Properties

Label 570.2.i.b.391.1
Level $570$
Weight $2$
Character 570.391
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 391.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.b.121.1

$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −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 0.995535 0.0943882i \(-0.0300895\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(14\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 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 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −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 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) −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 −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 2.50000 4.33013i 0.381246 0.660338i −0.609994 0.792406i \(-0.708828\pi\)
0.991241 + 0.132068i \(0.0421616\pi\)
\(44\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −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 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) −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 −0.793560 0.608492i \(-0.791775\pi\)
0.923749 + 0.382998i \(0.125108\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) −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 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i \(0.389279\pi\)
−0.984594 + 0.174855i \(0.944054\pi\)
\(74\) 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 −0.370907 0.928670i \(-0.620953\pi\)
0.989705 0.143120i \(-0.0457135\pi\)
\(80\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 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 −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 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 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 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 −0.00790932 0.999969i \(-0.502518\pi\)
0.869953 0.493135i \(-0.164149\pi\)
\(110\) 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 −0.964899 0.262620i \(-0.915413\pi\)
0.255014 0.966937i \(-0.417920\pi\)
\(128\) −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 −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 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 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) 4.50000 + 7.79423i 0.381685 + 0.661098i 0.991303 0.131597i \(-0.0420106\pi\)
−0.609618 + 0.792695i \(0.708677\pi\)
\(140\) 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 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) −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 −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 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 −0.998808 0.0488118i \(-0.984457\pi\)
0.457132 0.889399i \(-0.348877\pi\)
\(168\) 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 0.362500 0.931984i \(-0.381923\pi\)
0.625871 0.779926i \(-0.284744\pi\)
\(174\) 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 0.955714 0.294297i \(-0.0950855\pi\)
−0.732726 + 0.680524i \(0.761752\pi\)
\(182\) 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 −0.0719816 + 0.997406i \(0.522932\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 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 0.763707 0.645563i \(-0.223377\pi\)
−0.940927 + 0.338608i \(0.890044\pi\)
\(200\) −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 −0.767049 0.641588i \(-0.778276\pi\)
0.939156 + 0.343490i \(0.111609\pi\)
\(212\) 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 −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 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 −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) 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 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 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 0.895858 0.444340i \(-0.146562\pi\)
−0.832739 + 0.553666i \(0.813228\pi\)
\(252\) 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 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) −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 −0.669680 0.742650i \(-0.733569\pi\)
0.977993 + 0.208635i \(0.0669022\pi\)
\(264\) −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 −0.977229 0.212187i \(-0.931941\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i \(-0.755208\pi\)
0.961563 + 0.274586i \(0.0885408\pi\)
\(272\) −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 0.834021 + 0.551733i \(0.186033\pi\)
0.0608039 + 0.998150i \(0.480634\pi\)
\(282\) 0 0
\(283\) −4.00000 + 6.92820i −0.237775 + 0.411839i −0.960076 0.279741i \(-0.909752\pi\)
0.722300 + 0.691580i \(0.243085\pi\)
\(284\) 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 −0.917438 0.397879i \(-0.869747\pi\)
0.803292 + 0.595585i \(0.203080\pi\)
\(308\) 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 −0.999949 0.0100869i \(-0.996789\pi\)
0.491239 0.871025i \(-0.336544\pi\)
\(314\) 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 −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) 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 0.361815 + 0.932250i \(0.382157\pi\)
−0.988260 + 0.152784i \(0.951176\pi\)
\(338\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 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 −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) −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 0.942799 0.333363i \(-0.108183\pi\)
