Properties

Label 700.2.c.c.699.3
Level $700$
Weight $2$
Character 700.699
Analytic conductor $5.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 699.3
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.c.699.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(2.36603 + 0.633975i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(2.36603 + 0.633975i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.73205i q^{11} +(1.73205 - 3.00000i) q^{12} +6.46410 q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} -0.464102 q^{17} +6.00000 q^{19} +(3.00000 - 3.46410i) q^{21} +(5.09808 + 1.36603i) q^{22} -5.46410 q^{23} +(-3.46410 - 3.46410i) q^{24} +(2.36603 - 8.83013i) q^{26} +5.19615i q^{27} +(1.73205 + 5.00000i) q^{28} +5.92820 q^{29} +6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} -6.46410 q^{33} +(-0.169873 + 0.633975i) q^{34} -2.53590i q^{37} +(2.19615 - 8.19615i) q^{38} +11.1962i q^{39} +3.46410i q^{41} +(-3.63397 - 5.36603i) q^{42} +2.00000 q^{43} +(3.73205 - 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} +1.73205i q^{47} +(-6.00000 + 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} -0.803848i q^{51} +(-11.1962 - 6.46410i) q^{52} -2.00000i q^{53} +(7.09808 + 1.90192i) q^{54} +(7.46410 - 0.535898i) q^{56} +10.3923i q^{57} +(2.16987 - 8.09808i) q^{58} +3.46410 q^{59} +2.53590i q^{61} +(2.19615 - 8.19615i) q^{62} -8.00000i q^{64} +(-2.36603 + 8.83013i) q^{66} -3.46410 q^{67} +(0.803848 + 0.464102i) q^{68} -9.46410i q^{69} +0.535898i q^{71} -0.928203 q^{73} +(-3.46410 - 0.928203i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(6.46410 - 7.46410i) q^{77} +(15.2942 + 4.09808i) q^{78} +2.66025i q^{79} -9.00000 q^{81} +(4.73205 + 1.26795i) q^{82} +8.53590i q^{83} +(-8.66025 + 3.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} +10.2679i q^{87} +(-7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(-12.9282 - 11.1962i) q^{91} +(9.46410 + 5.46410i) q^{92} +10.3923i q^{93} +(2.36603 + 0.633975i) q^{94} +(2.53590 + 9.46410i) q^{96} -7.39230 q^{97} +(9.83013 + 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 6q^{6} - 8q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 6q^{6} - 8q^{7} - 8q^{8} + 12q^{13} - 2q^{14} + 8q^{16} + 12q^{17} + 24q^{19} + 12q^{21} + 10q^{22} - 8q^{23} + 6q^{26} - 4q^{29} + 24q^{31} + 8q^{32} - 12q^{33} - 18q^{34} - 12q^{38} - 18q^{42} + 8q^{43} + 8q^{44} - 8q^{46} - 24q^{48} + 4q^{49} - 24q^{52} + 18q^{54} + 16q^{56} + 26q^{58} - 12q^{62} - 6q^{66} + 24q^{68} + 24q^{73} + 12q^{77} + 30q^{78} - 36q^{81} + 12q^{82} - 4q^{86} - 16q^{88} - 24q^{91} + 24q^{92} + 6q^{94} + 24q^{96} + 12q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) 1.73205i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 0 0
\(6\) 2.36603 + 0.633975i 0.965926 + 0.258819i
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.73205i 1.12526i 0.826710 + 0.562628i \(0.190210\pi\)
−0.826710 + 0.562628i \(0.809790\pi\)
\(12\) 1.73205 3.00000i 0.500000 0.866025i
\(13\) 6.46410 1.79282 0.896410 0.443227i \(-0.146166\pi\)
0.896410 + 0.443227i \(0.146166\pi\)
\(14\) −3.09808 + 2.09808i −0.827996 + 0.560734i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −0.464102 −0.112561 −0.0562806 0.998415i \(-0.517924\pi\)
−0.0562806 + 0.998415i \(0.517924\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 3.00000 3.46410i 0.654654 0.755929i
\(22\) 5.09808 + 1.36603i 1.08691 + 0.291238i
\(23\) −5.46410 −1.13934 −0.569672 0.821872i \(-0.692930\pi\)
−0.569672 + 0.821872i \(0.692930\pi\)
\(24\) −3.46410 3.46410i −0.707107 0.707107i
\(25\) 0 0
\(26\) 2.36603 8.83013i 0.464016 1.73173i
\(27\) 5.19615i 1.00000i
\(28\) 1.73205 + 5.00000i 0.327327 + 0.944911i
\(29\) 5.92820 1.10084 0.550420 0.834888i \(-0.314468\pi\)
0.550420 + 0.834888i \(0.314468\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) −6.46410 −1.12526
\(34\) −0.169873 + 0.633975i −0.0291330 + 0.108726i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.53590i 0.416899i −0.978033 0.208450i \(-0.933158\pi\)
0.978033 0.208450i \(-0.0668417\pi\)
\(38\) 2.19615 8.19615i 0.356263 1.32959i
\(39\) 11.1962i 1.79282i
\(40\) 0 0
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) −3.63397 5.36603i −0.560734 0.827996i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 3.73205 6.46410i 0.562628 0.974500i
\(45\) 0 0
\(46\) −2.00000 + 7.46410i −0.294884 + 1.10052i
\(47\) 1.73205i 0.252646i 0.991989 + 0.126323i \(0.0403175\pi\)
−0.991989 + 0.126323i \(0.959682\pi\)
\(48\) −6.00000 + 3.46410i −0.866025 + 0.500000i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0.803848i 0.112561i
