Properties

Label 1323.2.h.h.226.1
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 226.1
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.h.802.1

$q$-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 0.688670 0.725075i \(-0.258195\pi\)
−0.972268 + 0.233868i \(0.924862\pi\)
\(6\) 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 \(0.395290\pi\)
−0.981117 + 0.193417i \(0.938043\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.98516 −0.496290
\(17\) 2.40822 + 4.17116i 0.584079 + 1.01165i 0.994990 + 0.0999785i \(0.0318774\pi\)
−0.410911 + 0.911676i \(0.634789\pi\)
\(18\) 0 0
\(19\) 2.69059 4.66025i 0.617265 1.06913i −0.372718 0.927945i \(-0.621574\pi\)
0.989983 0.141189i \(-0.0450925\pi\)
\(20\) −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 \(-0.458025\pi\)
0.131488 + 0.991318i \(0.458025\pi\)
\(32\) 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 −0.977092 0.212819i \(-0.931736\pi\)
0.672852 + 0.739777i \(0.265069\pi\)
\(42\) 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 \(-0.426083\pi\)
0.230135 + 0.973159i \(0.426083\pi\)
\(48\) 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 \(-0.493604\pi\)
0.0200935 + 0.999798i \(0.493604\pi\)
\(60\) 0 0
\(61\) −10.3429 −1.32427 −0.662134 0.749385i \(-0.730349\pi\)
−0.662134 + 0.749385i \(0.730349\pi\)
\(62\) −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 \(-0.954849\pi\)
0.372547 0.928013i \(-0.378484\pi\)
\(74\) 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 \(-0.978378\pi\)
0.440066 0.897965i \(-0.354955\pi\)
\(84\) 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 −0.970226 0.242200i \(-0.922131\pi\)
0.694864 + 0.719141i \(0.255464\pi\)
\(90\) 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 0.964168 0.265291i \(-0.0854682\pi\)
−0.711833 + 0.702348i \(0.752135\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.64005 8.03680i 0.464005 0.803680i
\(101\) −0.00266904 + 0.00462292i −0.000265580 + 0.000459997i −0.866158 0.499770i \(-0.833418\pi\)
0.865893 + 0.500230i \(0.166751\pi\)
\(102\) 0 0
\(103\) 6.51741 + 11.2885i 0.642180 + 1.11229i 0.984945 + 0.172867i \(0.0553030\pi\)
−0.342765 + 0.939421i \(0.611364\pi\)
\(104\) 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 0.869912 0.493207i \(-0.164175\pi\)
−0.862086 + 0.506763i \(0.830842\pi\)
\(132\) 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 \(0.461686\pi\)
−0.919798 + 0.392392i \(0.871648\pi\)
\(140\) 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 \(-0.517740\pi\)
−0.0557045 + 0.998447i \(0.517740\pi\)
\(158\) 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 −0.830313 0.557298i \(-0.811838\pi\)
0.897790 + 0.440423i \(0.145172\pi\)
\(168\) 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 \(-0.625119\pi\)
−0.383028 + 0.923737i \(0.625119\pi\)
\(174\) 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 \(-0.393823\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(182\) 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 0.992847 0.119393i \(-0.0380948\pi\)
−0.599821 + 0.800134i \(0.704761\pi\)
\(200\) −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 0.790114 0.612960i \(-0.210021\pi\)
−0.925896 + 0.377779i \(0.876688\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.68808 + 11.5841i −0.444884 + 0.770562i
\(227\) −0.667087 + 1.15543i −0.0442761 + 0.0766884i −0.887314 0.461165i \(-0.847431\pi\)
0.843038 + 0.537854i \(0.180765\pi\)
\(228\) 0 0
\(229\) −7.99832 13.8535i −0.528544 0.915465i −0.999446 0.0332795i \(-0.989405\pi\)
0.470902 0.882185i \(-0.343928\pi\)
\(230\) 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 \(-0.484897\pi\)
0.841336 0.540512i \(-0.181770\pi\)
\(242\) 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 \(-0.675061\pi\)
−0.522661 + 0.852541i \(0.675061\pi\)
\(252\) 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 0.832012 0.554758i \(-0.187189\pi\)
−0.896440 + 0.443164i \(0.853856\pi\)
\(258\) 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 0.998976 0.0452336i \(-0.0144032\pi\)
−0.538662 + 0.842522i \(0.681070\pi\)
\(270\) 0 0
\(271\) −14.4026 + 24.9459i −0.874893 + 1.51536i −0.0180156 + 0.999838i \(0.505735\pi\)
−0.856877 + 0.515521i \(0.827598\pi\)
\(272\) −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 \(-0.533949\pi\)
−0.106451 + 0.994318i \(0.533949\pi\)
\(284\) 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 \(-0.580910\pi\)
0.963928 0.266164i \(-0.0857563\pi\)
\(294\) 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 \(-0.261070\pi\)
0.682094 + 0.731265i \(0.261070\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.02072 + 3.49998i 0.114769 + 0.198786i
\(311\) −12.9416 −0.733853 −0.366926 0.930250i \(-0.619590\pi\)
