Properties

Label 1260.2.c.b.811.4
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.4
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.b.811.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-0.366025 + 1.36603i) q^{10} -3.73205i q^{11} +6.46410i q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} -0.464102i q^{17} -6.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(1.36603 - 5.09808i) q^{22} +5.46410i q^{23} -1.00000 q^{25} +(-2.36603 + 8.83013i) q^{26} +(-5.00000 + 1.73205i) q^{28} +5.92820 q^{29} +6.00000 q^{31} +(1.46410 + 5.46410i) q^{32} +(0.169873 - 0.633975i) q^{34} +(-2.00000 - 1.73205i) q^{35} -2.53590 q^{37} +(-8.19615 - 2.19615i) q^{38} +(-2.00000 + 2.00000i) q^{40} -3.46410i q^{41} +2.00000i q^{43} +(3.73205 - 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205 q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.36603 - 0.366025i) q^{50} +(-6.46410 + 11.1962i) q^{52} -2.00000 q^{53} +3.73205 q^{55} +(-7.46410 + 0.535898i) q^{56} +(8.09808 + 2.16987i) q^{58} +3.46410 q^{59} +2.53590i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} -6.46410 q^{65} +3.46410i q^{67} +(0.464102 - 0.803848i) q^{68} +(-2.09808 - 3.09808i) q^{70} -0.535898i q^{71} -0.928203i q^{73} +(-3.46410 - 0.928203i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(7.46410 + 6.46410i) q^{77} -2.66025i q^{79} +(-3.46410 + 2.00000i) q^{80} +(1.26795 - 4.73205i) q^{82} +8.53590 q^{83} +0.464102 q^{85} +(-0.732051 + 2.73205i) q^{86} +(7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(-12.9282 - 11.1962i) q^{91} +(-5.46410 + 9.46410i) q^{92} +(-2.36603 - 0.633975i) q^{94} -6.00000i q^{95} +7.39230i q^{97} +(1.16987 - 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 8 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} + 8 q^{8} + 2 q^{10} - 2 q^{14} + 8 q^{16} - 24 q^{19} - 4 q^{20} + 2 q^{22} - 4 q^{25} - 6 q^{26} - 20 q^{28} - 4 q^{29} + 24 q^{31} - 8 q^{32} + 18 q^{34} - 8 q^{35} - 24 q^{37} - 12 q^{38} - 8 q^{40} + 8 q^{44} - 8 q^{46} - 4 q^{49} - 2 q^{50} - 12 q^{52} - 8 q^{53} + 8 q^{55} - 16 q^{56} + 22 q^{58} + 12 q^{62} - 12 q^{65} - 12 q^{68} + 2 q^{70} + 16 q^{77} + 12 q^{82} + 48 q^{83} - 12 q^{85} + 4 q^{86} + 16 q^{88} - 24 q^{91} - 8 q^{92} - 6 q^{94} + 22 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i
\(3\) 0 0
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) −0.366025 + 1.36603i −0.115747 + 0.431975i
\(11\) 3.73205i 1.12526i −0.826710 0.562628i \(-0.809790\pi\)
0.826710 0.562628i \(-0.190210\pi\)
\(12\) 0 0
\(13\) 6.46410i 1.79282i 0.443227 + 0.896410i \(0.353834\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −3.09808 + 2.09808i −0.827996 + 0.560734i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0.464102i 0.112561i −0.998415 0.0562806i \(-0.982076\pi\)
0.998415 0.0562806i \(-0.0179241\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 0 0
\(22\) 1.36603 5.09808i 0.291238 1.08691i
\(23\) 5.46410i 1.13934i 0.821872 + 0.569672i \(0.192930\pi\)
−0.821872 + 0.569672i \(0.807070\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −2.36603 + 8.83013i −0.464016 + 1.73173i
\(27\) 0 0
\(28\) −5.00000 + 1.73205i −0.944911 + 0.327327i
\(29\) 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 \(0.318872\pi\)
\(32\) 1.46410 + 5.46410i 0.258819 + 0.965926i
\(33\) 0 0
\(34\) 0.169873 0.633975i 0.0291330 0.108726i
\(35\) −2.00000 1.73205i −0.338062 0.292770i
\(36\) 0 0
\(37\) −2.53590 −0.416899 −0.208450 0.978033i \(-0.566842\pi\)
−0.208450 + 0.978033i \(0.566842\pi\)
\(38\) −8.19615 2.19615i −1.32959 0.356263i
\(39\) 0 0
\(40\) −2.00000 + 2.00000i −0.316228 + 0.316228i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 3.73205 6.46410i 0.562628 0.974500i
\(45\) 0 0
\(46\) −2.00000 + 7.46410i −0.294884 + 1.10052i
\(47\) −1.73205 −0.252646 −0.126323 0.991989i \(-0.540318\pi\)
−0.126323 + 0.991989i \(0.540318\pi\)
\(48\) 0 0
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) −1.36603 0.366025i −0.193185 0.0517638i
\(51\) 0 0
