Properties

Label 1323.2.f.g.883.5
Level $1323$
Weight $2$
Character 1323.883
Analytic conductor $10.564$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 883.5
Root \(-1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 1323.883
Dual form 1323.2.f.g.442.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +(-1.82904 - 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})\) \(q+(1.23025 - 2.13086i) q^{2} +(-2.02704 - 3.51094i) q^{4} +(-1.82904 - 3.16799i) q^{5} -5.05408 q^{8} -9.00071 q^{10} +(0.203210 - 0.351971i) q^{11} +(0.243398 + 0.421578i) q^{13} +(-2.16372 + 3.74766i) q^{16} -4.85584 q^{17} -1.97351 q^{19} +(-7.41507 + 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(2.32383 + 4.02499i) q^{23} +(-4.19076 + 7.25860i) q^{25} +1.19777 q^{26} +(3.82383 - 6.62307i) q^{29} +(-3.51360 - 6.08573i) q^{31} +(0.269748 + 0.467216i) q^{32} +(-5.97391 + 10.3471i) q^{34} +2.32743 q^{37} +(-2.42792 + 4.20528i) q^{38} +(9.24411 + 16.0113i) q^{40} +(3.75700 + 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} -1.64766 q^{44} +11.4356 q^{46} +(-3.15811 + 5.47002i) q^{47} +(10.3114 + 17.8598i) q^{50} +(0.986757 - 1.70911i) q^{52} +3.56867 q^{53} -1.48672 q^{55} +(-9.40856 - 16.2961i) q^{58} +(3.05919 + 5.29868i) q^{59} +(4.01356 - 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 - 1.54216i) q^{65} +(-1.80039 - 3.11836i) q^{67} +(9.84299 + 17.0486i) q^{68} -8.46050 q^{71} +1.97351 q^{73} +(2.86333 - 4.95943i) q^{74} +(4.00040 + 6.92889i) q^{76} +(-4.08113 + 7.06872i) q^{79} +15.8301 q^{80} +18.4882 q^{82} +(6.08600 - 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(-2.86333 - 4.95943i) q^{86} +(-1.02704 + 1.77889i) q^{88} -14.8301 q^{89} +(9.42101 - 16.3177i) q^{92} +(7.77056 + 13.4590i) q^{94} +(3.60963 + 6.25206i) q^{95} +(4.74375 - 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} + O(q^{10}) \) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} + 8q^{11} - 6q^{16} - 6q^{22} + 4q^{23} - 12q^{25} + 22q^{29} + 16q^{32} - 12q^{37} - 6q^{43} + 28q^{44} + 24q^{46} + 56q^{50} - 56q^{53} - 18q^{58} - 48q^{64} - 6q^{65} - 76q^{71} + 36q^{74} + 6q^{79} + 30q^{85} - 36q^{86} + 6q^{88} + 62q^{92} + 60q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23025 2.13086i 0.869920 1.50675i 0.00784213 0.999969i \(-0.497504\pi\)
0.862078 0.506776i \(-0.169163\pi\)
\(3\) 0 0
\(4\) −2.02704 3.51094i −1.01352 1.75547i
\(5\) −1.82904 3.16799i −0.817970 1.41677i −0.907175 0.420753i \(-0.861766\pi\)
0.0892047 0.996013i \(-0.471567\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −5.05408 −1.78689
\(9\) 0 0
\(10\) −9.00071 −2.84628
\(11\) 0.203210 0.351971i 0.0612702 0.106123i −0.833763 0.552122i \(-0.813818\pi\)
0.895033 + 0.445999i \(0.147152\pi\)
\(12\) 0 0
\(13\) 0.243398 + 0.421578i 0.0675065 + 0.116925i 0.897803 0.440397i \(-0.145162\pi\)
−0.830297 + 0.557322i \(0.811829\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.16372 + 3.74766i −0.540929 + 0.936916i
\(17\) −4.85584 −1.17771 −0.588857 0.808237i \(-0.700422\pi\)
−0.588857 + 0.808237i \(0.700422\pi\)
\(18\) 0 0
\(19\) −1.97351 −0.452755 −0.226378 0.974040i \(-0.572688\pi\)
−0.226378 + 0.974040i \(0.572688\pi\)
\(20\) −7.41507 + 12.8433i −1.65806 + 2.87185i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 2.32383 + 4.02499i 0.484552 + 0.839269i 0.999843 0.0177464i \(-0.00564915\pi\)
−0.515290 + 0.857016i \(0.672316\pi\)
\(24\) 0 0
\(25\) −4.19076 + 7.25860i −0.838151 + 1.45172i
\(26\) 1.19777 0.234901
\(27\) 0 0
\(28\) 0 0
\(29\) 3.82383 6.62307i 0.710068 1.22987i −0.254764 0.967003i \(-0.581998\pi\)
0.964831 0.262870i \(-0.0846690\pi\)
\(30\) 0 0
\(31\) −3.51360 6.08573i −0.631061 1.09303i −0.987335 0.158648i \(-0.949286\pi\)
0.356274 0.934381i \(-0.384047\pi\)
\(32\) 0.269748 + 0.467216i 0.0476851 + 0.0825930i
\(33\) 0 0
\(34\) −5.97391 + 10.3471i −1.02452 + 1.77452i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.32743 0.382627 0.191314 0.981529i \(-0.438725\pi\)
0.191314 + 0.981529i \(0.438725\pi\)
\(38\) −2.42792 + 4.20528i −0.393861 + 0.682187i
\(39\) 0 0
\(40\) 9.24411 + 16.0113i 1.46162 + 2.53160i
\(41\) 3.75700 + 6.50731i 0.586744 + 1.01627i 0.994655 + 0.103249i \(0.0329240\pi\)
−0.407911 + 0.913022i \(0.633743\pi\)
\(42\) 0 0
\(43\) 1.16372 2.01561i 0.177465 0.307378i −0.763547 0.645753i \(-0.776544\pi\)
0.941012 + 0.338374i \(0.109877\pi\)