\(52\) −11.1962 6.46410i −1.55263 0.896410i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 7.09808 + 1.90192i 0.965926 + 0.258819i
\(55\) 0 0
\(56\) 7.46410 0.535898i 0.997433 0.0716124i
\(57\) 10.3923i 1.37649i
\(58\) 2.16987 8.09808i 0.284918 1.06333i
\(59\) 3.46410 0.450988 0.225494 0.974245i \(-0.427600\pi\)
0.225494 + 0.974245i \(0.427600\pi\)
\(60\) 0 0
\(61\) 2.53590i 0.324689i 0.986734 + 0.162344i \(0.0519055\pi\)
−0.986734 + 0.162344i \(0.948094\pi\)
\(62\) 2.19615 8.19615i 0.278912 1.04091i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −2.36603 + 8.83013i −0.291238 + 1.08691i
\(67\) −3.46410 −0.423207 −0.211604 0.977356i \(-0.567869\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 0.803848 + 0.464102i 0.0974808 + 0.0562806i
\(69\) 9.46410i 1.13934i
\(70\) 0 0
\(71\) 0.535898i 0.0635994i 0.999494 + 0.0317997i \(0.0101239\pi\)
−0.999494 + 0.0317997i \(0.989876\pi\)
\(72\) 0 0
\(73\) −0.928203 −0.108638 −0.0543190 0.998524i \(-0.517299\pi\)
−0.0543190 + 0.998524i \(0.517299\pi\)
\(74\) −3.46410 0.928203i −0.402694 0.107901i
\(75\) 0 0
\(76\) −10.3923 6.00000i −1.19208 0.688247i
\(77\) 6.46410 7.46410i 0.736653 0.850613i
\(78\) 15.2942 + 4.09808i 1.73173 + 0.464016i
\(79\) 2.66025i 0.299302i 0.988739 + 0.149651i \(0.0478150\pi\)
−0.988739 + 0.149651i \(0.952185\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 4.73205 + 1.26795i 0.522568 + 0.140022i
\(83\) 8.53590i 0.936937i 0.883480 + 0.468468i \(0.155194\pi\)
−0.883480 + 0.468468i \(0.844806\pi\)
\(84\) −8.66025 + 3.00000i −0.944911 + 0.327327i
\(85\) 0 0
\(86\) 0.732051 2.73205i 0.0789391 0.294605i
\(87\) 10.2679i 1.10084i
\(88\) −7.46410 7.46410i −0.795676 0.795676i
\(89\) 9.46410i 1.00319i −0.865102 0.501596i \(-0.832746\pi\)
0.865102 0.501596i \(-0.167254\pi\)
\(90\) 0 0
\(91\) −12.9282 11.1962i −1.35524 1.17368i
\(92\) 9.46410 + 5.46410i 0.986701 + 0.569672i
\(93\) 10.3923i 1.07763i
\(94\) 2.36603 + 0.633975i 0.244037 + 0.0653895i
\(95\) 0 0
\(96\) 2.53590 + 9.46410i 0.258819 + 0.965926i
\(97\) −7.39230 −0.750575 −0.375287 0.926908i \(-0.622456\pi\)
−0.375287 + 0.926908i \(0.622456\pi\)
\(98\) 9.83013 + 1.16987i 0.992993 + 0.118175i
\(99\) 0 0
\(100\) 0 0
\(101\) 8.53590i 0.849354i −0.905345 0.424677i \(-0.860388\pi\)
0.905345 0.424677i \(-0.139612\pi\)
\(102\) −1.09808 0.294229i −0.108726 0.0291330i
\(103\) 17.1962i 1.69439i −0.531284 0.847194i \(-0.678290\pi\)
0.531284 0.847194i \(-0.321710\pi\)
\(104\) −12.9282 + 12.9282i −1.26771 + 1.26771i
\(105\) 0 0
\(106\) −2.73205 0.732051i −0.265360 0.0711031i
\(107\) −18.3923 −1.77805 −0.889026 0.457857i \(-0.848617\pi\)
−0.889026 + 0.457857i \(0.848617\pi\)
\(108\) 5.19615 9.00000i 0.500000 0.866025i
\(109\) −15.9282 −1.52565 −0.762823 0.646608i \(-0.776187\pi\)
−0.762823 + 0.646608i \(0.776187\pi\)
\(110\) 0 0
\(111\) 4.39230 0.416899
\(112\) 2.00000 10.3923i 0.188982 0.981981i
\(113\) 1.46410i 0.137731i 0.997626 + 0.0688655i \(0.0219379\pi\)
−0.997626 + 0.0688655i \(0.978062\pi\)
\(114\) 14.1962 + 3.80385i 1.32959 + 0.356263i
\(115\) 0 0
\(116\) −10.2679 5.92820i −0.953355 0.550420i
\(117\) 0 0
\(118\) 1.26795 4.73205i 0.116724 0.435621i
\(119\) 0.928203 + 0.803848i 0.0850883 + 0.0736886i
\(120\) 0 0
\(121\) −2.92820 −0.266200
\(122\) 3.46410 + 0.928203i 0.313625 + 0.0840356i
\(123\) −6.00000 −0.541002
\(124\) −10.3923 6.00000i −0.933257 0.538816i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.53590 0.757438 0.378719 0.925512i \(-0.376365\pi\)
0.378719 + 0.925512i \(0.376365\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) 3.46410i 0.304997i
\(130\) 0 0
\(131\) −9.46410 −0.826882 −0.413441 0.910531i \(-0.635673\pi\)
−0.413441 + 0.910531i \(0.635673\pi\)
\(132\) 11.1962 + 6.46410i 0.974500 + 0.562628i
\(133\) −12.0000 10.3923i −1.04053 0.901127i
\(134\) −1.26795 + 4.73205i −0.109534 + 0.408787i
\(135\) 0 0
\(136\) 0.928203 0.928203i 0.0795928 0.0795928i
\(137\) 0.392305i 0.0335169i −0.999860 0.0167584i \(-0.994665\pi\)
0.999860 0.0167584i \(-0.00533462\pi\)
\(138\) −12.9282 3.46410i −1.10052 0.294884i
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0.732051 + 0.196152i 0.0614323 + 0.0164607i
\(143\) 24.1244i 2.01738i
\(144\) 0 0
\(145\) 0 0
\(146\) −0.339746 + 1.26795i −0.0281176 + 0.104936i
\(147\) −12.0000 + 1.73205i −0.989743 + 0.142857i
\(148\) −2.53590 + 4.39230i −0.208450 + 0.361045i
\(149\) −16.9282 −1.38681 −0.693406 0.720547i \(-0.743891\pi\)
−0.693406 + 0.720547i \(0.743891\pi\)
\(150\) 0 0
\(151\) 4.80385i 0.390932i 0.980711 + 0.195466i \(0.0626219\pi\)
−0.980711 + 0.195466i \(0.937378\pi\)
