Properties

Label 882.3.n.b.19.2
Level $882$
Weight $3$
Character 882.19
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.19
Dual form 882.3.n.b.325.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +(-8.12132 + 4.68885i) q^{10} +(-2.37868 - 4.11999i) q^{11} +15.2913i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.25736 + 1.88064i) q^{17} +(-3.62132 - 2.09077i) q^{19} +13.2621i q^{20} -6.72792 q^{22} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} +(18.7279 + 10.8126i) q^{26} -3.51472 q^{29} +(42.3198 - 24.4334i) q^{31} +(2.82843 + 4.89898i) q^{32} +5.31925i q^{34} +(1.47056 - 2.54709i) q^{37} +(-5.12132 + 2.95680i) q^{38} +(16.2426 + 9.37769i) q^{40} +27.9590i q^{41} -10.4853 q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(45.6213 + 26.3395i) q^{47} +26.8284 q^{50} +(26.4853 - 15.2913i) q^{52} +(27.9853 + 48.4719i) q^{53} +31.5462i q^{55} +(-2.48528 + 4.30463i) q^{58} +(33.5330 - 19.3603i) q^{59} +(78.3823 + 45.2540i) q^{61} -69.1080i q^{62} +8.00000 q^{64} +(50.6985 - 87.8124i) q^{65} +(17.3198 + 29.9988i) q^{67} +(6.51472 + 3.76127i) q^{68} -36.4264 q^{71} +(-45.5589 + 26.3034i) q^{73} +(-2.07969 - 3.60213i) q^{74} +8.36308i q^{76} +(16.8934 - 29.2602i) q^{79} +(22.9706 - 13.2621i) q^{80} +(34.2426 + 19.7700i) q^{82} +127.577i q^{83} +24.9411 q^{85} +(-7.41421 + 12.8418i) q^{86} +(6.72792 + 11.6531i) q^{88} +(-43.5883 - 25.1657i) q^{89} +55.4558 q^{92} +(64.5183 - 37.2497i) q^{94} +(13.8640 + 24.0131i) q^{95} +101.792i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 6 q^{5} + O(q^{10}) \) \( 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −5.74264 3.31552i −1.14853 0.663103i −0.200000 0.979796i \(-0.564094\pi\)
−0.948528 + 0.316693i \(0.897428\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) −8.12132 + 4.68885i −0.812132 + 0.468885i
\(11\) −2.37868 4.11999i −0.216244 0.374545i 0.737413 0.675442i \(-0.236047\pi\)
−0.953657 + 0.300897i \(0.902714\pi\)
\(12\) 0 0
\(13\) 15.2913i 1.17625i 0.808769 + 0.588126i \(0.200134\pi\)
−0.808769 + 0.588126i \(0.799866\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −3.25736 + 1.88064i −0.191609 + 0.110626i −0.592736 0.805397i \(-0.701952\pi\)
0.401126 + 0.916023i \(0.368619\pi\)
\(18\) 0 0
\(19\) −3.62132 2.09077i −0.190596 0.110041i 0.401666 0.915786i \(-0.368431\pi\)
−0.592261 + 0.805746i \(0.701765\pi\)
\(20\) 13.2621i 0.663103i
\(21\) 0 0
\(22\) −6.72792 −0.305815
\(23\) −13.8640 + 24.0131i −0.602781 + 1.04405i 0.389617 + 0.920977i \(0.372607\pi\)
−0.992398 + 0.123070i \(0.960726\pi\)
\(24\) 0 0
\(25\) 9.48528 + 16.4290i 0.379411 + 0.657160i
\(26\) 18.7279 + 10.8126i 0.720305 + 0.415868i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.51472 −0.121197 −0.0605986 0.998162i \(-0.519301\pi\)
−0.0605986 + 0.998162i \(0.519301\pi\)
\(30\) 0 0
\(31\) 42.3198 24.4334i 1.36516 0.788173i 0.374850 0.927085i \(-0.377694\pi\)
0.990305 + 0.138913i \(0.0443607\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 5.31925i 0.156448i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.47056 2.54709i 0.0397449 0.0688403i −0.845469 0.534025i \(-0.820679\pi\)
0.885214 + 0.465185i \(0.154012\pi\)
\(38\) −5.12132 + 2.95680i −0.134772 + 0.0778104i
\(39\) 0 0
\(40\) 16.2426 + 9.37769i 0.406066 + 0.234442i
\(41\) 27.9590i 0.681927i 0.940077 + 0.340963i \(0.110753\pi\)
−0.940077 + 0.340963i \(0.889247\pi\)
\(42\) 0 0
\(43\) −10.4853 −0.243844 −0.121922 0.992540i \(-0.538906\pi\)
−0.121922 + 0.992540i \(0.538906\pi\)
\(44\) −4.75736 + 8.23999i −0.108122 + 0.187272i
\(45\) 0 0
\(46\) 19.6066 + 33.9596i 0.426230 + 0.738253i
\(47\) 45.6213 + 26.3395i 0.970666 + 0.560415i 0.899439 0.437046i \(-0.143975\pi\)
0.0712271 + 0.997460i \(0.477309\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 26.8284 0.536569
\(51\) 0 0
\(52\) 26.4853 15.2913i 0.509332 0.294063i
\(53\) 27.9853 + 48.4719i 0.528024 + 0.914565i 0.999466 + 0.0326677i \(0.0104003\pi\)
−0.471442 + 0.881897i \(0.656266\pi\)
\(54\) 0 0
\(55\) 31.5462i 0.573567i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.48528 + 4.30463i −0.0428497 + 0.0742178i
\(59\) 33.5330 19.3603i 0.568356 0.328141i −0.188136 0.982143i \(-0.560245\pi\)
0.756492 + 0.654002i \(0.226911\pi\)
\(60\) 0 0
\(61\) 78.3823 + 45.2540i 1.28495 + 0.741869i 0.977750 0.209774i \(-0.0672729\pi\)
