Properties

Label 756.2.ba.a.575.3
Level $756$
Weight $2$
Character 756.575
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 575.3
Character \(\chi\) \(=\) 756.575
Dual form 756.2.ba.a.71.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +O(q^{10})\) \(q+(-1.37785 + 0.318634i) q^{2} +(1.79694 - 0.878061i) q^{4} +(-2.51813 + 1.45385i) q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.19614 + 1.78241i) q^{8} +(3.00637 - 2.80555i) q^{10} +(1.18430 - 2.05127i) q^{11} +(-0.125913 - 0.218087i) q^{13} +(1.35257 + 0.412980i) q^{14} +(2.45802 - 3.15565i) q^{16} -7.60859i q^{17} +2.60920i q^{19} +(-3.24838 + 4.82355i) q^{20} +(-0.978187 + 3.20371i) q^{22} +(4.51674 + 7.82323i) q^{23} +(1.72733 - 2.99183i) q^{25} +(0.242979 + 0.260371i) q^{26} +(-1.99523 - 0.138049i) q^{28} +(5.53448 + 3.19533i) q^{29} +(0.0905658 - 0.0522882i) q^{31} +(-2.38128 + 5.13123i) q^{32} +(2.42436 + 10.4835i) q^{34} +2.90769 q^{35} -3.15261 q^{37} +(-0.831380 - 3.59508i) q^{38} +(2.93883 - 7.68118i) q^{40} +(7.24183 - 4.18107i) q^{41} +(7.18102 + 4.14596i) q^{43} +(0.326984 - 4.72592i) q^{44} +(-8.71615 - 9.34005i) q^{46} +(0.248282 - 0.430036i) q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.42671 + 4.67268i) q^{50} +(-0.417752 - 0.281331i) q^{52} +2.38678i q^{53} +6.88718i q^{55} +(2.79312 - 0.445538i) q^{56} +(-8.64383 - 2.63922i) q^{58} +(3.99487 + 6.91932i) q^{59} +(3.69592 - 6.40151i) q^{61} +(-0.108125 + 0.100903i) q^{62} +(1.64606 - 7.82882i) q^{64} +(0.634129 + 0.366115i) q^{65} +(-0.444103 + 0.256403i) q^{67} +(-6.68081 - 13.6722i) q^{68} +(-4.00636 + 0.926490i) q^{70} +1.45233 q^{71} +4.06828 q^{73} +(4.34382 - 1.00453i) q^{74} +(2.29103 + 4.68858i) q^{76} +(-2.05127 + 1.18430i) q^{77} +(10.0369 + 5.79482i) q^{79} +(-1.60178 + 11.5199i) q^{80} +(-8.64592 + 8.06839i) q^{82} +(-0.439593 + 0.761398i) q^{83} +(11.0617 + 19.1594i) q^{85} +(-11.2154 - 3.42440i) q^{86} +(1.05531 + 6.61580i) q^{88} -14.6787i q^{89} +0.251825i q^{91} +(14.9856 + 10.0919i) q^{92} +(-0.205071 + 0.671637i) q^{94} +(-3.79337 - 6.57031i) q^{95} +(2.88066 - 4.98945i) q^{97} +(-0.964871 - 1.03394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37785 + 0.318634i −0.974287 + 0.225309i
\(3\) 0 0
\(4\) 1.79694 0.878061i 0.898472 0.439031i
\(5\) −2.51813 + 1.45385i −1.12614 + 0.650179i −0.942962 0.332900i \(-0.891973\pi\)
−0.183182 + 0.983079i \(0.558640\pi\)
\(6\) 0 0
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) −2.19614 + 1.78241i −0.776453 + 0.630175i
\(9\) 0 0
\(10\) 3.00637 2.80555i 0.950697 0.887191i
\(11\) 1.18430 2.05127i 0.357081 0.618483i −0.630391 0.776278i \(-0.717105\pi\)
0.987472 + 0.157795i \(0.0504387\pi\)
\(12\) 0 0
\(13\) −0.125913 0.218087i −0.0349219 0.0604864i 0.848036 0.529938i \(-0.177785\pi\)
−0.882958 + 0.469452i \(0.844452\pi\)
\(14\) 1.35257 + 0.412980i 0.361490 + 0.110373i
\(15\) 0 0
\(16\) 2.45802 3.15565i 0.614504 0.788913i
\(17\) 7.60859i 1.84535i −0.385574 0.922677i \(-0.625997\pi\)
0.385574 0.922677i \(-0.374003\pi\)
\(18\) 0 0
\(19\) 2.60920i 0.598591i 0.954160 + 0.299295i \(0.0967516\pi\)
−0.954160 + 0.299295i \(0.903248\pi\)
\(20\) −3.24838 + 4.82355i −0.726360 + 1.07858i
\(21\) 0 0
\(22\) −0.978187 + 3.20371i −0.208550 + 0.683033i
\(23\) 4.51674 + 7.82323i 0.941806 + 1.63126i 0.762024 + 0.647549i \(0.224206\pi\)
0.179782 + 0.983706i \(0.442461\pi\)
\(24\) 0 0
\(25\) 1.72733 2.99183i 0.345467 0.598366i
\(26\) 0.242979 + 0.260371i 0.0476520 + 0.0510630i
\(27\) 0 0
\(28\) −1.99523 0.138049i −0.377063 0.0260888i
\(29\) 5.53448 + 3.19533i 1.02773 + 0.593358i 0.916333 0.400418i \(-0.131135\pi\)
0.111394 + 0.993776i \(0.464468\pi\)
\(30\) 0 0
\(31\) 0.0905658 0.0522882i 0.0162661 0.00939124i −0.491845 0.870683i \(-0.663677\pi\)
0.508111 + 0.861292i \(0.330344\pi\)
\(32\) −2.38128 + 5.13123i −0.420955 + 0.907082i
\(33\) 0 0
\(34\) 2.42436 + 10.4835i 0.415774 + 1.79790i
\(35\) 2.90769 0.491489
\(36\) 0 0
\(37\) −3.15261 −0.518285 −0.259143 0.965839i \(-0.583440\pi\)
−0.259143 + 0.965839i \(0.583440\pi\)
\(38\) −0.831380 3.59508i −0.134868 0.583200i
\(39\) 0 0
\(40\) 2.93883 7.68118i 0.464670 1.21450i
\(41\) 7.24183 4.18107i 1.13098 0.652974i 0.186801 0.982398i \(-0.440188\pi\)
0.944182 + 0.329424i \(0.106855\pi\)
\(42\) 0 0
\(43\) 7.18102 + 4.14596i 1.09510 + 0.632254i 0.934928 0.354836i \(-0.115463\pi\)
0.160167 + 0.987090i \(0.448797\pi\)
\(44\) 0.326984 4.72592i 0.0492946 0.712459i
\(45\) 0 0
\(46\) −8.71615 9.34005i −1.28513 1.37712i
\(47\) 0.248282 0.430036i 0.0362156 0.0627273i −0.847349 0.531036i \(-0.821803\pi\)
0.883565 + 0.468308i \(0.155136\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −1.42671 + 4.67268i −0.201767 + 0.660817i
\(51\) 0 0
\(52\) −0.417752 0.281331i −0.0579317 0.0390136i
\(53\) 2.38678i 0.327849i 0.986473 + 0.163925i \(0.0524154\pi\)
−0.986473 + 0.163925i \(0.947585\pi\)
