Properties

Label 72.2.l.a.11.2
Level 72
Weight 2
Character 72.11
Analytic conductor 0.575
Analytic rank 0
Dimension 4
CM discriminant -8
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label 11.2
Root \(1.22474 + 0.707107i\) of \(x^{4} - 2 x^{2} + 4\)
Character \(\chi\) \(=\) 72.11
Dual form 72.2.l.a.59.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.224745 - 2.43916i) q^{6} +2.82843i q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.224745 - 2.43916i) q^{6} +2.82843i q^{8} +(-1.94949 + 2.28024i) q^{9} +(-5.72474 - 3.30518i) q^{11} +(2.00000 - 2.82843i) q^{12} +(-2.00000 + 3.46410i) q^{16} +2.36773i q^{17} +(-4.00000 + 1.41421i) q^{18} +6.34847 q^{19} +(-4.67423 - 8.09601i) q^{22} +(4.44949 - 2.04989i) q^{24} +(2.50000 - 4.33013i) q^{25} +(5.00000 + 1.41421i) q^{27} +(-4.89898 + 2.82843i) q^{32} +(-1.05051 + 11.4012i) q^{33} +(-1.67423 + 2.89986i) q^{34} +(-5.89898 - 1.09638i) q^{36} +(7.77526 + 4.48905i) q^{38} +(9.39898 - 5.42650i) q^{41} +(-6.17423 + 10.6941i) q^{43} -13.2207i q^{44} +(6.89898 + 0.635674i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(6.12372 - 3.53553i) q^{50} +(3.72474 - 1.71600i) q^{51} +(5.12372 + 5.26758i) q^{54} +(-4.60102 - 9.98698i) q^{57} +(-1.62372 + 0.937458i) q^{59} -8.00000 q^{64} +(-9.34847 + 13.2207i) q^{66} +(-0.174235 - 0.301783i) q^{67} +(-4.10102 + 2.36773i) q^{68} +(-6.44949 - 5.51399i) q^{72} -15.6969 q^{73} +(-8.62372 - 0.794593i) q^{75} +(6.34847 + 10.9959i) q^{76} +(-1.39898 - 8.89060i) q^{81} +15.3485 q^{82} +(2.44949 + 1.41421i) q^{83} +(-15.1237 + 8.73169i) q^{86} +(9.34847 - 16.1920i) q^{88} +5.65685i q^{89} +(8.00000 + 5.65685i) q^{96} +(4.84847 - 8.39780i) q^{97} -9.89949i q^{98} +(18.6969 - 6.61037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 4q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 4q^{4} - 4q^{6} + 2q^{9} - 18q^{11} + 8q^{12} - 8q^{16} - 16q^{18} - 4q^{19} - 4q^{22} + 8q^{24} + 10q^{25} + 20q^{27} - 14q^{33} + 8q^{34} - 4q^{36} + 36q^{38} + 18q^{41} - 10q^{43} + 8q^{48} - 14q^{49} + 10q^{51} - 4q^{54} - 38q^{57} + 18q^{59} - 32q^{64} - 8q^{66} + 14q^{67} - 36q^{68} - 16q^{72} - 4q^{73} - 10q^{75} - 4q^{76} + 14q^{81} + 32q^{82} - 36q^{86} + 8q^{88} + 32q^{96} - 10q^{97} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.866025 + 0.500000i
\(3\) −0.724745 1.57313i −0.418432 0.908248i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0.224745 2.43916i 0.0917517 0.995782i
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 2.82843i 1.00000i
\(9\) −1.94949 + 2.28024i −0.649830 + 0.760080i
\(10\) 0 0
\(11\) −5.72474 3.30518i −1.72608 0.996550i −0.904534 0.426401i \(-0.859781\pi\)
−0.821541 0.570149i \(-0.806886\pi\)
\(12\) 2.00000 2.82843i 0.577350 0.816497i
\(13\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 2.36773i 0.574258i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) −4.00000 + 1.41421i −0.942809 + 0.333333i
\(19\) 6.34847 1.45644 0.728219 0.685344i \(-0.240348\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.67423 8.09601i −0.996550 1.72608i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 4.44949 2.04989i 0.908248 0.418432i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 0 0