\(52\) −6.46410 + 11.1962i −0.896410 + 1.55263i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 3.73205 0.503230
\(56\) −7.46410 + 0.535898i −0.997433 + 0.0716124i
\(57\) 0 0
\(58\) 8.09808 + 2.16987i 1.06333 + 0.284918i
\(59\) 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 \(0.948094\pi\)
\(62\) 8.19615 + 2.19615i 1.04091 + 0.278912i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −6.46410 −0.801773
\(66\) 0 0
\(67\) 3.46410i 0.423207i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0.464102 0.803848i 0.0562806 0.0974808i
\(69\) 0 0
\(70\) −2.09808 3.09808i −0.250768 0.370291i
\(71\) 0.535898i 0.0635994i −0.999494 0.0317997i \(-0.989876\pi\)
0.999494 0.0317997i \(-0.0101239\pi\)
\(72\) 0 0
\(73\) 0.928203i 0.108638i −0.998524 0.0543190i \(-0.982701\pi\)
0.998524 0.0543190i \(-0.0172988\pi\)
\(74\) −3.46410 0.928203i −0.402694 0.107901i
\(75\) 0 0
\(76\) −10.3923 6.00000i −1.19208 0.688247i
\(77\) 7.46410 + 6.46410i 0.850613 + 0.736653i
\(78\) 0 0
\(79\) 2.66025i 0.299302i −0.988739 0.149651i \(-0.952185\pi\)
0.988739 0.149651i \(-0.0478150\pi\)
\(80\) −3.46410 + 2.00000i −0.387298 + 0.223607i
\(81\) 0 0
\(82\) 1.26795 4.73205i 0.140022 0.522568i
\(83\) 8.53590 0.936937 0.468468 0.883480i \(-0.344806\pi\)
0.468468 + 0.883480i \(0.344806\pi\)
\(84\) 0 0
\(85\) 0.464102 0.0503389
\(86\) −0.732051 + 2.73205i −0.0789391 + 0.294605i
\(87\) 0 0
\(88\) 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
\(92\) −5.46410 + 9.46410i −0.569672 + 0.986701i
\(93\) 0 0
\(94\) −2.36603 0.633975i −0.244037 0.0653895i
\(95\) 6.00000i 0.615587i
\(96\) 0 0
\(97\) 7.39230i 0.750575i 0.926908 + 0.375287i \(0.122456\pi\)
−0.926908 + 0.375287i \(0.877544\pi\)
\(98\) 1.16987 9.83013i 0.118175 0.992993i
\(99\) 0 0
\(100\) −1.73205 1.00000i −0.173205 0.100000i
\(101\) 8.53590i 0.849354i 0.905345 + 0.424677i \(0.139612\pi\)
−0.905345 + 0.424677i \(0.860388\pi\)
\(102\) 0 0
\(103\) 17.1962 1.69439 0.847194 0.531284i \(-0.178290\pi\)
0.847194 + 0.531284i \(0.178290\pi\)
\(104\) −12.9282 + 12.9282i −1.26771 + 1.26771i
\(105\) 0 0
\(106\) −2.73205 0.732051i −0.265360 0.0711031i
\(107\) 18.3923i 1.77805i −0.457857 0.889026i \(-0.651383\pi\)
0.457857 0.889026i \(-0.348617\pi\)
\(108\) 0 0
\(109\) 15.9282 1.52565 0.762823 0.646608i \(-0.223813\pi\)
0.762823 + 0.646608i \(0.223813\pi\)
\(110\) 5.09808 + 1.36603i 0.486082 + 0.130245i
\(111\) 0 0
\(112\) −10.3923 2.00000i −0.981981 0.188982i
\(113\) 1.46410 0.137731 0.0688655 0.997626i \(-0.478062\pi\)
0.0688655 + 0.997626i \(0.478062\pi\)
\(114\) 0 0
\(115\) −5.46410 −0.509530
\(116\) 10.2679 + 5.92820i 0.953355 + 0.550420i
\(117\) 0 0
\(118\) 4.73205 + 1.26795i 0.435621 + 0.116724i
\(119\) 0.928203 + 0.803848i 0.0850883 + 0.0736886i
\(120\) 0 0
\(121\) −2.92820 −0.266200
\(122\) −0.928203 + 3.46410i −0.0840356 + 0.313625i
\(123\) 0 0
\(124\) 10.3923 + 6.00000i 0.933257 + 0.538816i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 8.53590i 0.757438i −0.925512 0.378719i \(-0.876365\pi\)
0.925512 0.378719i \(-0.123635\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) 0 0
\(130\) −8.83013 2.36603i −0.774453 0.207514i
\(131\) 9.46410 0.826882 0.413441 0.910531i \(-0.364327\pi\)
0.413441 + 0.910531i \(0.364327\pi\)
\(132\) 0 0
\(133\) 10.3923 12.0000i 0.901127 1.04053i
\(134\) −1.26795 + 4.73205i −0.109534 + 0.408787i
\(135\) 0 0
\(136\) 0.928203 0.928203i 0.0795928 0.0795928i
\(137\) 0.392305 0.0335169 0.0167584 0.999860i \(-0.494665\pi\)
0.0167584 + 0.999860i \(0.494665\pi\)
\(138\) 0 0
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) −1.73205 5.00000i −0.146385 0.422577i
\(141\) 0 0
\(142\) 0.196152 0.732051i 0.0164607 0.0614323i
\(143\) 24.1244 2.01738
\(144\) 0 0
\(145\) 5.92820i 0.492310i
\(146\) 0.339746 1.26795i 0.0281176 0.104936i
\(147\) 0 0
\(148\) −4.39230 2.53590i −0.361045 0.208450i
\(149\) −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
\(155\) 6.00000i 0.481932i
\(156\) 0 0
\(157\) 19.8564i 1.58471i −0.610058 0.792357i \(-0.708854\pi\)
0.610058 0.792357i \(-0.291146\pi\)