0.307205 + 0.951643i \(0.400606\pi\)
\(62\) 69.1080i 1.11464i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 50.6985 87.8124i 0.779977 1.35096i
\(66\) 0 0
\(67\) 17.3198 + 29.9988i 0.258505 + 0.447743i 0.965842 0.259134i \(-0.0834370\pi\)
−0.707337 + 0.706877i \(0.750104\pi\)
\(68\) 6.51472 + 3.76127i 0.0958047 + 0.0553129i
\(69\) 0 0
\(70\) 0 0
\(71\) −36.4264 −0.513048 −0.256524 0.966538i \(-0.582577\pi\)
−0.256524 + 0.966538i \(0.582577\pi\)
\(72\) 0 0
\(73\) −45.5589 + 26.3034i −0.624094 + 0.360321i −0.778461 0.627693i \(-0.783999\pi\)
0.154367 + 0.988014i \(0.450666\pi\)
\(74\) −2.07969 3.60213i −0.0281039 0.0486774i
\(75\) 0 0
\(76\) 8.36308i 0.110041i
\(77\) 0 0
\(78\) 0 0
\(79\) 16.8934 29.2602i 0.213840 0.370383i −0.739073 0.673626i \(-0.764736\pi\)
0.952913 + 0.303243i \(0.0980694\pi\)
\(80\) 22.9706 13.2621i 0.287132 0.165776i
\(81\) 0 0
\(82\) 34.2426 + 19.7700i 0.417593 + 0.241098i
\(83\) 127.577i 1.53708i 0.639803 + 0.768539i \(0.279016\pi\)
−0.639803 + 0.768539i \(0.720984\pi\)
\(84\) 0 0
\(85\) 24.9411 0.293425
\(86\) −7.41421 + 12.8418i −0.0862118 + 0.149323i
\(87\) 0 0
\(88\) 6.72792 + 11.6531i 0.0764537 + 0.132422i
\(89\) −43.5883 25.1657i −0.489756 0.282761i 0.234717 0.972064i \(-0.424584\pi\)
−0.724473 + 0.689303i \(0.757917\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 55.4558 0.602781
\(93\) 0 0
\(94\) 64.5183 37.2497i 0.686365 0.396273i
\(95\) 13.8640 + 24.0131i 0.145936 + 0.252769i
\(96\) 0 0
\(97\) 101.792i 1.04940i 0.851287 + 0.524700i \(0.175823\pi\)
−0.851287 + 0.524700i \(0.824177\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 18.9706 32.8580i 0.189706 0.328580i
\(101\) −51.6838 + 29.8396i −0.511720 + 0.295442i −0.733541 0.679646i \(-0.762134\pi\)
0.221820 + 0.975088i \(0.428800\pi\)
\(102\) 0 0
\(103\) −104.077 60.0890i −1.01046 0.583388i −0.0991322 0.995074i \(-0.531607\pi\)
−0.911326 + 0.411686i \(0.864940\pi\)
\(104\) 43.2503i 0.415868i
\(105\) 0 0
\(106\) 79.1543 0.746739
\(107\) −56.8051 + 98.3893i −0.530889 + 0.919526i 0.468462 + 0.883484i \(0.344808\pi\)
−0.999350 + 0.0360423i \(0.988525\pi\)
\(108\) 0 0
\(109\) 72.6543 + 125.841i 0.666553 + 1.15450i 0.978862 + 0.204524i \(0.0655645\pi\)
−0.312308 + 0.949981i \(0.601102\pi\)
\(110\) 38.6360 + 22.3065i 0.351237 + 0.202787i
\(111\) 0 0
\(112\) 0 0
\(113\) −34.5442 −0.305700 −0.152850 0.988249i \(-0.548845\pi\)
−0.152850 + 0.988249i \(0.548845\pi\)
\(114\) 0 0
\(115\) 159.231 91.9323i 1.38462 0.799412i
\(116\) 3.51472 + 6.08767i 0.0302993 + 0.0524799i
\(117\) 0 0
\(118\) 54.7592i 0.464061i
\(119\) 0 0
\(120\) 0 0
\(121\) 49.1838 85.1888i 0.406477 0.704040i
\(122\) 110.849 63.9988i 0.908600 0.524581i
\(123\) 0 0
\(124\) −84.6396 48.8667i −0.682578 0.394086i
\(125\) 39.9814i 0.319851i
\(126\) 0 0
\(127\) −247.338 −1.94754 −0.973772 0.227526i \(-0.926936\pi\)
−0.973772 + 0.227526i \(0.926936\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −71.6985 124.185i −0.551527 0.955272i
\(131\) −127.864 73.8223i −0.976061 0.563529i −0.0749822 0.997185i \(-0.523890\pi\)
−0.901079 + 0.433656i \(0.857223\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 48.9878 0.365581
\(135\) 0 0
\(136\) 9.21320 5.31925i 0.0677441 0.0391121i
\(137\) −16.2868 28.2096i −0.118882 0.205909i 0.800443 0.599409i \(-0.204598\pi\)
−0.919325 + 0.393500i \(0.871264\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i 0.969089 + 0.246711i \(0.0793499\pi\)
−0.969089 + 0.246711i \(0.920650\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −25.7574 + 44.6131i −0.181390 + 0.314176i
\(143\) 63.0000 36.3731i 0.440559 0.254357i
\(144\) 0 0
\(145\) 20.1838 + 11.6531i 0.139198 + 0.0803662i
\(146\) 74.3973i 0.509571i
\(147\) 0 0
\(148\) −5.88225 −0.0397449
\(149\) 46.1985 80.0181i 0.310057 0.537034i −0.668317 0.743876i \(-0.732985\pi\)
0.978374 + 0.206842i \(0.0663185\pi\)
\(150\) 0 0
\(151\) 45.8934 + 79.4897i 0.303930 + 0.526422i 0.977022 0.213136i \(-0.0683678\pi\)
−0.673093 + 0.739558i \(0.735035\pi\)
\(152\) 10.2426 + 5.91359i 0.0673858 + 0.0389052i
\(153\) 0 0
\(154\) 0 0
\(155\) −324.037 −2.09056
\(156\) 0 0
\(157\) −7.32338 + 4.22815i −0.0466457 + 0.0269309i −0.523142 0.852246i \(-0.675240\pi\)
0.476496 + 0.879177i \(0.341907\pi\)
\(158\) −23.8909 41.3802i −0.151208 0.261900i
\(159\) 0 0
