Properties

Label 756.2.ba.a.71.3
Level $756$
Weight $2$
Character 756.71
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 71.3
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.3

$q$-expansion

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

Character values

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

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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 −0.183182 0.983079i \(-0.558640\pi\)
−0.942962 + 0.332900i \(0.891973\pi\)
\(6\) 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 0.987472 0.157795i \(-0.0504387\pi\)
−0.630391 + 0.776278i \(0.717105\pi\)
\(12\) 0 0
\(13\) −0.125913 + 0.218087i −0.0349219 + 0.0604864i −0.882958 0.469452i \(-0.844452\pi\)
0.848036 + 0.529938i \(0.177785\pi\)
\(14\) 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 \(0.374003\pi\)
−0.385574 + 0.922677i \(0.625997\pi\)
\(18\) 0 0
\(19\) 2.60920i 0.598591i −0.954160 0.299295i \(-0.903248\pi\)
0.954160 0.299295i \(-0.0967516\pi\)
\(20\) −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 0.179782 0.983706i \(-0.442461\pi\)
0.762024 0.647549i \(-0.224206\pi\)
\(24\) 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 0.111394 0.993776i \(-0.464468\pi\)
0.916333 + 0.400418i \(0.131135\pi\)
\(30\) 0 0
\(31\) 0.0905658 + 0.0522882i 0.0162661 + 0.00939124i 0.508111 0.861292i \(-0.330344\pi\)
−0.491845 + 0.870683i \(0.663677\pi\)
\(32\) −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 0.944182 0.329424i \(-0.106855\pi\)
0.186801 + 0.982398i \(0.440188\pi\)
\(42\) 0 0
\(43\) 7.18102 4.14596i 1.09510 0.632254i 0.160167 0.987090i \(-0.448797\pi\)
0.934928 + 0.354836i \(0.115463\pi\)
\(44\) 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 0.883565 0.468308i \(-0.155136\pi\)
−0.847349 + 0.531036i \(0.821803\pi\)
\(48\) 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 \(-0.947585\pi\)
0.986473 0.163925i \(-0.0524154\pi\)
\(54\) 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 −0.479640 0.877466i \(-0.659233\pi\)
0.999727 0.0233526i \(-0.00743403\pi\)
\(60\) 0 0
\(61\) 3.69592 + 6.40151i 0.473214 + 0.819630i 0.999530 0.0306589i \(-0.00976058\pi\)
−0.526316 + 0.850289i \(0.676427\pi\)
\(62\) −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 0.472627 0.881263i \(-0.343306\pi\)
−0.526883 + 0.849938i \(0.676639\pi\)
\(68\) −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 0.185498 0.982645i \(-0.440610\pi\)
0.943744 + 0.330677i \(0.107277\pi\)
\(80\) −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 0.840891 0.541205i \(-0.182032\pi\)
−0.889142 + 0.457630i \(0.848698\pi\)
\(84\) 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 \(0.283749\pi\)
−0.628304 + 0.777968i \(0.716251\pi\)
\(90\) 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 0.974397 0.224834i \(-0.0721839\pi\)
−0.681910 + 0.731436i \(0.738851\pi\)
\(98\) −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 0.273678 0.961821i \(-0.411760\pi\)
0.969801 + 0.243898i \(0.0784263\pi\)
\(102\) 0 0
\(103\) 10.3804 + 5.99314i 1.02281 + 0.590521i 0.914918 0.403641i \(-0.132255\pi\)
0.107896 + 0.994162i \(0.465589\pi\)
\(104\) 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 −0.494838 0.868985i \(-0.664772\pi\)
−0.999982 + 0.00595082i \(0.998106\pi\)
\(114\) 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 \(-0.794103\pi\)
0.797989 0.602672i \(-0.205897\pi\)
\(128\) 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 −0.831862 0.554983i \(-0.812725\pi\)
0.896560 + 0.442922i \(0.146058\pi\)
\(132\) 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 −0.985363 0.170469i \(-0.945472\pi\)
−0.345051 + 0.938584i \(0.612138\pi\)
\(138\) 0 0
\(139\) −7.21297 4.16441i −0.611796 0.353221i 0.161872 0.986812i \(-0.448247\pi\)
−0.773668 + 0.633591i \(0.781580\pi\)
\(140\) 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 0.612838 0.790208i \(-0.290028\pi\)
