Properties

Label 57.2.e.a.49.1
Level 57
Weight 2
Character 57.49
Analytic conductor 0.455
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 57.e (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.455147291521\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 57.49
Dual form 57.2.e.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} +1.00000 q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{21} +(1.00000 - 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 + 4.33013i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(4.00000 + 6.92820i) q^{29} -3.00000 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(0.500000 - 0.866025i) q^{36} +3.00000 q^{37} +(0.500000 - 4.33013i) q^{38} -5.00000 q^{39} +(6.00000 - 10.3923i) q^{41} +(0.500000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -5.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(0.500000 - 0.866025i) q^{54} -3.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} -8.00000 q^{58} +(-5.00000 + 8.66025i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{62} +(-0.500000 - 0.866025i) q^{63} +7.00000 q^{64} +(-1.00000 - 1.73205i) q^{66} +(-5.50000 - 9.52628i) q^{67} +4.00000 q^{68} +4.00000 q^{69} +(-3.00000 + 5.19615i) q^{71} +(1.50000 + 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-1.50000 + 2.59808i) q^{74} +5.00000 q^{75} +(-3.50000 - 2.59808i) q^{76} -2.00000 q^{77} +(2.50000 - 4.33013i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} +1.00000 q^{84} +(0.500000 + 0.866025i) q^{86} +8.00000 q^{87} +6.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(-2.50000 - 4.33013i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-1.50000 + 2.59808i) q^{93} -6.00000 q^{94} -5.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(3.00000 - 5.19615i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} - 6q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} - 6q^{8} - q^{9} - 4q^{11} + 2q^{12} - 5q^{13} - q^{14} + q^{16} + 4q^{17} + 2q^{18} - 8q^{19} + q^{21} + 2q^{22} + 4q^{23} - 3q^{24} + 5q^{25} + 10q^{26} - 2q^{27} + q^{28} + 8q^{29} - 6q^{31} - 5q^{32} - 2q^{33} + 4q^{34} + q^{36} + 6q^{37} + q^{38} - 10q^{39} + 12q^{41} + q^{42} + q^{43} - 2q^{44} - 8q^{46} + 6q^{47} - q^{48} - 12q^{49} - 10q^{50} - 4q^{51} + 5q^{52} - 4q^{53} + q^{54} - 6q^{56} - q^{57} - 16q^{58} - 10q^{59} + 13q^{61} + 3q^{62} - q^{63} + 14q^{64} - 2q^{66} - 11q^{67} + 8q^{68} + 8q^{69} - 6q^{71} + 3q^{72} + 11q^{73} - 3q^{74} + 10q^{75} - 7q^{76} - 4q^{77} + 5q^{78} - q^{79} - q^{81} + 12q^{82} + 2q^{84} + q^{86} + 16q^{87} + 12q^{88} + 6q^{89} - 5q^{91} - 4q^{92} - 3q^{93} - 12q^{94} - 10q^{96} - 2q^{97} + 6q^{98} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(40\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −3.00000 −1.06066
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.50000 4.33013i −0.693375 1.20096i −0.970725 0.240192i \(-0.922790\pi\)
0.277350 0.960769i \(-0.410544\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0.500000 0.866025i 0.109109 0.188982i
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 5.00000 0.980581
\(27\) −1.00000 −0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 4.00000 + 6.92820i 0.742781 + 1.28654i 0.951224 + 0.308500i \(0.0998271\pi\)
−0.208443 + 0.978035i \(0.566840\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0.500000 4.33013i 0.0811107 0.702439i
\(39\) −5.00000 −0.800641
\(40\) 0 0
\(41\) 6.00000 10.3923i 0.937043 1.62301i 0.166092 0.986110i \(-0.446885\pi\)
0.770950 0.636895i \(-0.219782\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −6.00000 −0.857143
\(50\) −5.00000 −0.707107
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 2.50000 4.33013i 0.346688 0.600481i
\(53\) −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i \(-0.255252\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) −0.500000 + 4.33013i −0.0662266 + 0.573539i
\(58\) −8.00000 −1.05045
