Properties

Label 1008.2.r.l.673.2
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.2091141441.1
Defining polynomial: \(x^{8} - x^{7} + x^{6} + 3 x^{5} - 15 x^{4} + 9 x^{3} + 9 x^{2} - 27 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(1.65525 + 0.510048i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.l.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.385911 - 1.68851i) q^{3} +(1.15525 + 2.00095i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.70215 + 1.30323i) q^{9} +O(q^{10})\) \(q+(-0.385911 - 1.68851i) q^{3} +(1.15525 + 2.00095i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.70215 + 1.30323i) q^{9} +(0.655250 - 1.13493i) q^{11} +(1.93281 + 3.34772i) q^{13} +(2.93281 - 2.72284i) q^{15} -0.326936 q^{17} -3.08232 q^{19} +(1.65525 + 0.510048i) q^{21} +(1.81872 + 3.15011i) q^{23} +(-0.169204 + 0.293069i) q^{25} +(3.24331 + 4.05968i) q^{27} +(-4.75152 + 8.22988i) q^{29} +(3.24904 + 5.62751i) q^{31} +(-2.16920 - 0.668417i) q^{33} -2.31050 q^{35} -2.31050 q^{37} +(4.90677 - 4.55549i) q^{39} +(4.74904 + 8.22558i) q^{41} +(0.0493786 - 0.0855263i) q^{43} +(-5.72935 - 3.90131i) q^{45} +(0.108354 - 0.187674i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.126168 + 0.552035i) q^{51} +13.7921 q^{53} +3.02791 q^{55} +(1.18950 + 5.20454i) q^{57} +(-1.22493 - 2.12163i) q^{59} +(7.68433 - 13.3097i) q^{61} +(0.222443 - 2.99174i) q^{63} +(-4.46575 + 7.73490i) q^{65} +(-2.93529 - 5.08407i) q^{67} +(4.61714 - 4.28659i) q^{69} +1.77182 q^{71} -5.99504 q^{73} +(0.560149 + 0.172604i) q^{75} +(0.655250 + 1.13493i) q^{77} +(-7.29594 + 12.6369i) q^{79} +(5.60318 - 7.04303i) q^{81} +(-3.04116 + 5.26744i) q^{83} +(-0.377692 - 0.654183i) q^{85} +(15.7299 + 4.84701i) q^{87} +5.52224 q^{89} -3.86561 q^{91} +(8.24827 - 7.65776i) q^{93} +(-3.56085 - 6.16757i) q^{95} +(2.99178 - 5.18192i) q^{97} +(-0.291511 + 3.92068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} - 7q^{11} + 3q^{13} + 11q^{15} + 6q^{17} + 8q^{19} + q^{21} - 2q^{23} - 5q^{25} - 11q^{27} - 9q^{29} - 3q^{31} - 21q^{33} + 6q^{35} + 6q^{37} - 2q^{39} + 9q^{41} - 8q^{43} + 7q^{45} - 3q^{47} - 4q^{49} + 18q^{51} + 12q^{53} + 56q^{55} + 34q^{57} - 10q^{59} + 20q^{61} + 2q^{63} + q^{65} - 11q^{67} - 17q^{69} + 6q^{71} - 48q^{73} - 52q^{75} - 7q^{77} - 21q^{79} - 25q^{81} - 8q^{83} + 9q^{85} + 15q^{87} + 12q^{89} - 6q^{91} + 29q^{93} - 36q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) −0.385911 1.68851i −0.222806 0.974863i
\(4\) 0 0
\(5\) 1.15525 + 2.00095i 0.516643 + 0.894853i 0.999813 + 0.0193259i \(0.00615202\pi\)
−0.483170 + 0.875527i \(0.660515\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) −2.70215 + 1.30323i −0.900715 + 0.434410i
\(10\) 0 0
\(11\) 0.655250 1.13493i 0.197565 0.342193i −0.750173 0.661241i \(-0.770030\pi\)
0.947738 + 0.319048i \(0.103363\pi\)
\(12\) 0 0
\(13\) 1.93281 + 3.34772i 0.536064 + 0.928490i 0.999111 + 0.0421566i \(0.0134228\pi\)
−0.463047 + 0.886334i \(0.653244\pi\)
\(14\) 0 0
\(15\) 2.93281 2.72284i 0.757247 0.703035i
\(16\) 0 0
\(17\) −0.326936 −0.0792936 −0.0396468 0.999214i \(-0.512623\pi\)
−0.0396468 + 0.999214i \(0.512623\pi\)
\(18\) 0 0
\(19\) −3.08232 −0.707133 −0.353566 0.935409i \(-0.615031\pi\)
−0.353566 + 0.935409i \(0.615031\pi\)
\(20\) 0 0
\(21\) 1.65525 + 0.510048i 0.361205 + 0.111301i
\(22\) 0 0
\(23\) 1.81872 + 3.15011i 0.379229 + 0.656844i 0.990950 0.134230i \(-0.0428560\pi\)
−0.611721 + 0.791073i \(0.709523\pi\)
\(24\) 0 0
\(25\) −0.169204 + 0.293069i −0.0338407 + 0.0586139i
\(26\) 0 0
\(27\) 3.24331 + 4.05968i 0.624175 + 0.781285i
\(28\) 0 0
\(29\) −4.75152 + 8.22988i −0.882336 + 1.52825i −0.0335990 + 0.999435i \(0.510697\pi\)
−0.848737 + 0.528815i \(0.822636\pi\)
\(30\) 0 0
\(31\) 3.24904 + 5.62751i 0.583545 + 1.01073i 0.995055 + 0.0993246i \(0.0316682\pi\)
−0.411510 + 0.911405i \(0.634998\pi\)
\(32\) 0 0
\(33\) −2.16920 0.668417i −0.377610 0.116356i
\(34\) 0 0
\(35\) −2.31050 −0.390546
\(36\) 0 0
\(37\) −2.31050 −0.379844 −0.189922 0.981799i \(-0.560823\pi\)
−0.189922 + 0.981799i \(0.560823\pi\)
\(38\) 0 0
\(39\) 4.90677 4.55549i 0.785713 0.729462i
\(40\) 0 0
\(41\) 4.74904 + 8.22558i 0.741676 + 1.28462i 0.951732 + 0.306931i \(0.0993020\pi\)
−0.210056 + 0.977689i \(0.567365\pi\)
\(42\) 0 0
\(43\) 0.0493786 0.0855263i 0.00753017 0.0130426i −0.862236 0.506507i \(-0.830936\pi\)
