Properties

Label 882.3.s.g.557.1
Level $882$
Weight $3$
Character 882.557
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 557.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.g.863.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +2.82843i q^{8} +(2.82843 - 4.89898i) q^{10} +(-2.44949 - 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.46410 + 2.00000i) q^{17} +(-11.3137 - 19.5959i) q^{19} +8.00000i q^{20} +4.00000 q^{22} +(-31.8434 + 18.3848i) q^{23} +(-4.50000 + 7.79423i) q^{25} +(-15.5885 + 9.00000i) q^{26} -32.5269i q^{29} +(25.4558 - 44.0908i) q^{31} +(4.89898 + 2.82843i) q^{32} -5.65685 q^{34} +(16.0000 + 27.7128i) q^{37} +(27.7128 + 16.0000i) q^{38} +(-5.65685 - 9.79796i) q^{40} +38.0000i q^{41} +20.0000 q^{43} +(-4.89898 + 2.82843i) q^{44} +(26.0000 - 45.0333i) q^{46} +(17.3205 - 10.0000i) q^{47} -12.7279i q^{50} +(12.7279 - 22.0454i) q^{52} +(82.0579 + 47.3762i) q^{53} +11.3137 q^{55} +(23.0000 + 39.8372i) q^{58} +(3.46410 + 2.00000i) q^{59} +(-41.7193 - 72.2599i) q^{61} +72.0000i q^{62} -8.00000 q^{64} +(-44.0908 + 25.4558i) q^{65} +(24.0000 - 41.5692i) q^{67} +(6.92820 - 4.00000i) q^{68} -76.3675i q^{71} +(60.1041 - 104.103i) q^{73} +(-39.1918 - 22.6274i) q^{74} -45.2548 q^{76} +(74.0000 + 128.172i) q^{79} +(13.8564 + 8.00000i) q^{80} +(-26.8701 - 46.5403i) q^{82} -80.0000i q^{83} -16.0000 q^{85} +(-24.4949 + 14.1421i) q^{86} +(4.00000 - 6.92820i) q^{88} +(91.7987 - 53.0000i) q^{89} +73.5391i q^{92} +(-14.1421 + 24.4949i) q^{94} +(78.3837 + 45.2548i) q^{95} +154.149 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 36 q^{25} + 128 q^{37} + 160 q^{43} + 208 q^{46} + 184 q^{58} - 64 q^{64} + 192 q^{67} + 592 q^{79} - 128 q^{85} + 32 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) −3.46410 + 2.00000i −0.692820 + 0.400000i −0.804668 0.593725i \(-0.797657\pi\)
0.111847 + 0.993725i \(0.464323\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 2.82843 4.89898i 0.282843 0.489898i
\(11\) −2.44949 1.41421i −0.222681 0.128565i 0.384510 0.923121i \(-0.374370\pi\)
−0.607191 + 0.794556i \(0.707704\pi\)
\(12\) 0 0
\(13\) 12.7279 0.979071 0.489535 0.871983i \(-0.337166\pi\)
0.489535 + 0.871983i \(0.337166\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 3.46410 + 2.00000i 0.203771 + 0.117647i 0.598413 0.801188i \(-0.295798\pi\)
−0.394642 + 0.918835i \(0.629132\pi\)
\(18\) 0 0
\(19\) −11.3137 19.5959i −0.595458 1.03136i −0.993482 0.113989i \(-0.963637\pi\)
0.398024 0.917375i \(-0.369696\pi\)
\(20\) 8.00000i 0.400000i
\(21\) 0 0
\(22\) 4.00000 0.181818
\(23\) −31.8434 + 18.3848i −1.38449 + 0.799338i −0.992688 0.120710i \(-0.961483\pi\)
−0.391806 + 0.920048i \(0.628150\pi\)
\(24\) 0 0
\(25\) −4.50000 + 7.79423i −0.180000 + 0.311769i
\(26\) −15.5885 + 9.00000i −0.599556 + 0.346154i
\(27\) 0 0
\(28\) 0 0
\(29\) 32.5269i 1.12162i −0.827945 0.560809i \(-0.810490\pi\)
0.827945 0.560809i \(-0.189510\pi\)
\(30\) 0 0
\(31\) 25.4558 44.0908i 0.821156 1.42228i −0.0836655 0.996494i \(-0.526663\pi\)
0.904822 0.425790i \(-0.140004\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −5.65685 −0.166378
\(35\) 0 0
\(36\) 0 0
\(37\) 16.0000 + 27.7128i 0.432432 + 0.748995i 0.997082 0.0763357i \(-0.0243221\pi\)
−0.564650 + 0.825331i \(0.690989\pi\)
\(38\) 27.7128 + 16.0000i 0.729285 + 0.421053i
\(39\) 0 0
\(40\) −5.65685 9.79796i −0.141421 0.244949i
\(41\) 38.0000i 0.926829i 0.886142 + 0.463415i \(0.153376\pi\)
−0.886142 + 0.463415i \(0.846624\pi\)
\(42\) 0 0
\(43\) 20.0000 0.465116 0.232558 0.972582i \(-0.425290\pi\)
0.232558 + 0.972582i \(0.425290\pi\)
\(44\) −4.89898 + 2.82843i −0.111340 + 0.0642824i
\(45\) 0 0
\(46\) 26.0000 45.0333i 0.565217 0.978985i
\(47\) 17.3205 10.0000i 0.368521 0.212766i −0.304291 0.952579i \(-0.598419\pi\)
0.672812 + 0.739813i \(0.265086\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 12.7279i 0.254558i
\(51\) 0 0
\(52\) 12.7279 22.0454i 0.244768 0.423950i
\(53\) 82.0579 + 47.3762i 1.54826 + 0.893890i 0.998275 + 0.0587170i \(0.0187009\pi\)
0.549988 + 0.835173i \(0.314632\pi\)
\(54\) 0 0
\(55\) 11.3137 0.205704
\(56\) 0 0
\(57\) 0 0
\(58\) 23.0000 + 39.8372i 0.396552 + 0.686848i
\(59\) 3.46410 + 2.00000i 0.0587136 + 0.0338983i 0.529069 0.848579i \(-0.322541\pi\)
−0.470356 + 0.882477i \(0.655874\pi\)
\(60\) 0 0
