Properties

Label 966.2.i.f.415.1
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.f.277.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +2.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(2.50000 - 0.866025i) q^{21} +3.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-1.00000 - 1.73205i) q^{39} +6.00000 q^{41} +(0.500000 - 2.59808i) q^{42} +2.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-1.00000 + 1.73205i) q^{61} -2.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 - 2.59808i) q^{68} -1.00000 q^{69} +3.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{75} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} -2.00000 q^{78} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-2.00000 - 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + q^{18} - 2 q^{19} + 5 q^{21} + 6 q^{22} + q^{23} + q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} - 2 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} + 12 q^{41} + q^{42} + 4 q^{43} + 3 q^{44} - q^{46} + 3 q^{47} + 2 q^{48} - 13 q^{49} + 10 q^{50} + 3 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} + q^{56} + 4 q^{57} + 3 q^{58} - 2 q^{61} - 4 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{66} - 2 q^{67} + 3 q^{68} - 2 q^{69} + 6 q^{71} + q^{72} - 11 q^{73} + 2 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} - 4 q^{78} - 11 q^{79} - q^{81} + 6 q^{82} - 4 q^{84} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 6 q^{89} - 2 q^{91} - 2 q^{92} - 2 q^{93} - 3 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −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 \(0.166667\pi\)
\(6\) −1.00000 −0.408248
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 3.00000 0.639602
\(23\) 0.500000 0.866025i 0.104257 0.180579i
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 1.00000 0.192450
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0.500000 2.59808i 0.0771517 0.400892i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 5.00000 0.707107
\(51\) 1.50000 2.59808i 0.210042 0.363803i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 2.00000 0.264906
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −2.00000 −0.254000
\(63\) −2.00000 1.73205i −0.251976 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 2.50000 4.33013i 0.288675 0.500000i
\(76\) 2.00000 0.229416
\(77\) −7.50000 + 2.59808i −0.854704 + 0.296078i
\(78\) −2.00000 −0.226455
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 0 0
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.19615i −0.104828 + 0.544705i
\(92\) −1.00000 −0.104257
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) −3.00000 −0.301511
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i \(-0.912559\pi\)
0.716173 + 0.697923i \(0.245892\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 0 0
\(119\) −7.50000 + 2.59808i −0.687524 + 0.238165i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) −2.50000 + 0.866025i −0.222718 + 0.0771517i
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) −3.00000 −0.261116
\(133\) −4.00000 3.46410i −0.346844 0.300376i
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) 10.5000 + 18.1865i 0.897076 + 1.55378i 0.831215 + 0.555952i \(0.187646\pi\)
0.0658609 + 0.997829i \(0.479021\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 1.50000 2.59808i 0.125877 0.218026i
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) 1.00000 + 6.92820i 0.0824786 + 0.571429i
\(148\) 2.00000 0.164399
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) −2.50000 4.33013i −0.204124 0.353553i
\(151\) 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i \(-0.114628\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) −3.00000 −0.242536
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 5.50000 + 9.52628i 0.437557 + 0.757870i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 2.00000 + 1.73205i 0.157622 + 0.136505i
