Properties

Label 624.2.cn.f.305.12
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.12
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.43567 - 0.968940i) q^{3} +(2.19967 + 2.19967i) q^{5} +(-1.17763 + 4.39498i) q^{7} +(1.12231 - 2.78216i) q^{9} +O(q^{10})\) \(q+(1.43567 - 0.968940i) q^{3} +(2.19967 + 2.19967i) q^{5} +(-1.17763 + 4.39498i) q^{7} +(1.12231 - 2.78216i) q^{9} +(-0.917595 - 3.42451i) q^{11} +(0.225112 + 3.59852i) q^{13} +(5.28937 + 1.02666i) q^{15} +(2.20507 + 3.81929i) q^{17} +(-1.06243 - 0.284677i) q^{19} +(2.56778 + 7.45081i) q^{21} +(0.812870 - 1.40793i) q^{23} +4.67714i q^{25} +(-1.08448 - 5.08172i) q^{27} +(-4.61533 - 2.66466i) q^{29} +(-3.28177 + 3.28177i) q^{31} +(-4.63551 - 4.02738i) q^{33} +(-12.2579 + 7.07712i) q^{35} +(2.75348 - 0.737792i) q^{37} +(3.80993 + 4.94817i) q^{39} +(9.76774 - 2.61726i) q^{41} +(6.07183 - 3.50557i) q^{43} +(8.58857 - 3.65113i) q^{45} +(4.14895 - 4.14895i) q^{47} +(-11.8669 - 6.85134i) q^{49} +(6.86643 + 3.34667i) q^{51} -8.33491i q^{53} +(5.51440 - 9.55122i) q^{55} +(-1.80113 + 0.620727i) q^{57} +(1.97653 + 0.529610i) q^{59} +(-4.77501 - 8.27056i) q^{61} +(10.9059 + 8.20890i) q^{63} +(-7.42039 + 8.41074i) q^{65} +(1.42966 + 5.33556i) q^{67} +(-0.197186 - 2.80895i) q^{69} +(1.43147 - 5.34234i) q^{71} +(2.99445 + 2.99445i) q^{73} +(4.53187 + 6.71484i) q^{75} +16.1312 q^{77} -15.4490 q^{79} +(-6.48084 - 6.24490i) q^{81} +(6.38106 + 6.38106i) q^{83} +(-3.55077 + 13.2516i) q^{85} +(-9.20800 + 0.646395i) q^{87} +(-1.98271 - 7.39957i) q^{89} +(-16.0805 - 3.24837i) q^{91} +(-1.53171 + 7.89138i) q^{93} +(-1.71080 - 2.96319i) q^{95} +(-8.75030 - 2.34464i) q^{97} +(-10.5574 - 1.29047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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 0
\(3\) 1.43567 0.968940i 0.828886 0.559418i
\(4\) 0 0
\(5\) 2.19967 + 2.19967i 0.983725 + 0.983725i 0.999870 0.0161451i \(-0.00513938\pi\)
−0.0161451 + 0.999870i \(0.505139\pi\)
\(6\) 0 0
\(7\) −1.17763 + 4.39498i −0.445103 + 1.66115i 0.270562 + 0.962703i \(0.412791\pi\)
−0.715665 + 0.698444i \(0.753876\pi\)
\(8\) 0 0
\(9\) 1.12231 2.78216i 0.374104 0.927387i
\(10\) 0 0
\(11\) −0.917595 3.42451i −0.276665 1.03253i −0.954717 0.297515i \(-0.903842\pi\)
0.678052 0.735014i \(-0.262824\pi\)
\(12\) 0 0
\(13\) 0.225112 + 3.59852i 0.0624348 + 0.998049i
\(14\) 0 0
\(15\) 5.28937 + 1.02666i 1.36571 + 0.265082i
\(16\) 0 0
\(17\) 2.20507 + 3.81929i 0.534808 + 0.926315i 0.999173 + 0.0406707i \(0.0129495\pi\)
−0.464364 + 0.885644i \(0.653717\pi\)
\(18\) 0 0
\(19\) −1.06243 0.284677i −0.243738 0.0653094i 0.134882 0.990862i \(-0.456935\pi\)
−0.378620 + 0.925552i \(0.623601\pi\)
\(20\) 0 0
\(21\) 2.56778 + 7.45081i 0.560335 + 1.62590i
\(22\) 0 0
\(23\) 0.812870 1.40793i 0.169495 0.293574i −0.768747 0.639553i \(-0.779120\pi\)
0.938242 + 0.345978i \(0.112453\pi\)
\(24\) 0 0
\(25\) 4.67714i 0.935428i
\(26\) 0 0
\(27\) −1.08448 5.08172i −0.208707 0.977978i
\(28\) 0 0
\(29\) −4.61533 2.66466i −0.857045 0.494815i 0.00597654 0.999982i \(-0.498098\pi\)
−0.863022 + 0.505167i \(0.831431\pi\)
\(30\) 0 0
\(31\) −3.28177 + 3.28177i −0.589423 + 0.589423i −0.937475 0.348052i \(-0.886843\pi\)
0.348052 + 0.937475i \(0.386843\pi\)
\(32\) 0 0
\(33\) −4.63551 4.02738i −0.806939 0.701077i
\(34\) 0 0
\(35\) −12.2579 + 7.07712i −2.07197 + 1.19625i
\(36\) 0 0
\(37\) 2.75348 0.737792i 0.452669 0.121292i −0.0252790 0.999680i \(-0.508047\pi\)
0.477948 + 0.878388i \(0.341381\pi\)
\(38\) 0 0
\(39\) 3.80993 + 4.94817i 0.610078 + 0.792342i
\(40\) 0 0
\(41\) 9.76774 2.61726i 1.52546 0.408747i 0.603928 0.797039i \(-0.293602\pi\)
0.921536 + 0.388292i \(0.126935\pi\)
\(42\) 0 0
\(43\) 6.07183 3.50557i 0.925946 0.534595i 0.0404187 0.999183i \(-0.487131\pi\)
0.885527 + 0.464588i \(0.153797\pi\)
\(44\) 0 0
\(45\) 8.58857 3.65113i 1.28031 0.544278i
\(46\) 0 0
\(47\) 4.14895 4.14895i 0.605186 0.605186i −0.336498 0.941684i \(-0.609243\pi\)
0.941684 + 0.336498i \(0.109243\pi\)
\(48\) 0 0
\(49\) −11.8669 6.85134i −1.69527 0.978762i
\(50\) 0 0
\(51\) 6.86643 + 3.34667i 0.961492 + 0.468628i
\(52\) 0 0
\(53\) 8.33491i 1.14489i −0.819944 0.572444i \(-0.805995\pi\)
0.819944 0.572444i \(-0.194005\pi\)
\(54\) 0 0
\(55\) 5.51440 9.55122i 0.743561 1.28789i
\(56\) 0 0
\(57\) −1.80113 + 0.620727i −0.238566 + 0.0822173i
\(58\) 0 0
