Properties

Label 570.2.i.b.121.1
Level $570$
Weight $2$
Character 570.121
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
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 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.b.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(1.50000 - 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -3.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(5.00000 - 8.66025i) q^{29} -1.00000 q^{30} +1.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-2.00000 + 3.46410i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} -5.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} -3.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.50000 + 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.50000 + 2.59808i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} -1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -10.0000 q^{58} +(1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.50000 + 4.33013i) q^{61} +(-0.500000 - 0.866025i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(2.50000 - 4.33013i) q^{67} +4.00000 q^{68} -6.00000 q^{69} +(-0.500000 + 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(2.50000 + 4.33013i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -2.00000 q^{77} +(1.50000 + 2.59808i) q^{78} +(5.50000 + 9.52628i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +2.00000 q^{83} -1.00000 q^{84} +(2.00000 - 3.46410i) q^{85} +(2.50000 - 4.33013i) q^{86} -10.0000 q^{87} +2.00000 q^{88} +(0.500000 + 0.866025i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-0.500000 - 0.866025i) q^{93} +(0.500000 + 4.33013i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + q^{10} + 4q^{11} + 2q^{12} + 3q^{13} + q^{14} + q^{15} - q^{16} - 4q^{17} + 2q^{18} + 8q^{19} - 2q^{20} + q^{21} - 2q^{22} + 6q^{23} - q^{24} - q^{25} - 6q^{26} + 2q^{27} + q^{28} + 10q^{29} - 2q^{30} + 2q^{31} - q^{32} - 2q^{33} - 4q^{34} - q^{35} - q^{36} - 10q^{37} - q^{38} - 6q^{39} + q^{40} - 2q^{41} + q^{42} + 5q^{43} - 2q^{44} - 2q^{45} - 12q^{46} - q^{48} - 12q^{49} + 2q^{50} - 4q^{51} + 3q^{52} + 12q^{53} - q^{54} + 2q^{55} - 2q^{56} - q^{57} - 20q^{58} + 2q^{59} + q^{60} - 5q^{61} - q^{62} + q^{63} + 2q^{64} + 6q^{65} - 2q^{66} + 5q^{67} + 8q^{68} - 12q^{69} - q^{70} - q^{72} - 11q^{73} + 5q^{74} + 2q^{75} - 7q^{76} - 4q^{77} + 3q^{78} + 11q^{79} + q^{80} - q^{81} - 2q^{82} + 4q^{83} - 2q^{84} + 4q^{85} + 5q^{86} - 20q^{87} + 4q^{88} + q^{90} - 3q^{91} + 6q^{92} - q^{93} + q^{95} + 2q^{96} + 2q^{97} + 6q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.50000 2.59808i 0.416025 0.720577i −0.579510 0.814965i \(-0.696756\pi\)
0.995535 + 0.0943882i \(0.0300895\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) −1.00000 −0.223607
\(21\) 0.500000 + 0.866025i 0.109109 + 0.188982i
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.00000 −0.588348
\(27\) 1.00000 0.192450
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i \(-0.454452\pi\)
0.785872 0.618389i \(-0.212214\pi\)
\(30\) −1.00000 −0.182574
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) −2.00000 + 3.46410i −0.342997 + 0.594089i
\(35\) −0.500000 0.866025i −0.0845154 0.146385i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −0.500000 4.33013i −0.0811107 0.702439i
\(39\) −3.00000 −0.480384
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −1.00000 1.73205i −0.156174 0.270501i 0.777312 0.629115i \(-0.216583\pi\)
−0.933486 + 0.358614i \(0.883249\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 2.50000 + 4.33013i 0.381246 + 0.660338i 0.991241 0.132068i \(-0.0421616\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) −1.00000 −0.149071
\(46\) −6.00000 −0.884652
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 1.50000 + 2.59808i 0.208013 + 0.360288i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) −1.00000 −0.133631
\(57\) −0.500000 4.33013i −0.0662266 0.573539i
\(58\) −10.0000 −1.31306
\(59\) 1.00000 + 1.73205i 0.130189 + 0.225494i 0.923749 0.382998i \(-0.125108\pi\)
−0.793560 + 0.608492i \(0.791775\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) −0.500000 0.866025i −0.0635001 0.109985i
\(63\) 0.500000 0.866025i 0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 3.00000 0.372104
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 4.00000 0.485071
