Properties

Label 2646.2.m.c.1763.21
Level $2646$
Weight $2$
Character 2646.1763
Analytic conductor $21.128$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1763.21
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.c.881.21

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.724499 - 1.25487i) q^{5} +1.00000i q^{8} -1.44900i q^{10} +(1.21051 + 0.698887i) q^{11} +(-3.03494 + 1.75222i) q^{13} +(-0.500000 + 0.866025i) q^{16} -7.90553 q^{17} +4.16869i q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 - 1.80925i) q^{23} +(1.45020 - 2.51182i) q^{25} -3.50444 q^{26} +(-4.06467 - 2.34674i) q^{29} +(0.794387 - 0.458640i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.84639 - 3.95277i) q^{34} -4.28351 q^{37} +(-2.08434 + 3.61019i) q^{38} +(1.25487 - 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +1.39777i q^{44} +3.61850 q^{46} +(-4.15872 + 7.20312i) q^{47} +(2.51182 - 1.45020i) q^{50} +(-3.03494 - 1.75222i) q^{52} -5.96029i q^{53} -2.02537i q^{55} +(-2.34674 - 4.06467i) q^{58} +(-4.72065 - 8.17641i) q^{59} +(-8.53864 - 4.92979i) q^{61} +0.917280 q^{62} -1.00000 q^{64} +(4.39762 + 2.53897i) q^{65} +(1.48540 + 2.57278i) q^{67} +(-3.95277 - 6.84639i) q^{68} +12.9436i q^{71} -11.3053i q^{73} +(-3.70963 - 2.14176i) q^{74} +(-3.61019 + 2.08434i) q^{76} +(-7.81709 + 13.5396i) q^{79} +1.44900 q^{80} +0.687454i q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 + 6.01497i) q^{86} +(-0.698887 + 1.21051i) q^{88} +1.06683 q^{89} +(3.13371 + 1.80925i) q^{92} +(-7.20312 + 4.15872i) q^{94} +(5.23116 - 3.02021i) q^{95} +(10.9670 + 6.33179i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} + O(q^{10}) \) \( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.724499 1.25487i −0.324006 0.561195i 0.657305 0.753625i \(-0.271696\pi\)
−0.981311 + 0.192430i \(0.938363\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.44900i 0.458214i
\(11\) 1.21051 + 0.698887i 0.364982 + 0.210722i 0.671264 0.741218i \(-0.265752\pi\)
−0.306282 + 0.951941i \(0.599085\pi\)
\(12\) 0 0
\(13\) −3.03494 + 1.75222i −0.841740 + 0.485979i −0.857855 0.513891i \(-0.828204\pi\)
0.0161150 + 0.999870i \(0.494870\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −7.90553 −1.91737 −0.958687 0.284464i \(-0.908184\pi\)
−0.958687 + 0.284464i \(0.908184\pi\)
\(18\) 0 0
\(19\) 4.16869i 0.956363i 0.878261 + 0.478181i \(0.158704\pi\)
−0.878261 + 0.478181i \(0.841296\pi\)
\(20\) 0.724499 1.25487i 0.162003 0.280597i
\(21\) 0 0
\(22\) 0.698887 + 1.21051i 0.149003 + 0.258081i
\(23\) 3.13371 1.80925i 0.653424 0.377255i −0.136343 0.990662i \(-0.543535\pi\)
0.789767 + 0.613407i \(0.210202\pi\)
\(24\) 0 0
\(25\) 1.45020 2.51182i 0.290040 0.502364i
\(26\) −3.50444 −0.687278
\(27\) 0 0
\(28\) 0 0
\(29\) −4.06467 2.34674i −0.754791 0.435779i 0.0726316 0.997359i \(-0.476860\pi\)
−0.827422 + 0.561580i \(0.810194\pi\)
\(30\) 0 0
\(31\) 0.794387 0.458640i 0.142676 0.0823741i −0.426963 0.904269i \(-0.640416\pi\)
0.569639 + 0.821895i \(0.307083\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −6.84639 3.95277i −1.17415 0.677894i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.28351 −0.704205 −0.352103 0.935961i \(-0.614533\pi\)
−0.352103 + 0.935961i \(0.614533\pi\)
\(38\) −2.08434 + 3.61019i −0.338125 + 0.585650i
\(39\) 0 0
\(40\) 1.25487 0.724499i 0.198412 0.114553i
\(41\) 0.343727 + 0.595352i 0.0536811 + 0.0929784i 0.891617 0.452790i \(-0.149571\pi\)
−0.837936 + 0.545768i \(0.816238\pi\)
\(42\) 0 0
\(43\) −6.01497 + 10.4182i −0.917275 + 1.58877i −0.113739 + 0.993511i \(0.536283\pi\)
−0.803536 + 0.595256i \(0.797051\pi\)
\(44\) 1.39777i 0.210722i
\(45\) 0 0
\(46\) 3.61850 0.533519
\(47\) −4.15872 + 7.20312i −0.606612 + 1.05068i 0.385182 + 0.922840i \(0.374139\pi\)
−0.991794 + 0.127842i \(0.959195\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.51182 1.45020i 0.355225 0.205089i
\(51\) 0 0
\(52\) −3.03494 1.75222i −0.420870 0.242990i
\(53\) 5.96029i 0.818709i −0.912375 0.409354i \(-0.865754\pi\)
0.912375 0.409354i \(-0.134246\pi\)
\(54\) 0 0
\(55\) 2.02537i 0.273101i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.34674 4.06467i −0.308142 0.533718i
\(59\) −4.72065 8.17641i −0.614577 1.06448i −0.990459 0.137810i \(-0.955994\pi\)
0.375882 0.926668i \(-0.377340\pi\)
\(60\) 0 0
\(61\) −8.53864 4.92979i −1.09326 0.631194i −0.158818 0.987308i \(-0.550768\pi\)