\(59\) 1.97653 + 0.529610i 0.257322 + 0.0689493i 0.385174 0.922844i \(-0.374141\pi\)
−0.127852 + 0.991793i \(0.540808\pi\)
\(60\) 0 0
\(61\) −4.77501 8.27056i −0.611378 1.05894i −0.991008 0.133799i \(-0.957282\pi\)
0.379631 0.925138i \(-0.376051\pi\)
\(62\) 0 0
\(63\) 10.9059 + 8.20890i 1.37401 + 1.03422i
\(64\) 0 0
\(65\) −7.42039 + 8.41074i −0.920387 + 1.04322i
\(66\) 0 0
\(67\) 1.42966 + 5.33556i 0.174661 + 0.651842i 0.996609 + 0.0822804i \(0.0262203\pi\)
−0.821949 + 0.569562i \(0.807113\pi\)
\(68\) 0 0
\(69\) −0.197186 2.80895i −0.0237385 0.338158i
\(70\) 0 0
\(71\) 1.43147 5.34234i 0.169885 0.634019i −0.827482 0.561493i \(-0.810227\pi\)
0.997367 0.0725259i \(-0.0231060\pi\)
\(72\) 0 0
\(73\) 2.99445 + 2.99445i 0.350473 + 0.350473i 0.860286 0.509812i \(-0.170285\pi\)
−0.509812 + 0.860286i \(0.670285\pi\)
\(74\) 0 0
\(75\) 4.53187 + 6.71484i 0.523295 + 0.775363i
\(76\) 0 0
\(77\) 16.1312 1.83833
\(78\) 0 0
\(79\) −15.4490 −1.73815 −0.869077 0.494677i \(-0.835286\pi\)
−0.869077 + 0.494677i \(0.835286\pi\)
\(80\) 0 0
\(81\) −6.48084 6.24490i −0.720093 0.693878i
\(82\) 0 0
\(83\) 6.38106 + 6.38106i 0.700413 + 0.700413i 0.964499 0.264086i \(-0.0850704\pi\)
−0.264086 + 0.964499i \(0.585070\pi\)
\(84\) 0 0
\(85\) −3.55077 + 13.2516i −0.385135 + 1.43734i
\(86\) 0 0
\(87\) −9.20800 + 0.646395i −0.987201 + 0.0693008i
\(88\) 0 0
\(89\) −1.98271 7.39957i −0.210167 0.784353i −0.987812 0.155650i \(-0.950253\pi\)
0.777646 0.628703i \(-0.216414\pi\)
\(90\) 0 0
\(91\) −16.0805 3.24837i −1.68570 0.340521i
\(92\) 0 0
\(93\) −1.53171 + 7.89138i −0.158831 + 0.818298i
\(94\) 0 0
\(95\) −1.71080 2.96319i −0.175525 0.304017i
\(96\) 0 0
\(97\) −8.75030 2.34464i −0.888458 0.238062i −0.214405 0.976745i \(-0.568781\pi\)
−0.674053 + 0.738683i \(0.735448\pi\)
\(98\) 0 0
\(99\) −10.5574 1.29047i −1.06106 0.129697i
\(100\) 0 0
\(101\) 3.52149 6.09939i 0.350401 0.606912i −0.635919 0.771756i \(-0.719379\pi\)
0.986320 + 0.164844i \(0.0527120\pi\)
\(102\) 0 0
\(103\) 7.10076i 0.699658i 0.936813 + 0.349829i \(0.113760\pi\)
−0.936813 + 0.349829i \(0.886240\pi\)
\(104\) 0 0
\(105\) −10.7411 + 22.0376i −1.04822 + 2.15065i
\(106\) 0 0
\(107\) 10.7690 + 6.21749i 1.04108 + 0.601068i 0.920139 0.391592i \(-0.128076\pi\)
0.120941 + 0.992660i \(0.461409\pi\)
\(108\) 0 0
\(109\) 5.09377 5.09377i 0.487895 0.487895i −0.419746 0.907641i \(-0.637881\pi\)
0.907641 + 0.419746i \(0.137881\pi\)
\(110\) 0 0
\(111\) 3.23822 3.72718i 0.307358 0.353769i
\(112\) 0 0
\(113\) −10.4784 + 6.04969i −0.985722 + 0.569107i −0.903993 0.427548i \(-0.859378\pi\)
−0.0817293 + 0.996655i \(0.526044\pi\)
\(114\) 0 0
\(115\) 4.88504 1.30894i 0.455533 0.122060i
\(116\) 0 0
\(117\) 10.2643 + 3.41236i 0.948935 + 0.315473i
\(118\) 0 0
\(119\) −19.3825 + 5.19352i −1.77679 + 0.476089i
\(120\) 0 0
\(121\) −1.35901 + 0.784625i −0.123546 + 0.0713296i
\(122\) 0 0
\(123\) 11.4873 13.2219i 1.03578 1.19218i
\(124\) 0 0
\(125\) 0.710189 0.710189i 0.0635212 0.0635212i
\(126\) 0 0
\(127\) −11.6158 6.70637i −1.03073 0.595094i −0.113539 0.993534i \(-0.536219\pi\)
−0.917195 + 0.398440i \(0.869552\pi\)
\(128\) 0 0
\(129\) 5.32047 10.9161i 0.468441 0.961109i
\(130\) 0 0
\(131\) 10.7616i 0.940244i −0.882601 0.470122i \(-0.844210\pi\)
0.882601 0.470122i \(-0.155790\pi\)
\(132\) 0 0
\(133\) 2.50230 4.33411i 0.216977 0.375815i
\(134\) 0 0
\(135\) 8.79265 13.5636i 0.756750 1.16737i
\(136\) 0 0
\(137\) −18.9042 5.06536i −1.61509 0.432763i −0.665539 0.746363i \(-0.731798\pi\)
−0.949555 + 0.313600i \(0.898465\pi\)
\(138\) 0 0
\(139\) −1.42992 2.47669i −0.121284 0.210070i 0.798990 0.601344i \(-0.205368\pi\)
−0.920274 + 0.391274i \(0.872034\pi\)
\(140\) 0 0
\(141\) 1.93645 9.97661i 0.163078 0.840182i
\(142\) 0 0
\(143\) 12.1166 4.07288i 1.01324 0.340591i
\(144\) 0 0
\(145\) −4.29083 16.0136i −0.356334 1.32986i
\(146\) 0 0
\(147\) −23.6755 + 1.66200i −1.95272 + 0.137080i
\(148\) 0 0
\(149\) −5.07006 + 18.9217i −0.415356 + 1.55013i 0.368766 + 0.929522i \(0.379780\pi\)
−0.784122 + 0.620607i \(0.786886\pi\)
\(150\) 0 0
\(151\) 15.8267 + 15.8267i 1.28796 + 1.28796i 0.936023 + 0.351940i \(0.114478\pi\)
0.351940 + 0.936023i \(0.385522\pi\)
\(152\) 0 0
\(153\) 13.1007 1.84842i 1.05913 0.149436i
\(154\) 0 0
\(155\) −14.4376 −1.15966
\(156\) 0 0
\(157\) 1.15713 0.0923494 0.0461747 0.998933i \(-0.485297\pi\)
0.0461747 + 0.998933i \(0.485297\pi\)
