{86} + 4 q^{87} + q^{88} + 10 q^{89} + 4 q^{90} + 8 q^{92} + 20 q^{93} - 10 q^{94} - 8 q^{95} - 2 q^{96} - 12 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) −1.00000 + 1.73205i −0.204124 + 0.353553i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 2.00000 + 3.46410i 0.365148 + 0.632456i
\(31\) −5.00000 + 8.66025i −0.898027 + 1.55543i −0.0680129 + 0.997684i \(0.521666\pi\)
−0.830014 + 0.557743i \(0.811667\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.00000 + 1.73205i 0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.00000 + 5.19615i 0.493197 + 0.854242i 0.999969 0.00783774i \(-0.00249486\pi\)
−0.506772 + 0.862080i \(0.669162\pi\)
\(38\) −2.00000 + 3.46410i −0.324443 + 0.561951i
\(39\) 4.00000 6.92820i 0.640513 1.10940i
\(40\) −1.00000 1.73205i −0.158114 0.273861i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 5.00000 + 8.66025i 0.729325 + 1.26323i 0.957169 + 0.289530i \(0.0934991\pi\)
−0.227844 + 0.973698i \(0.573168\pi\)
\(48\) −2.00000 −0.288675
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −2.00000 + 3.46410i −0.277350 + 0.480384i
\(53\) 7.00000 12.1244i 0.961524 1.66541i 0.242846 0.970065i \(-0.421919\pi\)
0.718677 0.695344i \(-0.244748\pi\)
\(54\) 2.00000 + 3.46410i 0.272166 + 0.471405i
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 8.00000 1.05963
\(58\) 1.00000 + 1.73205i 0.131306 + 0.227429i
\(59\) 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) −2.00000 + 3.46410i −0.258199 + 0.447214i
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) −10.0000 −1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.00000 + 6.92820i 0.496139 + 0.859338i
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 0 0
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) −8.00000 13.8564i −0.900070 1.55897i −0.827401 0.561611i \(-0.810182\pi\)
−0.0726692 0.997356i \(-0.523152\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 2.00000 3.46410i 0.214423 0.371391i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 10.0000 + 17.3205i 1.03695 + 1.79605i
\(94\) −5.00000 + 8.66025i −0.515711 + 0.893237i
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) −1.00000 1.73205i −0.102062 0.176777i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 0 0
\(103\) 1.00000 + 1.73205i 0.0985329 + 0.170664i 0.911078 0.412235i \(-0.135252\pi\)
−0.812545 + 0.582899i \(0.801918\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 14.0000 1.35980
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 12.0000 1.13899
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 4.00000 + 6.92820i 0.374634 + 0.648886i
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) −1.00000 + 1.73205i −0.0928477 + 0.160817i
\(117\) −2.00000 3.46410i −0.184900 0.320256i
\(118\) 10.0000 0.920575
\(119\) 0 0
\(120\) −4.00000 −0.365148
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 4.00000 6.92820i 0.362143 0.627250i
\(123\) 0 0
\(124\) −5.00000 8.66025i −0.449013 0.777714i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) −4.00000 + 6.92820i −0.350823 + 0.607644i
\(131\) 4.00000 + 6.92820i 0.349482 + 0.605320i 0.986157 0.165812i \(-0.0530244\pi\)
−0.636676 + 0.771132i \(0.719691\pi\)
\(132\) −2.00000 −0.174078
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 4.00000 + 6.92820i 0.344265 + 0.596285i
\(136\) 0 0
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) −4.00000 6.92820i −0.340503 0.589768i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 20.0000 1.68430
\(142\) −2.00000 3.46410i −0.167836 0.290701i
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 2.00000 + 3.46410i 0.166091 + 0.287678i
