Properties

Label 1078.2.e.h.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: \(x^{2} - x + 1\)
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.h.177.1

$q$-expansion

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

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 \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) −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 \(-0.833333\pi\)
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 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 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 \(-0.478334\pi\)
0.830014 0.557743i \(-0.188333\pi\)
\(32\) 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 \(-0.906501\pi\)
0.227844 0.973698i \(-0.426832\pi\)
\(48\) 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 \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) −2.00000 + 3.46410i −0.258199 + 0.447214i
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 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 −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) −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 \(-0.429548\pi\)
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 −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) −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 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −1.00000 1.73205i −0.0985329 0.170664i 0.812545 0.582899i \(-0.198082\pi\)
−0.911078 + 0.412235i \(0.864748\pi\)
\(104\) 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 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 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 \(-0.177693\pi\)
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 −0.825997 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 −0.993608 0.112884i \(-0.963991\pi\)
0.594565 + 0.804048i \(0.297324\pi\)
\(158\) 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 \(-0.600171\pi\)
−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 0.779926 0.625871i \(-0.215256\pi\)
−0.931984 + 0.362500i \(0.881923\pi\)
\(174\) −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 \(-0.325818\pi\)
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 0.684244 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 −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) −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 −0.967692 0.252136i \(-0.918867\pi\)
0.702202 + 0.711977i \(0.252200\pi\)
\(228\) −4.00000 + 6.92820i −0.264906 + 0.458831i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −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 −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 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 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 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 −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) −4.00000 + 6.92820i −0.243432 + 0.421637i
\(271\) 14.0000 + 24.2487i 0.850439 + 1.47300i 0.880812 + 0.473466i \(0.156997\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 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 \(-0.349073\pi\)
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 −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) −4.00000 + 6.92820i −0.226455 + 0.392232i
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) −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 \(-0.172659\pi\)
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 −0.891410 0.453197i \(-0.850283\pi\)
0.838186 + 0.545385i \(0.183617\pi\)
\(354\) 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 −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) −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 0.629890 0.776684i \(-0.283100\pi\)
−0.987573 + 0.157159i \(0.949767\pi\)
\(384\) −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 0.546795 0.837267i \(-0.315848\pi\)
−0.998492 + 0.0549046i \(0.982515\pi\)
\(398\) 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 −0.812333 0.583193i \(-0.801803\pi\)
0.911227 + 0.411905i \(0.135136\pi\)
\(410\) 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 −0.606471 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 \(-0.577241\pi\)
−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 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) −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 \(-0.232357\pi\)
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 0.657372 0.753566i \(-0.271668\pi\)
−0.981293 + 0.192518i \(0.938335\pi\)
\(468\) −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 −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 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 \(-0.413794\pi\)
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 −0.888065 0.459718i \(-0.847950\pi\)
0.0459045 0.998946i \(-0.485383\pi\)
\(510\) 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 \(-0.461500\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) 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 −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) −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 \(-0.494693\pi\)
0.857569 0.514370i \(-0.171974\pi\)
\(578\) −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 0.716131 0.697966i \(-0.245911\pi\)
−0.962522 + 0.271205i \(0.912578\pi\)
\(594\) 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 \(-0.662817\pi\)
−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 0.999889 0.0148722i \(-0.00473415\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(608\) −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 −0.845229 0.534404i \(-0.820536\pi\)
0.885422 + 0.464787i \(0.153869\pi\)
\(620\) 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 \(-0.357173\pi\)
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 −0.918952 0.394369i \(-0.870963\pi\)
0.801010 + 0.598651i \(0.204296\pi\)
\(648\) −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 \(-0.568625\pi\)
0.952940 0.303160i \(-0.0980418\pi\)
\(662\) −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 0.727386 0.686229i \(-0.240735\pi\)
−0.957984 + 0.286820i \(0.907402\pi\)
\(678\) 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 \(-0.872094\pi\)
0.121470 0.992595i \(-0.461239\pi\)
\(692\) 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 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 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 0.930393 0.366563i \(-0.119466\pi\)
−0.782650 + 0.622462i \(0.786132\pi\)
\(734\) −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 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 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 −0.379549 0.925172i \(-0.623921\pi\)
0.990997 0.133887i \(-0.0427458\pi\)
\(774\) −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
\(785\) 20.0000