Properties

Label 1323.2.h.h.226.2
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.h.802.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 + 1.09837i) q^{5} -1.60248 q^{8} +O(q^{10})\) \(q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 + 1.09837i) q^{5} -1.60248 q^{8} +(-1.38010 - 2.39040i) q^{10} +(-2.73867 + 4.74351i) q^{11} +(2.37268 - 4.10960i) q^{13} -1.98516 q^{16} +(-2.40822 - 4.17116i) q^{17} +(-2.69059 + 4.66025i) q^{19} +(1.73523 + 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} +(-2.58816 - 4.48282i) q^{23} +(1.69572 - 2.93707i) q^{25} +(-5.16368 + 8.94376i) q^{26} +(-2.01656 - 3.49278i) q^{29} -1.46419 q^{31} +7.52529 q^{32} +(5.24103 + 9.07773i) q^{34} +(-0.959170 + 1.66133i) q^{37} +(5.85557 - 10.1421i) q^{38} +(-1.01621 - 1.76012i) q^{40} +(1.94808 - 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} +(-7.49389 + 12.9798i) q^{44} +(5.63263 + 9.75600i) q^{46} -3.15546 q^{47} +(-3.69042 + 6.39199i) q^{50} +(6.49243 - 11.2452i) q^{52} +(-3.57149 - 6.18601i) q^{53} -6.94684 q^{55} +(4.38866 + 7.60138i) q^{58} -0.308683 q^{59} +10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} +6.01848 q^{65} +4.47310 q^{67} +(-6.58968 - 11.4137i) q^{68} +1.96688 q^{71} +(5.27515 + 9.13683i) q^{73} +(2.08745 - 3.61557i) q^{74} +(-7.36235 + 12.7520i) q^{76} -9.01643 q^{79} +(-1.25888 - 2.18044i) q^{80} +(-4.23963 + 7.34326i) q^{82} +(5.08023 + 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +(3.61303 + 6.25796i) q^{86} +(4.38866 - 7.60138i) q^{88} +(2.59776 - 4.49945i) q^{89} +(-7.08205 - 12.2665i) q^{92} +6.86726 q^{94} -6.82490 q^{95} +(-2.48521 - 4.30451i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17631 −1.53888 −0.769442 0.638717i \(-0.779466\pi\)
−0.769442 + 0.638717i \(0.779466\pi\)
\(3\) 0 0
\(4\) 2.73633 1.36816
\(5\) 0.634145 + 1.09837i 0.283598 + 0.491206i 0.972268 0.233868i \(-0.0751385\pi\)
−0.688670 + 0.725075i \(0.741805\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.60248 −0.566563
\(9\) 0 0
\(10\) −1.38010 2.39040i −0.436425 0.755910i
\(11\) −2.73867 + 4.74351i −0.825739 + 1.43022i 0.0756148 + 0.997137i \(0.475908\pi\)
−0.901353 + 0.433084i \(0.857425\pi\)
\(12\) 0 0
\(13\) 2.37268 4.10960i 0.658062 1.13980i −0.323054 0.946380i \(-0.604710\pi\)
0.981117 0.193417i \(-0.0619570\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.98516 −0.496290
\(17\) −2.40822 4.17116i −0.584079 1.01165i −0.994990 0.0999785i \(-0.968123\pi\)
0.410911 0.911676i \(-0.365211\pi\)
\(18\) 0 0
\(19\) −2.69059 + 4.66025i −0.617265 + 1.06913i 0.372718 + 0.927945i \(0.378426\pi\)
−0.989983 + 0.141189i \(0.954907\pi\)
\(20\) 1.73523 + 3.00550i 0.388009 + 0.672051i
\(21\) 0 0
\(22\) 5.96019 10.3233i 1.27072 2.20095i
\(23\) −2.58816 4.48282i −0.539668 0.934732i −0.998922 0.0464269i \(-0.985217\pi\)
0.459254 0.888305i \(-0.348117\pi\)
\(24\) 0 0
\(25\) 1.69572 2.93707i 0.339144 0.587415i
\(26\) −5.16368 + 8.94376i −1.01268 + 1.75402i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.01656 3.49278i −0.374466 0.648594i 0.615781 0.787917i \(-0.288841\pi\)
−0.990247 + 0.139324i \(0.955507\pi\)
\(30\) 0 0
\(31\) −1.46419 −0.262976 −0.131488 0.991318i \(-0.541975\pi\)
−0.131488 + 0.991318i \(0.541975\pi\)
\(32\) 7.52529 1.33030
\(33\) 0 0
\(34\) 5.24103 + 9.07773i 0.898830 + 1.55682i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.959170 + 1.66133i −0.157687 + 0.273121i −0.934034 0.357184i \(-0.883737\pi\)
0.776347 + 0.630305i \(0.217070\pi\)
\(38\) 5.85557 10.1421i 0.949899 1.64527i
\(39\) 0 0
\(40\) −1.01621 1.76012i −0.160676 0.278299i
\(41\) 1.94808 3.37418i 0.304239 0.526958i −0.672852 0.739777i \(-0.734931\pi\)
0.977092 + 0.212819i \(0.0682644\pi\)
\(42\) 0 0
\(43\) −1.66016 2.87549i −0.253173 0.438508i 0.711225 0.702964i \(-0.248141\pi\)
−0.964398 + 0.264457i \(0.914807\pi\)
\(44\) −7.49389 + 12.9798i −1.12975 + 1.95678i
\(45\) 0 0
\(46\) 5.63263 + 9.75600i 0.830486 + 1.43844i
\(47\) −3.15546 −0.460271 −0.230135 0.973159i \(-0.573917\pi\)
−0.230135 + 0.973159i \(0.573917\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.69042 + 6.39199i −0.521904 + 0.903964i
\(51\) 0 0
\(52\) 6.49243 11.2452i 0.900338 1.55943i
\(53\) −3.57149 6.18601i −0.490582 0.849714i 0.509359 0.860554i \(-0.329883\pi\)
−0.999941 + 0.0108405i \(0.996549\pi\)
\(54\) 0 0
\(55\) −6.94684 −0.936712
\(56\) 0 0