0.869766 + 0.493465i \(0.164270\pi\)
\(44\) 0 0
\(45\) −5.72935 3.90131i −0.854081 0.581572i
\(46\) 0 0
\(47\) 0.108354 0.187674i 0.0158050 0.0273750i −0.858015 0.513625i \(-0.828302\pi\)
0.873820 + 0.486250i \(0.161636\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 0.126168 + 0.552035i 0.0176671 + 0.0773004i
\(52\) 0 0
\(53\) 13.7921 1.89450 0.947249 0.320500i \(-0.103851\pi\)
0.947249 + 0.320500i \(0.103851\pi\)
\(54\) 0 0
\(55\) 3.02791 0.408283
\(56\) 0 0
\(57\) 1.18950 + 5.20454i 0.157553 + 0.689358i
\(58\) 0 0
\(59\) −1.22493 2.12163i −0.159472 0.276213i 0.775207 0.631708i \(-0.217646\pi\)
−0.934678 + 0.355495i \(0.884312\pi\)
\(60\) 0 0
\(61\) 7.68433 13.3097i 0.983878 1.70413i 0.337057 0.941484i \(-0.390568\pi\)
0.646821 0.762642i \(-0.276098\pi\)
\(62\) 0 0
\(63\) 0.222443 2.99174i 0.0280252 0.376924i
\(64\) 0 0
\(65\) −4.46575 + 7.73490i −0.553908 + 0.959397i
\(66\) 0 0
\(67\) −2.93529 5.08407i −0.358603 0.621118i 0.629125 0.777304i \(-0.283413\pi\)
−0.987728 + 0.156186i \(0.950080\pi\)
\(68\) 0 0
\(69\) 4.61714 4.28659i 0.555838 0.516045i
\(70\) 0 0
\(71\) 1.77182 0.210277 0.105138 0.994458i \(-0.466471\pi\)
0.105138 + 0.994458i \(0.466471\pi\)
\(72\) 0 0
\(73\) −5.99504 −0.701666 −0.350833 0.936438i \(-0.614101\pi\)
−0.350833 + 0.936438i \(0.614101\pi\)
\(74\) 0 0
\(75\) 0.560149 + 0.172604i 0.0646804 + 0.0199306i
\(76\) 0 0
\(77\) 0.655250 + 1.13493i 0.0746726 + 0.129337i
\(78\) 0 0
\(79\) −7.29594 + 12.6369i −0.820857 + 1.42177i 0.0841876 + 0.996450i \(0.473171\pi\)
−0.905045 + 0.425316i \(0.860163\pi\)
\(80\) 0 0
\(81\) 5.60318 7.04303i 0.622576 0.782559i
\(82\) 0 0
\(83\) −3.04116 + 5.26744i −0.333811 + 0.578177i −0.983256 0.182231i \(-0.941668\pi\)
0.649445 + 0.760409i \(0.275001\pi\)
\(84\) 0 0
\(85\) −0.377692 0.654183i −0.0409665 0.0709561i
\(86\) 0 0
\(87\) 15.7299 + 4.84701i 1.68642 + 0.519654i
\(88\) 0 0
\(89\) 5.52224 0.585356 0.292678 0.956211i \(-0.405454\pi\)
0.292678 + 0.956211i \(0.405454\pi\)
\(90\) 0 0
\(91\) −3.86561 −0.405226
\(92\) 0 0
\(93\) 8.24827 7.65776i 0.855306 0.794073i
\(94\) 0 0
\(95\) −3.56085 6.16757i −0.365336 0.632780i
\(96\) 0 0
\(97\) 2.99178 5.18192i 0.303769 0.526144i −0.673217 0.739445i \(-0.735088\pi\)
0.976987 + 0.213301i \(0.0684214\pi\)
\(98\) 0 0
\(99\) −0.291511 + 3.92068i −0.0292980 + 0.394043i
\(100\) 0 0
\(101\) 3.85105 6.67022i 0.383194 0.663712i −0.608323 0.793690i \(-0.708157\pi\)
0.991517 + 0.129978i \(0.0414907\pi\)
\(102\) 0 0
\(103\) 2.03046 + 3.51686i 0.200067 + 0.346526i 0.948550 0.316628i \(-0.102551\pi\)
−0.748483 + 0.663154i \(0.769217\pi\)
\(104\) 0 0
\(105\) 0.891646 + 3.90131i 0.0870158 + 0.380728i
\(106\) 0 0
\(107\) 14.0774 1.36091 0.680455 0.732790i \(-0.261782\pi\)
0.680455 + 0.732790i \(0.261782\pi\)
\(108\) 0 0
\(109\) −6.67306 −0.639164 −0.319582 0.947559i \(-0.603542\pi\)
−0.319582 + 0.947559i \(0.603542\pi\)
\(110\) 0 0
\(111\) 0.891646 + 3.90131i 0.0846313 + 0.370296i
\(112\) 0 0
\(113\) 3.84918 + 6.66697i 0.362100 + 0.627176i 0.988306 0.152482i \(-0.0487265\pi\)
−0.626206 + 0.779658i \(0.715393\pi\)
\(114\) 0 0
\(115\) −4.20215 + 7.27833i −0.391852 + 0.678708i
\(116\) 0 0
\(117\) −9.58557 6.52714i −0.886187 0.603434i
\(118\) 0 0
\(119\) 0.163468 0.283135i 0.0149851 0.0259549i
\(120\) 0 0
\(121\) 4.64130 + 8.03896i 0.421936 + 0.730815i
\(122\) 0 0
\(123\) 12.0563 11.1932i 1.08708 1.00925i
\(124\) 0 0
\(125\) 10.7706 0.963352
\(126\) 0 0
\(127\) −14.9847 −1.32968 −0.664838 0.746987i \(-0.731500\pi\)
−0.664838 + 0.746987i \(0.731500\pi\)
\(128\) 0 0
\(129\) −0.163468 0.0503709i −0.0143925 0.00443491i
\(130\) 0 0
\(131\) 5.20788 + 9.02032i 0.455015 + 0.788109i 0.998689 0.0511876i \(-0.0163007\pi\)
−0.543674 + 0.839296i \(0.682967\pi\)
\(132\) 0 0
\(133\) 1.54116 2.66937i 0.133636 0.231464i
\(134\) 0 0
\(135\) −4.37638 + 11.1796i −0.376659 + 0.962190i
\(136\) 0 0
\(137\) −3.13170 + 5.42426i −0.267559 + 0.463426i −0.968231 0.250058i \(-0.919550\pi\)
0.700672 + 0.713484i \(0.252884\pi\)
\(138\) 0 0
\(139\) −10.0798 17.4588i −0.854961 1.48084i −0.876681 0.481071i \(-0.840248\pi\)
0.0217207 0.999764i \(-0.493086\pi\)
\(140\) 0 0
\(141\) −0.358704 0.110531i −0.0302084 0.00930838i
\(142\) 0 0
\(143\) 5.06588 0.423631
\(144\) 0 0
\(145\) −21.9568 −1.82341
\(146\) 0 0