\(162\) −1.00000 −0.0785674
\(163\) −11.5000 + 19.9186i −0.900750 + 1.56014i −0.0742262 + 0.997241i \(0.523649\pi\)
−0.826523 + 0.562902i \(0.809685\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −2.50000 + 0.866025i −0.192879 + 0.0668153i
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) −3.00000 −0.227429
\(175\) −12.5000 + 4.33013i −0.944911 + 0.327327i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 4.00000 + 3.46410i 0.296500 + 0.256776i
\(183\) 2.00000 0.147844
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) −4.50000 + 7.79423i −0.329073 + 0.569970i
\(188\) −3.00000 −0.218797
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i \(-0.960818\pi\)
0.389885 0.920864i \(-0.372515\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) −1.00000 + 1.73205i −0.0705346 + 0.122169i
\(202\) 3.00000 0.211079
\(203\) −1.50000 + 7.79423i −0.105279 + 0.547048i
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 2.50000 + 4.33013i 0.174183 + 0.301694i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −19.0000 −1.30801 −0.654007 0.756489i \(-0.726913\pi\)
−0.654007 + 0.756489i \(0.726913\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) −1.50000 2.59808i −0.102778 0.178017i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 5.00000 1.73205i 0.339422 0.117579i
\(218\) 1.00000 0.0677285
\(219\) −5.50000 + 9.52628i −0.371656 + 0.643726i
\(220\) 0 0
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 1.00000 1.73205i 0.0671156 0.116248i
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) −5.00000 −0.333333
\(226\) 9.00000 15.5885i 0.598671 1.03693i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) 0 0
\(231\) 6.00000 + 5.19615i 0.394771 + 0.341882i
\(232\) −3.00000 −0.196960
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) 0 0
\(236\) 0 0
\(237\) 11.0000 0.714527
\(238\) −1.50000 + 7.79423i −0.0972306 + 0.505225i
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 0 0
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) −0.500000 + 2.59808i −0.0314970 + 0.163663i
\(253\) 3.00000 0.188608
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) −2.00000 −0.124515
\(259\) −4.00000 3.46410i −0.248548 0.215249i
\(260\) 0 0
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 0 0
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) −5.00000 + 1.73205i −0.306570 + 0.106199i
\(267\) −6.00000 −0.367194
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i \(-0.600397\pi\)
0.978406 0.206691i \(-0.0662693\pi\)
\(272\) −3.00000 −0.181902
\(273\) 5.00000 1.73205i 0.302614 0.104828i
\(274\) 21.0000 1.26866
\(275\) −7.50000 + 12.9904i −0.452267 + 0.783349i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −6.50000 + 11.2583i −0.389844 + 0.675230i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279741i \(0.909752\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) −3.00000 + 15.5885i −0.177084 + 0.920158i
\(288\) −1.00000 −0.0589256
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) −4.00000 6.92820i −0.234484 0.406138i
\(292\) −5.50000 + 9.52628i −0.321863 + 0.557483i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 6.50000 + 2.59808i 0.379088 + 0.151523i
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) 6.00000 + 10.3923i 0.347571 + 0.602010i
\(299\) 1.00000 1.73205i 0.0578315 0.100167i
\(300\) −5.00000 −0.288675
\(301\) −1.00000 + 5.19615i −0.0576390 + 0.299501i
\(302\) 4.00000 0.230174
\(303\) 1.50000 2.59808i 0.0861727 0.149256i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 6.00000 + 5.19615i 0.341882 + 0.296078i
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) 1.50000 + 2.59808i 0.0850572 + 0.147323i 0.905416 0.424526i \(-0.139559\pi\)
−0.820358 + 0.571850i \(0.806226\pi\)
\(312\) 1.00000 + 1.73205i 0.0566139 + 0.0980581i
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) −23.0000 −1.29797
\(315\) 0 0
\(316\) 11.0000 0.618798