\(152\) −12.0000 + 12.0000i −0.973329 + 0.973329i
\(153\) 0 0
\(154\) −7.83013 11.5622i −0.630970 0.931707i
\(155\) 0 0
\(156\) 11.1962 19.3923i 0.896410 1.55263i
\(157\) 19.8564 1.58471 0.792357 0.610058i \(-0.208854\pi\)
0.792357 + 0.610058i \(0.208854\pi\)
\(158\) 3.63397 + 0.973721i 0.289103 + 0.0774650i
\(159\) 3.46410 0.274721
\(160\) 0 0
\(161\) 10.9282 + 9.46410i 0.861263 + 0.745876i
\(162\) −3.29423 + 12.2942i −0.258819 + 0.965926i
\(163\) 20.7846 1.62798 0.813988 0.580881i \(-0.197292\pi\)
0.813988 + 0.580881i \(0.197292\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) 0 0
\(166\) 11.6603 + 3.12436i 0.905011 + 0.242497i
\(167\) 5.19615i 0.402090i −0.979582 0.201045i \(-0.935566\pi\)
0.979582 0.201045i \(-0.0644338\pi\)
\(168\) 0.928203 + 12.9282i 0.0716124 + 0.997433i
\(169\) 28.7846 2.21420
\(170\) 0 0
\(171\) 0 0
\(172\) −3.46410 2.00000i −0.264135 0.152499i
\(173\) 20.3205 1.54494 0.772470 0.635051i \(-0.219021\pi\)
0.772470 + 0.635051i \(0.219021\pi\)
\(174\) 14.0263 + 3.75833i 1.06333 + 0.284918i
\(175\) 0 0
\(176\) −12.9282 + 7.46410i −0.974500 + 0.562628i
\(177\) 6.00000i 0.450988i
\(178\) −12.9282 3.46410i −0.969010 0.259645i
\(179\) 14.3923i 1.07573i −0.843031 0.537866i \(-0.819231\pi\)
0.843031 0.537866i \(-0.180769\pi\)
\(180\) 0 0
\(181\) 12.9282i 0.960946i 0.877010 + 0.480473i \(0.159535\pi\)
−0.877010 + 0.480473i \(0.840465\pi\)
\(182\) −20.0263 + 13.5622i −1.48445 + 1.00530i
\(183\) −4.39230 −0.324689
\(184\) 10.9282 10.9282i 0.805638 0.805638i
\(185\) 0 0
\(186\) 14.1962 + 3.80385i 1.04091 + 0.278912i
\(187\) 1.73205i 0.126660i
\(188\) 1.73205 3.00000i 0.126323 0.218797i
\(189\) 9.00000 10.3923i 0.654654 0.755929i
\(190\) 0 0
\(191\) 3.19615i 0.231265i −0.993292 0.115633i \(-0.963110\pi\)
0.993292 0.115633i \(-0.0368896\pi\)
\(192\) 13.8564 1.00000
\(193\) 2.53590i 0.182538i 0.995826 + 0.0912690i \(0.0290923\pi\)
−0.995826 + 0.0912690i \(0.970908\pi\)
\(194\) −2.70577 + 10.0981i −0.194263 + 0.725000i
\(195\) 0 0
\(196\) 5.19615 13.0000i 0.371154 0.928571i
\(197\) 21.3205i 1.51902i 0.650494 + 0.759512i \(0.274562\pi\)
−0.650494 + 0.759512i \(0.725438\pi\)
\(198\) 0 0
\(199\) −3.46410 −0.245564 −0.122782 0.992434i \(-0.539182\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) 0 0
\(201\) 6.00000i 0.423207i
\(202\) −11.6603 3.12436i −0.820413 0.219829i
\(203\) −11.8564 10.2679i −0.832157 0.720669i
\(204\) −0.803848 + 1.39230i −0.0562806 + 0.0974808i
\(205\) 0 0
\(206\) −23.4904 6.29423i −1.63665 0.438540i
\(207\) 0 0
\(208\) 12.9282 + 22.3923i 0.896410 + 1.55263i
\(209\) 22.3923i 1.54891i
\(210\) 0 0
\(211\) 7.19615i 0.495404i −0.968836 0.247702i \(-0.920325\pi\)
0.968836 0.247702i \(-0.0796753\pi\)
\(212\) −2.00000 + 3.46410i −0.137361 + 0.237915i
\(213\) −0.928203 −0.0635994
\(214\) −6.73205 + 25.1244i −0.460194 + 1.71747i
\(215\) 0 0
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) −12.0000 10.3923i −0.814613 0.705476i
\(218\) −5.83013 + 21.7583i −0.394866 + 1.47366i
\(219\) 1.60770i 0.108638i
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 1.60770 6.00000i 0.107901 0.402694i
\(223\) 10.2679i 0.687593i −0.939044 0.343796i \(-0.888287\pi\)
0.939044 0.343796i \(-0.111713\pi\)
\(224\) −13.4641 6.53590i −0.899608 0.436698i
\(225\) 0 0
\(226\) 2.00000 + 0.535898i 0.133038 + 0.0356474i
\(227\) 3.33975i 0.221667i −0.993839 0.110833i \(-0.964648\pi\)
0.993839 0.110833i \(-0.0353520\pi\)
\(228\) 10.3923 18.0000i 0.688247 1.19208i
\(229\) 15.4641i 1.02190i 0.859611 + 0.510948i \(0.170706\pi\)
−0.859611 + 0.510948i \(0.829294\pi\)
\(230\) 0 0
\(231\) 12.9282 + 11.1962i 0.850613 + 0.736653i
\(232\) −11.8564 + 11.8564i −0.778411 + 0.778411i
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 3.46410i −0.390567 0.225494i
\(237\) −4.60770 −0.299302
\(238\) 1.43782 0.973721i 0.0932002 0.0631169i
\(239\) 27.9808i 1.80993i −0.425491 0.904963i \(-0.639899\pi\)
0.425491 0.904963i \(-0.360101\pi\)
\(240\) 0 0
\(241\) 4.39230i 0.282933i −0.989943 0.141467i \(-0.954818\pi\)
0.989943 0.141467i \(-0.0451818\pi\)
\(242\) −1.07180 + 4.00000i −0.0688977 + 0.257130i
\(243\) 0 0
\(244\) 2.53590 4.39230i 0.162344 0.281189i
\(245\) 0 0
\(246\) −2.19615 + 8.19615i −0.140022 + 0.522568i
\(247\) 38.7846 2.46781
\(248\) −12.0000 + 12.0000i −0.762001 + 0.762001i
\(249\) −14.7846 −0.936937
\(250\) 0 0
\(251\) −1.85641 −0.117175 −0.0585877 0.998282i \(-0.518660\pi\)
−0.0585877 + 0.998282i \(0.518660\pi\)
\(252\) 0 0
\(253\) 20.3923i 1.28205i
\(254\) 3.12436 11.6603i 0.196040 0.731629i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 4.73205 + 1.26795i 0.294605 + 0.0789391i