\(54\) 0 0
\(55\) 6.88718i 0.928667i
\(56\) 2.79312 0.445538i 0.373246 0.0595375i
\(57\) 0 0
\(58\) −8.64383 2.63922i −1.13499 0.346546i
\(59\) 3.99487 + 6.91932i 0.520088 + 0.900818i 0.999727 + 0.0233526i \(0.00743403\pi\)
−0.479640 + 0.877466i \(0.659233\pi\)
\(60\) 0 0
\(61\) 3.69592 6.40151i 0.473214 0.819630i −0.526316 0.850289i \(-0.676427\pi\)
0.999530 + 0.0306589i \(0.00976058\pi\)
\(62\) −0.108125 + 0.100903i −0.0137319 + 0.0128147i
\(63\) 0 0
\(64\) 1.64606 7.82882i 0.205758 0.978603i
\(65\) 0.634129 + 0.366115i 0.0786541 + 0.0454109i
\(66\) 0 0
\(67\) −0.444103 + 0.256403i −0.0542559 + 0.0313246i −0.526883 0.849938i \(-0.676639\pi\)
0.472627 + 0.881263i \(0.343306\pi\)
\(68\) −6.68081 13.6722i −0.810167 1.65800i
\(69\) 0 0
\(70\) −4.00636 + 0.926490i −0.478852 + 0.110737i
\(71\) 1.45233 0.172360 0.0861800 0.996280i \(-0.472534\pi\)
0.0861800 + 0.996280i \(0.472534\pi\)
\(72\) 0 0
\(73\) 4.06828 0.476157 0.238078 0.971246i \(-0.423483\pi\)
0.238078 + 0.971246i \(0.423483\pi\)
\(74\) 4.34382 1.00453i 0.504959 0.116774i
\(75\) 0 0
\(76\) 2.29103 + 4.68858i 0.262800 + 0.537817i
\(77\) −2.05127 + 1.18430i −0.233764 + 0.134964i
\(78\) 0 0
\(79\) 10.0369 + 5.79482i 1.12924 + 0.651968i 0.943744 0.330677i \(-0.107277\pi\)
0.185498 + 0.982645i \(0.440610\pi\)
\(80\) −1.60178 + 11.5199i −0.179085 + 1.28797i
\(81\) 0 0
\(82\) −8.64592 + 8.06839i −0.954782 + 0.891004i
\(83\) −0.439593 + 0.761398i −0.0482516 + 0.0835743i −0.889142 0.457630i \(-0.848698\pi\)
0.840891 + 0.541205i \(0.182032\pi\)
\(84\) 0 0
\(85\) 11.0617 + 19.1594i 1.19981 + 2.07813i
\(86\) −11.2154 3.42440i −1.20939 0.369262i
\(87\) 0 0
\(88\) 1.05531 + 6.61580i 0.112496 + 0.705246i
\(89\) 14.6787i 1.55594i −0.628304 0.777968i \(-0.716251\pi\)
0.628304 0.777968i \(-0.283749\pi\)
\(90\) 0 0
\(91\) 0.251825i 0.0263984i
\(92\) 14.9856 + 10.0919i 1.56236 + 1.05216i
\(93\) 0 0
\(94\) −0.205071 + 0.671637i −0.0211514 + 0.0692741i
\(95\) −3.79337 6.57031i −0.389191 0.674099i
\(96\) 0 0
\(97\) 2.88066 4.98945i 0.292487 0.506602i −0.681910 0.731436i \(-0.738851\pi\)
0.974397 + 0.224834i \(0.0721839\pi\)
\(98\) −0.964871 1.03394i −0.0974667 0.104443i
\(99\) 0 0
\(100\) 0.476913 6.89285i 0.0476913 0.689285i
\(101\) 12.4968 + 7.21504i 1.24348 + 0.717923i 0.969801 0.243898i \(-0.0784263\pi\)
0.273678 + 0.961821i \(0.411760\pi\)
\(102\) 0 0
\(103\) 10.3804 5.99314i 1.02281 0.590521i 0.107896 0.994162i \(-0.465589\pi\)
0.914918 + 0.403641i \(0.132255\pi\)
\(104\) 0.665241 + 0.254522i 0.0652322 + 0.0249580i
\(105\) 0 0
\(106\) −0.760510 3.28862i −0.0738672 0.319419i
\(107\) 6.10346 0.590043 0.295022 0.955491i \(-0.404673\pi\)
0.295022 + 0.955491i \(0.404673\pi\)
\(108\) 0 0
\(109\) 6.25509 0.599129 0.299564 0.954076i \(-0.403159\pi\)
0.299564 + 0.954076i \(0.403159\pi\)
\(110\) −2.19449 9.48950i −0.209237 0.904789i
\(111\) 0 0
\(112\) −3.70653 + 1.50387i −0.350234 + 0.142102i
\(113\) −15.8902 + 9.17418i −1.49482 + 0.863035i −0.999982 0.00595082i \(-0.998106\pi\)
−0.494838 + 0.868985i \(0.664772\pi\)
\(114\) 0 0
\(115\) −22.7475 13.1333i −2.12122 1.22469i
\(116\) 12.7508 + 0.882224i 1.18389 + 0.0819125i
\(117\) 0 0
\(118\) −7.70906 8.26088i −0.709677 0.760476i
\(119\) −3.80429 + 6.58923i −0.348739 + 0.604034i
\(120\) 0 0
\(121\) 2.69485 + 4.66762i 0.244986 + 0.424329i
\(122\) −3.05268 + 9.99798i −0.276376 + 0.905174i
\(123\) 0 0
\(124\) 0.116829 0.173481i 0.0104916 0.0155791i
\(125\) 4.49335i 0.401898i
\(126\) 0 0
\(127\) 13.5835i 1.20534i 0.797989 + 0.602672i \(0.205897\pi\)
−0.797989 + 0.602672i \(0.794103\pi\)
\(128\) 0.226504 + 11.3114i 0.0200203 + 0.999800i
\(129\) 0 0
\(130\) −0.990392 0.302396i −0.0868632 0.0265219i
\(131\) 0.740508 + 1.28260i 0.0646985 + 0.112061i 0.896560 0.442922i \(-0.146058\pi\)
−0.831862 + 0.554983i \(0.812725\pi\)
\(132\) 0 0
\(133\) 1.30460 2.25963i 0.113123 0.195935i
\(134\) 0.530209 0.494792i 0.0458031 0.0427435i
\(135\) 0 0
\(136\) 13.5616 + 16.7095i 1.16290 + 1.43283i
\(137\) −15.5721 8.99055i −1.33041 0.768115i −0.345051 0.938584i \(-0.612138\pi\)
−0.985363 + 0.170469i \(0.945472\pi\)
\(138\) 0 0
\(139\) −7.21297 + 4.16441i −0.611796 + 0.353221i −0.773668 0.633591i \(-0.781580\pi\)
0.161872 + 0.986812i \(0.448247\pi\)
\(140\) 5.22496 2.55313i 0.441590 0.215779i
\(141\) 0 0
\(142\) −2.00110 + 0.462763i −0.167928 + 0.0388342i
\(143\) −0.596475 −0.0498797
\(144\) 0 0
\(145\) −18.5821 −1.54316
\(146\) −5.60549 + 1.29629i −0.463913 + 0.107282i
\(147\) 0 0
\(148\) −5.66506 + 2.76818i −0.465665 + 0.227543i
\(149\) 2.86752 1.65557i 0.234917 0.135629i −0.377921 0.925838i \(-0.623361\pi\)
0.612838 + 0.790208i \(0.290028\pi\)
\(150\) 0 0
\(151\) −5.39261 3.11343i −0.438845 0.253367i 0.264263 0.964451i \(-0.414871\pi\)
−0.703107 + 0.711084i \(0.748205\pi\)
\(152\) −4.65065 5.73016i −0.377217 0.464778i
\(153\) 0 0