\(57\) 0 0
\(58\) 4.38866 + 7.60138i 0.576259 + 0.998111i
\(59\) −0.308683 −0.0401871 −0.0200935 0.999798i \(-0.506396\pi\)
−0.0200935 + 0.999798i \(0.506396\pi\)
\(60\) 0 0
\(61\) 10.3429 1.32427 0.662134 0.749385i \(-0.269651\pi\)
0.662134 + 0.749385i \(0.269651\pi\)
\(62\) 3.18652 0.404689
\(63\) 0 0
\(64\) −12.4070 −1.55088
\(65\) 6.01848 0.746501
\(66\) 0 0
\(67\) 4.47310 0.546476 0.273238 0.961946i \(-0.411905\pi\)
0.273238 + 0.961946i \(0.411905\pi\)
\(68\) −6.58968 11.4137i −0.799116 1.38411i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.96688 0.233426 0.116713 0.993166i \(-0.462764\pi\)
0.116713 + 0.993166i \(0.462764\pi\)
\(72\) 0 0
\(73\) 5.27515 + 9.13683i 0.617409 + 1.06938i 0.989957 + 0.141371i \(0.0451512\pi\)
−0.372547 + 0.928013i \(0.621516\pi\)
\(74\) 2.08745 3.61557i 0.242662 0.420302i
\(75\) 0 0
\(76\) −7.36235 + 12.7520i −0.844520 + 1.46275i
\(77\) 0 0
\(78\) 0 0
\(79\) −9.01643 −1.01443 −0.507214 0.861820i \(-0.669325\pi\)
−0.507214 + 0.861820i \(0.669325\pi\)
\(80\) −1.25888 2.18044i −0.140747 0.243781i
\(81\) 0 0
\(82\) −4.23963 + 7.34326i −0.468189 + 0.810927i
\(83\) 5.08023 + 8.79921i 0.557627 + 0.965839i 0.997694 + 0.0678739i \(0.0216216\pi\)
−0.440066 + 0.897965i \(0.645045\pi\)
\(84\) 0 0
\(85\) 3.05432 5.29023i 0.331287 0.573806i
\(86\) 3.61303 + 6.25796i 0.389603 + 0.674813i
\(87\) 0 0
\(88\) 4.38866 7.60138i 0.467833 0.810310i
\(89\) 2.59776 4.49945i 0.275362 0.476941i −0.694864 0.719141i \(-0.744536\pi\)
0.970226 + 0.242200i \(0.0778690\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.08205 12.2665i −0.738354 1.27887i
\(93\) 0 0
\(94\) 6.86726 0.708303
\(95\) −6.82490 −0.700220
\(96\) 0 0
\(97\) −2.48521 4.30451i −0.252335 0.437057i 0.711833 0.702348i \(-0.247865\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.64005 8.03680i 0.464005 0.803680i
\(101\) 0.00266904 0.00462292i 0.000265580 0.000459997i −0.865893 0.500230i \(-0.833249\pi\)
0.866158 + 0.499770i \(0.166582\pi\)
\(102\) 0 0
\(103\) −6.51741 11.2885i −0.642180 1.11229i −0.984945 0.172867i \(-0.944697\pi\)
0.342765 0.939421i \(-0.388636\pi\)
\(104\) −3.80217 + 6.58555i −0.372834 + 0.645767i
\(105\) 0 0
\(106\) 7.77268 + 13.4627i 0.754950 + 1.30761i
\(107\) 4.71081 8.15936i 0.455411 0.788795i −0.543301 0.839538i \(-0.682826\pi\)
0.998712 + 0.0507430i \(0.0161589\pi\)
\(108\) 0 0
\(109\) −8.44513 14.6274i −0.808896 1.40105i −0.913629 0.406549i \(-0.866732\pi\)
0.104732 0.994500i \(-0.466601\pi\)
\(110\) 15.1185 1.44149
\(111\) 0 0
\(112\) 0 0
\(113\) 3.07313 5.32281i 0.289095 0.500728i −0.684499 0.729014i \(-0.739979\pi\)
0.973594 + 0.228286i \(0.0733122\pi\)
\(114\) 0 0
\(115\) 3.28253 5.68551i 0.306098 0.530176i
\(116\) −5.51797 9.55741i −0.512331 0.887383i
\(117\) 0 0
\(118\) 0.671790 0.0618432
\(119\) 0 0
\(120\) 0 0
\(121\) −9.50058 16.4555i −0.863689 1.49595i
\(122\) −22.5093 −2.03790
\(123\) 0 0
\(124\) −4.00649 −0.359794
\(125\) 10.6428 0.951919
\(126\) 0 0
\(127\) −13.9305 −1.23613 −0.618065 0.786127i \(-0.712083\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(128\) 11.9510 1.05633
\(129\) 0 0
\(130\) −13.0981 −1.14878
\(131\) −0.0895778 0.155153i −0.00782645 0.0135558i 0.862086 0.506763i \(-0.169158\pi\)
−0.869912 + 0.493207i \(0.835825\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −9.73486 −0.840964
\(135\) 0 0
\(136\) 3.85913 + 6.68420i 0.330917 + 0.573166i
\(137\) 1.57603 2.72977i 0.134649 0.233220i −0.790814 0.612056i \(-0.790343\pi\)
0.925463 + 0.378837i \(0.123676\pi\)
\(138\) 0 0
\(139\) 9.42857 16.3308i 0.799721 1.38516i −0.120077 0.992765i \(-0.538314\pi\)
0.919798 0.392392i \(-0.128352\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.28054 −0.359215
\(143\) 12.9959 + 22.5096i 1.08677 + 1.88235i
\(144\) 0 0
\(145\) 2.55758 4.42986i 0.212396 0.367880i
\(146\) −11.4804 19.8846i −0.950122 1.64566i
\(147\) 0 0
\(148\) −2.62461 + 4.54595i −0.215741 + 0.373675i
\(149\) −10.6370 18.4238i −0.871418 1.50934i −0.860530 0.509400i \(-0.829868\pi\)
−0.0108879 0.999941i \(-0.503466\pi\)
\(150\) 0 0
\(151\) −3.18281 + 5.51278i −0.259013 + 0.448624i −0.965978 0.258625i \(-0.916731\pi\)
0.706965 + 0.707249i \(0.250064\pi\)
\(152\) 4.31163 7.46796i 0.349719 0.605731i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.928506 1.60822i −0.0745794 0.129175i
\(156\) 0 0