\(44\) −1.64766 −0.248395
\(45\) 0 0
\(46\) 11.4356 1.68609
\(47\) −3.15811 + 5.47002i −0.460658 + 0.797884i −0.998994 0.0448469i \(-0.985720\pi\)
0.538335 + 0.842731i \(0.319053\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 10.3114 + 17.8598i 1.45825 + 2.52576i
\(51\) 0 0
\(52\) 0.986757 1.70911i 0.136839 0.237011i
\(53\) 3.56867 0.490195 0.245097 0.969498i \(-0.421180\pi\)
0.245097 + 0.969498i \(0.421180\pi\)
\(54\) 0 0
\(55\) −1.48672 −0.200469
\(56\) 0 0
\(57\) 0 0
\(58\) −9.40856 16.2961i −1.23540 2.13978i
\(59\) 3.05919 + 5.29868i 0.398273 + 0.689829i 0.993513 0.113719i \(-0.0362763\pi\)
−0.595240 + 0.803548i \(0.702943\pi\)
\(60\) 0 0
\(61\) 4.01356 6.95169i 0.513884 0.890073i −0.485987 0.873966i \(-0.661540\pi\)
0.999870 0.0161063i \(-0.00512703\pi\)
\(62\) −17.2905 −2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 0.890369 1.54216i 0.110437 0.191282i
\(66\) 0 0
\(67\) −1.80039 3.11836i −0.219952 0.380969i 0.734841 0.678240i \(-0.237257\pi\)
−0.954793 + 0.297271i \(0.903924\pi\)
\(68\) 9.84299 + 17.0486i 1.19364 + 2.06744i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.46050 −1.00408 −0.502039 0.864845i \(-0.667416\pi\)
−0.502039 + 0.864845i \(0.667416\pi\)
\(72\) 0 0
\(73\) 1.97351 0.230982 0.115491 0.993309i \(-0.463156\pi\)
0.115491 + 0.993309i \(0.463156\pi\)
\(74\) 2.86333 4.95943i 0.332855 0.576522i
\(75\) 0 0
\(76\) 4.00040 + 6.92889i 0.458877 + 0.794798i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.08113 + 7.06872i −0.459163 + 0.795293i −0.998917 0.0465297i \(-0.985184\pi\)
0.539754 + 0.841823i \(0.318517\pi\)
\(80\) 15.8301 1.76986
\(81\) 0 0
\(82\) 18.4882 2.04168
\(83\) 6.08600 10.5413i 0.668025 1.15705i −0.310431 0.950596i \(-0.600473\pi\)
0.978456 0.206457i \(-0.0661933\pi\)
\(84\) 0 0
\(85\) 8.88151 + 15.3832i 0.963336 + 1.66855i
\(86\) −2.86333 4.95943i −0.308760 0.534789i
\(87\) 0 0
\(88\) −1.02704 + 1.77889i −0.109483 + 0.189630i
\(89\) −14.8301 −1.57199 −0.785996 0.618231i \(-0.787849\pi\)
−0.785996 + 0.618231i \(0.787849\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 9.42101 16.3177i 0.982208 1.70123i
\(93\) 0 0
\(94\) 7.77056 + 13.4590i 0.801472 + 1.38819i
\(95\) 3.60963 + 6.25206i 0.370340 + 0.641448i
\(96\) 0 0
\(97\) 4.74375 8.21642i 0.481655 0.834251i −0.518123 0.855306i \(-0.673369\pi\)
0.999778 + 0.0210547i \(0.00670241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 33.9794 3.39794
\(101\) 4.35588 7.54461i 0.433426 0.750716i −0.563739 0.825953i \(-0.690638\pi\)
0.997166 + 0.0752364i \(0.0239711\pi\)
\(102\) 0 0
\(103\) −4.01356 6.95169i −0.395468 0.684970i 0.597693 0.801725i \(-0.296084\pi\)
−0.993161 + 0.116755i \(0.962751\pi\)
\(104\) −1.23016 2.13069i −0.120627 0.208931i
\(105\) 0 0
\(106\) 4.39037 7.60434i 0.426430 0.738599i
\(107\) −12.8420 −1.24148 −0.620742 0.784015i \(-0.713169\pi\)
−0.620742 + 0.784015i \(0.713169\pi\)
\(108\) 0 0
\(109\) 2.60078 0.249109 0.124555 0.992213i \(-0.460250\pi\)
0.124555 + 0.992213i \(0.460250\pi\)
\(110\) −1.82904 + 3.16799i −0.174392 + 0.302056i
\(111\) 0 0
\(112\) 0 0
\(113\) −6.97509 12.0812i −0.656162 1.13651i −0.981601 0.190942i \(-0.938846\pi\)
0.325440 0.945563i \(-0.394488\pi\)
\(114\) 0 0
\(115\) 8.50075 14.7237i 0.792699 1.37300i
\(116\) −31.0043 −2.87867
\(117\) 0 0
\(118\) 15.0543 1.38586
\(119\) 0 0
\(120\) 0 0
\(121\) 5.41741 + 9.38323i 0.492492 + 0.853021i
\(122\) −9.87538 17.1047i −0.894075 1.54858i
\(123\) 0 0
\(124\) −14.2444 + 24.6721i −1.27919 + 2.21562i
\(125\) 12.3698 1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) −9.55408 + 16.5482i −0.844470 + 1.46266i
\(129\) 0 0
\(130\) −2.19076 3.79450i −0.192142 0.332800i
\(131\) −4.25696 7.37327i −0.371932 0.644205i 0.617931 0.786233i \(-0.287971\pi\)
−0.989863 + 0.142027i \(0.954638\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.85973 −0.765364
\(135\) 0 0
\(136\) 24.5418 2.10444
\(137\) 0.188621 0.326702i 0.0161150 0.0279120i −0.857855 0.513891i \(-0.828204\pi\)
0.873970 + 0.485979i \(0.161537\pi\)
\(138\) 0 0
\(139\) 9.50067 + 16.4556i 0.805837 + 1.39575i 0.915725 + 0.401806i \(0.131617\pi\)
−0.109888 + 0.993944i \(0.535049\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.4086 + 18.0281i −0.873467 + 1.51289i
\(143\) 0.197844 0.0165446
\(144\) 0 0
\(145\) −27.9757 −2.32326
\(146\) 2.42792 4.20528i 0.200936 0.348032i
\(147\) 0 0