\(59\) −5.00000 + 8.66025i −0.650945 + 1.12747i 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 1.50000 2.59808i 0.190500 0.329956i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −1.00000 1.73205i −0.123091 0.213201i
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 4.00000 0.485071
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 5.00000 0.577350
\(76\) −3.50000 2.59808i −0.401478 0.298020i
\(77\) −2.00000 −0.227921
\(78\) 2.50000 4.33013i 0.283069 0.490290i
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 6.00000 + 10.3923i 0.662589 + 1.14764i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 8.00000 0.857690
\(88\) 6.00000 0.639602
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) −2.50000 4.33013i −0.262071 0.453921i
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) −6.00000 −0.618853
\(95\) 0 0
\(96\) −5.00000 −0.510310
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 3.00000 5.19615i 0.303046 0.524891i
\(99\) 1.00000 + 1.73205i 0.100504 + 0.174078i
\(100\) −2.50000 + 4.33013i −0.250000 + 0.433013i
\(101\) −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) 4.00000 0.396059
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 7.50000 + 12.9904i 0.735436 + 1.27381i
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 1.50000 2.59808i 0.142374 0.246598i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −3.50000 2.59808i −0.327805 0.243332i
\(115\) 0 0
\(116\) −4.00000 + 6.92820i −0.371391 + 0.643268i
\(117\) −2.50000 + 4.33013i −0.231125 + 0.400320i
\(118\) −5.00000 8.66025i −0.460287 0.797241i
\(119\) 2.00000 3.46410i 0.183340 0.317554i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −13.0000 −1.17696
\(123\) −6.00000 10.3923i −0.541002 0.937043i
\(124\) −1.50000 2.59808i −0.134704 0.233314i
\(125\) 0 0
\(126\) 1.00000 0.0890871
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) −0.500000 0.866025i −0.0440225 0.0762493i
\(130\) 0 0
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) −2.00000 −0.174078
\(133\) −4.00000 + 1.73205i −0.346844 + 0.150188i
\(134\) 11.0000 0.950255
\(135\) 0 0
\(136\) −6.00000 + 10.3923i −0.514496 + 0.891133i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) −2.00000 + 3.46410i −0.170251 + 0.294884i
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 5.00000 + 8.66025i 0.418121 + 0.724207i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 5.50000 + 9.52628i 0.455183 + 0.788400i
\(147\) −3.00000 + 5.19615i −0.247436 + 0.428571i
\(148\) 1.50000 + 2.59808i 0.123299 + 0.213561i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) −2.50000 + 4.33013i −0.204124 + 0.353553i
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 12.0000 5.19615i 0.973329 0.421464i
\(153\) −4.00000 −0.323381
\(154\) 1.00000 1.73205i 0.0805823 0.139573i
\(155\) 0 0
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) −1.50000 + 2.59808i −0.119713 + 0.207349i −0.919654 0.392730i \(-0.871531\pi\)
0.799941 + 0.600079i \(0.204864\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) −4.00000 −0.317221
\(160\) 0 0
\(161\) 2.00000 + 3.46410i 0.157622 + 0.273009i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 3.00000 0.234978 0.117489 0.993074i \(-0.462515\pi\)
0.117489 + 0.993074i \(0.462515\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 + 1.73205i 0.0773823 + 0.134030i 0.902120 0.431486i \(-0.142010\pi\)
−0.824737 + 0.565516i \(0.808677\pi\)
\(168\) −1.50000 + 2.59808i −0.115728 + 0.200446i
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 3.50000 + 2.59808i 0.267652 + 0.198680i
\(172\) 1.00000 0.0762493
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) −4.00000 + 6.92820i −0.303239 + 0.525226i
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 5.00000 + 8.66025i 0.375823 + 0.650945i
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 1.00000 + 1.73205i 0.0743294 + 0.128742i 0.900794 0.434246i \(-0.142985\pi\)
−0.826465 + 0.562988i \(0.809652\pi\)
\(182\) 5.00000 0.370625
\(183\) 13.0000 0.960988
\(184\) −6.00000 10.3923i −0.442326 0.766131i