\(69\) −6.00000 −0.722315
\(70\) −0.500000 + 0.866025i −0.0597614 + 0.103510i
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) −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 \(-0.389279\pi\)
\(74\) 2.50000 + 4.33013i 0.290619 + 0.503367i
\(75\) 1.00000 0.115470
\(76\) −3.50000 + 2.59808i −0.401478 + 0.298020i
\(77\) −2.00000 −0.227921
\(78\) 1.50000 + 2.59808i 0.169842 + 0.294174i
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) −1.00000 −0.109109
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) 2.50000 4.33013i 0.269582 0.466930i
\(87\) −10.0000 −1.07211
\(88\) 2.00000 0.213201
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) −1.50000 + 2.59808i −0.157243 + 0.272352i
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) −0.500000 0.866025i −0.0518476 0.0898027i
\(94\) 0 0
\(95\) 0.500000 + 4.33013i 0.0512989 + 0.444262i
\(96\) 1.00000 0.102062
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 3.00000 + 5.19615i 0.303046 + 0.524891i
\(99\) −1.00000 + 1.73205i −0.100504 + 0.174078i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 4.00000 0.396059
\(103\) 19.0000 1.87213 0.936063 0.351833i \(-0.114441\pi\)
0.936063 + 0.351833i \(0.114441\pi\)
\(104\) 1.50000 2.59808i 0.147087 0.254762i
\(105\) −0.500000 + 0.866025i −0.0487950 + 0.0845154i
\(106\) −12.0000 −1.16554
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) 1.00000 1.73205i 0.0953463 0.165145i
\(111\) 2.50000 + 4.33013i 0.237289 + 0.410997i
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) −3.50000 + 2.59808i −0.327805 + 0.243332i
\(115\) 6.00000 0.559503
\(116\) 5.00000 + 8.66025i 0.464238 + 0.804084i
\(117\) 1.50000 + 2.59808i 0.138675 + 0.240192i
\(118\) 1.00000 1.73205i 0.0920575 0.159448i
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −7.00000 −0.636364
\(122\) 5.00000 0.452679
\(123\) −1.00000 + 1.73205i −0.0901670 + 0.156174i
\(124\) −0.500000 + 0.866025i −0.0449013 + 0.0777714i
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −8.00000 + 13.8564i −0.709885 + 1.22956i 0.255014 + 0.966937i \(0.417920\pi\)
−0.964899 + 0.262620i \(0.915413\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 2.50000 4.33013i 0.220113 0.381246i
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 2.00000 0.174078
\(133\) −4.00000 1.73205i −0.346844 0.150188i
\(134\) −5.00000 −0.431934
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 3.00000 + 5.19615i 0.255377 + 0.442326i
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 10.0000 0.830455
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 3.00000 + 5.19615i 0.247436 + 0.428571i
\(148\) 2.50000 4.33013i 0.205499 0.355934i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 4.00000 + 1.73205i 0.324443 + 0.140488i
\(153\) 4.00000 0.323381
\(154\) 1.00000 + 1.73205i 0.0805823 + 0.139573i
\(155\) 0.500000 + 0.866025i 0.0401610 + 0.0695608i
\(156\) 1.50000 2.59808i 0.120096 0.208013i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) −12.0000 −0.951662
\(160\) −1.00000 −0.0790569
\(161\) −3.00000 + 5.19615i −0.236433 + 0.409514i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −17.0000 −1.33154 −0.665771 0.746156i \(-0.731897\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) 2.00000 0.156174
\(165\) 1.00000 1.73205i 0.0778499 0.134840i
\(166\) −1.00000 1.73205i −0.0776151 0.134433i
\(167\) −7.00000 + 12.1244i −0.541676 + 0.938211i 0.457132 + 0.889399i \(0.348877\pi\)
−0.998808 + 0.0488118i \(0.984457\pi\)
\(168\) 0.500000 + 0.866025i 0.0385758 + 0.0668153i
\(169\) 2.00000 + 3.46410i 0.153846 + 0.266469i
\(170\) −4.00000 −0.306786
\(171\) −3.50000 + 2.59808i −0.267652 + 0.198680i
\(172\) −5.00000 −0.381246
\(173\) 13.0000 + 22.5167i 0.988372 + 1.71191i 0.625871 + 0.779926i \(0.284744\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(174\) 5.00000 + 8.66025i 0.379049 + 0.656532i
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) 1.00000 1.73205i 0.0751646 0.130189i
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 3.00000 5.19615i 0.222988 0.386227i −0.732726 0.680524i \(-0.761752\pi\)
0.955714 + 0.294297i \(0.0950855\pi\)
\(182\) 3.00000 0.222375
\(183\) 5.00000 0.369611
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −2.50000 4.33013i −0.183804 0.318357i
\(186\) −0.500000 + 0.866025i −0.0366618 + 0.0635001i