\(259\) −4.39230 + 5.07180i −0.272925 + 0.315146i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.46410 + 12.9282i −0.214013 + 0.798707i
\(263\) −4.53590 −0.279695 −0.139848 0.990173i \(-0.544661\pi\)
−0.139848 + 0.990173i \(0.544661\pi\)
\(264\) 12.9282 12.9282i 0.795676 0.795676i
\(265\) 0 0
\(266\) −18.5885 + 12.5885i −1.13973 + 0.771848i
\(267\) 16.3923 1.00319
\(268\) 6.00000 + 3.46410i 0.366508 + 0.211604i
\(269\) 12.0000i 0.731653i 0.930683 + 0.365826i \(0.119214\pi\)
−0.930683 + 0.365826i \(0.880786\pi\)
\(270\) 0 0
\(271\) −2.53590 −0.154045 −0.0770224 0.997029i \(-0.524541\pi\)
−0.0770224 + 0.997029i \(0.524541\pi\)
\(272\) −0.928203 1.60770i −0.0562806 0.0974808i
\(273\) 19.3923 22.3923i 1.17368 1.35524i
\(274\) −0.535898 0.143594i −0.0323748 0.00867480i
\(275\) 0 0
\(276\) −9.46410 + 16.3923i −0.569672 + 0.986701i
\(277\) 24.7846i 1.48916i −0.667532 0.744581i \(-0.732649\pi\)
0.667532 0.744581i \(-0.267351\pi\)
\(278\) −2.53590 + 9.46410i −0.152093 + 0.567619i
\(279\) 0 0
\(280\) 0 0
\(281\) 5.92820 0.353647 0.176823 0.984243i \(-0.443418\pi\)
0.176823 + 0.984243i \(0.443418\pi\)
\(282\) −1.09808 + 4.09808i −0.0653895 + 0.244037i
\(283\) 12.1244i 0.720718i −0.932814 0.360359i \(-0.882654\pi\)
0.932814 0.360359i \(-0.117346\pi\)
\(284\) 0.535898 0.928203i 0.0317997 0.0550787i
\(285\) 0 0
\(286\) 32.9545 + 8.83013i 1.94864 + 0.522136i
\(287\) 6.00000 6.92820i 0.354169 0.408959i
\(288\) 0 0
\(289\) −16.7846 −0.987330
\(290\) 0 0
\(291\) 12.8038i 0.750575i
\(292\) 1.60770 + 0.928203i 0.0940832 + 0.0543190i
\(293\) −14.3205 −0.836613 −0.418307 0.908306i \(-0.637376\pi\)
−0.418307 + 0.908306i \(0.637376\pi\)
\(294\) −2.02628 + 17.0263i −0.118175 + 0.992993i
\(295\) 0 0
\(296\) 5.07180 + 5.07180i 0.294792 + 0.294792i
\(297\) −19.3923 −1.12526
\(298\) −6.19615 + 23.1244i −0.358933 + 1.33956i
\(299\) −35.3205 −2.04264
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) 6.56218 + 1.75833i 0.377611 + 0.101181i
\(303\) 14.7846 0.849354
\(304\) 12.0000 + 20.7846i 0.688247 + 1.19208i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.73205i 0.0988534i 0.998778 + 0.0494267i \(0.0157394\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) −18.6603 + 6.46410i −1.06327 + 0.368326i
\(309\) 29.7846 1.69439
\(310\) 0 0
\(311\) 19.8564 1.12595 0.562977 0.826473i \(-0.309656\pi\)
0.562977 + 0.826473i \(0.309656\pi\)
\(312\) −22.3923 22.3923i −1.26771 1.26771i
\(313\) −24.4641 −1.38279 −0.691396 0.722476i \(-0.743004\pi\)
−0.691396 + 0.722476i \(0.743004\pi\)
\(314\) 7.26795 27.1244i 0.410154 1.53072i
\(315\) 0 0
\(316\) 2.66025 4.60770i 0.149651 0.259203i
\(317\) 16.9282i 0.950783i −0.879774 0.475391i \(-0.842306\pi\)
0.879774 0.475391i \(-0.157694\pi\)
\(318\) 1.26795 4.73205i 0.0711031 0.265360i
\(319\) 22.1244i 1.23873i
\(320\) 0 0
\(321\) 31.8564i 1.77805i
\(322\) 16.9282 11.4641i 0.943372 0.638869i
\(323\) −2.78461 −0.154940
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 0 0
\(326\) 7.60770 28.3923i 0.421351 1.57250i
\(327\) 27.5885i 1.52565i
\(328\) −6.92820 6.92820i −0.382546 0.382546i
\(329\) 3.00000 3.46410i 0.165395 0.190982i
\(330\) 0 0
\(331\) 5.60770i 0.308227i −0.988053 0.154113i \(-0.950748\pi\)
0.988053 0.154113i \(-0.0492521\pi\)
\(332\) 8.53590 14.7846i 0.468468 0.811411i
\(333\) 0 0
\(334\) −7.09808 1.90192i −0.388389 0.104069i
\(335\) 0 0
\(336\) 18.0000 + 3.46410i 0.981981 + 0.188982i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 10.5359 39.3205i 0.573077 2.13875i
\(339\) −2.53590 −0.137731
\(340\) 0 0
\(341\) 22.3923i 1.21261i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −4.00000 + 4.00000i −0.215666 + 0.215666i
\(345\) 0 0
\(346\) 7.43782 27.7583i 0.399860 1.49230i
\(347\) 14.2487 0.764911 0.382455 0.923974i \(-0.375079\pi\)
0.382455 + 0.923974i \(0.375079\pi\)
\(348\) 10.2679 17.7846i 0.550420 0.953355i
\(349\) 29.3205i 1.56949i −0.619818 0.784745i \(-0.712794\pi\)
0.619818 0.784745i \(-0.287206\pi\)
\(350\) 0 0
\(351\) 33.5885i 1.79282i
\(352\) 5.46410 + 20.3923i 0.291238 + 1.08691i
\(353\) 13.3923 0.712800 0.356400 0.934333i \(-0.384004\pi\)
0.356400 + 0.934333i \(0.384004\pi\)
\(354\) 8.19615 + 2.19615i 0.435621 + 0.116724i
\(355\) 0 0
\(356\) −9.46410 + 16.3923i −0.501596 + 0.868790i
\(357\) −1.39230 + 1.60770i −0.0736886 + 0.0850883i
\(358\) −19.6603 5.26795i −1.03908 0.278420i
\(359\) 9.32051i 0.491918i 0.969280 + 0.245959i \(0.0791028\pi\)
−0.969280 + 0.245959i \(0.920897\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 17.6603 + 4.73205i 0.928202 + 0.248711i