−0.934443 + 0.356113i \(0.884102\pi\)
\(62\) 0.917280 0.116495
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.39762 + 2.53897i 0.545458 + 0.314920i
\(66\) 0 0
\(67\) 1.48540 + 2.57278i 0.181470 + 0.314315i 0.942381 0.334541i \(-0.108581\pi\)
−0.760911 + 0.648856i \(0.775248\pi\)
\(68\) −3.95277 6.84639i −0.479343 0.830247i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.9436i 1.53612i 0.640377 + 0.768061i \(0.278778\pi\)
−0.640377 + 0.768061i \(0.721222\pi\)
\(72\) 0 0
\(73\) 11.3053i 1.32319i −0.749862 0.661595i \(-0.769880\pi\)
0.749862 0.661595i \(-0.230120\pi\)
\(74\) −3.70963 2.14176i −0.431236 0.248974i
\(75\) 0 0
\(76\) −3.61019 + 2.08434i −0.414117 + 0.239091i
\(77\) 0 0
\(78\) 0 0
\(79\) −7.81709 + 13.5396i −0.879491 + 1.52332i −0.0275906 + 0.999619i \(0.508783\pi\)
−0.851900 + 0.523704i \(0.824550\pi\)
\(80\) 1.44900 0.162003
\(81\) 0 0
\(82\) 0.687454i 0.0759166i
\(83\) −4.11183 + 7.12189i −0.451332 + 0.781729i −0.998469 0.0553135i \(-0.982384\pi\)
0.547137 + 0.837043i \(0.315718\pi\)
\(84\) 0 0
\(85\) 5.72755 + 9.92041i 0.621240 + 1.07602i
\(86\) −10.4182 + 6.01497i −1.12343 + 0.648611i
\(87\) 0 0
\(88\) −0.698887 + 1.21051i −0.0745016 + 0.129041i
\(89\) 1.06683 0.113084 0.0565421 0.998400i \(-0.481992\pi\)
0.0565421 + 0.998400i \(0.481992\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.13371 + 1.80925i 0.326712 + 0.188627i
\(93\) 0 0
\(94\) −7.20312 + 4.15872i −0.742945 + 0.428939i
\(95\) 5.23116 3.02021i 0.536706 0.309867i
\(96\) 0 0
\(97\) 10.9670 + 6.33179i 1.11353 + 0.642895i 0.939741 0.341888i \(-0.111066\pi\)
0.173787 + 0.984783i \(0.444400\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.90040 0.290040
\(101\) −8.77726 + 15.2027i −0.873370 + 1.51272i −0.0148801 + 0.999889i \(0.504737\pi\)
−0.858489 + 0.512831i \(0.828597\pi\)
\(102\) 0 0
\(103\) 3.86082 2.22905i 0.380418 0.219635i −0.297582 0.954696i \(-0.596180\pi\)
0.678000 + 0.735062i \(0.262847\pi\)
\(104\) −1.75222 3.03494i −0.171820 0.297600i
\(105\) 0 0
\(106\) 2.98014 5.16176i 0.289457 0.501355i
\(107\) 2.36213i 0.228356i 0.993460 + 0.114178i \(0.0364233\pi\)
−0.993460 + 0.114178i \(0.963577\pi\)
\(108\) 0 0
\(109\) 12.9955 1.24475 0.622373 0.782721i \(-0.286169\pi\)
0.622373 + 0.782721i \(0.286169\pi\)
\(110\) 1.01269 1.75402i 0.0965558 0.167240i
\(111\) 0 0
\(112\) 0 0
\(113\) −2.90616 + 1.67787i −0.273388 + 0.157841i −0.630426 0.776249i \(-0.717120\pi\)
0.357038 + 0.934090i \(0.383787\pi\)
\(114\) 0 0
\(115\) −4.54074 2.62160i −0.423427 0.244465i
\(116\) 4.69348i 0.435779i
\(117\) 0 0
\(118\) 9.44130i 0.869143i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.52311 7.83426i −0.411192 0.712206i
\(122\) −4.92979 8.53864i −0.446322 0.773052i
\(123\) 0 0
\(124\) 0.794387 + 0.458640i 0.0713381 + 0.0411871i
\(125\) −11.4477 −1.02391
\(126\) 0 0
\(127\) −12.9075 −1.14535 −0.572677 0.819781i \(-0.694095\pi\)
−0.572677 + 0.819781i \(0.694095\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 2.53897 + 4.39762i 0.222682 + 0.385697i
\(131\) −4.12856 7.15088i −0.360714 0.624775i 0.627364 0.778726i \(-0.284134\pi\)
−0.988079 + 0.153951i \(0.950800\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.97079i 0.256637i
\(135\) 0 0
\(136\) 7.90553i 0.677894i
\(137\) −11.3267 6.53946i −0.967703 0.558703i −0.0691676 0.997605i \(-0.522034\pi\)
−0.898535 + 0.438902i \(0.855368\pi\)
\(138\) 0 0
\(139\) 10.6722 6.16162i 0.905207 0.522621i 0.0263210 0.999654i \(-0.491621\pi\)
0.878886 + 0.477032i \(0.158287\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −6.47179 + 11.2095i −0.543101 + 0.940678i
\(143\) −4.89842 −0.409627
\(144\) 0 0
\(145\) 6.80085i 0.564780i
\(146\) 5.65267 9.79071i 0.467818 0.810285i
\(147\) 0 0
\(148\) −2.14176 3.70963i −0.176051 0.304930i
\(149\) 0.538692 0.311014i 0.0441314 0.0254792i −0.477772 0.878484i \(-0.658555\pi\)
0.521903 + 0.853005i \(0.325222\pi\)
\(150\) 0 0
\(151\) 10.5911 18.3443i 0.861889 1.49284i −0.00821353 0.999966i \(-0.502614\pi\)
0.870103 0.492870i \(-0.164052\pi\)
\(152\) −4.16869 −0.338125
\(153\) 0 0
\(154\) 0 0
\(155\) −1.15107 0.664569i −0.0924559 0.0533794i
\(156\) 0 0
\(157\) −13.0158 + 7.51469i −1.03878 + 0.599737i −0.919486 0.393122i \(-0.871395\pi\)
−0.119289 + 0.992860i \(0.538062\pi\)
\(158\) −13.5396 + 7.81709i −1.07715 + 0.621894i
\(159\) 0 0