\(154\) 2.44899 2.28540i 0.197345 0.184163i
\(155\) −0.152038 + 0.263337i −0.0122120 + 0.0211518i
\(156\) 0 0
\(157\) 1.48912 + 2.57922i 0.118844 + 0.205844i 0.919310 0.393534i \(-0.128748\pi\)
−0.800466 + 0.599379i \(0.795414\pi\)
\(158\) −15.6758 4.78629i −1.24710 0.380776i
\(159\) 0 0
\(160\) −1.46363 16.3831i −0.115710 1.29520i
\(161\) 9.03348i 0.711938i
\(162\) 0 0
\(163\) 8.29335i 0.649585i −0.945785 0.324793i \(-0.894706\pi\)
0.945785 0.324793i \(-0.105294\pi\)
\(164\) 9.34192 13.8719i 0.729482 1.08321i
\(165\) 0 0
\(166\) 0.363086 1.18916i 0.0281810 0.0922969i
\(167\) −9.34971 16.1942i −0.723503 1.25314i −0.959587 0.281411i \(-0.909198\pi\)
0.236085 0.971732i \(-0.424136\pi\)
\(168\) 0 0
\(169\) 6.46829 11.2034i 0.497561 0.861801i
\(170\) −21.3462 22.8742i −1.63718 1.75437i
\(171\) 0 0
\(172\) 16.5443 + 1.14469i 1.26149 + 0.0872819i
\(173\) −7.58848 4.38121i −0.576942 0.333097i 0.182975 0.983118i \(-0.441427\pi\)
−0.759917 + 0.650020i \(0.774760\pi\)
\(174\) 0 0
\(175\) −2.99183 + 1.72733i −0.226161 + 0.130574i
\(176\) −3.56207 8.77932i −0.268501 0.661766i
\(177\) 0 0
\(178\) 4.67713 + 20.2250i 0.350566 + 1.51593i
\(179\) −2.87709 −0.215044 −0.107522 0.994203i \(-0.534292\pi\)
−0.107522 + 0.994203i \(0.534292\pi\)
\(180\) 0 0
\(181\) −4.82998 −0.359010 −0.179505 0.983757i \(-0.557450\pi\)
−0.179505 + 0.983757i \(0.557450\pi\)
\(182\) −0.0802401 0.346977i −0.00594780 0.0257197i
\(183\) 0 0
\(184\) −23.8636 9.13024i −1.75925 0.673090i
\(185\) 7.93868 4.58340i 0.583664 0.336978i
\(186\) 0 0
\(187\) −15.6073 9.01088i −1.14132 0.658941i
\(188\) 0.0685500 0.990758i 0.00499952 0.0722584i
\(189\) 0 0
\(190\) 7.32022 + 7.84421i 0.531065 + 0.569078i
\(191\) 10.2584 17.7680i 0.742270 1.28565i −0.209189 0.977875i \(-0.567082\pi\)
0.951459 0.307775i \(-0.0995843\pi\)
\(192\) 0 0
\(193\) −9.29894 16.1062i −0.669352 1.15935i −0.978085 0.208204i \(-0.933238\pi\)
0.308733 0.951149i \(-0.400095\pi\)
\(194\) −2.37931 + 7.79260i −0.170824 + 0.559476i
\(195\) 0 0
\(196\) 1.65890 + 1.11717i 0.118493 + 0.0797978i
\(197\) 17.2523i 1.22917i 0.788850 + 0.614586i \(0.210677\pi\)
−0.788850 + 0.614586i \(0.789323\pi\)
\(198\) 0 0
\(199\) 1.17220i 0.0830948i −0.999137 0.0415474i \(-0.986771\pi\)
0.999137 0.0415474i \(-0.0132288\pi\)
\(200\) 1.53919 + 9.64928i 0.108837 + 0.682307i
\(201\) 0 0
\(202\) −19.5177 5.95933i −1.37326 0.419297i
\(203\) −3.19533 5.53448i −0.224268 0.388444i
\(204\) 0 0
\(205\) −12.1573 + 21.0570i −0.849100 + 1.47068i
\(206\) −12.3930 + 11.5652i −0.863464 + 0.805786i
\(207\) 0 0
\(208\) −0.997702 0.138725i −0.0691782 0.00961885i
\(209\) 5.35218 + 3.09008i 0.370218 + 0.213745i
\(210\) 0 0
\(211\) 8.81152 5.08733i 0.606610 0.350226i −0.165028 0.986289i \(-0.552771\pi\)
0.771637 + 0.636063i \(0.219438\pi\)
\(212\) 2.09574 + 4.28891i 0.143936 + 0.294563i
\(213\) 0 0
\(214\) −8.40965 + 1.94477i −0.574872 + 0.132942i
\(215\) −24.1104 −1.64431
\(216\) 0 0
\(217\) −0.104576 −0.00709911
\(218\) −8.61858 + 1.99309i −0.583724 + 0.134989i
\(219\) 0 0
\(220\) 6.04736 + 12.3759i 0.407713 + 0.834381i
\(221\) −1.65933 + 0.958017i −0.111619 + 0.0644432i
\(222\) 0 0
\(223\) −5.28069 3.04881i −0.353621 0.204163i 0.312658 0.949866i \(-0.398781\pi\)
−0.666279 + 0.745703i \(0.732114\pi\)
\(224\) 4.62786 3.25313i 0.309212 0.217359i
\(225\) 0 0
\(226\) 18.9710 17.7038i 1.26194 1.17764i
\(227\) −11.1581 + 19.3264i −0.740589 + 1.28274i 0.211639 + 0.977348i \(0.432120\pi\)
−0.952228 + 0.305390i \(0.901213\pi\)
\(228\) 0 0
\(229\) −2.70895 4.69204i −0.179013 0.310059i 0.762530 0.646953i \(-0.223957\pi\)
−0.941543 + 0.336894i \(0.890624\pi\)
\(230\) 35.5274 + 10.8476i 2.34261 + 0.715267i
\(231\) 0 0
\(232\) −17.8499 + 2.84729i −1.17190 + 0.186933i
\(233\) 6.08190i 0.398439i 0.979955 + 0.199219i \(0.0638406\pi\)
−0.979955 + 0.199219i \(0.936159\pi\)
\(234\) 0 0
\(235\) 1.44385i 0.0941865i
\(236\) 13.2541 + 8.92588i 0.862771 + 0.581026i
\(237\) 0 0
\(238\) 3.14219 10.2912i 0.203678 0.667076i
\(239\) −4.58910 7.94855i −0.296844 0.514149i 0.678568 0.734538i \(-0.262601\pi\)
−0.975412 + 0.220388i \(0.929268\pi\)
\(240\) 0 0
\(241\) −4.60034 + 7.96801i −0.296334 + 0.513265i −0.975294 0.220910i \(-0.929097\pi\)
0.678961 + 0.734175i \(0.262431\pi\)
\(242\) −5.20036 5.57260i −0.334292 0.358221i
\(243\) 0 0
\(244\) 1.02043 14.7484i 0.0653266 0.944170i
\(245\) −2.51813 1.45385i −0.160878 0.0928828i
\(246\) 0 0
\(247\) 0.569032 0.328531i 0.0362066 0.0209039i
\(248\) −0.105696 + 0.276257i −0.00671173 + 0.0175424i
\(249\) 0 0
\(250\) 1.43174 + 6.19117i 0.0905510 + 0.391564i
\(251\) 17.5771 1.10946 0.554729 0.832031i \(-0.312822\pi\)
0.554729 + 0.832031i \(0.312822\pi\)
\(252\) 0 0
\(253\) 21.3968 1.34520
\(254\) −4.32818 18.7161i −0.271574 1.17435i
\(255\) 0 0
\(256\) −3.91630 15.5133i −0.244769 0.969581i
\(257\) 9.36418 5.40641i 0.584122 0.337243i −0.178648 0.983913i \(-0.557172\pi\)