\(185\) 0 0
\(186\) −1.50000 2.59808i −0.109985 0.190500i
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 3.50000 6.06218i 0.252591 0.437500i
\(193\) −9.50000 + 16.4545i −0.683825 + 1.18442i 0.289980 + 0.957033i \(0.406351\pi\)
−0.973805 + 0.227387i \(0.926982\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) −3.00000 5.19615i −0.214286 0.371154i
\(197\) −26.0000 −1.85242 −0.926212 0.377004i \(-0.876954\pi\)
−0.926212 + 0.377004i \(0.876954\pi\)
\(198\) −2.00000 −0.142134
\(199\) −10.5000 18.1865i −0.744325 1.28921i −0.950509 0.310696i \(-0.899438\pi\)
0.206184 0.978513i \(-0.433895\pi\)
\(200\) −7.50000 12.9904i −0.530330 0.918559i
\(201\) −11.0000 −0.775880
\(202\) 14.0000 0.985037
\(203\) 4.00000 + 6.92820i 0.280745 + 0.486265i
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) −5.00000 −0.346688
\(209\) 8.00000 3.46410i 0.553372 0.239617i
\(210\) 0 0
\(211\) 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i \(-0.660634\pi\)
0.999820 0.0189499i \(-0.00603229\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) 9.00000 15.5885i 0.615227 1.06561i
\(215\) 0 0
\(216\) 3.00000 0.204124
\(217\) −3.00000 −0.203653
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) −5.50000 9.52628i −0.371656 0.643726i
\(220\) 0 0
\(221\) −20.0000 −1.34535
\(222\) 1.50000 + 2.59808i 0.100673 + 0.174371i
\(223\) −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i \(-0.930768\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(224\) −2.50000 4.33013i −0.167038 0.289319i
\(225\) 2.50000 4.33013i 0.166667 0.288675i
\(226\) −1.00000 + 1.73205i −0.0665190 + 0.115214i
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) −4.00000 + 1.73205i −0.264906 + 0.114708i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) −12.0000 20.7846i −0.787839 1.36458i
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −2.50000 4.33013i −0.163430 0.283069i
\(235\) 0 0
\(236\) −10.0000 −0.650945
\(237\) 0.500000 + 0.866025i 0.0324785 + 0.0562544i
\(238\) 2.00000 + 3.46410i 0.129641 + 0.224544i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −6.50000 + 11.2583i −0.416120 + 0.720741i
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 17.5000 + 12.9904i 1.11350 + 0.826558i
\(248\) 9.00000 0.571501
\(249\) 0 0
\(250\) 0 0
\(251\) 1.00000 + 1.73205i 0.0631194 + 0.109326i 0.895858 0.444340i \(-0.146562\pi\)
−0.832739 + 0.553666i \(0.813228\pi\)
\(252\) 0.500000 0.866025i 0.0314970 0.0545545i
\(253\) −4.00000 6.92820i −0.251478 0.435572i
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 10.0000 + 17.3205i 0.623783 + 1.08042i 0.988775 + 0.149413i \(0.0477384\pi\)
−0.364992 + 0.931011i \(0.618928\pi\)
\(258\) 1.00000 0.0622573
\(259\) 3.00000 0.186411
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 7.00000 + 12.1244i 0.432461 + 0.749045i
\(263\) −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i \(0.462692\pi\)
−0.918553 + 0.395298i \(0.870641\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 0 0
\(266\) 0.500000 4.33013i 0.0306570 0.265497i
\(267\) 6.00000 0.367194
\(268\) 5.50000 9.52628i 0.335966 0.581910i
\(269\) −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i \(-0.931941\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) −5.00000 −0.302614
\(274\) 18.0000 1.08742
\(275\) −5.00000 8.66025i −0.301511 0.522233i
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 5.00000 0.299880
\(279\) 1.50000 + 2.59808i 0.0898027 + 0.155543i
\(280\) 0 0
\(281\) 4.00000 + 6.92820i 0.238620 + 0.413302i 0.960319 0.278906i \(-0.0899716\pi\)
−0.721699 + 0.692207i \(0.756638\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) −10.0000 −0.591312
\(287\) 6.00000 10.3923i 0.354169 0.613438i
\(288\) −2.50000 + 4.33013i −0.147314 + 0.255155i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) 11.0000 0.643726
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) −3.00000 5.19615i −0.174964 0.303046i
\(295\) 0 0
\(296\) −9.00000 −0.523114