\(160\) 37.5108i 0.234442i
\(161\) 0 0
\(162\) 0 0
\(163\) −110.989 + 192.238i −0.680913 + 1.17938i 0.293789 + 0.955870i \(0.405084\pi\)
−0.974703 + 0.223506i \(0.928250\pi\)
\(164\) 48.4264 27.9590i 0.295283 0.170482i
\(165\) 0 0
\(166\) 156.250 + 90.2109i 0.941264 + 0.543439i
\(167\) 168.841i 1.01102i −0.862820 0.505511i \(-0.831304\pi\)
0.862820 0.505511i \(-0.168696\pi\)
\(168\) 0 0
\(169\) −64.8234 −0.383570
\(170\) 17.6360 30.5465i 0.103741 0.179685i
\(171\) 0 0
\(172\) 10.4853 + 18.1610i 0.0609609 + 0.105587i
\(173\) −142.323 82.1704i −0.822678 0.474974i 0.0286608 0.999589i \(-0.490876\pi\)
−0.851339 + 0.524616i \(0.824209\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 19.0294 0.108122
\(177\) 0 0
\(178\) −61.6432 + 35.5897i −0.346310 + 0.199942i
\(179\) 92.5919 + 160.374i 0.517273 + 0.895943i 0.999799 + 0.0200614i \(0.00638618\pi\)
−0.482526 + 0.875882i \(0.660280\pi\)
\(180\) 0 0
\(181\) 155.086i 0.856830i −0.903582 0.428415i \(-0.859072\pi\)
0.903582 0.428415i \(-0.140928\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 39.2132 67.9193i 0.213115 0.369126i
\(185\) −16.8898 + 9.75135i −0.0912964 + 0.0527100i
\(186\) 0 0
\(187\) 15.4964 + 8.94687i 0.0828686 + 0.0478442i
\(188\) 105.358i 0.560415i
\(189\) 0 0
\(190\) 39.2132 0.206385
\(191\) 124.048 214.857i 0.649465 1.12491i −0.333786 0.942649i \(-0.608326\pi\)
0.983251 0.182257i \(-0.0583402\pi\)
\(192\) 0 0
\(193\) −77.1690 133.661i −0.399840 0.692543i 0.593866 0.804564i \(-0.297601\pi\)
−0.993706 + 0.112021i \(0.964268\pi\)
\(194\) 124.669 + 71.9777i 0.642624 + 0.371019i
\(195\) 0 0
\(196\) 0 0
\(197\) 181.103 0.919303 0.459651 0.888099i \(-0.347974\pi\)
0.459651 + 0.888099i \(0.347974\pi\)
\(198\) 0 0
\(199\) −301.989 + 174.353i −1.51753 + 0.876147i −0.517744 + 0.855535i \(0.673228\pi\)
−0.999788 + 0.0206121i \(0.993439\pi\)
\(200\) −26.8284 46.4682i −0.134142 0.232341i
\(201\) 0 0
\(202\) 84.3992i 0.417818i
\(203\) 0 0
\(204\) 0 0
\(205\) 92.6985 160.558i 0.452188 0.783212i
\(206\) −147.187 + 84.9786i −0.714502 + 0.412518i
\(207\) 0 0
\(208\) −52.9706 30.5826i −0.254666 0.147032i
\(209\) 19.8931i 0.0951823i
\(210\) 0 0
\(211\) 364.073 1.72547 0.862733 0.505660i \(-0.168751\pi\)
0.862733 + 0.505660i \(0.168751\pi\)
\(212\) 55.9706 96.9439i 0.264012 0.457282i
\(213\) 0 0
\(214\) 80.3345 + 139.143i 0.375395 + 0.650203i
\(215\) 60.2132 + 34.7641i 0.280061 + 0.161694i
\(216\) 0 0
\(217\) 0 0
\(218\) 205.497 0.942649
\(219\) 0 0
\(220\) 54.6396 31.5462i 0.248362 0.143392i
\(221\) −28.7574 49.8092i −0.130124 0.225381i
\(222\) 0 0
\(223\) 123.231i 0.552603i 0.961071 + 0.276302i \(0.0891089\pi\)
−0.961071 + 0.276302i \(0.910891\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −24.4264 + 42.3078i −0.108081 + 0.187203i
\(227\) −66.1432 + 38.1878i −0.291380 + 0.168228i −0.638564 0.769569i \(-0.720471\pi\)
0.347184 + 0.937797i \(0.387138\pi\)
\(228\) 0 0
\(229\) −309.419 178.643i −1.35117 0.780101i −0.362760 0.931883i \(-0.618166\pi\)
−0.988414 + 0.151782i \(0.951499\pi\)
\(230\) 260.024i 1.13054i
\(231\) 0 0
\(232\) 9.94113 0.0428497
\(233\) −136.537 + 236.488i −0.585994 + 1.01497i 0.408757 + 0.912643i \(0.365962\pi\)
−0.994751 + 0.102328i \(0.967371\pi\)
\(234\) 0 0
\(235\) −174.658 302.516i −0.743225 1.28730i
\(236\) −67.0660 38.7206i −0.284178 0.164070i
\(237\) 0 0
\(238\) 0 0
\(239\) 265.103 1.10922 0.554608 0.832112i \(-0.312868\pi\)
0.554608 + 0.832112i \(0.312868\pi\)
\(240\) 0 0
\(241\) 75.8970 43.8191i 0.314925 0.181822i −0.334203 0.942501i \(-0.608467\pi\)
0.649128 + 0.760679i \(0.275134\pi\)
\(242\) −69.5563 120.475i −0.287423 0.497831i
\(243\) 0 0
\(244\) 181.016i 0.741869i
\(245\) 0 0
\(246\) 0 0
\(247\) 31.9706 55.3746i 0.129435 0.224189i
\(248\) −119.698 + 69.1080i −0.482655 + 0.278661i
\(249\) 0 0
\(250\) 48.9670 + 28.2711i 0.195868 + 0.113084i
\(251\) 495.655i 1.97472i 0.158491 + 0.987360i \(0.449337\pi\)
−0.158491 + 0.987360i \(0.550663\pi\)
\(252\) 0 0
\(253\) 131.912 0.521390
\(254\) −174.894 + 302.926i −0.688561 + 1.19262i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 346.875 + 200.268i 1.34971 + 0.779254i 0.988208 0.153119i \(-0.0489317\pi\)
0.361499 + 0.932372i \(0.382265\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −202.794 −0.779977
\(261\) 0 0
\(262\) −180.827 + 104.400i −0.690179 + 0.398475i