0.762770 + 0.646670i \(0.223839\pi\)
\(258\) 0 0
\(259\) 2.73024 + 1.57630i 0.169649 + 0.0979467i
\(260\) 1.46097 + 0.101083i 0.0906053 + 0.00626893i
\(261\) 0 0
\(262\) −1.42899 1.53128i −0.0882833 0.0946026i
\(263\) 1.23346 2.13642i 0.0760585 0.131737i −0.825488 0.564420i \(-0.809100\pi\)
0.901546 + 0.432683i \(0.142433\pi\)
\(264\) 0 0
\(265\) −3.47001 6.01023i −0.213161 0.369205i
\(266\) −1.07755 + 3.52912i −0.0660686 + 0.216384i
\(267\) 0 0
\(268\) −0.572891 + 0.850692i −0.0349949 + 0.0519643i
\(269\) 18.6417i 1.13661i 0.822820 + 0.568303i \(0.192400\pi\)
−0.822820 + 0.568303i \(0.807600\pi\)
\(270\) 0 0
\(271\) 11.9123i 0.723621i 0.932252 + 0.361811i \(0.117841\pi\)
−0.932252 + 0.361811i \(0.882159\pi\)
\(272\) −24.0101 18.7020i −1.45582 1.13398i
\(273\) 0 0
\(274\) 24.3207 + 7.42583i 1.46927 + 0.448611i
\(275\) −4.09137 7.08647i −0.246719 0.427330i
\(276\) 0 0
\(277\) 8.83024 15.2944i 0.530558 0.918953i −0.468807 0.883301i \(-0.655316\pi\)
0.999364 0.0356520i \(-0.0113508\pi\)
\(278\) 8.61147 8.03624i 0.516482 0.481981i
\(279\) 0 0
\(280\) −6.38570 + 5.18268i −0.381618 + 0.309725i
\(281\) 16.5651 + 9.56389i 0.988193 + 0.570534i 0.904734 0.425977i \(-0.140070\pi\)
0.0834596 + 0.996511i \(0.473403\pi\)
\(282\) 0 0
\(283\) 2.81044 1.62261i 0.167063 0.0964541i −0.414137 0.910215i \(-0.635917\pi\)
0.581200 + 0.813760i \(0.302583\pi\)
\(284\) 2.60976 1.27524i 0.154861 0.0756713i
\(285\) 0 0
\(286\) 0.821853 0.190057i 0.0485972 0.0112383i
\(287\) −8.36214 −0.493602
\(288\) 0 0
\(289\) −40.8906 −2.40533
\(290\) 25.6033 5.92089i 1.50348 0.347687i
\(291\) 0 0
\(292\) 7.31048 3.57220i 0.427813 0.209047i
\(293\) −11.1294 + 6.42555i −0.650185 + 0.375385i −0.788527 0.615000i \(-0.789156\pi\)
0.138342 + 0.990385i \(0.455823\pi\)
\(294\) 0 0
\(295\) −20.1192 11.6158i −1.17139 0.676300i
\(296\) 6.92356 5.61922i 0.402424 0.326611i
\(297\) 0 0
\(298\) −3.42350 + 3.19481i −0.198318 + 0.185071i
\(299\) 1.13743 1.97009i 0.0657792 0.113933i
\(300\) 0 0
\(301\) −4.14596 7.18102i −0.238969 0.413907i
\(302\) 8.42226 + 2.57156i 0.484647 + 0.147977i
\(303\) 0 0
\(304\) 8.23372 + 6.41345i 0.472236 + 0.367837i
\(305\) 21.4932i 1.23069i
\(306\) 0 0
\(307\) 17.7017i 1.01029i 0.863035 + 0.505144i \(0.168561\pi\)
−0.863035 + 0.505144i \(0.831439\pi\)
\(308\) −2.64613 + 3.92927i −0.150778 + 0.223891i
\(309\) 0 0
\(310\) 0.125577 0.411284i 0.00713230 0.0233594i
\(311\) 3.30345 + 5.72174i 0.187321 + 0.324450i 0.944356 0.328924i \(-0.106686\pi\)
−0.757035 + 0.653374i \(0.773353\pi\)
\(312\) 0 0
\(313\) 5.34114 9.25113i 0.301899 0.522905i −0.674667 0.738122i \(-0.735713\pi\)
0.976566 + 0.215217i \(0.0690460\pi\)
\(314\) −2.87361 3.07930i −0.162167 0.173775i
\(315\) 0 0
\(316\) 23.1240 + 1.59994i 1.30083 + 0.0900034i
\(317\) 22.1073 + 12.7636i 1.24167 + 0.716878i 0.969434 0.245353i \(-0.0789040\pi\)
0.272235 + 0.962231i \(0.412237\pi\)
\(318\) 0 0
\(319\) 13.1090 7.56849i 0.733964 0.423754i
\(320\) 7.23689 + 22.1071i 0.404555 + 1.23583i
\(321\) 0 0
\(322\) 2.87838 + 12.4468i 0.160406 + 0.693633i
\(323\) 19.8523 1.10461
\(324\) 0 0
\(325\) −0.869972 −0.0482573
\(326\) 2.64255 + 11.4270i 0.146357 + 0.632883i
\(327\) 0 0
\(328\) −8.45171 + 22.0901i −0.466667 + 1.21972i
\(329\) −0.430036 + 0.248282i −0.0237087 + 0.0136882i
\(330\) 0 0
\(331\) 23.0921 + 13.3322i 1.26925 + 0.732804i 0.974847 0.222876i \(-0.0715445\pi\)
0.294407 + 0.955680i \(0.404878\pi\)
\(332\) −0.121371 + 1.75418i −0.00666108 + 0.0962731i
\(333\) 0 0
\(334\) 18.0425 + 19.3340i 0.987243 + 1.05791i
\(335\) 0.745541 1.29132i 0.0407333 0.0705521i
\(336\) 0 0
\(337\) 3.17158 + 5.49333i 0.172767 + 0.299241i 0.939386 0.342861i \(-0.111396\pi\)
−0.766619 + 0.642102i \(0.778063\pi\)
\(338\) −5.34255 + 17.4976i −0.290596 + 0.951746i
\(339\) 0 0
\(340\) 36.7004 + 24.7156i 1.99036 + 1.34039i
\(341\) 0.247700i 0.0134137i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −23.1603 + 3.69437i −1.24872 + 0.199187i
\(345\) 0 0
\(346\) 11.8518 + 3.61871i 0.637157 + 0.194543i
\(347\) 2.10127 + 3.63950i 0.112802 + 0.195379i 0.916899 0.399119i \(-0.130684\pi\)
−0.804097 + 0.594498i \(0.797351\pi\)
\(348\) 0 0
\(349\) −17.6897 + 30.6395i −0.946908 + 1.64009i −0.195023 + 0.980799i \(0.562478\pi\)
−0.751885 + 0.659294i \(0.770855\pi\)
\(350\) 3.57190 3.33331i 0.190926 0.178173i
\(351\) 0 0
\(352\) 7.70540 + 10.9616i 0.410699 + 0.584255i
\(353\) −25.9389 14.9758i −1.38059 0.797082i −0.388358 0.921509i \(-0.626958\pi\)
−0.992229 + 0.124426i \(0.960291\pi\)
\(354\) 0 0
\(355\) −3.65716 + 2.11146i −0.194102 + 0.112065i
\(356\) −12.8888 26.3767i −0.683103 1.39796i
\(357\) 0 0
\(358\) 3.96420 0.916740i 0.209514 0.0484512i
\(359\) 5.48093 0.289272 0.144636 0.989485i \(-0.453799\pi\)
0.144636 + 0.989485i \(0.453799\pi\)
\(360\) 0 0
\(361\) 12.1921 0.641689