−0.377921 + 0.925838i \(0.623361\pi\)
\(150\) 0 0
\(151\) −5.39261 + 3.11343i −0.438845 + 0.253367i −0.703107 0.711084i \(-0.748205\pi\)
0.264263 + 0.964451i \(0.414871\pi\)
\(152\) −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 −0.800466 0.599379i \(-0.795414\pi\)
0.919310 + 0.393534i \(0.128748\pi\)
\(158\) −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 \(0.105294\pi\)
−0.945785 + 0.324793i \(0.894706\pi\)
\(164\) 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 0.236085 + 0.971732i \(0.424136\pi\)
−0.959587 + 0.281411i \(0.909198\pi\)
\(168\) 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 −0.759917 0.650020i \(-0.774760\pi\)
0.182975 + 0.983118i \(0.441427\pi\)
\(174\) 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 0.951459 + 0.307775i \(0.0995843\pi\)
−0.209189 + 0.977875i \(0.567082\pi\)
\(192\) 0 0
\(193\) −9.29894 + 16.1062i −0.669352 + 1.15935i 0.308733 + 0.951149i \(0.400095\pi\)
−0.978085 + 0.208204i \(0.933238\pi\)
\(194\) −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 \(-0.789323\pi\)
0.788850 0.614586i \(-0.210677\pi\)
\(198\) 0 0
\(199\) 1.17220i 0.0830948i 0.999137 + 0.0415474i \(0.0132288\pi\)
−0.999137 + 0.0415474i \(0.986771\pi\)
\(200\) 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 0.771637 0.636063i \(-0.219438\pi\)
−0.165028 + 0.986289i \(0.552771\pi\)
\(212\) 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 −0.666279 0.745703i \(-0.732114\pi\)
0.312658 + 0.949866i \(0.398781\pi\)
\(224\) 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 −0.952228 0.305390i \(-0.901213\pi\)
0.211639 0.977348i \(-0.432120\pi\)
\(228\) 0 0
\(229\) −2.70895 + 4.69204i −0.179013 + 0.310059i −0.941543 0.336894i \(-0.890624\pi\)
0.762530 + 0.646953i \(0.223957\pi\)
\(230\) 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 \(-0.936159\pi\)
0.979955 0.199219i \(-0.0638406\pi\)
\(234\) 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 −0.975412 0.220388i \(-0.929268\pi\)
0.678568 + 0.734538i \(0.262601\pi\)
\(240\) 0 0
\(241\) −4.60034 7.96801i −0.296334 0.513265i 0.678961 0.734175i \(-0.262431\pi\)
−0.975294 + 0.220910i \(0.929097\pi\)
\(242\) −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 0.762770 0.646670i \(-0.223839\pi\)
−0.178648 + 0.983913i \(0.557172\pi\)
\(258\) 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 0.901546 0.432683i \(-0.142433\pi\)
−0.825488 + 0.564420i \(0.809100\pi\)
\(264\) 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 \(-0.807600\pi\)
0.822820 0.568303i \(-0.192400\pi\)
\(270\) 0 0
\(271\) 11.9123i 0.723621i −0.932252 0.361811i \(-0.882159\pi\)
0.932252 0.361811i \(-0.117841\pi\)
\(272\) −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 0.999364 + 0.0356520i \(0.0113508\pi\)
−0.468807 + 0.883301i \(0.655316\pi\)
\(278\) 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 0.0834596 0.996511i \(-0.473403\pi\)
0.904734 + 0.425977i \(0.140070\pi\)
\(282\) 0 0
\(283\) 2.81044 + 1.62261i 0.167063 + 0.0964541i 0.581200 0.813760i \(-0.302583\pi\)
−0.414137 + 0.910215i \(0.635917\pi\)
\(284\) 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 0.138342 0.990385i \(-0.455823\pi\)
−0.788527 + 0.615000i \(0.789156\pi\)
\(294\) 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 \(-0.831439\pi\)
0.863035 0.505144i \(-0.168561\pi\)
\(308\) −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 −0.757035 0.653374i \(-0.773353\pi\)
0.944356 + 0.328924i \(0.106686\pi\)
\(312\) 0 0
\(313\) 5.34114 + 9.25113i 0.301899 + 0.522905i 0.976566 0.215217i \(-0.0690460\pi\)
−0.674667 + 0.738122i \(0.735713\pi\)
\(314\) −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 0.272235 0.962231i \(-0.412237\pi\)
0.969434 + 0.245353i \(0.0789040\pi\)
\(318\) 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 0.294407 0.955680i \(-0.404878\pi\)
0.974847 + 0.222876i \(0.0715445\pi\)