\(363\) 5.07180i 0.266200i
\(364\) 11.1962 + 32.3205i 0.586838 + 1.69405i
\(365\) 0 0
\(366\) −1.60770 + 6.00000i −0.0840356 + 0.313625i
\(367\) 36.1244i 1.88568i −0.333251 0.942838i \(-0.608146\pi\)
0.333251 0.942838i \(-0.391854\pi\)
\(368\) −10.9282 18.9282i −0.569672 0.986701i
\(369\) 0 0
\(370\) 0 0
\(371\) −3.46410 + 4.00000i −0.179847 + 0.207670i
\(372\) 10.3923 18.0000i 0.538816 0.933257i
\(373\) 24.3923i 1.26299i 0.775382 + 0.631493i \(0.217557\pi\)
−0.775382 + 0.631493i \(0.782443\pi\)
\(374\) −2.36603 0.633975i −0.122344 0.0327820i
\(375\) 0 0
\(376\) −3.46410 3.46410i −0.178647 0.178647i
\(377\) 38.3205 1.97361
\(378\) −10.9019 16.0981i −0.560734 0.827996i
\(379\) 26.3923i 1.35568i −0.735209 0.677841i \(-0.762916\pi\)
0.735209 0.677841i \(-0.237084\pi\)
\(380\) 0 0
\(381\) 14.7846i 0.757438i
\(382\) −4.36603 1.16987i −0.223385 0.0598559i
\(383\) 20.5359i 1.04934i 0.851307 + 0.524668i \(0.175810\pi\)
−0.851307 + 0.524668i \(0.824190\pi\)
\(384\) 5.07180 18.9282i 0.258819 0.965926i
\(385\) 0 0
\(386\) 3.46410 + 0.928203i 0.176318 + 0.0472443i
\(387\) 0 0
\(388\) 12.8038 + 7.39230i 0.650017 + 0.375287i
\(389\) −6.85641 −0.347634 −0.173817 0.984778i \(-0.555610\pi\)
−0.173817 + 0.984778i \(0.555610\pi\)
\(390\) 0 0
\(391\) 2.53590 0.128246
\(392\) −15.8564 11.8564i −0.800869 0.598839i
\(393\) 16.3923i 0.826882i
\(394\) 29.1244 + 7.80385i 1.46726 + 0.393152i
\(395\) 0 0
\(396\) 0 0
\(397\) −5.53590 −0.277839 −0.138919 0.990304i \(-0.544363\pi\)
−0.138919 + 0.990304i \(0.544363\pi\)
\(398\) −1.26795 + 4.73205i −0.0635566 + 0.237196i
\(399\) 18.0000 20.7846i 0.901127 1.04053i
\(400\) 0 0
\(401\) −23.9282 −1.19492 −0.597459 0.801900i \(-0.703823\pi\)
−0.597459 + 0.801900i \(0.703823\pi\)
\(402\) −8.19615 2.19615i −0.408787 0.109534i
\(403\) 38.7846 1.93200
\(404\) −8.53590 + 14.7846i −0.424677 + 0.735562i
\(405\) 0 0
\(406\) −18.3660 + 12.4378i −0.911491 + 0.617279i
\(407\) 9.46410 0.469118
\(408\) 1.60770 + 1.60770i 0.0795928 + 0.0795928i
\(409\) 31.8564i 1.57520i −0.616188 0.787599i \(-0.711324\pi\)
0.616188 0.787599i \(-0.288676\pi\)
\(410\) 0 0
\(411\) 0.679492 0.0335169
\(412\) −17.1962 + 29.7846i −0.847194 + 1.46738i
\(413\) −6.92820 6.00000i −0.340915 0.295241i
\(414\) 0 0
\(415\) 0 0
\(416\) 35.3205 9.46410i 1.73173 0.464016i
\(417\) 12.0000i 0.587643i
\(418\) 30.5885 + 8.19615i 1.49613 + 0.400887i
\(419\) 24.2487 1.18463 0.592314 0.805708i \(-0.298215\pi\)
0.592314 + 0.805708i \(0.298215\pi\)
\(420\) 0 0
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −9.83013 2.63397i −0.478523 0.128220i
\(423\) 0 0
\(424\) 4.00000 + 4.00000i 0.194257 + 0.194257i
\(425\) 0 0
\(426\) −0.339746 + 1.26795i −0.0164607 + 0.0614323i
\(427\) 4.39230 5.07180i 0.212559 0.245441i
\(428\) 31.8564 + 18.3923i 1.53984 + 0.889026i
\(429\) −41.7846 −2.01738
\(430\) 0 0
\(431\) 17.5885i 0.847206i 0.905848 + 0.423603i \(0.139235\pi\)
−0.905848 + 0.423603i \(0.860765\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) −4.14359 −0.199128 −0.0995642 0.995031i \(-0.531745\pi\)
−0.0995642 + 0.995031i \(0.531745\pi\)
\(434\) −18.5885 + 12.5885i −0.892275 + 0.604265i
\(435\) 0 0
\(436\) 27.5885 + 15.9282i 1.32125 + 0.762823i
\(437\) −32.7846 −1.56830
\(438\) −2.19615 0.588457i −0.104936 0.0281176i
\(439\) 15.7128 0.749932 0.374966 0.927039i \(-0.377654\pi\)
0.374966 + 0.927039i \(0.377654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.09808 + 4.09808i −0.0522302 + 0.194926i
\(443\) −26.0000 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) −7.60770 4.39230i −0.361045 0.208450i
\(445\) 0 0
\(446\) −14.0263 3.75833i −0.664164 0.177962i
\(447\) 29.3205i 1.38681i
\(448\) −13.8564 + 16.0000i −0.654654 + 0.755929i
\(449\) 1.92820 0.0909975 0.0454988 0.998964i \(-0.485512\pi\)
0.0454988 + 0.998964i \(0.485512\pi\)
\(450\) 0 0
\(451\) −12.9282 −0.608765
\(452\) 1.46410 2.53590i 0.0688655 0.119279i
\(453\) −8.32051 −0.390932
\(454\) −4.56218 1.22243i −0.214114 0.0573716i
\(455\) 0 0
\(456\) −20.7846 20.7846i −0.973329 0.973329i
\(457\) 27.4641i 1.28472i 0.766405 + 0.642358i \(0.222044\pi\)
−0.766405 + 0.642358i \(0.777956\pi\)
\(458\) 21.1244 + 5.66025i 0.987076 + 0.264486i
\(459\) 2.41154i 0.112561i
\(460\) 0 0
\(461\) 27.7128i 1.29071i −0.763881 0.645357i \(-0.776709\pi\)
0.763881 0.645357i \(-0.223291\pi\)
\(462\) 20.0263 13.5622i 0.931707 0.630970i
\(463\) 4.39230 0.204128 0.102064 0.994778i \(-0.467455\pi\)
0.102064 + 0.994778i \(0.467455\pi\)
\(464\) 11.8564 + 20.5359i 0.550420 + 0.953355i
\(465\) 0 0
\(466\) 31.3205 + 8.39230i 1.45089 + 0.388766i
