Properties

Label 700.2.c.f.699.1
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 699.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.f.699.2

$q$-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 \(-0.809790\pi\)
0.826710 0.562628i \(-0.190210\pi\)
\(12\) −1.73205 3.00000i −0.500000 0.866025i
\(13\) −6.46410 −1.79282 −0.896410 0.443227i \(-0.853834\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) −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 \(-0.482076\pi\)
0.0562806 + 0.998415i \(0.482076\pi\)
\(18\) 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 \(-0.307070\pi\)
0.569672 + 0.821872i \(0.307070\pi\)
\(24\) −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 \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 3.63397 5.36603i 0.560734 0.827996i
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 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 \(-0.948094\pi\)
0.986734 0.162344i \(-0.0519055\pi\)
\(62\) −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 \(-0.432131\pi\)
0.211604 + 0.977356i \(0.432131\pi\)
\(68\) −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 \(-0.989876\pi\)
0.999494 0.0317997i \(-0.0101239\pi\)
\(72\) 0 0
\(73\) 0.928203 0.108638 0.0543190 0.998524i \(-0.482701\pi\)
0.0543190 + 0.998524i \(0.482701\pi\)
\(74\) −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 \(-0.952185\pi\)
0.988739 0.149651i \(-0.0478150\pi\)
\(80\) 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 \(0.167254\pi\)
−0.865102 + 0.501596i \(0.832746\pi\)
\(90\) 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 \(-0.377544\pi\)
0.375287 + 0.926908i \(0.377544\pi\)
\(98\) −9.83013 + 1.16987i −0.992993 + 0.118175i
\(99\) 0 0
\(100\) 0 0
\(101\) 8.53590i 0.849354i 0.905345 + 0.424677i \(0.139612\pi\)
−0.905345 + 0.424677i \(0.860388\pi\)
\(102\) 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 \(-0.151383\pi\)
0.889026 + 0.457857i \(0.151383\pi\)
\(108\) −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 \(-0.623635\pi\)
−0.378719 + 0.925512i \(0.623635\pi\)
\(128\) 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 \(-0.937378\pi\)
0.980711 0.195466i \(-0.0626219\pi\)
\(152\) 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 \(-0.791146\pi\)
−0.792357 + 0.610058i \(0.791146\pi\)
\(158\) −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 \(-0.802708\pi\)
−0.813988 + 0.580881i \(0.802708\pi\)
\(164\) 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 \(-0.780979\pi\)
−0.772470 + 0.635051i \(0.780979\pi\)
\(174\) 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 \(0.180769\pi\)
−0.843031 + 0.537866i \(0.819231\pi\)
\(180\) 0 0
\(181\) 12.9282i 0.960946i −0.877010 0.480473i \(-0.840465\pi\)
0.877010 0.480473i \(-0.159535\pi\)
\(182\) 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 \(0.0368896\pi\)
−0.993292 + 0.115633i \(0.963110\pi\)
\(192\) −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 \(0.0796753\pi\)
−0.968836 + 0.247702i \(0.920325\pi\)
\(212\) 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 \(-0.829294\pi\)
0.859611 0.510948i \(-0.170706\pi\)
\(230\) 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 \(0.360101\pi\)
−0.425491 + 0.904963i \(0.639899\pi\)
\(240\) 0 0
\(241\) 4.39230i 0.282933i 0.989943 + 0.141467i \(0.0451818\pi\)
−0.989943 + 0.141467i \(0.954818\pi\)
\(242\) 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 \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −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 \(-0.455339\pi\)
0.139848 + 0.990173i \(0.455339\pi\)
\(264\) 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 \(-0.880786\pi\)
0.930683 0.365826i \(-0.119214\pi\)
\(270\) 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 \(-0.362624\pi\)
0.418307 + 0.908306i \(0.362624\pi\)
\(294\) −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 \(-0.256996\pi\)
0.691396 + 0.722476i \(0.256996\pi\)
\(314\) 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 \(0.0492521\pi\)
−0.988053 + 0.154113i \(0.950748\pi\)
\(332\) −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 \(-0.624921\pi\)
−0.382455 + 0.923974i \(0.624921\pi\)