\(147\) −1.26934 + 1.17846i −0.104693 + 0.0971981i
\(148\) 0 0
\(149\) −8.50878 14.7376i −0.697067 1.20736i −0.969479 0.245174i \(-0.921155\pi\)
0.272412 0.962181i \(-0.412179\pi\)
\(150\) 0 0
\(151\) −8.19641 + 14.1966i −0.667014 + 1.15530i 0.311721 + 0.950174i \(0.399095\pi\)
−0.978735 + 0.205129i \(0.934239\pi\)
\(152\) 0 0
\(153\) 0.883428 0.426072i 0.0714209 0.0344459i
\(154\) 0 0
\(155\) −7.50691 + 13.0023i −0.602969 + 1.04437i
\(156\) 0 0
\(157\) −10.2274 17.7144i −0.816238 1.41377i −0.908435 0.418025i \(-0.862722\pi\)
0.0921971 0.995741i \(-0.470611\pi\)
\(158\) 0 0
\(159\) −5.32254 23.2882i −0.422105 1.84687i
\(160\) 0 0
\(161\) −3.63744 −0.286670
\(162\) 0 0
\(163\) −16.8810 −1.32222 −0.661110 0.750289i \(-0.729914\pi\)
−0.661110 + 0.750289i \(0.729914\pi\)
\(164\) 0 0
\(165\) −1.16850 5.11266i −0.0909678 0.398020i
\(166\) 0 0
\(167\) −1.60587 2.78145i −0.124266 0.215235i 0.797180 0.603742i \(-0.206324\pi\)
−0.921446 + 0.388507i \(0.872991\pi\)
\(168\) 0 0
\(169\) −0.971485 + 1.68266i −0.0747296 + 0.129435i
\(170\) 0 0
\(171\) 8.32888 4.01697i 0.636925 0.307186i
\(172\) 0 0
\(173\) −0.306072 + 0.530133i −0.0232703 + 0.0403053i −0.877426 0.479712i \(-0.840741\pi\)
0.854156 + 0.520017i \(0.174074\pi\)
\(174\) 0 0
\(175\) −0.169204 0.293069i −0.0127906 0.0221540i
\(176\) 0 0
\(177\) −3.10969 + 2.88706i −0.233739 + 0.217005i
\(178\) 0 0
\(179\) −4.38135 −0.327477 −0.163739 0.986504i \(-0.552355\pi\)
−0.163739 + 0.986504i \(0.552355\pi\)
\(180\) 0 0
\(181\) −3.50192 −0.260295 −0.130148 0.991495i \(-0.541545\pi\)
−0.130148 + 0.991495i \(0.541545\pi\)
\(182\) 0 0
\(183\) −25.4390 7.83875i −1.88050 0.579457i
\(184\) 0 0
\(185\) −2.66920 4.62320i −0.196244 0.339904i
\(186\) 0 0
\(187\) −0.214225 + 0.371048i −0.0156657 + 0.0271337i
\(188\) 0 0
\(189\) −5.13744 + 0.778948i −0.373693 + 0.0566601i
\(190\) 0 0
\(191\) −2.71533 + 4.70309i −0.196474 + 0.340303i −0.947383 0.320103i \(-0.896283\pi\)
0.750909 + 0.660406i \(0.229616\pi\)
\(192\) 0 0
\(193\) 4.54193 + 7.86686i 0.326935 + 0.566269i 0.981902 0.189389i \(-0.0606507\pi\)
−0.654967 + 0.755658i \(0.727317\pi\)
\(194\) 0 0
\(195\) 14.7839 + 4.55549i 1.05869 + 0.326225i
\(196\) 0 0
\(197\) −8.58040 −0.611329 −0.305664 0.952139i \(-0.598879\pi\)
−0.305664 + 0.952139i \(0.598879\pi\)
\(198\) 0 0
\(199\) 25.4905 1.80697 0.903487 0.428616i \(-0.140999\pi\)
0.903487 + 0.428616i \(0.140999\pi\)
\(200\) 0 0
\(201\) −7.45175 + 6.91827i −0.525606 + 0.487977i
\(202\) 0 0
\(203\) −4.75152 8.22988i −0.333492 0.577624i
\(204\) 0 0
\(205\) −10.9727 + 19.0052i −0.766364 + 1.32738i
\(206\) 0 0
\(207\) −9.01976 6.14185i −0.626917 0.426888i
\(208\) 0 0
\(209\) −2.01969 + 3.49821i −0.139705 + 0.241976i
\(210\) 0 0
\(211\) −8.32066 14.4118i −0.572818 0.992150i −0.996275 0.0862336i \(-0.972517\pi\)
0.423457 0.905916i \(-0.360816\pi\)
\(212\) 0 0
\(213\) −0.683765 2.99174i −0.0468508 0.204991i
\(214\) 0 0
\(215\) 0.228179 0.0155616
\(216\) 0 0
\(217\) −6.49808 −0.441119
\(218\) 0 0
\(219\) 2.31355 + 10.1227i 0.156335 + 0.684028i
\(220\) 0 0
\(221\) −0.631904 1.09449i −0.0425064 0.0736233i
\(222\) 0 0
\(223\) 9.28503 16.0821i 0.621772 1.07694i −0.367384 0.930069i \(-0.619746\pi\)
0.989156 0.146871i \(-0.0469202\pi\)
\(224\) 0 0
\(225\) 0.0752763 1.01243i 0.00501842 0.0674952i
\(226\) 0 0
\(227\) −7.84096 + 13.5809i −0.520423 + 0.901399i 0.479295 + 0.877654i \(0.340892\pi\)
−0.999718 + 0.0237449i \(0.992441\pi\)
\(228\) 0 0
\(229\) −5.57024 9.64794i −0.368092 0.637554i 0.621175 0.783672i \(-0.286656\pi\)
−0.989267 + 0.146118i \(0.953322\pi\)
\(230\) 0 0
\(231\) 1.66347 1.54438i 0.109448 0.101613i
\(232\) 0 0
\(233\) −21.6831 −1.42050 −0.710252 0.703948i \(-0.751419\pi\)
−0.710252 + 0.703948i \(0.751419\pi\)
\(234\) 0 0
\(235\) 0.500702 0.0326622
\(236\) 0 0
\(237\) 24.1532 + 7.44255i 1.56892 + 0.483446i
\(238\) 0 0
\(239\) −6.20271 10.7434i −0.401220 0.694934i 0.592653 0.805458i \(-0.298080\pi\)
−0.993873 + 0.110524i \(0.964747\pi\)
\(240\) 0 0
\(241\) 8.35028 14.4631i 0.537889 0.931651i −0.461129 0.887333i \(-0.652555\pi\)
0.999017 0.0443176i \(-0.0141114\pi\)
\(242\) 0 0
\(243\) −14.0546 6.74306i −0.901601 0.432568i
\(244\) 0 0
\(245\) 1.15525 2.00095i 0.0738062 0.127836i
\(246\) 0 0
\(247\) −5.95753 10.3187i −0.379069 0.656566i
\(248\) 0 0
\(249\) 10.0678 + 3.10227i 0.638018 + 0.196599i