\(158\) 0 0
\(159\) −8.07603 11.9662i −0.640471 0.948982i
\(160\) 0 0
\(161\) 5.23057 + 5.23057i 0.412227 + 0.412227i
\(162\) 0 0
\(163\) 3.58002 13.3608i 0.280409 1.04650i −0.671720 0.740805i \(-0.734444\pi\)
0.952129 0.305696i \(-0.0988891\pi\)
\(164\) 0 0
\(165\) −1.33769 19.0555i −0.104139 1.48347i
\(166\) 0 0
\(167\) 2.53415 + 9.45758i 0.196098 + 0.731849i 0.991980 + 0.126397i \(0.0403412\pi\)
−0.795881 + 0.605453i \(0.792992\pi\)
\(168\) 0 0
\(169\) −12.8986 + 1.62014i −0.992204 + 0.124626i
\(170\) 0 0
\(171\) −1.98439 + 2.63635i −0.151750 + 0.201607i
\(172\) 0 0
\(173\) 2.36780 + 4.10115i 0.180020 + 0.311804i 0.941887 0.335929i \(-0.109050\pi\)
−0.761867 + 0.647734i \(0.775717\pi\)
\(174\) 0 0
\(175\) −20.5559 5.50795i −1.55388 0.416362i
\(176\) 0 0
\(177\) 3.35081 1.15479i 0.251862 0.0867995i
\(178\) 0 0
\(179\) −4.29215 + 7.43422i −0.320810 + 0.555660i −0.980655 0.195742i \(-0.937289\pi\)
0.659845 + 0.751402i \(0.270622\pi\)
\(180\) 0 0
\(181\) 6.64164i 0.493670i 0.969058 + 0.246835i \(0.0793905\pi\)
−0.969058 + 0.246835i \(0.920610\pi\)
\(182\) 0 0
\(183\) −14.8690 7.24712i −1.09915 0.535723i
\(184\) 0 0
\(185\) 7.67966 + 4.43385i 0.564620 + 0.325983i
\(186\) 0 0
\(187\) 11.0559 11.0559i 0.808484 0.808484i
\(188\) 0 0
\(189\) 23.6112 + 1.21815i 1.71746 + 0.0886073i
\(190\) 0 0
\(191\) −6.75249 + 3.89855i −0.488593 + 0.282089i −0.723991 0.689810i \(-0.757694\pi\)
0.235398 + 0.971899i \(0.424361\pi\)
\(192\) 0 0
\(193\) −2.57872 + 0.690967i −0.185621 + 0.0497369i −0.350432 0.936588i \(-0.613965\pi\)
0.164811 + 0.986325i \(0.447299\pi\)
\(194\) 0 0
\(195\) −2.50375 + 19.2650i −0.179298 + 1.37959i
\(196\) 0 0
\(197\) −18.6823 + 5.00590i −1.33106 + 0.356655i −0.853109 0.521733i \(-0.825286\pi\)
−0.477947 + 0.878388i \(0.658619\pi\)
\(198\) 0 0
\(199\) −6.95427 + 4.01505i −0.492975 + 0.284619i −0.725808 0.687898i \(-0.758534\pi\)
0.232833 + 0.972517i \(0.425200\pi\)
\(200\) 0 0
\(201\) 7.22235 + 6.27486i 0.509426 + 0.442594i
\(202\) 0 0
\(203\) 17.1463 17.1463i 1.20343 1.20343i
\(204\) 0 0
\(205\) 27.2430 + 15.7287i 1.90273 + 1.09854i
\(206\) 0 0
\(207\) −3.00480 3.84167i −0.208848 0.267015i
\(208\) 0 0
\(209\) 3.89952i 0.269735i
\(210\) 0 0
\(211\) −2.69364 + 4.66552i −0.185438 + 0.321187i −0.943724 0.330734i \(-0.892704\pi\)
0.758286 + 0.651922i \(0.226037\pi\)
\(212\) 0 0
\(213\) −3.12127 9.05686i −0.213866 0.620566i
\(214\) 0 0
\(215\) 21.0672 + 5.64493i 1.43677 + 0.384981i
\(216\) 0 0
\(217\) −10.5586 18.2880i −0.716764 1.24147i
\(218\) 0 0
\(219\) 7.20048 + 1.39761i 0.486564 + 0.0944415i
\(220\) 0 0
\(221\) −13.2474 + 8.79475i −0.891117 + 0.591599i
\(222\) 0 0
\(223\) −2.18490 8.15417i −0.146312 0.546044i −0.999693 0.0247569i \(-0.992119\pi\)
0.853381 0.521287i \(-0.174548\pi\)
\(224\) 0 0
\(225\) 13.0126 + 5.24920i 0.867504 + 0.349947i
\(226\) 0 0
\(227\) 0.237467 0.886239i 0.0157612 0.0588217i −0.957597 0.288110i \(-0.906973\pi\)
0.973359 + 0.229288i \(0.0736398\pi\)
\(228\) 0 0
\(229\) −2.28432 2.28432i −0.150952 0.150952i 0.627591 0.778543i \(-0.284041\pi\)
−0.778543 + 0.627591i \(0.784041\pi\)
\(230\) 0 0
\(231\) 23.1592 15.6302i 1.52376 1.02839i
\(232\) 0 0
\(233\) −9.30420 −0.609538 −0.304769 0.952426i \(-0.598579\pi\)
−0.304769 + 0.952426i \(0.598579\pi\)
\(234\) 0 0
\(235\) 18.2527 1.19067
\(236\) 0 0
\(237\) −22.1798 + 14.9692i −1.44073 + 0.972354i
\(238\) 0 0
\(239\) −18.5336 18.5336i −1.19884 1.19884i −0.974515 0.224323i \(-0.927983\pi\)
−0.224323 0.974515i \(-0.572017\pi\)
\(240\) 0 0
\(241\) −3.15760 + 11.7843i −0.203399 + 0.759094i 0.786533 + 0.617548i \(0.211874\pi\)
−0.989932 + 0.141546i \(0.954793\pi\)
\(242\) 0 0
\(243\) −15.3553 2.68609i −0.985042 0.172313i
\(244\) 0 0
\(245\) −11.0325 41.1740i −0.704842 2.63051i
\(246\) 0 0
\(247\) 0.785250 3.88725i 0.0499642 0.247340i
\(248\) 0 0
\(249\) 15.3440 + 2.97825i 0.972386 + 0.188739i
\(250\) 0 0
\(251\) 4.56257 + 7.90260i 0.287987 + 0.498808i 0.973329 0.229413i \(-0.0736808\pi\)
−0.685342 + 0.728221i \(0.740347\pi\)
\(252\) 0 0
\(253\) −5.56736 1.49177i −0.350017 0.0937868i
\(254\) 0 0
\(255\) 7.74231 + 22.4655i 0.484842 + 1.40684i
\(256\) 0 0
\(257\) 0.0791658 0.137119i 0.00493823 0.00855326i −0.863546 0.504271i \(-0.831761\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(258\) 0 0
\(259\) 12.9703i 0.805937i
\(260\) 0 0