\(148\) −4.71780 8.17147i −0.387801 0.671691i
\(149\) −4.85087 8.40196i −0.397399 0.688315i 0.596005 0.802981i \(-0.296754\pi\)
−0.993404 + 0.114665i \(0.963420\pi\)
\(150\) 0 0
\(151\) 6.41741 11.1153i 0.522242 0.904549i −0.477424 0.878673i \(-0.658429\pi\)
0.999665 0.0258756i \(-0.00823738\pi\)
\(152\) 9.97430 0.809023
\(153\) 0 0
\(154\) 0 0
\(155\) −12.8530 + 22.2621i −1.03238 + 1.78813i
\(156\) 0 0
\(157\) −10.4743 18.1420i −0.835937 1.44789i −0.893265 0.449531i \(-0.851591\pi\)
0.0573276 0.998355i \(-0.481742\pi\)
\(158\) 10.0416 + 17.3926i 0.798869 + 1.38368i
\(159\) 0 0
\(160\) 0.986757 1.70911i 0.0780100 0.135117i
\(161\) 0 0
\(162\) 0 0
\(163\) −11.1623 −0.874295 −0.437148 0.899390i \(-0.644011\pi\)
−0.437148 + 0.899390i \(0.644011\pi\)
\(164\) 15.2312 26.3812i 1.18936 2.06002i
\(165\) 0 0
\(166\) −14.9746 25.9368i −1.16226 2.01309i
\(167\) 1.73012 + 2.99665i 0.133880 + 0.231888i 0.925169 0.379555i \(-0.123923\pi\)
−0.791289 + 0.611443i \(0.790590\pi\)
\(168\) 0 0
\(169\) 6.38151 11.0531i 0.490886 0.850239i
\(170\) 43.7060 3.35210
\(171\) 0 0
\(172\) −9.43560 −0.719458
\(173\) −3.02680 + 5.24258i −0.230124 + 0.398586i −0.957844 0.287288i \(-0.907246\pi\)
0.727721 + 0.685874i \(0.240580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.879379 + 1.52313i 0.0662857 + 0.114810i
\(177\) 0 0
\(178\) −18.2448 + 31.6010i −1.36751 + 2.36859i
\(179\) −9.13307 −0.682638 −0.341319 0.939948i \(-0.610874\pi\)
−0.341319 + 0.939948i \(0.610874\pi\)
\(180\) 0 0
\(181\) 11.9478 0.888074 0.444037 0.896008i \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −11.7448 20.3427i −0.865841 1.49968i
\(185\) −4.25696 7.37327i −0.312978 0.542093i
\(186\) 0 0
\(187\) −0.986757 + 1.70911i −0.0721588 + 0.124983i
\(188\) 25.6065 1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) 4.57014 7.91571i 0.330683 0.572760i −0.651963 0.758251i \(-0.726054\pi\)
0.982646 + 0.185491i \(0.0593874\pi\)
\(192\) 0 0
\(193\) −8.47150 14.6731i −0.609792 1.05619i −0.991274 0.131814i \(-0.957920\pi\)
0.381483 0.924376i \(-0.375414\pi\)
\(194\) −11.6720 20.2165i −0.838003 1.45146i
\(195\) 0 0
\(196\) 0 0
\(197\) 21.3173 1.51880 0.759398 0.650627i \(-0.225494\pi\)
0.759398 + 0.650627i \(0.225494\pi\)
\(198\) 0 0
\(199\) 9.97430 0.707060 0.353530 0.935423i \(-0.384981\pi\)
0.353530 + 0.935423i \(0.384981\pi\)
\(200\) 21.1804 36.6856i 1.49768 2.59406i
\(201\) 0 0
\(202\) −10.7177 18.5635i −0.754092 1.30613i
\(203\) 0 0
\(204\) 0 0
\(205\) 13.7434 23.8042i 0.959879 1.66256i
\(206\) −19.7508 −1.37610
\(207\) 0 0
\(208\) −2.10658 −0.146065
\(209\) −0.401038 + 0.694619i −0.0277404 + 0.0480478i
\(210\) 0 0
\(211\) −2.44592 4.23645i −0.168384 0.291649i 0.769468 0.638685i \(-0.220521\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(212\) −7.23385 12.5294i −0.496823 0.860523i
\(213\) 0 0
\(214\) −15.7989 + 27.3645i −1.07999 + 1.87060i
\(215\) −8.51392 −0.580644
\(216\) 0 0
\(217\) 0 0
\(218\) 3.19961 5.54189i 0.216705 0.375344i
\(219\) 0 0
\(220\) 3.01364 + 5.21978i 0.203179 + 0.351917i
\(221\) −1.18190 2.04712i −0.0795034 0.137704i
\(222\) 0 0
\(223\) 11.7044 20.2727i 0.783786 1.35756i −0.145936 0.989294i \(-0.546619\pi\)
0.929722 0.368263i \(-0.120047\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −34.3245 −2.28323
\(227\) −3.05919 + 5.29868i −0.203046 + 0.351686i −0.949508 0.313742i \(-0.898417\pi\)
0.746463 + 0.665427i \(0.231751\pi\)
\(228\) 0 0
\(229\) −0.730195 1.26473i −0.0482526 0.0835760i 0.840890 0.541206i \(-0.182032\pi\)
−0.889143 + 0.457630i \(0.848699\pi\)
\(230\) −20.9161 36.2278i −1.37917 2.38879i
\(231\) 0 0
\(232\) −19.3260 + 33.4736i −1.26881 + 2.19765i
\(233\) 13.2484 0.867934 0.433967 0.900929i \(-0.357113\pi\)
0.433967 + 0.900929i \(0.357113\pi\)
\(234\) 0 0
\(235\) 23.1052 1.50722
\(236\) 12.4022 21.4813i 0.807316 1.39831i
\(237\) 0 0
\(238\) 0 0
\(239\) 9.69436 + 16.7911i 0.627076 + 1.08613i 0.988136 + 0.153584i \(0.0490817\pi\)
−0.361060 + 0.932543i \(0.617585\pi\)
\(240\) 0 0
\(241\) 2.52684 4.37662i 0.162768 0.281923i −0.773092 0.634294i \(-0.781291\pi\)
0.935860 + 0.352371i \(0.114624\pi\)
\(242\) 26.6591 1.71371
\(243\) 0 0
\(244\) −32.5426 −2.08333
\(245\) 0 0
\(246\) 0 0
\(247\) −0.480350 0.831990i −0.0305639 0.0529383i
\(248\) 17.7580 + 30.7578i 1.12764 + 1.95312i
\(249\) 0 0
\(250\) 15.2180 26.3584i 0.962472 1.66705i
\(251\) 15.0928 0.952647 0.476324 0.879270i \(-0.341969\pi\)