\(362\) 6.65499 1.53900i 0.349779 0.0808880i
\(363\) 0 0
\(364\) 0.221118 + 0.452516i 0.0115897 + 0.0237183i
\(365\) −10.2445 + 5.91465i −0.536221 + 0.309587i
\(366\) 0 0
\(367\) 14.7364 + 8.50804i 0.769232 + 0.444116i 0.832601 0.553874i \(-0.186851\pi\)
−0.0633686 + 0.997990i \(0.520184\pi\)
\(368\) 35.7896 + 4.97635i 1.86566 + 0.259410i
\(369\) 0 0
\(370\) −9.47789 + 8.84478i −0.492732 + 0.459818i
\(371\) 1.19339 2.06701i 0.0619577 0.107314i
\(372\) 0 0
\(373\) −0.570268 0.987733i −0.0295274 0.0511429i 0.850884 0.525353i \(-0.176067\pi\)
−0.880411 + 0.474211i \(0.842734\pi\)
\(374\) 24.3757 + 7.44262i 1.26044 + 0.384849i
\(375\) 0 0
\(376\) 0.221238 + 1.38696i 0.0114095 + 0.0715269i
\(377\) 1.60933i 0.0828847i
\(378\) 0 0
\(379\) 26.5456i 1.36356i −0.731559 0.681778i \(-0.761207\pi\)
0.731559 0.681778i \(-0.238793\pi\)
\(380\) −12.5856 8.47567i −0.645628 0.434793i
\(381\) 0 0
\(382\) −8.47301 + 27.7504i −0.433517 + 1.41983i
\(383\) 17.3272 + 30.0116i 0.885380 + 1.53352i 0.845277 + 0.534328i \(0.179435\pi\)
0.0401027 + 0.999196i \(0.487231\pi\)
\(384\) 0 0
\(385\) 3.44359 5.96447i 0.175502 0.303978i
\(386\) 17.9446 + 19.2290i 0.913354 + 0.978732i
\(387\) 0 0
\(388\) 0.795344 11.4952i 0.0403775 0.583578i
\(389\) −10.2165 5.89849i −0.517996 0.299065i 0.218118 0.975922i \(-0.430008\pi\)
−0.736114 + 0.676857i \(0.763341\pi\)
\(390\) 0 0
\(391\) 59.5237 34.3660i 3.01024 1.73796i
\(392\) −2.64168 1.01071i −0.133425 0.0510486i
\(393\) 0 0
\(394\) −5.49716 23.7710i −0.276943 1.19757i
\(395\) −33.6991 −1.69558
\(396\) 0 0
\(397\) −13.5577 −0.680441 −0.340221 0.940346i \(-0.610502\pi\)
−0.340221 + 0.940346i \(0.610502\pi\)
\(398\) 0.373502 + 1.61511i 0.0187220 + 0.0809583i
\(399\) 0 0
\(400\) −5.19536 12.8048i −0.259768 0.640241i
\(401\) 5.39384 3.11414i 0.269356 0.155513i −0.359239 0.933246i \(-0.616964\pi\)
0.628595 + 0.777733i \(0.283630\pi\)
\(402\) 0 0
\(403\) −0.0228067 0.0131675i −0.00113609 0.000655919i
\(404\) 28.7913 + 1.99206i 1.43242 + 0.0991085i
\(405\) 0 0
\(406\) 6.16617 + 6.60754i 0.306022 + 0.327927i
\(407\) −3.73364 + 6.46686i −0.185070 + 0.320550i
\(408\) 0 0
\(409\) −0.409311 0.708947i −0.0202391 0.0350552i 0.855728 0.517425i \(-0.173109\pi\)
−0.875968 + 0.482370i \(0.839776\pi\)
\(410\) 10.0414 32.8871i 0.495910 1.62418i
\(411\) 0 0
\(412\) 13.3907 19.8840i 0.659712 0.979613i
\(413\) 7.98974i 0.393149i
\(414\) 0 0
\(415\) 2.55640i 0.125489i
\(416\) 1.41889 0.126760i 0.0695667 0.00621491i
\(417\) 0 0
\(418\) −8.35911 2.55228i −0.408857 0.124836i
\(419\) 7.99122 + 13.8412i 0.390397 + 0.676187i 0.992502 0.122230i \(-0.0390045\pi\)
−0.602105 + 0.798417i \(0.705671\pi\)
\(420\) 0 0
\(421\) −4.02490 + 6.97133i −0.196161 + 0.339762i −0.947281 0.320405i \(-0.896181\pi\)
0.751119 + 0.660167i \(0.229514\pi\)
\(422\) −10.5200 + 9.81723i −0.512103 + 0.477896i
\(423\) 0 0
\(424\) −4.25421 5.24170i −0.206603 0.254559i
\(425\) −22.7636 13.1426i −1.10420 0.637508i
\(426\) 0 0
\(427\) −6.40151 + 3.69592i −0.309791 + 0.178858i
\(428\) 10.9676 5.35921i 0.530138 0.259047i
\(429\) 0 0
\(430\) 33.2205 7.68239i 1.60203 0.370478i
\(431\) −32.4604 −1.56356 −0.781780 0.623554i \(-0.785688\pi\)
−0.781780 + 0.623554i \(0.785688\pi\)
\(432\) 0 0
\(433\) −18.4266 −0.885525 −0.442762 0.896639i \(-0.646001\pi\)
−0.442762 + 0.896639i \(0.646001\pi\)
\(434\) 0.144091 0.0333216i 0.00691657 0.00159949i
\(435\) 0 0
\(436\) 11.2400 5.49235i 0.538301 0.263036i
\(437\) −20.4123 + 11.7851i −0.976455 + 0.563756i
\(438\) 0 0
\(439\) −31.5605 18.2214i −1.50630 0.869662i −0.999973 0.00731896i \(-0.997670\pi\)
−0.506325 0.862343i \(-0.668996\pi\)
\(440\) −12.2757 15.1252i −0.585223 0.721066i
\(441\) 0 0
\(442\) 1.98106 1.84872i 0.0942293 0.0879349i
\(443\) 11.3610 19.6778i 0.539776 0.934919i −0.459140 0.888364i \(-0.651842\pi\)
0.998916 0.0465549i \(-0.0148243\pi\)
\(444\) 0 0
\(445\) 21.3405 + 36.9628i 1.01164 + 1.75221i
\(446\) 8.24745 + 2.51819i 0.390528 + 0.119240i
\(447\) 0 0
\(448\) −5.33994 + 5.95693i −0.252289 + 0.281438i
\(449\) 9.26171i 0.437087i 0.975827 + 0.218544i \(0.0701306\pi\)
−0.975827 + 0.218544i \(0.929869\pi\)
\(450\) 0 0
\(451\) 19.8066i 0.932658i
\(452\) −20.4982 + 30.4380i −0.964155 + 1.43168i
\(453\) 0 0
\(454\) 9.21614 30.1842i 0.432535 1.41662i
\(455\) −0.366115 0.634129i −0.0171637 0.0297284i
\(456\) 0 0
\(457\) 5.90082 10.2205i 0.276029 0.478096i −0.694365 0.719623i \(-0.744315\pi\)
0.970394 + 0.241527i \(0.0776482\pi\)
\(458\) 5.22758 + 5.60177i 0.244269 + 0.261753i
\(459\) 0 0
\(460\) −52.4079 3.62607i −2.44353 0.169066i
\(461\) −2.21744 1.28024i −0.103276 0.0596266i 0.447472 0.894298i \(-0.352324\pi\)
−0.550749 + 0.834671i \(0.685658\pi\)
\(462\) 0 0
\(463\) −10.0234 + 5.78704i −0.465829 + 0.268947i −0.714492 0.699643i \(-0.753342\pi\)
0.248663 + 0.968590i \(0.420009\pi\)
\(464\) 23.6872 9.61072i 1.09965 0.446166i
\(465\) 0 0