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −11.0000 19.0526i −0.901155 1.56085i −0.825997 0.563675i \(-0.809387\pi\)
−0.0751583 0.997172i \(-0.523946\pi\)
\(150\) 1.00000 1.73205i 0.0816497 0.141421i
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 0 0
\(154\) 0 0
\(155\) −20.0000 −1.60644
\(156\) 4.00000 + 6.92820i 0.320256 + 0.554700i
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) −14.0000 24.2487i −1.11027 1.92305i
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −12.0000 20.7846i −0.939913 1.62798i −0.765631 0.643280i \(-0.777573\pi\)
−0.174282 0.984696i \(-0.555760\pi\)
\(164\) 0 0
\(165\) −2.00000 + 3.46410i −0.155700 + 0.269680i
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 2.00000 + 3.46410i 0.152057 + 0.263371i 0.931984 0.362500i \(-0.118077\pi\)
−0.779926 + 0.625871i \(0.784744\pi\)
\(174\) 4.00000 0.303239
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −10.0000 17.3205i −0.751646 1.30189i
\(178\) −5.00000 + 8.66025i −0.374766 + 0.649113i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −16.0000 −1.18275
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) −6.00000 + 10.3923i −0.441129 + 0.764057i
\(186\) −10.0000 + 17.3205i −0.733236 + 1.27000i
\(187\) 0 0
\(188\) −10.0000 −0.729325
\(189\) 0 0
\(190\) −8.00000 −0.580381
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 1.00000 1.73205i 0.0721688 0.125000i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) −3.00000 5.19615i −0.215387 0.373062i
\(195\) 16.0000 1.14578
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i \(-0.998611\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 8.00000 + 13.8564i 0.564276 + 0.977356i
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 + 1.73205i −0.0696733 + 0.120678i
\(207\) −2.00000 + 3.46410i −0.139010 + 0.240772i
\(208\) −2.00000 3.46410i −0.138675 0.240192i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 7.00000 + 12.1244i 0.480762 + 0.832704i
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) −4.00000 6.92820i −0.270295 0.468165i
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 0 0
\(222\) 6.00000 + 10.3923i 0.402694 + 0.697486i
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 4.00000 6.92820i 0.265489 0.459841i −0.702202 0.711977i \(-0.747800\pi\)
0.967692 + 0.252136i \(0.0811332\pi\)
\(228\) −4.00000 + 6.92820i −0.264906 + 0.458831i
\(229\) −5.00000 8.66025i −0.330409 0.572286i 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) −10.0000 + 17.3205i −0.652328 + 1.12987i
\(236\) 5.00000 + 8.66025i 0.325472 + 0.563735i
\(237\) −32.0000 −2.07862
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) −2.00000 3.46410i −0.129099 0.223607i
\(241\) 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i \(-0.750381\pi\)
0.965615 + 0.259975i \(0.0837143\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 + 13.8564i 0.509028 + 0.881662i
\(248\) 5.00000 8.66025i 0.317500 0.549927i
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 26.0000 1.64111 0.820553 0.571571i \(-0.193666\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.00000 + 1.73205i 0.0623783 + 0.108042i 0.895528 0.445005i \(-0.146798\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) −8.00000 −0.496139
\(261\) −1.00000 1.73205i −0.0618984 0.107211i
\(262\) −4.00000 + 6.92820i −0.247121 + 0.428026i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) 28.0000 1.72003
\(266\) 0 0
\(267\) 20.0000 1.22398
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −4.00000 + 6.92820i −0.243432 + 0.421637i
\(271\) −14.0000 24.2487i −0.850439 1.47300i −0.880812 0.473466i \(-0.843003\pi\)