0.476324 + 0.879270i \(0.341969\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) −19.1228 + 33.1216i −1.19987 + 2.07823i
\(255\) 0 0
\(256\) 16.1804 + 28.0253i 1.01128 + 1.75158i
\(257\) −3.85592 6.67865i −0.240526 0.416603i 0.720338 0.693623i \(-0.243986\pi\)
−0.960864 + 0.277020i \(0.910653\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7.21926 −0.447720
\(261\) 0 0
\(262\) −20.9485 −1.29420
\(263\) 2.10603 3.64776i 0.129864 0.224930i −0.793760 0.608231i \(-0.791879\pi\)
0.923624 + 0.383301i \(0.125213\pi\)
\(264\) 0 0
\(265\) −6.52724 11.3055i −0.400965 0.694492i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.29893 + 12.6421i −0.445853 + 0.772240i
\(269\) 20.7507 1.26519 0.632596 0.774482i \(-0.281989\pi\)
0.632596 + 0.774482i \(0.281989\pi\)
\(270\) 0 0
\(271\) 28.4889 1.73057 0.865287 0.501276i \(-0.167136\pi\)
0.865287 + 0.501276i \(0.167136\pi\)
\(272\) 10.5067 18.1981i 0.637060 1.10342i
\(273\) 0 0
\(274\) −0.464103 0.803851i −0.0280375 0.0485624i
\(275\) 1.70321 + 2.95005i 0.102707 + 0.177895i
\(276\) 0 0
\(277\) −8.58113 + 14.8629i −0.515590 + 0.893028i 0.484246 + 0.874932i \(0.339094\pi\)
−0.999836 + 0.0180962i \(0.994239\pi\)
\(278\) 46.7529 2.80405
\(279\) 0 0
\(280\) 0 0
\(281\) 4.72140 8.17770i 0.281655 0.487841i −0.690138 0.723678i \(-0.742450\pi\)
0.971793 + 0.235837i \(0.0757833\pi\)
\(282\) 0 0
\(283\) 8.43422 + 14.6085i 0.501362 + 0.868385i 0.999999 + 0.00157378i \(0.000500949\pi\)
−0.498636 + 0.866811i \(0.666166\pi\)
\(284\) 17.1498 + 29.7043i 1.01765 + 1.76263i
\(285\) 0 0
\(286\) 0.243398 0.421578i 0.0143924 0.0249284i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.57918 0.387011
\(290\) −34.4172 + 59.6124i −2.02105 + 3.50056i
\(291\) 0 0
\(292\) −4.00040 6.92889i −0.234105 0.405483i
\(293\) 1.86143 + 3.22409i 0.108746 + 0.188353i 0.915262 0.402858i \(-0.131983\pi\)
−0.806517 + 0.591211i \(0.798650\pi\)
\(294\) 0 0
\(295\) 11.1908 19.3830i 0.651551 1.12852i
\(296\) −11.7630 −0.683712
\(297\) 0 0
\(298\) −23.8712 −1.38282
\(299\) −1.13123 + 1.95935i −0.0654209 + 0.113312i
\(300\) 0 0
\(301\) 0 0
\(302\) −15.7901 27.3492i −0.908617 1.57377i
\(303\) 0 0
\(304\) 4.27012 7.39607i 0.244908 0.424194i
\(305\) −29.3638 −1.68137
\(306\) 0 0
\(307\) −30.5691 −1.74467 −0.872335 0.488908i \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 31.6249 + 54.7759i 1.79617 + 3.11106i
\(311\) 5.21739 + 9.03678i 0.295851 + 0.512429i 0.975182 0.221403i \(-0.0710635\pi\)
−0.679332 + 0.733831i \(0.737730\pi\)
\(312\) 0 0
\(313\) −0.309930 + 0.536815i −0.0175183 + 0.0303426i −0.874652 0.484752i \(-0.838910\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(314\) −51.5440 −2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) 5.12422 8.87541i 0.287805 0.498493i −0.685481 0.728091i \(-0.740408\pi\)
0.973285 + 0.229598i \(0.0737412\pi\)
\(318\) 0 0
\(319\) −1.55408 2.69175i −0.0870120 0.150709i
\(320\) 13.4021 + 23.2132i 0.749203 + 1.29766i
\(321\) 0 0
\(322\) 0 0
\(323\) 9.58307 0.533216
\(324\) 0 0
\(325\) −4.08009 −0.226323
\(326\) −13.7324 + 23.7852i −0.760567 + 1.31734i
\(327\) 0 0
\(328\) −18.9882 32.8885i −1.04845 1.81596i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.1819 17.6356i 0.559648 0.969339i −0.437878 0.899035i \(-0.644270\pi\)
0.997526 0.0703042i \(-0.0223970\pi\)
\(332\) −49.3463 −2.70823
\(333\) 0 0
\(334\) 8.51392 0.465861
\(335\) −6.58596 + 11.4072i −0.359829 + 0.623242i
\(336\) 0 0
\(337\) 2.85594 + 4.94662i 0.155573 + 0.269460i 0.933267 0.359182i \(-0.116944\pi\)
−0.777695 + 0.628642i \(0.783611\pi\)
\(338\) −15.7017 27.1962i −0.854062 1.47928i
\(339\) 0 0
\(340\) 36.0064 62.3649i 1.95272 3.38221i
\(341\) −2.85600 −0.154661
\(342\) 0 0
\(343\) 0 0
\(344\) −5.88151 + 10.1871i −0.317110 + 0.549251i
\(345\) 0 0
\(346\) 7.44746 + 12.8994i 0.400378 + 0.693475i
\(347\) 4.44066 + 7.69145i 0.238387 + 0.412899i 0.960252 0.279136i \(-0.0900480\pi\)
−0.721865 + 0.692034i \(0.756715\pi\)
\(348\) 0 0
\(349\) −10.4874 + 18.1648i −0.561379 + 0.972337i 0.435997 + 0.899948i \(0.356396\pi\)
−0.997376 + 0.0723893i \(0.976938\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.219262 0.0116867
\(353\) −7.38268 + 12.7872i −0.392941 + 0.680593i −0.992836 0.119485i \(-0.961876\pi\)
0.599895 + 0.800078i \(0.295209\pi\)
\(354\) 0 0
\(355\) 15.4746 + 26.8028i 0.821306 + 1.42254i