−0.760100 + 0.649806i \(0.774850\pi\)
\(368\) −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 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) −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 0.964490 0.264120i \(-0.0850816\pi\)
−0.710980 + 0.703213i \(0.751748\pi\)
\(390\) −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 −0.853206 0.521575i \(-0.825345\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) 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 0.200888 0.979614i \(-0.435617\pi\)
0.747927 0.663781i \(-0.231049\pi\)
\(402\) 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 0.951720 + 0.306968i \(0.0993146\pi\)
−0.210017 + 0.977698i \(0.567352\pi\)
\(410\) −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 −0.643489 0.765455i \(-0.722514\pi\)
0.984648 + 0.174550i \(0.0558472\pi\)
\(422\) 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 0.999779 0.0210230i \(-0.00669232\pi\)
−0.518096 + 0.855323i \(0.673359\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −14.5000 25.1147i −0.696826 1.20694i −0.969561 0.244848i \(-0.921262\pi\)
0.272736 0.962089i \(-0.412071\pi\)
\(434\) 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 0.310228 0.950662i \(-0.399595\pi\)
0.668184 0.743996i \(-0.267072\pi\)
\(440\) 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 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 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 −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(-0.575782\pi\)
\(480\) 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 0.355370 + 0.934726i \(0.384355\pi\)
−0.987181 + 0.159603i \(0.948978\pi\)
\(492\) −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 −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 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 −0.658781 0.752335i \(-0.728928\pi\)
−0.322151 0.946688i \(-0.604406\pi\)
\(504\) 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 0.940954 0.338535i \(-0.109931\pi\)
−0.763657 + 0.645622i \(0.776598\pi\)
\(510\) 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 0.960856 0.277047i \(-0.0893559\pi\)
−0.720358 + 0.693602i \(0.756023\pi\)
\(524\) −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 0.946398 0.323003i \(-0.104692\pi\)
−0.752928 + 0.658103i \(0.771359\pi\)
\(542\) 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 0.946047 0.324029i \(-0.105038\pi\)
−0.753641 + 0.657286i \(0.771704\pi\)
\(548\) 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 0.964686 0.263404i \(-0.0848453\pi\)
−0.710457 + 0.703740i \(0.751512\pi\)
\(558\) 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 −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) −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 −0.996051 0.0887797i \(-0.971703\pi\)
0.421140 0.906996i \(-0.361630\pi\)
\(594\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 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 −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) −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 0.516710 0.856161i \(-0.327157\pi\)
−0.999812 + 0.0194037i \(0.993823\pi\)
\(618\) −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 0.875806 + 0.482663i \(0.160330\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 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 −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) −20.5000 + 35.5070i −0.808441 + 1.40026i 0.105502 + 0.994419i \(0.466355\pi\)
−0.913943 + 0.405842i \(0.866978\pi\)
\(644\) −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 0.635763 0.771885i \(-0.280686\pi\)
−0.986353 + 0.164644i \(0.947352\pi\)
\(660\) 1.00000 1.73205i 0.0389249 0.0674200i
\(661\) −23.0000 39.8372i −0.894596 1.54949i −0.834303 0.551306i \(-0.814130\pi\)
−0.0602929 0.998181i \(-0.519203\pi\)
\(662\) −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 0.470664 + 0.882312i \(0.344014\pi\)
−0.999437 + 0.0335489i \(0.989319\pi\)
\(702\) −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 0.630641 0.776075i \(-0.282792\pi\)
−0.987421 + 0.158114i \(0.949459\pi\)
\(710\) 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 −0.999848 0.0174426i \(-0.994448\pi\)
0.515030 + 0.857172i \(0.327781\pi\)
\(720\) 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 −0.0599753 0.998200i \(-0.519102\pi\)
0.894454 0.447160i \(-0.147564\pi\)
\(728\) −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 −0.875075 0.483987i \(-0.839188\pi\)
0.856683 + 0.515844i \(0.172522\pi\)
\(740\) 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 −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) −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 0.874281 + 0.485421i \(0.161334\pi\)
−0.0167534 + 0.999860i \(0.505333\pi\)
\(752\) 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 −0.795385 0.606105i \(-0.792731\pi\)
0.922595 + 0.385771i \(0.126065\pi\)
\(758\) 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 0.993546 + 0.113429i \(0.0361834\pi\)
−0.398541 + 0.917151i \(0.630483\pi\)
\(770\) −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 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) 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