Properties

Label 722.2.c.c.429.1
Level 722
Weight 2
Character 722.429
Analytic conductor 5.765
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 722.429
Dual form 722.2.c.c.653.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -6.00000 q^{11} -1.00000 q^{12} +(2.50000 + 4.33013i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -2.00000 q^{18} +(-0.500000 + 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} -5.00000 q^{26} +5.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(3.00000 + 5.19615i) q^{44} +3.00000 q^{46} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -5.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +(2.50000 - 4.33013i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(-2.50000 + 4.33013i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(4.50000 - 7.79423i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{66} +(2.50000 + 4.33013i) q^{67} +3.00000 q^{68} -3.00000 q^{69} +(-3.00000 + 5.19615i) q^{71} +(1.00000 + 1.73205i) q^{72} +(3.50000 - 6.06218i) q^{73} +(1.00000 - 1.73205i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(-2.50000 + 4.33013i) q^{78} +(-5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{83} +1.00000 q^{84} +(-4.00000 - 6.92820i) q^{86} +9.00000 q^{87} -6.00000 q^{88} +(-6.00000 - 10.3923i) q^{89} +(-2.50000 - 4.33013i) q^{91} +(-1.50000 + 2.59808i) q^{92} +(2.00000 - 3.46410i) q^{93} -1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +(-6.00000 - 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} - 2q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} - 2q^{7} + 2q^{8} + 2q^{9} - 12q^{11} - 2q^{12} + 5q^{13} + q^{14} - q^{16} - 3q^{17} - 4q^{18} - q^{21} + 6q^{22} - 3q^{23} + q^{24} + 5q^{25} - 10q^{26} + 10q^{27} + q^{28} + 9q^{29} + 8q^{31} - q^{32} - 6q^{33} - 3q^{34} + 2q^{36} - 4q^{37} + 10q^{39} - q^{42} - 8q^{43} + 6q^{44} + 6q^{46} + q^{48} - 12q^{49} - 10q^{50} + 3q^{51} + 5q^{52} - 3q^{53} - 5q^{54} - 2q^{56} - 18q^{58} + 9q^{59} + 10q^{61} - 4q^{62} - 2q^{63} + 2q^{64} - 6q^{66} + 5q^{67} + 6q^{68} - 6q^{69} - 6q^{71} + 2q^{72} + 7q^{73} + 2q^{74} + 10q^{75} + 12q^{77} - 5q^{78} - 10q^{79} - q^{81} - 12q^{83} + 2q^{84} - 8q^{86} + 18q^{87} - 12q^{88} - 12q^{89} - 5q^{91} - 3q^{92} + 4q^{93} - 2q^{96} - 10q^{97} + 6q^{98} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0
\(20\) 0 0
\(21\) −0.500000 + 0.866025i −0.109109 + 0.188982i
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −5.00000 −0.980581
\(27\) 5.00000 0.962250
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) 0 0
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 3.00000 + 5.19615i 0.452267 + 0.783349i
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 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
\(50\) −5.00000 −0.707107
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 2.50000 4.33013i 0.346688 0.600481i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) −1.00000 1.73205i −0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 3.00000 0.363803
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 5.00000 0.577350
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) −2.50000 + 4.33013i −0.283069 + 0.490290i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 9.00000 0.964901
\(88\) −6.00000 −0.639602
\(89\) −6.00000 10.3923i −0.635999 1.10158i −0.986303 0.164946i \(-0.947255\pi\)
0.350304 0.936636i \(-0.386078\pi\)
\(90\) 0 0
\(91\) −2.50000 4.33013i −0.262071 0.453921i
\(92\) −1.50000 + 2.59808i −0.156386 + 0.270868i
\(93\) 2.00000 3.46410i 0.207390 0.359211i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i \(0.336161\pi\)
−0.999961 + 0.00888289i \(0.997172\pi\)