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) −4.89898 + 2.82843i −0.866025 + 0.500000i
\(33\) −1.05051 + 11.4012i −0.182870 + 1.98469i
\(34\) −1.67423 + 2.89986i −0.287129 + 0.497322i
\(35\) 0 0
\(36\) −5.89898 1.09638i −0.983163 0.182729i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 7.77526 + 4.48905i 1.26131 + 0.728219i
\(39\) 0 0
\(40\) 0 0
\(41\) 9.39898 5.42650i 1.46787 0.847477i 0.468521 0.883452i \(-0.344787\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) −6.17423 + 10.6941i −0.941562 + 1.63083i −0.179069 + 0.983836i \(0.557309\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 13.2207i 1.99310i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 6.89898 + 0.635674i 0.995782 + 0.0917517i
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 6.12372 3.53553i 0.866025 0.500000i
\(51\) 3.72474 1.71600i 0.521569 0.240288i
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 5.12372 + 5.26758i 0.697251 + 0.716827i
\(55\) 0 0
\(56\) 0 0
\(57\) −4.60102 9.98698i −0.609420 1.32281i
\(58\) 0 0
\(59\) −1.62372 + 0.937458i −0.211391 + 0.122047i −0.601958 0.798528i \(-0.705612\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) −9.34847 + 13.2207i −1.15072 + 1.62736i
\(67\) −0.174235 0.301783i −0.0212861 0.0368687i 0.855186 0.518321i \(-0.173443\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) −4.10102 + 2.36773i −0.497322 + 0.287129i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −6.44949 5.51399i −0.760080 0.649830i
\(73\) −15.6969 −1.83719 −0.918594 0.395203i \(-0.870674\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 0 0
\(75\) −8.62372 0.794593i −0.995782 0.0917517i
\(76\) 6.34847 + 10.9959i 0.728219 + 1.26131i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0 0
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) 15.3485 1.69495
\(83\) 2.44949 + 1.41421i 0.268866 + 0.155230i 0.628372 0.777913i \(-0.283721\pi\)
−0.359506 + 0.933143i \(0.617055\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −15.1237 + 8.73169i −1.63083 + 0.941562i
\(87\) 0 0
\(88\) 9.34847 16.1920i 0.996550 1.72608i
\(89\) 5.65685i 0.599625i 0.953998 + 0.299813i \(0.0969242\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 8.00000 + 5.65685i 0.816497 + 0.577350i
\(97\) 4.84847 8.39780i 0.492287 0.852667i −0.507673 0.861550i \(-0.669494\pi\)
0.999961 + 0.00888289i \(0.00282755\pi\)
\(98\) 9.89949i 1.00000i
\(99\) 18.6969 6.61037i 1.87911 0.664367i
\(100\) 10.0000 1.00000
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 5.77526 + 0.532134i 0.571835 + 0.0526891i
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.0956i 1.45935i 0.683793 + 0.729676i \(0.260329\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 2.55051 + 10.0745i 0.245423 + 0.969416i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.79796 + 5.65685i −0.921714 + 0.532152i −0.884182 0.467143i \(-0.845283\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 1.42679 15.4849i 0.133631 1.45030i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −2.65153 −0.244093
\(119\) 0 0
\(120\) 0 0
\(121\) 16.3485 + 28.3164i 1.48622 + 2.57422i
\(122\) 0 0
\(123\) −15.3485 10.8530i −1.38392 0.978583i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −9.79796 5.65685i −0.866025 0.500000i