\(157\) 1.39595 0.111409 0.0557045 0.998447i \(-0.482260\pi\)
0.0557045 + 0.998447i \(0.482260\pi\)
\(158\) 19.6226 1.56109
\(159\) 0 0
\(160\) 4.77212 + 8.26556i 0.377269 + 0.653450i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.53086 16.5079i 0.746515 1.29300i −0.202969 0.979185i \(-0.565059\pi\)
0.949484 0.313816i \(-0.101608\pi\)
\(164\) 5.33059 9.23286i 0.416249 0.720965i
\(165\) 0 0
\(166\) −11.0562 19.1498i −0.858124 1.48631i
\(167\) −0.872003 + 1.51035i −0.0674776 + 0.116875i −0.897790 0.440423i \(-0.854828\pi\)
0.830313 + 0.557298i \(0.188162\pi\)
\(168\) 0 0
\(169\) −4.75919 8.24317i −0.366092 0.634090i
\(170\) −6.64715 + 11.5132i −0.509813 + 0.883022i
\(171\) 0 0
\(172\) −4.54276 7.86828i −0.346382 0.599951i
\(173\) 10.0759 0.766056 0.383028 0.923737i \(-0.374881\pi\)
0.383028 + 0.923737i \(0.374881\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.43669 9.41662i 0.409806 0.709805i
\(177\) 0 0
\(178\) −5.65353 + 9.79221i −0.423750 + 0.733957i
\(179\) −9.27118 16.0582i −0.692961 1.20024i −0.970863 0.239634i \(-0.922973\pi\)
0.277902 0.960609i \(-0.410361\pi\)
\(180\) 0 0
\(181\) −8.80982 −0.654829 −0.327414 0.944881i \(-0.606177\pi\)
−0.327414 + 0.944881i \(0.606177\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.14747 + 7.18363i 0.305756 + 0.529584i
\(185\) −2.43301 −0.178879
\(186\) 0 0
\(187\) 26.3812 1.92919
\(188\) −8.63437 −0.629726
\(189\) 0 0
\(190\) 14.8531 1.07756
\(191\) −4.90939 −0.355231 −0.177615 0.984100i \(-0.556838\pi\)
−0.177615 + 0.984100i \(0.556838\pi\)
\(192\) 0 0
\(193\) −9.76760 −0.703087 −0.351544 0.936171i \(-0.614343\pi\)
−0.351544 + 0.936171i \(0.614343\pi\)
\(194\) 5.40859 + 9.36796i 0.388314 + 0.672580i
\(195\) 0 0
\(196\) 0 0
\(197\) −3.31445 −0.236145 −0.118073 0.993005i \(-0.537672\pi\)
−0.118073 + 0.993005i \(0.537672\pi\)
\(198\) 0 0
\(199\) −5.54432 9.60304i −0.393026 0.680742i 0.599821 0.800134i \(-0.295239\pi\)
−0.992847 + 0.119393i \(0.961905\pi\)
\(200\) −2.71736 + 4.70661i −0.192146 + 0.332807i
\(201\) 0 0
\(202\) −0.00580866 + 0.0100609i −0.000408696 + 0.000707883i
\(203\) 0 0
\(204\) 0 0
\(205\) 4.94146 0.345127
\(206\) 14.1839 + 24.5673i 0.988240 + 1.71168i
\(207\) 0 0
\(208\) −4.71014 + 8.15821i −0.326590 + 0.565670i
\(209\) −14.7373 25.5257i −1.01940 1.76565i
\(210\) 0 0
\(211\) −3.66118 + 6.34135i −0.252046 + 0.436557i −0.964089 0.265579i \(-0.914437\pi\)
0.712043 + 0.702136i \(0.247770\pi\)
\(212\) −9.77278 16.9270i −0.671198 1.16255i
\(213\) 0 0
\(214\) −10.2522 + 17.7573i −0.700825 + 1.21386i
\(215\) 2.10557 3.64695i 0.143599 0.248720i
\(216\) 0 0
\(217\) 0 0
\(218\) 18.3792 + 31.8337i 1.24480 + 2.15605i
\(219\) 0 0
\(220\) −19.0088 −1.28158
\(221\) −22.8557 −1.53744
\(222\) 0 0
\(223\) 2.02765 + 3.51199i 0.135782 + 0.235181i 0.925896 0.377779i \(-0.123312\pi\)
−0.790114 + 0.612960i \(0.789979\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.68808 + 11.5841i −0.444884 + 0.770562i
\(227\) 0.667087 1.15543i 0.0442761 0.0766884i −0.843038 0.537854i \(-0.819235\pi\)
0.887314 + 0.461165i \(0.152569\pi\)
\(228\) 0 0
\(229\) 7.99832 + 13.8535i 0.528544 + 0.915465i 0.999446 + 0.0332795i \(0.0105952\pi\)
−0.470902 + 0.882185i \(0.656072\pi\)
\(230\) −7.14381 + 12.3734i −0.471049 + 0.815880i
\(231\) 0 0
\(232\) 3.23150 + 5.59712i 0.212158 + 0.367469i
\(233\) 4.06542 7.04151i 0.266334 0.461305i −0.701578 0.712593i \(-0.747521\pi\)
0.967912 + 0.251288i \(0.0808542\pi\)
\(234\) 0 0
\(235\) −2.00102 3.46586i −0.130532 0.226088i
\(236\) −0.844658 −0.0549825
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0509 + 19.1407i −0.714823 + 1.23811i 0.248204 + 0.968708i \(0.420160\pi\)
−0.963028 + 0.269403i \(0.913174\pi\)
\(240\) 0 0
\(241\) −13.7973 + 23.8977i −0.888765 + 1.53939i −0.0474292 + 0.998875i \(0.515103\pi\)
−0.841336 + 0.540512i \(0.818230\pi\)
\(242\) 20.6762 + 35.8122i 1.32912 + 2.30210i
\(243\) 0 0
\(244\) 28.3015 1.81182
\(245\) 0 0
\(246\) 0 0
\(247\) 12.7678 + 22.1145i 0.812397 + 1.40711i
\(248\) 2.34633 0.148992
\(249\) 0 0
\(250\) −23.1620 −1.46489
\(251\) 16.5610 1.04532 0.522661 0.852541i \(-0.324939\pi\)
0.522661 + 0.852541i \(0.324939\pi\)
\(252\) 0 0
\(253\) 28.3524 1.78250
\(254\) 30.3171 1.90226
\(255\) 0 0
\(256\) −1.19503 −0.0746896
\(257\) 1.03287 + 1.78898i 0.0644285 + 0.111593i 0.896440 0.443164i \(-0.146144\pi\)