\(98\) 3.00000 5.19615i 0.303046 0.524891i
\(99\) −6.00000 10.3923i −0.603023 1.04447i
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) −3.00000 −0.297044
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 2.50000 + 4.33013i 0.245145 + 0.424604i
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.50000 7.79423i 0.417815 0.723676i
\(117\) −5.00000 + 8.66025i −0.462250 + 0.800641i
\(118\) 4.50000 + 7.79423i 0.414259 + 0.717517i
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.00000 + 6.92820i 0.352180 + 0.609994i
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 1.50000 2.59808i 0.127688 0.221163i
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −15.0000 25.9808i −1.25436 2.17262i
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 3.50000 + 6.06218i 0.289662 + 0.501709i
\(147\) −3.00000 + 5.19615i −0.247436 + 0.428571i
\(148\) 1.00000 + 1.73205i 0.0821995 + 0.142374i
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) −2.50000 + 4.33013i −0.204124 + 0.353553i
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) −3.00000 + 5.19615i −0.241747 + 0.418718i
\(155\) 0 0
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) 11.0000 19.0526i 0.877896 1.52056i 0.0242497 0.999706i \(-0.492280\pi\)
0.853646 0.520854i \(-0.174386\pi\)
\(158\) −5.00000 8.66025i −0.397779 0.688973i
\(159\) −3.00000 −0.237915
\(160\) 0 0
\(161\) 1.50000 + 2.59808i 0.118217 + 0.204757i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) −0.500000 + 0.866025i −0.0385758 + 0.0668153i
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −4.50000 + 7.79423i −0.341144 + 0.590879i
\(175\) −2.50000 4.33013i −0.188982 0.327327i
\(176\) 3.00000 5.19615i 0.226134 0.391675i
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 12.0000 0.899438
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 1.00000 + 1.73205i 0.0743294 + 0.128742i 0.900794 0.434246i \(-0.142985\pi\)
−0.826465 + 0.562988i \(0.809652\pi\)
\(182\) 5.00000 0.370625
\(183\) 10.0000 0.739221
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 0 0
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) 0 0
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 12.0000 0.852803
\(199\) −5.50000 9.52628i −0.389885 0.675300i 0.602549 0.798082i \(-0.294152\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) 5.00000 0.352673
\(202\) 18.0000 1.26648
\(203\) −4.50000 7.79423i −0.315838 0.547048i
\(204\) 1.50000 2.59808i 0.105021 0.181902i
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) −5.00000 −0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) 2.50000 4.33013i 0.172107 0.298098i −0.767049 0.641588i \(-0.778276\pi\)
0.939156 + 0.343490i \(0.111609\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) −4.50000 + 7.79423i −0.307614 + 0.532803i
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) −4.00000 −0.271538
\(218\) 5.50000 + 9.52628i 0.372507 + 0.645201i
\(219\) −3.50000 6.06218i −0.236508 0.409644i
\(220\) 0 0
\(221\) −15.0000 −1.00901
\(222\) −1.00000 1.73205i −0.0671156 0.116248i
\(223\) 13.0000 22.5167i 0.870544 1.50783i 0.00910984 0.999959i \(-0.497100\pi\)
0.861435 0.507869i \(-0.169566\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) −5.00000 + 8.66025i −0.333333 + 0.577350i
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 15.0000 0.995585 0.497792 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 3.00000 5.19615i 0.197386 0.341882i
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −5.00000 8.66025i −0.326860 0.566139i
\(235\) 0 0
\(236\) −9.00000 −0.585850
\(237\) 5.00000 + 8.66025i 0.324785 + 0.562544i
\(238\) 1.50000 + 2.59808i 0.0972306 + 0.168408i