\(466\) −1.93790 8.37995i −0.0897716 0.388194i
\(467\) 0.571766 0.0264582 0.0132291 0.999912i \(-0.495789\pi\)
0.0132291 + 0.999912i \(0.495789\pi\)
\(468\) 0 0
\(469\) 0.512806 0.0236792
\(470\) −0.460061 1.98941i −0.0212210 0.0917648i
\(471\) 0 0
\(472\) −21.1063 8.07531i −0.971497 0.371696i
\(473\) 17.0090 9.82016i 0.782076 0.451532i
\(474\) 0 0
\(475\) 7.80627 + 4.50695i 0.358176 + 0.206793i
\(476\) −1.05036 + 15.1809i −0.0481430 + 0.695815i
\(477\) 0 0
\(478\) 8.85578 + 9.48967i 0.405054 + 0.434048i
\(479\) 13.9036 24.0818i 0.635273 1.10033i −0.351184 0.936306i \(-0.614221\pi\)
0.986457 0.164019i \(-0.0524457\pi\)
\(480\) 0 0
\(481\) 0.396953 + 0.687542i 0.0180995 + 0.0313492i
\(482\) 3.79969 12.4446i 0.173071 0.566834i
\(483\) 0 0
\(484\) 8.94094 + 6.02120i 0.406407 + 0.273691i
\(485\) 16.7521i 0.760676i
\(486\) 0 0
\(487\) 10.3286i 0.468031i 0.972233 + 0.234016i \(0.0751867\pi\)
−0.972233 + 0.234016i \(0.924813\pi\)
\(488\) 3.29334 + 20.6462i 0.149083 + 0.934611i
\(489\) 0 0
\(490\) 3.93286 + 1.20082i 0.177668 + 0.0542474i
\(491\) −16.9157 29.2988i −0.763394 1.32224i −0.941091 0.338153i \(-0.890198\pi\)
0.177697 0.984085i \(-0.443135\pi\)
\(492\) 0 0
\(493\) 24.3120 42.1096i 1.09496 1.89652i
\(494\) −0.679360 + 0.633979i −0.0305658 + 0.0285241i
\(495\) 0 0
\(496\) 0.0576089 0.414320i 0.00258672 0.0186035i
\(497\) −1.25776 0.726166i −0.0564181 0.0325730i
\(498\) 0 0
\(499\) 5.27446 3.04521i 0.236117 0.136322i −0.377274 0.926102i \(-0.623138\pi\)
0.613391 + 0.789779i \(0.289805\pi\)
\(500\) −3.94544 8.07431i −0.176445 0.361094i
\(501\) 0 0
\(502\) −24.2187 + 5.60068i −1.08093 + 0.249971i
\(503\) 21.4710 0.957345 0.478673 0.877993i \(-0.341118\pi\)
0.478673 + 0.877993i \(0.341118\pi\)
\(504\) 0 0
\(505\) −41.9582 −1.86712
\(506\) −29.4816 + 6.81775i −1.31062 + 0.303086i
\(507\) 0 0
\(508\) 11.9272 + 24.4088i 0.529183 + 1.08297i
\(509\) 18.4897 10.6750i 0.819540 0.473161i −0.0307180 0.999528i \(-0.509779\pi\)
0.850258 + 0.526367i \(0.176446\pi\)
\(510\) 0 0
\(511\) −3.52324 2.03414i −0.155859 0.0899851i
\(512\) 10.3392 + 20.1271i 0.456930 + 0.889503i
\(513\) 0 0
\(514\) −11.1798 + 10.4330i −0.493119 + 0.460179i
\(515\) −17.4262 + 30.1830i −0.767890 + 1.33002i
\(516\) 0 0
\(517\) −0.588082 1.01859i −0.0258638 0.0447974i
\(518\) −4.26412 1.30196i −0.187355 0.0572050i
\(519\) 0 0
\(520\) −2.04520 + 0.326236i −0.0896880 + 0.0143064i
\(521\) 30.4799i 1.33535i −0.744453 0.667675i \(-0.767290\pi\)
0.744453 0.667675i \(-0.232710\pi\)
\(522\) 0 0
\(523\) 28.4494i 1.24401i −0.783014 0.622004i \(-0.786319\pi\)
0.783014 0.622004i \(-0.213681\pi\)
\(524\) 2.45685 + 1.65455i 0.107328 + 0.0722791i
\(525\) 0 0
\(526\) −1.01879 + 3.33669i −0.0444213 + 0.145486i
\(527\) −0.397839 0.689078i −0.0173302 0.0300167i
\(528\) 0 0
\(529\) −29.3019 + 50.7524i −1.27400 + 2.20663i
\(530\) 6.69622 + 7.17553i 0.290865 + 0.311685i
\(531\) 0 0
\(532\) 0.360197 5.20595i 0.0156165 0.225706i
\(533\) −1.82367 1.05290i −0.0789921 0.0456061i
\(534\) 0 0
\(535\) −15.3693 + 8.87348i −0.664474 + 0.383634i
\(536\) 0.518299 1.35467i 0.0223871 0.0585128i
\(537\) 0 0
\(538\) −5.93989 25.6855i −0.256087 1.10738i
\(539\) 2.36861 0.102023
\(540\) 0 0
\(541\) 28.9747 1.24572 0.622861 0.782333i \(-0.285970\pi\)
0.622861 + 0.782333i \(0.285970\pi\)
\(542\) −3.79567 16.4134i −0.163038 0.705015i
\(543\) 0 0
\(544\) 39.0414 + 18.1182i 1.67389 + 0.776811i
\(545\) −15.7512 + 9.09393i −0.674705 + 0.389541i
\(546\) 0 0
\(547\) 32.0274 + 18.4910i 1.36939 + 0.790619i 0.990850 0.134966i \(-0.0430924\pi\)
0.378541 + 0.925584i \(0.376426\pi\)
\(548\) −35.8764 2.48227i −1.53257 0.106037i
\(549\) 0 0
\(550\) 7.89529 + 8.46044i 0.336656 + 0.360754i
\(551\) −8.33725 + 14.4405i −0.355179 + 0.615188i
\(552\) 0 0
\(553\) −5.79482 10.0369i −0.246421 0.426813i
\(554\) −7.29342 + 23.8870i −0.309868 + 1.01486i
\(555\) 0 0
\(556\) −9.30470 + 13.8166i −0.394607 + 0.585956i
\(557\) 4.29428i 0.181955i −0.995853 0.0909773i \(-0.971001\pi\)
0.995853 0.0909773i \(-0.0289991\pi\)
\(558\) 0 0
\(559\) 2.08812i 0.0883179i
\(560\) 7.14715 9.17567i 0.302022 0.387743i
\(561\) 0 0
\(562\) −25.8717 7.89938i −1.09133 0.333215i
\(563\) 2.78657 + 4.82649i 0.117440 + 0.203412i 0.918753 0.394834i \(-0.129198\pi\)
−0.801312 + 0.598246i \(0.795865\pi\)
\(564\) 0 0
\(565\) 26.6757 46.2037i 1.12225 1.94380i
\(566\) −3.35535 + 3.13122i −0.141036 + 0.131615i
\(567\) 0 0
\(568\) −3.18952 + 2.58864i −0.133829 + 0.108617i
\(569\) 5.72734 + 3.30668i 0.240103 + 0.138623i 0.615224 0.788352i \(-0.289066\pi\)
−0.375121 + 0.926976i \(0.622399\pi\)
\(570\) 0 0
\(571\) −28.7640 + 16.6069i −1.20374 + 0.694978i −0.961384 0.275211i \(-0.911252\pi\)
−0.242353 + 0.970188i \(0.577919\pi\)
\(572\) −1.07183 + 0.523741i −0.0448156 + 0.0218987i
\(573\) 0 0
\(574\) 11.5218 2.66447i 0.480910 0.111213i
\(575\) 31.2077 1.30145