\(297\) 2.00000 0.116052
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 10.0000 17.3205i 0.578315 1.00167i
\(300\) 2.50000 + 4.33013i 0.144338 + 0.250000i
\(301\) 0.500000 0.866025i 0.0288195 0.0499169i
\(302\) −6.00000 + 10.3923i −0.345261 + 0.598010i
\(303\) −14.0000 −0.804279
\(304\) −0.500000 + 4.33013i −0.0286770 + 0.248350i
\(305\) 0 0
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i \(-0.722081\pi\)
0.984885 + 0.173210i \(0.0554140\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 6.50000 11.2583i 0.369772 0.640464i
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 15.0000 0.849208
\(313\) −11.0000 19.0526i −0.621757 1.07691i −0.989158 0.146852i \(-0.953086\pi\)
0.367402 0.930062i \(-0.380247\pi\)
\(314\) −1.50000 2.59808i −0.0846499 0.146618i
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 2.00000 + 3.46410i 0.112331 + 0.194563i 0.916710 0.399554i \(-0.130835\pi\)
−0.804379 + 0.594117i \(0.797502\pi\)
\(318\) 2.00000 3.46410i 0.112154 0.194257i
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) 0 0
\(321\) −9.00000 + 15.5885i −0.502331 + 0.870063i
\(322\) −4.00000 −0.222911
\(323\) −2.00000 + 17.3205i −0.111283 + 0.963739i
\(324\) −1.00000 −0.0555556
\(325\) 12.5000 21.6506i 0.693375 1.20096i
\(326\) −1.50000 + 2.59808i −0.0830773 + 0.143894i
\(327\) −1.00000 1.73205i −0.0553001 0.0957826i
\(328\) −18.0000 + 31.1769i −0.993884 + 1.72146i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) 0 0
\(333\) −1.50000 2.59808i −0.0821995 0.142374i
\(334\) −2.00000 −0.109435
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −6.50000 + 11.2583i −0.354078 + 0.613280i −0.986960 0.160968i \(-0.948538\pi\)
0.632882 + 0.774248i \(0.281872\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 1.00000 1.73205i 0.0543125 0.0940721i
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) −4.00000 + 1.73205i −0.216295 + 0.0936586i
\(343\) −13.0000 −0.701934
\(344\) −1.50000 + 2.59808i −0.0808746 + 0.140079i
\(345\) 0 0
\(346\) 0 0
\(347\) 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i \(-0.692036\pi\)
0.996826 + 0.0796169i \(0.0253697\pi\)
\(348\) 4.00000 + 6.92820i 0.214423 + 0.371391i
\(349\) −21.0000 −1.12410 −0.562052 0.827102i \(-0.689988\pi\)
−0.562052 + 0.827102i \(0.689988\pi\)
\(350\) −5.00000 −0.267261
\(351\) 2.50000 + 4.33013i 0.133440 + 0.231125i
\(352\) 5.00000 + 8.66025i 0.266501 + 0.461593i
\(353\) 4.00000 0.212899 0.106449 0.994318i \(-0.466052\pi\)
0.106449 + 0.994318i \(0.466052\pi\)
\(354\) −10.0000 −0.531494
\(355\) 0 0
\(356\) −3.00000 + 5.19615i −0.159000 + 0.275396i
\(357\) −2.00000 3.46410i −0.105851 0.183340i
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) 10.0000 17.3205i 0.527780 0.914141i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323801i \(-0.0103087\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) −2.00000 −0.105118
\(363\) −3.50000 + 6.06218i −0.183702 + 0.318182i
\(364\) 2.50000 4.33013i 0.131036 0.226960i
\(365\) 0 0
\(366\) −6.50000 + 11.2583i −0.339760 + 0.588482i
\(367\) −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i \(-0.225150\pi\)
−0.942799 + 0.333363i \(0.891817\pi\)
\(368\) 4.00000 0.208514
\(369\) −12.0000 −0.624695
\(370\) 0 0
\(371\) −2.00000 3.46410i −0.103835 0.179847i
\(372\) −3.00000 −0.155543
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 0 0
\(376\) −9.00000 15.5885i −0.464140 0.803913i
\(377\) 20.0000 34.6410i 1.03005 1.78410i
\(378\) 0.500000 0.866025i 0.0257172 0.0445435i
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) −12.0000 + 20.7846i −0.613973 + 1.06343i
\(383\) −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i \(-0.949767\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(384\) −1.50000 2.59808i −0.0765466 0.132583i
\(385\) 0 0
\(386\) −9.50000 16.4545i −0.483537 0.837511i
\(387\) −1.00000 −0.0508329
\(388\) −2.00000 −0.101535
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 18.0000 0.909137
\(393\) −7.00000 12.1244i −0.353103 0.611593i