−0.366926 + 0.930250i \(0.619590\pi\)
\(312\) 0 0
\(313\) 26.8681 1.51867 0.759336 0.650698i \(-0.225524\pi\)
0.759336 + 0.650698i \(0.225524\pi\)
\(314\) 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 \(-0.853639\pi\)
0.0637477 0.997966i \(-0.479695\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −20.6092 + 35.6963i −1.09848 + 1.90262i
\(353\) −1.32969 + 2.30309i −0.0707722 + 0.122581i −0.899240 0.437456i \(-0.855880\pi\)
0.828468 + 0.560037i \(0.189213\pi\)
\(354\) 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 −0.620068 0.784548i \(-0.712895\pi\)
0.989473 + 0.144720i \(0.0462283\pi\)
\(368\) 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 0.957705 0.287751i \(-0.0929075\pi\)
−0.728052 + 0.685522i \(0.759574\pi\)
\(384\) 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 \(-0.568019\pi\)
0.952361 0.304973i \(-0.0986475\pi\)
\(398\) −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 \(-0.587544\pi\)
−0.271574 + 0.962417i \(0.587544\pi\)
\(410\) −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 −0.935866 0.352357i \(-0.885380\pi\)
0.773083 + 0.634305i \(0.218714\pi\)
\(420\) 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 \(-0.809585\pi\)
−0.826348 + 0.563160i \(0.809585\pi\)
\(434\) 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 \(-0.545667\pi\)
−0.142977 + 0.989726i \(0.545667\pi\)
\(440\) −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 \(0.0724420\pi\)
−0.291711 + 0.956506i \(0.594225\pi\)
\(462\) 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 \(0.337641\pi\)
−0.999908 + 0.0135313i \(0.995693\pi\)
\(468\) 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 \(-0.638568\pi\)
0.996106 0.0881606i \(-0.0280989\pi\)
\(480\) 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 \(-0.281753\pi\)
0.633171 + 0.774012i \(0.281753\pi\)
\(504\) 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 0.901815 0.432122i \(-0.142235\pi\)
−0.825136 + 0.564934i \(0.808902\pi\)
\(510\) 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 0.777222 0.629227i \(-0.216628\pi\)
−0.933537 + 0.358480i \(0.883295\pi\)
\(522\) 0 0
\(523\) −6.53235 + 11.3144i −0.285640 + 0.494743i −0.972764 0.231797i \(-0.925539\pi\)
0.687124 + 0.726540i \(0.258873\pi\)
\(524\) 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 \(-0.531988\pi\)
−0.100325 + 0.994955i \(0.531988\pi\)
\(564\) 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 0.968387 0.249451i \(-0.0802502\pi\)
−0.700225 + 0.713923i \(0.746917\pi\)
\(578\) 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 \(-0.868814\pi\)
0.111235 0.993794i \(-0.464519\pi\)
\(588\) 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 \(0.476913\pi\)
−0.899982 + 0.435927i \(0.856421\pi\)
\(594\) 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 0.948000 0.318270i \(-0.103102\pi\)
−0.749630 + 0.661858i \(0.769768\pi\)
\(602\) 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 \(0.151931\pi\)
−0.0462763 + 0.998929i \(0.514735\pi\)
\(608\) 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 −0.964871 0.262726i \(-0.915379\pi\)
0.709962 + 0.704240i \(0.248712\pi\)
\(620\) −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 \(-0.458766\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −56.4060 −2.21926
\(647\) 19.5701 + 33.8964i 0.769379 + 1.33260i 0.937900 + 0.346905i \(0.112767\pi\)
−0.168521 + 0.985698i \(0.553899\pi\)
\(648\) 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 \(-0.771845\pi\)
−0.753932 + 0.656952i \(0.771845\pi\)
\(662\) −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 \(-0.472645\pi\)
0.0858322 + 0.996310i \(0.472645\pi\)
\(678\) 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 \(-0.214866\pi\)
0.780694 + 0.624913i \(0.214866\pi\)
\(692\) −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 \(-0.552891\pi\)
0.936797 0.349873i \(-0.113775\pi\)
\(720\) 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 0.942012 0.335580i \(-0.108932\pi\)
−0.761626 + 0.648016i \(0.775599\pi\)
\(728\) 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 \(0.0126158\pi\)
−0.465292 + 0.885157i \(0.654051\pi\)
\(734\) −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 \(-0.769248\pi\)
−0.199973 0.979801i \(-0.564085\pi\)
\(762\) 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 −0.886410 0.462901i \(-0.846809\pi\)
0.844089 + 0.536203i \(0.180142\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −26.7274 −0.961939
\(773\) −18.1814 31.4912i −0.653941 1.13266i −0.982158 0.188057i \(-0.939781\pi\)
0.328217 0.944602i \(-0.393552\pi\)
\(774\) 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 \(-0.308404\pi\)
0.566224 + 0.824251i \(0.308404\pi\)
\(788\) −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