\(261\) −12.5934 + 9.85001i −0.779509 + 0.609700i
\(262\) 0 0
\(263\) −3.05457 1.76356i −0.188353 0.108746i 0.402858 0.915262i \(-0.368017\pi\)
−0.591211 + 0.806517i \(0.701350\pi\)
\(264\) 0 0
\(265\) 18.3341 18.3341i 1.12625 1.12625i
\(266\) 0 0
\(267\) −10.0163 8.70223i −0.612985 0.532568i
\(268\) 0 0
\(269\) 16.2959 9.40842i 0.993576 0.573641i 0.0872346 0.996188i \(-0.472197\pi\)
0.906341 + 0.422546i \(0.138864\pi\)
\(270\) 0 0
\(271\) −1.95323 + 0.523366i −0.118650 + 0.0317922i −0.317656 0.948206i \(-0.602896\pi\)
0.199005 + 0.979998i \(0.436229\pi\)
\(272\) 0 0
\(273\) −26.2338 + 10.9175i −1.58774 + 0.660755i
\(274\) 0 0
\(275\) 16.0169 4.29172i 0.965856 0.258800i
\(276\) 0 0
\(277\) 15.1882 8.76890i 0.912569 0.526872i 0.0313123 0.999510i \(-0.490031\pi\)
0.881257 + 0.472638i \(0.156698\pi\)
\(278\) 0 0
\(279\) 5.44724 + 12.8136i 0.326118 + 0.767128i
\(280\) 0 0
\(281\) 13.8319 13.8319i 0.825142 0.825142i −0.161698 0.986840i \(-0.551697\pi\)
0.986840 + 0.161698i \(0.0516972\pi\)
\(282\) 0 0
\(283\) 15.2851 + 8.82488i 0.908607 + 0.524585i 0.879983 0.475006i \(-0.157554\pi\)
0.0286245 + 0.999590i \(0.490887\pi\)
\(284\) 0 0
\(285\) −5.32731 2.59651i −0.315562 0.153804i
\(286\) 0 0
\(287\) 46.0112i 2.71595i
\(288\) 0 0
\(289\) −1.22467 + 2.12120i −0.0720396 + 0.124776i
\(290\) 0 0
\(291\) −14.8344 + 5.11239i −0.869607 + 0.299693i
\(292\) 0 0
\(293\) −12.2454 3.28114i −0.715383 0.191686i −0.117272 0.993100i \(-0.537415\pi\)
−0.598111 + 0.801414i \(0.704082\pi\)
\(294\) 0 0
\(295\) 3.18275 + 5.51269i 0.185307 + 0.320961i
\(296\) 0 0
\(297\) −16.4073 + 8.37676i −0.952048 + 0.486069i
\(298\) 0 0
\(299\) 5.24945 + 2.60818i 0.303584 + 0.150835i
\(300\) 0 0
\(301\) 8.25655 + 30.8139i 0.475900 + 1.77608i
\(302\) 0 0
\(303\) −0.854244 12.1688i −0.0490751 0.699082i
\(304\) 0 0
\(305\) 7.68908 28.6960i 0.440275 1.64313i
\(306\) 0 0
\(307\) 6.09233 + 6.09233i 0.347707 + 0.347707i 0.859255 0.511548i \(-0.170928\pi\)
−0.511548 + 0.859255i \(0.670928\pi\)
\(308\) 0 0
\(309\) 6.88021 + 10.1944i 0.391401 + 0.579937i
\(310\) 0 0
\(311\) 9.87859 0.560164 0.280082 0.959976i \(-0.409638\pi\)
0.280082 + 0.959976i \(0.409638\pi\)
\(312\) 0 0
\(313\) 17.2222 0.973456 0.486728 0.873554i \(-0.338190\pi\)
0.486728 + 0.873554i \(0.338190\pi\)
\(314\) 0 0
\(315\) 5.93248 + 42.0463i 0.334257 + 2.36904i
\(316\) 0 0
\(317\) 0.00884596 + 0.00884596i 0.000496839 + 0.000496839i 0.707355 0.706858i \(-0.249888\pi\)
−0.706858 + 0.707355i \(0.749888\pi\)
\(318\) 0 0
\(319\) −4.89016 + 18.2503i −0.273796 + 1.02182i
\(320\) 0 0
\(321\) 21.4852 1.50824i 1.19918 0.0841819i
\(322\) 0 0
\(323\) −1.25547 4.68546i −0.0698560 0.260706i
\(324\) 0 0
\(325\) −16.8308 + 1.05288i −0.933603 + 0.0584032i
\(326\) 0 0
\(327\) 2.37743 12.2486i 0.131472 0.677346i
\(328\) 0 0
\(329\) 13.3486 + 23.1205i 0.735933 + 1.27467i
\(330\) 0 0
\(331\) −0.360355 0.0965567i −0.0198069 0.00530724i 0.248902 0.968529i \(-0.419930\pi\)
−0.268709 + 0.963221i \(0.586597\pi\)
\(332\) 0 0
\(333\) 1.03760 8.48865i 0.0568602 0.465175i
\(334\) 0 0
\(335\) −8.59171 + 14.8813i −0.469415 + 0.813051i
\(336\) 0 0
\(337\) 22.3015i 1.21484i 0.794381 + 0.607420i \(0.207796\pi\)
−0.794381 + 0.607420i \(0.792204\pi\)
\(338\) 0 0
\(339\) −9.18172 + 18.8383i −0.498683 + 1.02316i
\(340\) 0 0
\(341\) 14.2498 + 8.22711i 0.771669 + 0.445523i
\(342\) 0 0
\(343\) 21.5648 21.5648i 1.16439 1.16439i
\(344\) 0 0
\(345\) 5.74503 6.61253i 0.309302 0.356006i
\(346\) 0 0
\(347\) −0.801179 + 0.462561i −0.0430095 + 0.0248316i −0.521351 0.853343i \(-0.674572\pi\)
0.478341 + 0.878174i \(0.341238\pi\)
\(348\) 0 0
\(349\) −16.4270 + 4.40159i −0.879315 + 0.235612i −0.670112 0.742260i \(-0.733754\pi\)
−0.209204 + 0.977872i \(0.567087\pi\)
\(350\) 0 0
\(351\) 18.0425 5.04646i 0.963040 0.269360i
\(352\) 0 0
\(353\) 1.31686 0.352851i 0.0700893 0.0187804i −0.223604 0.974680i \(-0.571782\pi\)
0.293693 + 0.955900i \(0.405116\pi\)
\(354\) 0 0
\(355\) 14.9002 8.60262i 0.790819 0.456580i
\(356\) 0 0
\(357\) −22.7947 + 26.2367i −1.20642 + 1.38859i
\(358\) 0 0
\(359\) 23.2669 23.2669i 1.22798 1.22798i 0.263256 0.964726i \(-0.415204\pi\)
0.964726 0.263256i \(-0.0847963\pi\)
\(360\) 0 0
\(361\) −15.4068 8.89510i −0.810883 0.468163i
\(362\) 0 0
\(363\) −1.19084 + 2.44326i −0.0625029 + 0.128238i
\(364\) 0 0
\(365\) 13.1736i 0.689539i
\(366\) 0 0