\(129\) 21.2980 + 1.96240i 1.87518 + 0.172780i
\(130\) 0 0
\(131\) 12.2474 7.07107i 1.07006 0.617802i 0.141865 0.989886i \(-0.454690\pi\)
0.928199 + 0.372084i \(0.121357\pi\)
\(132\) −20.7980 + 9.58166i −1.81023 + 0.833976i
\(133\) 0 0
\(134\) 0.492810i 0.0425723i
\(135\) 0 0
\(136\) −6.69694 −0.574258
\(137\) 5.29796 + 3.05878i 0.452635 + 0.261329i 0.708942 0.705266i \(-0.249173\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −9.17423 15.8902i −0.778148 1.34779i −0.933008 0.359856i \(-0.882826\pi\)
0.154859 0.987937i \(-0.450508\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −4.00000 11.3137i −0.333333 0.942809i
\(145\) 0 0
\(146\) −19.2247 11.0994i −1.59105 0.918594i
\(147\) −7.00000 + 9.89949i −0.577350 + 0.816497i
\(148\) 0 0
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) −10.0000 7.07107i −0.816497 0.577350i
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 17.9562i 1.45644i
\(153\) −5.39898 4.61586i −0.436482 0.373170i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 4.57321 11.8780i 0.359306 0.933220i
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 18.7980 + 10.8530i 1.46787 + 0.847477i
\(165\) 0 0
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) −6.50000 + 11.2583i −0.500000 + 0.866025i
\(170\) 0 0
\(171\) −12.3763 + 14.4760i −0.946437 + 1.10701i
\(172\) −24.6969 −1.88312
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 22.8990 13.2207i 1.72608 0.996550i
\(177\) 2.65153 + 1.87492i 0.199301 + 0.140927i
\(178\) −4.00000 + 6.92820i −0.299813 + 0.519291i
\(179\) 19.7990i 1.47985i −0.672692 0.739923i \(-0.734862\pi\)
0.672692 0.739923i \(-0.265138\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 7.82577 13.5546i 0.572277 0.991212i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 5.79796 + 12.5851i 0.418432 + 0.908248i
\(193\) 1.84847 + 3.20164i 0.133056 + 0.230459i 0.924853 0.380325i \(-0.124188\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 11.8763 6.85677i 0.852667 0.492287i
\(195\) 0 0
\(196\) 7.00000 12.1244i 0.500000 0.866025i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 27.5732 + 5.12472i 1.95954 + 0.364198i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 12.2474 + 7.07107i 0.866025 + 0.500000i
\(201\) −0.348469 + 0.492810i −0.0245791 + 0.0347601i
\(202\) 0 0
\(203\) 0 0
\(204\) 6.69694 + 4.73545i 0.468879 + 0.331548i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −36.3434 20.9829i −2.51392 1.45141i
\(210\) 0 0
\(211\) −7.00000 12.1244i −0.481900 0.834675i 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −10.6742 + 18.4883i −0.729676 + 1.26384i
\(215\) 0 0
\(216\) −4.00000 + 14.1421i −0.272166 + 0.962250i
\(217\) 0 0
\(218\) 0 0
\(219\) 11.3763 + 24.6934i 0.768737 + 1.66862i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0 0
\(225\) 5.00000 + 14.1421i 0.333333 + 0.942809i
\(226\) −16.0000 −1.06430
\(227\) 21.2753 + 12.2833i 1.41209 + 0.815270i 0.995585 0.0938647i \(-0.0299221\pi\)
0.416503 + 0.909134i \(0.363255\pi\)
\(228\) 12.6969 17.9562i 0.840875 1.18918i
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 28.8092i 1.88735i −0.330870 0.943676i \(-0.607342\pi\)