\(394\) 13.0000 22.5167i 0.654931 1.13437i
\(395\) 0 0
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) −3.50000 + 6.06218i −0.175660 + 0.304252i −0.940389 0.340099i \(-0.889539\pi\)
0.764730 + 0.644351i \(0.222873\pi\)
\(398\) 21.0000 1.05263
\(399\) −0.500000 + 4.33013i −0.0250313 + 0.216777i
\(400\) 5.00000 0.250000
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) 5.50000 9.52628i 0.274315 0.475128i
\(403\) 7.50000 + 12.9904i 0.373602 + 0.647097i
\(404\) 7.00000 12.1244i 0.348263 0.603209i
\(405\) 0 0
\(406\) −8.00000 −0.397033
\(407\) −6.00000 −0.297409
\(408\) 6.00000 + 10.3923i 0.297044 + 0.514496i
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) −5.00000 + 8.66025i −0.246034 + 0.426143i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) 0 0
\(416\) −12.5000 + 21.6506i −0.612863 + 1.06151i
\(417\) −5.00000 −0.244851
\(418\) −1.00000 + 8.66025i −0.0489116 + 0.423587i
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) 11.0000 19.0526i 0.536107 0.928565i −0.463002 0.886357i \(-0.653228\pi\)
0.999109 0.0422075i \(-0.0134391\pi\)
\(422\) 7.50000 + 12.9904i 0.365094 + 0.632362i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 6.00000 + 10.3923i 0.291386 + 0.504695i
\(425\) 20.0000 0.970143
\(426\) −6.00000 −0.290701
\(427\) 6.50000 + 11.2583i 0.314557 + 0.544829i
\(428\) −9.00000 15.5885i −0.435031 0.753497i
\(429\) 10.0000 0.482805
\(430\) 0 0
\(431\) 5.00000 + 8.66025i 0.240842 + 0.417150i 0.960954 0.276707i \(-0.0892433\pi\)
−0.720113 + 0.693857i \(0.755910\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i \(-0.0972820\pi\)
−0.737404 + 0.675452i \(0.763949\pi\)
\(434\) 1.50000 2.59808i 0.0720023 0.124712i
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −14.0000 10.3923i −0.669711 0.497131i
\(438\) 11.0000 0.525600
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 0 0
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) 10.0000 17.3205i 0.475651 0.823853i
\(443\) 16.0000 + 27.7128i 0.760183 + 1.31668i 0.942756 + 0.333483i \(0.108224\pi\)
−0.182573 + 0.983192i \(0.558443\pi\)
\(444\) 3.00000 0.142374
\(445\) 0 0
\(446\) −4.50000 7.79423i −0.213081 0.369067i
\(447\) −3.00000 5.19615i −0.141895 0.245770i
\(448\) 7.00000 0.330719
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 2.50000 + 4.33013i 0.117851 + 0.204124i
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) 1.00000 + 1.73205i 0.0470360 + 0.0814688i
\(453\) 6.00000 10.3923i 0.281905 0.488273i
\(454\) 12.0000 20.7846i 0.563188 0.975470i
\(455\) 0 0
\(456\) 1.50000 12.9904i 0.0702439 0.608330i
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) −6.50000 + 11.2583i −0.303725 + 0.526067i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) −15.0000 + 25.9808i −0.698620 + 1.21004i 0.270326 + 0.962769i \(0.412869\pi\)
−0.968945 + 0.247276i \(0.920465\pi\)
\(462\) −1.00000 1.73205i −0.0465242 0.0805823i
\(463\) 23.0000 1.06890 0.534450 0.845200i \(-0.320519\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) −5.00000 −0.231125
\(469\) −5.50000 9.52628i −0.253966 0.439883i
\(470\) 0 0
\(471\) 1.50000 + 2.59808i 0.0691164 + 0.119713i
\(472\) 15.0000 25.9808i 0.690431 1.19586i
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) −1.00000 −0.0459315
\(475\) −17.5000 12.9904i −0.802955 0.596040i
\(476\) 4.00000 0.183340
\(477\) −2.00000 + 3.46410i −0.0915737 + 0.158610i
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) −7.00000 12.1244i −0.319838 0.553976i 0.660616 0.750724i \(-0.270295\pi\)
−0.980454 + 0.196748i \(0.936962\pi\)
\(480\) 0 0
\(481\) −7.50000 12.9904i −0.341971 0.592310i
\(482\) −7.00000 −0.318841
\(483\) 4.00000 0.182006
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −19.5000 33.7750i −0.882724 1.52892i
\(489\) 1.50000 2.59808i 0.0678323 0.117489i
\(490\) 0 0
\(491\) −3.00000 + 5.19615i −0.135388 + 0.234499i −0.925746 0.378147i \(-0.876561\pi\)
0.790358 + 0.612646i \(0.209895\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 32.0000 1.44121