\(61\) −41.7193 72.2599i −0.683923 1.18459i −0.973774 0.227518i \(-0.926939\pi\)
0.289851 0.957072i \(-0.406394\pi\)
\(62\) 72.0000i 1.16129i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −44.0908 + 25.4558i −0.678320 + 0.391628i
\(66\) 0 0
\(67\) 24.0000 41.5692i 0.358209 0.620436i −0.629453 0.777039i \(-0.716721\pi\)
0.987662 + 0.156603i \(0.0500542\pi\)
\(68\) 6.92820 4.00000i 0.101885 0.0588235i
\(69\) 0 0
\(70\) 0 0
\(71\) 76.3675i 1.07560i −0.843073 0.537800i \(-0.819256\pi\)
0.843073 0.537800i \(-0.180744\pi\)
\(72\) 0 0
\(73\) 60.1041 104.103i 0.823344 1.42607i −0.0798352 0.996808i \(-0.525439\pi\)
0.903179 0.429265i \(-0.141227\pi\)
\(74\) −39.1918 22.6274i −0.529619 0.305776i
\(75\) 0 0
\(76\) −45.2548 −0.595458
\(77\) 0 0
\(78\) 0 0
\(79\) 74.0000 + 128.172i 0.936709 + 1.62243i 0.771558 + 0.636159i \(0.219478\pi\)
0.165151 + 0.986268i \(0.447189\pi\)
\(80\) 13.8564 + 8.00000i 0.173205 + 0.100000i
\(81\) 0 0
\(82\) −26.8701 46.5403i −0.327684 0.567565i
\(83\) 80.0000i 0.963855i −0.876211 0.481928i \(-0.839937\pi\)
0.876211 0.481928i \(-0.160063\pi\)
\(84\) 0 0
\(85\) −16.0000 −0.188235
\(86\) −24.4949 + 14.1421i −0.284824 + 0.164443i
\(87\) 0 0
\(88\) 4.00000 6.92820i 0.0454545 0.0787296i
\(89\) 91.7987 53.0000i 1.03145 0.595506i 0.114047 0.993475i \(-0.463618\pi\)
0.917399 + 0.397970i \(0.130285\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 73.5391i 0.799338i
\(93\) 0 0
\(94\) −14.1421 + 24.4949i −0.150448 + 0.260584i
\(95\) 78.3837 + 45.2548i 0.825091 + 0.476367i
\(96\) 0 0
\(97\) 154.149 1.58917 0.794584 0.607154i \(-0.207689\pi\)
0.794584 + 0.607154i \(0.207689\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 9.00000 + 15.5885i 0.0900000 + 0.155885i
\(101\) 109.119 + 63.0000i 1.08039 + 0.623762i 0.931001 0.365016i \(-0.118937\pi\)
0.149387 + 0.988779i \(0.452270\pi\)
\(102\) 0 0
\(103\) 36.7696 + 63.6867i 0.356986 + 0.618318i 0.987456 0.157896i \(-0.0504711\pi\)
−0.630470 + 0.776214i \(0.717138\pi\)
\(104\) 36.0000i 0.346154i
\(105\) 0 0
\(106\) −134.000 −1.26415
\(107\) −61.2372 + 35.3553i −0.572311 + 0.330424i −0.758072 0.652171i \(-0.773858\pi\)
0.185761 + 0.982595i \(0.440525\pi\)
\(108\) 0 0
\(109\) 43.0000 74.4782i 0.394495 0.683286i −0.598541 0.801092i \(-0.704253\pi\)
0.993037 + 0.117806i \(0.0375861\pi\)
\(110\) −13.8564 + 8.00000i −0.125967 + 0.0727273i
\(111\) 0 0
\(112\) 0 0
\(113\) 21.2132i 0.187727i 0.995585 + 0.0938637i \(0.0299218\pi\)
−0.995585 + 0.0938637i \(0.970078\pi\)
\(114\) 0 0
\(115\) 73.5391 127.373i 0.639470 1.10760i
\(116\) −56.3383 32.5269i −0.485675 0.280404i
\(117\) 0 0
\(118\) −5.65685 −0.0479394
\(119\) 0 0
\(120\) 0 0
\(121\) −56.5000 97.8609i −0.466942 0.808768i
\(122\) 102.191 + 59.0000i 0.837631 + 0.483607i
\(123\) 0 0
\(124\) −50.9117 88.1816i −0.410578 0.711142i
\(125\) 136.000i 1.08800i
\(126\) 0 0
\(127\) 4.00000 0.0314961 0.0157480 0.999876i \(-0.494987\pi\)
0.0157480 + 0.999876i \(0.494987\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 36.0000 62.3538i 0.276923 0.479645i
\(131\) 20.7846 12.0000i 0.158661 0.0916031i −0.418567 0.908186i \(-0.637468\pi\)
0.577228 + 0.816583i \(0.304134\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 67.8823i 0.506584i
\(135\) 0 0
\(136\) −5.65685 + 9.79796i −0.0415945 + 0.0720438i
\(137\) 62.4620 + 36.0624i 0.455927 + 0.263230i 0.710330 0.703869i \(-0.248546\pi\)
−0.254403 + 0.967098i \(0.581879\pi\)
\(138\) 0 0
\(139\) 141.421 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 54.0000 + 93.5307i 0.380282 + 0.658667i
\(143\) −31.1769 18.0000i −0.218020 0.125874i
\(144\) 0 0
\(145\) 65.0538 + 112.677i 0.448647 + 0.777080i
\(146\) 170.000i 1.16438i
\(147\) 0 0
\(148\) 64.0000 0.432432
\(149\) −23.2702 + 13.4350i −0.156176 + 0.0901680i −0.576051 0.817414i \(-0.695407\pi\)
0.419876 + 0.907582i \(0.362074\pi\)
\(150\) 0 0
\(151\) −76.0000 + 131.636i −0.503311 + 0.871761i 0.496681 + 0.867933i \(0.334552\pi\)
−0.999993 + 0.00382774i \(0.998782\pi\)
\(152\) 55.4256 32.0000i 0.364642 0.210526i
\(153\) 0 0
\(154\) 0 0
\(155\) 203.647i 1.31385i
\(156\) 0 0
\(157\) −47.3762 + 82.0579i −0.301759 + 0.522662i −0.976534 0.215361i \(-0.930907\pi\)
0.674776 + 0.738023i \(0.264240\pi\)
\(158\) −181.262 104.652i −1.14723 0.662353i
\(159\) 0 0
\(160\) −22.6274 −0.141421
\(161\) 0 0
\(162\) 0 0