\(467\) 22.5167i 1.04195i 0.853573 + 0.520973i \(0.174431\pi\)
−0.853573 + 0.520973i \(0.825569\pi\)
\(468\) 0 0
\(469\) 6.92820 + 6.00000i 0.319915 + 0.277054i
\(470\) 0 0
\(471\) 34.3923i 1.58471i
\(472\) −6.92820 + 6.92820i −0.318896 + 0.318896i
\(473\) 7.46410i 0.343200i
\(474\) −1.68653 + 6.29423i −0.0774650 + 0.289103i
\(475\) 0 0
\(476\) −0.803848 2.32051i −0.0368443 0.106360i
\(477\) 0 0
\(478\) −38.2224 10.2417i −1.74825 0.468443i
\(479\) −37.1769 −1.69866 −0.849328 0.527865i \(-0.822993\pi\)
−0.849328 + 0.527865i \(0.822993\pi\)
\(480\) 0 0
\(481\) 16.3923i 0.747425i
\(482\) −6.00000 1.60770i −0.273293 0.0732285i
\(483\) −16.3923 + 18.9282i −0.745876 + 0.861263i
\(484\) 5.07180 + 2.92820i 0.230536 + 0.133100i
\(485\) 0 0
\(486\) 0 0
\(487\) −28.7846 −1.30436 −0.652178 0.758066i \(-0.726144\pi\)
−0.652178 + 0.758066i \(0.726144\pi\)
\(488\) −5.07180 5.07180i −0.229589 0.229589i
\(489\) 36.0000i 1.62798i
\(490\) 0 0
\(491\) 34.1244i 1.54001i −0.638037 0.770005i \(-0.720254\pi\)
0.638037 0.770005i \(-0.279746\pi\)
\(492\) 10.3923 + 6.00000i 0.468521 + 0.270501i
\(493\) −2.75129 −0.123912
\(494\) 14.1962 52.9808i 0.638715 2.38372i
\(495\) 0 0
\(496\) 12.0000 + 20.7846i 0.538816 + 0.933257i
\(497\) 0.928203 1.07180i 0.0416356 0.0480767i
\(498\) −5.41154 + 20.1962i −0.242497 + 0.905011i
\(499\) 5.58846i 0.250174i 0.992146 + 0.125087i \(0.0399210\pi\)
−0.992146 + 0.125087i \(0.960079\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) −0.679492 + 2.53590i −0.0303272 + 0.113183i
\(503\) 15.5885i 0.695055i 0.937670 + 0.347527i \(0.112979\pi\)
−0.937670 + 0.347527i \(0.887021\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −27.8564 7.46410i −1.23837 0.331820i
\(507\) 49.8564i 2.21420i
\(508\) −14.7846 8.53590i −0.655961 0.378719i
\(509\) 1.85641i 0.0822838i 0.999153 + 0.0411419i \(0.0130996\pi\)
−0.999153 + 0.0411419i \(0.986900\pi\)
\(510\) 0 0
\(511\) 1.85641 + 1.60770i 0.0821226 + 0.0711202i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 31.1769i 1.37649i
\(514\) −2.19615 + 8.19615i −0.0968681 + 0.361517i
\(515\) 0 0
\(516\) 3.46410 6.00000i 0.152499 0.264135i
\(517\) −6.46410 −0.284291
\(518\) 5.32051 + 7.85641i 0.233770 + 0.345191i
\(519\) 35.1962i 1.54494i
\(520\) 0 0
\(521\) 34.3923i 1.50675i 0.657589 + 0.753377i \(0.271576\pi\)
−0.657589 + 0.753377i \(0.728424\pi\)
\(522\) 0 0
\(523\) 24.2487i 1.06032i 0.847897 + 0.530161i \(0.177869\pi\)
−0.847897 + 0.530161i \(0.822131\pi\)
\(524\) 16.3923 + 9.46410i 0.716101 + 0.413441i
\(525\) 0 0
\(526\) −1.66025 + 6.19615i −0.0723905 + 0.270165i
\(527\) −2.78461 −0.121300
\(528\) −12.9282 22.3923i −0.562628 0.974500i
\(529\) 6.85641 0.298105
\(530\) 0 0
\(531\) 0 0
\(532\) 10.3923 + 30.0000i 0.450564 + 1.30066i
\(533\) 22.3923i 0.969918i
\(534\) 6.00000 22.3923i 0.259645 0.969010i
\(535\) 0 0
\(536\) 6.92820 6.92820i 0.299253 0.299253i
\(537\) 24.9282 1.07573
\(538\) 16.3923 + 4.39230i 0.706722 + 0.189366i
\(539\) −25.8564 + 3.73205i −1.11371 + 0.160751i
\(540\) 0 0
\(541\) −33.7846 −1.45251 −0.726257 0.687423i \(-0.758742\pi\)
−0.726257 + 0.687423i \(0.758742\pi\)
\(542\) −0.928203 + 3.46410i −0.0398697 + 0.148796i
\(543\) −22.3923 −0.960946
\(544\) −2.53590 + 0.679492i −0.108726 + 0.0291330i
\(545\) 0 0
\(546\) −23.4904 34.6865i −1.00530 1.48445i
\(547\) −14.5359 −0.621510 −0.310755 0.950490i \(-0.600582\pi\)
−0.310755 + 0.950490i \(0.600582\pi\)
\(548\) −0.392305 + 0.679492i −0.0167584 + 0.0290265i
\(549\) 0 0
\(550\) 0 0
\(551\) 35.5692 1.51530
\(552\) 18.9282 + 18.9282i 0.805638 + 0.805638i
\(553\) 4.60770 5.32051i 0.195939 0.226251i
\(554\) −33.8564 9.07180i −1.43842 0.385424i
\(555\) 0 0
\(556\) 12.0000 + 6.92820i 0.508913 + 0.293821i
\(557\) 5.85641i 0.248144i 0.992273 + 0.124072i \(0.0395954\pi\)
−0.992273 + 0.124072i \(0.960405\pi\)
\(558\) 0 0
\(559\) 12.9282 0.546805
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 2.16987 8.09808i 0.0915306 0.341597i
\(563\) 43.1769i 1.81969i −0.414948 0.909845i \(-0.636200\pi\)
0.414948 0.909845i \(-0.363800\pi\)
\(564\) 5.19615 + 3.00000i 0.218797 + 0.126323i
\(565\) 0 0
\(566\) −16.5622 4.43782i −0.696160 0.186536i
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −1.07180 1.07180i −0.0449716 0.0449716i
\(569\) −20.9282 −0.877356 −0.438678 0.898644i \(-0.644553\pi\)
−0.438678 + 0.898644i \(0.644553\pi\)
\(570\) 0 0
\(571\) 41.3205i 1.72921i −0.502453 0.864605i \(-0.667569\pi\)
0.502453 0.864605i \(-0.332431\pi\)
\(572\) 24.1244 41.7846i 1.00869 1.74710i
\(573\) 5.53590 0.231265
\(574\) −7.26795 10.7321i −0.303358 0.447947i
