Properties

Label 1323.2.o.e.440.9
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
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.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.9
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +O(q^{10})\) \(q+(-0.575298 - 0.332148i) q^{2} +(-0.779355 - 1.34988i) q^{4} +(-0.0141520 - 0.0245119i) q^{5} +2.36404i q^{8} +0.0188022i q^{10} +(0.885324 + 0.511142i) q^{11} +(-4.87844 + 2.81657i) q^{13} +(-0.773498 + 1.33974i) q^{16} +5.67880 q^{17} -2.09274i q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(2.49960 - 4.32943i) q^{25} +3.74208 q^{26} +(3.52577 + 2.03560i) q^{29} +(2.87364 - 1.65910i) q^{31} +(4.98462 - 2.87787i) q^{32} +(-3.26700 - 1.88620i) q^{34} -2.47265 q^{37} +(-0.695101 + 1.20395i) q^{38} +(0.0579471 - 0.0334558i) q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} -1.59344i q^{44} -4.82367 q^{46} +(-5.43997 + 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} +(7.60408 + 4.39022i) q^{52} -11.5995i q^{53} -0.0289346i q^{55} +(-1.35224 - 2.34215i) q^{58} +(3.01111 + 5.21540i) q^{59} +(2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(0.138079 + 0.0797200i) q^{65} +(-6.38995 - 11.0677i) q^{67} +(-4.42580 - 7.66571i) q^{68} -7.93415i q^{71} -10.8991i q^{73} +(1.42251 + 0.821285i) q^{74} +(-2.82496 + 1.63099i) q^{76} +(7.80018 - 13.5103i) q^{79} +0.0437861 q^{80} +4.68816i q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(-1.20836 + 2.09294i) q^{88} +12.0516 q^{89} +(-9.80194 - 5.65915i) q^{92} +(6.25921 - 3.61376i) q^{94} +(-0.0512971 + 0.0296164i) q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.575298 0.332148i −0.406797 0.234864i 0.282616 0.959233i \(-0.408798\pi\)
−0.689413 + 0.724369i \(0.742131\pi\)
\(3\) 0 0
\(4\) −0.779355 1.34988i −0.389677 0.674941i
\(5\) −0.0141520 0.0245119i −0.00632895 0.0109621i 0.862844 0.505471i \(-0.168681\pi\)
−0.869173 + 0.494509i \(0.835348\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.36404i 0.835814i
\(9\) 0 0
\(10\) 0.0188022i 0.00594578i
\(11\) 0.885324 + 0.511142i 0.266935 + 0.154115i 0.627494 0.778621i \(-0.284081\pi\)
−0.360559 + 0.932736i \(0.617414\pi\)
\(12\) 0 0
\(13\) −4.87844 + 2.81657i −1.35304 + 0.781176i −0.988674 0.150081i \(-0.952047\pi\)
−0.364363 + 0.931257i \(0.618713\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.773498 + 1.33974i −0.193375 + 0.334935i
\(17\) 5.67880 1.37731 0.688656 0.725089i \(-0.258201\pi\)
0.688656 + 0.725089i \(0.258201\pi\)
\(18\) 0 0
\(19\) 2.09274i 0.480108i −0.970760 0.240054i \(-0.922835\pi\)
0.970760 0.240054i \(-0.0771651\pi\)
\(20\) −0.0220588 + 0.0382070i −0.00493250 + 0.00854334i
\(21\) 0 0
\(22\) −0.339550 0.588118i −0.0723923 0.125387i
\(23\) 6.28849 3.63066i 1.31124 0.757046i 0.328940 0.944351i \(-0.393309\pi\)
0.982302 + 0.187305i \(0.0599754\pi\)
\(24\) 0 0
\(25\) 2.49960 4.32943i 0.499920 0.865887i
\(26\) 3.74208 0.733882
\(27\) 0 0
\(28\) 0 0
\(29\) 3.52577 + 2.03560i 0.654718 + 0.378002i 0.790262 0.612770i \(-0.209945\pi\)
−0.135543 + 0.990771i \(0.543278\pi\)
\(30\) 0 0
\(31\) 2.87364 1.65910i 0.516122 0.297983i −0.219225 0.975674i \(-0.570353\pi\)
0.735346 + 0.677691i \(0.237019\pi\)
\(32\) 4.98462 2.87787i 0.881165 0.508741i
\(33\) 0 0
\(34\) −3.26700 1.88620i −0.560286 0.323481i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.47265 −0.406501 −0.203250 0.979127i \(-0.565151\pi\)
−0.203250 + 0.979127i \(0.565151\pi\)
\(38\) −0.695101 + 1.20395i −0.112760 + 0.195306i
\(39\) 0 0
\(40\) 0.0579471 0.0334558i 0.00916224 0.00528982i
\(41\) −3.52867 6.11183i −0.551085 0.954508i −0.998197 0.0600295i \(-0.980881\pi\)
0.447111 0.894478i \(-0.352453\pi\)
\(42\) 0 0
\(43\) −1.15994 + 2.00908i −0.176890 + 0.306382i −0.940814 0.338924i \(-0.889937\pi\)
0.763924 + 0.645306i \(0.223270\pi\)
\(44\) 1.59344i 0.240221i
\(45\) 0 0
\(46\) −4.82367 −0.711212
\(47\) −5.43997 + 9.42231i −0.793502 + 1.37439i 0.130285 + 0.991477i \(0.458411\pi\)
−0.923786 + 0.382908i \(0.874922\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.87603 + 1.66048i −0.406732 + 0.234827i
\(51\) 0 0
\(52\) 7.60408 + 4.39022i 1.05450 + 0.608814i
\(53\) 11.5995i 1.59331i −0.604435 0.796655i \(-0.706601\pi\)
0.604435 0.796655i \(-0.293399\pi\)
\(54\) 0 0
\(55\) 0.0289346i 0.00390155i
\(56\) 0 0
\(57\) 0 0
\(58\) −1.35224 2.34215i −0.177558 0.307540i
\(59\) 3.01111 + 5.21540i 0.392013 + 0.678987i 0.992715 0.120486i \(-0.0384454\pi\)