\(367\) −8.66640 + 15.0106i −0.452382 + 0.783549i −0.998533 0.0541374i \(-0.982759\pi\)
0.546151 + 0.837687i \(0.316092\pi\)
\(368\) 0 0
\(369\) 3.68081 30.1128i 0.191615 1.56761i
\(370\) 0 0
\(371\) 36.6318 + 9.81545i 1.90183 + 0.509593i
\(372\) 0 0
\(373\) 1.40911 + 2.44066i 0.0729611 + 0.126372i 0.900198 0.435481i \(-0.143422\pi\)
−0.827237 + 0.561854i \(0.810088\pi\)
\(374\) 0 0
\(375\) 0.331468 1.70773i 0.0171169 0.0881867i
\(376\) 0 0
\(377\) 8.54986 17.2082i 0.440340 0.886267i
\(378\) 0 0
\(379\) 7.23342 + 26.9955i 0.371556 + 1.38667i 0.858312 + 0.513128i \(0.171513\pi\)
−0.486756 + 0.873538i \(0.661820\pi\)
\(380\) 0 0
\(381\) −23.1745 + 1.62684i −1.18727 + 0.0833453i
\(382\) 0 0
\(383\) −1.58764 + 5.92516i −0.0811248 + 0.302762i −0.994552 0.104240i \(-0.966759\pi\)
0.913427 + 0.407002i \(0.133426\pi\)
\(384\) 0 0
\(385\) 35.4835 + 35.4835i 1.80841 + 1.80841i
\(386\) 0 0
\(387\) −2.93859 20.8272i −0.149377 1.05870i
\(388\) 0 0
\(389\) 34.3070 1.73943 0.869717 0.493550i \(-0.164301\pi\)
0.869717 + 0.493550i \(0.164301\pi\)
\(390\) 0 0
\(391\) 7.16974 0.362589
\(392\) 0 0
\(393\) −10.4273 15.4501i −0.525989 0.779355i
\(394\) 0 0
\(395\) −33.9829 33.9829i −1.70986 1.70986i
\(396\) 0 0
\(397\) 2.44015 9.10677i 0.122468 0.457056i −0.877269 0.479999i \(-0.840637\pi\)
0.999737 + 0.0229433i \(0.00730371\pi\)
\(398\) 0 0
\(399\) −0.607009 8.64694i −0.0303885 0.432888i
\(400\) 0 0
\(401\) 7.09363 + 26.4738i 0.354239 + 1.32204i 0.881440 + 0.472297i \(0.156575\pi\)
−0.527201 + 0.849741i \(0.676758\pi\)
\(402\) 0 0
\(403\) −12.5483 11.0707i −0.625073 0.551472i
\(404\) 0 0
\(405\) −0.518985 27.9925i −0.0257886 1.39096i
\(406\) 0 0
\(407\) −5.05315 8.75232i −0.250476 0.433836i
\(408\) 0 0
\(409\) 13.8641 + 3.71487i 0.685535 + 0.183689i 0.584743 0.811219i \(-0.301195\pi\)
0.100793 + 0.994907i \(0.467862\pi\)
\(410\) 0 0
\(411\) −32.0483 + 11.0448i −1.58082 + 0.544801i
\(412\) 0 0
\(413\) −4.65525 + 8.06313i −0.229070 + 0.396761i
\(414\) 0 0
\(415\) 28.0725i 1.37803i
\(416\) 0 0
\(417\) −4.45265 2.17021i −0.218047 0.106276i
\(418\) 0 0
\(419\) −27.2181 15.7144i −1.32969 0.767697i −0.344438 0.938809i \(-0.611931\pi\)
−0.985252 + 0.171112i \(0.945264\pi\)
\(420\) 0 0
\(421\) 15.8765 15.8765i 0.773773 0.773773i −0.204991 0.978764i \(-0.565717\pi\)
0.978764 + 0.204991i \(0.0657165\pi\)
\(422\) 0 0
\(423\) −6.88663 16.1994i −0.334839 0.787644i
\(424\) 0 0
\(425\) −17.8634 + 10.3134i −0.866501 + 0.500274i
\(426\) 0 0
\(427\) 41.9722 11.2464i 2.03118 0.544252i
\(428\) 0 0
\(429\) 13.4491 17.5876i 0.649328 0.849136i
\(430\) 0 0
\(431\) 12.3582 3.31137i 0.595274 0.159503i 0.0514116 0.998678i \(-0.483628\pi\)
0.543862 + 0.839174i \(0.316961\pi\)
\(432\) 0 0
\(433\) 14.1339 8.16020i 0.679231 0.392154i −0.120335 0.992733i \(-0.538397\pi\)
0.799565 + 0.600579i \(0.205063\pi\)
\(434\) 0 0
\(435\) −21.6765 18.8327i −1.03931 0.902961i
\(436\) 0 0
\(437\) −1.26442 + 1.26442i −0.0604855 + 0.0604855i
\(438\) 0 0
\(439\) 20.2300 + 11.6798i 0.965525 + 0.557446i 0.897869 0.440262i \(-0.145115\pi\)
0.0676563 + 0.997709i \(0.478448\pi\)
\(440\) 0 0
\(441\) −32.3798 + 25.3262i −1.54190 + 1.20601i
\(442\) 0 0
\(443\) 19.6001i 0.931228i −0.884988 0.465614i \(-0.845834\pi\)
0.884988 0.465614i \(-0.154166\pi\)
\(444\) 0 0
\(445\) 11.9153 20.6380i 0.564841 0.978333i
\(446\) 0 0
\(447\) 11.0551 + 32.0780i 0.522887 + 1.51724i
\(448\) 0 0
\(449\) −11.4364 3.06438i −0.539717 0.144617i −0.0213456 0.999772i \(-0.506795\pi\)
−0.518372 + 0.855155i \(0.673462\pi\)
\(450\) 0 0
\(451\) −17.9256 31.0481i −0.844086 1.46200i
\(452\) 0 0
\(453\) 38.0572 + 7.38686i 1.78808 + 0.347065i
\(454\) 0 0
\(455\) −28.2266 42.5172i −1.32328 1.99324i
\(456\) 0 0
\(457\) 8.92124 + 33.2945i 0.417318 + 1.55745i 0.780147 + 0.625596i \(0.215144\pi\)
−0.362830 + 0.931856i \(0.618189\pi\)
\(458\) 0 0
\(459\) 17.0173 15.3475i 0.794297 0.716359i
\(460\) 0 0
\(461\) −4.84992 + 18.1002i −0.225883 + 0.843008i 0.756165 + 0.654381i \(0.227071\pi\)
−0.982049 + 0.188628i \(0.939596\pi\)
\(462\) 0 0
\(463\) −16.7806 16.7806i −0.779860 0.779860i 0.199947 0.979807i \(-0.435923\pi\)
−0.979807 + 0.199947i \(0.935923\pi\)
\(464\) 0 0
\(465\) −20.7277 + 13.9892i −0.961225 + 0.648734i
\(466\) 0 0
\(467\) −30.7628 −1.42353 −0.711767 0.702416i \(-0.752105\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(468\) 0 0