\(158\) 0.973721 3.63397i 0.0774650 0.289103i
\(159\) 0 0
\(160\) −5.46410 + 1.46410i −0.431975 + 0.115747i
\(161\) −10.9282 9.46410i −0.861263 0.745876i
\(162\) 0 0
\(163\) 20.7846i 1.62798i 0.580881 + 0.813988i \(0.302708\pi\)
−0.580881 + 0.813988i \(0.697292\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) 0 0
\(166\) 11.6603 + 3.12436i 0.905011 + 0.242497i
\(167\) 5.19615 0.402090 0.201045 0.979582i \(-0.435566\pi\)
0.201045 + 0.979582i \(0.435566\pi\)
\(168\) 0 0
\(169\) −28.7846 −2.21420
\(170\) 0.633975 + 0.169873i 0.0486236 + 0.0130287i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 20.3205i 1.54494i −0.635051 0.772470i \(-0.719021\pi\)
0.635051 0.772470i \(-0.280979\pi\)
\(174\) 0 0
\(175\) 1.73205 2.00000i 0.130931 0.151186i
\(176\) 12.9282 7.46410i 0.974500 0.562628i
\(177\) 0 0
\(178\) 3.46410 12.9282i 0.259645 0.969010i
\(179\) 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 \(0.840465\pi\)
\(182\) −13.5622 20.0263i −1.00530 1.48445i
\(183\) 0 0
\(184\) −10.9282 + 10.9282i −0.805638 + 0.805638i
\(185\) 2.53590i 0.186443i
\(186\) 0 0
\(187\) −1.73205 −0.126660
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) 0 0
\(190\) 2.19615 8.19615i 0.159326 0.594611i
\(191\) 3.19615i 0.231265i 0.993292 + 0.115633i \(0.0368896\pi\)
−0.993292 + 0.115633i \(0.963110\pi\)
\(192\) 0 0
\(193\) −2.53590 −0.182538 −0.0912690 0.995826i \(-0.529092\pi\)
−0.0912690 + 0.995826i \(0.529092\pi\)
\(194\) −2.70577 + 10.0981i −0.194263 + 0.725000i
\(195\) 0 0
\(196\) 5.19615 13.0000i 0.371154 0.928571i
\(197\) −21.3205 −1.51902 −0.759512 0.650494i \(-0.774562\pi\)
−0.759512 + 0.650494i \(0.774562\pi\)
\(198\) 0 0
\(199\) 3.46410 0.245564 0.122782 0.992434i \(-0.460818\pi\)
0.122782 + 0.992434i \(0.460818\pi\)
\(200\) −2.00000 2.00000i −0.141421 0.141421i
\(201\) 0 0
\(202\) −3.12436 + 11.6603i −0.219829 + 0.820413i
\(203\) −10.2679 + 11.8564i −0.720669 + 0.832157i
\(204\) 0 0
\(205\) 3.46410 0.241943
\(206\) 23.4904 + 6.29423i 1.63665 + 0.438540i
\(207\) 0 0
\(208\) −22.3923 + 12.9282i −1.55263 + 0.896410i
\(209\) 22.3923i 1.54891i
\(210\) 0 0
\(211\) 7.19615i 0.495404i −0.968836 0.247702i \(-0.920325\pi\)
0.968836 0.247702i \(-0.0796753\pi\)
\(212\) −3.46410 2.00000i −0.237915 0.137361i
\(213\) 0 0
\(214\) 6.73205 25.1244i 0.460194 1.71747i
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) −10.3923 + 12.0000i −0.705476 + 0.814613i
\(218\) 21.7583 + 5.83013i 1.47366 + 0.394866i
\(219\) 0 0
\(220\) 6.46410 + 3.73205i 0.435810 + 0.251615i
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) 10.2679 0.687593 0.343796 0.939044i \(-0.388287\pi\)
0.343796 + 0.939044i \(0.388287\pi\)
\(224\) −13.4641 6.53590i −0.899608 0.436698i
\(225\) 0 0
\(226\) 2.00000 + 0.535898i 0.133038 + 0.0356474i
\(227\) 3.33975 0.221667 0.110833 0.993839i \(-0.464648\pi\)
0.110833 + 0.993839i \(0.464648\pi\)
\(228\) 0 0
\(229\) 15.4641i 1.02190i −0.859611 0.510948i \(-0.829294\pi\)
0.859611 0.510948i \(-0.170706\pi\)
\(230\) −7.46410 2.00000i −0.492168 0.131876i
\(231\) 0 0
\(232\) 11.8564 + 11.8564i 0.778411 + 0.778411i
\(233\) 22.9282 1.50208 0.751038 0.660259i \(-0.229553\pi\)
0.751038 + 0.660259i \(0.229553\pi\)
\(234\) 0 0
\(235\) 1.73205i 0.112987i
\(236\) 6.00000 + 3.46410i 0.390567 + 0.225494i
\(237\) 0 0
\(238\) 0.973721 + 1.43782i 0.0631169 + 0.0932002i
\(239\) 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 \(-0.0451818\pi\)
\(242\) −4.00000 1.07180i −0.257130 0.0688977i
\(243\) 0 0
\(244\) −2.53590 + 4.39230i −0.162344 + 0.281189i
\(245\) 6.92820 1.00000i 0.442627 0.0638877i
\(246\) 0 0
\(247\) 38.7846i 2.46781i
\(248\) 12.0000 + 12.0000i 0.762001 + 0.762001i
\(249\) 0 0
\(250\) 0.366025 1.36603i 0.0231495 0.0863950i
\(251\) 1.85641 0.117175 0.0585877 0.998282i \(-0.481340\pi\)
0.0585877 + 0.998282i \(0.481340\pi\)
\(252\) 0 0
\(253\) 20.3923 1.28205
\(254\) 3.12436 11.6603i 0.196040 0.731629i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) 0 0
\(259\) 4.39230 5.07180i 0.272925 0.315146i