\(263\) −16.1726 28.0118i −0.0614928 0.106509i 0.833640 0.552308i \(-0.186253\pi\)
−0.895133 + 0.445799i \(0.852919\pi\)
\(264\) 0 0
\(265\) 371.142i 1.40054i
\(266\) 0 0
\(267\) 0 0
\(268\) 34.6396 59.9976i 0.129252 0.223872i
\(269\) −265.838 + 153.482i −0.988246 + 0.570564i −0.904749 0.425944i \(-0.859942\pi\)
−0.0834963 + 0.996508i \(0.526609\pi\)
\(270\) 0 0
\(271\) 65.8051 + 37.9926i 0.242823 + 0.140194i 0.616474 0.787376i \(-0.288561\pi\)
−0.373650 + 0.927570i \(0.621894\pi\)
\(272\) 15.0451i 0.0553129i
\(273\) 0 0
\(274\) −46.0660 −0.168124
\(275\) 45.1249 78.1586i 0.164091 0.284213i
\(276\) 0 0
\(277\) −139.206 241.111i −0.502547 0.870438i −0.999996 0.00294398i \(-0.999063\pi\)
0.497448 0.867494i \(-0.334270\pi\)
\(278\) 84.0000 + 48.4974i 0.302158 + 0.174451i
\(279\) 0 0
\(280\) 0 0
\(281\) −394.690 −1.40459 −0.702296 0.711885i \(-0.747842\pi\)
−0.702296 + 0.711885i \(0.747842\pi\)
\(282\) 0 0
\(283\) −126.783 + 73.1981i −0.447996 + 0.258650i −0.706983 0.707230i \(-0.749944\pi\)
0.258988 + 0.965881i \(0.416611\pi\)
\(284\) 36.4264 + 63.0924i 0.128262 + 0.222156i
\(285\) 0 0
\(286\) 102.879i 0.359715i
\(287\) 0 0
\(288\) 0 0
\(289\) −137.426 + 238.030i −0.475524 + 0.823632i
\(290\) 28.5442 16.4800i 0.0984281 0.0568275i
\(291\) 0 0
\(292\) 91.1177 + 52.6069i 0.312047 + 0.180160i
\(293\) 299.678i 1.02279i −0.859345 0.511396i \(-0.829128\pi\)
0.859345 0.511396i \(-0.170872\pi\)
\(294\) 0 0
\(295\) −256.757 −0.870364
\(296\) −4.15938 + 7.20426i −0.0140520 + 0.0243387i
\(297\) 0 0
\(298\) −65.3345 113.163i −0.219243 0.379741i
\(299\) −367.191 211.998i −1.22806 0.709023i
\(300\) 0 0
\(301\) 0 0
\(302\) 129.806 0.429822
\(303\) 0 0
\(304\) 14.4853 8.36308i 0.0476490 0.0275101i
\(305\) −300.081 519.755i −0.983871 1.70412i
\(306\) 0 0
\(307\) 20.9886i 0.0683666i −0.999416 0.0341833i \(-0.989117\pi\)
0.999416 0.0341833i \(-0.0108830\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −229.128 + 396.862i −0.739124 + 1.28020i
\(311\) 157.651 91.0197i 0.506916 0.292668i −0.224649 0.974440i \(-0.572124\pi\)
0.731565 + 0.681772i \(0.238790\pi\)
\(312\) 0 0
\(313\) 84.8087 + 48.9643i 0.270954 + 0.156435i 0.629321 0.777145i \(-0.283333\pi\)
−0.358367 + 0.933581i \(0.616666\pi\)
\(314\) 11.9590i 0.0380861i
\(315\) 0 0
\(316\) −67.5736 −0.213840
\(317\) −240.985 + 417.399i −0.760206 + 1.31672i 0.182538 + 0.983199i \(0.441569\pi\)
−0.942744 + 0.333517i \(0.891765\pi\)
\(318\) 0 0
\(319\) 8.36039 + 14.4806i 0.0262081 + 0.0453938i
\(320\) −45.9411 26.5241i −0.143566 0.0828879i
\(321\) 0 0
\(322\) 0 0
\(323\) 15.7279 0.0486933
\(324\) 0 0
\(325\) −251.220 + 145.042i −0.772986 + 0.446283i
\(326\) 156.962 + 271.866i 0.481478 + 0.833945i
\(327\) 0 0
\(328\) 79.0800i 0.241098i
\(329\) 0 0
\(330\) 0 0
\(331\) −112.504 + 194.862i −0.339890 + 0.588707i −0.984412 0.175879i \(-0.943723\pi\)
0.644522 + 0.764586i \(0.277056\pi\)
\(332\) 220.971 127.577i 0.665574 0.384269i
\(333\) 0 0
\(334\) −206.787 119.388i −0.619122 0.357450i
\(335\) 229.696i 0.685661i
\(336\) 0 0
\(337\) −264.368 −0.784473 −0.392237 0.919864i \(-0.628299\pi\)
−0.392237 + 0.919864i \(0.628299\pi\)
\(338\) −45.8370 + 79.3921i −0.135613 + 0.234888i
\(339\) 0 0
\(340\) −24.9411 43.1993i −0.0733563 0.127057i
\(341\) −201.331 116.238i −0.590412 0.340875i
\(342\) 0 0
\(343\) 0 0
\(344\) 29.6569 0.0862118
\(345\) 0 0
\(346\) −201.276 + 116.207i −0.581722 + 0.335857i
\(347\) −95.6285 165.633i −0.275586 0.477330i 0.694697 0.719303i \(-0.255539\pi\)
−0.970283 + 0.241973i \(0.922205\pi\)
\(348\) 0 0
\(349\) 135.448i 0.388104i 0.980991 + 0.194052i \(0.0621630\pi\)
−0.980991 + 0.194052i \(0.937837\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13.4558 23.3062i 0.0382268 0.0662108i
\(353\) −301.802 + 174.245i −0.854962 + 0.493612i −0.862322 0.506360i \(-0.830991\pi\)
0.00736010 + 0.999973i \(0.497657\pi\)
\(354\) 0 0
\(355\) 209.184 + 120.772i 0.589250 + 0.340204i
\(356\) 100.663i 0.282761i
\(357\) 0 0
\(358\) 261.889 0.731535
\(359\) 152.415 263.991i 0.424555 0.735351i −0.571824 0.820377i \(-0.693764\pi\)
0.996379 + 0.0850256i \(0.0270972\pi\)
\(360\) 0 0
\(361\) −171.757 297.492i −0.475782 0.824079i
\(362\) −189.941 109.663i −0.524699 0.302935i
\(363\) 0 0
\(364\) 0 0
\(365\) 348.838 0.955720
\(366\) 0 0