0.0303728 0.999539i \(-0.490331\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 4.00000 6.92820i 0.240772 0.417029i
\(277\) −3.00000 + 5.19615i −0.180253 + 0.312207i −0.941966 0.335707i \(-0.891025\pi\)
0.761714 + 0.647913i \(0.224358\pi\)
\(278\) −10.0000 17.3205i −0.599760 1.03882i
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 10.0000 + 17.3205i 0.595491 + 1.03142i
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 2.00000 3.46410i 0.118678 0.205557i
\(285\) 8.00000 + 13.8564i 0.473879 + 0.820783i
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −2.00000 + 3.46410i −0.117444 + 0.203419i
\(291\) −6.00000 + 10.3923i −0.351726 + 0.609208i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 20.0000 1.16445
\(296\) −3.00000 5.19615i −0.174371 0.302020i
\(297\) −2.00000 + 3.46410i −0.116052 + 0.201008i
\(298\) 11.0000 19.0526i 0.637213 1.10369i
\(299\) −8.00000 13.8564i −0.462652 0.801337i
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −12.0000 20.7846i −0.689382 1.19404i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 8.00000 13.8564i 0.458079 0.793416i
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) −10.0000 17.3205i −0.567962 0.983739i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) −4.00000 + 6.92820i −0.226455 + 0.392232i
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) 10.0000 0.564333
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 14.0000 24.2487i 0.785081 1.35980i
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) 1.00000 + 1.73205i 0.0559017 + 0.0968246i
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) 0 0
\(324\) 5.50000 + 9.52628i 0.305556 + 0.529238i
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) 12.0000 20.7846i 0.664619 1.15115i
\(327\) −14.0000 24.2487i −0.774202 1.34096i
\(328\) 0 0
\(329\) 0 0
\(330\) −4.00000 −0.220193
\(331\) 10.0000 + 17.3205i 0.549650 + 0.952021i 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 2.00000 3.46410i 0.109764 0.190117i
\(333\) 3.00000 5.19615i 0.164399 0.284747i
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −16.0000 −0.874173
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 1.50000 + 2.59808i 0.0815892 + 0.141317i
\(339\) −14.0000 + 24.2487i −0.760376 + 1.31701i
\(340\) 0 0
\(341\) −5.00000 8.66025i −0.270765 0.468979i
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) −8.00000 13.8564i −0.430706 0.746004i
\(346\) −2.00000 + 3.46410i −0.107521 + 0.186231i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 2.00000 + 3.46410i 0.107211 + 0.185695i
\(349\) −32.0000 −1.71292 −0.856460 0.516213i \(-0.827341\pi\)
−0.856460 + 0.516213i \(0.827341\pi\)
\(350\) 0 0
\(351\) 16.0000 0.854017
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 1.00000 1.73205i 0.0532246 0.0921878i −0.838186 0.545385i \(-0.816383\pi\)
0.891410 + 0.453197i \(0.149717\pi\)
\(354\) 10.0000 17.3205i 0.531494 0.920575i
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −7.00000 12.1244i −0.367912 0.637242i
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) −8.00000 13.8564i −0.418167 0.724286i
\(367\) 9.00000 15.5885i 0.469796 0.813711i −0.529607 0.848243i \(-0.677661\pi\)
0.999404 + 0.0345320i \(0.0109941\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) 0 0
\(372\) −20.0000 −1.03695
\(373\) 17.0000 + 29.4449i 0.880227 + 1.52460i 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) −5.00000 8.66025i −0.257855 0.446619i
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −4.00000 6.92820i −0.205196 0.355409i
\(381\) −16.0000 + 27.7128i −0.819705 + 1.41977i