\(260\) −11.1962 6.46410i −0.694356 0.400887i
\(261\) 0 0
\(262\) 12.9282 + 3.46410i 0.798707 + 0.214013i
\(263\) 4.53590i 0.279695i 0.990173 + 0.139848i \(0.0446613\pi\)
−0.990173 + 0.139848i \(0.955339\pi\)
\(264\) 0 0
\(265\) 2.00000i 0.122859i
\(266\) 18.5885 12.5885i 1.13973 0.771848i
\(267\) 0 0
\(268\) −3.46410 + 6.00000i −0.211604 + 0.366508i
\(269\) 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 \(0.524541\pi\)
\(272\) 1.60770 0.928203i 0.0974808 0.0562806i
\(273\) 0 0
\(274\) 0.535898 + 0.143594i 0.0323748 + 0.00867480i
\(275\) 3.73205i 0.225051i
\(276\) 0 0
\(277\) −24.7846 −1.48916 −0.744581 0.667532i \(-0.767351\pi\)
−0.744581 + 0.667532i \(0.767351\pi\)
\(278\) 9.46410 + 2.53590i 0.567619 + 0.152093i
\(279\) 0 0
\(280\) −0.535898 7.46410i −0.0320261 0.446065i
\(281\) −5.92820 −0.353647 −0.176823 0.984243i \(-0.556582\pi\)
−0.176823 + 0.984243i \(0.556582\pi\)
\(282\) 0 0
\(283\) 12.1244 0.720718 0.360359 0.932814i \(-0.382654\pi\)
0.360359 + 0.932814i \(0.382654\pi\)
\(284\) 0.535898 0.928203i 0.0317997 0.0550787i
\(285\) 0 0
\(286\) 32.9545 + 8.83013i 1.94864 + 0.522136i
\(287\) 6.92820 + 6.00000i 0.408959 + 0.354169i
\(288\) 0 0
\(289\) 16.7846 0.987330
\(290\) −2.16987 + 8.09808i −0.127419 + 0.475535i
\(291\) 0 0
\(292\) 0.928203 1.60770i 0.0543190 0.0940832i
\(293\) 14.3205i 0.836613i 0.908306 + 0.418307i \(0.137376\pi\)
−0.908306 + 0.418307i \(0.862624\pi\)
\(294\) 0 0
\(295\) 3.46410i 0.201688i
\(296\) −5.07180 5.07180i −0.294792 0.294792i
\(297\) 0 0
\(298\) −23.1244 6.19615i −1.33956 0.358933i
\(299\) −35.3205 −2.04264
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) −1.75833 + 6.56218i −0.101181 + 0.377611i
\(303\) 0 0
\(304\) −12.0000 20.7846i −0.688247 1.19208i
\(305\) −2.53590 −0.145205
\(306\) 0 0
\(307\) 1.73205 0.0988534 0.0494267 0.998778i \(-0.484261\pi\)
0.0494267 + 0.998778i \(0.484261\pi\)
\(308\) 6.46410 + 18.6603i 0.368326 + 1.06327i
\(309\) 0 0
\(310\) −2.19615 + 8.19615i −0.124733 + 0.465510i
\(311\) −19.8564 −1.12595 −0.562977 0.826473i \(-0.690344\pi\)
−0.562977 + 0.826473i \(0.690344\pi\)
\(312\) 0 0
\(313\) 24.4641i 1.38279i −0.722476 0.691396i \(-0.756996\pi\)
0.722476 0.691396i \(-0.243004\pi\)
\(314\) 7.26795 27.1244i 0.410154 1.53072i
\(315\) 0 0
\(316\) 2.66025 4.60770i 0.149651 0.259203i
\(317\) 16.9282 0.950783 0.475391 0.879774i \(-0.342306\pi\)
0.475391 + 0.879774i \(0.342306\pi\)
\(318\) 0 0
\(319\) 22.1244i 1.23873i
\(320\) −8.00000 −0.447214
\(321\) 0 0
\(322\) −11.4641 16.9282i −0.638869 0.943372i
\(323\) 2.78461i 0.154940i
\(324\) 0 0
\(325\) 6.46410i 0.358564i
\(326\) −7.60770 + 28.3923i −0.421351 + 1.57250i
\(327\) 0 0
\(328\) 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 \(-0.0492521\pi\)
\(332\) 14.7846 + 8.53590i 0.811411 + 0.468468i
\(333\) 0 0
\(334\) 7.09808 + 1.90192i 0.388389 + 0.104069i
\(335\) −3.46410 −0.189264
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −39.3205 10.5359i −2.13875 0.573077i
\(339\) 0 0
\(340\) 0.803848 + 0.464102i 0.0435948 + 0.0251694i
\(341\) 22.3923i 1.21261i
\(342\) 0 0
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −4.00000 + 4.00000i −0.215666 + 0.215666i
\(345\) 0 0
\(346\) 7.43782 27.7583i 0.399860 1.49230i
\(347\) 14.2487i 0.764911i 0.923974 + 0.382455i \(0.124921\pi\)
−0.923974 + 0.382455i \(0.875079\pi\)
\(348\) 0 0
\(349\) 29.3205i 1.56949i 0.619818 + 0.784745i \(0.287206\pi\)
−0.619818 + 0.784745i \(0.712794\pi\)
\(350\) 3.09808 2.09808i 0.165599 0.112147i
\(351\) 0 0
\(352\) 20.3923 5.46410i 1.08691 0.291238i
\(353\) 13.3923i 0.712800i −0.934333 0.356400i \(-0.884004\pi\)
0.934333 0.356400i \(-0.115996\pi\)
\(354\) 0 0
\(355\) 0.535898 0.0284425
\(356\) 9.46410 16.3923i 0.501596 0.868790i
\(357\) 0 0
\(358\) 5.26795 19.6603i 0.278420 1.03908i
\(359\) 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
\(362\) −4.73205 + 17.6603i −0.248711 + 0.928202i
\(363\) 0 0
\(364\) −11.1962 32.3205i −0.586838 1.69405i
\(365\) 0.928203 0.0485844
\(366\) 0 0