\(163\) 76.0000 + 131.636i 0.466258 + 0.807582i 0.999257 0.0385335i \(-0.0122686\pi\)
−0.533000 + 0.846115i \(0.678935\pi\)
\(164\) 65.8179 + 38.0000i 0.401329 + 0.231707i
\(165\) 0 0
\(166\) 56.5685 + 97.9796i 0.340774 + 0.590238i
\(167\) 116.000i 0.694611i −0.937752 0.347305i \(-0.887097\pi\)
0.937752 0.347305i \(-0.112903\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.0414201
\(170\) 19.5959 11.3137i 0.115270 0.0665512i
\(171\) 0 0
\(172\) 20.0000 34.6410i 0.116279 0.201401i
\(173\) 192.258 111.000i 1.11132 0.641618i 0.172146 0.985071i \(-0.444930\pi\)
0.939170 + 0.343453i \(0.111597\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 11.3137i 0.0642824i
\(177\) 0 0
\(178\) −74.9533 + 129.823i −0.421086 + 0.729342i
\(179\) 51.4393 + 29.6985i 0.287370 + 0.165913i 0.636755 0.771066i \(-0.280276\pi\)
−0.349385 + 0.936979i \(0.613609\pi\)
\(180\) 0 0
\(181\) 80.6102 0.445360 0.222680 0.974892i \(-0.428519\pi\)
0.222680 + 0.974892i \(0.428519\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −52.0000 90.0666i −0.282609 0.489493i
\(185\) −110.851 64.0000i −0.599196 0.345946i
\(186\) 0 0
\(187\) −5.65685 9.79796i −0.0302506 0.0523955i
\(188\) 40.0000i 0.212766i
\(189\) 0 0
\(190\) −128.000 −0.673684
\(191\) 262.095 151.321i 1.37223 0.792256i 0.381019 0.924567i \(-0.375573\pi\)
0.991208 + 0.132311i \(0.0422399\pi\)
\(192\) 0 0
\(193\) −109.000 + 188.794i −0.564767 + 0.978205i 0.432304 + 0.901728i \(0.357701\pi\)
−0.997071 + 0.0764772i \(0.975633\pi\)
\(194\) −188.794 + 109.000i −0.973163 + 0.561856i
\(195\) 0 0
\(196\) 0 0
\(197\) 287.085i 1.45729i −0.684894 0.728643i \(-0.740151\pi\)
0.684894 0.728643i \(-0.259849\pi\)
\(198\) 0 0
\(199\) 33.9411 58.7878i 0.170558 0.295416i −0.768057 0.640382i \(-0.778776\pi\)
0.938615 + 0.344966i \(0.112110\pi\)
\(200\) −22.0454 12.7279i −0.110227 0.0636396i
\(201\) 0 0
\(202\) −178.191 −0.882133
\(203\) 0 0
\(204\) 0 0
\(205\) −76.0000 131.636i −0.370732 0.642126i
\(206\) −90.0666 52.0000i −0.437217 0.252427i
\(207\) 0 0
\(208\) −25.4558 44.0908i −0.122384 0.211975i
\(209\) 64.0000i 0.306220i
\(210\) 0 0
\(211\) 132.000 0.625592 0.312796 0.949820i \(-0.398734\pi\)
0.312796 + 0.949820i \(0.398734\pi\)
\(212\) 164.116 94.7523i 0.774131 0.446945i
\(213\) 0 0
\(214\) 50.0000 86.6025i 0.233645 0.404685i
\(215\) −69.2820 + 40.0000i −0.322242 + 0.186047i
\(216\) 0 0
\(217\) 0 0
\(218\) 121.622i 0.557901i
\(219\) 0 0
\(220\) 11.3137 19.5959i 0.0514259 0.0890724i
\(221\) 44.0908 + 25.4558i 0.199506 + 0.115185i
\(222\) 0 0
\(223\) −169.706 −0.761012 −0.380506 0.924778i \(-0.624250\pi\)
−0.380506 + 0.924778i \(0.624250\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −15.0000 25.9808i −0.0663717 0.114959i
\(227\) −259.808 150.000i −1.14453 0.660793i −0.196979 0.980408i \(-0.563113\pi\)
−0.947548 + 0.319615i \(0.896447\pi\)
\(228\) 0 0
\(229\) 125.158 + 216.780i 0.546541 + 0.946637i 0.998508 + 0.0546023i \(0.0173891\pi\)
−0.451967 + 0.892035i \(0.649278\pi\)
\(230\) 208.000i 0.904348i
\(231\) 0 0
\(232\) 92.0000 0.396552
\(233\) −25.7196 + 14.8492i −0.110385 + 0.0637307i −0.554176 0.832400i \(-0.686967\pi\)
0.443791 + 0.896130i \(0.353633\pi\)
\(234\) 0 0
\(235\) −40.0000 + 69.2820i −0.170213 + 0.294817i
\(236\) 6.92820 4.00000i 0.0293568 0.0169492i
\(237\) 0 0
\(238\) 0 0
\(239\) 161.220i 0.674562i −0.941404 0.337281i \(-0.890493\pi\)
0.941404 0.337281i \(-0.109507\pi\)
\(240\) 0 0
\(241\) −188.798 + 327.007i −0.783392 + 1.35688i 0.146563 + 0.989201i \(0.453179\pi\)
−0.929955 + 0.367674i \(0.880154\pi\)
\(242\) 138.396 + 79.9031i 0.571885 + 0.330178i
\(243\) 0 0
\(244\) −166.877 −0.683923
\(245\) 0 0
\(246\) 0 0
\(247\) −144.000 249.415i −0.582996 1.00978i
\(248\) 124.708 + 72.0000i 0.502853 + 0.290323i
\(249\) 0 0
\(250\) 96.1665 + 166.565i 0.384666 + 0.666261i
\(251\) 476.000i 1.89641i −0.317653 0.948207i \(-0.602895\pi\)
0.317653 0.948207i \(-0.397105\pi\)
\(252\) 0 0
\(253\) 104.000 0.411067
\(254\) −4.89898 + 2.82843i −0.0192873 + 0.0111355i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −88.3346 + 51.0000i −0.343714 + 0.198444i −0.661913 0.749580i \(-0.730255\pi\)
0.318199 + 0.948024i \(0.396922\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 101.823i 0.391628i
\(261\) 0 0
\(262\) −16.9706 + 29.3939i −0.0647731 + 0.112190i