0.330870 0.943676i \(-0.392658\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.24745 1.87492i −0.211391 0.122047i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) 13.8485 23.9863i 0.892058 1.54509i 0.0546547 0.998505i \(-0.482594\pi\)
0.837404 0.546585i \(-0.184072\pi\)
\(242\) 46.2405i 2.97245i
\(243\) −12.9722 + 8.64420i −0.832167 + 0.554526i
\(244\) 0 0
\(245\) 0 0
\(246\) −11.1237 24.1452i −0.709223 1.53944i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.449490 4.87832i 0.0284853 0.309151i
\(250\) 0 0
\(251\) 10.3602i 0.653930i −0.945036 0.326965i \(-0.893974\pi\)
0.945036 0.326965i \(-0.106026\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −17.6010 + 10.1620i −1.09792 + 0.633885i −0.935674 0.352865i \(-0.885208\pi\)
−0.162247 + 0.986750i \(0.551874\pi\)
\(258\) 24.6969 + 17.4634i 1.53756 + 1.08722i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 20.0000 1.23560
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) −32.2474 2.97129i −1.98469 0.182870i
\(265\) 0 0
\(266\) 0 0
\(267\) 8.89898 4.09978i 0.544609 0.250902i
\(268\) 0.348469 0.603566i 0.0212861 0.0368687i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −8.20204 4.73545i −0.497322 0.287129i
\(273\) 0 0
\(274\) 4.32577 + 7.49245i 0.261329 + 0.452635i
\(275\) −28.6237 + 16.5259i −1.72608 + 0.996550i
\(276\) 0 0
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 25.9487i 1.55630i
\(279\) 0 0
\(280\) 0 0
\(281\) 24.4949 + 14.1421i 1.46124 + 0.843649i 0.999069 0.0431402i \(-0.0137362\pi\)
0.462174 + 0.886789i \(0.347070\pi\)
\(282\) 0 0
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 3.10102 16.6848i 0.182729 0.983163i
\(289\) 11.3939 0.670228
\(290\) 0 0
\(291\) −16.7247 1.54102i −0.980422 0.0903364i
\(292\) −15.6969 27.1879i −0.918594 1.59105i
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) −15.5732 + 7.17461i −0.908248 + 0.418432i
\(295\) 0 0
\(296\) 0 0
\(297\) −23.9495 24.6219i −1.38969 1.42871i
\(298\) 0 0
\(299\) 0 0
\(300\) −7.24745 15.7313i −0.418432 0.908248i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −12.6969 + 21.9917i −0.728219 + 1.26131i
\(305\) 0 0
\(306\) −3.34847 9.47090i −0.191419 0.541415i
\(307\) 24.3485 1.38964 0.694820 0.719183i \(-0.255484\pi\)
0.694820 + 0.719183i \(0.255484\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) −17.1969 + 29.7860i −0.972028 + 1.68360i −0.282617 + 0.959233i \(0.591202\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 23.7474 10.9405i 1.32545 0.610639i
\(322\) 0 0
\(323\) 15.0314i 0.836371i
\(324\) 14.0000 11.3137i 0.777778 0.628539i
\(325\) 0 0
\(326\) 2.44949 + 1.41421i 0.135665 + 0.0783260i
\(327\) 0 0
\(328\) 15.3485 + 26.5843i 0.847477 + 1.46787i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0000 + 22.5167i −0.714545 + 1.23763i 0.248590 + 0.968609i \(0.420033\pi\)
−0.963135 + 0.269019i \(0.913301\pi\)
\(332\) 5.65685i 0.310460i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.1969 19.3937i −0.609936 1.05644i −0.991250 0.131995i \(-0.957862\pi\)
0.381314 0.924445i \(-0.375472\pi\)
\(338\) −15.9217 + 9.19239i −0.866025 + 0.500000i
\(339\) 16.0000 + 11.3137i 0.869001 + 0.614476i
\(340\) 0 0
\(341\) 0 0
\(342\) −25.3939 + 8.97809i −1.37314 + 0.485480i
\(343\) 0 0
\(344\) −30.2474 17.4634i −1.63083 0.941562i
\(345\) 0 0
\(346\) 0 0
\(347\) 20.4217 11.7905i 1.09629 0.632945i 0.161048 0.986947i \(-0.448512\pi\)