\(332\) −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 −0.766619 0.642102i \(-0.778063\pi\)
0.939386 + 0.342861i \(0.111396\pi\)
\(338\) −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 −0.804097 0.594498i \(-0.797351\pi\)
0.916899 + 0.399119i \(0.130684\pi\)
\(348\) 0 0
\(349\) −17.6897 30.6395i −0.946908 1.64009i −0.751885 0.659294i \(-0.770855\pi\)
−0.195023 0.980799i \(-0.562478\pi\)
\(350\) 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 −0.992229 0.124426i \(-0.960291\pi\)
−0.388358 + 0.921509i \(0.626958\pi\)
\(354\) 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 −0.0633686 0.997990i \(-0.520184\pi\)
0.832601 + 0.553874i \(0.186851\pi\)
\(368\) 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 −0.880411 0.474211i \(-0.842734\pi\)
0.850884 + 0.525353i \(0.176067\pi\)
\(374\) 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 \(0.238793\pi\)
−0.731559 + 0.681778i \(0.761207\pi\)
\(380\) −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 0.0401027 0.999196i \(-0.487231\pi\)
0.845277 0.534328i \(-0.179435\pi\)
\(384\) 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 −0.736114 0.676857i \(-0.763341\pi\)
0.218118 + 0.975922i \(0.430008\pi\)
\(390\) 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 0.628595 0.777733i \(-0.283630\pi\)
−0.359239 + 0.933246i \(0.616964\pi\)
\(402\) 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 −0.875968 0.482370i \(-0.839776\pi\)
0.855728 + 0.517425i \(0.173109\pi\)
\(410\) 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 −0.602105 0.798417i \(-0.705671\pi\)
0.992502 + 0.122230i \(0.0390045\pi\)
\(420\) 0 0
\(421\) −4.02490 6.97133i −0.196161 0.339762i 0.751119 0.660167i \(-0.229514\pi\)
−0.947281 + 0.320405i \(0.896181\pi\)
\(422\) −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 −0.506325 + 0.862343i \(0.668996\pi\)
−0.999973 + 0.00731896i \(0.997670\pi\)
\(440\) −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 0.998916 + 0.0465549i \(0.0148243\pi\)
−0.459140 + 0.888364i \(0.651842\pi\)
\(444\) 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 \(-0.929869\pi\)
0.975827 0.218544i \(-0.0701306\pi\)
\(450\) 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 0.970394 0.241527i \(-0.0776482\pi\)
−0.694365 + 0.719623i \(0.744315\pi\)
\(458\) 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 −0.550749 0.834671i \(-0.685658\pi\)
0.447472 + 0.894298i \(0.352324\pi\)
\(462\) 0 0
\(463\) −10.0234 5.78704i −0.465829 0.268947i 0.248663 0.968590i \(-0.420009\pi\)
−0.714492 + 0.699643i \(0.753342\pi\)
\(464\) 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 0.986457 + 0.164019i \(0.0524457\pi\)
−0.351184 + 0.936306i \(0.614221\pi\)
\(480\) 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 \(-0.924813\pi\)
0.972233 0.234016i \(-0.0751867\pi\)
\(488\) 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 0.177697 + 0.984085i \(0.443135\pi\)
−0.941091 + 0.338153i \(0.890198\pi\)
\(492\) 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 0.613391 0.789779i \(-0.289805\pi\)
−0.377274 + 0.926102i \(0.623138\pi\)
\(500\) −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 0.850258 0.526367i \(-0.176446\pi\)
−0.0307180 + 0.999528i \(0.509779\pi\)
\(510\) 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 \(0.232710\pi\)
−0.744453 + 0.667675i \(0.767290\pi\)
\(522\) 0 0
\(523\) 28.4494i 1.24401i 0.783014 + 0.622004i \(0.213681\pi\)
−0.783014 + 0.622004i \(0.786319\pi\)
\(524\) 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 0.378541 0.925584i \(-0.376426\pi\)
0.990850 + 0.134966i \(0.0430924\pi\)
\(548\) −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 \(0.0289991\pi\)
−0.995853 + 0.0909773i \(0.971001\pi\)
\(558\) 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 −0.801312 0.598246i \(-0.795865\pi\)
0.918753 + 0.394834i \(0.129198\pi\)
\(564\) 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 −0.375121 0.926976i \(-0.622399\pi\)