\(367\) 82.2761 47.5021i 0.224186 0.129434i −0.383701 0.923457i \(-0.625351\pi\)
0.607887 + 0.794024i \(0.292017\pi\)
\(368\) −55.4558 96.0523i −0.150695 0.261012i
\(369\) 0 0
\(370\) 27.5810i 0.0745432i
\(371\) 0 0
\(372\) 0 0
\(373\) −126.779 + 219.588i −0.339891 + 0.588708i −0.984412 0.175879i \(-0.943723\pi\)
0.644521 + 0.764586i \(0.277057\pi\)
\(374\) 21.9153 12.6528i 0.0585970 0.0338310i
\(375\) 0 0
\(376\) −129.037 74.4993i −0.343182 0.198136i
\(377\) 53.7446i 0.142559i
\(378\) 0 0
\(379\) 508.250 1.34103 0.670514 0.741897i \(-0.266074\pi\)
0.670514 + 0.741897i \(0.266074\pi\)
\(380\) 27.7279 48.0262i 0.0729682 0.126385i
\(381\) 0 0
\(382\) −175.430 303.854i −0.459241 0.795428i
\(383\) 413.753 + 238.881i 1.08030 + 0.623709i 0.930976 0.365080i \(-0.118958\pi\)
0.149320 + 0.988789i \(0.452292\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −218.267 −0.565459
\(387\) 0 0
\(388\) 176.309 101.792i 0.454404 0.262350i
\(389\) 85.1102 + 147.415i 0.218792 + 0.378959i 0.954439 0.298406i \(-0.0964550\pi\)
−0.735647 + 0.677365i \(0.763122\pi\)
\(390\) 0 0
\(391\) 104.292i 0.266732i
\(392\) 0 0
\(393\) 0 0
\(394\) 128.059 221.804i 0.325023 0.562956i
\(395\) −194.025 + 112.021i −0.491204 + 0.283597i
\(396\) 0 0
\(397\) −211.786 122.275i −0.533467 0.307997i 0.208960 0.977924i \(-0.432992\pi\)
−0.742427 + 0.669927i \(0.766325\pi\)
\(398\) 493.146i 1.23906i
\(399\) 0 0
\(400\) −75.8823 −0.189706
\(401\) −208.786 + 361.629i −0.520664 + 0.901817i 0.479047 + 0.877789i \(0.340982\pi\)
−0.999711 + 0.0240277i \(0.992351\pi\)
\(402\) 0 0
\(403\) 373.617 + 647.124i 0.927090 + 1.60577i
\(404\) 103.368 + 59.6793i 0.255860 + 0.147721i
\(405\) 0 0
\(406\) 0 0
\(407\) −13.9920 −0.0343784
\(408\) 0 0
\(409\) −266.919 + 154.106i −0.652614 + 0.376787i −0.789457 0.613806i \(-0.789638\pi\)
0.136843 + 0.990593i \(0.456304\pi\)
\(410\) −131.095 227.064i −0.319745 0.553815i
\(411\) 0 0
\(412\) 240.356i 0.583388i
\(413\) 0 0
\(414\) 0 0
\(415\) 422.985 732.631i 1.01924 1.76538i
\(416\) −74.9117 + 43.2503i −0.180076 + 0.103967i
\(417\) 0 0
\(418\) 24.3640 + 14.0665i 0.0582870 + 0.0336520i
\(419\) 103.142i 0.246163i 0.992397 + 0.123081i \(0.0392776\pi\)
−0.992397 + 0.123081i \(0.960722\pi\)
\(420\) 0 0
\(421\) −165.220 −0.392447 −0.196224 0.980559i \(-0.562868\pi\)
−0.196224 + 0.980559i \(0.562868\pi\)
\(422\) 257.439 445.897i 0.610044 1.05663i
\(423\) 0 0
\(424\) −79.1543 137.099i −0.186685 0.323347i
\(425\) −61.7939 35.6767i −0.145398 0.0839453i
\(426\) 0 0
\(427\) 0 0
\(428\) 227.220 0.530889
\(429\) 0 0
\(430\) 85.1543 49.1639i 0.198033 0.114335i
\(431\) 297.268 + 514.883i 0.689717 + 1.19463i 0.971929 + 0.235273i \(0.0755984\pi\)
−0.282212 + 0.959352i \(0.591068\pi\)
\(432\) 0 0
\(433\) 40.6267i 0.0938261i −0.998899 0.0469131i \(-0.985062\pi\)
0.998899 0.0469131i \(-0.0149384\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 145.309 251.682i 0.333277 0.577252i
\(437\) 100.412 57.9727i 0.229775 0.132661i
\(438\) 0 0
\(439\) −126.959 73.3001i −0.289201 0.166971i 0.348380 0.937353i \(-0.386732\pi\)
−0.637582 + 0.770383i \(0.720065\pi\)
\(440\) 89.2261i 0.202787i
\(441\) 0 0
\(442\) −81.3381 −0.184023
\(443\) 53.6802 92.9768i 0.121174 0.209880i −0.799057 0.601256i \(-0.794667\pi\)
0.920231 + 0.391376i \(0.128001\pi\)
\(444\) 0 0
\(445\) 166.875 + 289.035i 0.374999 + 0.649518i
\(446\) 150.926 + 87.1372i 0.338399 + 0.195375i
\(447\) 0 0
\(448\) 0 0
\(449\) −135.161 −0.301028 −0.150514 0.988608i \(-0.548093\pi\)
−0.150514 + 0.988608i \(0.548093\pi\)
\(450\) 0 0
\(451\) 115.191 66.5055i 0.255412 0.147462i
\(452\) 34.5442 + 59.8322i 0.0764251 + 0.132372i
\(453\) 0 0
\(454\) 108.011i 0.237910i
\(455\) 0 0
\(456\) 0 0
\(457\) −79.8675 + 138.335i −0.174765 + 0.302702i −0.940080 0.340954i \(-0.889250\pi\)
0.765315 + 0.643656i \(0.222583\pi\)
\(458\) −437.584 + 252.639i −0.955424 + 0.551614i
\(459\) 0 0
\(460\) −318.463 183.865i −0.692311 0.399706i
\(461\) 310.250i 0.672993i −0.941685 0.336497i \(-0.890758\pi\)
0.941685 0.336497i \(-0.109242\pi\)
\(462\) 0 0
\(463\) −326.014 −0.704135 −0.352067 0.935975i \(-0.614521\pi\)
−0.352067 + 0.935975i \(0.614521\pi\)
\(464\) 7.02944 12.1753i 0.0151496 0.0262400i
\(465\) 0 0
\(466\) 193.092 + 334.445i 0.414360 + 0.717693i
\(467\) 515.769 + 297.779i 1.10443 + 0.637643i 0.937381 0.348306i \(-0.113243\pi\)