0.935245 + 0.354001i \(0.115179\pi\)
\(348\) 0 0
\(349\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 37.3939 1.99310
\(353\) 32.2980 + 18.6472i 1.71905 + 0.992492i 0.920677 + 0.390324i \(0.127637\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 1.92168 + 4.17121i 0.102136 + 0.221697i
\(355\) 0 0
\(356\) −9.79796 + 5.65685i −0.519291 + 0.299813i
\(357\) 0 0
\(358\) 14.0000 24.2487i 0.739923 1.28158i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 21.3031 1.12121
\(362\) 0 0
\(363\) 32.6969 46.2405i 1.71614 2.42699i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0 0
\(369\) −5.94949 + 32.0108i −0.309718 + 1.66642i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 19.1691 11.0673i 0.991212 0.572277i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −11.6515 −0.598499 −0.299249 0.954175i \(-0.596736\pi\)
−0.299249 + 0.954175i \(0.596736\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) −1.79796 + 19.5133i −0.0917517 + 0.995782i
\(385\) 0 0
\(386\) 5.22826i 0.266111i
\(387\) −12.3485 34.9267i −0.627708 1.77543i
\(388\) 19.3939 0.984575
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 17.1464 9.89949i 0.866025 0.500000i
\(393\) −20.0000 14.1421i −1.00887 0.713376i
\(394\) 0 0
\(395\) 0 0
\(396\) 30.1464 + 25.7737i 1.51492 + 1.29518i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 10.0000 + 17.3205i 0.500000 + 0.866025i
\(401\) −12.6464 + 7.30142i −0.631532 + 0.364615i −0.781345 0.624099i \(-0.785466\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −0.775255 + 0.357161i −0.0386662 + 0.0178136i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 4.85357 + 10.5352i 0.240288 + 0.521569i
\(409\) −20.1969 34.9821i −0.998674 1.72975i −0.543915 0.839140i \(-0.683059\pi\)
−0.454759 0.890614i \(-0.650275\pi\)
\(410\) 0 0
\(411\) 0.972194 10.5512i 0.0479548 0.520453i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −18.3485 + 25.9487i −0.898528 + 1.27071i
\(418\) −29.6742 51.3973i −1.45141 2.51392i
\(419\) −31.8434 + 18.3848i −1.55565 + 0.898155i −0.557986 + 0.829851i \(0.688426\pi\)
−0.997665 + 0.0683046i \(0.978241\pi\)
\(420\) 0 0
\(421\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 19.7990i 0.963800i
\(423\) 0 0
\(424\) 0 0
\(425\) 10.2526 + 5.91931i 0.497322 + 0.287129i
\(426\) 0 0
\(427\) 0 0
\(428\) −26.1464 + 15.0956i −1.26384 + 0.729676i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) −14.8990 + 14.4921i −0.716827 + 0.697251i
\(433\) −33.6969 −1.61937 −0.809686 0.586864i \(-0.800362\pi\)
−0.809686 + 0.586864i \(0.800362\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −3.52781 + 38.2873i −0.168565 + 1.82944i
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 20.6464 + 3.83732i 0.983163 + 0.182729i
\(442\) 0 0
\(443\) −32.7247 18.8936i −1.55480 0.897664i −0.997740 0.0671913i \(-0.978596\pi\)
−0.557059 0.830473i \(-0.688070\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 33.5446i 1.58307i 0.611124 + 0.791535i \(0.290718\pi\)
−0.611124 + 0.791535i \(0.709282\pi\)
\(450\) −3.87628 + 20.8560i −0.182729 + 0.983163i
\(451\) −71.7423 −3.37822
\(452\) −19.5959 11.3137i −0.921714 0.532152i
\(453\) 0 0
\(454\) 17.3712 + 30.0878i 0.815270 + 1.41209i
\(455\) 0 0