\(367\) −36.1244 −1.88568 −0.942838 0.333251i \(-0.891854\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(368\) −18.9282 + 10.9282i −0.986701 + 0.569672i
\(369\) 0 0
\(370\) 0.928203 3.46410i 0.0482550 0.180090i
\(371\) 3.46410 4.00000i 0.179847 0.207670i
\(372\) 0 0
\(373\) −24.3923 −1.26299 −0.631493 0.775382i \(-0.717557\pi\)
−0.631493 + 0.775382i \(0.717557\pi\)
\(374\) −2.36603 0.633975i −0.122344 0.0327820i
\(375\) 0 0
\(376\) −3.46410 3.46410i −0.178647 0.178647i
\(377\) 38.3205i 1.97361i
\(378\) 0 0
\(379\) 26.3923i 1.35568i 0.735209 + 0.677841i \(0.237084\pi\)
−0.735209 + 0.677841i \(0.762916\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 0 0
\(382\) −1.16987 + 4.36603i −0.0598559 + 0.223385i
\(383\) 20.5359 1.04934 0.524668 0.851307i \(-0.324190\pi\)
0.524668 + 0.851307i \(0.324190\pi\)
\(384\) 0 0
\(385\) −6.46410 + 7.46410i −0.329441 + 0.380406i
\(386\) −3.46410 0.928203i −0.176318 0.0472443i
\(387\) 0 0
\(388\) −7.39230 + 12.8038i −0.375287 + 0.650017i
\(389\) −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
\(392\) 11.8564 15.8564i 0.598839 0.800869i
\(393\) 0 0
\(394\) −29.1244 7.80385i −1.46726 0.393152i
\(395\) 2.66025 0.133852
\(396\) 0 0
\(397\) 5.53590i 0.277839i 0.990304 + 0.138919i \(0.0443629\pi\)
−0.990304 + 0.138919i \(0.955637\pi\)
\(398\) 4.73205 + 1.26795i 0.237196 + 0.0635566i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 23.9282 1.19492 0.597459 0.801900i \(-0.296177\pi\)
0.597459 + 0.801900i \(0.296177\pi\)
\(402\) 0 0
\(403\) 38.7846i 1.93200i
\(404\) −8.53590 + 14.7846i −0.424677 + 0.735562i
\(405\) 0 0
\(406\) −18.3660 + 12.4378i −0.911491 + 0.617279i
\(407\) 9.46410i 0.469118i
\(408\) 0 0
\(409\) 31.8564i 1.57520i 0.616188 + 0.787599i \(0.288676\pi\)
−0.616188 + 0.787599i \(0.711324\pi\)
\(410\) 4.73205 + 1.26795i 0.233699 + 0.0626195i
\(411\) 0 0
\(412\) 29.7846 + 17.1962i 1.46738 + 0.847194i
\(413\) −6.00000 + 6.92820i −0.295241 + 0.340915i
\(414\) 0 0
\(415\) 8.53590i 0.419011i
\(416\) −35.3205 + 9.46410i −1.73173 + 0.464016i
\(417\) 0 0
\(418\) −8.19615 + 30.5885i −0.400887 + 1.49613i
\(419\) 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 \(0.346772\pi\)
\(422\) 2.63397 9.83013i 0.128220 0.478523i
\(423\) 0 0
\(424\) −4.00000 4.00000i −0.194257 0.194257i
\(425\) 0.464102i 0.0225122i
\(426\) 0 0
\(427\) −5.07180 4.39230i −0.245441 0.212559i
\(428\) 18.3923 31.8564i 0.889026 1.53984i
\(429\) 0 0
\(430\) −2.73205 0.732051i −0.131751 0.0353026i
\(431\) 17.5885i 0.847206i −0.905848 0.423603i \(-0.860765\pi\)
0.905848 0.423603i \(-0.139235\pi\)
\(432\) 0 0
\(433\) 4.14359i 0.199128i −0.995031 0.0995642i \(-0.968255\pi\)
0.995031 0.0995642i \(-0.0317449\pi\)
\(434\) −18.5885 + 12.5885i −0.892275 + 0.604265i
\(435\) 0 0
\(436\) 27.5885 + 15.9282i 1.32125 + 0.762823i
\(437\) 32.7846i 1.56830i
\(438\) 0 0
\(439\) −15.7128 −0.749932 −0.374966 0.927039i \(-0.622346\pi\)
−0.374966 + 0.927039i \(0.622346\pi\)
\(440\) 7.46410 + 7.46410i 0.355837 + 0.355837i
\(441\) 0 0
\(442\) 4.09808 + 1.09808i 0.194926 + 0.0522302i
\(443\) 26.0000i 1.23530i 0.786454 + 0.617649i \(0.211915\pi\)
−0.786454 + 0.617649i \(0.788085\pi\)
\(444\) 0 0
\(445\) 9.46410 0.448641
\(446\) 14.0263 + 3.75833i 0.664164 + 0.177962i
\(447\) 0 0
\(448\) −16.0000 13.8564i −0.755929 0.654654i
\(449\) 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
\(452\) 2.53590 + 1.46410i 0.119279 + 0.0688655i
\(453\) 0 0
\(454\) 4.56218 + 1.22243i 0.214114 + 0.0573716i
\(455\) 11.1962 12.9282i 0.524884 0.606084i
\(456\) 0 0
\(457\) 27.4641 1.28472 0.642358 0.766405i \(-0.277956\pi\)
0.642358 + 0.766405i \(0.277956\pi\)
\(458\) 5.66025 21.1244i 0.264486 0.987076i
\(459\) 0 0
\(460\) −9.46410 5.46410i −0.441266 0.254765i
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 0 0
\(463\) 4.39230i 0.204128i 0.994778 + 0.102064i \(0.0325446\pi\)
−0.994778 + 0.102064i \(0.967455\pi\)
\(464\) 11.8564 + 20.5359i 0.550420 + 0.953355i
\(465\) 0 0
\(466\) 31.3205 + 8.39230i 1.45089 + 0.388766i
\(467\) −22.5167 −1.04195 −0.520973 0.853573i \(-0.674431\pi\)