0.615224 + 0.788352i \(0.289066\pi\)
\(570\) 0 0
\(571\) −28.7640 16.6069i −1.20374 0.694978i −0.242353 0.970188i \(-0.577919\pi\)
−0.961384 + 0.275211i \(0.911252\pi\)
\(572\) −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 0.503717 0.863869i \(-0.331965\pi\)
−0.999991 + 0.00429733i \(0.998632\pi\)
\(588\) 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 \(0.0461052\pi\)
−0.989528 + 0.144338i \(0.953895\pi\)
\(594\) 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 −0.388857 0.921298i \(-0.627130\pi\)
0.992296 0.123889i \(-0.0395366\pi\)
\(600\) 0 0
\(601\) −11.2326 19.4555i −0.458188 0.793605i 0.540677 0.841230i \(-0.318168\pi\)
−0.998865 + 0.0476250i \(0.984835\pi\)
\(602\) 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 −0.302748 0.953071i \(-0.597904\pi\)
−0.976757 + 0.214348i \(0.931237\pi\)
\(608\) −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 0.999879 + 0.0155564i \(0.00495195\pi\)
0.513412 + 0.858142i \(0.328381\pi\)
\(618\) 0 0
\(619\) 0.893596 0.515918i 0.0359167 0.0207365i −0.481934 0.876207i \(-0.660066\pi\)
0.517851 + 0.855471i \(0.326732\pi\)
\(620\) −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 \(-0.830951\pi\)
0.862258 0.506469i \(-0.169049\pi\)
\(632\) −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 0.0638607 0.997959i \(-0.479659\pi\)
0.896188 + 0.443674i \(0.146325\pi\)
\(642\) 0 0
\(643\) −11.1062 6.41216i −0.437985 0.252871i 0.264757 0.964315i \(-0.414708\pi\)
−0.702743 + 0.711444i \(0.748041\pi\)
\(644\) −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 0.396969 0.917832i \(-0.370062\pi\)
−0.596381 + 0.802701i \(0.703395\pi\)
\(654\) 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 −0.999981 0.00619658i \(-0.998028\pi\)
0.494624 0.869107i \(-0.335306\pi\)
\(660\) 0 0
\(661\) −19.8403 + 34.3644i −0.771699 + 1.33662i 0.164933 + 0.986305i \(0.447259\pi\)
−0.936631 + 0.350316i \(0.886074\pi\)
\(662\) −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 0.948291 0.317403i \(-0.102811\pi\)
−0.749024 + 0.662543i \(0.769477\pi\)
\(674\) −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 −0.407473 0.913217i \(-0.633590\pi\)
0.587132 + 0.809491i \(0.300257\pi\)
\(678\) 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 −0.166920 0.985970i \(-0.553382\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(692\) −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 \(0.0897222\pi\)
−0.960537 + 0.278153i \(0.910278\pi\)
\(702\) 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 0.861368 0.507982i \(-0.169608\pi\)
−0.870609 + 0.491975i \(0.836275\pi\)
\(710\) 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 −0.661215 0.750197i \(-0.729959\pi\)
0.319082 + 0.947727i \(0.396625\pi\)
\(728\) −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 0.251304 0.967908i \(-0.419141\pi\)
0.712581 0.701590i \(-0.247526\pi\)
\(734\) −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 \(0.216044\pi\)
−0.778376 + 0.627798i \(0.783956\pi\)
\(740\) 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 −0.705532 0.708678i \(-0.749292\pi\)
0.966499 + 0.256669i \(0.0826250\pi\)
\(744\) 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 −0.103844 0.994594i \(-0.533114\pi\)
−0.913265 + 0.407365i \(0.866448\pi\)
\(752\) −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 0.359915 0.932985i \(-0.382806\pi\)
−0.628031 + 0.778188i \(0.716139\pi\)
\(762\) 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 −0.999493 0.0318354i \(-0.989865\pi\)
0.527317 + 0.849669i \(0.323198\pi\)
\(770\) −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 \(0.0181364\pi\)
−0.998377 + 0.0569464i \(0.981864\pi\)
\(774\) 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 0.382722 0.923863i \(-0.374987\pi\)
−0.608728 + 0.793379i \(0.708320\pi\)
\(788\) 15.1485 31.0013i 0.539644 1.10438i
\(789\) 0 0
\(790\)