\(469\) −25.1333 −1.16055
\(470\) 0 0
\(471\) 1.66127 1.12119i 0.0765471 0.0516619i
\(472\) 0 0
\(473\) −17.5764 17.5764i −0.808162 0.808162i
\(474\) 0 0
\(475\) 1.33147 4.96913i 0.0610922 0.227999i
\(476\) 0 0
\(477\) −23.1891 9.35436i −1.06175 0.428307i
\(478\) 0 0
\(479\) 4.38660 + 16.3710i 0.200429 + 0.748010i 0.990794 + 0.135375i \(0.0432239\pi\)
−0.790366 + 0.612635i \(0.790109\pi\)
\(480\) 0 0
\(481\) 3.27480 + 9.74235i 0.149318 + 0.444213i
\(482\) 0 0
\(483\) 12.5775 + 2.44128i 0.572296 + 0.111082i
\(484\) 0 0
\(485\) −14.0904 24.4053i −0.639811 1.10819i
\(486\) 0 0
\(487\) −27.0620 7.25125i −1.22630 0.328585i −0.413161 0.910658i \(-0.635575\pi\)
−0.813137 + 0.582073i \(0.802242\pi\)
\(488\) 0 0
\(489\) −7.80610 22.6506i −0.353004 1.02430i
\(490\) 0 0
\(491\) −6.45173 + 11.1747i −0.291162 + 0.504308i −0.974085 0.226183i \(-0.927375\pi\)
0.682922 + 0.730491i \(0.260709\pi\)
\(492\) 0 0
\(493\) 23.5031i 1.05852i
\(494\) 0 0
\(495\) −20.3842 26.0614i −0.916200 1.17137i
\(496\) 0 0
\(497\) 21.7937 + 12.5826i 0.977582 + 0.564407i
\(498\) 0 0
\(499\) 2.22600 2.22600i 0.0996495 0.0996495i −0.655524 0.755174i \(-0.727552\pi\)
0.755174 + 0.655524i \(0.227552\pi\)
\(500\) 0 0
\(501\) 12.8020 + 11.1225i 0.571953 + 0.496919i
\(502\) 0 0
\(503\) −3.89079 + 2.24635i −0.173482 + 0.100160i −0.584226 0.811591i \(-0.698602\pi\)
0.410745 + 0.911750i \(0.365269\pi\)
\(504\) 0 0
\(505\) 21.1628 5.67056i 0.941733 0.252336i
\(506\) 0 0
\(507\) −16.9484 + 14.8240i −0.752706 + 0.658357i
\(508\) 0 0
\(509\) 22.9448 6.14805i 1.01701 0.272508i 0.288456 0.957493i \(-0.406858\pi\)
0.728556 + 0.684986i \(0.240192\pi\)
\(510\) 0 0
\(511\) −16.6869 + 9.63418i −0.738185 + 0.426191i
\(512\) 0 0
\(513\) −0.294472 + 5.70769i −0.0130012 + 0.252001i
\(514\) 0 0
\(515\) −15.6194 + 15.6194i −0.688271 + 0.688271i
\(516\) 0 0
\(517\) −18.0152 10.4011i −0.792306 0.457438i
\(518\) 0 0
\(519\) 7.37314 + 3.59365i 0.323645 + 0.157744i
\(520\) 0 0
\(521\) 9.05417i 0.396670i −0.980134 0.198335i \(-0.936447\pi\)
0.980134 0.198335i \(-0.0635534\pi\)
\(522\) 0 0
\(523\) 14.6521 25.3781i 0.640691 1.10971i −0.344588 0.938754i \(-0.611981\pi\)
0.985279 0.170955i \(-0.0546852\pi\)
\(524\) 0 0
\(525\) −34.8485 + 12.0099i −1.52091 + 0.524153i
\(526\) 0 0
\(527\) −19.7706 5.29751i −0.861219 0.230763i
\(528\) 0 0
\(529\) 10.1785 + 17.6297i 0.442543 + 0.766507i
\(530\) 0 0
\(531\) 3.69174 4.90464i 0.160208 0.212843i
\(532\) 0 0
\(533\) 11.6171 + 34.5602i 0.503191 + 1.49697i
\(534\) 0 0
\(535\) 10.0119 + 37.3648i 0.432851 + 1.61542i
\(536\) 0 0
\(537\) 1.04119 + 14.8319i 0.0449308 + 0.640045i
\(538\) 0 0
\(539\) −12.5735 + 46.9249i −0.541579 + 2.02120i
\(540\) 0 0
\(541\) −29.7524 29.7524i −1.27916 1.27916i −0.941141 0.338015i \(-0.890244\pi\)
−0.338015 0.941141i \(-0.609756\pi\)
\(542\) 0 0
\(543\) 6.43535 + 9.53523i 0.276167 + 0.409196i
\(544\) 0 0
\(545\) 22.4093 0.959909
\(546\) 0 0
\(547\) 9.72797 0.415938 0.207969 0.978135i \(-0.433315\pi\)
0.207969 + 0.978135i \(0.433315\pi\)
\(548\) 0 0
\(549\) −28.3691 + 4.00271i −1.21076 + 0.170831i
\(550\) 0 0
\(551\) 4.14489 + 4.14489i 0.176578 + 0.176578i
\(552\) 0 0
\(553\) 18.1933 67.8983i 0.773657 2.88733i
\(554\) 0 0
\(555\) 15.3216 1.07557i 0.650366 0.0456553i
\(556\) 0 0
\(557\) 2.30023 + 8.58457i 0.0974638 + 0.363740i 0.997381 0.0723199i \(-0.0230402\pi\)
−0.899918 + 0.436060i \(0.856374\pi\)
\(558\) 0 0
\(559\) 13.9817 + 21.0604i 0.591363 + 0.890762i
\(560\) 0 0
\(561\) 5.16013 26.5850i 0.217861 1.12242i
\(562\) 0 0
\(563\) 0.952635 + 1.65001i 0.0401488 + 0.0695398i 0.885402 0.464827i \(-0.153883\pi\)
−0.845253 + 0.534367i \(0.820550\pi\)
\(564\) 0 0
\(565\) −36.3564 9.74166i −1.52952 0.409835i
\(566\) 0 0
\(567\) 35.0782 21.1290i 1.47315 0.887333i
\(568\) 0 0
\(569\) 5.02931 8.71103i 0.210840 0.365185i −0.741138 0.671353i \(-0.765713\pi\)
0.951978 + 0.306168i \(0.0990468\pi\)
\(570\) 0 0
\(571\) 20.2231i 0.846309i −0.906057 0.423155i \(-0.860923\pi\)
0.906057 0.423155i \(-0.139077\pi\)
\(572\) 0 0
\(573\) −5.91690 + 12.1398i −0.247182 + 0.507147i
\(574\) 0 0
\(575\) 6.58509 + 3.80191i 0.274617 + 0.158550i
\(576\) 0 0
\(577\) −7.71564 + 7.71564i −0.321206 + 0.321206i −0.849230 0.528024i \(-0.822933\pi\)
0.528024 + 0.849230i \(0.322933\pi\)
\(578\) 0 0
\(579\) −3.03270 + 3.49063i −0.126035 + 0.145066i