\(576\) 0 0
\(577\) 27.6524 1.15119 0.575593 0.817736i \(-0.304771\pi\)
0.575593 + 0.817736i \(0.304771\pi\)
\(578\) 56.3411 13.0292i 2.34348 0.541941i
\(579\) 0 0
\(580\) −33.3910 + 16.3162i −1.38648 + 0.677494i
\(581\) 0.761398 0.439593i 0.0315881 0.0182374i
\(582\) 0 0
\(583\) 4.89594 + 2.82667i 0.202769 + 0.117069i
\(584\) −8.93452 + 7.25133i −0.369713 + 0.300062i
\(585\) 0 0
\(586\) 13.2872 12.3996i 0.548890 0.512225i
\(587\) −12.0238 + 20.8258i −0.496274 + 0.859571i −0.999991 0.00429733i \(-0.998632\pi\)
0.503717 + 0.863869i \(0.331965\pi\)
\(588\) 0 0
\(589\) 0.136430 + 0.236304i 0.00562151 + 0.00973674i
\(590\) 31.4225 + 9.59422i 1.29364 + 0.394988i
\(591\) 0 0
\(592\) −7.74916 + 9.94853i −0.318489 + 0.408882i
\(593\) 7.02971i 0.288675i −0.989528 0.144338i \(-0.953895\pi\)
0.989528 0.144338i \(-0.0461052\pi\)
\(594\) 0 0
\(595\) 22.1234i 0.906972i
\(596\) 3.69909 5.49282i 0.151521 0.224995i
\(597\) 0 0
\(598\) −0.939471 + 3.07691i −0.0384178 + 0.125824i
\(599\) 14.7689 + 25.5804i 0.603439 + 1.04519i 0.992296 + 0.123889i \(0.0395366\pi\)
−0.388857 + 0.921298i \(0.627130\pi\)
\(600\) 0 0
\(601\) −11.2326 + 19.4555i −0.458188 + 0.793605i −0.998865 0.0476250i \(-0.984835\pi\)
0.540677 + 0.841230i \(0.318168\pi\)
\(602\) 8.00064 + 8.57333i 0.326082 + 0.349423i
\(603\) 0 0
\(604\) −12.4240 0.859610i −0.505526 0.0349770i
\(605\) −13.5720 7.83579i −0.551780 0.318570i
\(606\) 0 0
\(607\) −31.5236 + 18.2002i −1.27950 + 0.738722i −0.976757 0.214348i \(-0.931237\pi\)
−0.302748 + 0.953071i \(0.597904\pi\)
\(608\) −13.3884 6.21323i −0.542971 0.251980i
\(609\) 0 0
\(610\) −6.84846 29.6144i −0.277286 1.19905i
\(611\) −0.125047 −0.00505886
\(612\) 0 0
\(613\) 12.8571 0.519293 0.259646 0.965704i \(-0.416394\pi\)
0.259646 + 0.965704i \(0.416394\pi\)
\(614\) −5.64036 24.3903i −0.227626 0.984310i
\(615\) 0 0
\(616\) 2.39398 6.25710i 0.0964561 0.252106i
\(617\) 37.5894 21.7022i 1.51329 0.873699i 0.513412 0.858142i \(-0.328381\pi\)
0.999879 0.0155564i \(-0.00495195\pi\)
\(618\) 0 0
\(619\) 0.893596 + 0.515918i 0.0359167 + 0.0207365i 0.517851 0.855471i \(-0.326732\pi\)
−0.481934 + 0.876207i \(0.660066\pi\)
\(620\) −0.0419773 + 0.606701i −0.00168585 + 0.0243657i
\(621\) 0 0
\(622\) −6.37480 6.83111i −0.255606 0.273903i
\(623\) −7.33933 + 12.7121i −0.294044 + 0.509299i
\(624\) 0 0
\(625\) 15.1693 + 26.2740i 0.606772 + 1.05096i
\(626\) −4.41157 + 14.4486i −0.176322 + 0.577480i
\(627\) 0 0
\(628\) 4.94057 + 3.32719i 0.197150 + 0.132769i
\(629\) 23.9869i 0.956420i
\(630\) 0 0
\(631\) 25.4447i 1.01294i 0.862258 + 0.506469i \(0.169049\pi\)
−0.862258 + 0.506469i \(0.830951\pi\)
\(632\) −32.3712 + 5.16363i −1.28766 + 0.205398i
\(633\) 0 0
\(634\) −34.5275 10.5423i −1.37126 0.418686i
\(635\) −19.7483 34.2051i −0.783689 1.35739i
\(636\) 0 0
\(637\) 0.125913 0.218087i 0.00498884 0.00864092i
\(638\) −15.6507 + 14.6052i −0.619616 + 0.578227i
\(639\) 0 0
\(640\) −17.0155 28.1544i −0.672595 1.11290i
\(641\) 24.3065 + 14.0334i 0.960049 + 0.554284i 0.896188 0.443674i \(-0.146325\pi\)
0.0638607 + 0.997959i \(0.479659\pi\)
\(642\) 0 0
\(643\) −11.1062 + 6.41216i −0.437985 + 0.252871i −0.702743 0.711444i \(-0.748041\pi\)
0.264757 + 0.964315i \(0.414708\pi\)
\(644\) −7.93195 16.2327i −0.312563 0.639657i
\(645\) 0 0
\(646\) −27.3535 + 6.32563i −1.07621 + 0.248878i
\(647\) −39.1711 −1.53998 −0.769988 0.638058i \(-0.779738\pi\)
−0.769988 + 0.638058i \(0.779738\pi\)
\(648\) 0 0
\(649\) 18.9246 0.742854
\(650\) 1.19869 0.277203i 0.0470165 0.0108728i
\(651\) 0 0
\(652\) −7.28207 14.9027i −0.285188 0.583634i
\(653\) −5.09574 + 2.94203i −0.199412 + 0.115130i −0.596381 0.802701i \(-0.703395\pi\)
0.396969 + 0.917832i \(0.370062\pi\)
\(654\) 0 0
\(655\) −3.72940 2.15317i −0.145720 0.0841313i
\(656\) 4.60652 33.1298i 0.179855 1.29350i
\(657\) 0 0
\(658\) 0.513415 0.479119i 0.0200150 0.0186780i
\(659\) −12.9730 + 22.4699i −0.505357 + 0.875304i 0.494624 + 0.869107i \(0.335306\pi\)
−0.999981 + 0.00619658i \(0.998028\pi\)
\(660\) 0 0
\(661\) −19.8403 34.3644i −0.771699 1.33662i −0.936631 0.350316i \(-0.886074\pi\)
0.164933 0.986305i \(-0.447259\pi\)
\(662\) −36.0655 11.0119i −1.40173 0.427988i
\(663\) 0 0
\(664\) −0.391711 2.45567i −0.0152013 0.0952985i
\(665\) 7.58674i 0.294201i
\(666\) 0 0
\(667\) 57.7300i 2.23531i
\(668\) −31.0204 20.8904i −1.20021 0.808274i
\(669\) 0 0
\(670\) −0.615787 + 2.01679i −0.0237899 + 0.0779156i
\(671\) −8.75417 15.1627i −0.337951 0.585349i
\(672\) 0 0
\(673\) 5.16943 8.95371i 0.199267 0.345140i −0.749024 0.662543i \(-0.769477\pi\)
0.948291 + 0.317403i \(0.102811\pi\)
\(674\) −6.12032 6.55842i −0.235746 0.252621i
\(675\) 0 0
\(676\) 1.78588 25.8115i 0.0686877 0.992748i
\(677\) 4.67459 + 2.69887i 0.179659 + 0.103726i 0.587132 0.809491i \(-0.300257\pi\)
−0.407473 + 0.913217i \(0.633590\pi\)
\(678\) 0 0