\(356\) 30.0613 + 52.0677i 1.59325 + 2.75959i
\(357\) 0 0
\(358\) −11.2360 + 19.4613i −0.593840 + 1.02856i
\(359\) −7.21206 −0.380638 −0.190319 0.981722i \(-0.560952\pi\)
−0.190319 + 0.981722i \(0.560952\pi\)
\(360\) 0 0
\(361\) −15.1052 −0.795013
\(362\) 14.6988 25.4591i 0.772554 1.33810i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.60963 6.25206i −0.188937 0.327248i
\(366\) 0 0
\(367\) 5.48711 9.50396i 0.286425 0.496103i −0.686529 0.727103i \(-0.740866\pi\)
0.972954 + 0.231000i \(0.0741998\pi\)
\(368\) −20.1124 −1.04843
\(369\) 0 0
\(370\) −20.9485 −1.08906
\(371\) 0 0
\(372\) 0 0
\(373\) 0.271884 + 0.470916i 0.0140776 + 0.0243831i 0.872978 0.487759i \(-0.162185\pi\)
−0.858901 + 0.512142i \(0.828852\pi\)
\(374\) 2.42792 + 4.20528i 0.125545 + 0.217450i
\(375\) 0 0
\(376\) 15.9614 27.6459i 0.823145 1.42573i
\(377\) 3.72286 0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) 14.6337 25.3464i 0.750695 1.30024i
\(381\) 0 0
\(382\) −11.2448 19.4766i −0.575336 0.996511i
\(383\) 17.8569 + 30.9291i 0.912447 + 1.58041i 0.810596 + 0.585606i \(0.199143\pi\)
0.101851 + 0.994800i \(0.467523\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −41.6883 −2.12188
\(387\) 0 0
\(388\) −38.4632 −1.95267
\(389\) 19.3296 33.4798i 0.980048 1.69749i 0.317892 0.948127i \(-0.397025\pi\)
0.662156 0.749366i \(-0.269641\pi\)
\(390\) 0 0
\(391\) −11.2842 19.5447i −0.570664 0.988420i
\(392\) 0 0
\(393\) 0 0
\(394\) 26.2257 45.4242i 1.32123 2.28844i
\(395\) 29.8581 1.50233
\(396\) 0 0
\(397\) −11.9478 −0.599644 −0.299822 0.953995i \(-0.596927\pi\)
−0.299822 + 0.953995i \(0.596927\pi\)
\(398\) 12.2709 21.2538i 0.615085 1.06536i
\(399\) 0 0
\(400\) −18.1352 31.4111i −0.906761 1.57056i
\(401\) 16.1783 + 28.0216i 0.807906 + 1.39933i 0.914312 + 0.405011i \(0.132732\pi\)
−0.106406 + 0.994323i \(0.533934\pi\)
\(402\) 0 0
\(403\) 1.71041 2.96251i 0.0852015 0.147573i
\(404\) −35.3182 −1.75715
\(405\) 0 0
\(406\) 0 0
\(407\) 0.472958 0.819187i 0.0234437 0.0406056i
\(408\) 0 0
\(409\) −9.48751 16.4328i −0.469127 0.812552i 0.530250 0.847841i \(-0.322098\pi\)
−0.999377 + 0.0352893i \(0.988765\pi\)
\(410\) −33.8157 58.5704i −1.67004 2.89259i
\(411\) 0 0
\(412\) −16.2713 + 28.1827i −0.801630 + 1.38846i
\(413\) 0 0
\(414\) 0 0
\(415\) −44.5261 −2.18570
\(416\) −0.131312 + 0.227439i −0.00643811 + 0.0111511i
\(417\) 0 0
\(418\) 0.986757 + 1.70911i 0.0482639 + 0.0835955i
\(419\) −8.64523 14.9740i −0.422347 0.731526i 0.573822 0.818980i \(-0.305460\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(420\) 0 0
\(421\) −9.30039 + 16.1087i −0.453273 + 0.785092i −0.998587 0.0531397i \(-0.983077\pi\)
0.545314 + 0.838232i \(0.316410\pi\)
\(422\) −12.0364 −0.585922
\(423\) 0 0
\(424\) −18.0364 −0.875924
\(425\) 20.3496 35.2466i 0.987103 1.70971i
\(426\) 0 0
\(427\) 0 0
\(428\) 26.0313 + 45.0876i 1.25827 + 2.17939i
\(429\) 0 0
\(430\) −10.4743 + 18.1420i −0.505114 + 0.874883i
\(431\) 15.8784 0.764835 0.382418 0.923990i \(-0.375092\pi\)
0.382418 + 0.923990i \(0.375092\pi\)
\(432\) 0 0
\(433\) 40.4367 1.94326 0.971631 0.236501i \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.27188 9.13117i −0.252477 0.437304i
\(437\) −4.58611 7.94338i −0.219384 0.379984i
\(438\) 0 0
\(439\) −6.23047 + 10.7915i −0.297364 + 0.515050i −0.975532 0.219857i \(-0.929441\pi\)
0.678168 + 0.734907i \(0.262774\pi\)
\(440\) 7.51399 0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) −4.11537 + 7.12802i −0.195527 + 0.338663i −0.947073 0.321018i \(-0.895975\pi\)
0.751546 + 0.659680i \(0.229308\pi\)
\(444\) 0 0
\(445\) 27.1249 + 46.9817i 1.28584 + 2.22715i
\(446\) −28.7988 49.8810i −1.36366 2.36193i
\(447\) 0 0
\(448\) 0 0
\(449\) −5.64474 −0.266392 −0.133196 0.991090i \(-0.542524\pi\)
−0.133196 + 0.991090i \(0.542524\pi\)
\(450\) 0 0
\(451\) 3.05384 0.143800
\(452\) −28.2776 + 48.9783i −1.33007 + 2.30374i
\(453\) 0 0
\(454\) 7.52716 + 13.0374i 0.353267 + 0.611876i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.53443 + 4.38977i −0.118556 + 0.205345i −0.919196 0.393801i \(-0.871160\pi\)
0.800640 + 0.599146i \(0.204493\pi\)
\(458\) −3.59330 −0.167904
\(459\) 0 0
\(460\) −68.9255 −3.21367
\(461\) −3.88831 + 6.73475i −0.181097 + 0.313669i −0.942254 0.334898i \(-0.891298\pi\)
0.761158 + 0.648567i \(0.224631\pi\)
\(462\) 0 0
\(463\) 4.58998 + 7.95008i 0.213314 + 0.369472i 0.952750 0.303756i \(-0.0982408\pi\)