0.167048 + 0.985949i \(0.446576\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −494.007 −1.05108
\(471\) 0 0
\(472\) −94.8457 + 54.7592i −0.200944 + 0.116015i
\(473\) 24.9411 + 43.1993i 0.0527297 + 0.0913304i
\(474\) 0 0
\(475\) 79.3262i 0.167002i
\(476\) 0 0
\(477\) 0 0
\(478\) 187.456 324.683i 0.392167 0.679253i
\(479\) 438.798 253.340i 0.916071 0.528894i 0.0336914 0.999432i \(-0.489274\pi\)
0.882379 + 0.470539i \(0.155940\pi\)
\(480\) 0 0
\(481\) 38.9483 + 22.4868i 0.0809735 + 0.0467501i
\(482\) 123.939i 0.257135i
\(483\) 0 0
\(484\) −196.735 −0.406477
\(485\) 337.492 584.554i 0.695861 1.20527i
\(486\) 0 0
\(487\) −105.651 182.992i −0.216942 0.375755i 0.736930 0.675970i \(-0.236275\pi\)
−0.953872 + 0.300215i \(0.902942\pi\)
\(488\) −221.698 127.998i −0.454300 0.262290i
\(489\) 0 0
\(490\) 0 0
\(491\) 784.161 1.59707 0.798534 0.601949i \(-0.205609\pi\)
0.798534 + 0.601949i \(0.205609\pi\)
\(492\) 0 0
\(493\) 11.4487 6.60991i 0.0232225 0.0134075i
\(494\) −45.2132 78.3116i −0.0915247 0.158525i
\(495\) 0 0
\(496\) 195.467i 0.394086i
\(497\) 0 0
\(498\) 0 0
\(499\) 85.7462 148.517i 0.171836 0.297629i −0.767226 0.641377i \(-0.778363\pi\)
0.939062 + 0.343748i \(0.111697\pi\)
\(500\) 69.2498 39.9814i 0.138500 0.0799628i
\(501\) 0 0
\(502\) 607.051 + 350.481i 1.20926 + 0.698169i
\(503\) 20.0883i 0.0399370i 0.999801 + 0.0199685i \(0.00635659\pi\)
−0.999801 + 0.0199685i \(0.993643\pi\)
\(504\) 0 0
\(505\) 395.735 0.783634
\(506\) 93.2756 161.558i 0.184339 0.319285i
\(507\) 0 0
\(508\) 247.338 + 428.402i 0.486886 + 0.843311i
\(509\) −412.890 238.382i −0.811178 0.468334i 0.0361865 0.999345i \(-0.488479\pi\)
−0.847365 + 0.531011i \(0.821812\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) 490.555 283.222i 0.954387 0.551016i
\(515\) 398.452 + 690.139i 0.773693 + 1.34008i
\(516\) 0 0
\(517\) 250.613i 0.484744i
\(518\) 0 0
\(519\) 0 0
\(520\) −143.397 + 248.371i −0.275763 + 0.477636i
\(521\) 739.823 427.137i 1.42001 0.819841i 0.423707 0.905799i \(-0.360729\pi\)
0.996299 + 0.0859587i \(0.0273953\pi\)
\(522\) 0 0
\(523\) 513.554 + 296.501i 0.981940 + 0.566923i 0.902855 0.429945i \(-0.141467\pi\)
0.0790845 + 0.996868i \(0.474800\pi\)
\(524\) 295.289i 0.563529i
\(525\) 0 0
\(526\) −45.7431 −0.0869640
\(527\) −91.9005 + 159.176i −0.174384 + 0.302043i
\(528\) 0 0
\(529\) −119.919 207.706i −0.226690 0.392638i
\(530\) −454.555 262.437i −0.857651 0.495165i
\(531\) 0 0
\(532\) 0 0
\(533\) −427.529 −0.802118
\(534\) 0 0
\(535\) 652.422 376.676i 1.21948 0.704068i
\(536\) −48.9878 84.8494i −0.0913952 0.158301i
\(537\) 0 0
\(538\) 434.112i 0.806899i
\(539\) 0 0
\(540\) 0 0
\(541\) −427.595 + 740.617i −0.790380 + 1.36898i 0.135352 + 0.990798i \(0.456783\pi\)
−0.925732 + 0.378180i \(0.876550\pi\)
\(542\) 93.0624 53.7296i 0.171702 0.0991322i
\(543\) 0 0
\(544\) −18.4264 10.6385i −0.0338721 0.0195560i
\(545\) 963.546i 1.76797i
\(546\) 0 0
\(547\) 415.897 0.760323 0.380161 0.924920i \(-0.375868\pi\)
0.380161 + 0.924920i \(0.375868\pi\)
\(548\) −32.5736 + 56.4191i −0.0594409 + 0.102955i
\(549\) 0 0
\(550\) −63.8162 110.533i −0.116030 0.200969i
\(551\) 12.7279 + 7.34847i 0.0230997 + 0.0133366i
\(552\) 0 0
\(553\) 0 0
\(554\) −393.733 −0.710709
\(555\) 0 0
\(556\) 118.794 68.5857i 0.213658 0.123356i
\(557\) −292.110 505.950i −0.524435 0.908348i −0.999595 0.0284485i \(-0.990943\pi\)
0.475160 0.879899i \(-0.342390\pi\)
\(558\) 0 0
\(559\) 160.333i 0.286822i
\(560\) 0 0
\(561\) 0 0
\(562\) −279.088 + 483.395i −0.496598 + 0.860134i
\(563\) 789.076 455.573i 1.40156 0.809189i 0.407004 0.913426i \(-0.366573\pi\)
0.994552 + 0.104237i \(0.0332402\pi\)
\(564\) 0 0
\(565\) 198.375 + 114.532i 0.351106 + 0.202711i
\(566\) 207.035i 0.365787i
\(567\) 0 0
\(568\) 103.029 0.181390
\(569\) 350.000 606.217i 0.615113 1.06541i −0.375251 0.926923i \(-0.622444\pi\)
0.990365 0.138485i \(-0.0442231\pi\)
\(570\) 0 0
\(571\) 281.231 + 487.107i 0.492525 + 0.853077i 0.999963 0.00861055i \(-0.00274086\pi\)
−0.507438 + 0.861688i \(0.669408\pi\)
\(572\) −126.000 72.7461i −0.220280 0.127179i
\(573\) 0 0
\(574\) 0 0
\(575\) −526.014 −0.914807
\(576\) 0 0
\(577\) 573.014 330.830i 0.993092 0.573362i 0.0868946 0.996218i \(-0.472306\pi\)
0.906197 + 0.422856i \(0.138972\pi\)
\(578\) 194.350 + 336.625i 0.336246 + 0.582395i