−0.600702 + 0.799473i \(0.705112\pi\)
\(60\) 0 0
\(61\) 2.05220 + 1.18484i 0.262757 + 0.151703i 0.625592 0.780151i \(-0.284858\pi\)
−0.362834 + 0.931854i \(0.618191\pi\)
\(62\) −2.20427 −0.279942
\(63\) 0 0
\(64\) −0.729528 −0.0911909
\(65\) 0.138079 + 0.0797200i 0.0171266 + 0.00988805i
\(66\) 0 0
\(67\) −6.38995 11.0677i −0.780656 1.35214i −0.931560 0.363588i \(-0.881552\pi\)
0.150903 0.988549i \(-0.451782\pi\)
\(68\) −4.42580 7.66571i −0.536707 0.929604i
\(69\) 0 0
\(70\) 0 0
\(71\) 7.93415i 0.941610i −0.882237 0.470805i \(-0.843964\pi\)
0.882237 0.470805i \(-0.156036\pi\)
\(72\) 0 0
\(73\) 10.8991i 1.27564i −0.770185 0.637821i \(-0.779836\pi\)
0.770185 0.637821i \(-0.220164\pi\)
\(74\) 1.42251 + 0.821285i 0.165363 + 0.0954725i
\(75\) 0 0
\(76\) −2.82496 + 1.63099i −0.324045 + 0.187087i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.80018 13.5103i 0.877588 1.52003i 0.0236086 0.999721i \(-0.492484\pi\)
0.853980 0.520306i \(-0.174182\pi\)
\(80\) 0.0437861 0.00489543
\(81\) 0 0
\(82\) 4.68816i 0.517721i
\(83\) −3.07406 + 5.32442i −0.337421 + 0.584431i −0.983947 0.178461i \(-0.942888\pi\)
0.646526 + 0.762892i \(0.276221\pi\)
\(84\) 0 0
\(85\) −0.0803661 0.139198i −0.00871693 0.0150982i
\(86\) 1.33463 0.770546i 0.143916 0.0830902i
\(87\) 0 0
\(88\) −1.20836 + 2.09294i −0.128812 + 0.223108i
\(89\) 12.0516 1.27747 0.638736 0.769426i \(-0.279458\pi\)
0.638736 + 0.769426i \(0.279458\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −9.80194 5.65915i −1.02192 0.590007i
\(93\) 0 0
\(94\) 6.25921 3.61376i 0.645588 0.372730i
\(95\) −0.0512971 + 0.0296164i −0.00526297 + 0.00303858i
\(96\) 0 0
\(97\) 6.77565 + 3.91192i 0.687963 + 0.397196i 0.802848 0.596183i \(-0.203317\pi\)
−0.114885 + 0.993379i \(0.536650\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −7.79230 −0.779230
\(101\) 0.226924 0.393043i 0.0225797 0.0391093i −0.854515 0.519427i \(-0.826145\pi\)
0.877094 + 0.480318i \(0.159479\pi\)
\(102\) 0 0
\(103\) 4.58316 2.64609i 0.451592 0.260727i −0.256910 0.966435i \(-0.582704\pi\)
0.708502 + 0.705708i \(0.249371\pi\)
\(104\) −6.65848 11.5328i −0.652918 1.13089i
\(105\) 0 0
\(106\) −3.85274 + 6.67315i −0.374212 + 0.648153i
\(107\) 9.06755i 0.876593i 0.898830 + 0.438296i \(0.144418\pi\)
−0.898830 + 0.438296i \(0.855582\pi\)
\(108\) 0 0
\(109\) 4.73027 0.453078 0.226539 0.974002i \(-0.427259\pi\)
0.226539 + 0.974002i \(0.427259\pi\)
\(110\) −0.00961059 + 0.0166460i −0.000916334 + 0.00158714i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.21108 4.74067i 0.772433 0.445965i −0.0613086 0.998119i \(-0.519527\pi\)
0.833742 + 0.552154i \(0.186194\pi\)
\(114\) 0 0
\(115\) −0.177989 0.102762i −0.0165976 0.00958261i
\(116\) 6.34583i 0.589195i
\(117\) 0 0
\(118\) 4.00054i 0.368280i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.97747 8.62123i −0.452497 0.783748i
\(122\) −0.787084 1.36327i −0.0712593 0.123425i
\(123\) 0 0
\(124\) −4.47918 2.58606i −0.402242 0.232235i
\(125\) −0.283017 −0.0253138
\(126\) 0 0
\(127\) 4.37297 0.388039 0.194019 0.980998i \(-0.437848\pi\)
0.194019 + 0.980998i \(0.437848\pi\)
\(128\) −9.54954 5.51343i −0.844068 0.487323i
\(129\) 0 0
\(130\) −0.0529577 0.0917255i −0.00464470 0.00804486i
\(131\) −1.27231 2.20371i −0.111162 0.192539i 0.805077 0.593171i \(-0.202124\pi\)
−0.916239 + 0.400632i \(0.868791\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.48964i 0.733393i
\(135\) 0 0
\(136\) 13.4249i 1.15118i
\(137\) 9.82536 + 5.67267i 0.839437 + 0.484649i 0.857073 0.515195i \(-0.172281\pi\)
−0.0176357 + 0.999844i \(0.505614\pi\)
\(138\) 0 0
\(139\) 3.04891 1.76029i 0.258605 0.149306i −0.365093 0.930971i \(-0.618963\pi\)
0.623698 + 0.781665i \(0.285629\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.63531 + 4.56450i −0.221151 + 0.383044i
\(143\) −5.75867 −0.481564
\(144\) 0 0
\(145\) 0.115231i 0.00956942i
\(146\) −3.62012 + 6.27022i −0.299603 + 0.518927i
\(147\) 0 0
\(148\) 1.92707 + 3.33778i 0.158404 + 0.274364i
\(149\) 13.7806 7.95623i 1.12895 0.651800i 0.185279 0.982686i \(-0.440681\pi\)
0.943671 + 0.330886i \(0.107348\pi\)
\(150\) 0 0
\(151\) −1.73008 + 2.99659i −0.140792 + 0.243859i −0.927795 0.373090i \(-0.878298\pi\)
0.787003 + 0.616949i \(0.211632\pi\)
\(152\) 4.94732 0.401281
\(153\) 0 0
\(154\) 0 0
\(155\) −0.0813354 0.0469590i −0.00653302 0.00377184i
\(156\) 0 0
\(157\) −14.1585 + 8.17442i −1.12997 + 0.652390i −0.943928 0.330151i \(-0.892900\pi\)
