Properties

Label 882.3.n.b.325.2
Level $882$
Weight $3$
Character 882.325
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 325.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.325
Dual form 882.3.n.b.19.2

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 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 −0.948528 0.316693i \(-0.897428\pi\)
−0.200000 + 0.979796i \(0.564094\pi\)
\(6\) 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 −0.953657 0.300897i \(-0.902714\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(12\) 0 0
\(13\) 15.2913i 1.17625i −0.808769 0.588126i \(-0.799866\pi\)
0.808769 0.588126i \(-0.200134\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −3.25736 1.88064i −0.191609 0.110626i 0.401126 0.916023i \(-0.368619\pi\)
−0.592736 + 0.805397i \(0.701952\pi\)
\(18\) 0 0
\(19\) −3.62132 + 2.09077i −0.190596 + 0.110041i −0.592261 0.805746i \(-0.701765\pi\)
0.401666 + 0.915786i \(0.368431\pi\)
\(20\) 13.2621i 0.663103i
\(21\) 0 0
\(22\) −6.72792 −0.305815
\(23\) −13.8640 24.0131i −0.602781 1.04405i −0.992398 0.123070i \(-0.960726\pi\)
0.389617 0.920977i \(-0.372607\pi\)
\(24\) 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 0.990305 0.138913i \(-0.0443607\pi\)
0.374850 + 0.927085i \(0.377694\pi\)
\(32\) 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 0.885214 0.465185i \(-0.154012\pi\)
−0.845469 + 0.534025i \(0.820679\pi\)
\(38\) −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 \(-0.889247\pi\)
0.940077 0.340963i \(-0.110753\pi\)
\(42\) 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 0.0712271 0.997460i \(-0.477309\pi\)
0.899439 + 0.437046i \(0.143975\pi\)
\(48\) 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 −0.471442 0.881897i \(-0.656266\pi\)
0.999466 0.0326677i \(-0.0104003\pi\)
\(54\) 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 0.756492 0.654002i \(-0.226911\pi\)
−0.188136 + 0.982143i \(0.560245\pi\)
\(60\) 0 0
\(61\) 78.3823 45.2540i 1.28495 0.741869i 0.307205 0.951643i \(-0.400606\pi\)
0.977750 + 0.209774i \(0.0672729\pi\)
\(62\) 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 −0.707337 0.706877i \(-0.750104\pi\)
0.965842 + 0.259134i \(0.0834370\pi\)
\(68\) 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 0.154367 0.988014i \(-0.450666\pi\)
−0.778461 + 0.627693i \(0.783999\pi\)
\(74\) −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 0.952913 0.303243i \(-0.0980694\pi\)
−0.739073 + 0.673626i \(0.764736\pi\)
\(80\) 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 \(-0.720984\pi\)
0.639803 0.768539i \(-0.279016\pi\)
\(84\) 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 −0.724473 0.689303i \(-0.757917\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(90\) 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 \(-0.824177\pi\)
0.851287 0.524700i \(-0.175823\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 18.9706 + 32.8580i 0.189706 + 0.328580i
\(101\) −51.6838 29.8396i −0.511720 0.295442i 0.221820 0.975088i \(-0.428800\pi\)
−0.733541 + 0.679646i \(0.762134\pi\)
\(102\) 0 0
\(103\) −104.077 + 60.0890i −1.01046 + 0.583388i −0.911326 0.411686i \(-0.864940\pi\)
−0.0991322 + 0.995074i \(0.531607\pi\)
\(104\) 43.2503i 0.415868i
\(105\) 0 0
\(106\) 79.1543 0.746739
\(107\) −56.8051 98.3893i −0.530889 0.919526i −0.999350 0.0360423i \(-0.988525\pi\)
0.468462 0.883484i \(-0.344808\pi\)
\(108\) 0 0
\(109\) 72.6543 125.841i 0.666553 1.15450i −0.312308 0.949981i \(-0.601102\pi\)
0.978862 0.204524i \(-0.0655645\pi\)
\(110\) 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 −0.901079 0.433656i \(-0.857223\pi\)
−0.0749822 + 0.997185i \(0.523890\pi\)
\(132\) 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 −0.919325 0.393500i \(-0.871264\pi\)
0.800443 + 0.599409i \(0.204598\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i −0.969089 0.246711i \(-0.920650\pi\)
0.969089 0.246711i \(-0.0793499\pi\)
\(140\) 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 0.978374 0.206842i \(-0.0663185\pi\)