\(579\) 0 0
\(580\) 46.6124i 0.0803662i
\(581\) 0 0
\(582\) 0 0
\(583\) 133.136 230.598i 0.228364 0.395538i
\(584\) 128.860 74.3973i 0.220651 0.127393i
\(585\) 0 0
\(586\) −367.029 211.905i −0.626330 0.361612i
\(587\) 823.029i 1.40209i 0.713116 + 0.701046i \(0.247283\pi\)
−0.713116 + 0.701046i \(0.752717\pi\)
\(588\) 0 0
\(589\) −204.338 −0.346924
\(590\) −181.555 + 314.462i −0.307720 + 0.532987i
\(591\) 0 0
\(592\) 5.88225 + 10.1884i 0.00993623 + 0.0172101i
\(593\) −538.890 311.128i −0.908752 0.524668i −0.0287225 0.999587i \(-0.509144\pi\)
−0.880029 + 0.474919i \(0.842477\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −184.794 −0.310057
\(597\) 0 0
\(598\) −519.286 + 299.810i −0.868372 + 0.501355i
\(599\) −256.422 444.137i −0.428084 0.741463i 0.568619 0.822601i \(-0.307478\pi\)
−0.996703 + 0.0811377i \(0.974145\pi\)
\(600\) 0 0
\(601\) 680.160i 1.13171i 0.824504 + 0.565857i \(0.191454\pi\)
−0.824504 + 0.565857i \(0.808546\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 91.7868 158.979i 0.151965 0.263211i
\(605\) −564.889 + 326.139i −0.933701 + 0.539073i
\(606\) 0 0
\(607\) −33.5482 19.3690i −0.0552688 0.0319095i 0.472111 0.881539i \(-0.343492\pi\)
−0.527380 + 0.849630i \(0.676825\pi\)
\(608\) 23.6544i 0.0389052i
\(609\) 0 0
\(610\) −848.756 −1.39140
\(611\) −402.765 + 697.609i −0.659189 + 1.14175i
\(612\) 0 0
\(613\) −200.552 347.366i −0.327164 0.566665i 0.654784 0.755816i \(-0.272760\pi\)
−0.981948 + 0.189151i \(0.939426\pi\)
\(614\) −25.7056 14.8412i −0.0418658 0.0241713i
\(615\) 0 0
\(616\) 0 0
\(617\) 959.044 1.55437 0.777183 0.629275i \(-0.216648\pi\)
0.777183 + 0.629275i \(0.216648\pi\)
\(618\) 0 0
\(619\) 869.951 502.267i 1.40541 0.811416i 0.410473 0.911873i \(-0.365364\pi\)
0.994941 + 0.100457i \(0.0320303\pi\)
\(620\) 324.037 + 561.248i 0.522640 + 0.905238i
\(621\) 0 0
\(622\) 257.443i 0.413895i
\(623\) 0 0
\(624\) 0 0
\(625\) 369.691 640.323i 0.591505 1.02452i
\(626\) 119.938 69.2460i 0.191594 0.110617i
\(627\) 0 0
\(628\) 14.6468 + 8.45631i 0.0233229 + 0.0134655i
\(629\) 11.0624i 0.0175873i
\(630\) 0 0
\(631\) −386.514 −0.612542 −0.306271 0.951944i \(-0.599081\pi\)
−0.306271 + 0.951944i \(0.599081\pi\)
\(632\) −47.7817 + 82.7604i −0.0756040 + 0.130950i
\(633\) 0 0
\(634\) 340.805 + 590.291i 0.537547 + 0.931058i
\(635\) 1420.37 + 820.053i 2.23681 + 1.29142i
\(636\) 0 0
\(637\) 0 0
\(638\) 23.6468 0.0370639
\(639\) 0 0
\(640\) −64.9706 + 37.5108i −0.101517 + 0.0586106i
\(641\) −496.074 859.225i −0.773906 1.34044i −0.935407 0.353572i \(-0.884967\pi\)
0.161502 0.986872i \(-0.448366\pi\)
\(642\) 0 0
\(643\) 944.986i 1.46965i 0.678256 + 0.734826i \(0.262736\pi\)
−0.678256 + 0.734826i \(0.737264\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.1213 19.2627i 0.0172157 0.0298184i
\(647\) 2.50357 1.44544i 0.00386951 0.00223406i −0.498064 0.867140i \(-0.665956\pi\)
0.501934 + 0.864906i \(0.332622\pi\)
\(648\) 0 0
\(649\) −159.529 92.1039i −0.245807 0.141917i
\(650\) 410.241i 0.631140i
\(651\) 0 0
\(652\) 443.955 0.680913
\(653\) −161.529 + 279.777i −0.247365 + 0.428449i −0.962794 0.270237i \(-0.912898\pi\)
0.715429 + 0.698686i \(0.246231\pi\)
\(654\) 0 0
\(655\) 489.518 + 847.870i 0.747356 + 1.29446i
\(656\) −96.8528 55.9180i −0.147641 0.0852409i
\(657\) 0 0
\(658\) 0 0
\(659\) −295.955 −0.449098 −0.224549 0.974463i \(-0.572091\pi\)
−0.224549 + 0.974463i \(0.572091\pi\)
\(660\) 0 0
\(661\) −17.9710 + 10.3756i −0.0271876 + 0.0156968i −0.513532 0.858070i \(-0.671663\pi\)
0.486345 + 0.873767i \(0.338330\pi\)
\(662\) 159.104 + 275.576i 0.240338 + 0.416278i
\(663\) 0 0
\(664\) 360.843i 0.543439i
\(665\) 0 0
\(666\) 0 0
\(667\) 48.7279 84.3992i 0.0730554 0.126536i
\(668\) −292.441 + 168.841i −0.437785 + 0.252756i
\(669\) 0 0
\(670\) −281.319 162.420i −0.419880 0.242418i
\(671\) 430.579i 0.641698i
\(672\) 0 0
\(673\) 627.044 0.931714 0.465857 0.884860i \(-0.345746\pi\)
0.465857 + 0.884860i \(0.345746\pi\)
\(674\) −186.936 + 323.783i −0.277353 + 0.480390i
\(675\) 0 0
\(676\) 64.8234 + 112.277i 0.0958926 + 0.166091i
\(677\) −94.6097 54.6230i −0.139749 0.0806838i 0.428496 0.903544i \(-0.359044\pi\)
−0.568244 + 0.822860i \(0.692377\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −70.5442 −0.103741
\(681\) 0 0
\(682\) −284.724 + 164.386i −0.417484 + 0.241035i