−0.739435 + 0.673228i \(0.764907\pi\)
\(464\) 16.5474 + 28.6609i 0.768192 + 1.33055i
\(465\) 0 0
\(466\) 16.2989 28.2306i 0.755033 1.30776i
\(467\) 13.7654 0.636989 0.318494 0.947925i \(-0.396823\pi\)
0.318494 + 0.947925i \(0.396823\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 28.4253 49.2340i 1.31116 2.27100i
\(471\) 0 0
\(472\) −15.4614 26.7800i −0.711669 1.23265i
\(473\) −0.472958 0.819187i −0.0217466 0.0376663i
\(474\) 0 0
\(475\) 8.27052 14.3250i 0.379477 0.657274i
\(476\) 0 0
\(477\) 0 0
\(478\) 47.7060 2.18202
\(479\) 4.35588 7.54461i 0.199025 0.344722i −0.749187 0.662358i \(-0.769556\pi\)
0.948213 + 0.317636i \(0.102889\pi\)
\(480\) 0 0
\(481\) 0.566492 + 0.981194i 0.0258298 + 0.0447386i
\(482\) −6.21731 10.7687i −0.283191 0.490501i
\(483\) 0 0
\(484\) 21.9626 38.0404i 0.998302 1.72911i
\(485\) −34.7060 −1.57592
\(486\) 0 0
\(487\) −18.0364 −0.817306 −0.408653 0.912690i \(-0.634001\pi\)
−0.408653 + 0.912690i \(0.634001\pi\)
\(488\) −20.2849 + 35.1344i −0.918253 + 1.59046i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.02344 + 1.77266i 0.0461874 + 0.0799989i 0.888195 0.459467i \(-0.151960\pi\)
−0.842007 + 0.539466i \(0.818626\pi\)
\(492\) 0 0
\(493\) −18.5679 + 32.1606i −0.836257 + 1.44844i
\(494\) −2.36381 −0.106353
\(495\) 0 0
\(496\) 30.4097 1.36544
\(497\) 0 0
\(498\) 0 0
\(499\) 19.5438 + 33.8508i 0.874899 + 1.51537i 0.856870 + 0.515532i \(0.172406\pi\)
0.0180291 + 0.999837i \(0.494261\pi\)
\(500\) −25.0742 43.4297i −1.12135 1.94224i
\(501\) 0 0
\(502\) 18.5679 32.1606i 0.828727 1.43540i
\(503\) −5.11846 −0.228221 −0.114111 0.993468i \(-0.536402\pi\)
−0.114111 + 0.993468i \(0.536402\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) 2.32383 4.02499i 0.103307 0.178933i
\(507\) 0 0
\(508\) 31.5079 + 54.5732i 1.39794 + 2.42130i
\(509\) −14.7636 25.5713i −0.654386 1.13343i −0.982047 0.188634i \(-0.939594\pi\)
0.327662 0.944795i \(-0.393739\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 41.4078 1.82998
\(513\) 0 0
\(514\) −18.9750 −0.836952
\(515\) −14.6819 + 25.4298i −0.646962 + 1.12057i
\(516\) 0 0
\(517\) 1.28352 + 2.22313i 0.0564493 + 0.0977730i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.50000 + 7.79423i −0.197338 + 0.341800i
\(521\) −1.06470 −0.0466454 −0.0233227 0.999728i \(-0.507425\pi\)
−0.0233227 + 0.999728i \(0.507425\pi\)
\(522\) 0 0
\(523\) 13.3819 0.585149 0.292574 0.956243i \(-0.405488\pi\)
0.292574 + 0.956243i \(0.405488\pi\)
\(524\) −17.2581 + 29.8918i −0.753922 + 1.30583i
\(525\) 0 0
\(526\) −5.18190 8.97532i −0.225942 0.391343i
\(527\) 17.0615 + 29.5513i 0.743210 + 1.28728i
\(528\) 0 0
\(529\) 0.699612 1.21176i 0.0304179 0.0526853i
\(530\) −32.1206 −1.39523
\(531\) 0 0
\(532\) 0 0
\(533\) −1.82889 + 3.16774i −0.0792181 + 0.137210i
\(534\) 0 0
\(535\) 23.4885 + 40.6833i 1.01550 + 1.75889i
\(536\) 9.09931 + 15.7605i 0.393031 + 0.680749i
\(537\) 0 0
\(538\) 25.5286 44.2168i 1.10062 1.90632i
\(539\) 0 0
\(540\) 0 0
\(541\) −34.0875 −1.46554 −0.732769 0.680478i \(-0.761772\pi\)
−0.732769 + 0.680478i \(0.761772\pi\)
\(542\) 35.0485 60.7058i 1.50546 2.60754i
\(543\) 0 0
\(544\) −1.30985 2.26873i −0.0561594 0.0972709i
\(545\) −4.75692 8.23922i −0.203764 0.352930i
\(546\) 0 0
\(547\) 2.97150 5.14678i 0.127052 0.220060i −0.795481 0.605978i \(-0.792782\pi\)
0.922533 + 0.385918i \(0.126115\pi\)
\(548\) −1.52937 −0.0653316
\(549\) 0 0
\(550\) 8.38151 0.357389
\(551\) −7.54638 + 13.0707i −0.321487 + 0.556831i
\(552\) 0 0
\(553\) 0 0
\(554\) 21.1139 + 36.5704i 0.897044 + 1.55373i
\(555\) 0 0
\(556\) 38.5165 66.7126i 1.63346 2.82924i
\(557\) 30.0803 1.27454 0.637272 0.770639i \(-0.280063\pi\)
0.637272 + 0.770639i \(0.280063\pi\)
\(558\) 0 0
\(559\) 1.13298 0.0479202
\(560\) 0 0
\(561\) 0 0
\(562\) −11.6170 20.1213i −0.490035 0.848765i
\(563\) 9.81060 + 16.9925i 0.413468 + 0.716147i 0.995266 0.0971860i \(-0.0309842\pi\)
−0.581799 + 0.813333i \(0.697651\pi\)
\(564\) 0 0
\(565\) −25.5154 + 44.1940i −1.07344 + 1.85926i
\(566\) 41.5049 1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) −0.687159 + 1.19019i −0.0288072 + 0.0498955i −0.880070 0.474845i \(-0.842504\pi\)
0.851262 + 0.524740i \(0.175838\pi\)
\(570\) 0 0
\(571\) −8.69076 15.0528i −0.363697 0.629941i 0.624869 0.780729i \(-0.285152\pi\)
−0.988566 + 0.150788i \(0.951819\pi\)
\(572\) −0.401038 0.694619i −0.0167683 0.0290435i
\(573\) 0 0