\(239\) −21.0000 −1.35838 −0.679189 0.733964i \(-0.737668\pi\)
−0.679189 + 0.733964i \(0.737668\pi\)
\(240\) 0 0
\(241\) 4.00000 + 6.92820i 0.257663 + 0.446285i 0.965615 0.259975i \(-0.0837143\pi\)
−0.707953 + 0.706260i \(0.750381\pi\)
\(242\) −12.5000 + 21.6506i −0.803530 + 1.39176i
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 5.00000 8.66025i 0.320092 0.554416i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0 0
\(251\) −3.00000 5.19615i −0.189358 0.327978i 0.755678 0.654943i \(-0.227307\pi\)
−0.945036 + 0.326965i \(0.893974\pi\)
\(252\) −1.00000 + 1.73205i −0.0629941 + 0.109109i
\(253\) 9.00000 + 15.5885i 0.565825 + 0.980038i
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) −8.00000 −0.498058
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) −9.00000 + 15.5885i −0.557086 + 0.964901i
\(262\) 0 0
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 2.50000 4.33013i 0.152712 0.264505i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) −5.00000 −0.302614
\(274\) −9.00000 −0.543710
\(275\) −15.0000 25.9808i −0.904534 1.56670i
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −4.00000 −0.239904
\(279\) 4.00000 + 6.92820i 0.239474 + 0.414781i
\(280\) 0 0
\(281\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(282\) 0 0
\(283\) 11.0000 19.0526i 0.653882 1.13256i −0.328291 0.944577i \(-0.606473\pi\)
0.982173 0.187980i \(-0.0601941\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 0 0
\(288\) 1.00000 1.73205i 0.0589256 0.102062i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) −7.00000 −0.409644
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) −3.00000 5.19615i −0.174964 0.303046i
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) −30.0000 −1.74078
\(298\) 0 0
\(299\) 7.50000 12.9904i 0.433736 0.751253i
\(300\) −2.50000 4.33013i −0.144338 0.250000i
\(301\) 4.00000 6.92820i 0.230556 0.399335i
\(302\) −5.00000 + 8.66025i −0.287718 + 0.498342i
\(303\) −18.0000 −1.03407
\(304\) 0 0
\(305\) 0 0
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) 10.0000 17.3205i 0.570730 0.988534i −0.425761 0.904836i \(-0.639994\pi\)
0.996491 0.0836980i \(-0.0266731\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 0 0
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) 5.00000 0.283069
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 11.0000 + 19.0526i 0.620766 + 1.07520i
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i \(-0.248000\pi\)
−0.964281 + 0.264883i \(0.914667\pi\)
\(318\) 1.50000 2.59808i 0.0841158 0.145693i
\(319\) −27.0000 46.7654i −1.51171 2.61836i
\(320\) 0 0
\(321\) 4.50000 7.79423i 0.251166 0.435031i
\(322\) −3.00000 −0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −12.5000 + 21.6506i −0.693375 + 1.20096i
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) −5.50000 9.52628i −0.304151 0.526804i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.00000 0.0549650 0.0274825 0.999622i \(-0.491251\pi\)
0.0274825 + 0.999622i \(0.491251\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −2.00000 + 3.46410i −0.108947 + 0.188702i −0.915344 0.402673i \(-0.868081\pi\)
0.806397 + 0.591375i \(0.201415\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) −4.50000 7.79423i −0.241225 0.417815i
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 5.00000 0.267261
\(351\) 12.5000 + 21.6506i 0.667201 + 1.15563i
\(352\) 3.00000 + 5.19615i 0.159901 + 0.276956i
\(353\) −15.0000 −0.798369 −0.399185 0.916871i \(-0.630707\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(354\) 9.00000 0.478345
\(355\) 0 0
\(356\) −6.00000 + 10.3923i −0.317999 + 0.550791i