−0.186045 + 0.982541i \(0.559567\pi\)
\(158\) −8.97485 + 5.18163i −0.714001 + 0.412228i
\(159\) 0 0
\(160\) −0.141084 0.0814550i −0.0111537 0.00643959i
\(161\) 0 0
\(162\) 0 0
\(163\) 10.3556 0.811116 0.405558 0.914069i \(-0.367077\pi\)
0.405558 + 0.914069i \(0.367077\pi\)
\(164\) −5.50017 + 9.52657i −0.429491 + 0.743900i
\(165\) 0 0
\(166\) 3.53699 2.04208i 0.274524 0.158497i
\(167\) 2.94297 + 5.09738i 0.227734 + 0.394447i 0.957136 0.289638i \(-0.0935349\pi\)
−0.729402 + 0.684085i \(0.760202\pi\)
\(168\) 0 0
\(169\) 9.36614 16.2226i 0.720473 1.24790i
\(170\) 0.106774i 0.00818919i
\(171\) 0 0
\(172\) 3.61603 0.275720
\(173\) −2.43276 + 4.21366i −0.184959 + 0.320359i −0.943563 0.331194i \(-0.892549\pi\)
0.758604 + 0.651552i \(0.225882\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.36959 + 0.790735i −0.103237 + 0.0596039i
\(177\) 0 0
\(178\) −6.93328 4.00293i −0.519671 0.300032i
\(179\) 0.202645i 0.0151464i −0.999971 0.00757319i \(-0.997589\pi\)
0.999971 0.00757319i \(-0.00241064\pi\)
\(180\) 0 0
\(181\) 6.26273i 0.465505i 0.972536 + 0.232753i \(0.0747732\pi\)
−0.972536 + 0.232753i \(0.925227\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8.58303 + 14.8662i 0.632749 + 1.09595i
\(185\) 0.0349928 + 0.0606093i 0.00257272 + 0.00445608i
\(186\) 0 0
\(187\) 5.02758 + 2.90267i 0.367653 + 0.212264i
\(188\) 16.9587 1.23684
\(189\) 0 0
\(190\) 0.0393482 0.00285462
\(191\) −11.9541 6.90168i −0.864965 0.499388i 0.000706698 1.00000i \(-0.499775\pi\)
−0.865672 + 0.500612i \(0.833108\pi\)
\(192\) 0 0
\(193\) 10.5387 + 18.2536i 0.758593 + 1.31392i 0.943568 + 0.331178i \(0.107446\pi\)
−0.184976 + 0.982743i \(0.559221\pi\)
\(194\) −2.59868 4.50104i −0.186574 0.323156i
\(195\) 0 0
\(196\) 0 0
\(197\) 15.1679i 1.08067i 0.841451 + 0.540334i \(0.181702\pi\)
−0.841451 + 0.540334i \(0.818298\pi\)
\(198\) 0 0
\(199\) 9.68724i 0.686710i −0.939206 0.343355i \(-0.888437\pi\)
0.939206 0.343355i \(-0.111563\pi\)
\(200\) 10.2349 + 5.90915i 0.723720 + 0.417840i
\(201\) 0 0
\(202\) −0.261097 + 0.150745i −0.0183707 + 0.0106064i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0998751 + 0.172989i −0.00697558 + 0.0120821i
\(206\) −3.51558 −0.244942
\(207\) 0 0
\(208\) 8.71445i 0.604238i
\(209\) 1.06969 1.85275i 0.0739919 0.128158i
\(210\) 0 0
\(211\) −7.05942 12.2273i −0.485991 0.841761i 0.513880 0.857862i \(-0.328208\pi\)
−0.999870 + 0.0161017i \(0.994874\pi\)
\(212\) −15.6579 + 9.04010i −1.07539 + 0.620877i
\(213\) 0 0
\(214\) 3.01177 5.21654i 0.205880 0.356595i
\(215\) 0.0656619 0.00447810
\(216\) 0 0
\(217\) 0 0
\(218\) −2.72132 1.57115i −0.184311 0.106412i
\(219\) 0 0
\(220\) −0.0390584 + 0.0225504i −0.00263331 + 0.00152034i
\(221\) −27.7037 + 15.9947i −1.86355 + 1.07592i
\(222\) 0 0
\(223\) −2.58777 1.49405i −0.173290 0.100049i 0.410846 0.911705i \(-0.365233\pi\)
−0.584136 + 0.811656i \(0.698567\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.29842 −0.418965
\(227\) 14.3867 24.9184i 0.954876 1.65389i 0.220224 0.975449i \(-0.429321\pi\)
0.734652 0.678444i \(-0.237346\pi\)
\(228\) 0 0
\(229\) −7.67401 + 4.43059i −0.507113 + 0.292782i −0.731646 0.681685i \(-0.761248\pi\)
0.224533 + 0.974466i \(0.427914\pi\)
\(230\) 0.0682645 + 0.118238i 0.00450122 + 0.00779635i
\(231\) 0 0
\(232\) −4.81224 + 8.33505i −0.315939 + 0.547223i
\(233\) 12.9082i 0.845646i 0.906212 + 0.422823i \(0.138961\pi\)
−0.906212 + 0.422823i \(0.861039\pi\)
\(234\) 0 0
\(235\) 0.307945 0.0200881
\(236\) 4.69345 8.12929i 0.305518 0.529172i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.85712 2.80426i 0.314181 0.181392i −0.334615 0.942355i \(-0.608606\pi\)
0.648796 + 0.760963i \(0.275273\pi\)
\(240\) 0 0
\(241\) −9.51481 5.49338i −0.612903 0.353860i 0.161198 0.986922i \(-0.448464\pi\)
−0.774101 + 0.633063i \(0.781798\pi\)
\(242\) 6.61303i 0.425102i
\(243\) 0 0
\(244\) 3.69364i 0.236461i
\(245\) 0 0
\(246\) 0 0
\(247\) 5.89436 + 10.2093i 0.375049 + 0.649604i
\(248\) 3.92218 + 6.79341i 0.249058 + 0.431382i
\(249\) 0 0
\(250\) 0.162819 + 0.0940035i 0.0102976 + 0.00594530i
\(251\) 24.2241 1.52901 0.764505 0.644618i \(-0.222984\pi\)
0.764505 + 0.644618i \(0.222984\pi\)
\(252\) 0 0
\(253\) 7.42314 0.466689
\(254\) −2.51576 1.45248i −0.157853 0.0911365i
\(255\) 0 0
\(256\) 4.39208 + 7.60731i 0.274505 + 0.475457i
\(257\) −8.86142 15.3484i −0.552760 0.957409i −0.998074 0.0620341i \(-0.980241\pi\)
