Properties

Label 576.2.bb.e.49.12
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.12
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.795173 - 1.53873i) q^{3} +(-2.41406 + 0.646846i) q^{5} +(-2.82197 + 1.62927i) q^{7} +(-1.73540 - 2.44712i) q^{9} +O(q^{10})\) \(q+(0.795173 - 1.53873i) q^{3} +(-2.41406 + 0.646846i) q^{5} +(-2.82197 + 1.62927i) q^{7} +(-1.73540 - 2.44712i) q^{9} +(-0.356120 + 1.32906i) q^{11} +(1.42802 + 5.32945i) q^{13} +(-0.924273 + 4.22895i) q^{15} +5.37452 q^{17} +(-4.71269 + 4.71269i) q^{19} +(0.263051 + 5.63781i) q^{21} +(2.88877 + 1.66783i) q^{23} +(1.07916 - 0.623053i) q^{25} +(-5.14540 + 0.724438i) q^{27} +(-3.03883 - 0.814251i) q^{29} +(-0.621800 + 1.07699i) q^{31} +(1.76189 + 1.60481i) q^{33} +(5.75853 - 5.75853i) q^{35} +(-5.86087 - 5.86087i) q^{37} +(9.33612 + 2.04049i) q^{39} +(-2.81108 - 1.62298i) q^{41} +(-1.61636 + 6.03232i) q^{43} +(5.77227 + 4.78496i) q^{45} +(-2.17485 - 3.76695i) q^{47} +(1.80902 - 3.13331i) q^{49} +(4.27367 - 8.26995i) q^{51} +(-0.134334 - 0.134334i) q^{53} -3.43879i q^{55} +(3.50417 + 10.9990i) q^{57} +(2.21088 - 0.592405i) q^{59} +(-2.29879 - 0.615960i) q^{61} +(8.88426 + 4.07827i) q^{63} +(-6.89466 - 11.9419i) q^{65} +(0.0300838 + 0.112274i) q^{67} +(4.86343 - 3.11884i) q^{69} +3.21118i q^{71} +9.75441i q^{73} +(-0.100594 - 2.15597i) q^{75} +(-1.16043 - 4.33078i) q^{77} +(-1.11184 - 1.92576i) q^{79} +(-2.97677 + 8.49346i) q^{81} +(-5.74772 - 1.54010i) q^{83} +(-12.9744 + 3.47649i) q^{85} +(-3.66931 + 4.02848i) q^{87} -6.12376i q^{89} +(-12.7129 - 12.7129i) q^{91} +(1.16276 + 1.81318i) q^{93} +(8.32833 - 14.4251i) q^{95} +(-2.21495 - 3.83640i) q^{97} +(3.87037 - 1.43498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.795173 1.53873i 0.459093 0.888388i
\(4\) 0 0
\(5\) −2.41406 + 0.646846i −1.07960 + 0.289278i −0.754433 0.656378i \(-0.772088\pi\)
−0.325169 + 0.945656i \(0.605421\pi\)
\(6\) 0 0
\(7\) −2.82197 + 1.62927i −1.06661 + 0.615805i −0.927252 0.374438i \(-0.877836\pi\)
−0.139353 + 0.990243i \(0.544502\pi\)
\(8\) 0 0
\(9\) −1.73540 2.44712i −0.578467 0.815706i
\(10\) 0 0
\(11\) −0.356120 + 1.32906i −0.107374 + 0.400726i −0.998604 0.0528265i \(-0.983177\pi\)
0.891229 + 0.453553i \(0.149844\pi\)
\(12\) 0 0
\(13\) 1.42802 + 5.32945i 0.396062 + 1.47812i 0.819964 + 0.572415i \(0.193993\pi\)
−0.423903 + 0.905708i \(0.639340\pi\)
\(14\) 0 0
\(15\) −0.924273 + 4.22895i −0.238646 + 1.09191i
\(16\) 0 0
\(17\) 5.37452 1.30351 0.651756 0.758428i \(-0.274032\pi\)
0.651756 + 0.758428i \(0.274032\pi\)
\(18\) 0 0
\(19\) −4.71269 + 4.71269i −1.08116 + 1.08116i −0.0847630 + 0.996401i \(0.527013\pi\)
−0.996401 + 0.0847630i \(0.972987\pi\)
\(20\) 0 0
\(21\) 0.263051 + 5.63781i 0.0574025 + 1.23027i
\(22\) 0 0
\(23\) 2.88877 + 1.66783i 0.602351 + 0.347767i 0.769966 0.638085i \(-0.220273\pi\)
−0.167615 + 0.985853i \(0.553607\pi\)
\(24\) 0 0
\(25\) 1.07916 0.623053i 0.215832 0.124611i
\(26\) 0 0