\(357\) −1.50000 2.59808i −0.0793884 0.137505i
\(358\) 0 0
\(359\) −10.5000 + 18.1865i −0.554169 + 0.959849i 0.443799 + 0.896126i \(0.353630\pi\)
−0.997968 + 0.0637221i \(0.979703\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −0.105118
\(363\) 12.5000 21.6506i 0.656080 1.13636i
\(364\) −2.50000 + 4.33013i −0.131036 + 0.226960i
\(365\) 0 0
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 0 0
\(371\) 1.50000 + 2.59808i 0.0778761 + 0.134885i
\(372\) −4.00000 −0.207390
\(373\) −23.0000 −1.19089 −0.595447 0.803394i \(-0.703025\pi\)
−0.595447 + 0.803394i \(0.703025\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 0 0
\(377\) −22.5000 + 38.9711i −1.15881 + 2.00712i
\(378\) 2.50000 4.33013i 0.128586 0.222718i
\(379\) 7.00000 0.359566 0.179783 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) −1.50000 + 2.59808i −0.0767467 + 0.132929i
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 7.00000 + 12.1244i 0.356291 + 0.617113i
\(387\) −16.0000 −0.813326
\(388\) 10.0000 0.507673
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) −6.00000 −0.303046
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −6.00000 + 10.3923i −0.301511 + 0.522233i
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) −2.50000 + 4.33013i −0.124689 + 0.215967i
\(403\) 10.0000 + 17.3205i 0.498135 + 0.862796i
\(404\) −9.00000 + 15.5885i −0.447767 + 0.775555i
\(405\) 0 0
\(406\) 9.00000 0.446663
\(407\) 12.0000 0.594818
\(408\) 1.50000 + 2.59808i 0.0742611 + 0.128624i
\(409\) 16.0000 + 27.7128i 0.791149 + 1.37031i 0.925256 + 0.379344i \(0.123850\pi\)
−0.134107 + 0.990967i \(0.542817\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) −4.50000 + 7.79423i −0.221431 + 0.383529i
\(414\) 3.00000 + 5.19615i 0.147442 + 0.255377i
\(415\) 0 0
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 8.50000 14.7224i 0.414265 0.717527i −0.581086 0.813842i \(-0.697372\pi\)
0.995351 + 0.0963145i \(0.0307055\pi\)
\(422\) 2.50000 + 4.33013i 0.121698 + 0.210787i
\(423\) 0 0
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) −15.0000 −0.727607
\(426\) −6.00000 −0.290701
\(427\) −5.00000 8.66025i −0.241967 0.419099i
\(428\) −4.50000 7.79423i −0.217516 0.376748i
\(429\) −30.0000 −1.44841
\(430\) 0 0
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 1.00000 + 1.73205i 0.0480569 + 0.0832370i 0.889053 0.457804i \(-0.151364\pi\)
−0.840996 + 0.541041i \(0.818030\pi\)
\(434\) 2.00000 3.46410i 0.0960031 0.166282i
\(435\) 0 0
\(436\) −11.0000 −0.526804
\(437\) 0 0
\(438\) 7.00000 0.334473
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) −6.00000 10.3923i −0.285714 0.494872i
\(442\) 7.50000 12.9904i 0.356739 0.617889i
\(443\) 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i \(-0.0260248\pi\)
−0.569057 + 0.822298i \(0.692691\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 13.0000 + 22.5167i 0.615568 + 1.06619i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −5.00000 8.66025i −0.235702 0.408248i
\(451\) 0 0
\(452\) 3.00000 + 5.19615i 0.141108 + 0.244406i
\(453\) 5.00000 8.66025i 0.234920 0.406894i
\(454\) −7.50000 + 12.9904i −0.351992 + 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 11.0000 19.0526i 0.513996 0.890268i
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 0 0
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) 3.00000 + 5.19615i 0.139573 + 0.241747i
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −9.00000 −0.417815
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 10.0000 0.462250
\(469\) −2.50000 4.33013i −0.115439 0.199947i
\(470\) 0 0
\(471\) −11.0000 19.0526i −0.506853 0.877896i
\(472\) 4.50000 7.79423i 0.207129 0.358758i