\(263\) −315.984 182.434i −1.20146 0.693664i −0.240581 0.970629i \(-0.577338\pi\)
−0.960880 + 0.276965i \(0.910671\pi\)
\(264\) 0 0
\(265\) −379.009 −1.43022
\(266\) 0 0
\(267\) 0 0
\(268\) −48.0000 83.1384i −0.179104 0.310218i
\(269\) −169.741 98.0000i −0.631007 0.364312i 0.150135 0.988666i \(-0.452029\pi\)
−0.781142 + 0.624353i \(0.785363\pi\)
\(270\) 0 0
\(271\) −87.6812 151.868i −0.323547 0.560400i 0.657670 0.753306i \(-0.271542\pi\)
−0.981217 + 0.192906i \(0.938209\pi\)
\(272\) 16.0000i 0.0588235i
\(273\) 0 0
\(274\) −102.000 −0.372263
\(275\) 22.0454 12.7279i 0.0801651 0.0462834i
\(276\) 0 0
\(277\) −128.000 + 221.703i −0.462094 + 0.800370i −0.999065 0.0432305i \(-0.986235\pi\)
0.536971 + 0.843601i \(0.319568\pi\)
\(278\) −173.205 + 100.000i −0.623040 + 0.359712i
\(279\) 0 0
\(280\) 0 0
\(281\) 26.8701i 0.0956230i −0.998856 0.0478115i \(-0.984775\pi\)
0.998856 0.0478115i \(-0.0152247\pi\)
\(282\) 0 0
\(283\) −251.730 + 436.009i −0.889505 + 1.54067i −0.0490442 + 0.998797i \(0.515618\pi\)
−0.840461 + 0.541872i \(0.817716\pi\)
\(284\) −132.272 76.3675i −0.465748 0.268900i
\(285\) 0 0
\(286\) 50.9117 0.178013
\(287\) 0 0
\(288\) 0 0
\(289\) −136.500 236.425i −0.472318 0.818079i
\(290\) −159.349 92.0000i −0.549478 0.317241i
\(291\) 0 0
\(292\) −120.208 208.207i −0.411672 0.713036i
\(293\) 190.000i 0.648464i 0.945978 + 0.324232i \(0.105106\pi\)
−0.945978 + 0.324232i \(0.894894\pi\)
\(294\) 0 0
\(295\) −16.0000 −0.0542373
\(296\) −78.3837 + 45.2548i −0.264810 + 0.152888i
\(297\) 0 0
\(298\) 19.0000 32.9090i 0.0637584 0.110433i
\(299\) −405.300 + 234.000i −1.35552 + 0.782609i
\(300\) 0 0
\(301\) 0 0
\(302\) 214.960i 0.711790i
\(303\) 0 0
\(304\) −45.2548 + 78.3837i −0.148865 + 0.257841i
\(305\) 289.040 + 166.877i 0.947671 + 0.547138i
\(306\) 0 0
\(307\) 265.872 0.866033 0.433017 0.901386i \(-0.357449\pi\)
0.433017 + 0.901386i \(0.357449\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −144.000 249.415i −0.464516 0.804566i
\(311\) −460.726 266.000i −1.48143 0.855305i −0.481654 0.876361i \(-0.659964\pi\)
−0.999778 + 0.0210559i \(0.993297\pi\)
\(312\) 0 0
\(313\) −74.2462 128.598i −0.237208 0.410857i 0.722704 0.691158i \(-0.242899\pi\)
−0.959912 + 0.280301i \(0.909566\pi\)
\(314\) 134.000i 0.426752i
\(315\) 0 0
\(316\) 296.000 0.936709
\(317\) −199.633 + 115.258i −0.629758 + 0.363591i −0.780659 0.624958i \(-0.785116\pi\)
0.150900 + 0.988549i \(0.451783\pi\)
\(318\) 0 0
\(319\) −46.0000 + 79.6743i −0.144201 + 0.249763i
\(320\) 27.7128 16.0000i 0.0866025 0.0500000i
\(321\) 0 0
\(322\) 0 0
\(323\) 90.5097i 0.280216i
\(324\) 0 0
\(325\) −57.2756 + 99.2043i −0.176233 + 0.305244i
\(326\) −186.161 107.480i −0.571047 0.329694i
\(327\) 0 0
\(328\) −107.480 −0.327684
\(329\) 0 0
\(330\) 0 0
\(331\) −134.000 232.095i −0.404834 0.701193i 0.589468 0.807792i \(-0.299337\pi\)
−0.994302 + 0.106599i \(0.966004\pi\)
\(332\) −138.564 80.0000i −0.417362 0.240964i
\(333\) 0 0
\(334\) 82.0244 + 142.070i 0.245582 + 0.425360i
\(335\) 192.000i 0.573134i
\(336\) 0 0
\(337\) 170.000 0.504451 0.252226 0.967668i \(-0.418838\pi\)
0.252226 + 0.967668i \(0.418838\pi\)
\(338\) 8.57321 4.94975i 0.0253645 0.0146442i
\(339\) 0 0
\(340\) −16.0000 + 27.7128i −0.0470588 + 0.0815083i
\(341\) −124.708 + 72.0000i −0.365712 + 0.211144i
\(342\) 0 0
\(343\) 0 0
\(344\) 56.5685i 0.164443i
\(345\) 0 0
\(346\) −156.978 + 271.893i −0.453693 + 0.785819i
\(347\) −242.499 140.007i −0.698846 0.403479i 0.108072 0.994143i \(-0.465532\pi\)
−0.806917 + 0.590664i \(0.798866\pi\)
\(348\) 0 0
\(349\) −241.831 −0.692924 −0.346462 0.938064i \(-0.612617\pi\)
−0.346462 + 0.938064i \(0.612617\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.00000 13.8564i −0.0227273 0.0393648i
\(353\) 460.726 + 266.000i 1.30517 + 0.753541i 0.981286 0.192555i \(-0.0616775\pi\)
0.323885 + 0.946096i \(0.395011\pi\)
\(354\) 0 0
\(355\) 152.735 + 264.545i 0.430240 + 0.745197i
\(356\) 212.000i 0.595506i
\(357\) 0 0
\(358\) −84.0000 −0.234637
\(359\) 296.388 171.120i 0.825594 0.476657i −0.0267477 0.999642i \(-0.508515\pi\)
0.852342 + 0.522985i \(0.175182\pi\)
\(360\) 0 0
\(361\) −75.5000 + 130.770i −0.209141 + 0.362243i
\(362\) −98.7269 + 57.0000i −0.272726 + 0.157459i
\(363\) 0 0
\(364\) 0 0
\(365\) 480.833i 1.31735i
\(366\) 0 0
\(367\) 342.240 592.777i 0.932533 1.61519i 0.153558 0.988140i \(-0.450927\pi\)