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 3.50000 2.59808i 0.253917 0.188484i
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −12.5000 21.6506i −0.899770 1.55845i −0.827788 0.561041i \(-0.810401\pi\)
−0.0719816 0.997406i \(-0.522932\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) −1.50000 2.59808i −0.107417 0.186052i
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 2.00000 0.142134
\(199\) −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i \(-0.890044\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −5.00000 −0.352673
\(202\) 6.00000 0.422159
\(203\) −5.00000 + 8.66025i −0.350931 + 0.607831i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) −9.50000 16.4545i −0.661896 1.14644i
\(207\) 3.00000 + 5.19615i 0.208514 + 0.361158i
\(208\) −3.00000 −0.208013
\(209\) 8.00000 + 3.46410i 0.553372 + 0.239617i
\(210\) 1.00000 0.0690066
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) −2.50000 + 4.33013i −0.170499 + 0.295312i
\(216\) 1.00000 0.0680414
\(217\) −1.00000 −0.0678844
\(218\) 9.00000 15.5885i 0.609557 1.05578i
\(219\) −5.50000 + 9.52628i −0.371656 + 0.643726i
\(220\) −2.00000 −0.134840
\(221\) −12.0000 −0.807207
\(222\) 2.50000 4.33013i 0.167789 0.290619i
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 4.00000 + 1.73205i 0.264906 + 0.114708i
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) −3.00000 5.19615i −0.197814 0.342624i
\(231\) 1.00000 + 1.73205i 0.0657952 + 0.113961i
\(232\) 5.00000 8.66025i 0.328266 0.568574i
\(233\) 2.00000 + 3.46410i 0.131024 + 0.226941i 0.924072 0.382219i \(-0.124840\pi\)
−0.793047 + 0.609160i \(0.791507\pi\)
\(234\) 1.50000 2.59808i 0.0980581 0.169842i
\(235\) 0 0
\(236\) −2.00000 −0.130189
\(237\) 5.50000 9.52628i 0.357263 0.618798i
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.50000 4.33013i −0.160046 0.277208i
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) 2.00000 0.127515
\(247\) 10.5000 7.79423i 0.668099 0.495935i
\(248\) 1.00000 0.0635001
\(249\) −1.00000 1.73205i −0.0633724 0.109764i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 1.00000 1.73205i 0.0631194 0.109326i −0.832739 0.553666i \(-0.813228\pi\)
0.895858 + 0.444340i \(0.146562\pi\)
\(252\) 0.500000 + 0.866025i 0.0314970 + 0.0545545i
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) 16.0000 1.00393
\(255\) −4.00000 −0.250490
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) −5.00000 −0.311286
\(259\) 5.00000 0.310685
\(260\) −1.50000 + 2.59808i −0.0930261 + 0.161126i
\(261\) 5.00000 + 8.66025i 0.309492 + 0.536056i
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) 5.00000 + 8.66025i 0.308313 + 0.534014i 0.977993 0.208635i \(-0.0669022\pi\)
−0.669680 + 0.742650i \(0.733569\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) 12.0000 0.737154
\(266\) 0.500000 + 4.33013i 0.0306570 + 0.265497i
\(267\) 0 0
\(268\) 2.50000 + 4.33013i 0.152712 + 0.264505i
\(269\) −5.00000 8.66025i −0.304855 0.528025i 0.672374 0.740212i \(-0.265275\pi\)
−0.977229 + 0.212187i \(0.931941\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) −2.00000 + 3.46410i −0.121268 + 0.210042i
\(273\) 3.00000 0.181568
\(274\) −2.00000 −0.120824
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −9.00000 −0.539784
\(279\) −0.500000 + 0.866025i −0.0299342 + 0.0518476i
\(280\) −0.500000 0.866025i −0.0298807 0.0517549i
\(281\) 15.0000 25.9808i 0.894825 1.54988i 0.0608039 0.998150i \(-0.480634\pi\)
0.834021 0.551733i \(-0.186033\pi\)
\(282\) 0 0
\(283\) −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279741i \(0.909752\pi\)
\(284\) 0 0
\(285\) 3.50000 2.59808i 0.207322 0.153897i
\(286\) −6.00000 −0.354787
\(287\) 1.00000 + 1.73205i 0.0590281 + 0.102240i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −5.00000 8.66025i −0.293610 0.508548i
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 11.0000 0.643726
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 3.00000 5.19615i 0.174964 0.303046i
\(295\) −1.00000 + 1.73205i −0.0582223 + 0.100844i
\(296\) −5.00000 −0.290619
\(297\) 2.00000 0.116052
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) −9.00000 15.5885i −0.520483 0.901504i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −2.50000 4.33013i −0.144098 0.249584i