\(348\) −10.2679 17.7846i −0.550420 0.953355i
\(349\) 29.3205i 1.56949i 0.619818 + 0.784745i \(0.287206\pi\)
−0.619818 + 0.784745i \(0.712794\pi\)
\(350\) 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 \(-0.615996\pi\)
−0.356400 + 0.934333i \(0.615996\pi\)
\(354\) 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 \(-0.920897\pi\)
0.969280 0.245959i \(-0.0791028\pi\)
\(360\) 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 \(0.237084\pi\)
−0.735209 + 0.677841i \(0.762916\pi\)
\(380\) 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 \(-0.455637\pi\)
0.138919 + 0.990304i \(0.455637\pi\)
\(398\) 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 \(0.288676\pi\)
−0.616188 + 0.787599i \(0.711324\pi\)
\(410\) 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 \(-0.860765\pi\)
0.905848 0.423603i \(-0.139235\pi\)
\(432\) 18.0000 + 10.3923i 0.866025 + 0.500000i
\(433\) 4.14359 0.199128 0.0995642 0.995031i \(-0.468255\pi\)
0.0995642 + 0.995031i \(0.468255\pi\)
\(434\) −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 \(-0.288085\pi\)
0.617649 + 0.786454i \(0.288085\pi\)
\(444\) −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 \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) −20.0263 13.5622i −0.931707 0.630970i
\(463\) −4.39230 −0.204128 −0.102064 0.994778i \(-0.532545\pi\)
−0.102064 + 0.994778i \(0.532545\pi\)
\(464\) 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 \(-0.273856\pi\)
0.652178 + 0.758066i \(0.273856\pi\)
\(488\) 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 \(0.279746\pi\)
−0.638037 + 0.770005i \(0.720254\pi\)
\(492\) −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 \(-0.960079\pi\)
0.992146 0.125087i \(-0.0399210\pi\)
\(500\) 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 \(-0.986900\pi\)
0.999153 0.0411419i \(-0.0130996\pi\)
\(510\) 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 \(-0.728424\pi\)
0.657589 0.753377i \(-0.271576\pi\)
\(522\) 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 \(-0.399418\pi\)
0.310755 + 0.950490i \(0.399418\pi\)
\(548\) 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 \(0.332431\pi\)
−0.502453 + 0.864605i \(0.667569\pi\)
\(572\) −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 \(-0.509226\pi\)
−0.0289812 + 0.999580i \(0.509226\pi\)
\(578\) 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 \(-0.660544\pi\)
−0.483252 + 0.875481i \(0.660544\pi\)
\(594\) −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 \(0.0931741\pi\)
−0.957464 + 0.288553i \(0.906826\pi\)
\(600\) 0 0
\(601\) 26.7846i 1.09257i −0.837600 0.546284i \(-0.816042\pi\)
0.837600 0.546284i \(-0.183958\pi\)
\(602\) 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 \(0.179920\pi\)
−0.844463 + 0.535614i \(0.820080\pi\)
\(632\) 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 \(-0.867201\pi\)
0.914227 0.405201i \(-0.132799\pi\)
\(660\) 0 0
\(661\) 15.7128i 0.611158i 0.952167 + 0.305579i \(0.0988499\pi\)
−0.952167 + 0.305579i \(0.901150\pi\)
\(662\) 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 \(-0.528221\pi\)
−0.0885441 + 0.996072i \(0.528221\pi\)
\(678\) 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 \(-0.324927\pi\)
0.522695 + 0.852520i \(0.324927\pi\)
\(684\) 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 \(-0.610763\pi\)
−0.340994 + 0.940066i \(0.610763\pi\)
\(734\) −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 \(-0.954578\pi\)
0.989836 0.142214i \(-0.0454221\pi\)
\(740\) 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 \(-0.556392\pi\)
−0.176236 + 0.984348i \(0.556392\pi\)
\(744\) −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 \(-0.967488\pi\)
0.994788 0.101963i \(-0.0325123\pi\)
\(752\) 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 \(-0.963871\pi\)
0.993566 0.113258i \(-0.0361286\pi\)
\(762\) −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 \(0.105212\pi\)
−0.945869 + 0.324548i \(0.894788\pi\)
\(770\) 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 \(-0.428039\pi\)
0.224151 + 0.974554i \(0.428039\pi\)
\(774\) 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 \(-0.0881487\pi\)