\(160\) 1.25487 + 0.724499i 0.0992062 + 0.0572767i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.03527 −0.237741 −0.118871 0.992910i \(-0.537927\pi\)
−0.118871 + 0.992910i \(0.537927\pi\)
\(164\) −0.343727 + 0.595352i −0.0268406 + 0.0464892i
\(165\) 0 0
\(166\) −7.12189 + 4.11183i −0.552766 + 0.319140i
\(167\) 3.05895 + 5.29826i 0.236709 + 0.409992i 0.959768 0.280794i \(-0.0905979\pi\)
−0.723059 + 0.690786i \(0.757265\pi\)
\(168\) 0 0
\(169\) −0.359433 + 0.622557i −0.0276487 + 0.0478890i
\(170\) 11.4551i 0.878567i
\(171\) 0 0
\(172\) −12.0299 −0.917275
\(173\) 1.14757 1.98766i 0.0872484 0.151119i −0.819099 0.573653i \(-0.805526\pi\)
0.906347 + 0.422534i \(0.138859\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.21051 + 0.698887i −0.0912454 + 0.0526806i
\(177\) 0 0
\(178\) 0.923906 + 0.533417i 0.0692497 + 0.0399813i
\(179\) 3.37592i 0.252328i −0.992009 0.126164i \(-0.959733\pi\)
0.992009 0.126164i \(-0.0402666\pi\)
\(180\) 0 0
\(181\) 1.68857i 0.125511i −0.998029 0.0627553i \(-0.980011\pi\)
0.998029 0.0627553i \(-0.0199888\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.80925 + 3.13371i 0.133380 + 0.231020i
\(185\) 3.10340 + 5.37525i 0.228167 + 0.395196i
\(186\) 0 0
\(187\) −9.56971 5.52507i −0.699806 0.404033i
\(188\) −8.31745 −0.606612
\(189\) 0 0
\(190\) 6.04043 0.438219
\(191\) 7.74947 + 4.47416i 0.560732 + 0.323739i 0.753439 0.657517i \(-0.228393\pi\)
−0.192707 + 0.981256i \(0.561727\pi\)
\(192\) 0 0
\(193\) −12.8028 22.1751i −0.921564 1.59620i −0.796996 0.603984i \(-0.793579\pi\)
−0.124568 0.992211i \(-0.539754\pi\)
\(194\) 6.33179 + 10.9670i 0.454596 + 0.787383i
\(195\) 0 0
\(196\) 0 0
\(197\) 23.5602i 1.67860i 0.543670 + 0.839299i \(0.317034\pi\)
−0.543670 + 0.839299i \(0.682966\pi\)
\(198\) 0 0
\(199\) 13.6242i 0.965796i −0.875677 0.482898i \(-0.839584\pi\)
0.875677 0.482898i \(-0.160416\pi\)
\(200\) 2.51182 + 1.45020i 0.177613 + 0.102545i
\(201\) 0 0
\(202\) −15.2027 + 8.77726i −1.06965 + 0.617566i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.498060 0.862665i 0.0347860 0.0602511i
\(206\) 4.45810 0.310610
\(207\) 0 0
\(208\) 3.50444i 0.242990i
\(209\) −2.91344 + 5.04623i −0.201527 + 0.349055i
\(210\) 0 0
\(211\) −10.7961 18.6994i −0.743235 1.28732i −0.951015 0.309145i \(-0.899957\pi\)
0.207780 0.978176i \(-0.433376\pi\)
\(212\) 5.16176 2.98014i 0.354511 0.204677i
\(213\) 0 0
\(214\) −1.18106 + 2.04566i −0.0807359 + 0.139839i
\(215\) 17.4314 1.18881
\(216\) 0 0
\(217\) 0 0
\(218\) 11.2545 + 6.49776i 0.762248 + 0.440084i
\(219\) 0 0
\(220\) 1.75402 1.01269i 0.118256 0.0682753i
\(221\) 23.9928 13.8523i 1.61393 0.931803i
\(222\) 0 0
\(223\) 14.5710 + 8.41256i 0.975745 + 0.563347i 0.900983 0.433855i \(-0.142847\pi\)
0.0747620 + 0.997201i \(0.476180\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.35574 −0.223221
\(227\) 6.11065 10.5840i 0.405578 0.702482i −0.588810 0.808271i \(-0.700404\pi\)
0.994389 + 0.105789i \(0.0337369\pi\)
\(228\) 0 0
\(229\) 16.8458 9.72591i 1.11320 0.642706i 0.173543 0.984826i \(-0.444478\pi\)
0.939656 + 0.342120i \(0.111145\pi\)
\(230\) −2.62160 4.54074i −0.172863 0.299408i
\(231\) 0 0
\(232\) 2.34674 4.06467i 0.154071 0.266859i
\(233\) 28.5651i 1.87136i 0.352848 + 0.935681i \(0.385213\pi\)
−0.352848 + 0.935681i \(0.614787\pi\)
\(234\) 0 0
\(235\) 12.0520 0.786184
\(236\) 4.72065 8.17641i 0.307288 0.532239i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0020 5.77465i 0.646975 0.373531i −0.140322 0.990106i \(-0.544814\pi\)
0.787296 + 0.616575i \(0.211480\pi\)
\(240\) 0 0
\(241\) 0.0299000 + 0.0172628i 0.00192603 + 0.00111199i 0.500963 0.865469i \(-0.332979\pi\)
−0.499037 + 0.866581i \(0.666313\pi\)
\(242\) 9.04623i 0.581514i
\(243\) 0 0
\(244\) 9.85957i 0.631194i
\(245\) 0 0
\(246\) 0 0
\(247\) −7.30447 12.6517i −0.464772 0.805009i
\(248\) 0.458640 + 0.794387i 0.0291237 + 0.0504437i
\(249\) 0 0
\(250\) −9.91398 5.72384i −0.627015 0.362007i
\(251\) 3.26317 0.205969 0.102985 0.994683i \(-0.467161\pi\)
0.102985 + 0.994683i \(0.467161\pi\)
\(252\) 0 0
\(253\) 5.05784 0.317984
\(254\) −11.1782 6.45374i −0.701383 0.404944i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.89851 + 17.1447i 0.617452 + 1.06946i 0.989949 + 0.141425i \(0.0451685\pi\)
−0.372497 + 0.928034i \(0.621498\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 5.07794i 0.314920i
\(261\) 0 0
\(262\) 8.25713i 0.510127i