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) −0.500000 4.33013i −0.0286770 0.248350i
\(305\) −5.00000 −0.286299
\(306\) −2.00000 3.46410i −0.114332 0.198030i
\(307\) −2.00000 3.46410i −0.114146 0.197707i 0.803292 0.595585i \(-0.203080\pi\)
−0.917438 + 0.397879i \(0.869747\pi\)
\(308\) 1.00000 1.73205i 0.0569803 0.0986928i
\(309\) −9.50000 16.4545i −0.540436 0.936063i
\(310\) 0.500000 0.866025i 0.0283981 0.0491869i
\(311\) −10.0000 −0.567048 −0.283524 0.958965i \(-0.591504\pi\)
−0.283524 + 0.958965i \(0.591504\pi\)
\(312\) −3.00000 −0.169842
\(313\) −9.00000 + 15.5885i −0.508710 + 0.881112i 0.491239 + 0.871025i \(0.336544\pi\)
−0.999949 + 0.0100869i \(0.996789\pi\)
\(314\) 6.50000 11.2583i 0.366816 0.635344i
\(315\) 1.00000 0.0563436
\(316\) −11.0000 −0.618798
\(317\) −15.0000 + 25.9808i −0.842484 + 1.45922i 0.0453045 + 0.998973i \(0.485574\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(318\) 6.00000 + 10.3923i 0.336463 + 0.582772i
\(319\) 10.0000 17.3205i 0.559893 0.969762i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 2.00000 + 3.46410i 0.111629 + 0.193347i
\(322\) 6.00000 0.334367
\(323\) −2.00000 17.3205i −0.111283 0.963739i
\(324\) 1.00000 0.0555556
\(325\) 1.50000 + 2.59808i 0.0832050 + 0.144115i
\(326\) 8.50000 + 14.7224i 0.470771 + 0.815400i
\(327\) 9.00000 15.5885i 0.497701 0.862044i
\(328\) −1.00000 1.73205i −0.0552158 0.0956365i
\(329\) 0 0
\(330\) −2.00000 −0.110096
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) −1.00000 + 1.73205i −0.0548821 + 0.0950586i
\(333\) 2.50000 4.33013i 0.136999 0.237289i
\(334\) 14.0000 0.766046
\(335\) 5.00000 0.273179
\(336\) 0.500000 0.866025i 0.0272772 0.0472456i
\(337\) −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i \(-0.951176\pi\)
0.361815 0.932250i \(-0.382157\pi\)
\(338\) 2.00000 3.46410i 0.108786 0.188422i
\(339\) −7.00000 12.1244i −0.380188 0.658505i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 2.00000 0.108306
\(342\) 4.00000 + 1.73205i 0.216295 + 0.0936586i
\(343\) 13.0000 0.701934
\(344\) 2.50000 + 4.33013i 0.134791 + 0.233465i
\(345\) −3.00000 5.19615i −0.161515 0.279751i
\(346\) 13.0000 22.5167i 0.698884 1.21050i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 5.00000 8.66025i 0.268028 0.464238i
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 1.50000 2.59808i 0.0800641 0.138675i
\(352\) −1.00000 + 1.73205i −0.0533002 + 0.0923186i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −2.00000 −0.106299
\(355\) 0 0
\(356\) 0 0
\(357\) 2.00000 3.46410i 0.105851 0.183340i
\(358\) 5.00000 + 8.66025i 0.264258 + 0.457709i
\(359\) 1.00000 + 1.73205i 0.0527780 + 0.0914141i 0.891207 0.453596i \(-0.149859\pi\)
−0.838429 + 0.545010i \(0.816526\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) −6.00000 −0.315353
\(363\) 3.50000 + 6.06218i 0.183702 + 0.318182i
\(364\) −1.50000 2.59808i −0.0786214 0.136176i
\(365\) 5.50000 9.52628i 0.287883 0.498628i
\(366\) −2.50000 4.33013i −0.130677 0.226339i
\(367\) 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i \(-0.774850\pi\)
0.942799 + 0.333363i \(0.108183\pi\)
\(368\) −6.00000 −0.312772
\(369\) 2.00000 0.104116
\(370\) −2.50000 + 4.33013i −0.129969 + 0.225113i
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 1.00000 0.0518476
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) −15.0000 25.9808i −0.772539 1.33808i
\(378\) 0.500000 + 0.866025i 0.0257172 + 0.0445435i
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) −4.00000 1.73205i −0.205196 0.0888523i
\(381\) 16.0000 0.819705
\(382\) −8.00000 13.8564i −0.409316 0.708955i
\(383\) 18.0000 + 31.1769i 0.919757 + 1.59307i 0.799783 + 0.600289i \(0.204948\pi\)
0.119974 + 0.992777i \(0.461719\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) −12.5000 + 21.6506i −0.636233 + 1.10199i
\(387\) −5.00000 −0.254164
\(388\) −2.00000 −0.101535
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) −1.50000 + 2.59808i −0.0759555 + 0.131559i
\(391\) −24.0000 −1.21373
\(392\) −6.00000 −0.303046
\(393\) 3.00000 5.19615i 0.151330 0.262111i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) −5.50000 + 9.52628i −0.276735 + 0.479319i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 5.00000 0.250627
\(399\) 0.500000 + 4.33013i 0.0250313 + 0.216777i
\(400\) 1.00000 0.0500000
\(401\) 19.0000 + 32.9090i 0.948815 + 1.64340i 0.747927 + 0.663781i \(0.231049\pi\)