−0.832012 + 0.554758i \(0.812811\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 16.4686 1.02134
\(261\) 0 0
\(262\) 0.194949 + 0.337662i 0.0120440 + 0.0208608i
\(263\) 5.06482 8.77252i 0.312310 0.540937i −0.666552 0.745458i \(-0.732231\pi\)
0.978862 + 0.204522i \(0.0655639\pi\)
\(264\) 0 0
\(265\) 4.52969 7.84565i 0.278257 0.481954i
\(266\) 0 0
\(267\) 0 0
\(268\) 12.2399 0.747670
\(269\) −7.54972 13.0765i −0.460315 0.797289i 0.538662 0.842522i \(-0.318930\pi\)
−0.998976 + 0.0452336i \(0.985597\pi\)
\(270\) 0 0
\(271\) 14.4026 24.9459i 0.874893 1.51536i 0.0180156 0.999838i \(-0.494265\pi\)
0.856877 0.515521i \(-0.172402\pi\)
\(272\) 4.78070 + 8.28041i 0.289872 + 0.502074i
\(273\) 0 0
\(274\) −3.42993 + 5.94082i −0.207210 + 0.358898i
\(275\) 9.28802 + 16.0873i 0.560089 + 0.970102i
\(276\) 0 0
\(277\) 1.34982 2.33795i 0.0811026 0.140474i −0.822621 0.568590i \(-0.807489\pi\)
0.903724 + 0.428116i \(0.140823\pi\)
\(278\) −20.5195 + 35.5408i −1.23068 + 2.13160i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.46312 + 4.26626i 0.146938 + 0.254503i 0.930094 0.367321i \(-0.119725\pi\)
−0.783157 + 0.621825i \(0.786392\pi\)
\(282\) 0 0
\(283\) 3.58157 0.212903 0.106451 0.994318i \(-0.466051\pi\)
0.106451 + 0.994318i \(0.466051\pi\)
\(284\) 5.38203 0.319365
\(285\) 0 0
\(286\) −28.2832 48.9879i −1.67242 2.89672i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.09903 + 5.36768i −0.182296 + 0.315746i
\(290\) −5.56609 + 9.64075i −0.326852 + 0.566125i
\(291\) 0 0
\(292\) 14.4345 + 25.0014i 0.844718 + 1.46309i
\(293\) −12.1955 + 21.1232i −0.712469 + 1.23403i 0.251459 + 0.967868i \(0.419090\pi\)
−0.963928 + 0.266164i \(0.914244\pi\)
\(294\) 0 0
\(295\) −0.195750 0.339048i −0.0113970 0.0197401i
\(296\) 1.53705 2.66225i 0.0893394 0.154740i
\(297\) 0 0
\(298\) 23.1494 + 40.0960i 1.34101 + 2.32270i
\(299\) −24.5634 −1.42054
\(300\) 0 0
\(301\) 0 0
\(302\) 6.92678 11.9975i 0.398591 0.690380i
\(303\) 0 0
\(304\) 5.34126 9.25134i 0.306342 0.530600i
\(305\) 6.55887 + 11.3603i 0.375560 + 0.650489i
\(306\) 0 0
\(307\) −23.9025 −1.36419 −0.682094 0.731265i \(-0.738930\pi\)
−0.682094 + 0.731265i \(0.738930\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.02072 + 3.49998i 0.114769 + 0.198786i
\(311\) 12.9416 0.733853 0.366926 0.930250i \(-0.380410\pi\)
0.366926 + 0.930250i \(0.380410\pi\)
\(312\) 0 0
\(313\) −26.8681 −1.51867 −0.759336 0.650698i \(-0.774476\pi\)
−0.759336 + 0.650698i \(0.774476\pi\)
\(314\) −3.03802 −0.171446
\(315\) 0 0
\(316\) −24.6719 −1.38790
\(317\) −8.31169 −0.466831 −0.233415 0.972377i \(-0.574990\pi\)
−0.233415 + 0.972377i \(0.574990\pi\)
\(318\) 0 0
\(319\) 22.0907 1.23684
\(320\) −7.86786 13.6275i −0.439827 0.761803i
\(321\) 0 0
\(322\) 0 0
\(323\) 25.9182 1.44212
\(324\) 0 0
\(325\) −8.04680 13.9375i −0.446356 0.773111i
\(326\) −20.7421 + 35.9264i −1.14880 + 1.98978i
\(327\) 0 0
\(328\) −3.12177 + 5.40706i −0.172371 + 0.298555i
\(329\) 0 0
\(330\) 0 0
\(331\) 12.3978 0.681443 0.340722 0.940164i \(-0.389329\pi\)
0.340722 + 0.940164i \(0.389329\pi\)
\(332\) 13.9012 + 24.0775i 0.762926 + 1.32143i
\(333\) 0 0
\(334\) 1.89775 3.28700i 0.103840 0.179857i
\(335\) 2.83659 + 4.91312i 0.154980 + 0.268433i
\(336\) 0 0
\(337\) −12.9588 + 22.4454i −0.705913 + 1.22268i 0.260448 + 0.965488i \(0.416130\pi\)
−0.966361 + 0.257189i \(0.917204\pi\)
\(338\) 10.3575 + 17.9397i 0.563373 + 0.975791i
\(339\) 0 0
\(340\) 8.35762 14.4758i 0.453256 0.785062i
\(341\) 4.00992 6.94538i 0.217149 0.376113i
\(342\) 0 0
\(343\) 0 0
\(344\) 2.66038 + 4.60792i 0.143438 + 0.248442i
\(345\) 0 0
\(346\) −21.9283 −1.17887
\(347\) 16.8483 0.904464 0.452232 0.891900i \(-0.350628\pi\)
0.452232 + 0.891900i \(0.350628\pi\)
\(348\) 0 0
\(349\) 15.5503 + 26.9340i 0.832390 + 1.44174i 0.896138 + 0.443776i \(0.146361\pi\)
−0.0637477 + 0.997966i \(0.520305\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −20.6092 + 35.6963i −1.09848 + 1.90262i
\(353\) 1.32969 2.30309i 0.0707722 0.122581i −0.828468 0.560037i \(-0.810787\pi\)
0.899240 + 0.437456i \(0.144120\pi\)
\(354\) 0 0
\(355\) 1.24729 + 2.16036i 0.0661991 + 0.114660i
\(356\) 7.10833 12.3120i 0.376741 0.652534i
\(357\) 0 0
\(358\) 20.1770 + 34.9476i 1.06639 + 1.84704i
\(359\) −16.2715 + 28.1830i −0.858775 + 1.48744i 0.0143230 + 0.999897i \(0.495441\pi\)
−0.873098 + 0.487545i \(0.837893\pi\)
\(360\) 0 0
\(361\) −4.97859 8.62318i −0.262031 0.453852i