\(27\) −5.14540 + 0.724438i −0.990234 + 0.139418i
\(28\) 0 0
\(29\) −3.03883 0.814251i −0.564296 0.151203i −0.0346168 0.999401i \(-0.511021\pi\)
−0.529679 + 0.848198i \(0.677688\pi\)
\(30\) 0 0
\(31\) −0.621800 + 1.07699i −0.111679 + 0.193433i −0.916447 0.400156i \(-0.868956\pi\)
0.804769 + 0.593589i \(0.202289\pi\)
\(32\) 0 0
\(33\) 1.76189 + 1.60481i 0.306706 + 0.279361i
\(34\) 0 0
\(35\) 5.75853 5.75853i 0.973369 0.973369i
\(36\) 0 0
\(37\) −5.86087 5.86087i −0.963521 0.963521i 0.0358368 0.999358i \(-0.488590\pi\)
−0.999358 + 0.0358368i \(0.988590\pi\)
\(38\) 0 0
\(39\) 9.33612 + 2.04049i 1.49498 + 0.326739i
\(40\) 0 0
\(41\) −2.81108 1.62298i −0.439017 0.253467i 0.264163 0.964478i \(-0.414904\pi\)
−0.703181 + 0.711011i \(0.748237\pi\)
\(42\) 0 0
\(43\) −1.61636 + 6.03232i −0.246492 + 0.919920i 0.726136 + 0.687551i \(0.241314\pi\)
−0.972628 + 0.232369i \(0.925352\pi\)
\(44\) 0 0
\(45\) 5.77227 + 4.78496i 0.860480 + 0.713299i
\(46\) 0 0
\(47\) −2.17485 3.76695i −0.317234 0.549466i 0.662676 0.748907i \(-0.269421\pi\)
−0.979910 + 0.199441i \(0.936088\pi\)
\(48\) 0 0
\(49\) 1.80902 3.13331i 0.258431 0.447615i
\(50\) 0 0
\(51\) 4.27367 8.26995i 0.598434 1.15803i
\(52\) 0 0
\(53\) −0.134334 0.134334i −0.0184522 0.0184522i 0.697820 0.716273i \(-0.254153\pi\)
−0.716273 + 0.697820i \(0.754153\pi\)
\(54\) 0 0
\(55\) 3.43879i 0.463686i
\(56\) 0 0
\(57\) 3.50417 + 10.9990i 0.464138 + 1.45685i
\(58\) 0 0
\(59\) 2.21088 0.592405i 0.287833 0.0771245i −0.112014 0.993707i \(-0.535730\pi\)
0.399846 + 0.916582i \(0.369063\pi\)
\(60\) 0 0
\(61\) −2.29879 0.615960i −0.294330 0.0788656i 0.108632 0.994082i \(-0.465353\pi\)
−0.402963 + 0.915216i \(0.632020\pi\)
\(62\) 0 0
\(63\) 8.88426 + 4.07827i 1.11931 + 0.513813i
\(64\) 0 0
\(65\) −6.89466 11.9419i −0.855178 1.48121i
\(66\) 0 0
\(67\) 0.0300838 + 0.112274i 0.00367532 + 0.0137165i 0.967739 0.251954i \(-0.0810733\pi\)
−0.964064 + 0.265671i \(0.914407\pi\)
\(68\) 0 0
\(69\) 4.86343 3.11884i 0.585488 0.375464i
\(70\) 0 0
\(71\) 3.21118i 0.381097i 0.981678 + 0.190548i \(0.0610266\pi\)
−0.981678 + 0.190548i \(0.938973\pi\)
\(72\) 0 0
\(73\) 9.75441i 1.14167i 0.821066 + 0.570833i \(0.193380\pi\)
−0.821066 + 0.570833i \(0.806620\pi\)
\(74\) 0 0
\(75\) −0.100594 2.15597i −0.0116156 0.248950i
\(76\) 0 0
\(77\) −1.16043 4.33078i −0.132243 0.493538i
\(78\) 0 0
\(79\) −1.11184 1.92576i −0.125092 0.216665i 0.796677 0.604405i \(-0.206589\pi\)
−0.921769 + 0.387740i \(0.873256\pi\)
\(80\) 0 0
\(81\) −2.97677 + 8.49346i −0.330752 + 0.943718i
\(82\) 0 0
\(83\) −5.74772 1.54010i −0.630895 0.169048i −0.0708190 0.997489i \(-0.522561\pi\)
−0.560076 + 0.828441i \(0.689228\pi\)
\(84\) 0 0
\(85\) −12.9744 + 3.47649i −1.40727 + 0.377078i
\(86\) 0 0
\(87\) −3.66931 + 4.02848i −0.393391 + 0.431898i
\(88\) 0 0
\(89\) 6.12376i 0.649118i −0.945866 0.324559i \(-0.894784\pi\)
0.945866 0.324559i \(-0.105216\pi\)
\(90\) 0 0
\(91\) −12.7129 12.7129i −1.33268 1.33268i