−0.668317 + 0.743876i \(0.732985\pi\)
\(150\) 0 0
\(151\) 45.8934 79.4897i 0.303930 0.526422i −0.673093 0.739558i \(-0.735035\pi\)
0.977022 + 0.213136i \(0.0683678\pi\)
\(152\) 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 0.476496 0.879177i \(-0.341907\pi\)
−0.523142 + 0.852246i \(0.675240\pi\)
\(158\) −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 −0.974703 0.223506i \(-0.928250\pi\)
0.293789 0.955870i \(-0.405084\pi\)
\(164\) 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 \(0.168696\pi\)
−0.862820 + 0.505511i \(0.831304\pi\)
\(168\) 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 −0.851339 0.524616i \(-0.824209\pi\)
0.0286608 + 0.999589i \(0.490876\pi\)
\(174\) 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 −0.482526 0.875882i \(-0.660280\pi\)
0.999799 0.0200614i \(-0.00638618\pi\)
\(180\) 0 0
\(181\) 155.086i 0.856830i 0.903582 + 0.428415i \(0.140928\pi\)
−0.903582 + 0.428415i \(0.859072\pi\)
\(182\) 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 0.983251 + 0.182257i \(0.0583402\pi\)
−0.333786 + 0.942649i \(0.608326\pi\)
\(192\) 0 0
\(193\) −77.1690 + 133.661i −0.399840 + 0.692543i −0.993706 0.112021i \(-0.964268\pi\)
0.593866 + 0.804564i \(0.297601\pi\)
\(194\) 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 −0.999788 0.0206121i \(-0.993439\pi\)
−0.517744 0.855535i \(-0.673228\pi\)
\(200\) −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 \(-0.910891\pi\)
0.961071 0.276302i \(-0.0891089\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −24.4264 42.3078i −0.108081 0.187203i
\(227\) −66.1432 38.1878i −0.291380 0.168228i 0.347184 0.937797i \(-0.387138\pi\)
−0.638564 + 0.769569i \(0.720471\pi\)
\(228\) 0 0
\(229\) −309.419 + 178.643i −1.35117 + 0.780101i −0.988414 0.151782i \(-0.951499\pi\)
−0.362760 + 0.931883i \(0.618166\pi\)
\(230\) 260.024i 1.13054i
\(231\) 0 0
\(232\) 9.94113 0.0428497
\(233\) −136.537 236.488i −0.585994 1.01497i −0.994751 0.102328i \(-0.967371\pi\)
0.408757 0.912643i \(-0.365962\pi\)
\(234\) 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 0.649128 0.760679i \(-0.275134\pi\)
−0.334203 + 0.942501i \(0.608467\pi\)
\(242\) −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 \(-0.550663\pi\)
0.158491 0.987360i \(-0.449337\pi\)
\(252\) 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 0.361499 0.932372i \(-0.382265\pi\)
0.988208 + 0.153119i \(0.0489317\pi\)
\(258\) 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 −0.895133 0.445799i \(-0.852919\pi\)
0.833640 + 0.552308i \(0.186253\pi\)
\(264\) 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 −0.0834963 0.996508i \(-0.526609\pi\)
−0.904749 + 0.425944i \(0.859942\pi\)
\(270\) 0 0
\(271\) 65.8051 37.9926i 0.242823 0.140194i −0.373650 0.927570i \(-0.621894\pi\)
0.616474 + 0.787376i \(0.288561\pi\)
\(272\) 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 0.497448 + 0.867494i \(0.334270\pi\)
−0.999996 + 0.00294398i \(0.999063\pi\)
\(278\) 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 0.258988 0.965881i \(-0.416611\pi\)
−0.706983 + 0.707230i \(0.749944\pi\)
\(284\) 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 \(0.170872\pi\)
−0.859345 + 0.511396i \(0.829128\pi\)
\(294\) 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 \(0.0108830\pi\)
−0.999416 + 0.0341833i \(0.989117\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −229.128 396.862i −0.739124 1.28020i
\(311\) 157.651 + 91.0197i 0.506916 + 0.292668i 0.731565 0.681772i \(-0.238790\pi\)
−0.224649 + 0.974440i \(0.572124\pi\)
\(312\) 0 0
\(313\) 84.8087 48.9643i 0.270954 0.156435i −0.358367 0.933581i \(-0.616666\pi\)
0.629321 + 0.777145i \(0.283333\pi\)
\(314\) 11.9590i 0.0380861i
\(315\) 0 0
\(316\) −67.5736 −0.213840
\(317\) −240.985 417.399i −0.760206 1.31672i −0.942744 0.333517i \(-0.891765\pi\)
0.182538 0.983199i \(-0.441569\pi\)
\(318\) 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 0.644522 0.764586i \(-0.277056\pi\)
−0.984412 + 0.175879i \(0.943723\pi\)