\(362\) 19.1729 1.00771
\(363\) 0 0
\(364\) 0 0
\(365\) −6.69042 + 11.5881i −0.350192 + 0.606551i
\(366\) 0 0
\(367\) −7.07678 + 12.2573i −0.369405 + 0.639828i −0.989473 0.144720i \(-0.953772\pi\)
0.620068 + 0.784548i \(0.287105\pi\)
\(368\) 5.13790 + 8.89911i 0.267832 + 0.463898i
\(369\) 0 0
\(370\) 5.29499 0.275273
\(371\) 0 0
\(372\) 0 0
\(373\) −1.33814 2.31773i −0.0692863 0.120007i 0.829301 0.558802i \(-0.188739\pi\)
−0.898587 + 0.438795i \(0.855406\pi\)
\(374\) −57.4137 −2.96879
\(375\) 0 0
\(376\) 5.05656 0.260772
\(377\) −19.1386 −0.985687
\(378\) 0 0
\(379\) −0.312929 −0.0160741 −0.00803705 0.999968i \(-0.502558\pi\)
−0.00803705 + 0.999968i \(0.502558\pi\)
\(380\) −18.6752 −0.958017
\(381\) 0 0
\(382\) 10.6844 0.546659
\(383\) −4.49440 7.78453i −0.229653 0.397771i 0.728052 0.685522i \(-0.240426\pi\)
−0.957705 + 0.287751i \(0.907093\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.2573 1.08197
\(387\) 0 0
\(388\) −6.80036 11.7786i −0.345236 0.597966i
\(389\) −13.4934 + 23.3713i −0.684144 + 1.18497i 0.289560 + 0.957160i \(0.406491\pi\)
−0.973705 + 0.227813i \(0.926842\pi\)
\(390\) 0 0
\(391\) −12.4657 + 21.5912i −0.630417 + 1.09191i
\(392\) 0 0
\(393\) 0 0
\(394\) 7.21328 0.363400
\(395\) −5.71772 9.90339i −0.287690 0.498293i
\(396\) 0 0
\(397\) −14.7503 + 25.5482i −0.740295 + 1.28223i 0.212066 + 0.977255i \(0.431981\pi\)
−0.952361 + 0.304973i \(0.901352\pi\)
\(398\) 12.0662 + 20.8992i 0.604822 + 1.04758i
\(399\) 0 0
\(400\) −3.36628 + 5.83056i −0.168314 + 0.291528i
\(401\) −17.1392 29.6860i −0.855891 1.48245i −0.875816 0.482645i \(-0.839676\pi\)
0.0199251 0.999801i \(-0.493657\pi\)
\(402\) 0 0
\(403\) −3.47404 + 6.01721i −0.173054 + 0.299739i
\(404\) 0.00730338 0.0126498i 0.000363357 0.000629352i
\(405\) 0 0
\(406\) 0 0
\(407\) −5.25369 9.09966i −0.260416 0.451054i
\(408\) 0 0
\(409\) 10.9845 0.543149 0.271574 0.962417i \(-0.412456\pi\)
0.271574 + 0.962417i \(0.412456\pi\)
\(410\) −10.7542 −0.531110
\(411\) 0 0
\(412\) −17.8338 30.8890i −0.878608 1.52179i
\(413\) 0 0
\(414\) 0 0
\(415\) −6.44320 + 11.1599i −0.316284 + 0.547820i
\(416\) 17.8551 30.9259i 0.875417 1.51627i
\(417\) 0 0
\(418\) 32.0729 + 55.5519i 1.56874 + 2.71713i
\(419\) 3.33207 5.77132i 0.162782 0.281947i −0.773083 0.634305i \(-0.781286\pi\)
0.935866 + 0.352357i \(0.114620\pi\)
\(420\) 0 0
\(421\) −17.0430 29.5193i −0.830625 1.43868i −0.897543 0.440926i \(-0.854650\pi\)
0.0669186 0.997758i \(-0.478683\pi\)
\(422\) 7.96787 13.8008i 0.387870 0.671810i
\(423\) 0 0
\(424\) 5.72325 + 9.91297i 0.277946 + 0.481416i
\(425\) −16.3347 −0.792348
\(426\) 0 0
\(427\) 0 0
\(428\) 12.8903 22.3267i 0.623077 1.07920i
\(429\) 0 0
\(430\) −4.58237 + 7.93690i −0.220982 + 0.382751i
\(431\) 1.12969 + 1.95669i 0.0544155 + 0.0942504i 0.891950 0.452134i \(-0.149337\pi\)
−0.837535 + 0.546384i \(0.816004\pi\)
\(432\) 0 0
\(433\) 34.3904 1.65270 0.826348 0.563160i \(-0.190415\pi\)
0.826348 + 0.563160i \(0.190415\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −23.1086 40.0254i −1.10670 1.91687i
\(437\) 27.8547 1.33247
\(438\) 0 0
\(439\) 5.99139 0.285953 0.142977 0.989726i \(-0.454333\pi\)
0.142977 + 0.989726i \(0.454333\pi\)
\(440\) 11.1322 0.530706
\(441\) 0 0
\(442\) 49.7411 2.36594
\(443\) 39.4380 1.87376 0.936879 0.349654i \(-0.113701\pi\)
0.936879 + 0.349654i \(0.113701\pi\)
\(444\) 0 0
\(445\) 6.58942 0.312369
\(446\) −4.41280 7.64319i −0.208952 0.361916i
\(447\) 0 0
\(448\) 0 0
\(449\) −2.45092 −0.115666 −0.0578330 0.998326i \(-0.518419\pi\)
−0.0578330 + 0.998326i \(0.518419\pi\)
\(450\) 0 0
\(451\) 10.6703 + 18.4815i 0.502444 + 0.870259i
\(452\) 8.40909 14.5650i 0.395530 0.685078i
\(453\) 0 0
\(454\) −1.45179 + 2.51457i −0.0681358 + 0.118015i
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0212 0.515548 0.257774 0.966205i \(-0.417011\pi\)
0.257774 + 0.966205i \(0.417011\pi\)
\(458\) −17.4068 30.1495i −0.813368 1.40879i
\(459\) 0 0
\(460\) 8.98208 15.5574i 0.418792 0.725369i
\(461\) −14.6540 25.3814i −0.682503 1.18213i −0.974215 0.225624i \(-0.927558\pi\)
0.291711 0.956506i \(-0.405775\pi\)
\(462\) 0 0
\(463\) 0.593566 1.02809i 0.0275853 0.0477792i −0.851903 0.523699i \(-0.824552\pi\)
0.879489 + 0.475920i \(0.157885\pi\)
\(464\) 4.00319 + 6.93374i 0.185844 + 0.321891i
\(465\) 0 0
\(466\) −8.84761 + 15.3245i −0.409858 + 0.709894i
