Properties

Label 1078.2.e.h.177.1
Level $1078$
Weight $2$
Character 1078.177
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 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.h.67.1

$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

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

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 −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) −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 \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 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 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) 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 −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 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 0.227844 + 0.973698i \(0.426832\pi\)
−0.957169 + 0.289530i \(0.906501\pi\)
\(48\) 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 0.718677 + 0.695344i \(0.244748\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) −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 −0.982894 0.184172i \(-0.941040\pi\)
0.331949 0.943297i \(-0.392294\pi\)
\(60\) −2.00000 3.46410i −0.258199 0.447214i
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 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 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 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 \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) −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 −0.0726692 + 0.997356i \(0.523152\pi\)
−0.827401 + 0.561611i \(0.810182\pi\)
\(80\) −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 \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 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 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) −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 \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 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 −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −1.00000 + 1.73205i −0.0985329 + 0.170664i −0.911078 0.412235i \(-0.864748\pi\)
0.812545 + 0.582899i \(0.198082\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 14.0000 1.35980
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 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 \(-0.946976\pi\)
0.636676 + 0.771132i \(0.280309\pi\)
\(132\) 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 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 4.00000 6.92820i 0.340503 0.589768i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 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 −0.0751583 + 0.997172i \(0.523946\pi\)
−0.825997 + 0.563675i \(0.809387\pi\)
\(150\) −1.00000 1.73205i −0.0816497 0.141421i
\(151\) −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i \(-0.941004\pi\)
0.331842 0.943335i \(-0.392330\pi\)
\(152\) 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 \(-0.297324\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(158\) 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 −0.174282 + 0.984696i \(0.555760\pi\)
−0.765631 + 0.643280i \(0.777573\pi\)
\(164\) 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 \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 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 \(-0.881923\pi\)
0.779926 + 0.625871i \(0.215256\pi\)
\(174\) −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 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −1.00000 + 1.73205i −0.0745356 + 0.129099i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 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 −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) −1.00000 1.73205i −0.0721688 0.125000i
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 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 \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) −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 \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) 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 \(-0.252200\pi\)
−0.967692 + 0.252136i \(0.918867\pi\)
\(228\) −4.00000 6.92820i −0.264906 0.458831i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −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 \(-0.249619\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) 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 \(-0.806334\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(252\) 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 \(-0.853202\pi\)
0.833150 + 0.553047i \(0.186535\pi\)
\(258\) 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 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 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 \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) −4.00000 6.92820i −0.243432 0.421637i
\(271\) 14.0000 24.2487i 0.850439 1.47300i −0.0303728 0.999539i \(-0.509669\pi\)
0.880812 0.473466i \(-0.156997\pi\)
\(272\) 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 0.761714 0.647913i \(-0.224358\pi\)
−0.941966 + 0.335707i \(0.891025\pi\)
\(278\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 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 \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 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 \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) −4.00000 6.92820i −0.226455 0.392232i
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) −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 −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) −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 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) −2.00000 + 3.46410i −0.107211 + 0.185695i
\(349\) 32.0000 1.71292 0.856460 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) 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 \(-0.183617\pi\)
−0.891410 + 0.453197i \(0.850283\pi\)
\(354\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 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 \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) −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 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 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 \(-0.949767\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(384\) −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 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) −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 \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) 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 \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 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 \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 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 0.991817 0.127666i \(-0.0407486\pi\)
−0.606471 + 0.795106i \(0.707415\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 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 −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(444\) 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 0.0474665 0.998873i \(-0.484885\pi\)
0.841316 0.540544i \(-0.181781\pi\)
\(458\) −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 \(-0.232357\pi\)
0.745194 + 0.666847i \(0.232357\pi\)
\(462\) 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 \(-0.938335\pi\)
0.657372 + 0.753566i \(0.271668\pi\)
\(468\) −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 \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 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 0.697459 0.716625i \(-0.254314\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(488\) −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 −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) 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 \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 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 0.0459045 + 0.998946i \(0.485383\pi\)
−0.888065 + 0.459718i \(0.847950\pi\)
\(510\) 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 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 1.00000 + 1.73205i 0.0437688 + 0.0758098i
\(523\) −8.00000 + 13.8564i −0.349816 + 0.605898i −0.986216 0.165460i \(-0.947089\pi\)
0.636401 + 0.771358i \(0.280422\pi\)
\(524\) 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 −0.843728 0.536771i \(-0.819644\pi\)
0.886721 + 0.462304i \(0.152977\pi\)
\(542\) −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 −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) −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 \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) −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 −0.974624 0.223847i \(-0.928139\pi\)
0.681169 + 0.732126i \(0.261472\pi\)
\(570\) 8.00000 + 13.8564i 0.335083 + 0.580381i
\(571\) 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i \(0.0325850\pi\)
−0.408883 + 0.912587i \(0.634082\pi\)
\(572\) 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 0.857569 + 0.514370i \(0.171974\pi\)
0.0166728 + 0.999861i \(0.494693\pi\)
\(578\) −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 \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 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 \(-0.912578\pi\)
0.716131 + 0.697966i \(0.245911\pi\)
\(594\) 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 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) −1.00000 + 1.73205i −0.0408248 + 0.0707107i
\(601\) −24.0000 −0.978980 −0.489490 0.872009i \(-0.662817\pi\)
−0.489490 + 0.872009i \(0.662817\pi\)
\(602\) 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 \(-0.671401\pi\)
0.999889 + 0.0148722i \(0.00473415\pi\)
\(608\) −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 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 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 \(-0.153869\pi\)
−0.845229 + 0.534404i \(0.820536\pi\)
\(620\) 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 0.987200 0.159489i \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) 22.0000 0.867595 0.433798 0.901010i \(-0.357173\pi\)
0.433798 + 0.901010i \(0.357173\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) −3.00000 5.19615i −0.117942 0.204282i 0.801010 0.598651i \(-0.204296\pi\)
−0.918952 + 0.394369i \(0.870963\pi\)
\(648\) −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 −0.0726446 + 0.997358i \(0.523144\pi\)
−0.827415 + 0.561591i \(0.810189\pi\)
\(654\) −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 0.952940 + 0.303160i \(0.0980418\pi\)
−0.213925 + 0.976850i \(0.568625\pi\)
\(662\) −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 \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 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 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −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 0.121470 + 0.992595i \(0.461239\pi\)
−0.920348 + 0.391102i \(0.872094\pi\)
\(692\) 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 −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) −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 \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 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 \(-0.174767\pi\)
0.853023 + 0.521874i \(0.174767\pi\)
\(728\) 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 \(-0.786132\pi\)
0.930393 + 0.366563i \(0.119466\pi\)
\(734\) −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 0.731072 + 0.682300i \(0.239020\pi\)
0.225354 + 0.974277i \(0.427646\pi\)
\(740\) 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 −0.988761 0.149505i \(-0.952232\pi\)
0.623856 + 0.781540i \(0.285565\pi\)
\(752\) −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 \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 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 \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 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 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) −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