\(250\) 0 0
\(251\) 27.0215 1.70558 0.852790 0.522255i \(-0.174909\pi\)
0.852790 + 0.522255i \(0.174909\pi\)
\(252\) 0 0
\(253\) 4.76686 0.299690
\(254\) 0 0
\(255\) −0.958840 + 0.890194i −0.0600449 + 0.0557461i
\(256\) 0 0
\(257\) 9.97645 + 17.2797i 0.622314 + 1.07788i 0.989054 + 0.147556i \(0.0471406\pi\)
−0.366740 + 0.930324i \(0.619526\pi\)
\(258\) 0 0
\(259\) 1.15525 2.00095i 0.0717837 0.124333i
\(260\) 0 0
\(261\) 2.11388 28.4307i 0.130846 1.75981i
\(262\) 0 0
\(263\) 7.92841 13.7324i 0.488887 0.846776i −0.511032 0.859562i \(-0.670737\pi\)
0.999918 + 0.0127855i \(0.00406985\pi\)
\(264\) 0 0
\(265\) 15.9334 + 27.5974i 0.978779 + 1.69530i
\(266\) 0 0
\(267\) −2.13109 9.32437i −0.130421 0.570642i
\(268\) 0 0
\(269\) 0.694466 0.0423423 0.0211712 0.999776i \(-0.493261\pi\)
0.0211712 + 0.999776i \(0.493261\pi\)
\(270\) 0 0
\(271\) 9.08883 0.552107 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(272\) 0 0
\(273\) 1.49178 + 6.52714i 0.0902867 + 0.395040i
\(274\) 0 0
\(275\) 0.221741 + 0.384067i 0.0133715 + 0.0231601i
\(276\) 0 0
\(277\) −7.20084 + 12.4722i −0.432656 + 0.749383i −0.997101 0.0760880i \(-0.975757\pi\)
0.564445 + 0.825471i \(0.309090\pi\)
\(278\) 0 0
\(279\) −16.1133 10.9721i −0.964679 0.656882i
\(280\) 0 0
\(281\) 4.68356 8.11216i 0.279398 0.483931i −0.691837 0.722053i \(-0.743199\pi\)
0.971235 + 0.238122i \(0.0765319\pi\)
\(282\) 0 0
\(283\) −9.54310 16.5291i −0.567279 0.982556i −0.996834 0.0795148i \(-0.974663\pi\)
0.429555 0.903041i \(-0.358670\pi\)
\(284\) 0 0
\(285\) −9.03985 + 8.39267i −0.535475 + 0.497139i
\(286\) 0 0
\(287\) −9.49808 −0.560654
\(288\) 0 0
\(289\) −16.8931 −0.993713
\(290\) 0 0
\(291\) −9.90429 3.05190i −0.580600 0.178906i
\(292\) 0 0
\(293\) −9.10262 15.7662i −0.531781 0.921071i −0.999312 0.0370944i \(-0.988190\pi\)
0.467531 0.883977i \(-0.345144\pi\)
\(294\) 0 0
\(295\) 2.83019 4.90203i 0.164780 0.285407i
\(296\) 0 0
\(297\) 6.73261 1.02081i 0.390665 0.0592334i
\(298\) 0 0
\(299\) −7.03046 + 12.1771i −0.406582 + 0.704221i
\(300\) 0 0
\(301\) 0.0493786 + 0.0855263i 0.00284614 + 0.00492965i
\(302\) 0 0
\(303\) −12.7489 3.92844i −0.732406 0.225683i
\(304\) 0 0
\(305\) 35.5093 2.03326
\(306\) 0 0
\(307\) 26.8537 1.53262 0.766312 0.642469i \(-0.222090\pi\)
0.766312 + 0.642469i \(0.222090\pi\)
\(308\) 0 0
\(309\) 5.15468 4.78565i 0.293240 0.272246i
\(310\) 0 0
\(311\) −0.790243 1.36874i −0.0448106 0.0776142i 0.842750 0.538305i \(-0.180935\pi\)
−0.887561 + 0.460691i \(0.847602\pi\)
\(312\) 0 0
\(313\) −10.2617 + 17.7738i −0.580025 + 1.00463i 0.415451 + 0.909616i \(0.363624\pi\)
−0.995476 + 0.0950169i \(0.969709\pi\)
\(314\) 0 0
\(315\) 6.24331 3.01111i 0.351770 0.169657i
\(316\) 0 0
\(317\) −15.9323 + 27.5955i −0.894845 + 1.54992i −0.0608495 + 0.998147i \(0.519381\pi\)
−0.833996 + 0.551771i \(0.813952\pi\)
\(318\) 0 0
\(319\) 6.22687 + 10.7853i 0.348638 + 0.603858i
\(320\) 0 0
\(321\) −5.43260 23.7698i −0.303218 1.32670i
\(322\) 0 0
\(323\) 1.00772 0.0560711
\(324\) 0 0
\(325\) −1.30815 −0.0725632
\(326\) 0 0
\(327\) 2.57521 + 11.2675i 0.142409 + 0.623097i
\(328\) 0 0
\(329\) 0.108354 + 0.187674i 0.00597372 + 0.0103468i
\(330\) 0 0
\(331\) 17.0714 29.5686i 0.938330 1.62524i 0.169744 0.985488i \(-0.445706\pi\)
0.768586 0.639747i \(-0.220961\pi\)
\(332\) 0 0
\(333\) 6.24331 3.01111i 0.342131 0.165008i
\(334\) 0 0
\(335\) 6.78198 11.7467i 0.370539 0.641793i
\(336\) 0 0
\(337\) −0.252833 0.437920i −0.0137727 0.0238550i 0.859057 0.511880i \(-0.171051\pi\)
−0.872830 + 0.488025i \(0.837717\pi\)
\(338\) 0 0
\(339\) 9.77182 9.07224i 0.530732 0.492736i
\(340\) 0 0
\(341\) 8.51573 0.461153
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 13.9112 + 4.28659i 0.748954 + 0.230782i
\(346\) 0 0
\(347\) 14.2154 + 24.6217i 0.763120 + 1.32176i 0.941235 + 0.337753i \(0.109667\pi\)
−0.178114 + 0.984010i \(0.557000\pi\)
\(348\) 0 0
\(349\) 17.5804 30.4502i 0.941057 1.62996i 0.177599 0.984103i \(-0.443167\pi\)
0.763459 0.645856i \(-0.223500\pi\)
\(350\) 0 0
\(351\) −7.32197 + 18.7042i −0.390818 + 0.998359i
\(352\) 0 0
\(353\) −0.496139 + 0.859339i −0.0264068 + 0.0457380i −0.878927 0.476957i \(-0.841740\pi\)
0.852520 + 0.522695i \(0.175073\pi\)
\(354\) 0 0
\(355\) 2.04690 + 3.54533i 0.108638 + 0.188166i
\(356\) 0 0
\(357\) −0.541160 0.166753i −0.0286412 0.00882549i
\(358\) 0 0