0.445314 0.895375i \(-0.353092\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.248521i 0.0154126i
\(261\) 0 0
\(262\) 1.69039i 0.104432i
\(263\) −2.51031 1.44933i −0.154793 0.0893695i 0.420603 0.907245i \(-0.361819\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(264\) 0 0
\(265\) −0.284325 + 0.164155i −0.0174660 + 0.0100840i
\(266\) 0 0
\(267\) 0 0
\(268\) −9.96008 + 17.2514i −0.608408 + 1.05379i
\(269\) −21.8938 −1.33489 −0.667444 0.744660i \(-0.732612\pi\)
−0.667444 + 0.744660i \(0.732612\pi\)
\(270\) 0 0
\(271\) 8.98347i 0.545707i 0.962056 + 0.272854i \(0.0879675\pi\)
−0.962056 + 0.272854i \(0.912033\pi\)
\(272\) −4.39254 + 7.60811i −0.266337 + 0.461309i
\(273\) 0 0
\(274\) −3.76834 6.52695i −0.227654 0.394308i
\(275\) 4.42591 2.55530i 0.266892 0.154090i
\(276\) 0 0
\(277\) −7.95091 + 13.7714i −0.477724 + 0.827442i −0.999674 0.0255339i \(-0.991871\pi\)
0.521950 + 0.852976i \(0.325205\pi\)
\(278\) −2.33871 −0.140267
\(279\) 0 0
\(280\) 0 0
\(281\) 4.50324 + 2.59995i 0.268641 + 0.155100i 0.628270 0.777996i \(-0.283763\pi\)
−0.359629 + 0.933095i \(0.617097\pi\)
\(282\) 0 0
\(283\) −16.2587 + 9.38694i −0.966476 + 0.557995i −0.898160 0.439668i \(-0.855096\pi\)
−0.0683162 + 0.997664i \(0.521763\pi\)
\(284\) −10.7102 + 6.18352i −0.635531 + 0.366924i
\(285\) 0 0
\(286\) 3.31295 + 1.91273i 0.195899 + 0.113102i
\(287\) 0 0
\(288\) 0 0
\(289\) 15.2488 0.896986
\(290\) −0.0382738 + 0.0662922i −0.00224751 + 0.00389281i
\(291\) 0 0
\(292\) −14.7125 + 8.49426i −0.860983 + 0.497089i
\(293\) 11.4201 + 19.7802i 0.667169 + 1.15557i 0.978692 + 0.205332i \(0.0658274\pi\)
−0.311523 + 0.950238i \(0.600839\pi\)
\(294\) 0 0
\(295\) 0.0852263 0.147616i 0.00496206 0.00859455i
\(296\) 5.84543i 0.339759i
\(297\) 0 0
\(298\) −10.5706 −0.612338
\(299\) −20.4520 + 35.4240i −1.18277 + 2.04862i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.99062 1.14929i 0.114548 0.0661341i
\(303\) 0 0
\(304\) 2.80373 + 1.61873i 0.160805 + 0.0928407i
\(305\) 0.0670711i 0.00384048i
\(306\) 0 0
\(307\) 18.6325i 1.06341i −0.846928 0.531707i \(-0.821551\pi\)
0.846928 0.531707i \(-0.178449\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.0311947 + 0.0540308i 0.00177174 + 0.00306875i
\(311\) −10.2747 17.7964i −0.582628 1.00914i −0.995167 0.0982007i \(-0.968691\pi\)
0.412539 0.910940i \(-0.364642\pi\)
\(312\) 0 0
\(313\) 0.624466 + 0.360536i 0.0352969 + 0.0203787i 0.517545 0.855656i \(-0.326846\pi\)
−0.482248 + 0.876035i \(0.660179\pi\)
\(314\) 10.8605 0.612893
\(315\) 0 0
\(316\) −24.3164 −1.36791
\(317\) 18.9915 + 10.9647i 1.06667 + 0.615841i 0.927269 0.374396i \(-0.122150\pi\)
0.139398 + 0.990236i \(0.455483\pi\)
\(318\) 0 0
\(319\) 2.08096 + 3.60433i 0.116512 + 0.201804i
\(320\) 0.0103242 + 0.0178821i 0.000577143 + 0.000999641i
\(321\) 0 0
\(322\) 0 0
\(323\) 11.8843i 0.661258i
\(324\) 0 0
\(325\) 28.1612i 1.56210i
\(326\) −5.95757 3.43961i −0.329959 0.190502i
\(327\) 0 0
\(328\) 14.4486 8.34191i 0.797791 0.460605i
\(329\) 0 0
\(330\) 0 0
\(331\) −10.8338 + 18.7647i −0.595480 + 1.03140i 0.397999 + 0.917386i \(0.369705\pi\)
−0.993479 + 0.114016i \(0.963629\pi\)
\(332\) 9.58312 0.525942
\(333\) 0 0
\(334\) 3.91002i 0.213947i
\(335\) −0.180861 + 0.313260i −0.00988147 + 0.0171152i
\(336\) 0 0
\(337\) 12.6455 + 21.9026i 0.688844 + 1.19311i 0.972212 + 0.234101i \(0.0752147\pi\)
−0.283369 + 0.959011i \(0.591452\pi\)
\(338\) −10.7766 + 6.22190i −0.586172 + 0.338427i
\(339\) 0 0
\(340\) −0.125268 + 0.216970i −0.00679358 + 0.0117668i
\(341\) 3.39214 0.183695
\(342\) 0 0
\(343\) 0 0
\(344\) −4.74955 2.74215i −0.256078 0.147847i
\(345\) 0 0
\(346\) 2.79912 1.61607i 0.150482 0.0868806i
\(347\) 4.92420 2.84299i 0.264345 0.152620i −0.361970 0.932190i \(-0.617896\pi\)
0.626315 + 0.779570i \(0.284562\pi\)
\(348\) 0 0
\(349\) 9.68412 + 5.59113i 0.518379 + 0.299286i 0.736271 0.676687i \(-0.236585\pi\)
−0.217892 + 0.975973i \(0.569918\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5.88400 0.313618
\(353\) 7.02111 12.1609i 0.373696 0.647260i −0.616435 0.787406i \(-0.711424\pi\)
0.990131 + 0.140146i \(0.0447571\pi\)
\(354\) 0 0
\(355\) −0.194481 + 0.112284i −0.0103220 + 0.00595940i
\(356\) −9.39250 16.2683i −0.497802 0.862218i
\(357\) 0 0
\(358\) −0.0673081 + 0.116581i −0.00355734 + 0.00616150i
\(359\) 27.1414i 1.43247i 0.697859 + 0.716235i \(0.254136\pi\)
−0.697859 + 0.716235i \(0.745864\pi\)
\(360\) 0 0
\(361\) 14.6204 0.769496