\(473\) 24.0000 41.5692i 1.10352 1.91135i
\(474\) −10.0000 −0.459315
\(475\) 0 0
\(476\) −3.00000 −0.137505
\(477\) 3.00000 5.19615i 0.137361 0.237915i
\(478\) 10.5000 18.1865i 0.480259 0.831833i
\(479\) −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 0 0
\(481\) −5.00000 8.66025i −0.227980 0.394874i
\(482\) −8.00000 −0.364390
\(483\) 3.00000 0.136505
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 0 0
\(486\) −16.0000 −0.725775
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 10.0000 17.3205i 0.452216 0.783260i
\(490\) 0 0
\(491\) 18.0000 31.1769i 0.812329 1.40699i −0.0989017 0.995097i \(-0.531533\pi\)
0.911230 0.411897i \(-0.135134\pi\)
\(492\) 0 0
\(493\) −27.0000 −1.21602
\(494\) 0 0
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 6.00000 0.267793
\(503\) 10.5000 + 18.1865i 0.468172 + 0.810897i 0.999338 0.0363700i \(-0.0115795\pi\)
−0.531167 + 0.847267i \(0.678246\pi\)
\(504\) −1.00000 1.73205i −0.0445435 0.0771517i
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 1.00000 1.73205i 0.0443678 0.0768473i
\(509\) 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 0 0
\(511\) −3.50000 + 6.06218i −0.154831 + 0.268175i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) 0 0
\(518\) −1.00000 + 1.73205i −0.0439375 + 0.0761019i
\(519\) −3.00000 5.19615i −0.131685 0.228086i
\(520\) 0 0
\(521\) 36.0000 1.57719 0.788594 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) 5.50000 + 9.52628i 0.240498 + 0.416555i 0.960856 0.277047i \(-0.0893559\pi\)
−0.720358 + 0.693602i \(0.756023\pi\)
\(524\) 0 0
\(525\) −5.00000 −0.218218
\(526\) −12.0000 20.7846i −0.523225 0.906252i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) −3.00000 5.19615i −0.130558 0.226134i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 0 0
\(534\) 6.00000 10.3923i 0.259645 0.449719i
\(535\) 0 0
\(536\) 2.50000 + 4.33013i 0.107984 + 0.187033i
\(537\) 0 0
\(538\) −3.00000 5.19615i −0.129339 0.224022i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) −5.50000 9.52628i −0.236245 0.409189i
\(543\) 2.00000 0.0858282
\(544\) 3.00000 0.128624
\(545\) 0 0
\(546\) 2.50000 4.33013i 0.106990 0.185312i
\(547\) 22.0000 + 38.1051i 0.940652 + 1.62926i 0.764231 + 0.644942i \(0.223119\pi\)
0.176421 + 0.984315i \(0.443548\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) −10.0000 + 17.3205i −0.426790 + 0.739221i
\(550\) 30.0000 1.27920
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) 5.00000 8.66025i 0.212622 0.368271i
\(554\) −4.00000 + 6.92820i −0.169944 + 0.294351i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −12.0000 20.7846i −0.508456 0.880672i −0.999952 0.00979220i \(-0.996883\pi\)
0.491496 0.870880i \(-0.336450\pi\)
\(558\) −8.00000 −0.338667
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) −9.00000 15.5885i −0.379980 0.658145i
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 11.0000 + 19.0526i 0.462364 + 0.800839i
\(567\) 0.500000 0.866025i 0.0209980 0.0363696i
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) −15.0000 + 25.9808i −0.627182 + 1.08631i
\(573\) 1.50000 2.59808i 0.0626634 0.108536i
\(574\) 0 0
\(575\) 7.50000 12.9904i 0.312772 0.541736i
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −8.00000 −0.332756
\(579\) −7.00000 12.1244i −0.290910 0.503871i
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) −10.0000 −0.414513
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 3.50000 6.06218i 0.144831 0.250855i
\(585\) 0 0
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 6.00000 0.247436
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 15.0000 + 25.9808i 0.615976 + 1.06690i 0.990212 + 0.139569i \(0.0445716\pi\)