\(332\) 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 −0.970283 0.241973i \(-0.922205\pi\)
0.694697 + 0.719303i \(0.255539\pi\)
\(348\) 0 0
\(349\) 135.448i 0.388104i −0.980991 0.194052i \(-0.937837\pi\)
0.980991 0.194052i \(-0.0621630\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13.4558 + 23.3062i 0.0382268 + 0.0662108i
\(353\) −301.802 174.245i −0.854962 0.493612i 0.00736010 0.999973i \(-0.497657\pi\)
−0.862322 + 0.506360i \(0.830991\pi\)
\(354\) 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 0.996379 0.0850256i \(-0.0270972\pi\)
−0.571824 + 0.820377i \(0.693764\pi\)
\(360\) 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 0.607887 0.794024i \(-0.292017\pi\)
−0.383701 + 0.923457i \(0.625351\pi\)
\(368\) −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 0.644521 0.764586i \(-0.277057\pi\)
−0.984412 + 0.175879i \(0.943723\pi\)
\(374\) 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 0.149320 0.988789i \(-0.452292\pi\)
0.930976 + 0.365080i \(0.118958\pi\)
\(384\) 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 −0.735647 0.677365i \(-0.763122\pi\)
0.954439 + 0.298406i \(0.0964550\pi\)
\(390\) 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 −0.742427 0.669927i \(-0.766325\pi\)
0.208960 + 0.977924i \(0.432992\pi\)
\(398\) 493.146i 1.23906i
\(399\) 0 0
\(400\) −75.8823 −0.189706
\(401\) −208.786 361.629i −0.520664 0.901817i −0.999711 0.0240277i \(-0.992351\pi\)
0.479047 0.877789i \(-0.340982\pi\)
\(402\) 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 0.136843 0.990593i \(-0.456304\pi\)
−0.789457 + 0.613806i \(0.789638\pi\)
\(410\) −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 \(-0.960722\pi\)
0.992397 0.123081i \(-0.0392776\pi\)
\(420\) 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 −0.282212 0.959352i \(-0.591068\pi\)
0.971929 0.235273i \(-0.0755984\pi\)
\(432\) 0 0
\(433\) 40.6267i 0.0938261i 0.998899 + 0.0469131i \(0.0149384\pi\)
−0.998899 + 0.0469131i \(0.985062\pi\)
\(434\) 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 −0.637582 0.770383i \(-0.720065\pi\)
0.348380 + 0.937353i \(0.386732\pi\)
\(440\) 89.2261i 0.202787i
\(441\) 0 0
\(442\) −81.3381 −0.184023
\(443\) 53.6802 + 92.9768i 0.121174 + 0.209880i 0.920231 0.391376i \(-0.128001\pi\)
−0.799057 + 0.601256i \(0.794667\pi\)
\(444\) 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 0.765315 0.643656i \(-0.222583\pi\)
−0.940080 + 0.340954i \(0.889250\pi\)
\(458\) −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 \(0.109242\pi\)
−0.941685 + 0.336497i \(0.890758\pi\)
\(462\) 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 0.167048 0.985949i \(-0.446576\pi\)
0.937381 + 0.348306i \(0.113243\pi\)
\(468\) 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 0.882379 0.470539i \(-0.155940\pi\)
0.0336914 + 0.999432i \(0.489274\pi\)
\(480\) 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 −0.953872 0.300215i \(-0.902942\pi\)
0.736930 + 0.675970i \(0.236275\pi\)
\(488\) −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 0.939062 0.343748i \(-0.111697\pi\)
−0.767226 + 0.641377i \(0.778363\pi\)
\(500\) 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 \(-0.993643\pi\)
0.999801 0.0199685i \(-0.00635659\pi\)
\(504\) 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 −0.847365 0.531011i \(-0.821812\pi\)
0.0361865 + 0.999345i \(0.488479\pi\)
\(510\) 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 0.996299 0.0859587i \(-0.0273953\pi\)
0.423707 + 0.905799i \(0.360729\pi\)
\(522\) 0 0
\(523\) 513.554 296.501i 0.981940 0.566923i 0.0790845 0.996868i \(-0.474800\pi\)
0.902855 + 0.429945i \(0.141467\pi\)
\(524\) 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 −0.925732 0.378180i \(-0.876550\pi\)
0.135352 0.990798i \(-0.456783\pi\)
\(542\) 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 0.475160 + 0.879899i \(0.342390\pi\)
−0.999595 + 0.0284485i \(0.990943\pi\)
\(558\) 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 0.994552 0.104237i \(-0.0332402\pi\)