\(683\) 396.783 + 687.248i 0.580941 + 1.00622i 0.995368 + 0.0961370i \(0.0306487\pi\)
−0.414427 + 0.910083i \(0.636018\pi\)
\(684\) 0 0
\(685\) 215.996i 0.315323i
\(686\) 0 0
\(687\) 0 0
\(688\) 20.9706 36.3221i 0.0304805 0.0527937i
\(689\) −741.198 + 427.931i −1.07576 + 0.621090i
\(690\) 0 0
\(691\) −159.253 91.9447i −0.230467 0.133060i 0.380320 0.924855i \(-0.375814\pi\)
−0.610788 + 0.791794i \(0.709147\pi\)
\(692\) 328.682i 0.474974i
\(693\) 0 0
\(694\) −270.478 −0.389738
\(695\) 227.397 393.863i 0.327190 0.566710i
\(696\) 0 0
\(697\) −52.5807 91.0725i −0.0754386 0.130664i
\(698\) 165.889 + 95.7763i 0.237664 + 0.137215i
\(699\) 0 0
\(700\) 0 0
\(701\) 1043.82 1.48905 0.744525 0.667595i \(-0.232676\pi\)
0.744525 + 0.667595i \(0.232676\pi\)
\(702\) 0 0
\(703\) −10.6508 + 6.14922i −0.0151504 + 0.00874711i
\(704\) −19.0294 32.9600i −0.0270305 0.0468181i
\(705\) 0 0
\(706\) 492.840i 0.698073i
\(707\) 0 0
\(708\) 0 0
\(709\) 490.279 849.188i 0.691507 1.19773i −0.279836 0.960048i \(-0.590280\pi\)
0.971344 0.237678i \(-0.0763864\pi\)
\(710\) 295.831 170.798i 0.416663 0.240560i
\(711\) 0 0
\(712\) 123.286 + 71.1794i 0.173155 + 0.0999711i
\(713\) 1354.97i 1.90038i
\(714\) 0 0
\(715\) −482.382 −0.674660
\(716\) 185.184 320.748i 0.258637 0.447972i
\(717\) 0 0
\(718\) −215.548 373.340i −0.300206 0.519972i
\(719\) −674.187 389.242i −0.937673 0.541366i −0.0484429 0.998826i \(-0.515426\pi\)
−0.889230 + 0.457460i \(0.848759\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −485.803 −0.672858
\(723\) 0 0
\(724\) −268.617 + 155.086i −0.371018 + 0.214208i
\(725\) −33.3381 57.7433i −0.0459836 0.0796459i
\(726\) 0 0
\(727\) 735.255i 1.01135i −0.862723 0.505677i \(-0.831243\pi\)
0.862723 0.505677i \(-0.168757\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 246.665 427.237i 0.337898 0.585256i
\(731\) 34.1543 19.7190i 0.0467227 0.0269754i
\(732\) 0 0
\(733\) 414.705 + 239.430i 0.565764 + 0.326644i 0.755456 0.655200i \(-0.227415\pi\)
−0.189692 + 0.981844i \(0.560749\pi\)
\(734\) 134.356i 0.183047i
\(735\) 0 0
\(736\) −156.853 −0.213115
\(737\) 82.3965 142.715i 0.111800 0.193643i
\(738\) 0 0
\(739\) 9.95227 + 17.2378i 0.0134672 + 0.0233259i 0.872680 0.488292i \(-0.162380\pi\)
−0.859213 + 0.511618i \(0.829046\pi\)
\(740\) 33.7797 + 19.5027i 0.0456482 + 0.0263550i
\(741\) 0 0
\(742\) 0 0
\(743\) −43.3095 −0.0582901 −0.0291450 0.999575i \(-0.509278\pi\)
−0.0291450 + 0.999575i \(0.509278\pi\)
\(744\) 0 0
\(745\) −530.603 + 306.344i −0.712218 + 0.411199i
\(746\) 179.293 + 310.544i 0.240339 + 0.416279i
\(747\) 0 0
\(748\) 35.7875i 0.0478442i
\(749\) 0 0
\(750\) 0 0
\(751\) −112.665 + 195.142i −0.150020 + 0.259842i −0.931235 0.364420i \(-0.881267\pi\)
0.781215 + 0.624263i \(0.214600\pi\)
\(752\) −182.485 + 105.358i −0.242667 + 0.140104i
\(753\) 0 0
\(754\) −65.8234 38.0031i −0.0872989 0.0504020i
\(755\) 608.641i 0.806147i
\(756\) 0 0
\(757\) 935.779 1.23617 0.618084 0.786112i \(-0.287909\pi\)
0.618084 + 0.786112i \(0.287909\pi\)
\(758\) 359.387 622.476i 0.474125 0.821209i
\(759\) 0 0
\(760\) −39.2132 67.9193i −0.0515963 0.0893674i
\(761\) 1214.79 + 701.357i 1.59630 + 0.921625i 0.992191 + 0.124724i \(0.0398046\pi\)
0.604110 + 0.796901i \(0.293529\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −496.191 −0.649465
\(765\) 0 0
\(766\) 585.136 337.828i 0.763885 0.441029i
\(767\) 296.044 + 512.763i 0.385976 + 0.668530i
\(768\) 0 0
\(769\) 1.72330i 0.00224097i 0.999999 + 0.00112048i \(0.000356661\pi\)
−0.999999 + 0.00112048i \(0.999643\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −154.338 + 267.321i −0.199920 + 0.346271i
\(773\) 194.213 112.129i 0.251245 0.145057i −0.369089 0.929394i \(-0.620330\pi\)
0.620334 + 0.784337i \(0.286997\pi\)
\(774\) 0 0
\(775\) 802.831 + 463.514i 1.03591 + 0.598083i
\(776\) 287.911i 0.371019i
\(777\) 0 0
\(778\) 240.728 0.309419
\(779\) 58.4558 101.248i 0.0750396 0.129972i
\(780\) 0 0
\(781\) 86.6468 + 150.077i 0.110943 + 0.192160i
\(782\) −127.731 73.7458i −0.163340 0.0943041i
\(783\) 0 0
\(784\) 0 0
\(785\) 56.0740 0.0714319
\(786\) 0 0
\(787\) −60.7979 + 35.1017i −0.0772528 + 0.0446019i −0.538129 0.842863i \(-0.680869\pi\)
0.460876 + 0.887465i \(0.347535\pi\)
\(788\) −181.103 313.679i −0.229826 0.398070i
\(789\) 0 0
\(790\) 316.842i 0.401066i
\(791\) 0 0