\(494\) −20.0000 + 8.66025i −0.899843 + 0.389643i
\(495\) 0 0
\(496\) −1.50000 + 2.59808i −0.0673520 + 0.116657i
\(497\) −3.00000 + 5.19615i −0.134568 + 0.233079i
\(498\) 0 0
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) 2.00000 0.0893534
\(502\) −2.00000 −0.0892644
\(503\) −20.0000 34.6410i −0.891756 1.54457i −0.837769 0.546025i \(-0.816140\pi\)
−0.0539870 0.998542i \(-0.517193\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 0 0
\(506\) 8.00000 0.355643
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) −4.00000 + 6.92820i −0.177471 + 0.307389i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) 5.50000 9.52628i 0.243306 0.421418i
\(512\) −11.0000 −0.486136
\(513\) 4.00000 1.73205i 0.176604 0.0764719i
\(514\) −20.0000 −0.882162
\(515\) 0 0
\(516\) 0.500000 0.866025i 0.0220113 0.0381246i
\(517\) −6.00000 10.3923i −0.263880 0.457053i
\(518\) −1.50000 + 2.59808i −0.0659062 + 0.114153i
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 4.00000 + 6.92820i 0.175075 + 0.303239i
\(523\) −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) 14.0000 0.611593
\(525\) 5.00000 0.218218
\(526\) −13.0000 22.5167i −0.566827 0.981773i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 1.00000 + 1.73205i 0.0435194 + 0.0753778i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 10.0000 0.433963
\(532\) −3.50000 2.59808i −0.151744 0.112641i
\(533\) −60.0000 −2.59889
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) 16.5000 + 28.5788i 0.712691 + 1.23442i
\(537\) 6.00000 10.3923i 0.258919 0.448461i
\(538\) −5.00000 8.66025i −0.215565 0.373370i
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 19.5000 + 33.7750i 0.838370 + 1.45210i 0.891256 + 0.453500i \(0.149825\pi\)
−0.0528859 + 0.998601i \(0.516842\pi\)
\(542\) 0 0
\(543\) 2.00000 0.0858282
\(544\) −20.0000 −0.857493
\(545\) 0 0
\(546\) 2.50000 4.33013i 0.106990 0.185312i
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) 6.50000 11.2583i 0.277413 0.480494i
\(550\) 10.0000 0.426401
\(551\) −28.0000 20.7846i −1.19284 0.885454i
\(552\) −12.0000 −0.510754
\(553\) −0.500000 + 0.866025i −0.0212622 + 0.0368271i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) 2.50000 4.33013i 0.106024 0.183638i
\(557\) 19.0000 + 32.9090i 0.805056 + 1.39440i 0.916253 + 0.400599i \(0.131198\pi\)
−0.111198 + 0.993798i \(0.535469\pi\)
\(558\) −3.00000 −0.127000
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 4.00000 + 6.92820i 0.168880 + 0.292509i
\(562\) −8.00000 −0.337460
\(563\) 18.0000 0.758610 0.379305 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 0 0
\(566\) 2.00000 + 3.46410i 0.0840663 + 0.145607i
\(567\) −0.500000 + 0.866025i −0.0209980 + 0.0363696i
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) 33.0000 1.38101 0.690504 0.723329i \(-0.257389\pi\)
0.690504 + 0.723329i \(0.257389\pi\)
\(572\) −5.00000 + 8.66025i −0.209061 + 0.362103i
\(573\) 12.0000 20.7846i 0.501307 0.868290i
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) −10.0000 + 17.3205i −0.417029 + 0.722315i
\(576\) −3.50000 6.06218i −0.145833 0.252591i
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 9.50000 + 16.4545i 0.394807 + 0.683825i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) −16.5000 + 28.5788i −0.682775 + 1.18260i
\(585\) 0 0
\(586\) −7.00000 + 12.1244i −0.289167 + 0.500853i
\(587\) 13.0000 22.5167i 0.536567 0.929362i −0.462518 0.886610i \(-0.653054\pi\)
0.999086 0.0427523i \(-0.0136126\pi\)
\(588\) −6.00000 −0.247436
\(589\) 12.0000 5.19615i 0.494451 0.214104i
\(590\) 0 0
\(591\) −13.0000 + 22.5167i −0.534749 + 0.926212i
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) −1.00000 + 1.73205i −0.0410305 + 0.0710669i
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −21.0000 −0.859473
\(598\) 10.0000 + 17.3205i 0.408930 + 0.708288i
\(599\) −9.00000 15.5885i −0.367730 0.636927i 0.621480 0.783430i \(-0.286532\pi\)
−0.989210 + 0.146503i \(0.953198\pi\)
\(600\) −15.0000 −0.612372