\(679\) −4.98945 + 2.88066i −0.191478 + 0.110550i
\(680\) −58.4430 22.3604i −2.24119 0.857481i
\(681\) 0 0
\(682\) 0.0789259 + 0.341294i 0.00302223 + 0.0130688i
\(683\) 39.2840 1.50316 0.751581 0.659641i \(-0.229292\pi\)
0.751581 + 0.659641i \(0.229292\pi\)
\(684\) 0 0
\(685\) 52.2835 1.99765
\(686\) 0.318634 + 1.37785i 0.0121655 + 0.0526066i
\(687\) 0 0
\(688\) 30.7343 12.4700i 1.17173 0.475413i
\(689\) 0.520525 0.300525i 0.0198304 0.0114491i
\(690\) 0 0
\(691\) 15.8640 + 9.15909i 0.603495 + 0.348428i 0.770415 0.637542i \(-0.220049\pi\)
−0.166920 + 0.985970i \(0.553382\pi\)
\(692\) −17.4831 1.20964i −0.664606 0.0459837i
\(693\) 0 0
\(694\) −4.05490 4.34515i −0.153922 0.164940i
\(695\) 12.1088 20.9731i 0.459314 0.795555i
\(696\) 0 0
\(697\) −31.8120 55.1001i −1.20497 2.08706i
\(698\) 14.6110 47.8532i 0.553034 1.81127i
\(699\) 0 0
\(700\) −3.85944 + 5.73093i −0.145873 + 0.216609i
\(701\) 14.7290i 0.556306i −0.960537 0.278153i \(-0.910278\pi\)
0.960537 0.278153i \(-0.0897222\pi\)
\(702\) 0 0
\(703\) 8.22577i 0.310241i
\(704\) −14.1096 12.6482i −0.531777 0.476698i
\(705\) 0 0
\(706\) 40.5117 + 12.3694i 1.52468 + 0.465529i
\(707\) −7.21504 12.4968i −0.271349 0.469991i
\(708\) 0 0
\(709\) −0.246081 + 0.426224i −0.00924175 + 0.0160072i −0.870609 0.491975i \(-0.836275\pi\)
0.861368 + 0.507982i \(0.169608\pi\)
\(710\) 4.36624 4.07458i 0.163862 0.152916i
\(711\) 0 0
\(712\) 26.1633 + 32.2364i 0.980512 + 1.20811i
\(713\) 0.818125 + 0.472345i 0.0306390 + 0.0176894i
\(714\) 0 0
\(715\) 1.50200 0.867182i 0.0561718 0.0324308i
\(716\) −5.16997 + 2.52626i −0.193211 + 0.0944108i
\(717\) 0 0
\(718\) −7.55190 + 1.74641i −0.281834 + 0.0651755i
\(719\) −7.89549 −0.294452 −0.147226 0.989103i \(-0.547034\pi\)
−0.147226 + 0.989103i \(0.547034\pi\)
\(720\) 0 0
\(721\) −11.9863 −0.446392
\(722\) −16.7989 + 3.88482i −0.625189 + 0.144578i
\(723\) 0 0
\(724\) −8.67921 + 4.24102i −0.322560 + 0.157616i
\(725\) 19.1198 11.0388i 0.710091 0.409971i
\(726\) 0 0
\(727\) −9.22490 5.32600i −0.342133 0.197530i 0.319082 0.947727i \(-0.396625\pi\)
−0.661215 + 0.750197i \(0.729959\pi\)
\(728\) −0.448854 0.553043i −0.0166357 0.0204971i
\(729\) 0 0
\(730\) 12.2308 11.4138i 0.452681 0.422442i
\(731\) 31.5449 54.6374i 1.16673 2.02084i
\(732\) 0 0
\(733\) 26.0962 + 45.1999i 0.963885 + 1.66950i 0.712581 + 0.701590i \(0.247526\pi\)
0.251304 + 0.967908i \(0.419141\pi\)
\(734\) −23.0155 7.02730i −0.849516 0.259382i
\(735\) 0 0
\(736\) −50.8984 + 4.54714i −1.87614 + 0.167610i
\(737\) 1.21464i 0.0447417i
\(738\) 0 0
\(739\) 34.1328i 1.25560i −0.778376 0.627798i \(-0.783956\pi\)
0.778376 0.627798i \(-0.216044\pi\)
\(740\) 10.2409 15.2068i 0.376462 0.559012i
\(741\) 0 0
\(742\) −0.985691 + 3.22829i −0.0361859 + 0.118514i
\(743\) 7.11347 + 12.3209i 0.260968 + 0.452009i 0.966499 0.256669i \(-0.0826250\pi\)
−0.705532 + 0.708678i \(0.749292\pi\)
\(744\) 0 0
\(745\) −4.81387 + 8.33787i −0.176367 + 0.305476i
\(746\) 1.10047 + 1.17924i 0.0402911 + 0.0431751i
\(747\) 0 0
\(748\) −35.9576 2.48788i −1.31474 0.0909660i
\(749\) −5.28575 3.05173i −0.193137 0.111508i
\(750\) 0 0
\(751\) −27.8733 + 16.0926i −1.01711 + 0.587228i −0.913265 0.407365i \(-0.866448\pi\)
−0.103844 + 0.994594i \(0.533114\pi\)
\(752\) −0.746765 1.84053i −0.0272317 0.0671171i
\(753\) 0 0
\(754\) 0.512788 + 2.21742i 0.0186746 + 0.0807536i
\(755\) 18.1058 0.658936
\(756\) 0 0
\(757\) −33.8024 −1.22857 −0.614284 0.789085i \(-0.710555\pi\)
−0.614284 + 0.789085i \(0.710555\pi\)
\(758\) 8.45835 + 36.5759i 0.307221 + 1.32850i
\(759\) 0 0
\(760\) 20.0417 + 7.66800i 0.726990 + 0.278147i
\(761\) −7.39633 + 4.27027i −0.268117 + 0.154797i −0.628031 0.778188i \(-0.716139\pi\)
0.359915 + 0.932985i \(0.382806\pi\)
\(762\) 0 0
\(763\) −5.41707 3.12754i −0.196111 0.113225i
\(764\) 2.83232 40.9357i 0.102470 1.48100i
\(765\) 0 0
\(766\) −33.4371 35.8305i −1.20813 1.29461i
\(767\) 1.00601 1.74246i 0.0363249 0.0629165i
\(768\) 0 0
\(769\) −13.0938 22.6792i −0.472176 0.817833i 0.527317 0.849669i \(-0.323198\pi\)
−0.999493 + 0.0318354i \(0.989865\pi\)
\(770\) −2.84427 + 9.31540i −0.102500 + 0.335704i
\(771\) 0 0
\(772\) −30.8519 20.7770i −1.11039 0.747780i
\(773\) 3.16655i 0.113893i −0.998377 0.0569464i \(-0.981864\pi\)
0.998377 0.0569464i \(-0.0181364\pi\)
\(774\) 0 0
\(775\) 0.361277i 0.0129774i
\(776\) 2.56689 + 16.0920i 0.0921459 + 0.577671i
\(777\) 0 0
\(778\) 15.9562 + 4.87191i 0.572059 + 0.174667i
\(779\) 10.9092 + 18.8954i 0.390864 + 0.676996i
\(780\) 0 0
\(781\) 1.72000 2.97913i 0.0615465 0.106602i
\(782\) −71.0646 + 66.3176i −2.54126 + 2.37151i
\(783\) 0 0
\(784\) 3.96189 + 0.550878i 0.141496 + 0.0196742i
\(785\) −7.49959 4.32989i −0.267672 0.154540i
\(786\) 0 0
\(787\) −6.34026 + 3.66055i −0.226006 + 0.130485i −0.608728 0.793379i \(-0.708320\pi\)
0.382722 + 0.923863i \(0.374987\pi\)
\(788\) 15.1485 + 31.0013i 0.539644 + 1.10438i