\(359\) 23.2914 1.22928 0.614638 0.788810i \(-0.289302\pi\)
0.614638 + 0.788810i \(0.289302\pi\)
\(360\) 0 0
\(361\) −9.49930 −0.499963
\(362\) 0 0
\(363\) 11.7828 10.9392i 0.618434 0.574159i
\(364\) 0 0
\(365\) −6.92576 11.9958i −0.362511 0.627887i
\(366\) 0 0
\(367\) −5.89144 + 10.2043i −0.307531 + 0.532659i −0.977822 0.209440i \(-0.932836\pi\)
0.670291 + 0.742099i \(0.266169\pi\)
\(368\) 0 0
\(369\) −23.5524 16.0376i −1.22609 0.834886i
\(370\) 0 0
\(371\) −6.89607 + 11.9443i −0.358026 + 0.620120i
\(372\) 0 0
\(373\) 6.91714 + 11.9808i 0.358156 + 0.620344i 0.987653 0.156659i \(-0.0500723\pi\)
−0.629497 + 0.777003i \(0.716739\pi\)
\(374\) 0 0
\(375\) −4.15649 18.1863i −0.214640 0.939136i
\(376\) 0 0
\(377\) −36.7351 −1.89195
\(378\) 0 0
\(379\) 21.5877 1.10889 0.554443 0.832222i \(-0.312931\pi\)
0.554443 + 0.832222i \(0.312931\pi\)
\(380\) 0 0
\(381\) 5.78275 + 25.3018i 0.296260 + 1.29625i
\(382\) 0 0
\(383\) 8.31989 + 14.4105i 0.425127 + 0.736341i 0.996432 0.0843965i \(-0.0268962\pi\)
−0.571306 + 0.820737i \(0.693563\pi\)
\(384\) 0 0
\(385\) −1.51395 + 2.62225i −0.0771582 + 0.133642i
\(386\) 0 0
\(387\) −0.0219678 + 0.295456i −0.00111669 + 0.0150189i
\(388\) 0 0
\(389\) 9.46709 16.3975i 0.480000 0.831385i −0.519736 0.854327i \(-0.673970\pi\)
0.999737 + 0.0229417i \(0.00730320\pi\)
\(390\) 0 0
\(391\) −0.594604 1.02988i −0.0300704 0.0520835i
\(392\) 0 0
\(393\) 13.2211 12.2746i 0.666918 0.619172i
\(394\) 0 0
\(395\) −33.7145 −1.69636
\(396\) 0 0
\(397\) 16.0746 0.806761 0.403381 0.915032i \(-0.367835\pi\)
0.403381 + 0.915032i \(0.367835\pi\)
\(398\) 0 0
\(399\) −5.10201 1.57213i −0.255420 0.0787049i
\(400\) 0 0
\(401\) −19.4409 33.6726i −0.970832 1.68153i −0.693056 0.720884i \(-0.743736\pi\)
−0.277776 0.960646i \(-0.589597\pi\)
\(402\) 0 0
\(403\) −12.5595 + 21.7538i −0.625635 + 1.08363i
\(404\) 0 0
\(405\) 20.5658 + 3.07524i 1.02192 + 0.152810i
\(406\) 0 0
\(407\) −1.51395 + 2.62225i −0.0750439 + 0.129980i
\(408\) 0 0
\(409\) −6.39993 11.0850i −0.316456 0.548119i 0.663290 0.748363i \(-0.269160\pi\)
−0.979746 + 0.200244i \(0.935826\pi\)
\(410\) 0 0
\(411\) 10.3675 + 3.19463i 0.511391 + 0.157580i
\(412\) 0 0
\(413\) 2.44985 0.120549
\(414\) 0 0
\(415\) −14.0532 −0.689844
\(416\) 0 0
\(417\) −25.5895 + 23.7575i −1.25312 + 1.16341i
\(418\) 0 0
\(419\) 0.597046 + 1.03411i 0.0291676 + 0.0505197i 0.880241 0.474527i \(-0.157381\pi\)
−0.851073 + 0.525047i \(0.824048\pi\)
\(420\) 0 0
\(421\) −8.19067 + 14.1867i −0.399189 + 0.691416i −0.993626 0.112726i \(-0.964042\pi\)
0.594437 + 0.804142i \(0.297375\pi\)
\(422\) 0 0
\(423\) −0.0482049 + 0.648332i −0.00234380 + 0.0315230i
\(424\) 0 0
\(425\) 0.0553187 0.0958149i 0.00268335 0.00464770i
\(426\) 0 0
\(427\) 7.68433 + 13.3097i 0.371871 + 0.644099i
\(428\) 0 0
\(429\) −1.95498 8.55381i −0.0943873 0.412982i
\(430\) 0 0
\(431\) 26.3928 1.27130 0.635649 0.771978i \(-0.280733\pi\)
0.635649 + 0.771978i \(0.280733\pi\)
\(432\) 0 0
\(433\) 23.7503 1.14137 0.570684 0.821170i \(-0.306678\pi\)
0.570684 + 0.821170i \(0.306678\pi\)
\(434\) 0 0
\(435\) 8.47336 + 37.0743i 0.406267 + 1.77758i
\(436\) 0 0
\(437\) −5.60587 9.70965i −0.268165 0.464476i
\(438\) 0 0
\(439\) −10.2431 + 17.7416i −0.488877 + 0.846759i −0.999918 0.0127969i \(-0.995926\pi\)
0.511042 + 0.859556i \(0.329260\pi\)
\(440\) 0 0
\(441\) 2.47970 + 1.68851i 0.118081 + 0.0804053i
\(442\) 0 0
\(443\) −3.89909 + 6.75343i −0.185252 + 0.320865i −0.943661 0.330913i \(-0.892643\pi\)
0.758410 + 0.651778i \(0.225977\pi\)
\(444\) 0 0
\(445\) 6.37957 + 11.0497i 0.302421 + 0.523808i
\(446\) 0 0
\(447\) −21.6011 + 20.0546i −1.02170 + 0.948550i
\(448\) 0 0
\(449\) 2.35981 0.111366 0.0556831 0.998448i \(-0.482266\pi\)
0.0556831 + 0.998448i \(0.482266\pi\)
\(450\) 0 0
\(451\) 12.4472 0.586117
\(452\) 0 0
\(453\) 27.1342 + 8.36112i 1.27488 + 0.392840i
\(454\) 0 0
\(455\) −4.46575 7.73490i −0.209358 0.362618i
\(456\) 0 0
\(457\) −10.1012 + 17.4959i −0.472516 + 0.818422i −0.999505 0.0314501i \(-0.989987\pi\)
0.526989 + 0.849872i \(0.323321\pi\)
\(458\) 0 0
\(459\) −1.06035 1.32725i −0.0494930 0.0619509i
\(460\) 0 0
\(461\) 6.02197 10.4304i 0.280471 0.485790i −0.691030 0.722826i \(-0.742843\pi\)
0.971501 + 0.237036i \(0.0761760\pi\)
\(462\) 0 0
\(463\) −11.6437 20.1675i −0.541130 0.937265i −0.998839 0.0481633i \(-0.984663\pi\)