\(601\) −21.0000 −0.856608 −0.428304 0.903635i \(-0.640889\pi\)
−0.428304 + 0.903635i \(0.640889\pi\)
\(602\) 0.500000 + 0.866025i 0.0203785 + 0.0352966i
\(603\) −5.50000 + 9.52628i −0.223977 + 0.387940i
\(604\) 6.00000 + 10.3923i 0.244137 + 0.422857i
\(605\) 0 0
\(606\) 7.00000 12.1244i 0.284356 0.492518i
\(607\) −43.0000 −1.74532 −0.872658 0.488332i \(-0.837606\pi\)
−0.872658 + 0.488332i \(0.837606\pi\)
\(608\) 17.5000 + 12.9904i 0.709719 + 0.526830i
\(609\) 8.00000 0.324176
\(610\) 0 0
\(611\) 15.0000 25.9808i 0.606835 1.05107i
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −3.00000 5.19615i −0.120775 0.209189i 0.799298 0.600935i \(-0.205205\pi\)
−0.920074 + 0.391745i \(0.871871\pi\)
\(618\) 6.50000 + 11.2583i 0.261468 + 0.452876i
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −9.00000 + 15.5885i −0.360867 + 0.625040i
\(623\) 3.00000 + 5.19615i 0.120192 + 0.208179i
\(624\) −2.50000 + 4.33013i −0.100080 + 0.173344i
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 22.0000 0.879297
\(627\) 1.00000 8.66025i 0.0399362 0.345857i
\(628\) −3.00000 −0.119713
\(629\) 6.00000 10.3923i 0.239236 0.414368i
\(630\) 0 0
\(631\) 7.50000 + 12.9904i 0.298570 + 0.517139i 0.975809 0.218624i \(-0.0701569\pi\)
−0.677239 + 0.735763i \(0.736824\pi\)
\(632\) 1.50000 2.59808i 0.0596668 0.103346i
\(633\) −7.50000 12.9904i −0.298098 0.516321i
\(634\) −4.00000 −0.158860
\(635\) 0 0
\(636\) −2.00000 3.46410i −0.0793052 0.137361i
\(637\) 15.0000 + 25.9808i 0.594322 + 1.02940i
\(638\) 16.0000 0.633446
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) −9.00000 15.5885i −0.355202 0.615227i
\(643\) 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) −2.00000 + 3.46410i −0.0788110 + 0.136505i
\(645\) 0 0
\(646\) −14.0000 10.3923i −0.550823 0.408880i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 1.50000 2.59808i 0.0589256 0.102062i
\(649\) 10.0000 17.3205i 0.392534 0.679889i
\(650\) 12.5000 + 21.6506i 0.490290 + 0.849208i
\(651\) −1.50000 + 2.59808i −0.0587896 + 0.101827i
\(652\) 1.50000 + 2.59808i 0.0587445 + 0.101749i
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) −6.00000 10.3923i −0.234261 0.405751i
\(657\) −11.0000 −0.429151
\(658\) −6.00000 −0.233904
\(659\) −17.0000 29.4449i −0.662226 1.14701i −0.980029 0.198852i \(-0.936279\pi\)
0.317803 0.948157i \(-0.397055\pi\)
\(660\) 0 0
\(661\) −21.0000 36.3731i −0.816805 1.41475i −0.908024 0.418917i \(-0.862410\pi\)
0.0912190 0.995831i \(-0.470924\pi\)
\(662\) 12.5000 21.6506i 0.485826 0.841476i
\(663\) −10.0000 + 17.3205i −0.388368 + 0.672673i
\(664\) 0 0
\(665\) 0 0
\(666\) 3.00000 0.116248
\(667\) −16.0000 + 27.7128i −0.619522 + 1.07304i
\(668\) −1.00000 + 1.73205i −0.0386912 + 0.0670151i
\(669\) 4.50000 + 7.79423i 0.173980 + 0.301342i
\(670\) 0 0
\(671\) −13.0000 22.5167i −0.501859 0.869246i
\(672\) −5.00000 −0.192879
\(673\) −33.0000 −1.27206 −0.636028 0.771666i \(-0.719424\pi\)
−0.636028 + 0.771666i \(0.719424\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) −12.0000 −0.461538
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 1.00000 + 1.73205i 0.0384048 + 0.0665190i
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) −12.0000 + 20.7846i −0.459841 + 0.796468i
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −0.500000 + 4.33013i −0.0191180 + 0.165567i
\(685\) 0 0
\(686\) 6.50000 11.2583i 0.248171 0.429845i
\(687\) 6.50000 11.2583i 0.247990 0.429532i
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) −10.0000 + 17.3205i −0.380970 + 0.659859i
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 0 0
\(693\) 1.00000 + 1.73205i 0.0379869 + 0.0657952i
\(694\) 8.00000 + 13.8564i 0.303676 + 0.525982i
\(695\) 0 0
\(696\) −24.0000 −0.909718
\(697\) −24.0000 41.5692i −0.909065 1.57455i
\(698\) 10.5000 18.1865i 0.397431 0.688370i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) −2.50000 + 4.33013i −0.0944911 + 0.163663i
\(701\) −10.0000 + 17.3205i −0.377695 + 0.654187i −0.990726 0.135872i \(-0.956616\pi\)