−0.374236 + 0.927333i \(0.622095\pi\)
\(594\) 15.0000 25.9808i 0.615457 1.06600i
\(595\) 0 0
\(596\) 0 0
\(597\) −11.0000 −0.450200
\(598\) 7.50000 + 12.9904i 0.306698 + 0.531216i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 5.00000 0.204124
\(601\) 28.0000 1.14214 0.571072 0.820900i \(-0.306528\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(602\) 4.00000 + 6.92820i 0.163028 + 0.282372i
\(603\) −5.00000 + 8.66025i −0.203616 + 0.352673i
\(604\) −5.00000 8.66025i −0.203447 0.352381i
\(605\) 0 0
\(606\) 9.00000 15.5885i 0.365600 0.633238i
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) −9.00000 −0.364698
\(610\) 0 0
\(611\) 0 0
\(612\) 3.00000 + 5.19615i 0.121268 + 0.210042i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 10.0000 + 17.3205i 0.403567 + 0.698999i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) −7.50000 12.9904i −0.300965 0.521286i
\(622\) 10.5000 18.1865i 0.421012 0.729214i
\(623\) 6.00000 + 10.3923i 0.240385 + 0.416359i
\(624\) −2.50000 + 4.33013i −0.100080 + 0.173344i
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) 3.00000 5.19615i 0.119618 0.207184i
\(630\) 0 0
\(631\) 8.00000 + 13.8564i 0.318475 + 0.551615i 0.980170 0.198158i \(-0.0634960\pi\)
−0.661695 + 0.749773i \(0.730163\pi\)
\(632\) −5.00000 + 8.66025i −0.198889 + 0.344486i
\(633\) −2.50000 4.33013i −0.0993661 0.172107i
\(634\) 9.00000 0.357436
\(635\) 0 0
\(636\) 1.50000 + 2.59808i 0.0594789 + 0.103020i
\(637\) −15.0000 25.9808i −0.594322 1.02940i
\(638\) 54.0000 2.13788
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 3.00000 5.19615i 0.118493 0.205236i −0.800678 0.599095i \(-0.795527\pi\)
0.919171 + 0.393860i \(0.128860\pi\)
\(642\) 4.50000 + 7.79423i 0.177601 + 0.307614i
\(643\) 11.0000 19.0526i 0.433798 0.751360i −0.563399 0.826185i \(-0.690507\pi\)
0.997197 + 0.0748254i \(0.0238399\pi\)
\(644\) 1.50000 2.59808i 0.0591083 0.102379i
\(645\) 0 0
\(646\) 0 0
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −27.0000 + 46.7654i −1.05984 + 1.83570i
\(650\) −12.5000 21.6506i −0.490290 0.849208i
\(651\) −2.00000 + 3.46410i −0.0783862 + 0.135769i
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 11.0000 0.430134
\(655\) 0 0
\(656\) 0 0
\(657\) 14.0000 0.546192
\(658\) 0 0
\(659\) −22.5000 38.9711i −0.876476 1.51810i −0.855183 0.518327i \(-0.826555\pi\)
−0.0212930 0.999773i \(-0.506778\pi\)
\(660\) 0 0
\(661\) −6.50000 11.2583i −0.252821 0.437898i 0.711481 0.702706i \(-0.248025\pi\)
−0.964301 + 0.264807i \(0.914692\pi\)
\(662\) −0.500000 + 0.866025i −0.0194331 + 0.0336590i
\(663\) −7.50000 + 12.9904i −0.291276 + 0.504505i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 13.5000 23.3827i 0.522722 0.905381i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) −13.0000 22.5167i −0.502609 0.870544i
\(670\) 0 0
\(671\) −30.0000 51.9615i −1.15814 2.00595i
\(672\) 1.00000 0.0385758
\(673\) −44.0000 −1.69608 −0.848038 0.529936i \(-0.822216\pi\)
−0.848038 + 0.529936i \(0.822216\pi\)
\(674\) −2.00000 3.46410i −0.0770371 0.133432i
\(675\) 12.5000 + 21.6506i 0.481125 + 0.833333i
\(676\) 12.0000 0.461538
\(677\) 33.0000 1.26829 0.634147 0.773213i \(-0.281352\pi\)
0.634147 + 0.773213i \(0.281352\pi\)
\(678\) −3.00000 5.19615i −0.115214 0.199557i
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 0 0
\(681\) 7.50000 12.9904i 0.287401 0.497792i
\(682\) 12.0000 20.7846i 0.459504 0.795884i
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) −11.0000 + 19.0526i −0.419676 + 0.726900i
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 7.50000 12.9904i 0.285727 0.494894i
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) −6.00000 −0.228086