0.200888 + 0.979614i \(0.435617\pi\)
\(402\) 2.50000 + 4.33013i 0.124689 + 0.215967i
\(403\) 1.50000 2.59808i 0.0747203 0.129419i
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 10.0000 0.496292
\(407\) −10.0000 −0.495682
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) 15.0000 25.9808i 0.741702 1.28467i −0.210017 0.977698i \(-0.567352\pi\)
0.951720 0.306968i \(-0.0993146\pi\)
\(410\) −2.00000 −0.0987730
\(411\) −2.00000 −0.0986527
\(412\) −9.50000 + 16.4545i −0.468031 + 0.810654i
\(413\) −1.00000 1.73205i −0.0492068 0.0852286i
\(414\) 3.00000 5.19615i 0.147442 0.255377i
\(415\) 1.00000 + 1.73205i 0.0490881 + 0.0850230i
\(416\) 1.50000 + 2.59808i 0.0735436 + 0.127381i
\(417\) −9.00000 −0.440732
\(418\) −1.00000 8.66025i −0.0489116 0.423587i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) −0.500000 0.866025i −0.0243975 0.0422577i
\(421\) 7.00000 + 12.1244i 0.341159 + 0.590905i 0.984648 0.174550i \(-0.0558472\pi\)
−0.643489 + 0.765455i \(0.722514\pi\)
\(422\) 2.50000 4.33013i 0.121698 0.210787i
\(423\) 0 0
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) 2.50000 4.33013i 0.120983 0.209550i
\(428\) 2.00000 3.46410i 0.0966736 0.167444i
\(429\) −6.00000 −0.289683
\(430\) 5.00000 0.241121
\(431\) 10.0000 17.3205i 0.481683 0.834300i −0.518096 0.855323i \(-0.673359\pi\)
0.999779 + 0.0210230i \(0.00669232\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −14.5000 + 25.1147i −0.696826 + 1.20694i 0.272736 + 0.962089i \(0.412071\pi\)
−0.969561 + 0.244848i \(0.921262\pi\)
\(434\) 0.500000 + 0.866025i 0.0240008 + 0.0415705i
\(435\) −5.00000 8.66025i −0.239732 0.415227i
\(436\) −18.0000 −0.862044
\(437\) 21.0000 15.5885i 1.00457 0.745697i
\(438\) 11.0000 0.525600
\(439\) 20.5000 + 35.5070i 0.978412 + 1.69466i 0.668184 + 0.743996i \(0.267072\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(440\) 1.00000 + 1.73205i 0.0476731 + 0.0825723i
\(441\) 3.00000 5.19615i 0.142857 0.247436i
\(442\) 6.00000 + 10.3923i 0.285391 + 0.494312i
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) −5.00000 −0.237289
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) −9.00000 + 15.5885i −0.425685 + 0.737309i
\(448\) −1.00000 −0.0472456
\(449\) 28.0000 1.32140 0.660701 0.750649i \(-0.270259\pi\)
0.660701 + 0.750649i \(0.270259\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −2.00000 3.46410i −0.0941763 0.163118i
\(452\) −7.00000 + 12.1244i −0.329252 + 0.570282i
\(453\) 0 0
\(454\) 9.00000 + 15.5885i 0.422391 + 0.731603i
\(455\) −3.00000 −0.140642
\(456\) −0.500000 4.33013i −0.0234146 0.202777i
\(457\) 23.0000 1.07589 0.537947 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) 2.50000 + 4.33013i 0.116817 + 0.202334i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(462\) 1.00000 1.73205i 0.0465242 0.0805823i
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) −10.0000 −0.464238
\(465\) 0.500000 0.866025i 0.0231869 0.0401610i
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 30.0000 1.38823 0.694117 0.719862i \(-0.255795\pi\)
0.694117 + 0.719862i \(0.255795\pi\)
\(468\) −3.00000 −0.138675
\(469\) −2.50000 + 4.33013i −0.115439 + 0.199947i
\(470\) 0 0
\(471\) 6.50000 11.2583i 0.299504 0.518756i
\(472\) 1.00000 + 1.73205i 0.0460287 + 0.0797241i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) −11.0000 −0.505247
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) −4.00000 −0.183340
\(477\) 6.00000 + 10.3923i 0.274721 + 0.475831i
\(478\) 9.00000 + 15.5885i 0.411650 + 0.712999i
\(479\) −21.0000 + 36.3731i −0.959514 + 1.66193i −0.235833 + 0.971794i \(0.575782\pi\)
−0.723681 + 0.690134i \(0.757551\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −7.50000 + 12.9904i −0.341971 + 0.592310i
\(482\) 5.00000 0.227744
\(483\) 6.00000 0.273009
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) −2.50000 + 4.33013i −0.113170 + 0.196016i
\(489\) 8.50000 + 14.7224i 0.384383 + 0.665771i
\(490\) −3.00000 + 5.19615i −0.135526 + 0.234738i
\(491\) −14.0000 24.2487i −0.631811 1.09433i −0.987181 0.159603i \(-0.948978\pi\)
0.355370 0.934726i \(-0.384355\pi\)
\(492\) −1.00000 1.73205i −0.0450835 0.0780869i
\(493\) −40.0000 −1.80151
\(494\) −12.0000 5.19615i −0.539906 0.233786i
\(495\) −2.00000 −0.0898933
\(496\) −0.500000 0.866025i −0.0224507 0.0388857i