0.613032 + 0.790058i \(0.289950\pi\)
\(702\) −5.00000 −0.188713
\(703\) −12.0000 + 5.19615i −0.452589 + 0.195977i
\(704\) −14.0000 −0.527645
\(705\) 0 0
\(706\) −2.00000 + 3.46410i −0.0752710 + 0.130373i
\(707\) −7.00000 12.1244i −0.263262 0.455983i
\(708\) −5.00000 + 8.66025i −0.187912 + 0.325472i
\(709\) 19.5000 + 33.7750i 0.732338 + 1.26845i 0.955882 + 0.293752i \(0.0949041\pi\)
−0.223544 + 0.974694i \(0.571763\pi\)
\(710\) 0 0
\(711\) 1.00000 0.0375029
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) −6.00000 10.3923i −0.224702 0.389195i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 10.0000 + 17.3205i 0.373197 + 0.646396i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) 13.0000 0.484145
\(722\) 5.50000 + 18.1865i 0.204689 + 0.676833i
\(723\) 7.00000 0.260333
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −20.0000 + 34.6410i −0.742781 + 1.28654i
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 23.5000 40.7032i 0.871567 1.50960i 0.0111912 0.999937i \(-0.496438\pi\)
0.860376 0.509661i \(-0.170229\pi\)
\(728\) 7.50000 + 12.9904i 0.277968 + 0.481456i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.00000 3.46410i −0.0739727 0.128124i
\(732\) 6.50000 + 11.2583i 0.240247 + 0.416120i
\(733\) −50.0000 −1.84679 −0.923396 0.383849i \(-0.874598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) 7.00000 0.258375
\(735\) 0 0
\(736\) 10.0000 17.3205i 0.368605 0.638442i
\(737\) 11.0000 + 19.0526i 0.405190 + 0.701810i
\(738\) 6.00000 10.3923i 0.220863 0.382546i
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) 0 0
\(741\) 20.0000 8.66025i 0.734718 0.318142i
\(742\) 4.00000 0.146845
\(743\) 25.0000 43.3013i 0.917161 1.58857i 0.113455 0.993543i \(-0.463808\pi\)
0.803706 0.595026i \(-0.202858\pi\)
\(744\) 4.50000 7.79423i 0.164978 0.285750i
\(745\) 0 0
\(746\) −5.00000 + 8.66025i −0.183063 + 0.317074i
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −22.5000 38.9711i −0.821037 1.42208i −0.904911 0.425601i \(-0.860063\pi\)
0.0838743 0.996476i \(-0.473271\pi\)
\(752\) 6.00000 0.218797
\(753\) 2.00000 0.0728841
\(754\) 20.0000 + 34.6410i 0.728357 + 1.26155i
\(755\) 0 0
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) −6.50000 + 11.2583i −0.236247 + 0.409191i −0.959634 0.281251i \(-0.909251\pi\)
0.723388 + 0.690442i \(0.242584\pi\)
\(758\) 2.50000 4.33013i 0.0908041 0.157277i
\(759\) −8.00000 −0.290382
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −4.00000 + 6.92820i −0.144905 + 0.250982i
\(763\) 1.00000 1.73205i 0.0362024 0.0627044i
\(764\) 12.0000 + 20.7846i 0.434145 + 0.751961i
\(765\) 0 0
\(766\) −7.00000 12.1244i −0.252920 0.438071i
\(767\) 50.0000 1.80540
\(768\) 17.0000 0.613435
\(769\) 18.5000 + 32.0429i 0.667127 + 1.15550i 0.978704 + 0.205277i \(0.0658095\pi\)
−0.311577 + 0.950221i \(0.600857\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) −19.0000 −0.683825
\(773\) −7.00000 12.1244i −0.251773 0.436083i 0.712241 0.701935i \(-0.247680\pi\)
−0.964014 + 0.265852i \(0.914347\pi\)
\(774\) 0.500000 0.866025i 0.0179721 0.0311286i
\(775\) −7.50000 12.9904i −0.269408 0.466628i
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) 1.50000 2.59808i 0.0538122 0.0932055i
\(778\) −24.0000 −0.860442
\(779\) −6.00000 + 51.9615i −0.214972 + 1.86171i
\(780\) 0 0
\(781\) 6.00000 10.3923i 0.214697 0.371866i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) −4.00000 6.92820i −0.142948 0.247594i
\(784\) −3.00000 + 5.19615i −0.107143 + 0.185577i
\(785\) 0 0
\(786\) 14.0000 0.499363
\(787\) 25.0000 0.891154 0.445577 0.895244i \(-0.352999\pi\)
0.445577 + 0.895244i \(0.352999\pi\)
\(788\) −13.0000 22.5167i −0.463106 0.802123i
\(789\) 13.0000 + 22.5167i 0.462812 + 0.801614i
\(790\) 0 0
\(791\) 2.00000 0.0711118
\(792\) −3.00000 5.19615i −0.106600 0.184637i
\(793\) 32.5000 56.2917i 1.15411 1.99898i
\(794\) −3.50000 6.06218i −0.124210 0.215139i
\(795\) 0 0
\(796\) 10.5000 18.1865i 0.372163 0.644605i
\(797\) −14.0000 −0.495905