\(382\) 4.00000 6.92820i 0.204658 0.354478i
\(383\) 7.00000 + 12.1244i 0.357683 + 0.619526i 0.987573 0.157159i \(-0.0502334\pi\)
−0.629890 + 0.776684i \(0.716900\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 3.00000 5.19615i 0.152302 0.263795i
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 8.00000 + 13.8564i 0.405096 + 0.701646i
\(391\) 0 0
\(392\) 0 0
\(393\) 16.0000 0.807093
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 16.0000 27.7128i 0.805047 1.39438i
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) −14.0000 −0.701757
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −5.00000 8.66025i −0.249688 0.432472i 0.713751 0.700399i \(-0.246995\pi\)
−0.963439 + 0.267927i \(0.913661\pi\)
\(402\) −8.00000 + 13.8564i −0.399004 + 0.691095i
\(403\) −20.0000 + 34.6410i −0.996271 + 1.72559i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 22.0000 1.09319
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −2.00000 + 3.46410i −0.0988936 + 0.171289i −0.911227 0.411905i \(-0.864864\pi\)
0.812333 + 0.583193i \(0.198197\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) −2.00000 −0.0985329
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) −4.00000 6.92820i −0.196352 0.340092i
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) −20.0000 + 34.6410i −0.979404 + 1.69638i
\(418\) −2.00000 3.46410i −0.0978232 0.169435i
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) 5.00000 8.66025i 0.243108 0.421076i
\(424\) −7.00000 + 12.1244i −0.339950 + 0.588811i
\(425\) 0 0
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 4.00000 + 6.92820i 0.193122 + 0.334497i
\(430\) 4.00000 6.92820i 0.192897 0.334108i
\(431\) 8.00000 13.8564i 0.385346 0.667440i −0.606471 0.795106i \(-0.707415\pi\)
0.991817 + 0.127666i \(0.0407486\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) 10.0000 0.480569 0.240285 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 8.00000 13.8564i 0.382692 0.662842i
\(438\) 4.00000 6.92820i 0.191127 0.331042i
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) −10.0000 + 17.3205i −0.474045 + 0.821071i
\(446\) 7.00000 + 12.1244i 0.331460 + 0.574105i
\(447\) −44.0000 −2.08113
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) 0 0
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) 16.0000 + 27.7128i 0.751746 + 1.30206i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) 19.0000 + 32.9090i 0.888783 + 1.53942i 0.841316 + 0.540544i \(0.181781\pi\)
0.0474665 + 0.998873i \(0.484885\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) 0 0
\(460\) 4.00000 + 6.92820i 0.186501 + 0.323029i
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 0 0
\(463\) 12.0000 0.557687 0.278844 0.960337i \(-0.410049\pi\)
0.278844 + 0.960337i \(0.410049\pi\)
\(464\) −1.00000 1.73205i −0.0464238 0.0804084i
\(465\) −20.0000 + 34.6410i −0.927478 + 1.60644i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) 7.00000 + 12.1244i 0.323921 + 0.561048i 0.981293 0.192518i \(-0.0616653\pi\)
−0.657372 + 0.753566i \(0.728332\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) −20.0000 −0.922531
\(471\) −10.0000 17.3205i −0.460776 0.798087i
\(472\) −5.00000 + 8.66025i −0.230144 + 0.398621i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) −16.0000 27.7128i −0.734904 1.27289i
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −14.0000 −0.641016
\(478\) −4.00000 6.92820i −0.182956 0.316889i
\(479\) 6.00000 10.3923i 0.274147 0.474837i −0.695773 0.718262i \(-0.744938\pi\)
0.969920 + 0.243426i \(0.0782712\pi\)
\(480\) 2.00000 3.46410i 0.0912871 0.158114i