\(263\) 15.2576 + 8.80897i 0.940823 + 0.543184i 0.890218 0.455535i \(-0.150552\pi\)
0.0506045 + 0.998719i \(0.483885\pi\)
\(264\) 0 0
\(265\) −7.47939 + 4.31823i −0.459455 + 0.265266i
\(266\) 0 0
\(267\) 0 0
\(268\) −1.48540 + 2.57278i −0.0907350 + 0.157158i
\(269\) 7.67344 0.467858 0.233929 0.972254i \(-0.424842\pi\)
0.233929 + 0.972254i \(0.424842\pi\)
\(270\) 0 0
\(271\) 7.03381i 0.427273i 0.976913 + 0.213637i \(0.0685309\pi\)
−0.976913 + 0.213637i \(0.931469\pi\)
\(272\) 3.95277 6.84639i 0.239672 0.415123i
\(273\) 0 0
\(274\) −6.53946 11.3267i −0.395063 0.684269i
\(275\) 3.51096 2.02705i 0.211719 0.122236i
\(276\) 0 0
\(277\) −8.65364 + 14.9885i −0.519947 + 0.900575i 0.479784 + 0.877387i \(0.340715\pi\)
−0.999731 + 0.0231880i \(0.992618\pi\)
\(278\) 12.3232 0.739098
\(279\) 0 0
\(280\) 0 0
\(281\) −14.3155 8.26508i −0.853994 0.493053i 0.00800273 0.999968i \(-0.497453\pi\)
−0.861996 + 0.506915i \(0.830786\pi\)
\(282\) 0 0
\(283\) −2.73910 + 1.58142i −0.162823 + 0.0940057i −0.579197 0.815187i \(-0.696634\pi\)
0.416374 + 0.909193i \(0.363301\pi\)
\(284\) −11.2095 + 6.47179i −0.665160 + 0.384030i
\(285\) 0 0
\(286\) −4.24216 2.44921i −0.250844 0.144825i
\(287\) 0 0
\(288\) 0 0
\(289\) 45.4974 2.67632
\(290\) −3.40042 + 5.88971i −0.199680 + 0.345855i
\(291\) 0 0
\(292\) 9.79071 5.65267i 0.572958 0.330797i
\(293\) 4.26045 + 7.37932i 0.248898 + 0.431104i 0.963220 0.268713i \(-0.0865982\pi\)
−0.714322 + 0.699817i \(0.753265\pi\)
\(294\) 0 0
\(295\) −6.84022 + 11.8476i −0.398253 + 0.689794i
\(296\) 4.28351i 0.248974i
\(297\) 0 0
\(298\) 0.622028 0.0360331
\(299\) −6.34042 + 10.9819i −0.366676 + 0.635101i
\(300\) 0 0
\(301\) 0 0
\(302\) 18.3443 10.5911i 1.05559 0.609448i
\(303\) 0 0
\(304\) −3.61019 2.08434i −0.207059 0.119545i
\(305\) 14.2865i 0.818043i
\(306\) 0 0
\(307\) 25.0805i 1.43142i −0.698398 0.715710i \(-0.746103\pi\)
0.698398 0.715710i \(-0.253897\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.664569 1.15107i −0.0377450 0.0653762i
\(311\) 1.78678 + 3.09479i 0.101319 + 0.175489i 0.912228 0.409682i \(-0.134360\pi\)
−0.810909 + 0.585172i \(0.801027\pi\)
\(312\) 0 0
\(313\) 11.8033 + 6.81464i 0.667162 + 0.385186i 0.795000 0.606609i \(-0.207471\pi\)
−0.127838 + 0.991795i \(0.540804\pi\)
\(314\) −15.0294 −0.848157
\(315\) 0 0
\(316\) −15.6342 −0.879491
\(317\) −3.71520 2.14497i −0.208666 0.120474i 0.392025 0.919955i \(-0.371775\pi\)
−0.600692 + 0.799481i \(0.705108\pi\)
\(318\) 0 0
\(319\) −3.28021 5.68149i −0.183657 0.318102i
\(320\) 0.724499 + 1.25487i 0.0405007 + 0.0701494i
\(321\) 0 0
\(322\) 0 0
\(323\) 32.9557i 1.83370i
\(324\) 0 0
\(325\) 10.1643i 0.563814i
\(326\) −2.62863 1.51764i −0.145586 0.0840542i
\(327\) 0 0
\(328\) −0.595352 + 0.343727i −0.0328728 + 0.0189791i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.46962 + 7.74160i −0.245672 + 0.425517i −0.962320 0.271918i \(-0.912342\pi\)
0.716648 + 0.697435i \(0.245675\pi\)
\(332\) −8.22365 −0.451332
\(333\) 0 0
\(334\) 6.11791i 0.334757i
\(335\) 2.15234 3.72796i 0.117595 0.203680i
\(336\) 0 0
\(337\) 0.0729773 + 0.126400i 0.00397532 + 0.00688546i 0.868006 0.496553i \(-0.165401\pi\)
−0.864031 + 0.503439i \(0.832068\pi\)
\(338\) −0.622557 + 0.359433i −0.0338626 + 0.0195506i
\(339\) 0 0
\(340\) −5.72755 + 9.92041i −0.310620 + 0.538010i
\(341\) 1.28215 0.0694323
\(342\) 0 0
\(343\) 0 0
\(344\) −10.4182 6.01497i −0.561714 0.324306i
\(345\) 0 0
\(346\) 1.98766 1.14757i 0.106857 0.0616939i
\(347\) 19.2988 11.1422i 1.03602 0.598144i 0.117313 0.993095i \(-0.462572\pi\)
0.918702 + 0.394951i \(0.129238\pi\)
\(348\) 0 0
\(349\) 2.79851 + 1.61572i 0.149801 + 0.0864876i 0.573027 0.819537i \(-0.305769\pi\)
−0.423226 + 0.906024i \(0.639102\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.39777 −0.0745016
\(353\) −3.13232 + 5.42533i −0.166716 + 0.288761i −0.937263 0.348622i \(-0.886650\pi\)
0.770547 + 0.637383i \(0.219983\pi\)
\(354\) 0 0
\(355\) 16.2425 9.37762i 0.862063 0.497712i
\(356\) 0.533417 + 0.923906i 0.0282711 + 0.0489669i
\(357\) 0 0
\(358\) 1.68796 2.92364i 0.0892116 0.154519i
\(359\) 12.0693i 0.636991i −0.947924 0.318496i \(-0.896822\pi\)
0.947924 0.318496i \(-0.103178\pi\)
\(360\) 0 0
\(361\) 1.62203 0.0853700
\(362\) 0.844286 1.46235i 0.0443747 0.0768592i
\(363\) 0 0
\(364\) 0 0
\(365\) −14.1867 + 8.19071i −0.742567 + 0.428721i
\(366\) 0 0