\(467\) 11.0573 19.1519i 0.511673 0.886243i −0.488236 0.872712i \(-0.662359\pi\)
0.999908 0.0135313i \(-0.00430729\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4.35483 + 7.54280i 0.200874 + 0.347923i
\(471\) 0 0
\(472\) 0.494658 0.0227685
\(473\) 18.1865 0.836218
\(474\) 0 0
\(475\) 9.12499 + 15.8050i 0.418683 + 0.725181i
\(476\) 0 0
\(477\) 0 0
\(478\) 24.0502 41.6562i 1.10003 1.90531i
\(479\) −12.5714 + 21.7743i −0.574402 + 0.994894i 0.421704 + 0.906734i \(0.361432\pi\)
−0.996106 + 0.0881606i \(0.971901\pi\)
\(480\) 0 0
\(481\) 4.55160 + 7.88361i 0.207535 + 0.359462i
\(482\) 30.0273 52.0088i 1.36771 2.36894i
\(483\) 0 0
\(484\) −25.9967 45.0276i −1.18167 2.04671i
\(485\) 3.15197 5.45937i 0.143123 0.247897i
\(486\) 0 0
\(487\) −6.78904 11.7590i −0.307641 0.532849i 0.670205 0.742176i \(-0.266206\pi\)
−0.977846 + 0.209327i \(0.932873\pi\)
\(488\) −16.5743 −0.750281
\(489\) 0 0
\(490\) 0 0
\(491\) −7.25177 + 12.5604i −0.327268 + 0.566844i −0.981969 0.189044i \(-0.939461\pi\)
0.654701 + 0.755888i \(0.272795\pi\)
\(492\) 0 0
\(493\) −9.71263 + 16.8228i −0.437435 + 0.757659i
\(494\) −27.7868 48.1281i −1.25019 2.16538i
\(495\) 0 0
\(496\) 2.90664 0.130512
\(497\) 0 0
\(498\) 0 0
\(499\) −6.99574 12.1170i −0.313172 0.542431i 0.665875 0.746063i \(-0.268058\pi\)
−0.979047 + 0.203633i \(0.934725\pi\)
\(500\) 29.1221 1.30238
\(501\) 0 0
\(502\) −36.0419 −1.60863
\(503\) −28.4011 −1.26634 −0.633171 0.774012i \(-0.718247\pi\)
−0.633171 + 0.774012i \(0.718247\pi\)
\(504\) 0 0
\(505\) 0.00677023 0.000301271
\(506\) −61.7036 −2.74306
\(507\) 0 0
\(508\) −38.1184 −1.69123
\(509\) −1.72997 2.99639i −0.0766794 0.132813i 0.825136 0.564934i \(-0.191098\pi\)
−0.901815 + 0.432122i \(0.857765\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −21.3013 −0.941392
\(513\) 0 0
\(514\) −2.24784 3.89337i −0.0991480 0.171729i
\(515\) 8.26597 14.3171i 0.364242 0.630886i
\(516\) 0 0
\(517\) 8.64174 14.9679i 0.380063 0.658289i
\(518\) 0 0
\(519\) 0 0
\(520\) −9.64451 −0.422940
\(521\) 3.56797 + 6.17991i 0.156316 + 0.270747i 0.933537 0.358480i \(-0.116705\pi\)
−0.777222 + 0.629227i \(0.783372\pi\)
\(522\) 0 0
\(523\) 6.53235 11.3144i 0.285640 0.494743i −0.687124 0.726540i \(-0.741127\pi\)
0.972764 + 0.231797i \(0.0744606\pi\)
\(524\) −0.245114 0.424551i −0.0107079 0.0185466i
\(525\) 0 0
\(526\) −11.0226 + 19.0917i −0.480609 + 0.832439i
\(527\) 3.52608 + 6.10735i 0.153598 + 0.266040i
\(528\) 0 0
\(529\) −1.89710 + 3.28587i −0.0824825 + 0.142864i
\(530\) −9.85801 + 17.0746i −0.428205 + 0.741672i
\(531\) 0 0
\(532\) 0 0
\(533\) −9.24434 16.0117i −0.400417 0.693542i
\(534\) 0 0
\(535\) 11.9493 0.516615
\(536\) −7.16806 −0.309613
\(537\) 0 0
\(538\) 16.4305 + 28.4585i 0.708371 + 1.22693i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.46788 + 4.27450i −0.106103 + 0.183775i −0.914188 0.405290i \(-0.867171\pi\)
0.808086 + 0.589065i \(0.200504\pi\)
\(542\) −31.3444 + 54.2901i −1.34636 + 2.33196i
\(543\) 0 0
\(544\) −18.1225 31.3892i −0.776997 1.34580i
\(545\) 10.7109 18.5518i 0.458803 0.794670i
\(546\) 0 0
\(547\) 0.559964 + 0.969887i 0.0239423 + 0.0414694i 0.877748 0.479122i \(-0.159045\pi\)
−0.853806 + 0.520591i \(0.825712\pi\)
\(548\) 4.31254 7.46954i 0.184223 0.319083i
\(549\) 0 0
\(550\) −20.2136 35.0110i −0.861912 1.49288i
\(551\) 21.7030 0.924578
\(552\) 0 0
\(553\) 0 0
\(554\) −2.93762 + 5.08811i −0.124808 + 0.216173i
\(555\) 0 0
\(556\) 25.7997 44.6863i 1.09415 1.89512i
\(557\) −5.47832 9.48873i −0.232124 0.402050i 0.726309 0.687368i \(-0.241234\pi\)
−0.958433 + 0.285318i \(0.907901\pi\)
\(558\) 0 0
\(559\) −15.7561 −0.666413
\(560\) 0 0
\(561\) 0 0
\(562\) −5.36052 9.28470i −0.226120 0.391651i
\(563\) 4.76096 0.200650 0.100325 0.994955i \(-0.468012\pi\)
0.100325 + 0.994955i \(0.468012\pi\)
\(564\) 0 0
\(565\) 7.79523 0.327948
\(566\) −7.79462 −0.327632
\(567\) 0 0
\(568\) −3.15189 −0.132250
\(569\) −3.49976 −0.146718 −0.0733588 0.997306i \(-0.523372\pi\)
−0.0733588 + 0.997306i \(0.523372\pi\)
\(570\) 0 0
\(571\) 7.06101 0.295494 0.147747 0.989025i \(-0.452798\pi\)
0.147747 + 0.989025i \(0.452798\pi\)
\(572\) 35.5612 + 61.5937i 1.48689 + 2.57536i
\(573\) 0 0
\(574\) 0 0
\(575\) −17.5552 −0.732101
\(576\) 0 0
\(577\) −6.44149 11.1570i −0.268163 0.464472i 0.700225 0.713923i \(-0.253083\pi\)
−0.968387 + 0.249451i \(0.919750\pi\)
\(578\) 6.74445 11.6817i 0.280532 0.485896i