\(580\) 0 0
\(581\) −35.5592 + 20.5301i −1.47524 + 0.851733i
\(582\) 0 0
\(583\) −28.5430 + 7.64807i −1.18213 + 0.316751i
\(584\) 0 0
\(585\) 15.0720 + 30.0842i 0.623152 + 1.24383i
\(586\) 0 0
\(587\) −1.87678 + 0.502881i −0.0774630 + 0.0207561i −0.297342 0.954771i \(-0.596100\pi\)
0.219879 + 0.975527i \(0.429434\pi\)
\(588\) 0 0
\(589\) 4.42089 2.55240i 0.182159 0.105170i
\(590\) 0 0
\(591\) −21.9712 + 25.2888i −0.903774 + 1.04024i
\(592\) 0 0
\(593\) −23.1037 + 23.1037i −0.948756 + 0.948756i −0.998750 0.0499940i \(-0.984080\pi\)
0.0499940 + 0.998750i \(0.484080\pi\)
\(594\) 0 0
\(595\) −54.0592 31.2111i −2.21621 1.27953i
\(596\) 0 0
\(597\) −6.09371 + 12.5026i −0.249399 + 0.511696i
\(598\) 0 0
\(599\) 8.98472i 0.367106i 0.983010 + 0.183553i \(0.0587598\pi\)
−0.983010 + 0.183553i \(0.941240\pi\)
\(600\) 0 0
\(601\) −16.6602 + 28.8563i −0.679583 + 1.17707i 0.295523 + 0.955336i \(0.404506\pi\)
−0.975107 + 0.221737i \(0.928827\pi\)
\(602\) 0 0
\(603\) 16.4489 + 2.01062i 0.669851 + 0.0818786i
\(604\) 0 0
\(605\) −4.71530 1.26346i −0.191704 0.0513670i
\(606\) 0 0
\(607\) −22.1672 38.3948i −0.899740 1.55840i −0.827826 0.560984i \(-0.810423\pi\)
−0.0719135 0.997411i \(-0.522911\pi\)
\(608\) 0 0
\(609\) 8.00273 41.2302i 0.324287 1.67073i
\(610\) 0 0
\(611\) 15.8640 + 13.9961i 0.641790 + 0.566221i
\(612\) 0 0
\(613\) 11.5021 + 42.9265i 0.464566 + 1.73379i 0.658323 + 0.752736i \(0.271266\pi\)
−0.193756 + 0.981050i \(0.562067\pi\)
\(614\) 0 0
\(615\) 54.3522 3.81549i 2.19169 0.153855i
\(616\) 0 0
\(617\) −2.01395 + 7.51616i −0.0810785 + 0.302589i −0.994543 0.104330i \(-0.966730\pi\)
0.913464 + 0.406919i \(0.133397\pi\)
\(618\) 0 0
\(619\) 3.82416 + 3.82416i 0.153706 + 0.153706i 0.779771 0.626065i \(-0.215336\pi\)
−0.626065 + 0.779771i \(0.715336\pi\)
\(620\) 0 0
\(621\) −8.03626 2.60391i −0.322484 0.104491i
\(622\) 0 0
\(623\) 34.8559 1.39647
\(624\) 0 0
\(625\) 26.5101 1.06040
\(626\) 0 0
\(627\) 3.77840 + 5.59843i 0.150895 + 0.223580i
\(628\) 0 0
\(629\) 8.88946 + 8.88946i 0.354446 + 0.354446i
\(630\) 0 0
\(631\) 4.24796 15.8536i 0.169109 0.631122i −0.828372 0.560179i \(-0.810732\pi\)
0.997480 0.0709434i \(-0.0226010\pi\)
\(632\) 0 0
\(633\) 0.653424 + 9.30812i 0.0259713 + 0.369965i
\(634\) 0 0
\(635\) −10.7991 40.3028i −0.428549 1.59937i
\(636\) 0 0
\(637\) 21.9833 44.2454i 0.871009 1.75307i
\(638\) 0 0
\(639\) −13.2567 9.97835i −0.524426 0.394738i
\(640\) 0 0
\(641\) −24.3557 42.1853i −0.961993 1.66622i −0.717487 0.696572i \(-0.754708\pi\)
−0.244506 0.969648i \(-0.578626\pi\)
\(642\) 0 0
\(643\) 16.3066 + 4.36934i 0.643069 + 0.172310i 0.565593 0.824684i \(-0.308647\pi\)
0.0774759 + 0.996994i \(0.475314\pi\)
\(644\) 0 0
\(645\) 35.7152 12.3086i 1.40628 0.484649i
\(646\) 0 0
\(647\) −10.9410 + 18.9504i −0.430137 + 0.745018i −0.996885 0.0788727i \(-0.974868\pi\)
0.566748 + 0.823891i \(0.308201\pi\)
\(648\) 0 0
\(649\) 7.25461i 0.284769i
\(650\) 0 0
\(651\) −32.8787 16.0250i −1.28862 0.628068i
\(652\) 0 0
\(653\) 19.2265 + 11.1004i 0.752392 + 0.434393i 0.826557 0.562852i \(-0.190296\pi\)
−0.0741658 + 0.997246i \(0.523629\pi\)
\(654\) 0 0
\(655\) 23.6720 23.6720i 0.924941 0.924941i
\(656\) 0 0
\(657\) 11.6917 4.97033i 0.456138 0.193911i
\(658\) 0 0
\(659\) 37.6857 21.7578i 1.46803 0.847565i 0.468667 0.883375i \(-0.344734\pi\)
0.999359 + 0.0358100i \(0.0114011\pi\)
\(660\) 0 0
\(661\) −5.55235 + 1.48775i −0.215961 + 0.0578667i −0.365177 0.930938i \(-0.618992\pi\)
0.149216 + 0.988805i \(0.452325\pi\)
\(662\) 0 0
\(663\) −10.4974 + 25.4623i −0.407683 + 0.988875i
\(664\) 0 0
\(665\) 15.0379 4.02939i 0.583144 0.156253i
\(666\) 0 0
\(667\) −7.50332 + 4.33205i −0.290530 + 0.167738i
\(668\) 0 0
\(669\) −11.0377 9.58968i −0.426743 0.370759i
\(670\) 0 0
\(671\) −23.9411 + 23.9411i −0.924236 + 0.924236i
\(672\) 0 0
\(673\) −19.1318 11.0458i −0.737478 0.425783i 0.0836738 0.996493i \(-0.473335\pi\)
−0.821152 + 0.570710i \(0.806668\pi\)
\(674\) 0 0
\(675\) 23.7679 5.07224i 0.914828 0.195231i
\(676\) 0 0
\(677\) 29.1088i 1.11874i −0.828917 0.559371i \(-0.811043\pi\)
0.828917 0.559371i \(-0.188957\pi\)
\(678\) 0 0
\(679\) 20.6093 35.6963i 0.790911 1.36990i
\(680\) 0 0
\(681\) −0.517787 1.50244i −0.0198416 0.0575736i
\(682\) 0 0
\(683\) −19.8514 5.31917i −0.759593 0.203532i −0.141824 0.989892i \(-0.545297\pi\)
−0.617769 + 0.786360i \(0.711963\pi\)