0.457709 0.889102i \(-0.348670\pi\)
\(464\) 0 0
\(465\) 24.8516 + 7.65776i 1.15247 + 0.355120i
\(466\) 0 0
\(467\) −34.0682 −1.57649 −0.788243 0.615364i \(-0.789009\pi\)
−0.788243 + 0.615364i \(0.789009\pi\)
\(468\) 0 0
\(469\) 5.87058 0.271078
\(470\) 0 0
\(471\) −25.9642 + 24.1053i −1.19637 + 1.11072i
\(472\) 0 0
\(473\) −0.0647107 0.112082i −0.00297540 0.00515354i
\(474\) 0 0
\(475\) 0.521540 0.903334i 0.0239299 0.0414478i
\(476\) 0 0
\(477\) −37.2684 + 17.9743i −1.70640 + 0.822988i
\(478\) 0 0
\(479\) −9.38477 + 16.2549i −0.428801 + 0.742705i −0.996767 0.0803471i \(-0.974397\pi\)
0.567966 + 0.823052i \(0.307730\pi\)
\(480\) 0 0
\(481\) −4.46575 7.73490i −0.203621 0.352681i
\(482\) 0 0
\(483\) 1.40373 + 6.14185i 0.0638717 + 0.279464i
\(484\) 0 0
\(485\) 13.8250 0.627762
\(486\) 0 0
\(487\) 13.8837 0.629132 0.314566 0.949236i \(-0.398141\pi\)
0.314566 + 0.949236i \(0.398141\pi\)
\(488\) 0 0
\(489\) 6.51455 + 28.5037i 0.294598 + 1.28898i
\(490\) 0 0
\(491\) 4.54250 + 7.86784i 0.205000 + 0.355071i 0.950133 0.311846i \(-0.100947\pi\)
−0.745133 + 0.666916i \(0.767614\pi\)
\(492\) 0 0
\(493\) 1.55344 2.69064i 0.0699636 0.121180i
\(494\) 0 0
\(495\) −8.18185 + 3.94606i −0.367747 + 0.177362i
\(496\) 0 0
\(497\) −0.885911 + 1.53444i −0.0397385 + 0.0688291i
\(498\) 0 0
\(499\) −11.8788 20.5747i −0.531769 0.921051i −0.999312 0.0370810i \(-0.988194\pi\)
0.467543 0.883970i \(-0.345139\pi\)
\(500\) 0 0
\(501\) −4.07679 + 3.78492i −0.182138 + 0.169098i
\(502\) 0 0
\(503\) 22.5612 1.00595 0.502977 0.864300i \(-0.332238\pi\)
0.502977 + 0.864300i \(0.332238\pi\)
\(504\) 0 0
\(505\) 17.7957 0.791899
\(506\) 0 0
\(507\) 3.21610 + 0.991007i 0.142832 + 0.0440122i
\(508\) 0 0
\(509\) −3.94814 6.83838i −0.174998 0.303106i 0.765162 0.643837i \(-0.222659\pi\)
−0.940161 + 0.340732i \(0.889325\pi\)
\(510\) 0 0
\(511\) 2.99752 5.19185i 0.132602 0.229674i
\(512\) 0 0
\(513\) −9.99691 12.5132i −0.441374 0.552472i
\(514\) 0 0
\(515\) −4.69138 + 8.12570i −0.206727 + 0.358061i
\(516\) 0 0
\(517\) −0.141997 0.245946i −0.00624503 0.0108167i
\(518\) 0 0
\(519\) 1.01325 + 0.312223i 0.0444768 + 0.0137051i
\(520\) 0 0
\(521\) 9.86440 0.432167 0.216084 0.976375i \(-0.430672\pi\)
0.216084 + 0.976375i \(0.430672\pi\)
\(522\) 0 0
\(523\) −22.9097 −1.00177 −0.500885 0.865514i \(-0.666992\pi\)
−0.500885 + 0.865514i \(0.666992\pi\)
\(524\) 0 0
\(525\) −0.429554 + 0.398801i −0.0187473 + 0.0174051i
\(526\) 0 0
\(527\) −1.06223 1.83983i −0.0462714 0.0801444i
\(528\) 0 0
\(529\) 4.88453 8.46026i 0.212371 0.367837i
\(530\) 0 0
\(531\) 6.07490 + 4.13660i 0.263628 + 0.179513i
\(532\) 0 0
\(533\) −18.3580 + 31.7969i −0.795172 + 1.37728i
\(534\) 0 0
\(535\) 16.2629 + 28.1681i 0.703105 + 1.21781i
\(536\) 0 0
\(537\) 1.69081 + 7.39796i 0.0729638 + 0.319246i
\(538\) 0 0
\(539\) −1.31050 −0.0564472
\(540\) 0 0
\(541\) 29.7187 1.27771 0.638853 0.769329i \(-0.279409\pi\)
0.638853 + 0.769329i \(0.279409\pi\)
\(542\) 0 0
\(543\) 1.35143 + 5.91303i 0.0579953 + 0.253752i
\(544\) 0 0
\(545\) −7.70906 13.3525i −0.330220 0.571957i
\(546\) 0 0
\(547\) −1.30472 + 2.25985i −0.0557859 + 0.0966240i −0.892570 0.450909i \(-0.851100\pi\)
0.836784 + 0.547533i \(0.184433\pi\)
\(548\) 0 0
\(549\) −3.41865 + 45.9791i −0.145904 + 1.96234i
\(550\) 0 0
\(551\) 14.6457 25.3671i 0.623929 1.08068i
\(552\) 0 0
\(553\) −7.29594 12.6369i −0.310255 0.537377i
\(554\) 0 0
\(555\) −6.77625 + 6.29112i −0.287636 + 0.267043i
\(556\) 0 0
\(557\) 26.0406 1.10338 0.551688 0.834051i \(-0.313984\pi\)
0.551688 + 0.834051i \(0.313984\pi\)
\(558\) 0 0
\(559\) 0.381757 0.0161466
\(560\) 0 0
\(561\) 0.709190 + 0.218529i 0.0299420 + 0.00922632i
\(562\) 0 0
\(563\) −22.3876 38.7765i −0.943525 1.63423i −0.758677 0.651467i \(-0.774154\pi\)
−0.184848 0.982767i \(-0.559179\pi\)
\(564\) 0 0
\(565\) −8.89352 + 15.4040i −0.374153 + 0.648052i
\(566\) 0 0
\(567\) 3.29785 + 8.37402i 0.138497 + 0.351676i
\(568\) 0 0
\(569\) 14.6290 25.3382i 0.613280 1.06223i −0.377404 0.926049i \(-0.623183\pi\)
0.990684 0.136183i \(-0.0434836\pi\)
\(570\) 0 0
\(571\) 18.2628 + 31.6321i 0.764275 + 1.32376i 0.940629 + 0.339437i \(0.110236\pi\)
−0.176354 + 0.984327i \(0.556430\pi\)
\(572\) 0 0
\(573\) 8.98909 + 2.76989i 0.375525 + 0.115714i
\(574\) 0 0
\(575\) −1.23093 −0.0513335
\(576\) 0 0