\(574\) 0 0
\(575\) −38.9545 −1.62451
\(576\) 0 0
\(577\) 27.0548 1.12631 0.563153 0.826353i \(-0.309588\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(578\) 8.09406 14.0193i 0.336668 0.583127i
\(579\) 0 0
\(580\) 56.7080 + 98.2211i 2.35467 + 4.07841i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.725191 1.25607i 0.0300344 0.0520210i
\(584\) −9.97430 −0.412740
\(585\) 0 0
\(586\) 9.16010 0.378400
\(587\) −3.75700 + 6.50731i −0.155068 + 0.268585i −0.933084 0.359659i \(-0.882893\pi\)
0.778016 + 0.628245i \(0.216226\pi\)
\(588\) 0 0
\(589\) 6.93414 + 12.0103i 0.285716 + 0.494875i
\(590\) −27.5349 47.6919i −1.13359 1.96344i
\(591\) 0 0
\(592\) −5.03590 + 8.72243i −0.206974 + 0.358490i
\(593\) 35.5808 1.46113 0.730565 0.682843i \(-0.239257\pi\)
0.730565 + 0.682843i \(0.239257\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −19.6659 + 34.0623i −0.805545 + 1.39524i
\(597\) 0 0
\(598\) 2.78340 + 4.82100i 0.113822 + 0.197145i
\(599\) −5.74105 9.94379i −0.234573 0.406292i 0.724576 0.689195i \(-0.242036\pi\)
−0.959148 + 0.282903i \(0.908702\pi\)
\(600\) 0 0
\(601\) −0.190030 + 0.329142i −0.00775150 + 0.0134260i −0.869875 0.493272i \(-0.835801\pi\)
0.862124 + 0.506698i \(0.169134\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −52.0335 −2.11721
\(605\) 19.8173 34.3246i 0.805688 1.39549i
\(606\) 0 0
\(607\) −9.27044 16.0569i −0.376275 0.651728i 0.614242 0.789118i \(-0.289462\pi\)
−0.990517 + 0.137390i \(0.956129\pi\)
\(608\) −0.532351 0.922058i −0.0215897 0.0373944i
\(609\) 0 0
\(610\) −36.1249 + 62.5702i −1.46265 + 2.53339i
\(611\) −3.07472 −0.124390
\(612\) 0 0
\(613\) 7.32451 0.295834 0.147917 0.989000i \(-0.452743\pi\)
0.147917 + 0.989000i \(0.452743\pi\)
\(614\) −37.6077 + 65.1385i −1.51772 + 2.62877i
\(615\) 0 0
\(616\) 0 0
\(617\) −12.7427 22.0710i −0.513002 0.888546i −0.999886 0.0150791i \(-0.995200\pi\)
0.486884 0.873466i \(-0.338133\pi\)
\(618\) 0 0
\(619\) 16.4482 28.4891i 0.661108 1.14507i −0.319217 0.947682i \(-0.603420\pi\)
0.980325 0.197391i \(-0.0632468\pi\)
\(620\) 104.214 4.18535
\(621\) 0 0
\(622\) 25.6748 1.02947
\(623\) 0 0
\(624\) 0 0
\(625\) −1.67111 2.89444i −0.0668443 0.115778i
\(626\) 0.762585 + 1.32084i 0.0304790 + 0.0527912i
\(627\) 0 0
\(628\) −42.4636 + 73.5490i −1.69448 + 2.93493i
\(629\) −11.3016 −0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) 20.6264 35.7259i 0.820472 1.42110i
\(633\) 0 0
\(634\) −12.6082 21.8380i −0.500734 0.867297i
\(635\) 28.4301 + 49.2424i 1.12822 + 1.95413i
\(636\) 0 0
\(637\) 0 0
\(638\) −7.64766 −0.302774
\(639\) 0 0
\(640\) 69.8991 2.76301
\(641\) 5.73025 9.92509i 0.226331 0.392017i −0.730387 0.683034i \(-0.760660\pi\)
0.956718 + 0.291016i \(0.0939934\pi\)
\(642\) 0 0
\(643\) −8.69078 15.0529i −0.342731 0.593627i 0.642208 0.766531i \(-0.278019\pi\)
−0.984939 + 0.172903i \(0.944685\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.7896 20.4202i 0.463855 0.803421i
\(647\) 25.3439 0.996372 0.498186 0.867070i \(-0.334000\pi\)
0.498186 + 0.867070i \(0.334000\pi\)
\(648\) 0 0
\(649\) 2.48664 0.0976091
\(650\) −5.01954 + 8.69410i −0.196883 + 0.341011i
\(651\) 0 0
\(652\) 22.6264 + 39.1900i 0.886116 + 1.53480i
\(653\) 7.04163 + 12.1965i 0.275560 + 0.477284i 0.970276 0.242000i \(-0.0778033\pi\)
−0.694716 + 0.719284i \(0.744470\pi\)
\(654\) 0 0
\(655\) −15.5723 + 26.9720i −0.608459 + 1.05388i
\(656\) −32.5163 −1.26955
\(657\) 0 0
\(658\) 0 0
\(659\) 19.0854 33.0569i 0.743462 1.28771i −0.207449 0.978246i \(-0.566516\pi\)
0.950910 0.309467i \(-0.100151\pi\)
\(660\) 0 0
\(661\) −0.176866 0.306341i −0.00687930 0.0119153i 0.862565 0.505946i \(-0.168856\pi\)
−0.869445 + 0.494031i \(0.835523\pi\)
\(662\) −25.0526 43.3924i −0.973698 1.68649i
\(663\) 0 0
\(664\) −30.7591 + 53.2764i −1.19369 + 2.06752i
\(665\) 0 0
\(666\) 0 0
\(667\) 35.5438 1.37626
\(668\) 7.01403 12.1487i 0.271381 0.470046i
\(669\) 0 0
\(670\) 16.2048 + 28.0675i 0.626045 + 1.08434i
\(671\) −1.63119 2.82531i −0.0629715 0.109070i
\(672\) 0 0
\(673\) 10.5555 18.2827i 0.406886 0.704748i −0.587653 0.809113i \(-0.699948\pi\)
0.994539 + 0.104365i \(0.0332811\pi\)
\(674\) 14.0541 0.541343
\(675\) 0 0
\(676\) −51.7424 −1.99009
\(677\) −10.5732 + 18.3133i −0.406361 + 0.703837i −0.994479 0.104938i \(-0.966536\pi\)
0.588118 + 0.808775i \(0.299869\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −44.8879 77.7482i −1.72137 2.98151i