0.407004 + 0.913426i \(0.366573\pi\)
\(564\) 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 0.990365 + 0.138485i \(0.0442231\pi\)
−0.375251 + 0.926923i \(0.622444\pi\)
\(570\) 0 0
\(571\) 281.231 487.107i 0.492525 0.853077i −0.507438 0.861688i \(-0.669408\pi\)
0.999963 + 0.00861055i \(0.00274086\pi\)
\(572\) −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 0.906197 0.422856i \(-0.138972\pi\)
0.0868946 + 0.996218i \(0.472306\pi\)
\(578\) 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 \(-0.752717\pi\)
0.713116 0.701046i \(-0.247283\pi\)
\(588\) 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 −0.880029 0.474919i \(-0.842477\pi\)
−0.0287225 + 0.999587i \(0.509144\pi\)
\(594\) 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 −0.996703 0.0811377i \(-0.974145\pi\)
0.568619 + 0.822601i \(0.307478\pi\)
\(600\) 0 0
\(601\) 680.160i 1.13171i −0.824504 0.565857i \(-0.808546\pi\)
0.824504 0.565857i \(-0.191454\pi\)
\(602\) 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 −0.527380 0.849630i \(-0.676825\pi\)
0.472111 + 0.881539i \(0.343492\pi\)
\(608\) 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 −0.981948 0.189151i \(-0.939426\pi\)
0.654784 + 0.755816i \(0.272760\pi\)
\(614\) −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 0.994941 0.100457i \(-0.0320303\pi\)
0.410473 + 0.911873i \(0.365364\pi\)
\(620\) 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 0.161502 + 0.986872i \(0.448366\pi\)
−0.935407 + 0.353572i \(0.884967\pi\)
\(642\) 0 0
\(643\) 944.986i 1.46965i −0.678256 0.734826i \(-0.737264\pi\)
0.678256 0.734826i \(-0.262736\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.1213 + 19.2627i 0.0172157 + 0.0298184i
\(647\) 2.50357 + 1.44544i 0.00386951 + 0.00223406i 0.501934 0.864906i \(-0.332622\pi\)
−0.498064 + 0.867140i \(0.665956\pi\)
\(648\) 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 0.715429 0.698686i \(-0.246231\pi\)
−0.962794 + 0.270237i \(0.912898\pi\)
\(654\) 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 0.486345 0.873767i \(-0.338330\pi\)
−0.513532 + 0.858070i \(0.671663\pi\)
\(662\) 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 −0.568244 0.822860i \(-0.692377\pi\)
0.428496 + 0.903544i \(0.359044\pi\)
\(678\) 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 −0.414427 0.910083i \(-0.636018\pi\)
0.995368 0.0961370i \(-0.0306487\pi\)
\(684\) 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 −0.610788 0.791794i \(-0.709147\pi\)
0.380320 + 0.924855i \(0.375814\pi\)
\(692\) 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 0.971344 + 0.237678i \(0.0763864\pi\)
−0.279836 + 0.960048i \(0.590280\pi\)
\(710\) 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 −0.889230 0.457460i \(-0.848759\pi\)
−0.0484429 + 0.998826i \(0.515426\pi\)
\(720\) 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 \(0.168757\pi\)
−0.862723 + 0.505677i \(0.831243\pi\)
\(728\) 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 −0.189692 0.981844i \(-0.560749\pi\)
0.755456 + 0.655200i \(0.227415\pi\)
\(734\) 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 −0.859213 0.511618i \(-0.829046\pi\)
0.872680 + 0.488292i \(0.162380\pi\)
\(740\) 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 0.781215 0.624263i \(-0.214600\pi\)
−0.931235 + 0.364420i \(0.881267\pi\)
\(752\) −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 0.604110 0.796901i \(-0.293529\pi\)
0.992191 0.124724i \(-0.0398046\pi\)
\(762\) 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 \(-0.999643\pi\)
0.999999 0.00112048i \(-0.000356661\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −154.338 267.321i −0.199920 0.346271i
\(773\) 194.213 + 112.129i 0.251245 + 0.145057i 0.620334 0.784337i \(-0.286997\pi\)
−0.369089 + 0.929394i \(0.620330\pi\)
\(774\) 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 0.460876 0.887465i \(-0.347535\pi\)
−0.538129 + 0.842863i \(0.680869\pi\)
\(788\) −181.103 + 313.679i −0.229826 + 0.398070i
\(789\) 0 0
\(790\) 316.842i 0.401066i
\(791\) 0 0