0.778975 0.627055i \(-0.215740\pi\)
\(368\) 127.373 + 73.5391i 0.346124 + 0.199835i
\(369\) 0 0
\(370\) 181.019 0.489241
\(371\) 0 0
\(372\) 0 0
\(373\) −191.000 330.822i −0.512064 0.886921i −0.999902 0.0139872i \(-0.995548\pi\)
0.487838 0.872934i \(-0.337786\pi\)
\(374\) 13.8564 + 8.00000i 0.0370492 + 0.0213904i
\(375\) 0 0
\(376\) 28.2843 + 48.9898i 0.0752241 + 0.130292i
\(377\) 414.000i 1.09814i
\(378\) 0 0
\(379\) −140.000 −0.369393 −0.184697 0.982796i \(-0.559130\pi\)
−0.184697 + 0.982796i \(0.559130\pi\)
\(380\) 156.767 90.5097i 0.412546 0.238183i
\(381\) 0 0
\(382\) −214.000 + 370.659i −0.560209 + 0.970311i
\(383\) −214.774 + 124.000i −0.560768 + 0.323760i −0.753454 0.657501i \(-0.771614\pi\)
0.192685 + 0.981261i \(0.438280\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 308.299i 0.798701i
\(387\) 0 0
\(388\) 154.149 266.994i 0.397292 0.688130i
\(389\) −295.164 170.413i −0.758775 0.438079i 0.0700807 0.997541i \(-0.477674\pi\)
−0.828856 + 0.559462i \(0.811008\pi\)
\(390\) 0 0
\(391\) −147.078 −0.376159
\(392\) 0 0
\(393\) 0 0
\(394\) 203.000 + 351.606i 0.515228 + 0.892402i
\(395\) −512.687 296.000i −1.29794 0.749367i
\(396\) 0 0
\(397\) 122.329 + 211.881i 0.308135 + 0.533705i 0.977954 0.208819i \(-0.0669619\pi\)
−0.669820 + 0.742524i \(0.733629\pi\)
\(398\) 96.0000i 0.241206i
\(399\) 0 0
\(400\) 36.0000 0.0900000
\(401\) −25.7196 + 14.8492i −0.0641388 + 0.0370305i −0.531726 0.846916i \(-0.678457\pi\)
0.467588 + 0.883947i \(0.345123\pi\)
\(402\) 0 0
\(403\) 324.000 561.184i 0.803970 1.39252i
\(404\) 218.238 126.000i 0.540194 0.311881i
\(405\) 0 0
\(406\) 0 0
\(407\) 90.5097i 0.222382i
\(408\) 0 0
\(409\) −303.349 + 525.416i −0.741684 + 1.28463i 0.210044 + 0.977692i \(0.432639\pi\)
−0.951728 + 0.306943i \(0.900694\pi\)
\(410\) 186.161 + 107.480i 0.454052 + 0.262147i
\(411\) 0 0
\(412\) 147.078 0.356986
\(413\) 0 0
\(414\) 0 0
\(415\) 160.000 + 277.128i 0.385542 + 0.667779i
\(416\) 62.3538 + 36.0000i 0.149889 + 0.0865385i
\(417\) 0 0
\(418\) −45.2548 78.3837i −0.108265 0.187521i
\(419\) 692.000i 1.65155i 0.563999 + 0.825776i \(0.309262\pi\)
−0.563999 + 0.825776i \(0.690738\pi\)
\(420\) 0 0
\(421\) 384.000 0.912114 0.456057 0.889951i \(-0.349261\pi\)
0.456057 + 0.889951i \(0.349261\pi\)
\(422\) −161.666 + 93.3381i −0.383096 + 0.221180i
\(423\) 0 0
\(424\) −134.000 + 232.095i −0.316038 + 0.547393i
\(425\) −31.1769 + 18.0000i −0.0733574 + 0.0423529i
\(426\) 0 0
\(427\) 0 0
\(428\) 141.421i 0.330424i
\(429\) 0 0
\(430\) 56.5685 97.9796i 0.131555 0.227860i
\(431\) 95.5301 + 55.1543i 0.221648 + 0.127968i 0.606713 0.794921i \(-0.292488\pi\)
−0.385065 + 0.922889i \(0.625821\pi\)
\(432\) 0 0
\(433\) −156.978 −0.362535 −0.181268 0.983434i \(-0.558020\pi\)
−0.181268 + 0.983434i \(0.558020\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −86.0000 148.956i −0.197248 0.341643i
\(437\) 720.533 + 416.000i 1.64882 + 0.951945i
\(438\) 0 0
\(439\) −101.823 176.363i −0.231944 0.401739i 0.726436 0.687234i \(-0.241175\pi\)
−0.958380 + 0.285495i \(0.907842\pi\)
\(440\) 32.0000i 0.0727273i
\(441\) 0 0
\(442\) −72.0000 −0.162896
\(443\) 703.004 405.879i 1.58692 0.916206i 0.593104 0.805126i \(-0.297902\pi\)
0.993811 0.111080i \(-0.0354311\pi\)
\(444\) 0 0
\(445\) −212.000 + 367.195i −0.476404 + 0.825157i
\(446\) 207.846 120.000i 0.466023 0.269058i
\(447\) 0 0
\(448\) 0 0
\(449\) 284.257i 0.633089i −0.948578 0.316544i \(-0.897477\pi\)
0.948578 0.316544i \(-0.102523\pi\)
\(450\) 0 0
\(451\) 53.7401 93.0806i 0.119158 0.206387i
\(452\) 36.7423 + 21.2132i 0.0812884 + 0.0469319i
\(453\) 0 0
\(454\) 424.264 0.934502
\(455\) 0 0
\(456\) 0 0
\(457\) 144.000 + 249.415i 0.315098 + 0.545767i 0.979458 0.201646i \(-0.0646291\pi\)
−0.664360 + 0.747413i \(0.731296\pi\)
\(458\) −306.573 177.000i −0.669373 0.386463i
\(459\) 0 0
\(460\) −147.078 254.747i −0.319735 0.553798i
\(461\) 706.000i 1.53145i 0.643166 + 0.765727i \(0.277620\pi\)
−0.643166 + 0.765727i \(0.722380\pi\)
\(462\) 0 0
\(463\) −356.000 −0.768898 −0.384449 0.923146i \(-0.625609\pi\)
−0.384449 + 0.923146i \(0.625609\pi\)
\(464\) −112.677 + 65.0538i −0.242837 + 0.140202i
\(465\) 0 0
\(466\) 21.0000 36.3731i 0.0450644 0.0780538i
\(467\) 765.566 442.000i 1.63933 0.946467i 0.658264 0.752787i \(-0.271291\pi\)