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 8.00000 0.364390
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −6.00000 10.3923i −0.272446 0.471890i
\(486\) 5.00000 8.66025i 0.226805 0.392837i
\(487\) −6.00000 + 10.3923i −0.271886 + 0.470920i −0.969345 0.245705i \(-0.920981\pi\)
0.697459 + 0.716625i \(0.254314\pi\)
\(488\) 4.00000 + 6.92820i 0.181071 + 0.313625i
\(489\) −48.0000 −2.17064
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 1.00000 + 1.73205i 0.0449467 + 0.0778499i
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) −8.00000 −0.358489
\(499\) 8.00000 + 13.8564i 0.358129 + 0.620298i 0.987648 0.156687i \(-0.0500814\pi\)
−0.629519 + 0.776985i \(0.716748\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 8.00000 13.8564i 0.357414 0.619059i
\(502\) 13.0000 + 22.5167i 0.580218 + 1.00497i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 2.00000 + 3.46410i 0.0889108 + 0.153998i
\(507\) 3.00000 5.19615i 0.133235 0.230769i
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) 19.0000 + 32.9090i 0.842160 + 1.45866i 0.888065 + 0.459718i \(0.152050\pi\)
−0.0459045 + 0.998946i \(0.514617\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 8.00000 + 13.8564i 0.353209 + 0.611775i
\(514\) −1.00000 + 1.73205i −0.0441081 + 0.0763975i
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) −10.0000 −0.439799
\(518\) 0 0
\(519\) 8.00000 0.351161
\(520\) −4.00000 6.92820i −0.175412 0.303822i
\(521\) −21.0000 + 36.3731i −0.920027 + 1.59353i −0.120656 + 0.992694i \(0.538500\pi\)
−0.799370 + 0.600839i \(0.794833\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 1.00000 1.73205i 0.0435194 0.0753778i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 14.0000 + 24.2487i 0.608121 + 1.05330i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 0 0
\(534\) 10.0000 + 17.3205i 0.432742 + 0.749532i
\(535\) −12.0000 + 20.7846i −0.518805 + 0.898597i
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) 12.0000 + 20.7846i 0.517838 + 0.896922i
\(538\) 14.0000 0.603583
\(539\) 0 0
\(540\) −8.00000 −0.344265
\(541\) 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i \(-0.152977\pi\)
−0.843728 + 0.536771i \(0.819644\pi\)
\(542\) 14.0000 24.2487i 0.601351 1.04157i
\(543\) −14.0000 + 24.2487i −0.600798 + 1.04061i
\(544\) 0 0
\(545\) 28.0000 1.19939
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 8.00000 0.340503
\(553\) 0 0
\(554\) −6.00000 −0.254916
\(555\) 12.0000 + 20.7846i 0.509372 + 0.882258i
\(556\) 10.0000 17.3205i 0.424094 0.734553i
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 5.00000 + 8.66025i 0.211667 + 0.366618i
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 15.0000 + 25.9808i 0.632737 + 1.09593i
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) −10.0000 + 17.3205i −0.421076 + 0.729325i
\(565\) −14.0000 24.2487i −0.588984 1.02015i
\(566\) 0 0
\(567\) 0 0
\(568\) 4.00000 0.167836
\(569\) −7.00000 12.1244i −0.293455 0.508279i 0.681169 0.732126i \(-0.261472\pi\)
−0.974624 + 0.223847i \(0.928139\pi\)
\(570\) −8.00000 + 13.8564i −0.335083 + 0.580381i
\(571\) 14.0000 24.2487i 0.585882 1.01478i −0.408883 0.912587i \(-0.634082\pi\)
0.994765 0.102190i \(-0.0325850\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) −16.0000 −0.668410
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −21.0000 + 36.3731i −0.874241 + 1.51423i −0.0166728 + 0.999861i \(0.505307\pi\)
−0.857569 + 0.514370i \(0.828026\pi\)
\(578\) −8.50000 + 14.7224i −0.353553 + 0.612372i
\(579\) −6.00000 10.3923i −0.249351 0.431889i