\(362\) 2.08016 3.60294i 0.109331 0.189366i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.267158 + 0.154244i −0.0139837 + 0.00807347i
\(366\) 0 0
\(367\) −5.95891 3.44038i −0.311053 0.179586i 0.336345 0.941739i \(-0.390809\pi\)
−0.647397 + 0.762153i \(0.724143\pi\)
\(368\) 11.2332i 0.585573i
\(369\) 0 0
\(370\) 0.0464912i 0.00241696i
\(371\) 0 0
\(372\) 0 0
\(373\) 0.123926 + 0.214645i 0.00641662 + 0.0111139i 0.869216 0.494433i \(-0.164624\pi\)
−0.862799 + 0.505547i \(0.831291\pi\)
\(374\) −1.92824 3.33980i −0.0997067 0.172697i
\(375\) 0 0
\(376\) −22.2747 12.8603i −1.14873 0.663220i
\(377\) −22.9337 −1.18114
\(378\) 0 0
\(379\) −8.91863 −0.458119 −0.229060 0.973412i \(-0.573565\pi\)
−0.229060 + 0.973412i \(0.573565\pi\)
\(380\) 0.0799573 + 0.0461634i 0.00410172 + 0.00236813i
\(381\) 0 0
\(382\) 4.58476 + 7.94104i 0.234577 + 0.406299i
\(383\) 0.163545 + 0.283268i 0.00835675 + 0.0144743i 0.870174 0.492745i \(-0.164007\pi\)
−0.861817 + 0.507220i \(0.830673\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0017i 0.712665i
\(387\) 0 0
\(388\) 12.1951i 0.619113i
\(389\) 5.72348 + 3.30445i 0.290192 + 0.167542i 0.638028 0.770013i \(-0.279750\pi\)
−0.347837 + 0.937555i \(0.613084\pi\)
\(390\) 0 0
\(391\) 35.7111 20.6178i 1.80599 1.04269i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.03799 8.72606i 0.253810 0.439613i
\(395\) −0.441551 −0.0222168
\(396\) 0 0
\(397\) 7.51057i 0.376945i 0.982078 + 0.188472i \(0.0603536\pi\)
−0.982078 + 0.188472i \(0.939646\pi\)
\(398\) −3.21760 + 5.57305i −0.161284 + 0.279352i
\(399\) 0 0
\(400\) 3.86687 + 6.69762i 0.193344 + 0.334881i
\(401\) 5.48595 3.16732i 0.273956 0.158168i −0.356728 0.934208i \(-0.616108\pi\)
0.630684 + 0.776040i \(0.282774\pi\)
\(402\) 0 0
\(403\) −9.34594 + 16.1876i −0.465555 + 0.806364i
\(404\) −0.707416 −0.0351953
\(405\) 0 0
\(406\) 0 0
\(407\) −2.18909 1.26387i −0.108509 0.0626479i
\(408\) 0 0
\(409\) 29.0045 16.7457i 1.43418 0.828024i 0.436743 0.899586i \(-0.356132\pi\)
0.997436 + 0.0715625i \(0.0227986\pi\)
\(410\) 0.114916 0.0663467i 0.00567529 0.00327663i
\(411\) 0 0
\(412\) −7.14382 4.12448i −0.351951 0.203199i
\(413\) 0 0
\(414\) 0 0
\(415\) 0.174016 0.00854209
\(416\) −16.2115 + 28.0791i −0.794832 + 1.37669i
\(417\) 0 0
\(418\) −1.23078 + 0.710590i −0.0601993 + 0.0347561i
\(419\) 0.896459 + 1.55271i 0.0437949 + 0.0758550i 0.887092 0.461593i \(-0.152722\pi\)
−0.843297 + 0.537448i \(0.819389\pi\)
\(420\) 0 0
\(421\) 1.90262 3.29543i 0.0927278 0.160609i −0.815930 0.578150i \(-0.803775\pi\)
0.908658 + 0.417541i \(0.137108\pi\)
\(422\) 9.37910i 0.456568i
\(423\) 0 0
\(424\) 27.4216 1.33171
\(425\) 14.1947 24.5860i 0.688545 1.19260i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.2401 7.06684i 0.591649 0.341589i
\(429\) 0 0
\(430\) −0.0377751 0.0218095i −0.00182168 0.00105175i
\(431\) 1.32957i 0.0640434i −0.999487 0.0320217i \(-0.989805\pi\)
0.999487 0.0320217i \(-0.0101946\pi\)
\(432\) 0 0
\(433\) 37.4292i 1.79873i 0.437194 + 0.899367i \(0.355972\pi\)
−0.437194 + 0.899367i \(0.644028\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3.68656 6.38531i −0.176554 0.305801i
\(437\) −7.59804 13.1602i −0.363464 0.629537i
\(438\) 0 0
\(439\) 20.5584 + 11.8694i 0.981201 + 0.566496i 0.902632 0.430412i \(-0.141632\pi\)
0.0785682 + 0.996909i \(0.474965\pi\)
\(440\) 0.0684026 0.00326097
\(441\) 0 0
\(442\) 21.2505 1.01078
\(443\) −9.74317 5.62522i −0.462912 0.267262i 0.250356 0.968154i \(-0.419452\pi\)
−0.713268 + 0.700891i \(0.752786\pi\)
\(444\) 0 0
\(445\) −0.170554 0.295409i −0.00808505 0.0140037i
\(446\) 0.992491 + 1.71904i 0.0469958 + 0.0813991i
\(447\) 0 0
\(448\) 0 0
\(449\) 14.3953i 0.679357i 0.940542 + 0.339679i \(0.110318\pi\)
−0.940542 + 0.339679i \(0.889682\pi\)
\(450\) 0 0
\(451\) 7.21460i 0.339722i
\(452\) −12.7987 7.38933i −0.602000 0.347565i
\(453\) 0 0
\(454\) −16.5532 + 9.55701i −0.776881 + 0.448533i
\(455\) 0 0
\(456\) 0 0
\(457\) 10.3135 17.8635i 0.482444 0.835617i −0.517353 0.855772i \(-0.673083\pi\)
0.999797 + 0.0201547i \(0.00641589\pi\)
\(458\) 5.88646 0.275056
\(459\) 0 0
\(460\) 0.320352i 0.0149365i
\(461\) −0.832511 + 1.44195i −0.0387739 + 0.0671584i −0.884761 0.466045i \(-0.845679\pi\)
0.845987 + 0.533203i \(0.179012\pi\)
\(462\) 0 0
\(463\) 0.604175 + 1.04646i 0.0280784 + 0.0486332i 0.879723 0.475486i \(-0.157728\pi\)
−0.851645 + 0.524119i \(0.824395\pi\)
\(464\) −5.45435 + 3.14907i −0.253212 + 0.146192i
\(465\) 0 0
\(466\) 4.28745 7.42608i 0.198612 0.344006i