\(684\) 0 0
\(685\) −30.4409 52.7252i −1.16309 2.01453i
\(686\) 0 0
\(687\) −5.49290 1.06617i −0.209567 0.0406768i
\(688\) 0 0
\(689\) 29.9933 1.87629i 1.14265 0.0714808i
\(690\) 0 0
\(691\) 7.53183 + 28.1092i 0.286524 + 1.06932i 0.947718 + 0.319109i \(0.103383\pi\)
−0.661194 + 0.750215i \(0.729950\pi\)
\(692\) 0 0
\(693\) 18.1043 44.8797i 0.687724 1.70484i
\(694\) 0 0
\(695\) 2.30256 8.59325i 0.0873409 0.325961i
\(696\) 0 0
\(697\) 31.5346 + 31.5346i 1.19446 + 1.19446i
\(698\) 0 0
\(699\) −13.3578 + 9.01521i −0.505238 + 0.340986i
\(700\) 0 0
\(701\) −47.9676 −1.81171 −0.905855 0.423588i \(-0.860770\pi\)
−0.905855 + 0.423588i \(0.860770\pi\)
\(702\) 0 0
\(703\) −3.13541 −0.118254
\(704\) 0 0
\(705\) 26.2048 17.6857i 0.986932 0.666083i
\(706\) 0 0
\(707\) 22.6597 + 22.6597i 0.852206 + 0.852206i
\(708\) 0 0
\(709\) −13.0177 + 48.5829i −0.488891 + 1.82457i 0.0729667 + 0.997334i \(0.476753\pi\)
−0.561858 + 0.827234i \(0.689913\pi\)
\(710\) 0 0
\(711\) −17.3386 + 42.9817i −0.650250 + 1.61194i
\(712\) 0 0
\(713\) 1.95285 + 7.28815i 0.0731350 + 0.272943i
\(714\) 0 0
\(715\) 35.6116 + 17.6936i 1.33180 + 0.661702i
\(716\) 0 0
\(717\) −44.5661 8.65023i −1.66435 0.323049i
\(718\) 0 0
\(719\) −4.43706 7.68521i −0.165474 0.286610i 0.771349 0.636412i \(-0.219582\pi\)
−0.936824 + 0.349802i \(0.886249\pi\)
\(720\) 0 0
\(721\) −31.2077 8.36208i −1.16224 0.311420i
\(722\) 0 0
\(723\) 6.88501 + 19.9779i 0.256056 + 0.742987i
\(724\) 0 0
\(725\) 12.4630 21.5865i 0.462864 0.801704i
\(726\) 0 0
\(727\) 11.4138i 0.423315i 0.977344 + 0.211658i \(0.0678861\pi\)
−0.977344 + 0.211658i \(0.932114\pi\)
\(728\) 0 0
\(729\) −24.6478 + 11.0220i −0.912882 + 0.408223i
\(730\) 0 0
\(731\) 26.7776 + 15.4601i 0.990407 + 0.571812i
\(732\) 0 0
\(733\) −14.4825 + 14.4825i −0.534923 + 0.534923i −0.922033 0.387110i \(-0.873473\pi\)
0.387110 + 0.922033i \(0.373473\pi\)
\(734\) 0 0
\(735\) −55.7342 48.4225i −2.05579 1.78609i
\(736\) 0 0
\(737\) 16.9598 9.79176i 0.624723 0.360684i
\(738\) 0 0
\(739\) −35.8764 + 9.61305i −1.31973 + 0.353622i −0.848879 0.528588i \(-0.822722\pi\)
−0.470856 + 0.882210i \(0.656055\pi\)
\(740\) 0 0
\(741\) −2.63915 6.34168i −0.0969517 0.232967i
\(742\) 0 0
\(743\) −12.1935 + 3.26724i −0.447337 + 0.119864i −0.475453 0.879741i \(-0.657716\pi\)
0.0281161 + 0.999605i \(0.491049\pi\)
\(744\) 0 0
\(745\) −52.7741 + 30.4692i −1.93350 + 1.11630i
\(746\) 0 0
\(747\) 24.9147 10.5916i 0.911581 0.387527i
\(748\) 0 0
\(749\) −40.0077 + 40.0077i −1.46185 + 1.46185i
\(750\) 0 0
\(751\) 2.30561 + 1.33114i 0.0841328 + 0.0485741i 0.541476 0.840716i \(-0.317866\pi\)
−0.457343 + 0.889290i \(0.651199\pi\)
\(752\) 0 0
\(753\) 14.2075 + 6.92469i 0.517750 + 0.252350i
\(754\) 0 0
\(755\) 69.6274i 2.53400i
\(756\) 0 0
\(757\) −4.12709 + 7.14833i −0.150002 + 0.259810i −0.931228 0.364438i \(-0.881261\pi\)
0.781226 + 0.624248i \(0.214595\pi\)
\(758\) 0 0
\(759\) −9.43834 + 3.25275i −0.342590 + 0.118067i
\(760\) 0 0
\(761\) −17.6088 4.71825i −0.638317 0.171037i −0.0748761 0.997193i \(-0.523856\pi\)
−0.563441 + 0.826156i \(0.690523\pi\)
\(762\) 0 0
\(763\) 16.3884 + 28.3856i 0.593302 + 1.02763i
\(764\) 0 0
\(765\) 32.8831 + 24.7513i 1.18889 + 0.894884i
\(766\) 0 0
\(767\) −1.46087 + 7.23180i −0.0527489 + 0.261125i
\(768\) 0 0
\(769\) 1.20203 + 4.48602i 0.0433462 + 0.161770i 0.984206 0.177025i \(-0.0566473\pi\)
−0.940860 + 0.338795i \(0.889981\pi\)
\(770\) 0 0
\(771\) −0.0192041 0.273565i −0.000691618 0.00985221i
\(772\) 0 0
\(773\) 4.06155 15.1579i 0.146084 0.545193i −0.853621 0.520895i \(-0.825598\pi\)
0.999705 0.0242978i \(-0.00773498\pi\)
\(774\) 0 0
\(775\) −15.3493 15.3493i −0.551362 0.551362i
\(776\) 0 0
\(777\) 12.5675 + 18.6211i 0.450855 + 0.668030i
\(778\) 0 0
\(779\) −11.1226 −0.398508
\(780\) 0 0
\(781\) −19.6084 −0.701644
\(782\) 0 0
\(783\) −8.53586 + 26.3436i −0.305047 + 0.941443i
\(784\) 0 0
\(785\) 2.54532 + 2.54532i 0.0908464 + 0.0908464i
\(786\) 0 0
\(787\) −12.6603 + 47.2487i −0.451290 + 1.68424i 0.247483 + 0.968892i \(0.420396\pi\)
−0.698773 + 0.715343i \(0.746270\pi\)
\(788\) 0 0
\(789\) −6.09415 + 0.427805i −0.216957 + 0.0152303i
\(790\) 0 0
\(791\) −14.2486 53.1765i −0.506622 1.89074i
\(792\) 0 0
\(793\) 28.6869 19.0448i 1.01870 0.676299i
\(794\) 0 0
\(795\) 8.55712 44.0864i 0.303490 1.56358i
\(796\) 0 0
\(797\) −22.4830 38.9417i