\(367\) 14.7907 + 8.53940i 0.772067 + 0.445753i 0.833611 0.552351i \(-0.186269\pi\)
−0.0615446 + 0.998104i \(0.519603\pi\)
\(368\) 3.61850i 0.188627i
\(369\) 0 0
\(370\) 6.20681i 0.322677i
\(371\) 0 0
\(372\) 0 0
\(373\) −1.93680 3.35463i −0.100284 0.173696i 0.811518 0.584328i \(-0.198642\pi\)
−0.911801 + 0.410631i \(0.865308\pi\)
\(374\) −5.52507 9.56971i −0.285695 0.494838i
\(375\) 0 0
\(376\) −7.20312 4.15872i −0.371472 0.214470i
\(377\) 16.4480 0.847117
\(378\) 0 0
\(379\) 8.21884 0.422173 0.211087 0.977467i \(-0.432300\pi\)
0.211087 + 0.977467i \(0.432300\pi\)
\(380\) 5.23116 + 3.02021i 0.268353 + 0.154934i
\(381\) 0 0
\(382\) 4.47416 + 7.74947i 0.228918 + 0.396498i
\(383\) −15.1513 26.2428i −0.774195 1.34095i −0.935246 0.353999i \(-0.884821\pi\)
0.161050 0.986946i \(-0.448512\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 25.6055i 1.30329i
\(387\) 0 0
\(388\) 12.6636i 0.642895i
\(389\) −18.2352 10.5281i −0.924562 0.533796i −0.0394744 0.999221i \(-0.512568\pi\)
−0.885088 + 0.465424i \(0.845902\pi\)
\(390\) 0 0
\(391\) −24.7737 + 14.3031i −1.25286 + 0.723338i
\(392\) 0 0
\(393\) 0 0
\(394\) −11.7801 + 20.4038i −0.593474 + 1.02793i
\(395\) 22.6539 1.13984
\(396\) 0 0
\(397\) 0.596428i 0.0299338i 0.999888 + 0.0149669i \(0.00476430\pi\)
−0.999888 + 0.0149669i \(0.995236\pi\)
\(398\) 6.81212 11.7989i 0.341461 0.591427i
\(399\) 0 0
\(400\) 1.45020 + 2.51182i 0.0725101 + 0.125591i
\(401\) 2.02316 1.16807i 0.101032 0.0583309i −0.448633 0.893716i \(-0.648089\pi\)
0.549665 + 0.835385i \(0.314755\pi\)
\(402\) 0 0
\(403\) −1.60728 + 2.78389i −0.0800642 + 0.138675i
\(404\) −17.5545 −0.873370
\(405\) 0 0
\(406\) 0 0
\(407\) −5.18523 2.99369i −0.257022 0.148392i
\(408\) 0 0
\(409\) 8.35337 4.82282i 0.413048 0.238473i −0.279051 0.960276i \(-0.590020\pi\)
0.692098 + 0.721803i \(0.256686\pi\)
\(410\) 0.862665 0.498060i 0.0426040 0.0245974i
\(411\) 0 0
\(412\) 3.86082 + 2.22905i 0.190209 + 0.109817i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.9161 0.584937
\(416\) 1.75222 3.03494i 0.0859098 0.148800i
\(417\) 0 0
\(418\) −5.04623 + 2.91344i −0.246819 + 0.142501i
\(419\) 14.4297 + 24.9930i 0.704939 + 1.22099i 0.966714 + 0.255861i \(0.0823590\pi\)
−0.261775 + 0.965129i \(0.584308\pi\)
\(420\) 0 0
\(421\) 6.14672 10.6464i 0.299573 0.518875i −0.676466 0.736474i \(-0.736489\pi\)
0.976038 + 0.217599i \(0.0698226\pi\)
\(422\) 21.5922i 1.05109i
\(423\) 0 0
\(424\) 5.96029 0.289457
\(425\) −11.4646 + 19.8573i −0.556115 + 0.963220i
\(426\) 0 0
\(427\) 0 0
\(428\) −2.04566 + 1.18106i −0.0988808 + 0.0570889i
\(429\) 0 0
\(430\) 15.0960 + 8.71569i 0.727995 + 0.420308i
\(431\) 27.7631i 1.33730i 0.743577 + 0.668650i \(0.233128\pi\)
−0.743577 + 0.668650i \(0.766872\pi\)
\(432\) 0 0
\(433\) 21.3927i 1.02807i 0.857769 + 0.514035i \(0.171850\pi\)
−0.857769 + 0.514035i \(0.828150\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.49776 + 11.2545i 0.311186 + 0.538990i
\(437\) 7.54220 + 13.0635i 0.360792 + 0.624911i
\(438\) 0 0
\(439\) 2.28558 + 1.31958i 0.109085 + 0.0629801i 0.553550 0.832816i \(-0.313273\pi\)
−0.444465 + 0.895796i \(0.646606\pi\)
\(440\) 2.02537 0.0965558
\(441\) 0 0
\(442\) 27.7045 1.31777
\(443\) −10.5439 6.08750i −0.500954 0.289226i 0.228153 0.973625i \(-0.426731\pi\)
−0.729107 + 0.684399i \(0.760065\pi\)
\(444\) 0 0
\(445\) −0.772921 1.33874i −0.0366400 0.0634623i
\(446\) 8.41256 + 14.5710i 0.398346 + 0.689956i
\(447\) 0 0
\(448\) 0 0
\(449\) 14.2454i 0.672283i −0.941811 0.336142i \(-0.890878\pi\)
0.941811 0.336142i \(-0.109122\pi\)
\(450\) 0 0
\(451\) 0.960905i 0.0452472i
\(452\) −2.90616 1.67787i −0.136694 0.0789204i
\(453\) 0 0
\(454\) 10.5840 6.11065i 0.496730 0.286787i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.78156 10.0140i 0.270450 0.468433i −0.698527 0.715583i \(-0.746161\pi\)
0.968977 + 0.247151i \(0.0794942\pi\)
\(458\) 19.4518 0.908924
\(459\) 0 0
\(460\) 5.24320i 0.244465i
\(461\) −11.0041 + 19.0597i −0.512513 + 0.887698i 0.487382 + 0.873189i \(0.337952\pi\)
−0.999895 + 0.0145095i \(0.995381\pi\)
\(462\) 0 0
\(463\) 6.47862 + 11.2213i 0.301087 + 0.521498i 0.976382 0.216049i \(-0.0693171\pi\)
−0.675295 + 0.737547i \(0.735984\pi\)
\(464\) 4.06467 2.34674i 0.188698 0.108945i
\(465\) 0 0
\(466\) −14.2825 + 24.7381i −0.661626 + 1.14597i
\(467\) 2.85090 0.131924 0.0659619 0.997822i \(-0.478988\pi\)