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) −9.00000 15.5885i −0.341635 0.591730i
\(695\) 0 0
\(696\) 9.00000 0.341144
\(697\) 0 0
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) −2.50000 + 4.33013i −0.0944911 + 0.163663i
\(701\) −6.00000 + 10.3923i −0.226617 + 0.392512i −0.956803 0.290736i \(-0.906100\pi\)
0.730186 + 0.683248i \(0.239433\pi\)
\(702\) −25.0000 −0.943564
\(703\) 0 0
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) 7.50000 12.9904i 0.282266 0.488899i
\(707\) 9.00000 + 15.5885i 0.338480 + 0.586264i
\(708\) −4.50000 + 7.79423i −0.169120 + 0.292925i
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −20.0000 −0.750059
\(712\) −6.00000 10.3923i −0.224860 0.389468i
\(713\) −6.00000 10.3923i −0.224702 0.389195i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 0 0
\(717\) −10.5000 + 18.1865i −0.392130 + 0.679189i
\(718\) −10.5000 18.1865i −0.391857 0.678715i
\(719\) −19.5000 + 33.7750i −0.727227 + 1.25959i 0.230823 + 0.972996i \(0.425858\pi\)
−0.958051 + 0.286599i \(0.907475\pi\)
\(720\) 0 0
\(721\) 14.0000 0.521387
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −22.5000 + 38.9711i −0.835629 + 1.44735i
\(726\) 12.5000 + 21.6506i 0.463919 + 0.803530i
\(727\) 18.5000 32.0429i 0.686127 1.18841i −0.286954 0.957944i \(-0.592643\pi\)
0.973081 0.230463i \(-0.0740239\pi\)
\(728\) −2.50000 4.33013i −0.0926562 0.160485i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) −5.00000 8.66025i −0.184805 0.320092i
\(733\) 32.0000 1.18195 0.590973 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) 0 0
\(746\) 11.5000 19.9186i 0.421045 0.729271i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) −18.0000 −0.658145
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i \(-0.906275\pi\)
0.227153 0.973859i \(-0.427058\pi\)
\(752\) 0 0
\(753\) −6.00000 −0.218652
\(754\) −22.5000 38.9711i −0.819402 1.41925i
\(755\) 0 0
\(756\) 2.50000 + 4.33013i 0.0909241 + 0.157485i
\(757\) −1.00000 + 1.73205i −0.0363456 + 0.0629525i −0.883626 0.468193i \(-0.844905\pi\)
0.847280 + 0.531146i \(0.178238\pi\)
\(758\) −3.50000 + 6.06218i −0.127126 + 0.220188i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) −1.00000 + 1.73205i −0.0362262 + 0.0627456i
\(763\) −5.50000 + 9.52628i −0.199113 + 0.344874i
\(764\) −1.50000 2.59808i −0.0542681 0.0939951i
\(765\) 0 0
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) 45.0000 1.62486
\(768\) −1.00000 −0.0360844
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) −14.0000 −0.503871
\(773\) 25.5000 + 44.1673i 0.917171 + 1.58859i 0.803691 + 0.595047i \(0.202867\pi\)
0.113480 + 0.993540i \(0.463800\pi\)
\(774\) 8.00000 13.8564i 0.287554 0.498058i
\(775\) 10.0000 + 17.3205i 0.359211 + 0.622171i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) 1.00000 1.73205i 0.0358748 0.0621370i
\(778\) 18.0000 0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) −4.50000 + 7.79423i −0.160920 + 0.278721i
\(783\) 22.5000 + 38.9711i 0.804084 + 1.39272i
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0
\(786\) 0 0
\(787\) 31.0000 1.10503 0.552515 0.833503i \(-0.313668\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(788\) 0 0
\(789\) 12.0000 + 20.7846i 0.427211 + 0.739952i
\(790\) 0 0
\(791\) 6.00000 0.213335
\(792\) −6.00000 10.3923i −0.213201 0.369274i
\(793\) −25.0000 + 43.3013i −0.887776 + 1.53767i
\(794\) −10.0000 17.3205i −0.354887 0.614682i
\(795\) 0 0
\(796\) −5.50000 + 9.52628i −0.194942 + 0.337650i
\(797\) 39.0000 1.38145 0.690725 0.723117i \(-0.257291\pi\)
0.690725 + 0.723117i \(0.257291\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.50000 4.33013i 0.0883883