0.981065 0.193679i \(-0.0620422\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 113.137i 0.240717i
\(471\) 0 0
\(472\) −5.65685 + 9.79796i −0.0119849 + 0.0207584i
\(473\) −48.9898 28.2843i −0.103573 0.0597976i
\(474\) 0 0
\(475\) 203.647 0.428730
\(476\) 0 0
\(477\) 0 0
\(478\) 114.000 + 197.454i 0.238494 + 0.413083i
\(479\) 439.941 + 254.000i 0.918457 + 0.530271i 0.883142 0.469105i \(-0.155423\pi\)
0.0353145 + 0.999376i \(0.488757\pi\)
\(480\) 0 0
\(481\) 203.647 + 352.727i 0.423382 + 0.733319i
\(482\) 534.000i 1.10788i
\(483\) 0 0
\(484\) −226.000 −0.466942
\(485\) −533.989 + 308.299i −1.10101 + 0.635667i
\(486\) 0 0
\(487\) 312.000 540.400i 0.640657 1.10965i −0.344629 0.938739i \(-0.611995\pi\)
0.985286 0.170912i \(-0.0546713\pi\)
\(488\) 204.382 118.000i 0.418816 0.241803i
\(489\) 0 0
\(490\) 0 0
\(491\) 840.043i 1.71088i 0.517901 + 0.855441i \(0.326714\pi\)
−0.517901 + 0.855441i \(0.673286\pi\)
\(492\) 0 0
\(493\) 65.0538 112.677i 0.131955 0.228553i
\(494\) 352.727 + 203.647i 0.714021 + 0.412240i
\(495\) 0 0
\(496\) −203.647 −0.410578
\(497\) 0 0
\(498\) 0 0
\(499\) 470.000 + 814.064i 0.941884 + 1.63139i 0.761874 + 0.647726i \(0.224280\pi\)
0.180010 + 0.983665i \(0.442387\pi\)
\(500\) −235.559 136.000i −0.471118 0.272000i
\(501\) 0 0
\(502\) 336.583 + 582.979i 0.670484 + 1.16131i
\(503\) 632.000i 1.25646i −0.778027 0.628231i \(-0.783779\pi\)
0.778027 0.628231i \(-0.216221\pi\)
\(504\) 0 0
\(505\) −504.000 −0.998020
\(506\) −127.373 + 73.5391i −0.251726 + 0.145334i
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.00787402 0.0136382i
\(509\) 190.526 110.000i 0.374314 0.216110i −0.301028 0.953615i \(-0.597330\pi\)
0.675341 + 0.737505i \(0.263996\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 72.1249 124.924i 0.140321 0.243043i
\(515\) −254.747 147.078i −0.494654 0.285589i
\(516\) 0 0
\(517\) −56.5685 −0.109417
\(518\) 0 0
\(519\) 0 0
\(520\) −72.0000 124.708i −0.138462 0.239822i
\(521\) 439.941 + 254.000i 0.844416 + 0.487524i 0.858763 0.512373i \(-0.171233\pi\)
−0.0143466 + 0.999897i \(0.504567\pi\)
\(522\) 0 0
\(523\) −407.294 705.453i −0.778764 1.34886i −0.932655 0.360771i \(-0.882514\pi\)
0.153891 0.988088i \(-0.450820\pi\)
\(524\) 48.0000i 0.0916031i
\(525\) 0 0
\(526\) 516.000 0.980989
\(527\) 176.363 101.823i 0.334655 0.193213i
\(528\) 0 0
\(529\) 411.500 712.739i 0.777883 1.34733i
\(530\) 464.190 268.000i 0.875829 0.505660i
\(531\) 0 0
\(532\) 0 0
\(533\) 483.661i 0.907432i
\(534\) 0 0
\(535\) 141.421 244.949i 0.264339 0.457849i
\(536\) 117.576 + 67.8823i 0.219357 + 0.126646i
\(537\) 0 0
\(538\) 277.186 0.515215
\(539\) 0 0
\(540\) 0 0
\(541\) 232.000 + 401.836i 0.428835 + 0.742765i 0.996770 0.0803089i \(-0.0255907\pi\)
−0.567935 + 0.823074i \(0.692257\pi\)
\(542\) 214.774 + 124.000i 0.396263 + 0.228782i
\(543\) 0 0
\(544\) 11.3137 + 19.5959i 0.0207973 + 0.0360219i
\(545\) 344.000i 0.631193i
\(546\) 0 0
\(547\) −80.0000 −0.146252 −0.0731261 0.997323i \(-0.523298\pi\)
−0.0731261 + 0.997323i \(0.523298\pi\)
\(548\) 124.924 72.1249i 0.227963 0.131615i
\(549\) 0 0
\(550\) −18.0000 + 31.1769i −0.0327273 + 0.0566853i
\(551\) −637.395 + 368.000i −1.15680 + 0.667877i
\(552\) 0 0
\(553\) 0 0
\(554\) 362.039i 0.653499i
\(555\) 0 0
\(556\) 141.421 244.949i 0.254355 0.440556i
\(557\) 789.960 + 456.084i 1.41824 + 0.818822i 0.996144 0.0877287i \(-0.0279608\pi\)
0.422097 + 0.906551i \(0.361294\pi\)
\(558\) 0 0
\(559\) 254.558 0.455382
\(560\) 0 0
\(561\) 0 0
\(562\) 19.0000 + 32.9090i 0.0338078 + 0.0585569i
\(563\) 273.664 + 158.000i 0.486082 + 0.280639i 0.722948 0.690903i \(-0.242787\pi\)
−0.236866 + 0.971542i \(0.576120\pi\)
\(564\) 0 0
\(565\) −42.4264 73.4847i −0.0750910 0.130061i
\(566\) 712.000i 1.25795i
\(567\) 0 0
\(568\) 216.000 0.380282
\(569\) −963.874 + 556.493i −1.69398 + 0.978019i −0.742733 + 0.669588i \(0.766471\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(570\) 0 0
\(571\) 220.000 381.051i 0.385289 0.667340i −0.606520 0.795068i \(-0.707435\pi\)
0.991809 + 0.127728i \(0.0407684\pi\)
\(572\) −62.3538 + 36.0000i −0.109010 + 0.0629371i
\(573\) 0 0
\(574\) 0 0
\(575\) 330.926i 0.575523i
\(576\) 0 0
\(577\) 159.099 275.568i 0.275735 0.477587i −0.694585 0.719410i \(-0.744412\pi\)
0.970320 + 0.241823i \(0.0777455\pi\)
\(578\) 334.355 + 193.040i 0.578469 + 0.333980i