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) −3.00000 5.19615i −0.168232 0.291386i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 2.50000 0.866025i 0.139320 0.0482617i
\(323\) −6.00000 −0.333849
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 5.00000 + 8.66025i 0.277350 + 0.480384i
\(326\) 11.5000 + 19.9186i 0.636926 + 1.10319i
\(327\) 0.500000 0.866025i 0.0276501 0.0478913i
\(328\) −6.00000 −0.331295
\(329\) 6.00000 + 5.19615i 0.330791 + 0.286473i
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 0 0
\(333\) −1.00000 1.73205i −0.0547997 0.0949158i
\(334\) 0 0
\(335\) 0 0
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) −9.00000 15.5885i −0.488813 0.846649i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) −2.00000 −0.108148
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) −7.50000 12.9904i −0.403202 0.698367i
\(347\) −3.00000 5.19615i −0.161048 0.278944i 0.774197 0.632945i \(-0.218154\pi\)
−0.935245 + 0.354001i \(0.884821\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) −2.50000 + 12.9904i −0.133631 + 0.694365i
\(351\) 2.00000 0.106752
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 6.00000 + 5.19615i 0.317554 + 0.275010i
\(358\) −6.00000 −0.317110
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 5.50000 9.52628i 0.289074 0.500690i
\(363\) −2.00000 −0.104973
\(364\) 5.00000 1.73205i 0.262071 0.0907841i
\(365\) 0 0
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 0.500000 + 0.866025i 0.0260643 + 0.0451447i
\(369\) −3.00000 + 5.19615i −0.156174 + 0.270501i
\(370\) 0 0
\(371\) −15.0000 + 5.19615i −0.778761 + 0.269771i
\(372\) 2.00000 0.103695
\(373\) 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 4.50000 + 7.79423i 0.232689 + 0.403030i
\(375\) 0 0
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) 6.00000 0.309016
\(378\) 2.00000 + 1.73205i 0.102869 + 0.0890871i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) −1.00000 1.73205i −0.0512316 0.0887357i
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) −4.00000 6.92820i −0.203069 0.351726i
\(389\) −12.0000 20.7846i −0.608424 1.05382i −0.991500 0.130105i \(-0.958469\pi\)
0.383076 0.923717i \(-0.374865\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) 0 0
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) 0 0
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 17.0000 29.4449i 0.853206 1.47780i −0.0250943 0.999685i \(-0.507989\pi\)
0.878300 0.478110i \(-0.158678\pi\)
\(398\) −17.0000 −0.852133
\(399\) −1.00000 + 5.19615i −0.0500626 + 0.260133i
\(400\) −5.00000 −0.250000
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) 1.00000 + 1.73205i 0.0498755 + 0.0863868i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 0 0
\(406\) 6.00000 + 5.19615i 0.297775 + 0.257881i
\(407\) −6.00000 −0.297409
\(408\) −1.50000 + 2.59808i −0.0742611 + 0.128624i
\(409\) −14.5000 25.1147i −0.716979 1.24184i −0.962191 0.272374i \(-0.912191\pi\)
0.245212 0.969469i \(-0.421142\pi\)
\(410\) 0 0
\(411\) 10.5000 18.1865i 0.517927 0.897076i
\(412\) 5.00000 0.246332
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 6.50000 + 11.2583i 0.318306 + 0.551323i
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) −21.0000 −1.02592 −0.512959 0.858413i \(-0.671451\pi\)
−0.512959 + 0.858413i \(0.671451\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) −9.50000 + 16.4545i −0.462453 + 0.800992i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) −7.50000 + 12.9904i −0.363803 + 0.630126i
\(426\) −3.00000 −0.145350
\(427\) −4.00000 3.46410i −0.193574 0.167640i
\(428\) 12.0000 0.580042
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 1.00000 5.19615i 0.0480015 0.249423i
\(435\) 0 0
\(436\) 0.500000 0.866025i 0.0239457 0.0414751i
\(437\) 1.00000 + 1.73205i 0.0478365 + 0.0828552i
\(438\) 5.50000 + 9.52628i 0.262800 + 0.455183i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 6.00000 0.285391