\(575\) 0 0
\(576\) 0 0
\(577\) 1.39230 0.0579624 0.0289812 0.999580i \(-0.490774\pi\)
0.0289812 + 0.999580i \(0.490774\pi\)
\(578\) −6.14359 + 22.9282i −0.255540 + 0.953688i
\(579\) −4.39230 −0.182538
\(580\) 0 0
\(581\) 14.7846 17.0718i 0.613369 0.708257i
\(582\) −17.4904 4.68653i −0.725000 0.194263i
\(583\) 7.46410 0.309132
\(584\) 1.85641 1.85641i 0.0768186 0.0768186i
\(585\) 0 0
\(586\) −5.24167 + 19.5622i −0.216531 + 0.808106i
\(587\) 27.4641i 1.13356i 0.823868 + 0.566782i \(0.191812\pi\)
−0.823868 + 0.566782i \(0.808188\pi\)
\(588\) 22.5167 + 9.00000i 0.928571 + 0.371154i
\(589\) 36.0000 1.48335
\(590\) 0 0
\(591\) −36.9282 −1.51902
\(592\) 8.78461 5.07180i 0.361045 0.208450i
\(593\) 23.5359 0.966504 0.483252 0.875481i \(-0.339456\pi\)
0.483252 + 0.875481i \(0.339456\pi\)
\(594\) −7.09808 + 26.4904i −0.291238 + 1.08691i
\(595\) 0 0
\(596\) 29.3205 + 16.9282i 1.20101 + 0.693406i
\(597\) 6.00000i 0.245564i
\(598\) −12.9282 + 48.2487i −0.528674 + 1.97304i
\(599\) 14.1244i 0.577106i −0.957464 0.288553i \(-0.906826\pi\)
0.957464 0.288553i \(-0.0931741\pi\)
\(600\) 0 0
\(601\) 26.7846i 1.09257i 0.837600 + 0.546284i \(0.183958\pi\)
−0.837600 + 0.546284i \(0.816042\pi\)
\(602\) −6.19615 + 4.19615i −0.252536 + 0.171022i
\(603\) 0 0
\(604\) 4.80385 8.32051i 0.195466 0.338557i
\(605\) 0 0
\(606\) 5.41154 20.1962i 0.219829 0.820413i
\(607\) 18.8038i 0.763225i 0.924322 + 0.381612i \(0.124631\pi\)
−0.924322 + 0.381612i \(0.875369\pi\)
\(608\) 32.7846 8.78461i 1.32959 0.356263i
\(609\) 17.7846 20.5359i 0.720669 0.832157i
\(610\) 0 0
\(611\) 11.1962i 0.452948i
\(612\) 0 0
\(613\) 10.0000i 0.403896i 0.979396 + 0.201948i \(0.0647272\pi\)
−0.979396 + 0.201948i \(0.935273\pi\)
\(614\) 2.36603 + 0.633975i 0.0954850 + 0.0255851i
\(615\) 0 0
\(616\) 2.00000 + 27.8564i 0.0805823 + 1.12237i
\(617\) 9.07180i 0.365217i −0.983186 0.182608i \(-0.941546\pi\)
0.983186 0.182608i \(-0.0584540\pi\)
\(618\) 10.9019 40.6865i 0.438540 1.63665i
\(619\) 35.3205 1.41965 0.709826 0.704378i \(-0.248774\pi\)
0.709826 + 0.704378i \(0.248774\pi\)
\(620\) 0 0
\(621\) 28.3923i 1.13934i
\(622\) 7.26795 27.1244i 0.291418 1.08759i
\(623\) −16.3923 + 18.9282i −0.656744 + 0.758342i
\(624\) −38.7846 + 22.3923i −1.55263 + 0.896410i
\(625\) 0 0
\(626\) −8.95448 + 33.4186i −0.357893 + 1.33568i
\(627\) −38.7846 −1.54891
\(628\) −34.3923 19.8564i −1.37240 0.792357i
\(629\) 1.17691i 0.0469267i
\(630\) 0 0
\(631\) 26.9090i 1.07123i −0.844463 0.535614i \(-0.820080\pi\)
0.844463 0.535614i \(-0.179920\pi\)
\(632\) −5.32051 5.32051i −0.211638 0.211638i
\(633\) 12.4641 0.495404
\(634\) −23.1244 6.19615i −0.918385 0.246081i
\(635\) 0 0
\(636\) −6.00000 3.46410i −0.237915 0.137361i
\(637\) 6.46410 + 44.7846i 0.256117 + 1.77443i
\(638\) 30.2224 + 8.09808i 1.19652 + 0.320606i
\(639\) 0 0
\(640\) 0 0
\(641\) −4.92820 −0.194652 −0.0973262 0.995253i \(-0.531029\pi\)
−0.0973262 + 0.995253i \(0.531029\pi\)
\(642\) −43.5167 11.6603i −1.71747 0.460194i
\(643\) 31.0526i 1.22459i −0.790628 0.612297i \(-0.790246\pi\)
0.790628 0.612297i \(-0.209754\pi\)
\(644\) −9.46410 27.3205i −0.372938 1.07658i
\(645\) 0 0
\(646\) −1.01924 + 3.80385i −0.0401014 + 0.149660i
\(647\) 10.3923i 0.408564i −0.978912 0.204282i \(-0.934514\pi\)
0.978912 0.204282i \(-0.0654859\pi\)
\(648\) 18.0000 18.0000i 0.707107 0.707107i
\(649\) 12.9282i 0.507476i
\(650\) 0 0
\(651\) 18.0000 20.7846i 0.705476 0.814613i
\(652\) −36.0000 20.7846i −1.40987 0.813988i
\(653\) 38.3923i 1.50241i −0.660071 0.751203i \(-0.729474\pi\)
0.660071 0.751203i \(-0.270526\pi\)
\(654\) −37.6865 10.0981i −1.47366 0.394866i
\(655\) 0 0
\(656\) −12.0000 + 6.92820i −0.468521 + 0.270501i
\(657\) 0 0
\(658\) −3.63397 5.36603i −0.141667 0.209189i
\(659\) 20.8038i 0.810403i 0.914227 + 0.405201i \(0.132799\pi\)
−0.914227 + 0.405201i \(0.867201\pi\)
\(660\) 0 0
\(661\) 15.7128i 0.611158i −0.952167 0.305579i \(-0.901150\pi\)
0.952167 0.305579i \(-0.0988499\pi\)
\(662\) −7.66025 2.05256i −0.297724 0.0797750i
\(663\) 5.19615i 0.201802i
\(664\) −17.0718 17.0718i −0.662514 0.662514i
\(665\) 0 0
\(666\) 0 0
\(667\) −32.3923 −1.25424
\(668\) −5.19615 + 9.00000i −0.201045 + 0.348220i
\(669\) 17.7846 0.687593
\(670\) 0 0
\(671\) −9.46410 −0.365358
\(672\) 11.3205 23.3205i 0.436698 0.899608i
\(673\) 49.1769i 1.89563i −0.318820 0.947815i \(-0.603286\pi\)
0.318820 0.947815i \(-0.396714\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −49.8564 28.7846i −1.91755 1.10710i
\(677\) 4.60770 0.177088 0.0885441 0.996072i \(-0.471779\pi\)
0.0885441 + 0.996072i \(0.471779\pi\)
\(678\) −0.928203 + 3.46410i −0.0356474 + 0.133038i