−0.520973 + 0.853573i \(0.674431\pi\)
\(468\) 0 0
\(469\) −6.92820 6.00000i −0.319915 0.277054i
\(470\) 0.633975 2.36603i 0.0292431 0.109137i
\(471\) 0 0
\(472\) 6.92820 + 6.92820i 0.318896 + 0.318896i
\(473\) 7.46410 0.343200
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0.803848 + 2.32051i 0.0368443 + 0.106360i
\(477\) 0 0
\(478\) 10.2417 38.2224i 0.468443 1.74825i
\(479\) −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
\(482\) 1.60770 6.00000i 0.0732285 0.273293i
\(483\) 0 0
\(484\) −5.07180 2.92820i −0.230536 0.133100i
\(485\) −7.39230 −0.335667
\(486\) 0 0
\(487\) 28.7846i 1.30436i 0.758066 + 0.652178i \(0.226144\pi\)
−0.758066 + 0.652178i \(0.773856\pi\)
\(488\) −5.07180 + 5.07180i −0.229589 + 0.229589i
\(489\) 0 0
\(490\) 9.83013 + 1.16987i 0.444080 + 0.0528495i
\(491\) 34.1244i 1.54001i 0.638037 + 0.770005i \(0.279746\pi\)
−0.638037 + 0.770005i \(0.720254\pi\)
\(492\) 0 0
\(493\) 2.75129i 0.123912i
\(494\) 14.1962 52.9808i 0.638715 2.38372i
\(495\) 0 0
\(496\) 12.0000 + 20.7846i 0.538816 + 0.933257i
\(497\) 1.07180 + 0.928203i 0.0480767 + 0.0416356i
\(498\) 0 0
\(499\) 5.58846i 0.250174i −0.992146 0.125087i \(-0.960079\pi\)
0.992146 0.125087i \(-0.0399210\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 0 0
\(502\) 2.53590 + 0.679492i 0.113183 + 0.0303272i
\(503\) 15.5885 0.695055 0.347527 0.937670i \(-0.387021\pi\)
0.347527 + 0.937670i \(0.387021\pi\)
\(504\) 0 0
\(505\) −8.53590 −0.379842
\(506\) 27.8564 + 7.46410i 1.23837 + 0.331820i
\(507\) 0 0
\(508\) 8.53590 14.7846i 0.378719 0.655961i
\(509\) 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
\(513\) 0 0
\(514\) 2.19615 8.19615i 0.0968681 0.361517i
\(515\) 17.1962i 0.757753i
\(516\) 0 0
\(517\) 6.46410i 0.284291i
\(518\) 7.85641 5.32051i 0.345191 0.233770i
\(519\) 0 0
\(520\) −12.9282 12.9282i −0.566939 0.566939i
\(521\) 34.3923i 1.50675i −0.657589 0.753377i \(-0.728424\pi\)
0.657589 0.753377i \(-0.271576\pi\)
\(522\) 0 0
\(523\) −24.2487 −1.06032 −0.530161 0.847897i \(-0.677869\pi\)
−0.530161 + 0.847897i \(0.677869\pi\)
\(524\) 16.3923 + 9.46410i 0.716101 + 0.413441i
\(525\) 0 0
\(526\) −1.66025 + 6.19615i −0.0723905 + 0.270165i
\(527\) 2.78461i 0.121300i
\(528\) 0 0
\(529\) −6.85641 −0.298105
\(530\) 0.732051 2.73205i 0.0317983 0.118673i
\(531\) 0 0
\(532\) 30.0000 10.3923i 1.30066 0.450564i
\(533\) 22.3923 0.969918
\(534\) 0 0
\(535\) 18.3923 0.795169
\(536\) −6.92820 + 6.92820i −0.299253 + 0.299253i
\(537\) 0 0
\(538\) −4.39230 + 16.3923i −0.189366 + 0.706722i
\(539\) −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 \(0.758742\pi\)
\(542\) −3.46410 0.928203i −0.148796 0.0398697i
\(543\) 0 0
\(544\) 2.53590 0.679492i 0.108726 0.0291330i
\(545\) 15.9282i 0.682289i
\(546\) 0 0
\(547\) 14.5359i 0.621510i 0.950490 + 0.310755i \(0.100582\pi\)
−0.950490 + 0.310755i \(0.899418\pi\)
\(548\) 0.679492 + 0.392305i 0.0290265 + 0.0167584i
\(549\) 0 0
\(550\) −1.36603 + 5.09808i −0.0582475 + 0.217383i
\(551\) −35.5692 −1.51530
\(552\) 0 0
\(553\) 5.32051 + 4.60770i 0.226251 + 0.195939i
\(554\) −33.8564 9.07180i −1.43842 0.385424i
\(555\) 0 0
\(556\) 12.0000 + 6.92820i 0.508913 + 0.293821i
\(557\) −5.85641 −0.248144 −0.124072 0.992273i \(-0.539595\pi\)
−0.124072 + 0.992273i \(0.539595\pi\)
\(558\) 0 0
\(559\) −12.9282 −0.546805
\(560\) 2.00000 10.3923i 0.0845154 0.439155i
\(561\) 0 0
\(562\) −8.09808 2.16987i −0.341597 0.0915306i
\(563\) −43.1769 −1.81969 −0.909845 0.414948i \(-0.863800\pi\)
−0.909845 + 0.414948i \(0.863800\pi\)
\(564\) 0 0
\(565\) 1.46410i 0.0615952i
\(566\) 16.5622 + 4.43782i 0.696160 + 0.186536i
\(567\) 0 0
\(568\) 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 \(-0.332431\pi\)
\(572\) 41.7846 + 24.1244i 1.74710 + 1.00869i
\(573\) 0 0
\(574\) 7.26795 + 10.7321i 0.303358 + 0.447947i
\(575\) 5.46410i 0.227869i
\(576\) 0 0
\(577\) 1.39230i 0.0579624i −0.999580 0.0289812i \(-0.990774\pi\)
0.999580 0.0289812i \(-0.00922630\pi\)
\(578\) 22.9282 + 6.14359i 0.953688 + 0.255540i