\(579\) 0 0
\(580\) 6.99838 12.1216i 0.290592 0.503320i
\(581\) 0 0
\(582\) 0 0
\(583\) 39.1245 1.62037
\(584\) −8.45333 14.6416i −0.349801 0.605874i
\(585\) 0 0
\(586\) 26.5412 45.9707i 1.09641 1.89903i
\(587\) 19.5044 + 33.7826i 0.805034 + 1.39436i 0.916268 + 0.400565i \(0.131186\pi\)
−0.111235 + 0.993794i \(0.535481\pi\)
\(588\) 0 0
\(589\) 3.93953 6.82347i 0.162326 0.281156i
\(590\) 0.426012 + 0.737874i 0.0175386 + 0.0303778i
\(591\) 0 0
\(592\) 1.90411 3.29801i 0.0782583 0.135547i
\(593\) 20.1513 34.9031i 0.827515 1.43330i −0.0724676 0.997371i \(-0.523087\pi\)
0.899982 0.435927i \(-0.143579\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −29.1064 50.4137i −1.19224 2.06503i
\(597\) 0 0
\(598\) 53.4577 2.18605
\(599\) 12.7821 0.522261 0.261130 0.965304i \(-0.415905\pi\)
0.261130 + 0.965304i \(0.415905\pi\)
\(600\) 0 0
\(601\) −4.86311 8.42316i −0.198371 0.343588i 0.749630 0.661858i \(-0.230232\pi\)
−0.948000 + 0.318270i \(0.896898\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.70921 + 15.0848i −0.354373 + 0.613792i
\(605\) 12.0495 20.8703i 0.489881 0.848499i
\(606\) 0 0
\(607\) −20.7437 35.9291i −0.841959 1.45832i −0.888236 0.459388i \(-0.848069\pi\)
0.0462763 0.998929i \(-0.485265\pi\)
\(608\) −20.2475 + 35.0697i −0.821145 + 1.42226i
\(609\) 0 0
\(610\) −14.2742 24.7236i −0.577943 1.00103i
\(611\) −7.48688 + 12.9677i −0.302887 + 0.524615i
\(612\) 0 0
\(613\) −7.64783 13.2464i −0.308893 0.535018i 0.669228 0.743057i \(-0.266625\pi\)
−0.978120 + 0.208039i \(0.933292\pi\)
\(614\) 52.0193 2.09933
\(615\) 0 0
\(616\) 0 0
\(617\) 2.66563 4.61700i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(618\) 0 0
\(619\) 6.34205 10.9847i 0.254908 0.441514i −0.709962 0.704240i \(-0.751288\pi\)
0.964871 + 0.262726i \(0.0846214\pi\)
\(620\) −2.54070 4.40062i −0.102037 0.176733i
\(621\) 0 0
\(622\) −28.1650 −1.12931
\(623\) 0 0
\(624\) 0 0
\(625\) −1.72954 2.99566i −0.0691817 0.119826i
\(626\) 58.4733 2.33706
\(627\) 0 0
\(628\) 3.81978 0.152426
\(629\) 9.23957 0.368406
\(630\) 0 0
\(631\) 0.123764 0.00492698 0.00246349 0.999997i \(-0.499216\pi\)
0.00246349 + 0.999997i \(0.499216\pi\)
\(632\) 14.4487 0.574737
\(633\) 0 0
\(634\) 18.0888 0.718399
\(635\) −8.83394 15.3008i −0.350564 0.607195i
\(636\) 0 0
\(637\) 0 0
\(638\) −48.0763 −1.90336
\(639\) 0 0
\(640\) 7.57868 + 13.1267i 0.299573 + 0.518876i
\(641\) 2.96588 5.13706i 0.117145 0.202902i −0.801490 0.598008i \(-0.795959\pi\)
0.918635 + 0.395107i \(0.129292\pi\)
\(642\) 0 0
\(643\) −23.4140 + 40.5542i −0.923358 + 1.59930i −0.129178 + 0.991621i \(0.541234\pi\)
−0.794180 + 0.607682i \(0.792100\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −56.4060 −2.21926
\(647\) −19.5701 33.8964i −0.769379 1.33260i −0.937900 0.346905i \(-0.887233\pi\)
0.168521 0.985698i \(-0.446101\pi\)
\(648\) 0 0
\(649\) 0.845379 1.46424i 0.0331840 0.0574764i
\(650\) 17.5123 + 30.3322i 0.686890 + 1.18973i
\(651\) 0 0
\(652\) 26.0796 45.1711i 1.02135 1.76904i
\(653\) 21.6640 + 37.5232i 0.847779 + 1.46840i 0.883186 + 0.469023i \(0.155394\pi\)
−0.0354068 + 0.999373i \(0.511273\pi\)
\(654\) 0 0
\(655\) 0.113611 0.196779i 0.00443913 0.00768881i
\(656\) −3.86726 + 6.69828i −0.150991 + 0.261524i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.43895 5.95643i −0.133962 0.232030i 0.791238 0.611508i \(-0.209437\pi\)
−0.925201 + 0.379478i \(0.876103\pi\)
\(660\) 0 0
\(661\) 38.7671 1.50786 0.753932 0.656952i \(-0.228155\pi\)
0.753932 + 0.656952i \(0.228155\pi\)
\(662\) −26.9814 −1.04866
\(663\) 0 0
\(664\) −8.14097 14.1006i −0.315931 0.547209i
\(665\) 0 0
\(666\) 0 0
\(667\) −10.4383 + 18.0797i −0.404174 + 0.700050i
\(668\) −2.38609 + 4.13282i −0.0923205 + 0.159904i
\(669\) 0 0
\(670\) −6.17331 10.6925i −0.238496 0.413087i
\(671\) −28.3257 + 49.0615i −1.09350 + 1.89400i
\(672\) 0 0
\(673\) 17.9897 + 31.1591i 0.693452 + 1.20109i 0.970700 + 0.240295i \(0.0772443\pi\)
−0.277248 + 0.960798i \(0.589422\pi\)
\(674\) 28.2025 48.8481i 1.08632 1.88156i
\(675\) 0 0
\(676\) −13.0227 22.5560i −0.500874 0.867539i
\(677\) −4.46658 −0.171664 −0.0858322 0.996310i \(-0.527355\pi\)
−0.0858322 + 0.996310i \(0.527355\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.89449 + 8.47750i −0.187695 + 0.325097i
\(681\) 0 0
\(682\) −8.72682 + 15.1153i −0.334167 + 0.578795i