\(456\) 28.2474 13.0137i 1.32281 0.609420i
\(457\) −8.19694 + 14.1975i −0.383437 + 0.664132i −0.991551 0.129718i \(-0.958593\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) 0 0
\(459\) −3.34847 + 11.8386i −0.156293 + 0.552580i
\(460\) 0 0
\(461\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0 0
\(463\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 20.3712 35.2839i 0.943676 1.63450i
\(467\) 41.5371i 1.92211i −0.276360 0.961054i \(-0.589128\pi\)
0.276360 0.961054i \(-0.410872\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −2.65153 4.59259i −0.122047 0.211391i
\(473\) 70.6918 40.8140i 3.25041 1.87663i
\(474\) 0 0
\(475\) 15.8712 27.4897i 0.728219 1.26131i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 33.9217 19.5847i 1.54509 0.892058i
\(483\) 0 0
\(484\) −32.6969 + 56.6328i −1.48622 + 2.57422i
\(485\) 0 0
\(486\) −22.0000 + 1.41421i −0.997940 + 0.0641500i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −1.44949 3.14626i −0.0655482 0.142279i
\(490\) 0 0
\(491\) 25.3763 14.6510i 1.14522 0.661190i 0.197499 0.980303i \(-0.436718\pi\)
0.947717 + 0.319113i \(0.103385\pi\)
\(492\) 3.44949 37.4373i 0.155515 1.68781i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 4.00000 5.65685i 0.179244 0.253490i
\(499\) 21.8712 + 37.8820i 0.979088 + 1.69583i 0.665725 + 0.746197i \(0.268122\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 7.32577 12.6886i 0.326965 0.566320i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 22.4217 + 2.06594i 0.995782 + 0.0917517i
\(508\) 0 0
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 1.00000i
\(513\) 31.7423 + 8.97809i 1.40146 + 0.396392i
\(514\) −28.7423 −1.26777
\(515\) 0 0
\(516\) 17.8990 + 38.8515i 0.787959 + 1.71034i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 27.8236i 1.21897i 0.792797 + 0.609486i \(0.208624\pi\)
−0.792797 + 0.609486i \(0.791376\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 24.4949 + 14.1421i 1.07006 + 0.617802i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −37.3939 26.4415i −1.62736 1.15072i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) 1.02781 5.53004i 0.0446030 0.239983i
\(532\) 0 0
\(533\) 0 0
\(534\) 13.7980 + 1.27135i 0.597096 + 0.0550167i
\(535\) 0 0
\(536\) 0.853572 0.492810i 0.0368687 0.0212861i
\(537\) −31.1464 + 14.3492i −1.34407 + 0.619214i
\(538\) 0 0
\(539\) 46.2726i 1.99310i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −6.69694 11.5994i −0.287129 0.497322i
\(545\) 0 0
\(546\) 0 0
\(547\) −15.1742 + 26.2825i −0.648803 + 1.12376i 0.334606 + 0.942358i \(0.391397\pi\)
−0.983409 + 0.181402i \(0.941936\pi\)
\(548\) 12.2351i 0.522658i
\(549\) 0 0
\(550\) −46.7423 −1.99310
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 18.3485 31.7805i 0.778148 1.34779i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −26.9949 2.48732i −1.13973 0.105015i
\(562\) 20.0000 + 34.6410i 0.843649 + 1.46124i
\(563\) −6.57832 + 3.79799i −0.277243 + 0.160066i −0.632175 0.774826i \(-0.717837\pi\)
0.354932 + 0.934892i \(0.384504\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 31.1127i 1.30776i
\(567\) 0 0
\(568\) 0 0