\(497\) 0 0
\(498\) −1.00000 + 1.73205i −0.0448111 + 0.0776151i
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 14.0000 0.625474
\(502\) −2.00000 −0.0892644
\(503\) −22.0000 + 38.1051i −0.980932 + 1.69902i −0.322151 + 0.946688i \(0.604406\pi\)
−0.658781 + 0.752335i \(0.728928\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) −6.00000 −0.266996
\(506\) −12.0000 −0.533465
\(507\) 2.00000 3.46410i 0.0888231 0.153846i
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) 4.00000 6.92820i 0.177297 0.307087i −0.763657 0.645622i \(-0.776598\pi\)
0.940954 + 0.338535i \(0.109931\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) 5.50000 + 9.52628i 0.243306 + 0.421418i
\(512\) 1.00000 0.0441942
\(513\) 4.00000 + 1.73205i 0.176604 + 0.0764719i
\(514\) −6.00000 −0.264649
\(515\) 9.50000 + 16.4545i 0.418620 + 0.725071i
\(516\) 2.50000 + 4.33013i 0.110056 + 0.190623i
\(517\) 0 0
\(518\) −2.50000 4.33013i −0.109844 0.190255i
\(519\) 13.0000 22.5167i 0.570637 0.988372i
\(520\) 3.00000 0.131559
\(521\) 8.00000 0.350486 0.175243 0.984525i \(-0.443929\pi\)
0.175243 + 0.984525i \(0.443929\pi\)
\(522\) 5.00000 8.66025i 0.218844 0.379049i
\(523\) 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i \(-0.756023\pi\)
0.960856 + 0.277047i \(0.0893559\pi\)
\(524\) −6.00000 −0.262111
\(525\) −1.00000 −0.0436436
\(526\) 5.00000 8.66025i 0.218010 0.377605i
\(527\) −2.00000 3.46410i −0.0871214 0.150899i
\(528\) −1.00000 + 1.73205i −0.0435194 + 0.0753778i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) −2.00000 −0.0867926
\(532\) 3.50000 2.59808i 0.151744 0.112641i
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) −2.00000 3.46410i −0.0864675 0.149766i
\(536\) 2.50000 4.33013i 0.107984 0.187033i
\(537\) 5.00000 + 8.66025i 0.215766 + 0.373718i
\(538\) −5.00000 + 8.66025i −0.215565 + 0.373370i
\(539\) −12.0000 −0.516877
\(540\) −1.00000 −0.0430331
\(541\) 4.50000 7.79423i 0.193470 0.335100i −0.752928 0.658103i \(-0.771359\pi\)
0.946398 + 0.323003i \(0.104692\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) −6.00000 −0.257485
\(544\) 4.00000 0.171499
\(545\) −9.00000 + 15.5885i −0.385518 + 0.667736i
\(546\) −1.50000 2.59808i −0.0641941 0.111187i
\(547\) 4.50000 7.79423i 0.192406 0.333257i −0.753641 0.657286i \(-0.771704\pi\)
0.946047 + 0.324029i \(0.105038\pi\)
\(548\) 1.00000 + 1.73205i 0.0427179 + 0.0739895i
\(549\) −2.50000 4.33013i −0.106697 0.184805i
\(550\) 2.00000 0.0852803
\(551\) 35.0000 25.9808i 1.49105 1.10682i
\(552\) −6.00000 −0.255377
\(553\) −5.50000 9.52628i −0.233884 0.405099i
\(554\) 5.00000 + 8.66025i 0.212430 + 0.367939i
\(555\) −2.50000 + 4.33013i −0.106119 + 0.183804i
\(556\) 4.50000 + 7.79423i 0.190843 + 0.330549i
\(557\) 6.00000 10.3923i 0.254228 0.440336i −0.710457 0.703740i \(-0.751512\pi\)
0.964686 + 0.263404i \(0.0848453\pi\)
\(558\) 1.00000 0.0423334
\(559\) 15.0000 0.634432
\(560\) −0.500000 + 0.866025i −0.0211289 + 0.0365963i
\(561\) −4.00000 + 6.92820i −0.168880 + 0.292509i
\(562\) −30.0000 −1.26547
\(563\) 22.0000 0.927189 0.463595 0.886047i \(-0.346559\pi\)
0.463595 + 0.886047i \(0.346559\pi\)
\(564\) 0 0
\(565\) 7.00000 + 12.1244i 0.294492 + 0.510075i
\(566\) −4.00000 + 6.92820i −0.168133 + 0.291214i
\(567\) 0.500000 + 0.866025i 0.0209980 + 0.0363696i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) −4.00000 1.73205i −0.167542 0.0725476i
\(571\) 39.0000 1.63210 0.816050 0.577982i \(-0.196160\pi\)
0.816050 + 0.577982i \(0.196160\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −8.00000 13.8564i −0.334205 0.578860i
\(574\) 1.00000 1.73205i 0.0417392 0.0722944i
\(575\) 3.00000 + 5.19615i 0.125109 + 0.216695i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −12.5000 + 21.6506i −0.519482 + 0.899770i
\(580\) −5.00000 + 8.66025i −0.207614 + 0.359597i
\(581\) −2.00000 −0.0829740
\(582\) −2.00000 −0.0829027
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) −5.50000 9.52628i −0.227592 0.394200i
\(585\) −1.50000 + 2.59808i −0.0620174 + 0.107417i
\(586\) 13.0000 + 22.5167i 0.537025 + 0.930155i
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) −6.00000 −0.247436
\(589\) 4.00000 + 1.73205i 0.164817 + 0.0713679i
\(590\) 2.00000 0.0823387
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) 2.50000 + 4.33013i 0.102749 + 0.177967i