\(443\) 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i \(-0.640223\pi\)
0.996551 0.0829786i \(-0.0264433\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) 0 0
\(446\) −5.00000 + 8.66025i −0.236757 + 0.410075i
\(447\) 12.0000 0.567581
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) −2.50000 + 4.33013i −0.117851 + 0.204124i
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) −9.00000 15.5885i −0.423324 0.733219i
\(453\) 2.00000 3.46410i 0.0939682 0.162758i
\(454\) 3.00000 0.140797
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −10.0000 + 17.3205i −0.467780 + 0.810219i −0.999322 0.0368128i \(-0.988279\pi\)
0.531542 + 0.847032i \(0.321613\pi\)
\(458\) −0.500000 0.866025i −0.0233635 0.0404667i
\(459\) 1.50000 + 2.59808i 0.0700140 + 0.121268i
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 7.50000 2.59808i 0.348932 0.120873i
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 0 0
\(467\) 10.5000 18.1865i 0.485882 0.841572i −0.513986 0.857798i \(-0.671832\pi\)
0.999868 + 0.0162260i \(0.00516512\pi\)
\(468\) 2.00000 0.0924500
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) 0 0
\(471\) −11.5000 + 19.9186i −0.529892 + 0.917800i
\(472\) 0 0
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 5.50000 9.52628i 0.252623 0.437557i
\(475\) −10.0000 −0.458831
\(476\) 6.00000 + 5.19615i 0.275010 + 0.238165i
\(477\) −6.00000 −0.274721
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i \(-0.926308\pi\)
0.287954 0.957644i \(-0.407025\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −2.00000 −0.0910975
\(483\) 0.500000 2.59808i 0.0227508 0.118217i
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) 23.0000 1.04010
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −3.00000 + 5.19615i −0.135250 + 0.234261i
\(493\) 4.50000 + 7.79423i 0.202670 + 0.351034i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −1.50000 + 7.79423i −0.0672842 + 0.349619i
\(498\) 0 0
\(499\) −17.5000 + 30.3109i −0.783408 + 1.35690i 0.146538 + 0.989205i \(0.453187\pi\)
−0.929946 + 0.367697i \(0.880146\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 2.00000 + 1.73205i 0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) 1.50000 2.59808i 0.0666831 0.115499i
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 10.5000 18.1865i 0.465404 0.806104i −0.533815 0.845601i \(-0.679242\pi\)
0.999220 + 0.0394971i \(0.0125756\pi\)
\(510\) 0 0
\(511\) 27.5000 9.52628i 1.21653 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 9.00000 0.395820
\(518\) −5.00000 + 1.73205i −0.219687 + 0.0761019i
\(519\) −15.0000 −0.658427
\(520\) 0 0
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) 11.0000 19.0526i 0.480996 0.833110i −0.518766 0.854916i \(-0.673608\pi\)
0.999762 + 0.0218062i \(0.00694167\pi\)
\(524\) 0 0
\(525\) 10.0000 + 8.66025i 0.436436 + 0.377964i
\(526\) −24.0000 −1.04645
\(527\) 3.00000 5.19615i 0.130682 0.226348i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 + 5.19615i −0.0433555 + 0.225282i
\(533\) 12.0000 0.519778
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) −15.0000 −0.646696
\(539\) −3.00000 20.7846i −0.129219 0.895257i
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) −11.0000 19.0526i −0.472490 0.818377i
\(543\) −5.50000 9.52628i −0.236028 0.408812i
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) 0 0
\(546\) 1.00000 5.19615i 0.0427960 0.222375i
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 10.5000 18.1865i 0.448538 0.776890i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 7.50000 + 12.9904i 0.319801 + 0.553912i
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) 1.00000 0.0425628
\(553\) −22.0000 19.0526i −0.935535 0.810197i
\(554\) −8.00000 −0.339887
\(555\) 0 0
\(556\) 6.50000 + 11.2583i 0.275661 + 0.477460i
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 1.00000 1.73205i 0.0423334 0.0733236i
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 9.00000 0.379980