\(569\) −21.7020 12.5297i −0.909797 0.525271i −0.0294311 0.999567i \(-0.509370\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) 12.8712 + 22.2935i 0.538642 + 0.932955i 0.998978 + 0.0452101i \(0.0143957\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 15.5959 18.2419i 0.649830 0.760080i
\(577\) 46.3939 1.93140 0.965701 0.259656i \(-0.0836092\pi\)
0.965701 + 0.259656i \(0.0836092\pi\)
\(578\) 13.9546 + 8.05669i 0.580435 + 0.335114i
\(579\) 3.69694 5.22826i 0.153640 0.217279i
\(580\) 0 0
\(581\) 0 0
\(582\) −19.3939 13.7135i −0.803902 0.568445i
\(583\) 0 0
\(584\) 44.3976i 1.83719i
\(585\) 0 0
\(586\) 0 0
\(587\) 16.3207 + 9.42274i 0.673626 + 0.388918i 0.797449 0.603386i \(-0.206182\pi\)
−0.123823 + 0.992304i \(0.539516\pi\)
\(588\) −24.1464 2.22486i −0.995782 0.0917517i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 45.2548i 1.85839i −0.369586 0.929197i \(-0.620500\pi\)
0.369586 0.929197i \(-0.379500\pi\)
\(594\) −11.9217 47.0904i −0.489153 1.93214i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 2.24745 24.3916i 0.0917517 0.995782i
\(601\) −4.15153 + 7.19066i −0.169344 + 0.293313i −0.938190 0.346122i \(-0.887498\pi\)
0.768845 + 0.639435i \(0.220832\pi\)
\(602\) 0 0
\(603\) 1.02781 + 0.191027i 0.0418555 + 0.00777921i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) −31.1010 + 17.9562i −1.26131 + 0.728219i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 2.59592 13.9672i 0.104934 0.564589i
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 29.8207 + 17.2170i 1.20346 + 0.694820i
\(615\) 0 0
\(616\) 0 0
\(617\) −39.6464 + 22.8899i −1.59611 + 0.921512i −0.603877 + 0.797077i \(0.706378\pi\)
−0.992228 + 0.124434i \(0.960288\pi\)
\(618\) 0 0
\(619\) 24.8712 43.0781i 0.999657 1.73146i 0.477143 0.878826i \(-0.341672\pi\)
0.522514 0.852631i \(-0.324994\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −42.1237 + 24.3201i −1.68360 + 0.972028i
\(627\) −6.66913 + 72.3801i −0.266339 + 2.89058i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −14.0000 + 19.7990i −0.556450 + 0.786939i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −43.7474 25.2576i −1.72792 0.997615i −0.898470 0.439034i \(-0.855321\pi\)
−0.829450 0.558581i \(-0.811346\pi\)
\(642\) 36.8207 + 3.39267i 1.45320 + 0.133898i
\(643\) 8.82577 + 15.2867i 0.348054 + 0.602848i 0.985904 0.167313i \(-0.0535092\pi\)
−0.637850 + 0.770161i \(0.720176\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.6288 + 18.4097i −0.418186 + 0.724319i
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 25.1464 3.95691i 0.987845 0.155442i
\(649\) 12.3939 0.486502
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 43.4120i 1.69495i
\(657\) 30.6010 35.7928i 1.19386 1.39641i
\(658\) 0 0
\(659\) −41.6413 24.0416i −1.62212 0.936529i −0.986353 0.164644i \(-0.947352\pi\)
−0.635763 0.771885i \(-0.719314\pi\)
\(660\) 0 0
\(661\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) −31.8434 + 18.3848i −1.23763 + 0.714545i
\(663\) 0 0
\(664\) −4.00000 + 6.92820i −0.155230 + 0.268866i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 5.00000 8.66025i 0.192736 0.333828i −0.753420 0.657539i \(-0.771597\pi\)
0.946156 + 0.323711i \(0.104931\pi\)
\(674\) 31.6697i 1.21987i
\(675\) 18.6237 18.1151i 0.716827 0.697251i
\(676\) −26.0000 −1.00000
\(677\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 11.5959 + 25.1701i 0.445339 + 0.966652i