\(679\) 14.7846 + 12.8038i 0.567381 + 0.491367i
\(680\) 0 0
\(681\) 5.78461 0.221667
\(682\) 30.5885 + 8.19615i 1.17129 + 0.313847i
\(683\) −27.3205 −1.04539 −0.522695 0.852520i \(-0.675073\pi\)
−0.522695 + 0.852520i \(0.675073\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −17.6340 19.3660i −0.673268 0.739398i
\(687\) −26.7846 −1.02190
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 12.9282i 0.492525i
\(690\) 0 0
\(691\) −46.6410 −1.77431 −0.887154 0.461474i \(-0.847321\pi\)
−0.887154 + 0.461474i \(0.847321\pi\)
\(692\) −35.1962 20.3205i −1.33796 0.772470i
\(693\) 0 0
\(694\) 5.21539 19.4641i 0.197974 0.738847i
\(695\) 0 0
\(696\) −20.5359 20.5359i −0.778411 0.778411i
\(697\) 1.60770i 0.0608958i
\(698\) −40.0526 10.7321i −1.51601 0.406214i
\(699\) −39.7128 −1.50208
\(700\) 0 0
\(701\) 3.78461 0.142943 0.0714714 0.997443i \(-0.477231\pi\)
0.0714714 + 0.997443i \(0.477231\pi\)
\(702\) 45.8827 + 12.2942i 1.73173 + 0.464016i
\(703\) 15.2154i 0.573859i
\(704\) 29.8564 1.12526
\(705\) 0 0
\(706\) 4.90192 18.2942i 0.184486 0.688512i
\(707\) −14.7846 + 17.0718i −0.556032 + 0.642051i
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) −21.0000 −0.788672 −0.394336 0.918966i \(-0.629025\pi\)
−0.394336 + 0.918966i \(0.629025\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 18.9282 + 18.9282i 0.709364 + 0.709364i
\(713\) −32.7846 −1.22779
\(714\) 1.68653 + 2.49038i 0.0631169 + 0.0932002i
\(715\) 0 0
\(716\) −14.3923 + 24.9282i −0.537866 + 0.931611i
\(717\) 48.4641 1.80993
\(718\) 12.7321 + 3.41154i 0.475156 + 0.127318i
\(719\) 45.4641 1.69552 0.847762 0.530376i \(-0.177949\pi\)
0.847762 + 0.530376i \(0.177949\pi\)
\(720\) 0 0
\(721\) −29.7846 + 34.3923i −1.10924 + 1.28084i
\(722\) 6.22243 23.2224i 0.231575 0.864249i
\(723\) 7.60770 0.282933
\(724\) 12.9282 22.3923i 0.480473 0.832203i
\(725\) 0 0
\(726\) −6.92820 1.85641i −0.257130 0.0688977i
\(727\) 34.3923i 1.27554i 0.770227 + 0.637770i \(0.220143\pi\)
−0.770227 + 0.637770i \(0.779857\pi\)
\(728\) 48.2487 3.46410i 1.78822 0.128388i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −0.928203 −0.0343308
\(732\) 7.60770 + 4.39230i 0.281189 + 0.162344i
\(733\) 18.4641 0.681987 0.340994 0.940066i \(-0.389237\pi\)
0.340994 + 0.940066i \(0.389237\pi\)
\(734\) −49.3468 13.2224i −1.82142 0.488049i
\(735\) 0 0
\(736\) −29.8564 + 8.00000i −1.10052 + 0.294884i
\(737\) 12.9282i 0.476216i
\(738\) 0 0
\(739\) 7.73205i 0.284428i 0.989836 + 0.142214i \(0.0454221\pi\)
−0.989836 + 0.142214i \(0.954578\pi\)
\(740\) 0 0
\(741\) 67.1769i 2.46781i
\(742\) 4.19615 + 6.19615i 0.154046 + 0.227468i
\(743\) 9.60770 0.352472 0.176236 0.984348i \(-0.443608\pi\)
0.176236 + 0.984348i \(0.443608\pi\)
\(744\) −20.7846 20.7846i −0.762001 0.762001i
\(745\) 0 0
\(746\) 33.3205 + 8.92820i 1.21995 + 0.326885i
\(747\) 0 0
\(748\) −1.73205 + 3.00000i −0.0633300 + 0.109691i
\(749\) 36.7846 + 31.8564i 1.34408 + 1.16401i
\(750\) 0 0
\(751\) 5.58846i 0.203926i 0.994788 + 0.101963i \(0.0325123\pi\)
−0.994788 + 0.101963i \(0.967488\pi\)
\(752\) −6.00000 + 3.46410i −0.218797 + 0.126323i
\(753\) 3.21539i 0.117175i
\(754\) 14.0263 52.3468i 0.510807 1.90636i
\(755\) 0 0
\(756\) −25.9808 + 9.00000i −0.944911 + 0.327327i
\(757\) 10.1436i 0.368675i 0.982863 + 0.184338i \(0.0590140\pi\)
−0.982863 + 0.184338i \(0.940986\pi\)
\(758\) −36.0526 9.66025i −1.30949 0.350876i
\(759\) 35.3205 1.28205
\(760\) 0 0
\(761\) 6.24871i 0.226516i 0.993566 + 0.113258i \(0.0361286\pi\)
−0.993566 + 0.113258i \(0.963871\pi\)
\(762\) 20.1962 + 5.41154i 0.731629 + 0.196040i
\(763\) 31.8564 + 27.5885i 1.15328 + 0.998769i
\(764\) −3.19615 + 5.53590i −0.115633 + 0.200282i
\(765\) 0 0
\(766\) 28.0526 + 7.51666i 1.01358 + 0.271588i
\(767\) 22.3923 0.808539
\(768\) −24.0000 13.8564i −0.866025 0.500000i
\(769\) 18.0000i 0.649097i −0.945869 0.324548i \(-0.894788\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) 2.53590 4.39230i 0.0912690 0.158083i
\(773\) −12.4641 −0.448303 −0.224151 0.974554i \(-0.571961\pi\)
−0.224151 + 0.974554i \(0.571961\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 14.7846 14.7846i 0.530737 0.530737i
\(777\) −8.78461 7.60770i −0.315146 0.272925i
\(778\) −2.50962 + 9.36603i −0.0899742 + 0.335788i
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 0.928203 3.46410i 0.0331925 0.123876i
\(783\) 30.8038i 1.10084i
\(784\) −22.0000 + 17.3205i −0.785714 + 0.618590i
\(785\) 0 0
\(786\) −22.3923 6.00000i −0.798707 0.214013i
\(787\) 15.3397i 0.546803i −0.961900 0.273401i \(-0.911851\pi\)
0.961900 0.273401i \(-0.0881487\pi\)