\(467\) −9.23988 −0.427571 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.177160 0.102283i −0.00817179 0.00471798i
\(471\) 0 0
\(472\) −12.3294 + 7.11839i −0.567507 + 0.327650i
\(473\) −2.05385 + 1.18579i −0.0944361 + 0.0545227i
\(474\) 0 0
\(475\) −9.06039 5.23102i −0.415719 0.240016i
\(476\) 0 0
\(477\) 0 0
\(478\) −3.72572 −0.170410
\(479\) −8.77241 + 15.1943i −0.400822 + 0.694243i −0.993825 0.110956i \(-0.964609\pi\)
0.593004 + 0.805200i \(0.297942\pi\)
\(480\) 0 0
\(481\) 12.0627 6.96438i 0.550010 0.317549i
\(482\) 3.64923 + 6.32066i 0.166218 + 0.287898i
\(483\) 0 0
\(484\) −7.75843 + 13.4380i −0.352656 + 0.610818i
\(485\) 0.221446i 0.0100553i
\(486\) 0 0
\(487\) −43.1898 −1.95712 −0.978558 0.205974i \(-0.933964\pi\)
−0.978558 + 0.205974i \(0.933964\pi\)
\(488\) −2.80100 + 4.85148i −0.126796 + 0.219616i
\(489\) 0 0
\(490\) 0 0
\(491\) −23.0046 + 13.2817i −1.03818 + 0.599396i −0.919319 0.393514i \(-0.871259\pi\)
−0.118866 + 0.992910i \(0.537926\pi\)
\(492\) 0 0
\(493\) 20.0221 + 11.5598i 0.901751 + 0.520626i
\(494\) 7.83120i 0.352342i
\(495\) 0 0
\(496\) 5.13324i 0.230489i
\(497\) 0 0
\(498\) 0 0
\(499\) −2.65759 4.60308i −0.118970 0.206062i 0.800390 0.599480i \(-0.204626\pi\)
−0.919360 + 0.393418i \(0.871293\pi\)
\(500\) 0.220570 + 0.382039i 0.00986421 + 0.0170853i
\(501\) 0 0
\(502\) −13.9361 8.04598i −0.621996 0.359110i
\(503\) −35.5334 −1.58436 −0.792178 0.610290i \(-0.791053\pi\)
−0.792178 + 0.610290i \(0.791053\pi\)
\(504\) 0 0
\(505\) −0.0128457 −0.000571624
\(506\) −4.27051 2.46558i −0.189847 0.109608i
\(507\) 0 0
\(508\) −3.40810 5.90300i −0.151210 0.261903i
\(509\) 6.81654 + 11.8066i 0.302138 + 0.523318i 0.976620 0.214973i \(-0.0689663\pi\)
−0.674482 + 0.738291i \(0.735633\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.2184i 0.716760i
\(513\) 0 0
\(514\) 11.7732i 0.519295i
\(515\) −0.129721 0.0748947i −0.00571621 0.00330025i
\(516\) 0 0
\(517\) −9.63227 + 5.56120i −0.423627 + 0.244581i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.188461 + 0.326424i −0.00826457 + 0.0143147i
\(521\) −10.2252 −0.447973 −0.223987 0.974592i \(-0.571907\pi\)
−0.223987 + 0.974592i \(0.571907\pi\)
\(522\) 0 0
\(523\) 5.17480i 0.226278i −0.993579 0.113139i \(-0.963909\pi\)
0.993579 0.113139i \(-0.0360905\pi\)
\(524\) −1.98317 + 3.43495i −0.0866350 + 0.150056i
\(525\) 0 0
\(526\) 0.962785 + 1.66759i 0.0419794 + 0.0727105i
\(527\) 16.3189 9.42169i 0.710860 0.410415i
\(528\) 0 0
\(529\) 14.8634 25.7442i 0.646236 1.11931i
\(530\) 0.218096 0.00947346
\(531\) 0 0
\(532\) 0 0
\(533\) 34.4288 + 19.8775i 1.49128 + 0.860990i
\(534\) 0 0
\(535\) 0.222263 0.128324i 0.00960927 0.00554791i
\(536\) 26.1645 15.1061i 1.13013 0.652484i
\(537\) 0 0
\(538\) 12.5955 + 7.27199i 0.543029 + 0.313518i
\(539\) 0 0
\(540\) 0 0
\(541\) −25.4395 −1.09373 −0.546864 0.837222i \(-0.684178\pi\)
−0.546864 + 0.837222i \(0.684178\pi\)
\(542\) 2.98385 5.16817i 0.128167 0.221992i
\(543\) 0 0
\(544\) 28.3067 16.3429i 1.21364 0.700694i
\(545\) −0.0669427 0.115948i −0.00286751 0.00496667i
\(546\) 0 0
\(547\) 14.7771 25.5947i 0.631824 1.09435i −0.355355 0.934732i \(-0.615640\pi\)
0.987179 0.159620i \(-0.0510267\pi\)
\(548\) 17.6841i 0.755428i
\(549\) 0 0
\(550\) −3.39495 −0.144761
\(551\) 4.25999 7.37852i 0.181482 0.314336i
\(552\) 0 0
\(553\) 0 0
\(554\) 9.14828 5.28176i 0.388673 0.224401i
\(555\) 0 0
\(556\) −4.75237 2.74378i −0.201545 0.116362i
\(557\) 19.6054i 0.830706i 0.909660 + 0.415353i \(0.136342\pi\)
−0.909660 + 0.415353i \(0.863658\pi\)
\(558\) 0 0
\(559\) 13.0683i 0.552728i
\(560\) 0 0
\(561\) 0 0
\(562\) −1.72714 2.99149i −0.0728548 0.126188i
\(563\) 7.23796 + 12.5365i 0.305044 + 0.528351i 0.977271 0.211994i \(-0.0679956\pi\)
−0.672227 + 0.740345i \(0.734662\pi\)
\(564\) 0 0
\(565\) −0.232406 0.134180i −0.00977738 0.00564497i
\(566\) 12.4714 0.524213
\(567\) 0 0
\(568\) 18.7566 0.787011
\(569\) −6.70970 3.87385i −0.281285 0.162400i 0.352720 0.935729i \(-0.385257\pi\)
−0.634005 + 0.773329i \(0.718590\pi\)
\(570\) 0 0
\(571\) −8.06856 13.9752i −0.337659 0.584842i 0.646333 0.763055i \(-0.276302\pi\)
−0.983992 + 0.178213i \(0.942968\pi\)
\(572\) 4.48805 + 7.77353i 0.187655 + 0.325027i
\(573\) 0 0
\(574\) 0 0
\(575\) 36.3008i 1.51385i
\(576\) 0 0
\(577\) 12.1708i 0.506679i −0.967377 0.253339i \(-0.918471\pi\)
0.967377 0.253339i \(-0.0815290\pi\)
\(578\) −8.77258 5.06485i −0.364891 0.210670i