\(593\) −14.0000 + 24.2487i −0.574911 + 0.995775i 0.421140 + 0.906996i \(0.361630\pi\)
−0.996051 + 0.0887797i \(0.971703\pi\)
\(594\) −1.00000 1.73205i −0.0410305 0.0710669i
\(595\) −2.00000 + 3.46410i −0.0819920 + 0.142014i
\(596\) 18.0000 0.737309
\(597\) 5.00000 0.204636
\(598\) −9.00000 + 15.5885i −0.368037 + 0.637459i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 1.00000 0.0408248
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) −2.50000 + 4.33013i −0.101892 + 0.176483i
\(603\) 2.50000 + 4.33013i 0.101808 + 0.176336i
\(604\) 0 0
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −9.00000 −0.365299 −0.182649 0.983178i \(-0.558467\pi\)
−0.182649 + 0.983178i \(0.558467\pi\)
\(608\) −3.50000 + 2.59808i −0.141944 + 0.105366i
\(609\) 10.0000 0.405220
\(610\) 2.50000 + 4.33013i 0.101222 + 0.175322i
\(611\) 0 0
\(612\) −2.00000 + 3.46410i −0.0808452 + 0.140028i
\(613\) 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i \(-0.0201241\pi\)
−0.553716 + 0.832705i \(0.686791\pi\)
\(614\) −2.00000 + 3.46410i −0.0807134 + 0.139800i
\(615\) −2.00000 −0.0806478
\(616\) −2.00000 −0.0805823
\(617\) −12.0000 + 20.7846i −0.483102 + 0.836757i −0.999812 0.0194037i \(-0.993823\pi\)
0.516710 + 0.856161i \(0.327157\pi\)
\(618\) −9.50000 + 16.4545i −0.382146 + 0.661896i
\(619\) −29.0000 −1.16561 −0.582804 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) −1.00000 −0.0401610
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) 5.00000 + 8.66025i 0.200482 + 0.347245i
\(623\) 0 0
\(624\) 1.50000 + 2.59808i 0.0600481 + 0.104006i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 18.0000 0.719425
\(627\) −1.00000 8.66025i −0.0399362 0.345857i
\(628\) −13.0000 −0.518756
\(629\) 10.0000 + 17.3205i 0.398726 + 0.690614i
\(630\) −0.500000 0.866025i −0.0199205 0.0345033i
\(631\) 21.5000 37.2391i 0.855901 1.48246i −0.0199047 0.999802i \(-0.506336\pi\)
0.875806 0.482663i \(-0.160330\pi\)
\(632\) 5.50000 + 9.52628i 0.218778 + 0.378935i
\(633\) 2.50000 4.33013i 0.0993661 0.172107i
\(634\) 30.0000 1.19145
\(635\) −16.0000 −0.634941
\(636\) 6.00000 10.3923i 0.237915 0.412082i
\(637\) −9.00000 + 15.5885i −0.356593 + 0.617637i
\(638\) −20.0000 −0.791808
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) 2.00000 3.46410i 0.0789337 0.136717i
\(643\) −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) −3.00000 5.19615i −0.118217 0.204757i
\(645\) 5.00000 0.196875
\(646\) −14.0000 + 10.3923i −0.550823 + 0.408880i
\(647\) 46.0000 1.80845 0.904223 0.427060i \(-0.140451\pi\)
0.904223 + 0.427060i \(0.140451\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) 1.50000 2.59808i 0.0588348 0.101905i
\(651\) 0.500000 + 0.866025i 0.0195965 + 0.0339422i
\(652\) 8.50000 14.7224i 0.332886 0.576575i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) −18.0000 −0.703856
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) −1.00000 + 1.73205i −0.0390434 + 0.0676252i
\(657\) 11.0000 0.429151
\(658\) 0 0
\(659\) −9.00000 + 15.5885i −0.350590 + 0.607240i −0.986353 0.164644i \(-0.947352\pi\)
0.635763 + 0.771885i \(0.280686\pi\)
\(660\) 1.00000 + 1.73205i 0.0389249 + 0.0674200i
\(661\) −23.0000 + 39.8372i −0.894596 + 1.54949i −0.0602929 + 0.998181i \(0.519203\pi\)
−0.834303 + 0.551306i \(0.814130\pi\)
\(662\) −2.50000 4.33013i −0.0971653 0.168295i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 2.00000 0.0776151
\(665\) −0.500000 4.33013i −0.0193892 0.167915i
\(666\) −5.00000 −0.193746
\(667\) −30.0000 51.9615i −1.16160 2.01196i
\(668\) −7.00000 12.1244i −0.270838 0.469105i
\(669\) 0.500000 0.866025i 0.0193311 0.0334825i
\(670\) −2.50000 4.33013i −0.0965834 0.167287i
\(671\) −5.00000 + 8.66025i −0.193023 + 0.334325i
\(672\) −1.00000 −0.0385758
\(673\) −23.0000 −0.886585 −0.443292 0.896377i \(-0.646190\pi\)
−0.443292 + 0.896377i \(0.646190\pi\)
\(674\) −11.5000 + 19.9186i −0.442963 + 0.767235i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −4.00000 −0.153846
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) −7.00000 + 12.1244i −0.268833 + 0.465633i
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 9.00000 + 15.5885i 0.344881 + 0.597351i
\(682\) −1.00000 1.73205i −0.0382920 0.0663237i
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −0.500000 4.33013i −0.0191180 0.165567i
\(685\) 2.00000 0.0764161