\(562\) −1.50000 + 2.59808i −0.0632737 + 0.109593i
\(563\) 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i \(-0.105931\pi\)
−0.755482 + 0.655169i \(0.772597\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 0 0
\(566\) −8.00000 −0.336265
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) −3.00000 −0.125877
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 3.00000 5.19615i 0.125436 0.217262i
\(573\) 12.0000 0.501307
\(574\) 12.0000 + 10.3923i 0.500870 + 0.433766i
\(575\) 5.00000 0.208514
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 0 0
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 5.50000 4.33013i 0.226816 0.178571i
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) −7.50000 12.9904i −0.308509 0.534353i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 21.0000 36.3731i 0.862367 1.49366i −0.00727173 0.999974i \(-0.502315\pi\)
0.869638 0.493689i \(-0.164352\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −8.50000 + 14.7224i −0.347882 + 0.602549i
\(598\) −1.00000 1.73205i −0.0408930 0.0708288i
\(599\) −7.50000 12.9904i −0.306442 0.530773i 0.671140 0.741331i \(-0.265805\pi\)
−0.977581 + 0.210558i \(0.932472\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 4.00000 + 3.46410i 0.163028 + 0.141186i
\(603\) 2.00000 0.0814463
\(604\) 2.00000 3.46410i 0.0813788 0.140952i
\(605\) 0 0
\(606\) −1.50000 2.59808i −0.0609333 0.105540i
\(607\) −7.00000 + 12.1244i −0.284121 + 0.492112i −0.972396 0.233338i \(-0.925035\pi\)
0.688274 + 0.725450i \(0.258368\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 7.50000 2.59808i 0.303915 0.105279i
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 1.50000 + 2.59808i 0.0606339 + 0.105021i
\(613\) −2.50000 4.33013i −0.100974 0.174892i 0.811112 0.584891i \(-0.198863\pi\)
−0.912086 + 0.409998i \(0.865529\pi\)
\(614\) 5.50000 9.52628i 0.221962 0.384449i
\(615\) 0 0
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) 33.0000 1.32853 0.664265 0.747497i \(-0.268745\pi\)
0.664265 + 0.747497i \(0.268745\pi\)
\(618\) 2.50000 4.33013i 0.100565 0.174183i
\(619\) −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i \(-0.944317\pi\)
0.341644 0.939829i \(-0.389016\pi\)
\(620\) 0 0
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 3.00000 0.120289
\(623\) 12.0000 + 10.3923i 0.480770 + 0.416359i
\(624\) 2.00000 0.0800641
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) 3.00000 + 5.19615i 0.119808 + 0.207514i
\(628\) −11.5000 + 19.9186i −0.458900 + 0.794838i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 17.0000 0.676759 0.338380 0.941010i \(-0.390121\pi\)
0.338380 + 0.941010i \(0.390121\pi\)
\(632\) 5.50000 9.52628i 0.218778 0.378935i
\(633\) 9.50000 + 16.4545i 0.377591 + 0.654007i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) −13.0000 5.19615i −0.515079 0.205879i
\(638\) 9.00000 0.356313
\(639\) −1.50000 + 2.59808i −0.0593391 + 0.102778i
\(640\) 0 0
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) 6.00000 10.3923i 0.236801 0.410152i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 0.500000 2.59808i 0.0197028 0.102379i
\(645\) 0 0
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 7.50000 + 12.9904i 0.294855 + 0.510705i 0.974951 0.222419i \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 10.0000 0.392232
\(651\) −4.00000 3.46410i −0.156772 0.135769i
\(652\) 23.0000 0.900750
\(653\) −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) −0.500000 0.866025i −0.0195515 0.0338643i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 11.0000 0.429151
\(658\) 7.50000 2.59808i 0.292380 0.101284i
\(659\) 3.00000 0.116863 0.0584317 0.998291i \(-0.481390\pi\)
0.0584317 + 0.998291i \(0.481390\pi\)
\(660\) 0 0
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 4.00000 + 6.92820i 0.155464 + 0.269272i
\(663\) 3.00000 5.19615i 0.116510 0.201802i
\(664\) 0 0
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 1.50000 2.59808i 0.0580802 0.100598i