\(681\) 0 0
\(682\) −3.51360 + 6.08573i −0.134543 + 0.233035i
\(683\) −34.7716 −1.33050 −0.665249 0.746622i \(-0.731674\pi\)
−0.665249 + 0.746622i \(0.731674\pi\)
\(684\) 0 0
\(685\) −1.37998 −0.0527264
\(686\) 0 0
\(687\) 0 0
\(688\) 5.03590 + 8.72243i 0.191992 + 0.332539i
\(689\) 0.868609 + 1.50447i 0.0330914 + 0.0573159i
\(690\) 0 0
\(691\) 17.3246 30.0071i 0.659059 1.14152i −0.321801 0.946807i \(-0.604288\pi\)
0.980860 0.194716i \(-0.0623785\pi\)
\(692\) 24.5418 0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) 34.7542 60.1960i 1.31830 2.28336i
\(696\) 0 0
\(697\) −18.2434 31.5985i −0.691017 1.19688i
\(698\) 25.8044 + 44.6945i 0.976710 + 1.69171i
\(699\) 0 0
\(700\) 0 0
\(701\) 48.6050 1.83579 0.917894 0.396826i \(-0.129889\pi\)
0.917894 + 0.396826i \(0.129889\pi\)
\(702\) 0 0
\(703\) −4.59322 −0.173236
\(704\) −1.48901 + 2.57904i −0.0561192 + 0.0972012i
\(705\) 0 0
\(706\) 18.1651 + 31.4629i 0.683654 + 1.18412i
\(707\) 0 0
\(708\) 0 0
\(709\) −2.05408 + 3.55778i −0.0771428 + 0.133615i −0.902016 0.431702i \(-0.857913\pi\)
0.824873 + 0.565318i \(0.191246\pi\)
\(710\) 76.1506 2.85788
\(711\) 0 0
\(712\) 74.9528 2.80898
\(713\) 16.3300 28.2844i 0.611564 1.05926i
\(714\) 0 0
\(715\) −0.361864 0.626767i −0.0135330 0.0234398i
\(716\) 18.5131 + 32.0657i 0.691868 + 1.19835i
\(717\) 0 0
\(718\) −8.87266 + 15.3679i −0.331125 + 0.573525i
\(719\) 48.2816 1.80060 0.900299 0.435271i \(-0.143347\pi\)
0.900299 + 0.435271i \(0.143347\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −18.5833 + 32.1872i −0.691597 + 1.19788i
\(723\) 0 0
\(724\) −24.2187 41.9481i −0.900082 1.55899i
\(725\) 32.0495 + 55.5114i 1.19029 + 2.06164i
\(726\) 0 0
\(727\) −20.5151 + 35.5332i −0.760863 + 1.31785i 0.181543 + 0.983383i \(0.441891\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −17.7630 −0.657439
\(731\) −5.65082 + 9.78750i −0.209003 + 0.362004i
\(732\) 0 0
\(733\) 15.2714 + 26.4508i 0.564062 + 0.976983i 0.997136 + 0.0756253i \(0.0240953\pi\)
−0.433075 + 0.901358i \(0.642571\pi\)
\(734\) −13.5011 23.3845i −0.498334 0.863139i
\(735\) 0 0
\(736\) −1.25370 + 2.17147i −0.0462118 + 0.0800413i
\(737\) −1.46343 −0.0539061
\(738\) 0 0
\(739\) 23.8200 0.876234 0.438117 0.898918i \(-0.355646\pi\)
0.438117 + 0.898918i \(0.355646\pi\)
\(740\) −17.2581 + 29.8918i −0.634419 + 1.09885i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.26089 + 9.11213i 0.193003 + 0.334292i 0.946244 0.323453i \(-0.104844\pi\)
−0.753241 + 0.657745i \(0.771510\pi\)
\(744\) 0 0
\(745\) −17.7449 + 30.7350i −0.650121 + 1.12604i
\(746\) 1.33794 0.0489855
\(747\) 0 0
\(748\) 8.00079 0.292538
\(749\) 0 0
\(750\) 0 0
\(751\) 5.13521 + 8.89445i 0.187386 + 0.324563i 0.944378 0.328862i \(-0.106665\pi\)
−0.756992 + 0.653425i \(0.773332\pi\)
\(752\) −13.6665 23.6711i −0.498367 0.863197i
\(753\) 0 0
\(754\) 4.58005 7.93288i 0.166796 0.288899i
\(755\) −46.9507 −1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) −27.9159 + 48.3518i −1.01395 + 1.75622i
\(759\) 0 0
\(760\) −18.2434 31.5985i −0.661757 1.14620i
\(761\) −13.8302 23.9547i −0.501345 0.868355i −0.999999 0.00155404i \(-0.999505\pi\)
0.498654 0.866801i \(-0.333828\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −37.0554 −1.34062
\(765\) 0 0
\(766\) 87.8742 3.17502
\(767\) −1.48920 + 2.57938i −0.0537720 + 0.0931359i
\(768\) 0 0
\(769\) −16.9613 29.3778i −0.611640 1.05939i −0.990964 0.134128i \(-0.957177\pi\)
0.379324 0.925264i \(-0.376157\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −34.3442 + 59.4858i −1.23607 + 2.14094i
\(773\) −28.5956 −1.02851 −0.514256 0.857637i \(-0.671932\pi\)
−0.514256 + 0.857637i \(0.671932\pi\)
\(774\) 0 0
\(775\) 58.8986 2.11570
\(776\) −23.9753 + 41.5265i −0.860664 + 1.49071i
\(777\) 0 0
\(778\) −47.5605 82.3772i −1.70513 2.95337i
\(779\) −7.41449 12.8423i −0.265652 0.460122i
\(780\) 0 0
\(781\) −1.71926 + 2.97785i −0.0615200 + 0.106556i
\(782\) −55.5294 −1.98573
\(783\) 0 0
\(784\) 0 0
\(785\) −38.3157 + 66.3647i −1.36754 + 2.36866i
\(786\) 0 0
\(787\) 23.0017 + 39.8402i 0.819923 + 1.42015i 0.905738 + 0.423838i \(0.139317\pi\)
−0.0858145 + 0.996311i \(0.527349\pi\)
\(788\) −43.2111 74.8438i −1.53933 2.66620i
\(789\) 0 0
\(790\) 36.7330 63.6235i 1.30690 2.26362i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.90757 0.138762
\(794\) −14.6988 + 25.4591i −0.521642 + 0.903511i
\(795\) 0