0.0659619 + 0.997822i \(0.478988\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 10.4373 + 6.02598i 0.481437 + 0.277958i
\(471\) 0 0
\(472\) 8.17641 4.72065i 0.376350 0.217286i
\(473\) −14.5623 + 8.40757i −0.669577 + 0.386581i
\(474\) 0 0
\(475\) 10.4710 + 6.04544i 0.480443 + 0.277384i
\(476\) 0 0
\(477\) 0 0
\(478\) 11.5493 0.528253
\(479\) 16.6352 28.8130i 0.760081 1.31650i −0.182727 0.983164i \(-0.558492\pi\)
0.942808 0.333336i \(-0.108174\pi\)
\(480\) 0 0
\(481\) 13.0002 7.50567i 0.592758 0.342229i
\(482\) 0.0172628 + 0.0299000i 0.000786298 + 0.00136191i
\(483\) 0 0
\(484\) 4.52311 7.83426i 0.205596 0.356103i
\(485\) 18.3495i 0.833208i
\(486\) 0 0
\(487\) −10.4500 −0.473535 −0.236767 0.971566i \(-0.576088\pi\)
−0.236767 + 0.971566i \(0.576088\pi\)
\(488\) 4.92979 8.53864i 0.223161 0.386526i
\(489\) 0 0
\(490\) 0 0
\(491\) −2.03404 + 1.17436i −0.0917952 + 0.0529980i −0.545195 0.838309i \(-0.683544\pi\)
0.453400 + 0.891307i \(0.350211\pi\)
\(492\) 0 0
\(493\) 32.1334 + 18.5522i 1.44722 + 0.835550i
\(494\) 14.6089i 0.657287i
\(495\) 0 0
\(496\) 0.917280i 0.0411871i
\(497\) 0 0
\(498\) 0 0
\(499\) −17.3895 30.1195i −0.778462 1.34834i −0.932828 0.360322i \(-0.882667\pi\)
0.154366 0.988014i \(-0.450667\pi\)
\(500\) −5.72384 9.91398i −0.255978 0.443366i
\(501\) 0 0
\(502\) 2.82599 + 1.63158i 0.126130 + 0.0728211i
\(503\) 17.8290 0.794956 0.397478 0.917612i \(-0.369886\pi\)
0.397478 + 0.917612i \(0.369886\pi\)
\(504\) 0 0
\(505\) 25.4365 1.13191
\(506\) 4.38022 + 2.52892i 0.194725 + 0.112424i
\(507\) 0 0
\(508\) −6.45374 11.1782i −0.286338 0.495953i
\(509\) −7.78061 13.4764i −0.344869 0.597331i 0.640461 0.767991i \(-0.278743\pi\)
−0.985330 + 0.170660i \(0.945410\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 19.7970i 0.873209i
\(515\) −5.59433 3.22989i −0.246516 0.142326i
\(516\) 0 0
\(517\) −10.0683 + 5.81295i −0.442805 + 0.255653i
\(518\) 0 0
\(519\) 0 0
\(520\) −2.53897 + 4.39762i −0.111341 + 0.192848i
\(521\) −29.6376 −1.29844 −0.649222 0.760599i \(-0.724906\pi\)
−0.649222 + 0.760599i \(0.724906\pi\)
\(522\) 0 0
\(523\) 22.2110i 0.971220i 0.874176 + 0.485610i \(0.161403\pi\)
−0.874176 + 0.485610i \(0.838597\pi\)
\(524\) 4.12856 7.15088i 0.180357 0.312388i
\(525\) 0 0
\(526\) 8.80897 + 15.2576i 0.384089 + 0.665262i
\(527\) −6.28006 + 3.62579i −0.273564 + 0.157942i
\(528\) 0 0
\(529\) −4.95323 + 8.57925i −0.215358 + 0.373011i
\(530\) −8.63645 −0.375143
\(531\) 0 0
\(532\) 0 0
\(533\) −2.08638 1.20457i −0.0903711 0.0521758i
\(534\) 0 0
\(535\) 2.96416 1.71136i 0.128152 0.0739886i
\(536\) −2.57278 + 1.48540i −0.111127 + 0.0641593i
\(537\) 0 0
\(538\) 6.64540 + 3.83672i 0.286503 + 0.165413i
\(539\) 0 0
\(540\) 0 0
\(541\) 22.0342 0.947324 0.473662 0.880707i \(-0.342932\pi\)
0.473662 + 0.880707i \(0.342932\pi\)
\(542\) −3.51690 + 6.09146i −0.151064 + 0.261650i
\(543\) 0 0
\(544\) 6.84639 3.95277i 0.293537 0.169473i
\(545\) −9.41525 16.3077i −0.403305 0.698545i
\(546\) 0 0
\(547\) −14.5256 + 25.1592i −0.621072 + 1.07573i 0.368215 + 0.929741i \(0.379969\pi\)
−0.989286 + 0.145987i \(0.953364\pi\)
\(548\) 13.0789i 0.558703i
\(549\) 0 0
\(550\) 4.05411 0.172868
\(551\) 9.78283 16.9444i 0.416762 0.721854i
\(552\) 0 0
\(553\) 0 0
\(554\) −14.9885 + 8.65364i −0.636802 + 0.367658i
\(555\) 0 0
\(556\) 10.6722 + 6.16162i 0.452603 + 0.261311i
\(557\) 17.3143i 0.733632i 0.930294 + 0.366816i \(0.119552\pi\)
−0.930294 + 0.366816i \(0.880448\pi\)
\(558\) 0 0
\(559\) 42.1583i 1.78311i
\(560\) 0 0
\(561\) 0 0
\(562\) −8.26508 14.3155i −0.348641 0.603865i
\(563\) 10.3834 + 17.9846i 0.437608 + 0.757959i 0.997504 0.0706035i \(-0.0224925\pi\)
−0.559897 + 0.828562i \(0.689159\pi\)
\(564\) 0 0
\(565\) 4.21102 + 2.43123i 0.177159 + 0.102283i
\(566\) −3.16284 −0.132944
\(567\) 0 0
\(568\) −12.9436 −0.543101
\(569\) −12.7829 7.38020i −0.535887 0.309394i 0.207524 0.978230i \(-0.433460\pi\)
−0.743410 + 0.668836i \(0.766793\pi\)
\(570\) 0 0
\(571\) 11.1208 + 19.2618i 0.465390 + 0.806080i 0.999219 0.0395130i \(-0.0125806\pi\)
−0.533829 + 0.845593i \(0.679247\pi\)
\(572\) −2.44921 4.24216i −0.102407 0.177373i
\(573\) 0 0
\(574\) 0 0
\(575\) 10.4951i 0.437676i
\(576\) 0 0
\(577\) 18.7182i 0.779249i 0.920974 + 0.389625i \(0.127395\pi\)
−0.920974 + 0.389625i \(0.872605\pi\)
\(578\) 39.4019 + 22.7487i 1.63890 + 0.946222i
\(579\) 0 0