\(577\) 9.88205 0.411395 0.205698 0.978616i \(-0.434054\pi\)
0.205698 + 0.978616i \(0.434054\pi\)
\(578\) 0 0
\(579\) 11.5305 10.7050i 0.479191 0.444885i
\(580\) 0 0
\(581\) −3.04116 5.26744i −0.126169 0.218530i
\(582\) 0 0
\(583\) 9.03730 15.6531i 0.374287 0.648284i
\(584\) 0 0
\(585\) 1.98675 26.7207i 0.0821419 1.10477i
\(586\) 0 0
\(587\) −4.05954 + 7.03133i −0.167555 + 0.290214i −0.937560 0.347824i \(-0.886921\pi\)
0.770005 + 0.638038i \(0.220254\pi\)
\(588\) 0 0
\(589\) −10.0146 17.3458i −0.412644 0.714720i
\(590\) 0 0
\(591\) 3.31127 + 14.4881i 0.136207 + 0.595961i
\(592\) 0 0
\(593\) 29.6969 1.21950 0.609752 0.792592i \(-0.291269\pi\)
0.609752 + 0.792592i \(0.291269\pi\)
\(594\) 0 0
\(595\) 0.755385 0.0309678
\(596\) 0 0
\(597\) −9.83706 43.0410i −0.402604 1.76155i
\(598\) 0 0
\(599\) −8.19531 14.1947i −0.334851 0.579979i 0.648605 0.761125i \(-0.275353\pi\)
−0.983456 + 0.181146i \(0.942019\pi\)
\(600\) 0 0
\(601\) 24.4424 42.3355i 0.997028 1.72690i 0.431790 0.901974i \(-0.357882\pi\)
0.565237 0.824928i \(-0.308785\pi\)
\(602\) 0 0
\(603\) 14.5573 + 9.91254i 0.592819 + 0.403670i
\(604\) 0 0
\(605\) −10.7237 + 18.5740i −0.435981 + 0.755141i
\(606\) 0 0
\(607\) 23.6033 + 40.8820i 0.958027 + 1.65935i 0.727285 + 0.686335i \(0.240782\pi\)
0.230741 + 0.973015i \(0.425885\pi\)
\(608\) 0 0
\(609\) −12.0626 + 11.1990i −0.488801 + 0.453807i
\(610\) 0 0
\(611\) 0.837706 0.0338899
\(612\) 0 0
\(613\) −15.6396 −0.631679 −0.315840 0.948813i \(-0.602286\pi\)
−0.315840 + 0.948813i \(0.602286\pi\)
\(614\) 0 0
\(615\) 36.3250 + 11.1932i 1.46476 + 0.451352i
\(616\) 0 0
\(617\) −15.7793 27.3305i −0.635251 1.10029i −0.986462 0.163990i \(-0.947563\pi\)
0.351211 0.936296i \(-0.385770\pi\)
\(618\) 0 0
\(619\) 7.31619 12.6720i 0.294063 0.509331i −0.680704 0.732559i \(-0.738326\pi\)
0.974766 + 0.223227i \(0.0716592\pi\)
\(620\) 0 0
\(621\) −6.88977 + 17.6002i −0.276477 + 0.706271i
\(622\) 0 0
\(623\) −2.76112 + 4.78240i −0.110622 + 0.191603i
\(624\) 0 0
\(625\) 13.2888 + 23.0168i 0.531550 + 0.920672i
\(626\) 0 0
\(627\) 6.68618 + 2.06028i 0.267020 + 0.0822795i
\(628\) 0 0
\(629\) 0.755385 0.0301192
\(630\) 0 0
\(631\) 36.3101 1.44548 0.722742 0.691118i \(-0.242881\pi\)
0.722742 + 0.691118i \(0.242881\pi\)
\(632\) 0 0
\(633\) −21.1235 + 19.6112i −0.839583 + 0.779476i
\(634\) 0 0
\(635\) −17.3111 29.9836i −0.686969 1.18986i
\(636\) 0 0
\(637\) 1.93281 3.34772i 0.0765806 0.132641i
\(638\) 0 0
\(639\) −4.78772 + 2.30909i −0.189399 + 0.0913462i
\(640\) 0 0
\(641\) −5.40731 + 9.36574i −0.213576 + 0.369924i −0.952831 0.303501i \(-0.901844\pi\)
0.739255 + 0.673425i \(0.235178\pi\)
\(642\) 0 0
\(643\) −6.97535 12.0817i −0.275081 0.476454i 0.695075 0.718937i \(-0.255371\pi\)
−0.970155 + 0.242484i \(0.922038\pi\)
\(644\) 0 0
\(645\) −0.0880566 0.385282i −0.00346722 0.0151705i
\(646\) 0 0
\(647\) 34.5634 1.35883 0.679414 0.733755i \(-0.262234\pi\)
0.679414 + 0.733755i \(0.262234\pi\)
\(648\) 0 0
\(649\) −3.21053 −0.126024
\(650\) 0 0
\(651\) 2.50768 + 10.9721i 0.0982837 + 0.430030i
\(652\) 0 0
\(653\) 13.7927 + 23.8897i 0.539751 + 0.934875i 0.998917 + 0.0465252i \(0.0148148\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(654\) 0 0
\(655\) −12.0328 + 20.8414i −0.470161 + 0.814342i
\(656\) 0 0
\(657\) 16.1995 7.81291i 0.632001 0.304811i
\(658\) 0 0
\(659\) 10.3059 17.8503i 0.401460 0.695348i −0.592443 0.805613i \(-0.701836\pi\)
0.993902 + 0.110264i \(0.0351697\pi\)
\(660\) 0 0
\(661\) 13.5815 + 23.5239i 0.528259 + 0.914972i 0.999457 + 0.0329446i \(0.0104885\pi\)
−0.471198 + 0.882028i \(0.656178\pi\)
\(662\) 0 0
\(663\) −1.60420 + 1.48935i −0.0623020 + 0.0578417i
\(664\) 0 0
\(665\) 7.12170 0.276168
\(666\) 0 0
\(667\) −34.5667 −1.33843
\(668\) 0 0
\(669\) −30.7381 9.47162i −1.18840 0.366194i
\(670\) 0 0
\(671\) −10.0703 17.4423i −0.388760 0.673352i
\(672\) 0 0
\(673\) −9.52644 + 16.5003i −0.367217 + 0.636039i −0.989129 0.147048i \(-0.953023\pi\)
0.621912 + 0.783087i \(0.286356\pi\)
\(674\) 0 0
\(675\) −1.73855 + 0.263602i −0.0669167 + 0.0101460i
\(676\) 0 0
\(677\) 10.8695 18.8265i 0.417748 0.723560i −0.577965 0.816062i \(-0.696153\pi\)
0.995713 + 0.0925013i \(0.0294862\pi\)
\(678\) 0 0
\(679\) 2.99178 + 5.18192i 0.114814 + 0.198864i
\(680\) 0 0
\(681\) 25.9575 + 7.99852i 0.994693 + 0.306504i
\(682\) 0 0
\(683\) 41.0808 1.57191 0.785957 0.618281i \(-0.212171\pi\)