\(686\) −6.50000 11.2583i −0.248171 0.429845i
\(687\) 2.50000 + 4.33013i 0.0953809 + 0.165205i
\(688\) 2.50000 4.33013i 0.0953116 0.165085i
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) −3.00000 + 5.19615i −0.114208 + 0.197814i
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) −26.0000 −0.988372
\(693\) 1.00000 1.73205i 0.0379869 0.0657952i
\(694\) 0 0
\(695\) 9.00000 0.341389
\(696\) −10.0000 −0.379049
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) −8.50000 14.7224i −0.321730 0.557252i
\(699\) 2.00000 3.46410i 0.0756469 0.131024i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) −14.0000 24.2487i −0.528773 0.915861i −0.999437 0.0335489i \(-0.989319\pi\)
0.470664 0.882312i \(-0.344014\pi\)
\(702\) −3.00000 −0.113228
\(703\) −20.0000 8.66025i −0.754314 0.326628i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 1.00000 + 1.73205i 0.0375823 + 0.0650945i
\(709\) −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i \(-0.949459\pi\)
0.630641 + 0.776075i \(0.282792\pi\)
\(710\) 0 0
\(711\) −11.0000 −0.412532
\(712\) 0 0
\(713\) 3.00000 5.19615i 0.112351 0.194597i
\(714\) −4.00000 −0.149696
\(715\) 6.00000 0.224387
\(716\) 5.00000 8.66025i 0.186859 0.323649i
\(717\) 9.00000 + 15.5885i 0.336111 + 0.582162i
\(718\) 1.00000 1.73205i 0.0373197 0.0646396i
\(719\) −13.0000 22.5167i −0.484818 0.839730i 0.515030 0.857172i \(-0.327781\pi\)
−0.999848 + 0.0174426i \(0.994448\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −19.0000 −0.707597
\(722\) 5.50000 18.1865i 0.204689 0.676833i
\(723\) 5.00000 0.185952
\(724\) 3.00000 + 5.19615i 0.111494 + 0.193113i
\(725\) 5.00000 + 8.66025i 0.185695 + 0.321634i
\(726\) 3.50000 6.06218i 0.129897 0.224989i
\(727\) 22.5000 + 38.9711i 0.834479 + 1.44536i 0.894454 + 0.447160i \(0.147564\pi\)
−0.0599753 + 0.998200i \(0.519102\pi\)
\(728\) −1.50000 + 2.59808i −0.0555937 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) −11.0000 −0.407128
\(731\) 10.0000 17.3205i 0.369863 0.640622i
\(732\) −2.50000 + 4.33013i −0.0924027 + 0.160046i
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) −7.00000 −0.258375
\(735\) −3.00000 + 5.19615i −0.110657 + 0.191663i
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) −1.00000 1.73205i −0.0368105 0.0637577i
\(739\) −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i \(-0.172522\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(740\) 5.00000 0.183804
\(741\) −12.0000 5.19615i −0.440831 0.190885i
\(742\) 12.0000 0.440534
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) −0.500000 0.866025i −0.0183309 0.0317500i
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 11.0000 + 19.0526i 0.402739 + 0.697564i
\(747\) −1.00000 + 1.73205i −0.0365881 + 0.0633724i
\(748\) 8.00000 0.292509
\(749\) 4.00000 0.146157
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) 23.5000 40.7032i 0.857527 1.48528i −0.0167534 0.999860i \(-0.505333\pi\)
0.874281 0.485421i \(-0.161334\pi\)
\(752\) 0 0
\(753\) −2.00000 −0.0728841
\(754\) −15.0000 + 25.9808i −0.546268 + 0.946164i
\(755\) 0 0
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) 3.50000 + 6.06218i 0.127210 + 0.220334i 0.922595 0.385771i \(-0.126065\pi\)
−0.795385 + 0.606105i \(0.792731\pi\)
\(758\) 5.50000 + 9.52628i 0.199769 + 0.346010i
\(759\) −12.0000 −0.435572
\(760\) 0.500000 + 4.33013i 0.0181369 + 0.157070i
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) −8.00000 13.8564i −0.289809 0.501965i
\(763\) −9.00000 15.5885i −0.325822 0.564340i
\(764\) −8.00000 + 13.8564i −0.289430 + 0.501307i
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 18.0000 31.1769i 0.650366 1.12647i
\(767\) 6.00000 0.216647
\(768\) 1.00000 0.0360844
\(769\) 16.5000 28.5788i 0.595005 1.03058i −0.398541 0.917151i \(-0.630483\pi\)
0.993546 0.113429i \(-0.0361834\pi\)
\(770\) −1.00000 + 1.73205i −0.0360375 + 0.0624188i
\(771\) −6.00000 −0.216085
\(772\) 25.0000 0.899770
\(773\) 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i \(-0.798920\pi\)
0.914920 + 0.403634i \(0.132253\pi\)
\(774\) 2.50000 + 4.33013i 0.0898606 + 0.155643i
\(775\) −0.500000 + 0.866025i −0.0179605 + 0.0311086i
\(776\) 1.00000 + 1.73205i 0.0358979 + 0.0621770i
\(777\) −2.50000 4.33013i −0.0896870 0.155342i
\(778\) −10.0000 −0.358517
\(779\) −1.00000 8.66025i −0.0358287 0.310286i
\(780\)