\(579\) 0 0
\(580\) 260.215 0.448647
\(581\) 0 0
\(582\) 0 0
\(583\) −134.000 232.095i −0.229846 0.398104i
\(584\) 294.449 + 170.000i 0.504193 + 0.291096i
\(585\) 0 0
\(586\) −134.350 232.702i −0.229267 0.397102i
\(587\) 300.000i 0.511073i 0.966799 + 0.255537i \(0.0822521\pi\)
−0.966799 + 0.255537i \(0.917748\pi\)
\(588\) 0 0
\(589\) −1152.00 −1.95586
\(590\) 19.5959 11.3137i 0.0332134 0.0191758i
\(591\) 0 0
\(592\) 64.0000 110.851i 0.108108 0.187249i
\(593\) 897.202 518.000i 1.51299 0.873524i 0.513104 0.858326i \(-0.328495\pi\)
0.999885 0.0151981i \(-0.00483791\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 53.7401i 0.0901680i
\(597\) 0 0
\(598\) 330.926 573.181i 0.553388 0.958496i
\(599\) −849.973 490.732i −1.41899 0.819252i −0.422777 0.906234i \(-0.638945\pi\)
−0.996210 + 0.0869817i \(0.972278\pi\)
\(600\) 0 0
\(601\) −352.139 −0.585922 −0.292961 0.956124i \(-0.594641\pi\)
−0.292961 + 0.956124i \(0.594641\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 152.000 + 263.272i 0.251656 + 0.435880i
\(605\) 391.443 + 226.000i 0.647014 + 0.373554i
\(606\) 0 0
\(607\) −432.749 749.544i −0.712931 1.23483i −0.963752 0.266800i \(-0.914034\pi\)
0.250821 0.968034i \(-0.419300\pi\)
\(608\) 128.000i 0.210526i
\(609\) 0 0
\(610\) −472.000 −0.773770
\(611\) 220.454 127.279i 0.360809 0.208313i
\(612\) 0 0
\(613\) 132.000 228.631i 0.215334 0.372970i −0.738042 0.674755i \(-0.764249\pi\)
0.953376 + 0.301785i \(0.0975825\pi\)
\(614\) −325.626 + 188.000i −0.530335 + 0.306189i
\(615\) 0 0
\(616\) 0 0
\(617\) 15.5563i 0.0252129i 0.999921 + 0.0126064i \(0.00401286\pi\)
−0.999921 + 0.0126064i \(0.995987\pi\)
\(618\) 0 0
\(619\) 200.818 347.828i 0.324424 0.561918i −0.656972 0.753915i \(-0.728163\pi\)
0.981396 + 0.191997i \(0.0614963\pi\)
\(620\) 352.727 + 203.647i 0.568914 + 0.328463i
\(621\) 0 0
\(622\) 752.362 1.20958
\(623\) 0 0
\(624\) 0 0
\(625\) 159.500 + 276.262i 0.255200 + 0.442019i
\(626\) 181.865 + 105.000i 0.290520 + 0.167732i
\(627\) 0 0
\(628\) 94.7523 + 164.116i 0.150879 + 0.261331i
\(629\) 128.000i 0.203498i
\(630\) 0 0
\(631\) −676.000 −1.07132 −0.535658 0.844435i \(-0.679936\pi\)
−0.535658 + 0.844435i \(0.679936\pi\)
\(632\) −362.524 + 209.304i −0.573615 + 0.331177i
\(633\) 0 0
\(634\) 163.000 282.324i 0.257098 0.445306i
\(635\) −13.8564 + 8.00000i −0.0218211 + 0.0125984i
\(636\) 0 0
\(637\) 0 0
\(638\) 130.108i 0.203930i
\(639\) 0 0
\(640\) −22.6274 + 39.1918i −0.0353553 + 0.0612372i
\(641\) −787.511 454.670i −1.22857 0.709313i −0.261836 0.965112i \(-0.584328\pi\)
−0.966730 + 0.255799i \(0.917661\pi\)
\(642\) 0 0
\(643\) 480.833 0.747796 0.373898 0.927470i \(-0.378021\pi\)
0.373898 + 0.927470i \(0.378021\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 64.0000 + 110.851i 0.0990712 + 0.171596i
\(647\) −509.223 294.000i −0.787052 0.454405i 0.0518714 0.998654i \(-0.483481\pi\)
−0.838924 + 0.544249i \(0.816815\pi\)
\(648\) 0 0
\(649\) −5.65685 9.79796i −0.00871626 0.0150970i
\(650\) 162.000i 0.249231i
\(651\) 0 0
\(652\) 304.000 0.466258
\(653\) −393.143 + 226.981i −0.602057 + 0.347598i −0.769850 0.638225i \(-0.779669\pi\)
0.167793 + 0.985822i \(0.446336\pi\)
\(654\) 0 0
\(655\) −48.0000 + 83.1384i −0.0732824 + 0.126929i
\(656\) 131.636 76.0000i 0.200664 0.115854i
\(657\) 0 0
\(658\) 0 0
\(659\) 755.190i 1.14596i 0.819568 + 0.572982i \(0.194213\pi\)
−0.819568 + 0.572982i \(0.805787\pi\)
\(660\) 0 0
\(661\) −120.915 + 209.431i −0.182928 + 0.316840i −0.942876 0.333143i \(-0.891891\pi\)
0.759949 + 0.649983i \(0.225224\pi\)
\(662\) 328.232 + 189.505i 0.495818 + 0.286261i
\(663\) 0 0
\(664\) 226.274 0.340774
\(665\) 0 0
\(666\) 0 0
\(667\) 598.000 + 1035.77i 0.896552 + 1.55287i
\(668\) −200.918 116.000i −0.300775 0.173653i
\(669\) 0 0
\(670\) −135.765 235.151i −0.202634 0.350972i
\(671\) 236.000i 0.351714i
\(672\) 0 0
\(673\) 1176.00 1.74740 0.873700 0.486465i \(-0.161714\pi\)
0.873700 + 0.486465i \(0.161714\pi\)
\(674\) −208.207 + 120.208i −0.308912 + 0.178350i
\(675\) 0 0
\(676\) −7.00000 + 12.1244i −0.0103550 + 0.0179354i
\(677\) 192.258 111.000i 0.283985 0.163959i −0.351241 0.936285i \(-0.614240\pi\)
0.635226 + 0.772326i \(0.280907\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 45.2548i 0.0665512i
\(681\) 0 0
\(682\) 101.823 176.363i 0.149301 0.258597i