\(580\) −5.88971 + 3.40042i −0.244557 + 0.141195i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.16557 7.21497i 0.172520 0.298814i
\(584\) 11.3053 0.467818
\(585\) 0 0
\(586\) 8.52090i 0.351995i
\(587\) 10.7433 18.6079i 0.443423 0.768031i −0.554518 0.832172i \(-0.687097\pi\)
0.997941 + 0.0641405i \(0.0204306\pi\)
\(588\) 0 0
\(589\) 1.91193 + 3.31155i 0.0787796 + 0.136450i
\(590\) −11.8476 + 6.84022i −0.487758 + 0.281607i
\(591\) 0 0
\(592\) 2.14176 3.70963i 0.0880257 0.152465i
\(593\) −14.0949 −0.578809 −0.289404 0.957207i \(-0.593457\pi\)
−0.289404 + 0.957207i \(0.593457\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.538692 + 0.311014i 0.0220657 + 0.0127396i
\(597\) 0 0
\(598\) −10.9819 + 6.34042i −0.449084 + 0.259279i
\(599\) −16.6024 + 9.58537i −0.678354 + 0.391648i −0.799235 0.601019i \(-0.794761\pi\)
0.120881 + 0.992667i \(0.461428\pi\)
\(600\) 0 0
\(601\) 34.6795 + 20.0222i 1.41460 + 0.816723i 0.995818 0.0913619i \(-0.0291220\pi\)
0.418787 + 0.908084i \(0.362455\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 21.1821 0.861889
\(605\) −6.55399 + 11.3518i −0.266457 + 0.461518i
\(606\) 0 0
\(607\) −39.6529 + 22.8936i −1.60946 + 0.929223i −0.619971 + 0.784625i \(0.712856\pi\)
−0.989490 + 0.144599i \(0.953811\pi\)
\(608\) −2.08434 3.61019i −0.0845313 0.146413i
\(609\) 0 0
\(610\) −7.14325 + 12.3725i −0.289222 + 0.500947i
\(611\) 29.1480i 1.17920i
\(612\) 0 0
\(613\) −45.2962 −1.82950 −0.914748 0.404026i \(-0.867611\pi\)
−0.914748 + 0.404026i \(0.867611\pi\)
\(614\) 12.5403 21.7204i 0.506083 0.876562i
\(615\) 0 0
\(616\) 0 0
\(617\) 28.6323 16.5308i 1.15269 0.665506i 0.203149 0.979148i \(-0.434882\pi\)
0.949542 + 0.313641i \(0.101549\pi\)
\(618\) 0 0
\(619\) 9.35801 + 5.40285i 0.376130 + 0.217159i 0.676133 0.736779i \(-0.263654\pi\)
−0.300003 + 0.953938i \(0.596988\pi\)
\(620\) 1.32914i 0.0533794i
\(621\) 0 0
\(622\) 3.57355i 0.143286i
\(623\) 0 0
\(624\) 0 0
\(625\) 1.04283 + 1.80623i 0.0417131 + 0.0722491i
\(626\) 6.81464 + 11.8033i 0.272368 + 0.471755i
\(627\) 0 0
\(628\) −13.0158 7.51469i −0.519388 0.299869i
\(629\) 33.8635 1.35022
\(630\) 0 0
\(631\) −30.0554 −1.19648 −0.598242 0.801315i \(-0.704134\pi\)
−0.598242 + 0.801315i \(0.704134\pi\)
\(632\) −13.5396 7.81709i −0.538576 0.310947i
\(633\) 0 0
\(634\) −2.14497 3.71520i −0.0851877 0.147549i
\(635\) 9.35146 + 16.1972i 0.371101 + 0.642767i
\(636\) 0 0
\(637\) 0 0
\(638\) 6.56042i 0.259730i
\(639\) 0 0
\(640\) 1.44900i 0.0572767i
\(641\) 9.66957 + 5.58273i 0.381925 + 0.220505i 0.678655 0.734457i \(-0.262563\pi\)
−0.296730 + 0.954961i \(0.595896\pi\)
\(642\) 0 0
\(643\) −4.40588 + 2.54373i −0.173751 + 0.100315i −0.584353 0.811499i \(-0.698652\pi\)
0.410602 + 0.911814i \(0.365318\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 16.4779 28.5405i 0.648312 1.12291i
\(647\) 12.9142 0.507710 0.253855 0.967242i \(-0.418301\pi\)
0.253855 + 0.967242i \(0.418301\pi\)
\(648\) 0 0
\(649\) 13.1968i 0.518020i
\(650\) −5.08215 + 8.80254i −0.199338 + 0.345264i
\(651\) 0 0
\(652\) −1.51764 2.62863i −0.0594353 0.102945i
\(653\) 31.5843 18.2352i 1.23599 0.713598i 0.267716 0.963498i \(-0.413731\pi\)
0.968272 + 0.249900i \(0.0803977\pi\)
\(654\) 0 0
\(655\) −5.98228 + 10.3616i −0.233747 + 0.404862i
\(656\) −0.687454 −0.0268406
\(657\) 0 0
\(658\) 0 0
\(659\) −2.04111 1.17844i −0.0795104 0.0459054i 0.459718 0.888065i \(-0.347951\pi\)
−0.539228 + 0.842160i \(0.681284\pi\)
\(660\) 0 0
\(661\) −6.72135 + 3.88057i −0.261430 + 0.150937i −0.624987 0.780635i \(-0.714896\pi\)
0.363557 + 0.931572i \(0.381562\pi\)
\(662\) −7.74160 + 4.46962i −0.300886 + 0.173717i
\(663\) 0 0
\(664\) −7.12189 4.11183i −0.276383 0.159570i
\(665\) 0 0
\(666\) 0 0
\(667\) −16.9833 −0.657598
\(668\) −3.05895 + 5.29826i −0.118354 + 0.204996i
\(669\) 0 0
\(670\) 3.72796 2.15234i 0.144024 0.0831520i
\(671\) −6.89072 11.9351i −0.266013 0.460749i
\(672\) 0 0
\(673\) 17.5783 30.4465i 0.677594 1.17363i −0.298109 0.954532i \(-0.596356\pi\)
0.975703 0.219096i \(-0.0703106\pi\)
\(674\) 0.145955i 0.00562196i
\(675\) 0 0
\(676\) −0.718866 −0.0276487
\(677\) −7.03074 + 12.1776i −0.270213 + 0.468023i −0.968916 0.247389i \(-0.920428\pi\)
0.698703 + 0.715412i \(0.253761\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −9.92041 + 5.72755i −0.380430 + 0.219642i
\(681\) 0 0
\(682\) 1.11037 + 0.641075i 0.0425184 + 0.0245480i
\(683\) 33.6363i 1.28706i 0.765422 + 0.643529i \(0.222530\pi\)