\(579\) 0 0
\(580\) −0.155548 + 0.0898059i −0.00645879 + 0.00372899i
\(581\) 0 0
\(582\) 0 0
\(583\) 5.92897 10.2693i 0.245553 0.425310i
\(584\) 25.7659 1.06620
\(585\) 0 0
\(586\) 15.1727i 0.626777i
\(587\) 16.8761 29.2302i 0.696550 1.20646i −0.273106 0.961984i \(-0.588051\pi\)
0.969655 0.244476i \(-0.0786158\pi\)
\(588\) 0 0
\(589\) −3.47207 6.01380i −0.143064 0.247794i
\(590\) −0.0980610 + 0.0566155i −0.00403711 + 0.00233082i
\(591\) 0 0
\(592\) 1.91259 3.31270i 0.0786069 0.136151i
\(593\) 18.3025 0.751592 0.375796 0.926702i \(-0.377369\pi\)
0.375796 + 0.926702i \(0.377369\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −21.4799 12.4015i −0.879853 0.507983i
\(597\) 0 0
\(598\) 23.5320 13.5862i 0.962296 0.555582i
\(599\) 34.1905 19.7399i 1.39699 0.806551i 0.402911 0.915239i \(-0.367998\pi\)
0.994076 + 0.108689i \(0.0346651\pi\)
\(600\) 0 0
\(601\) −34.4865 19.9108i −1.40673 0.812177i −0.411661 0.911337i \(-0.635051\pi\)
−0.995072 + 0.0991600i \(0.968384\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.39339 0.219454
\(605\) −0.140882 + 0.244015i −0.00572766 + 0.00992060i
\(606\) 0 0
\(607\) −21.6104 + 12.4768i −0.877140 + 0.506417i −0.869714 0.493555i \(-0.835697\pi\)
−0.00742570 + 0.999972i \(0.502364\pi\)
\(608\) −6.02264 10.4315i −0.244250 0.423054i
\(609\) 0 0
\(610\) −0.0222776 + 0.0385859i −0.000901992 + 0.00156230i
\(611\) 61.2883i 2.47946i
\(612\) 0 0
\(613\) 28.0570 1.13321 0.566605 0.823990i \(-0.308257\pi\)
0.566605 + 0.823990i \(0.308257\pi\)
\(614\) −6.18876 + 10.7192i −0.249758 + 0.432594i
\(615\) 0 0
\(616\) 0 0
\(617\) −29.8093 + 17.2104i −1.20008 + 0.692865i −0.960573 0.278030i \(-0.910319\pi\)
−0.239506 + 0.970895i \(0.576985\pi\)
\(618\) 0 0
\(619\) −17.2889 9.98173i −0.694898 0.401200i 0.110546 0.993871i \(-0.464740\pi\)
−0.805444 + 0.592671i \(0.798073\pi\)
\(620\) 0.146391i 0.00587920i
\(621\) 0 0
\(622\) 13.6510i 0.547354i
\(623\) 0 0
\(624\) 0 0
\(625\) −12.4940 21.6402i −0.499760 0.865609i
\(626\) −0.239503 0.414831i −0.00957245 0.0165800i
\(627\) 0 0
\(628\) 22.0690 + 12.7416i 0.880650 + 0.508443i
\(629\) −14.0417 −0.559878
\(630\) 0 0
\(631\) −46.8447 −1.86486 −0.932429 0.361354i \(-0.882314\pi\)
−0.932429 + 0.361354i \(0.882314\pi\)
\(632\) 31.9389 + 18.4399i 1.27046 + 0.733501i
\(633\) 0 0
\(634\) −7.28384 12.6160i −0.289278 0.501044i
\(635\) −0.0618862 0.107190i −0.00245588 0.00425370i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.76475i 0.109458i
\(639\) 0 0
\(640\) 0.312103i 0.0123370i
\(641\) 3.34281 + 1.92997i 0.132033 + 0.0762293i 0.564562 0.825391i \(-0.309045\pi\)
−0.432529 + 0.901620i \(0.642379\pi\)
\(642\) 0 0
\(643\) −31.0233 + 17.9113i −1.22344 + 0.706352i −0.965649 0.259849i \(-0.916327\pi\)
−0.257789 + 0.966201i \(0.582994\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.94734 + 6.83699i −0.155306 + 0.268998i
\(647\) 43.6492 1.71603 0.858013 0.513627i \(-0.171699\pi\)
0.858013 + 0.513627i \(0.171699\pi\)
\(648\) 0 0
\(649\) 6.15642i 0.241661i
\(650\) 9.35369 16.2011i 0.366882 0.635458i
\(651\) 0 0
\(652\) −8.07072 13.9789i −0.316074 0.547456i
\(653\) −6.45191 + 3.72501i −0.252483 + 0.145771i −0.620901 0.783889i \(-0.713233\pi\)
0.368418 + 0.929660i \(0.379900\pi\)
\(654\) 0 0
\(655\) −0.0360114 + 0.0623736i −0.00140708 + 0.00243714i
\(656\) 10.9177 0.426264
\(657\) 0 0
\(658\) 0 0
\(659\) 7.52607 + 4.34518i 0.293174 + 0.169264i 0.639372 0.768897i \(-0.279194\pi\)
−0.346198 + 0.938161i \(0.612528\pi\)
\(660\) 0 0
\(661\) −24.9853 + 14.4253i −0.971815 + 0.561077i −0.899789 0.436325i \(-0.856280\pi\)
−0.0720256 + 0.997403i \(0.522946\pi\)
\(662\) 12.4653 7.19686i 0.484479 0.279714i
\(663\) 0 0
\(664\) −12.5871 7.26719i −0.488476 0.282022i
\(665\) 0 0
\(666\) 0 0
\(667\) 29.5623 1.14466
\(668\) 4.58724 7.94534i 0.177486 0.307414i
\(669\) 0 0
\(670\) 0.208097 0.120145i 0.00803950 0.00464161i
\(671\) 1.21124 + 2.09793i 0.0467594 + 0.0809897i
\(672\) 0 0
\(673\) −3.60695 + 6.24742i −0.139038 + 0.240820i −0.927133 0.374733i \(-0.877734\pi\)
0.788095 + 0.615554i \(0.211068\pi\)
\(674\) 16.8007i 0.647139i
\(675\) 0 0
\(676\) −29.1982 −1.12301
\(677\) 18.1911 31.5079i 0.699140 1.21095i −0.269626 0.962965i \(-0.586900\pi\)
0.968765 0.247980i \(-0.0797667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.329070 0.189989i 0.0126193 0.00728573i
\(681\) 0 0
\(682\) −1.95149 1.12669i −0.0747265 0.0431433i
\(683\) 23.7326i 0.908101i −0.890976 0.454050i \(-0.849979\pi\)