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) 7.00000 + 12.1244i 0.289910 + 0.502140i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 4.00000 6.92820i 0.165380 0.286446i
\(586\) 0 0
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) 0 0
\(589\) −40.0000 −1.64817
\(590\) 10.0000 + 17.3205i 0.411693 + 0.713074i
\(591\) −18.0000 + 31.1769i −0.740421 + 1.28245i
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) 6.00000 + 10.3923i 0.246390 + 0.426761i 0.962522 0.271205i \(-0.0874221\pi\)
−0.716131 + 0.697966i \(0.754089\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 22.0000 0.901155
\(597\) 14.0000 + 24.2487i 0.572982 + 0.992434i
\(598\) 8.00000 13.8564i 0.327144 0.566631i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 1.00000 + 1.73205i 0.0408248 + 0.0707107i
\(601\) 24.0000 0.978980 0.489490 0.872009i \(-0.337183\pi\)
0.489490 + 0.872009i \(0.337183\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 12.0000 20.7846i 0.487467 0.844317i
\(607\) −12.0000 20.7846i −0.487065 0.843621i 0.512824 0.858494i \(-0.328599\pi\)
−0.999889 + 0.0148722i \(0.995266\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 16.0000 0.647821
\(611\) 20.0000 + 34.6410i 0.809113 + 1.40143i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) −8.00000 13.8564i −0.322854 0.559199i
\(615\) 0 0
\(616\) 0 0
\(617\) 38.0000 1.52982 0.764911 0.644136i \(-0.222783\pi\)
0.764911 + 0.644136i \(0.222783\pi\)
\(618\) 2.00000 + 3.46410i 0.0804518 + 0.139347i
\(619\) −1.00000 + 1.73205i −0.0401934 + 0.0696170i −0.885422 0.464787i \(-0.846131\pi\)
0.845229 + 0.534404i \(0.179464\pi\)
\(620\) 10.0000 17.3205i 0.401610 0.695608i
\(621\) −8.00000 13.8564i −0.321029 0.556038i
\(622\) −6.00000 −0.240578
\(623\) 0 0
\(624\) −8.00000 −0.320256
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) −4.00000 + 6.92820i −0.159745 + 0.276686i
\(628\) 5.00000 + 8.66025i 0.199522 + 0.345582i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −16.0000 27.7128i −0.634941 1.09975i
\(636\) 28.0000 1.11027
\(637\) 0 0
\(638\) −2.00000 −0.0791808
\(639\) 2.00000 + 3.46410i 0.0791188 + 0.137038i
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 12.0000 + 20.7846i 0.473602 + 0.820303i
\(643\) −22.0000 −0.867595 −0.433798 0.901010i \(-0.642827\pi\)
−0.433798 + 0.901010i \(0.642827\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) 3.00000 5.19615i 0.117942 0.204282i −0.801010 0.598651i \(-0.795704\pi\)
0.918952 + 0.394369i \(0.129037\pi\)
\(648\) −5.50000 + 9.52628i −0.216060 + 0.374228i
\(649\) 5.00000 + 8.66025i 0.196267 + 0.339945i
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) 24.0000 0.939913
\(653\) −23.0000 39.8372i −0.900060 1.55895i −0.827415 0.561591i \(-0.810189\pi\)
−0.0726446 0.997358i \(-0.523144\pi\)
\(654\) 14.0000 24.2487i 0.547443 0.948200i
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) −2.00000 3.46410i −0.0778499 0.134840i
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −10.0000 + 17.3205i −0.388661 + 0.673181i
\(663\) 0 0
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −4.00000 6.92820i −0.154881 0.268261i
\(668\) −4.00000 + 6.92820i −0.154765 + 0.268060i
\(669\) 14.0000 24.2487i 0.541271 0.937509i
\(670\) −8.00000 13.8564i −0.309067 0.535320i
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) −17.0000 29.4449i −0.654816 1.13417i
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) −28.0000 −1.07533
\(679\) 0 0
\(680\) 0 0
\(681\) −8.00000 13.8564i −0.306561 0.530979i
\(682\) 5.00000 8.66025i 0.191460 0.331618i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 2.00000 + 3.46410i 0.0764719 + 0.132453i
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −20.0000 −0.763048