\(679\) 0 0
\(680\) 0 0
\(681\) 3.90408 42.3710i 0.149605 1.62366i
\(682\) 0 0
\(683\) 20.8167i 0.796530i 0.917270 + 0.398265i \(0.130387\pi\)
−0.917270 + 0.398265i \(0.869613\pi\)
\(684\) −37.4495 6.96031i −1.43192 0.266134i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −24.6969 42.7764i −0.941562 1.63083i
\(689\) 0 0
\(690\) 0 0
\(691\) 23.0000 39.8372i 0.874961 1.51548i 0.0181572 0.999835i \(-0.494220\pi\)
0.856804 0.515642i \(-0.172447\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 33.3485 1.26589
\(695\) 0 0
\(696\) 0 0
\(697\) 12.8485 + 22.2542i 0.486670 + 0.842938i
\(698\) 0 0
\(699\) −45.3207 + 20.8793i −1.71418 + 0.789728i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 45.7980 + 26.4415i 1.72608 + 0.996550i
\(705\) 0 0
\(706\) 26.3712 + 45.6762i 0.992492 + 1.71905i
\(707\) 0 0
\(708\) −0.595918 + 6.46750i −0.0223960 + 0.243064i
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −16.0000 −0.599625
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 34.2929 19.7990i 1.28158 0.739923i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 26.0908 + 15.0635i 0.971000 + 0.560607i
\(723\) −47.7702 4.40156i −1.77659 0.163696i
\(724\) 0 0
\(725\) 0 0
\(726\) 72.7423 33.5125i 2.69972 1.24377i
\(727\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) −25.3207 14.6189i −0.936519 0.540699i
\(732\) 0 0
\(733\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.30351i 0.0848508i
\(738\) −29.9217 + 34.9982i −1.10143 + 1.28830i
\(739\) −19.7423 −0.726234 −0.363117 0.931744i \(-0.618287\pi\)
−0.363117 + 0.931744i \(0.618287\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −8.00000 + 2.82843i −0.292705 + 0.103487i
\(748\) 31.3031 1.14455
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) −16.2980 + 7.50850i −0.593931 + 0.273625i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −14.2702 8.23888i −0.518315 0.299249i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.79796 + 5.65685i −0.355176 + 0.205061i −0.666962 0.745091i \(-0.732406\pi\)
0.311787 + 0.950152i \(0.399073\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −16.0000 + 22.6274i −0.577350 + 0.816497i
\(769\) 11.0000 + 19.0526i 0.396670 + 0.687053i 0.993313 0.115454i \(-0.0368323\pi\)
−0.596643 + 0.802507i \(0.703499\pi\)
\(770\) 0 0
\(771\) 28.7423 + 20.3239i 1.03513 + 0.731948i
\(772\) −3.69694 + 6.40329i −0.133056 + 0.230459i
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 9.57321 51.5080i 0.344102 1.85142i
\(775\) 0 0
\(776\) 23.7526 + 13.7135i 0.852667 + 0.492287i
\(777\) 0 0
\(778\) 0 0
\(779\) 59.6691 34.4500i 2.13787 1.23430i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 28.0000 1.00000
\(785\) 0 0
\(786\) −14.4949 31.4626i −0.517016 1.12224i
\(787\) −25.0000 43.3013i −0.891154 1.54352i −0.838494 0.544911i \(-0.816563\pi\)
−0.0526599 0.998613i \(-0.516770\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 18.6969 + 52.8829i 0.664367 + 1.87911i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 28.2843i 1.00000i
\(801\) −12.8990 11.0280i −0.455763 0.389654i
\(802\) −20.6515 −0.729231
\(803\) 89.8610 + 51.8813i 3.17112 + 1.83085i
\(804\) −1.20204 0.110756i −0.0423927 0.00390608i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0