\(579\) 0 0
\(580\) −5.92820 + 10.2679i −0.246155 + 0.426353i
\(581\) −14.7846 + 17.0718i −0.613369 + 0.708257i
\(582\) 0 0
\(583\) 7.46410i 0.309132i
\(584\) 1.85641 1.85641i 0.0768186 0.0768186i
\(585\) 0 0
\(586\) −5.24167 + 19.5622i −0.216531 + 0.808106i
\(587\) −27.4641 −1.13356 −0.566782 0.823868i \(-0.691812\pi\)
−0.566782 + 0.823868i \(0.691812\pi\)
\(588\) 0 0
\(589\) −36.0000 −1.48335
\(590\) −1.26795 + 4.73205i −0.0522006 + 0.194815i
\(591\) 0 0
\(592\) −5.07180 8.78461i −0.208450 0.361045i
\(593\) 23.5359i 0.966504i −0.875481 0.483252i \(-0.839456\pi\)
0.875481 0.483252i \(-0.160544\pi\)
\(594\) 0 0
\(595\) −0.803848 + 0.928203i −0.0329545 + 0.0380526i
\(596\) −29.3205 16.9282i −1.20101 0.693406i
\(597\) 0 0
\(598\) −48.2487 12.9282i −1.97304 0.528674i
\(599\) 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 \(0.816042\pi\)
\(602\) −4.19615 6.19615i −0.171022 0.252536i
\(603\) 0 0
\(604\) −4.80385 + 8.32051i −0.195466 + 0.338557i
\(605\) 2.92820i 0.119048i
\(606\) 0 0
\(607\) 18.8038 0.763225 0.381612 0.924322i \(-0.375369\pi\)
0.381612 + 0.924322i \(0.375369\pi\)
\(608\) −8.78461 32.7846i −0.356263 1.32959i
\(609\) 0 0
\(610\) −3.46410 0.928203i −0.140257 0.0375819i
\(611\) 11.1962i 0.452948i
\(612\) 0 0
\(613\) −10.0000 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 2.36603 + 0.633975i 0.0954850 + 0.0255851i
\(615\) 0 0
\(616\) 2.00000 + 27.8564i 0.0805823 + 1.12237i
\(617\) 9.07180 0.365217 0.182608 0.983186i \(-0.441546\pi\)
0.182608 + 0.983186i \(0.441546\pi\)
\(618\) 0 0
\(619\) −35.3205 −1.41965 −0.709826 0.704378i \(-0.751226\pi\)
−0.709826 + 0.704378i \(0.751226\pi\)
\(620\) −6.00000 + 10.3923i −0.240966 + 0.417365i
\(621\) 0 0
\(622\) −27.1244 7.26795i −1.08759 0.291418i
\(623\) 18.9282 + 16.3923i 0.758342 + 0.656744i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 8.95448 33.4186i 0.357893 1.33568i
\(627\) 0 0
\(628\) 19.8564 34.3923i 0.792357 1.37240i
\(629\) 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
\(633\) 0 0
\(634\) 23.1244 + 6.19615i 0.918385 + 0.246081i
\(635\) 8.53590 0.338737
\(636\) 0 0
\(637\) 44.7846 6.46410i 1.77443 0.256117i
\(638\) 8.09808 30.2224i 0.320606 1.19652i
\(639\) 0 0
\(640\) −10.9282 2.92820i −0.431975 0.115747i
\(641\) 4.92820 0.194652 0.0973262 0.995253i \(-0.468971\pi\)
0.0973262 + 0.995253i \(0.468971\pi\)
\(642\) 0 0
\(643\) 31.0526 1.22459 0.612297 0.790628i \(-0.290246\pi\)
0.612297 + 0.790628i \(0.290246\pi\)
\(644\) −9.46410 27.3205i −0.372938 1.07658i
\(645\) 0 0
\(646\) −1.01924 + 3.80385i −0.0401014 + 0.149660i
\(647\) 10.3923 0.408564 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(648\) 0 0
\(649\) 12.9282i 0.507476i
\(650\) 2.36603 8.83013i 0.0928032 0.346346i
\(651\) 0 0
\(652\) −20.7846 + 36.0000i −0.813988 + 1.40987i
\(653\) −38.3923 −1.50241 −0.751203 0.660071i \(-0.770526\pi\)
−0.751203 + 0.660071i \(0.770526\pi\)
\(654\) 0 0
\(655\) 9.46410i 0.369793i
\(656\) 12.0000 6.92820i 0.468521 0.270501i
\(657\) 0 0
\(658\) 5.36603 3.63397i 0.209189 0.141667i
\(659\) 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 \(-0.0988499\pi\)
\(662\) 2.05256 7.66025i 0.0797750 0.297724i
\(663\) 0 0
\(664\) 17.0718 + 17.0718i 0.662514 + 0.662514i
\(665\) 12.0000 + 10.3923i 0.465340 + 0.402996i
\(666\) 0 0
\(667\) 32.3923i 1.25424i
\(668\) 9.00000 + 5.19615i 0.348220 + 0.201045i
\(669\) 0 0
\(670\) −4.73205 1.26795i −0.182815 0.0489852i
\(671\) 9.46410 0.365358
\(672\) 0 0
\(673\) 49.1769 1.89563 0.947815 0.318820i \(-0.103286\pi\)
0.947815 + 0.318820i \(0.103286\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −49.8564 28.7846i −1.91755 1.10710i
\(677\) 4.60770i 0.177088i 0.996072 + 0.0885441i \(0.0282214\pi\)
−0.996072 + 0.0885441i \(0.971779\pi\)
\(678\) 0 0
\(679\) −14.7846 12.8038i −0.567381 0.491367i
\(680\) 0.928203 + 0.928203i 0.0355950 + 0.0355950i
\(681\) 0 0
\(682\) 8.19615 30.5885i 0.313847 1.17129i
\(683\) 27.3205i 1.04539i 0.852520 + 0.522695i \(0.175073\pi\)
−0.852520 + 0.522695i \(0.824927\pi\)