\(683\) 448.257 + 258.801i 0.656305 + 0.378918i 0.790868 0.611987i \(-0.209630\pi\)
−0.134562 + 0.990905i \(0.542963\pi\)
\(684\) 0 0
\(685\) −288.500 −0.421167
\(686\) 0 0
\(687\) 0 0
\(688\) −40.0000 69.2820i −0.0581395 0.100701i
\(689\) 1044.43 + 603.000i 1.51586 + 0.875181i
\(690\) 0 0
\(691\) −322.441 558.484i −0.466629 0.808225i 0.532644 0.846339i \(-0.321198\pi\)
−0.999273 + 0.0381139i \(0.987865\pi\)
\(692\) 444.000i 0.641618i
\(693\) 0 0
\(694\) 396.000 0.570605
\(695\) −489.898 + 282.843i −0.704889 + 0.406968i
\(696\) 0 0
\(697\) −76.0000 + 131.636i −0.109039 + 0.188861i
\(698\) 296.181 171.000i 0.424328 0.244986i
\(699\) 0 0
\(700\) 0 0
\(701\) 657.609i 0.938102i −0.883171 0.469051i \(-0.844596\pi\)
0.883171 0.469051i \(-0.155404\pi\)
\(702\) 0 0
\(703\) 362.039 627.069i 0.514991 0.891991i
\(704\) 19.5959 + 11.3137i 0.0278351 + 0.0160706i
\(705\) 0 0
\(706\) −752.362 −1.06567
\(707\) 0 0
\(708\) 0 0
\(709\) −53.0000 91.7987i −0.0747532 0.129476i 0.826226 0.563339i \(-0.190484\pi\)
−0.900979 + 0.433863i \(0.857150\pi\)
\(710\) −374.123 216.000i −0.526934 0.304225i
\(711\) 0 0
\(712\) 149.907 + 259.646i 0.210543 + 0.364671i
\(713\) 1872.00i 2.62553i
\(714\) 0 0
\(715\) 144.000 0.201399
\(716\) 102.879 59.3970i 0.143685 0.0829567i
\(717\) 0 0
\(718\) −242.000 + 419.156i −0.337047 + 0.583783i
\(719\) −1053.09 + 608.000i −1.46465 + 0.845619i −0.999221 0.0394637i \(-0.987435\pi\)
−0.465434 + 0.885083i \(0.654102\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 213.546i 0.295770i
\(723\) 0 0
\(724\) 80.6102 139.621i 0.111340 0.192847i
\(725\) 253.522 + 146.371i 0.349686 + 0.201891i
\(726\) 0 0
\(727\) 73.5391 0.101154 0.0505771 0.998720i \(-0.483894\pi\)
0.0505771 + 0.998720i \(0.483894\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −340.000 588.897i −0.465753 0.806709i
\(731\) 69.2820 + 40.0000i 0.0947771 + 0.0547196i
\(732\) 0 0
\(733\) −210.011 363.749i −0.286508 0.496247i 0.686465 0.727162i \(-0.259161\pi\)
−0.972974 + 0.230915i \(0.925828\pi\)
\(734\) 968.000i 1.31880i
\(735\) 0 0
\(736\) −208.000 −0.282609
\(737\) −117.576 + 67.8823i −0.159533 + 0.0921062i
\(738\) 0 0
\(739\) 204.000 353.338i 0.276049 0.478130i −0.694350 0.719637i \(-0.744308\pi\)
0.970399 + 0.241507i \(0.0776416\pi\)
\(740\) −221.703 + 128.000i −0.299598 + 0.172973i
\(741\) 0 0
\(742\) 0 0
\(743\) 489.318i 0.658571i −0.944230 0.329285i \(-0.893192\pi\)
0.944230 0.329285i \(-0.106808\pi\)
\(744\) 0 0
\(745\) 53.7401 93.0806i 0.0721344 0.124940i
\(746\) 467.853 + 270.115i 0.627148 + 0.362084i
\(747\) 0 0
\(748\) −22.6274 −0.0302506
\(749\) 0 0
\(750\) 0 0
\(751\) 68.0000 + 117.779i 0.0905459 + 0.156830i 0.907741 0.419531i \(-0.137805\pi\)
−0.817195 + 0.576361i \(0.804472\pi\)
\(752\) −69.2820 40.0000i −0.0921304 0.0531915i
\(753\) 0 0
\(754\) 292.742 + 507.044i 0.388252 + 0.672473i
\(755\) 608.000i 0.805298i
\(756\) 0 0
\(757\) 758.000 1.00132 0.500661 0.865644i \(-0.333091\pi\)
0.500661 + 0.865644i \(0.333091\pi\)
\(758\) 171.464 98.9949i 0.226206 0.130600i
\(759\) 0 0
\(760\) −128.000 + 221.703i −0.168421 + 0.291714i
\(761\) 50.2295 29.0000i 0.0660046 0.0381078i −0.466635 0.884450i \(-0.654534\pi\)
0.532639 + 0.846342i \(0.321200\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 605.283i 0.792256i
\(765\) 0 0
\(766\) 175.362 303.737i 0.228933 0.396523i
\(767\) 44.0908 + 25.4558i 0.0574848 + 0.0331888i
\(768\) 0 0
\(769\) 292.742 0.380679 0.190340 0.981718i \(-0.439041\pi\)
0.190340 + 0.981718i \(0.439041\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 218.000 + 377.587i 0.282383 + 0.489102i
\(773\) 261.540 + 151.000i 0.338344 + 0.195343i 0.659539 0.751670i \(-0.270751\pi\)
−0.321196 + 0.947013i \(0.604085\pi\)
\(774\) 0 0
\(775\) 229.103 + 396.817i 0.295616 + 0.512022i
\(776\) 436.000i 0.561856i
\(777\) 0 0
\(778\) 482.000 0.619537
\(779\) 744.645 429.921i 0.955898 0.551888i
\(780\) 0 0
\(781\) −108.000 + 187.061i −0.138284 + 0.239515i
\(782\) 180.133 104.000i 0.230349 0.132992i
\(783\) 0 0
\(784\) 0 0
\(785\) 379.009i 0.482814i
\(786\) 0 0
\(787\) 248.902 431.110i 0.316266 0.547789i −0.663440 0.748230i \(-0.730904\pi\)
0.979706 + 0.200441i \(0.0642374\pi\)
\(788\) −497.246 287.085i −0.631023 0.364322i
\(789\) 0 0
\(790\) 837.214 1.05977
\(791\) 0 0
\(792\) 0 0
\(793\) −531.000 919.719i −0.669609