0.785957 + 0.618281i \(0.212171\pi\)
\(684\) 0 0
\(685\) −14.4716 −0.552931
\(686\) 0 0
\(687\) −14.1411 + 13.1287i −0.539515 + 0.500890i
\(688\) 0 0
\(689\) 26.6576 + 46.1722i 1.01557 + 1.75902i
\(690\) 0 0
\(691\) 9.03599 15.6508i 0.343745 0.595384i −0.641380 0.767224i \(-0.721638\pi\)
0.985125 + 0.171839i \(0.0549710\pi\)
\(692\) 0 0
\(693\) −3.24965 2.21279i −0.123444 0.0840571i
\(694\) 0 0
\(695\) 23.2895 40.3385i 0.883420 1.53013i
\(696\) 0 0
\(697\) −1.55263 2.68924i −0.0588101 0.101862i
\(698\) 0 0
\(699\) 8.36772 + 36.6121i 0.316496 + 1.38480i
\(700\) 0 0
\(701\) −41.5130 −1.56793 −0.783963 0.620808i \(-0.786805\pi\)
−0.783963 + 0.620808i \(0.786805\pi\)
\(702\) 0 0
\(703\) 7.12170 0.268600
\(704\) 0 0
\(705\) −0.193226 0.845441i −0.00727732 0.0318411i
\(706\) 0 0
\(707\) 3.85105 + 6.67022i 0.144834 + 0.250859i
\(708\) 0 0
\(709\) −0.684536 + 1.18565i −0.0257083 + 0.0445280i −0.878593 0.477571i \(-0.841517\pi\)
0.852885 + 0.522099i \(0.174851\pi\)
\(710\) 0 0
\(711\) 3.24586 43.6551i 0.121729 1.63720i
\(712\) 0 0
\(713\) −11.8182 + 20.4697i −0.442594 + 0.766596i
\(714\) 0 0
\(715\) 5.85236 + 10.1366i 0.218866 + 0.379087i
\(716\) 0 0
\(717\) −15.7467 + 14.6194i −0.588071 + 0.545970i
\(718\) 0 0
\(719\) −20.1854 −0.752787 −0.376394 0.926460i \(-0.622836\pi\)
−0.376394 + 0.926460i \(0.622836\pi\)
\(720\) 0 0
\(721\) −4.06092 −0.151237
\(722\) 0 0
\(723\) −27.6436 8.51808i −1.02808 0.316791i
\(724\) 0 0
\(725\) −1.60795 2.78505i −0.0597178 0.103434i
\(726\) 0 0
\(727\) 1.69393 2.93397i 0.0628243 0.108815i −0.832903 0.553420i \(-0.813323\pi\)
0.895727 + 0.444605i \(0.146656\pi\)
\(728\) 0 0
\(729\) −5.96193 + 26.3335i −0.220812 + 0.975316i
\(730\) 0 0
\(731\) −0.0161436 + 0.0279616i −0.000597094 + 0.00103420i
\(732\) 0 0
\(733\) 8.90603 + 15.4257i 0.328952 + 0.569761i 0.982304 0.187293i \(-0.0599713\pi\)
−0.653352 + 0.757054i \(0.726638\pi\)
\(734\) 0 0
\(735\) −3.82445 1.17846i −0.141067 0.0434683i
\(736\) 0 0
\(737\) −7.69339 −0.283390
\(738\) 0 0
\(739\) 1.15512 0.0424918 0.0212459 0.999774i \(-0.493237\pi\)
0.0212459 + 0.999774i \(0.493237\pi\)
\(740\) 0 0
\(741\) −15.1243 + 14.0415i −0.555603 + 0.515827i
\(742\) 0 0
\(743\) −13.5863 23.5322i −0.498435 0.863314i 0.501564 0.865121i \(-0.332758\pi\)
−0.999998 + 0.00180657i \(0.999425\pi\)
\(744\) 0 0
\(745\) 19.6595 34.0513i 0.720270 1.24754i
\(746\) 0 0
\(747\) 1.35297 18.1967i 0.0495025 0.665784i
\(748\) 0 0
\(749\) −7.03868 + 12.1913i −0.257188 + 0.445462i
\(750\) 0 0
\(751\) 11.2959 + 19.5651i 0.412195 + 0.713942i 0.995129 0.0985769i \(-0.0314290\pi\)
−0.582935 + 0.812519i \(0.698096\pi\)
\(752\) 0 0
\(753\) −10.4279 45.6261i −0.380013 1.66271i
\(754\) 0 0
\(755\) −37.8756 −1.37843
\(756\) 0 0
\(757\) 13.9989 0.508797 0.254399 0.967099i \(-0.418122\pi\)
0.254399 + 0.967099i \(0.418122\pi\)
\(758\) 0 0
\(759\) −1.83958 8.04889i −0.0667726 0.292156i
\(760\) 0 0
\(761\) 0.252336 + 0.437059i 0.00914718 + 0.0158434i 0.870563 0.492057i \(-0.163755\pi\)
−0.861416 + 0.507901i \(0.830422\pi\)
\(762\) 0 0
\(763\) 3.33653 5.77904i 0.120791 0.209215i
\(764\) 0 0
\(765\) 1.87313 + 1.27548i 0.0677232 + 0.0461150i
\(766\) 0 0
\(767\) 4.73509 8.20141i 0.170974 0.296136i
\(768\) 0 0
\(769\) 4.89218 + 8.47351i 0.176417 + 0.305563i 0.940651 0.339376i \(-0.110216\pi\)
−0.764234 + 0.644939i \(0.776883\pi\)
\(770\) 0 0
\(771\) 25.3270 23.5138i 0.912129 0.846828i
\(772\) 0 0
\(773\) 26.5907 0.956403 0.478201 0.878250i \(-0.341289\pi\)
0.478201 + 0.878250i \(0.341289\pi\)
\(774\) 0 0
\(775\) −2.19900 −0.0789904
\(776\) 0 0
\(777\) −3.82445 1.17846i −0.137201 0.0422772i
\(778\) 0 0
\(779\) −14.6381 25.3539i −0.524463 0.908397i
\(780\) 0 0
\(781\) 1.16099 2.01089i 0.0415433 0.0719551i
\(782\) 0 0
\(783\) −48.8213 + 7.40238i −1.74473 + 0.264539i
\(784\) 0 0
\(785\) 23.6305 40.9292i 0.843408 1.46083i
\(786\) 0 0
\(787\) −19.1108 33.1009i −0.681227 1.17992i −0.974607 0.223924i \(-0.928113\pi\)
0.293379 0.955996i \(-0.405220\pi\)
\(788\) 0 0
\(789\) −26.2470 8.08773i −0.934418 0.287931i
\(790\) 0 0
\(791\) −7.69835 −0.273722
\(792\) 0 0
\(793\) 59.4093 2.10969
\(794\) 0 0
\(795\) 40.4497 37.5538i 1.43460 1.33190i
\(796\) 0 0
\(797\) −11.1866 19.3758i −0.396250 0.686325i 0.597010 0.802234i \(-0.296355\pi\)
−0.993260 + 0.115909i \(0.963022\pi\)