\(668\) 0 0
\(669\) 5.00000 + 8.66025i 0.193311 + 0.334825i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) 2.00000 + 1.73205i 0.0771517 + 0.0668153i
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) −18.0000 −0.691286
\(679\) −4.00000 + 20.7846i −0.153506 + 0.797640i
\(680\) 0 0
\(681\) 1.50000 2.59808i 0.0574801 0.0995585i
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i \(-0.796201\pi\)
−0.116390 0.993204i \(-0.537132\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) −1.00000 −0.0381524
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) −15.0000 −0.570214
\(693\) 1.50000 7.79423i 0.0569803 0.296078i
\(694\) −6.00000 −0.227757
\(695\) 0 0
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) 9.00000 + 15.5885i 0.340899 + 0.590455i
\(698\) −11.0000 + 19.0526i −0.416356 + 0.721150i
\(699\) 0 0
\(700\) 10.0000 + 8.66025i 0.377964 + 0.327327i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 1.00000 1.73205i 0.0377426 0.0653720i
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) −7.50000 + 2.59808i −0.282067 + 0.0977107i
\(708\) 0 0
\(709\) 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i \(-0.635559\pi\)
0.995228 0.0975728i \(-0.0311079\pi\)
\(710\) 0 0
\(711\) −5.50000 9.52628i −0.206266 0.357263i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −2.00000 −0.0749006
\(714\) 7.50000 2.59808i 0.280680 0.0972306i
\(715\) 0 0
\(716\) −3.00000 + 5.19615i −0.112115 + 0.194189i
\(717\) −7.50000 12.9904i −0.280093 0.485135i
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 0 0
\(721\) −10.0000 8.66025i −0.372419 0.322525i
\(722\) 15.0000 0.558242
\(723\) −1.00000 + 1.73205i −0.0371904 + 0.0644157i
\(724\) −5.50000 9.52628i −0.204406 0.354041i
\(725\) 7.50000 + 12.9904i 0.278543 + 0.482451i
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 1.00000 5.19615i 0.0370625 0.192582i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 3.00000 + 5.19615i 0.110959 + 0.192187i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −20.5000 + 35.5070i −0.757185 + 1.31148i 0.187096 + 0.982342i \(0.440092\pi\)
−0.944281 + 0.329141i \(0.893241\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 3.00000 5.19615i 0.110506 0.191403i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) 12.5000 + 21.6506i 0.459820 + 0.796431i 0.998951 0.0457903i \(-0.0145806\pi\)
−0.539131 + 0.842222i \(0.681247\pi\)
\(740\) 0 0
\(741\) 4.00000 0.146944
\(742\) −3.00000 + 15.5885i −0.110133 + 0.572270i
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) −6.50000 11.2583i −0.237982 0.412197i
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) −24.0000 20.7846i −0.876941 0.759453i
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) −1.50000 2.59808i −0.0546630 0.0946792i
\(754\) 3.00000 5.19615i 0.109254 0.189233i
\(755\) 0 0
\(756\) 2.50000 0.866025i 0.0909241 0.0314970i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 10.0000 17.3205i 0.363216 0.629109i
\(759\) −1.50000 2.59808i −0.0544466 0.0943042i
\(760\) 0 0
\(761\) −24.0000 + 41.5692i −0.869999 + 1.50688i −0.00800331 + 0.999968i \(0.502548\pi\)
−0.861996 + 0.506915i \(0.830786\pi\)
\(762\) −2.00000 −0.0724524
\(763\) −2.50000 + 0.866025i −0.0905061 + 0.0313522i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −3.00000 5.19615i −0.108394 0.187745i
\(767\) 0 0
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 18.0000 + 31.1769i 0.647415 + 1.12136i 0.983738 + 0.179609i \(0.0574833\pi\)
−0.336323 + 0.941747i \(0.609183\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 5.00000 8.66025i 0.179605 0.311086i
\(776\) −8.00000 −0.287183
\(777\) −1.00000 + 5.19615i −0.0358748 + 0.186411i
\(778\) −24.0000 −0.860442
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 4.50000 + 7.79423i 0.161023 + 0.278899i
\(782\) 1.50000 2.59808i 0.0536399 0.0929070i
\(783\) 3.00000 0.107211
\(784\) 5.50000 4.33013i 0.196429 0.154647i