\(684\) 0 0
\(685\) 0.392305i 0.0149892i
\(686\) 17.6340 + 19.3660i 0.673268 + 0.739398i
\(687\) 0 0
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 12.9282i 0.492525i
\(690\) 0 0
\(691\) −46.6410 −1.77431 −0.887154 0.461474i \(-0.847321\pi\)
−0.887154 + 0.461474i \(0.847321\pi\)
\(692\) 20.3205 35.1962i 0.772470 1.33796i
\(693\) 0 0
\(694\) −5.21539 + 19.4641i −0.197974 + 0.738847i
\(695\) 6.92820i 0.262802i
\(696\) 0 0
\(697\) −1.60770 −0.0608958
\(698\) −10.7321 + 40.0526i −0.406214 + 1.51601i
\(699\) 0 0
\(700\) 5.00000 1.73205i 0.188982 0.0654654i
\(701\) −3.78461 −0.142943 −0.0714714 0.997443i \(-0.522769\pi\)
−0.0714714 + 0.997443i \(0.522769\pi\)
\(702\) 0 0
\(703\) 15.2154 0.573859
\(704\) 29.8564 1.12526
\(705\) 0 0
\(706\) 4.90192 18.2942i 0.184486 0.688512i
\(707\) −17.0718 14.7846i −0.642051 0.556032i
\(708\) 0 0
\(709\) 21.0000 0.788672 0.394336 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(710\) 0.732051 + 0.196152i 0.0274734 + 0.00736147i
\(711\) 0 0
\(712\) 18.9282 18.9282i 0.709364 0.709364i
\(713\) 32.7846i 1.22779i
\(714\) 0 0
\(715\) 24.1244i 0.902200i
\(716\) 14.3923 24.9282i 0.537866 0.931611i
\(717\) 0 0
\(718\) −3.41154 + 12.7321i −0.127318 + 0.475156i
\(719\) 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
\(722\) 23.2224 + 6.22243i 0.864249 + 0.231575i
\(723\) 0 0
\(724\) −12.9282 + 22.3923i −0.480473 + 0.832203i
\(725\) −5.92820 −0.220168
\(726\) 0 0
\(727\) 34.3923 1.27554 0.637770 0.770227i \(-0.279857\pi\)
0.637770 + 0.770227i \(0.279857\pi\)
\(728\) −3.46410 48.2487i −0.128388 1.78822i
\(729\) 0 0
\(730\) 1.26795 + 0.339746i 0.0469289 + 0.0125746i
\(731\) 0.928203 0.0343308
\(732\) 0 0
\(733\) 18.4641i 0.681987i 0.940066 + 0.340994i \(0.110763\pi\)
−0.940066 + 0.340994i \(0.889237\pi\)
\(734\) −49.3468 13.2224i −1.82142 0.488049i
\(735\) 0 0
\(736\) −29.8564 + 8.00000i −1.10052 + 0.294884i
\(737\) 12.9282 0.476216
\(738\) 0 0
\(739\) 7.73205i 0.284428i −0.989836 0.142214i \(-0.954578\pi\)
0.989836 0.142214i \(-0.0454221\pi\)
\(740\) 2.53590 4.39230i 0.0932215 0.161464i
\(741\) 0 0
\(742\) 6.19615 4.19615i 0.227468 0.154046i
\(743\) 9.60770i 0.352472i −0.984348 0.176236i \(-0.943608\pi\)
0.984348 0.176236i \(-0.0563922\pi\)
\(744\) 0 0
\(745\) 16.9282i 0.620201i
\(746\) −33.3205 8.92820i −1.21995 0.326885i
\(747\) 0 0
\(748\) −3.00000 1.73205i −0.109691 0.0633300i
\(749\) 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 \(0.967488\pi\)
\(752\) −3.46410 6.00000i −0.126323 0.218797i
\(753\) 0 0
\(754\) −14.0263 + 52.3468i −0.510807 + 1.90636i
\(755\) −4.80385 −0.174830
\(756\) 0 0
\(757\) 10.1436 0.368675 0.184338 0.982863i \(-0.440986\pi\)
0.184338 + 0.982863i \(0.440986\pi\)
\(758\) −9.66025 + 36.0526i −0.350876 + 1.30949i
\(759\) 0 0
\(760\) 12.0000 12.0000i 0.435286 0.435286i
\(761\) 6.24871i 0.226516i −0.993566 0.113258i \(-0.963871\pi\)
0.993566 0.113258i \(-0.0361286\pi\)
\(762\) 0 0
\(763\) −27.5885 + 31.8564i −0.998769 + 1.15328i
\(764\) −3.19615 + 5.53590i −0.115633 + 0.200282i
\(765\) 0 0
\(766\) 28.0526 + 7.51666i 1.01358 + 0.271588i
\(767\) 22.3923i 0.808539i
\(768\) 0 0
\(769\) 18.0000i 0.649097i 0.945869 + 0.324548i \(0.105212\pi\)
−0.945869 + 0.324548i \(0.894788\pi\)
\(770\) −11.5622 + 7.83013i −0.416672 + 0.282178i
\(771\) 0 0
\(772\) −4.39230 2.53590i −0.158083 0.0912690i
\(773\) 12.4641i 0.448303i 0.974554 + 0.224151i \(0.0719610\pi\)
−0.974554 + 0.224151i \(0.928039\pi\)
\(774\) 0 0
\(775\) −6.00000 −0.215526
\(776\) −14.7846 + 14.7846i −0.530737 + 0.530737i
\(777\) 0 0
\(778\) −9.36603 2.50962i −0.335788 0.0899742i
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 3.46410 + 0.928203i 0.123876 + 0.0331925i
\(783\) 0 0
\(784\) 22.0000 17.3205i 0.785714 0.618590i
\(785\) 19.8564 0.708706
\(786\) 0 0
\(787\) −15.3397 −0.546803 −0.273401 0.961900i \(-0.588149\pi\)
−0.273401 + 0.961900i \(0.588149\pi\)
\(788\) −36.9282 21.3205i −1.31551 0.759512i
\(789\) 0 0
\(790\) 3.63397 + 0.973721i 0.129291 + 0.0346434i
\(791\) −2.53590 + 2.92820i</