−0.765422 + 0.643529i \(0.777470\pi\)
\(684\) 0 0
\(685\) 18.9513i 0.724093i
\(686\) 0 0
\(687\) 0 0
\(688\) −6.01497 10.4182i −0.229319 0.397192i
\(689\) 10.4438 + 18.0891i 0.397875 + 0.689140i
\(690\) 0 0
\(691\) 3.81269 + 2.20126i 0.145042 + 0.0837399i 0.570765 0.821114i \(-0.306647\pi\)
−0.425723 + 0.904854i \(0.639980\pi\)
\(692\) 2.29515 0.0872484
\(693\) 0 0
\(694\) 22.2844 0.845903
\(695\) −15.4640 8.92817i −0.586585 0.338665i
\(696\) 0 0
\(697\) −2.71734 4.70658i −0.102927 0.178274i
\(698\) 1.61572 + 2.79851i 0.0611560 + 0.105925i
\(699\) 0 0
\(700\) 0 0
\(701\) 31.5424i 1.19134i 0.803229 + 0.595670i \(0.203113\pi\)
−0.803229 + 0.595670i \(0.796887\pi\)
\(702\) 0 0
\(703\) 17.8566i 0.673476i
\(704\) −1.21051 0.698887i −0.0456227 0.0263403i
\(705\) 0 0
\(706\) −5.42533 + 3.13232i −0.204185 + 0.117886i
\(707\) 0 0
\(708\) 0 0
\(709\) −2.17269 + 3.76320i −0.0815970 + 0.141330i −0.903936 0.427668i \(-0.859335\pi\)
0.822339 + 0.568998i \(0.192669\pi\)
\(710\) 18.7552 0.703872
\(711\) 0 0
\(712\) 1.06683i 0.0399813i
\(713\) 1.65959 2.87449i 0.0621520 0.107651i
\(714\) 0 0
\(715\) 3.54890 + 6.14688i 0.132721 + 0.229880i
\(716\) 2.92364 1.68796i 0.109261 0.0630821i
\(717\) 0 0
\(718\) 6.03463 10.4523i 0.225210 0.390076i
\(719\) 28.3001 1.05541 0.527707 0.849426i \(-0.323052\pi\)
0.527707 + 0.849426i \(0.323052\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.40472 + 0.811015i 0.0522782 + 0.0301829i
\(723\) 0 0
\(724\) 1.46235 0.844286i 0.0543477 0.0313776i
\(725\) −11.7892 + 6.80649i −0.437839 + 0.252787i
\(726\) 0 0
\(727\) −11.7770 6.79945i −0.436784 0.252178i 0.265448 0.964125i \(-0.414480\pi\)
−0.702233 + 0.711948i \(0.747813\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.3814 −0.606303
\(731\) 47.5516 82.3617i 1.75876 3.04626i
\(732\) 0 0
\(733\) −41.0236 + 23.6850i −1.51524 + 0.874825i −0.515401 + 0.856949i \(0.672357\pi\)
−0.999840 + 0.0178757i \(0.994310\pi\)
\(734\) 8.53940 + 14.7907i 0.315195 + 0.545934i
\(735\) 0 0
\(736\) −1.80925 + 3.13371i −0.0666898 + 0.115510i
\(737\) 4.15250i 0.152959i
\(738\) 0 0
\(739\) 33.7203 1.24042 0.620210 0.784435i \(-0.287047\pi\)
0.620210 + 0.784435i \(0.287047\pi\)
\(740\) −3.10340 + 5.37525i −0.114083 + 0.197598i
\(741\) 0 0
\(742\) 0 0
\(743\) −6.86253 + 3.96208i −0.251762 + 0.145355i −0.620571 0.784151i \(-0.713099\pi\)
0.368809 + 0.929505i \(0.379766\pi\)
\(744\) 0 0
\(745\) −0.780564 0.450659i −0.0285976 0.0165109i
\(746\) 3.87360i 0.141822i
\(747\) 0 0
\(748\) 11.0501i 0.404033i
\(749\) 0 0
\(750\) 0 0
\(751\) −2.06865 3.58301i −0.0754861 0.130746i 0.825811 0.563946i \(-0.190718\pi\)
−0.901298 + 0.433201i \(0.857384\pi\)
\(752\) −4.15872 7.20312i −0.151653 0.262671i
\(753\) 0 0
\(754\) 14.2444 + 8.22402i 0.518751 + 0.299501i
\(755\) −30.6929 −1.11703
\(756\) 0 0
\(757\) 35.2411 1.28086 0.640430 0.768017i \(-0.278756\pi\)
0.640430 + 0.768017i \(0.278756\pi\)
\(758\) 7.11772 + 4.10942i 0.258527 + 0.149261i
\(759\) 0 0
\(760\) 3.02021 + 5.23116i 0.109555 + 0.189754i
\(761\) −4.93597 8.54935i −0.178929 0.309914i 0.762585 0.646888i \(-0.223930\pi\)
−0.941514 + 0.336974i \(0.890596\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.94832i 0.323739i
\(765\) 0 0
\(766\) 30.3026i 1.09488i
\(767\) 28.6538 + 16.5433i 1.03463 + 0.597343i
\(768\) 0 0
\(769\) 18.6213 10.7510i 0.671503 0.387692i −0.125143 0.992139i \(-0.539939\pi\)
0.796646 + 0.604446i \(0.206606\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 12.8028 22.1751i 0.460782 0.798098i
\(773\) −7.39549 −0.265997 −0.132999 0.991116i \(-0.542461\pi\)
−0.132999 + 0.991116i \(0.542461\pi\)
\(774\) 0 0
\(775\) 2.66048i 0.0955673i
\(776\) −6.33179 + 10.9670i −0.227298 + 0.393691i
\(777\) 0 0
\(778\) −10.5281 18.2352i −0.377451 0.653764i
\(779\) −2.48184 + 1.43289i −0.0889211 + 0.0513386i
\(780\) 0 0
\(781\) −9.04610 + 15.6683i −0.323695 + 0.560656i
\(782\) −28.6062 −1.02295
\(783\) 0 0
\(784\) 0 0
\(785\) 18.8599 + 10.8888i 0.673139 + 0.388637i
\(786\) 0 0
\(787\) −15.4285 + 8.90768i −0.549968 + 0.317524i −0.749109 0.662446i \(-0.769518\pi\)
0.199141 + 0.979971i \(0.436185\pi\)
\(788\) −20.4038 + 11.7801i −0.726854 + 0.419649i
\(789\) 0 0
\(790\) 19.6189 + 11.3269i 0.698007 + 0.402995i
\(791\) 0 0
\(792\) 0 0
\(793\) 34.5523 1.22699
\(794\) −0.298214 + 0.516521i −0.0105832 + 0.0183307i
\(795\) 0 0
\(796\) 11.7989