\(683\) −13.3356 23.0980i −0.510274 0.883821i −0.999929 0.0119046i \(-0.996211\pi\)
0.489655 0.871916i \(-0.337123\pi\)
\(684\) 0 0
\(685\) 3.99773 0.152745
\(686\) 0 0
\(687\) 0 0
\(688\) 3.29569 + 5.70831i 0.125647 + 0.217627i
\(689\) −33.8960 −1.29134
\(690\) 0 0
\(691\) −41.0440 −1.56139 −0.780694 0.624913i \(-0.785134\pi\)
−0.780694 + 0.624913i \(0.785134\pi\)
\(692\) 27.5709 1.04809
\(693\) 0 0
\(694\) −36.6671 −1.39187
\(695\) 23.9163 0.907197
\(696\) 0 0
\(697\) −18.7656 −0.710799
\(698\) −33.8424 58.6167i −1.28095 2.21867i
\(699\) 0 0
\(700\) 0 0
\(701\) −9.63355 −0.363854 −0.181927 0.983312i \(-0.558233\pi\)
−0.181927 + 0.983312i \(0.558233\pi\)
\(702\) 0 0
\(703\) −5.16148 8.93994i −0.194669 0.337176i
\(704\) 33.9788 58.8529i 1.28062 2.21810i
\(705\) 0 0
\(706\) −2.89382 + 5.01224i −0.108910 + 0.188638i
\(707\) 0 0
\(708\) 0 0
\(709\) −10.1426 −0.380914 −0.190457 0.981696i \(-0.560997\pi\)
−0.190457 + 0.981696i \(0.560997\pi\)
\(710\) −2.71448 4.70162i −0.101873 0.176449i
\(711\) 0 0
\(712\) −4.16286 + 7.21029i −0.156010 + 0.270217i
\(713\) 3.78954 + 6.56368i 0.141919 + 0.245812i
\(714\) 0 0
\(715\) −16.4826 + 28.5487i −0.616415 + 1.06766i
\(716\) −25.3690 43.9404i −0.948085 1.64213i
\(717\) 0 0
\(718\) 35.4118 61.3350i 1.32156 2.28900i
\(719\) −20.6844 + 35.8264i −0.771397 + 1.33610i 0.165400 + 0.986227i \(0.447109\pi\)
−0.936797 + 0.349873i \(0.886225\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10.8350 + 18.7667i 0.403236 + 0.698425i
\(723\) 0 0
\(724\) −24.1066 −0.895914
\(725\) −13.6781 −0.507991
\(726\) 0 0
\(727\) −4.86372 8.42422i −0.180386 0.312437i 0.761626 0.648016i \(-0.224401\pi\)
−0.942012 + 0.335580i \(0.891068\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 14.5604 25.2194i 0.538906 0.933412i
\(731\) −7.99607 + 13.8496i −0.295745 + 0.512246i
\(732\) 0 0
\(733\) −14.4554 25.0375i −0.533922 0.924780i −0.999215 0.0396234i \(-0.987384\pi\)
0.465292 0.885157i \(-0.345949\pi\)
\(734\) 15.4013 26.6758i 0.568471 0.984621i
\(735\) 0 0
\(736\) −19.4766 33.7345i −0.717918 1.24347i
\(737\) −12.2503 + 21.2182i −0.451247 + 0.781582i
\(738\) 0 0
\(739\) 6.67467 + 11.5609i 0.245532 + 0.425273i 0.962281 0.272058i \(-0.0877041\pi\)
−0.716749 + 0.697331i \(0.754371\pi\)
\(740\) −6.65752 −0.244735
\(741\) 0 0
\(742\) 0 0
\(743\) −19.9100 + 34.4851i −0.730425 + 1.26513i 0.226276 + 0.974063i \(0.427345\pi\)
−0.956702 + 0.291071i \(0.905988\pi\)
\(744\) 0 0
\(745\) 13.4908 23.3668i 0.494265 0.856092i
\(746\) 2.91221 + 5.04410i 0.106624 + 0.184678i
\(747\) 0 0
\(748\) 72.1877 2.63944
\(749\) 0 0
\(750\) 0 0
\(751\) 19.2173 + 33.2853i 0.701248 + 1.21460i 0.968029 + 0.250840i \(0.0807069\pi\)
−0.266780 + 0.963757i \(0.585960\pi\)
\(752\) 6.26409 0.228428
\(753\) 0 0
\(754\) 41.6515 1.51686
\(755\) −8.07344 −0.293823
\(756\) 0 0
\(757\) −5.66698 −0.205970 −0.102985 0.994683i \(-0.532839\pi\)
−0.102985 + 0.994683i \(0.532839\pi\)
\(758\) 0.681032 0.0247362
\(759\) 0 0
\(760\) 10.9368 0.396719
\(761\) 26.1661 + 45.3210i 0.948519 + 1.64288i 0.748546 + 0.663082i \(0.230752\pi\)
0.199973 + 0.979801i \(0.435915\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13.4337 −0.486014
\(765\) 0 0
\(766\) 9.78121 + 16.9416i 0.353410 + 0.612123i
\(767\) −0.732404 + 1.26856i −0.0264456 + 0.0458051i
\(768\) 0 0
\(769\) 1.17360 2.03274i 0.0423212 0.0733025i −0.844089 0.536203i \(-0.819858\pi\)
0.886410 + 0.462901i \(0.153191\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −26.7274 −0.961939
\(773\) 18.1814 + 31.4912i 0.653941 + 1.13266i 0.982158 + 0.188057i \(0.0602189\pi\)
−0.328217 + 0.944602i \(0.606448\pi\)
\(774\) 0 0
\(775\) −2.48285 + 4.30042i −0.0891866 + 0.154476i
\(776\) 3.98251 + 6.89790i 0.142964 + 0.247620i
\(777\) 0 0
\(778\) 29.3659 50.8633i 1.05282 1.82354i
\(779\) 10.4830 + 18.1571i 0.375592 + 0.650545i
\(780\) 0 0
\(781\) −5.38663 + 9.32991i −0.192749 + 0.333851i
\(782\) 27.1292 46.9892i 0.970139 1.68033i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.885235 + 1.53327i 0.0315954 + 0.0547248i
\(786\) 0 0
\(787\) −31.7692 −1.13245 −0.566224 0.824251i \(-0.691596\pi\)
−0.566224 + 0.824251i \(0.691596\pi\)
\(788\) −9.06944 −0.323085
\(789\) 0 0
\(790\) 12.4435 + 21.5528i 0.442721 + 0.766816i
\(791\) 0 0
\(792\) 0 0
\(793\) 24.5403 42.5050i 0.871451 1.50940i
\(794\) 32.1012 55.6009i 1.13923 1.97320i
\(795\) 0 0
\(796\) −15.1711 26.2771i