0.890976 0.454050i \(-0.150021\pi\)
\(684\) 0 0
\(685\) 0.321118i 0.0122693i
\(686\) 0 0
\(687\) 0 0
\(688\) −1.79443 3.10804i −0.0684119 0.118493i
\(689\) 32.6707 + 56.5874i 1.24466 + 2.15581i
\(690\) 0 0
\(691\) 2.86127 + 1.65195i 0.108848 + 0.0628433i 0.553436 0.832892i \(-0.313316\pi\)
−0.444588 + 0.895735i \(0.646650\pi\)
\(692\) 7.58393 0.288298
\(693\) 0 0
\(694\) −3.77718 −0.143380
\(695\) −0.0862962 0.0498231i −0.00327340 0.00188990i
\(696\) 0 0
\(697\) −20.0386 34.7079i −0.759016 1.31465i
\(698\) −3.71417 6.43313i −0.140583 0.243498i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.873603i 0.0329955i 0.999864 + 0.0164978i \(0.00525164\pi\)
−0.999864 + 0.0164978i \(0.994748\pi\)
\(702\) 0 0
\(703\) 5.17461i 0.195164i
\(704\) −0.645868 0.372892i −0.0243421 0.0140539i
\(705\) 0 0
\(706\) −8.07845 + 4.66410i −0.304037 + 0.175536i
\(707\) 0 0
\(708\) 0 0
\(709\) −8.07767 + 13.9909i −0.303363 + 0.525441i −0.976896 0.213717i \(-0.931443\pi\)
0.673532 + 0.739158i \(0.264776\pi\)
\(710\) 0.149179 0.00559860
\(711\) 0 0
\(712\) 28.4905i 1.06773i
\(713\) 12.0473 20.8665i 0.451174 0.781456i
\(714\) 0 0
\(715\) 0.0814965 + 0.141156i 0.00304779 + 0.00527894i
\(716\) −0.273546 + 0.157932i −0.0102229 + 0.00590220i
\(717\) 0 0
\(718\) 9.01498 15.6144i 0.336436 0.582724i
\(719\) −45.1905 −1.68532 −0.842661 0.538445i \(-0.819012\pi\)
−0.842661 + 0.538445i \(0.819012\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8.41110 4.85615i −0.313029 0.180727i
\(723\) 0 0
\(724\) 8.45395 4.88089i 0.314189 0.181397i
\(725\) 17.6260 10.1764i 0.654613 0.377941i
\(726\) 0 0
\(727\) 7.15775 + 4.13253i 0.265466 + 0.153267i 0.626826 0.779160i \(-0.284354\pi\)
−0.361359 + 0.932427i \(0.617687\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.204927 0.00758468
\(731\) −6.58709 + 11.4092i −0.243632 + 0.421983i
\(732\) 0 0
\(733\) 10.5799 6.10830i 0.390777 0.225615i −0.291720 0.956504i \(-0.594227\pi\)
0.682497 + 0.730889i \(0.260894\pi\)
\(734\) 2.28543 + 3.95849i 0.0843569 + 0.146110i
\(735\) 0 0
\(736\) 20.8972 36.1949i 0.770280 1.33416i
\(737\) 13.0647i 0.481244i
\(738\) 0 0
\(739\) −20.7072 −0.761726 −0.380863 0.924631i \(-0.624373\pi\)
−0.380863 + 0.924631i \(0.624373\pi\)
\(740\) 0.0545436 0.0944723i 0.00200506 0.00347287i
\(741\) 0 0
\(742\) 0 0
\(743\) −10.2862 + 5.93873i −0.377363 + 0.217871i −0.676670 0.736286i \(-0.736578\pi\)
0.299307 + 0.954157i \(0.403244\pi\)
\(744\) 0 0
\(745\) −0.390045 0.225192i −0.0142901 0.00825041i
\(746\) 0.164647i 0.00602814i
\(747\) 0 0
\(748\) 9.04885i 0.330859i
\(749\) 0 0
\(750\) 0 0
\(751\) −11.8554 20.5342i −0.432610 0.749303i 0.564487 0.825442i \(-0.309074\pi\)
−0.997097 + 0.0761390i \(0.975741\pi\)
\(752\) −8.41562 14.5763i −0.306886 0.531542i
\(753\) 0 0
\(754\) 13.1937 + 7.61738i 0.480486 + 0.277409i
\(755\) 0.0979362 0.00356426
\(756\) 0 0
\(757\) 44.2494 1.60827 0.804136 0.594446i \(-0.202628\pi\)
0.804136 + 0.594446i \(0.202628\pi\)
\(758\) 5.13087 + 2.96231i 0.186362 + 0.107596i
\(759\) 0 0
\(760\) −0.0700143 0.121268i −0.00253969 0.00439887i
\(761\) 24.3767 + 42.2217i 0.883656 + 1.53054i 0.847246 + 0.531200i \(0.178259\pi\)
0.0364098 + 0.999337i \(0.488408\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.5154i 0.778401i
\(765\) 0 0
\(766\) 0.217284i 0.00785081i
\(767\) −29.3791 16.9620i −1.06082 0.612463i
\(768\) 0 0
\(769\) −23.3870 + 13.5025i −0.843357 + 0.486912i −0.858404 0.512975i \(-0.828543\pi\)
0.0150472 + 0.999887i \(0.495210\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 16.4268 28.4520i 0.591213 1.02401i
\(773\) −26.7135 −0.960817 −0.480408 0.877045i \(-0.659512\pi\)
−0.480408 + 0.877045i \(0.659512\pi\)
\(774\) 0 0
\(775\) 16.5883i 0.595871i
\(776\) −9.24794 + 16.0179i −0.331982 + 0.575009i
\(777\) 0 0
\(778\) −2.19514 3.80209i −0.0786994 0.136311i
\(779\) −12.7905 + 7.38459i −0.458267 + 0.264580i
\(780\) 0 0
\(781\) 4.05547 7.02429i 0.145116 0.251349i
\(782\) −27.3927 −0.979560
\(783\) 0 0
\(784\) 0 0
\(785\) 0.400742 + 0.231368i 0.0143031 + 0.00825789i
\(786\) 0 0
\(787\) 41.0093 23.6767i 1.46182 0.843983i 0.462726 0.886501i \(-0.346871\pi\)
0.999096 + 0.0425177i \(0.0135379\pi\)
\(788\) 20.4749 11.8212i 0.729388 0.421112i
\(789\) 0 0
\(790\) 0.254023 + 0.146660i 0.00903775 + 0.00521795i
\(791\) 0 0
\(792\) 0 0
\(793\) −13.3487 −0.474027
\(794\) 2.49462 4.32082i 0.0885309 0.153340i
\(795\) 0 0
\(796\)