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) 28.0000 48.4974i 1.06672 1.84760i
\(690\) 8.00000 13.8564i 0.304555 0.527504i
\(691\) 21.0000 + 36.3731i 0.798878 + 1.38370i 0.920348 + 0.391102i \(0.127906\pi\)
−0.121470 + 0.992595i \(0.538761\pi\)
\(692\) −4.00000 −0.152057
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −20.0000 34.6410i −0.758643 1.31401i
\(696\) −2.00000 + 3.46410i −0.0758098 + 0.131306i
\(697\) 0 0
\(698\) −16.0000 27.7128i −0.605609 1.04895i
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 8.00000 + 13.8564i 0.301941 + 0.522976i
\(703\) −12.0000 + 20.7846i −0.452589 + 0.783906i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 20.0000 + 34.6410i 0.753244 + 1.30466i
\(706\) 2.00000 0.0752710
\(707\) 0 0
\(708\) 20.0000 0.751646
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 4.00000 6.92820i 0.150117 0.260011i
\(711\) −8.00000 + 13.8564i −0.300023 + 0.519656i
\(712\) −5.00000 8.66025i −0.187383 0.324557i
\(713\) 40.0000 1.49801
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) −8.00000 + 13.8564i −0.298765 + 0.517477i
\(718\) 0 0
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −8.00000 13.8564i −0.297523 0.515325i
\(724\) 7.00000 12.1244i 0.260153 0.450598i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −46.0000 −1.70605 −0.853023 0.521874i \(-0.825233\pi\)
−0.853023 + 0.521874i \(0.825233\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 4.00000 + 6.92820i 0.148047 + 0.256424i
\(731\) 0 0
\(732\) 8.00000 13.8564i 0.295689 0.512148i
\(733\) −4.00000 6.92820i −0.147743 0.255899i 0.782650 0.622462i \(-0.213868\pi\)
−0.930393 + 0.366563i \(0.880534\pi\)
\(734\) 18.0000 0.664392
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −4.00000 6.92820i −0.147342 0.255204i
\(738\) 0 0
\(739\) 26.0000 45.0333i 0.956425 1.65658i 0.225354 0.974277i \(-0.427646\pi\)
0.731072 0.682300i \(-0.239020\pi\)
\(740\) −6.00000 10.3923i −0.220564 0.382029i
\(741\) 32.0000 1.17555
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) −10.0000 17.3205i −0.366618 0.635001i
\(745\) 22.0000 38.1051i 0.806018 1.39606i
\(746\) −17.0000 + 29.4449i −0.622414 + 1.07805i
\(747\) 2.00000 + 3.46410i 0.0731762 + 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 24.0000 0.876356
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 5.00000 8.66025i 0.182331 0.315807i
\(753\) 26.0000 45.0333i 0.947493 1.64111i
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) 30.0000 1.09037 0.545184 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) 4.00000 + 6.92820i 0.145287 + 0.251644i
\(759\) 4.00000 6.92820i 0.145191 0.251478i
\(760\) 4.00000 6.92820i 0.145095 0.251312i
\(761\) −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i \(-0.236457\pi\)
−0.954043 + 0.299670i \(0.903123\pi\)
\(762\) −32.0000 −1.15924
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −7.00000 + 12.1244i −0.252920 + 0.438071i
\(767\) 20.0000 34.6410i 0.722158 1.25081i
\(768\) 1.00000 + 1.73205i 0.0360844 + 0.0625000i
\(769\) −4.00000 −0.144244 −0.0721218 0.997396i \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 0 0
\(771\) 4.00000 0.144056
\(772\) 3.00000 + 5.19615i 0.107972 + 0.187014i
\(773\) −17.0000 + 29.4449i −0.611448 + 1.05906i 0.379549 + 0.925172i \(0.376079\pi\)
−0.990997 + 0.133887i \(0.957254\pi\)
\(774\) −2.00000 + 3.46410i −0.0718885 + 0.124515i
\(775\) 5.00000 + 8.66025i 0.179605 + 0.311086i
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) 0 0
\(780\) −8.00000 + 13.8564i −0.286446 + 0.496139i
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0