\(92\) 0 0
\(93\) 1.16276 + 1.81318i 0.120573 + 0.188018i
\(94\) 0 0
\(95\) 8.32833 14.4251i 0.854469 1.47998i
\(96\) 0 0
\(97\) −2.21495 3.83640i −0.224894 0.389528i 0.731394 0.681956i \(-0.238870\pi\)
−0.956288 + 0.292428i \(0.905537\pi\)
\(98\) 0 0
\(99\) 3.87037 1.43498i 0.388987 0.144221i
\(100\) 0 0
\(101\) −4.62330 + 17.2544i −0.460035 + 1.71688i 0.212811 + 0.977093i \(0.431738\pi\)
−0.672847 + 0.739782i \(0.734929\pi\)
\(102\) 0 0
\(103\) 8.73448 + 5.04285i 0.860634 + 0.496887i 0.864224 0.503106i \(-0.167810\pi\)
−0.00359067 + 0.999994i \(0.501143\pi\)
\(104\) 0 0
\(105\) −4.28182 13.4399i −0.417863 1.31160i
\(106\) 0 0
\(107\) −3.59876 3.59876i −0.347905 0.347905i 0.511423 0.859329i \(-0.329118\pi\)
−0.859329 + 0.511423i \(0.829118\pi\)
\(108\) 0 0
\(109\) −7.27011 + 7.27011i −0.696351 + 0.696351i −0.963621 0.267271i \(-0.913878\pi\)
0.267271 + 0.963621i \(0.413878\pi\)
\(110\) 0 0
\(111\) −13.6787 + 4.35791i −1.29833 + 0.413635i
\(112\) 0 0
\(113\) 5.81099 10.0649i 0.546652 0.946828i −0.451849 0.892094i \(-0.649236\pi\)
0.998501 0.0547341i \(-0.0174311\pi\)
\(114\) 0 0
\(115\) −8.05251 2.15766i −0.750900 0.201203i
\(116\) 0 0
\(117\) 10.5636 12.7433i 0.976604 1.17811i
\(118\) 0 0
\(119\) −15.1667 + 8.75652i −1.39033 + 0.802709i
\(120\) 0 0
\(121\) 7.88670 + 4.55339i 0.716973 + 0.413945i
\(122\) 0 0
\(123\) −4.73263 + 3.03496i −0.426727 + 0.273653i
\(124\) 0 0
\(125\) 6.63394 6.63394i 0.593358 0.593358i
\(126\) 0 0
\(127\) 7.37772 0.654667 0.327333 0.944909i \(-0.393850\pi\)
0.327333 + 0.944909i \(0.393850\pi\)
\(128\) 0 0
\(129\) 7.99685 + 7.28387i 0.704083 + 0.641309i
\(130\) 0 0
\(131\) 3.93512 + 14.6861i 0.343813 + 1.28313i 0.893992 + 0.448082i \(0.147893\pi\)
−0.550179 + 0.835047i \(0.685440\pi\)
\(132\) 0 0
\(133\) 5.62085 20.9773i 0.487389 1.81896i
\(134\) 0 0
\(135\) 11.9527 5.07712i 1.02873 0.436969i
\(136\) 0 0
\(137\) 11.5397 6.66247i 0.985906 0.569213i 0.0818576 0.996644i \(-0.473915\pi\)
0.904048 + 0.427431i \(0.140581\pi\)
\(138\) 0 0
\(139\) 16.2127 4.34417i 1.37514 0.368468i 0.505787 0.862658i \(-0.331202\pi\)
0.869354 + 0.494191i \(0.164535\pi\)
\(140\) 0 0
\(141\) −7.52571 + 0.351138i −0.633779 + 0.0295712i
\(142\) 0 0
\(143\) −7.59170 −0.634849
\(144\) 0 0
\(145\) 7.86261 0.652955
\(146\) 0 0
\(147\) −3.38285 5.27511i −0.279012 0.435084i
\(148\) 0 0
\(149\) 12.7771 3.42362i 1.04674 0.280474i 0.305838 0.952084i \(-0.401063\pi\)
0.740905 + 0.671610i \(0.234397\pi\)
\(150\) 0 0
\(151\) 10.3438 5.97202i 0.841769 0.485996i −0.0160959 0.999870i \(-0.505124\pi\)
0.857865 + 0.513875i \(0.171790\pi\)
\(152\) 0 0
\(153\) −9.32695 13.1521i −0.754039 1.06328i
\(154\) 0 0
\(155\) 0.804418 3.00213i 0.0646124 0.241137i
\(156\) 0 0
\(157\) −3.88412 14.4957i −0.309986 1.15689i −0.928567 0.371164i \(-0.878959\pi\)
0.618581 0.785721i \(-0.287708\pi\)
\(158\) 0 0
\(159\) −0.313524 + 0.0998858i −0.0248641 + 0.00792146i
\(160\) 0 0
\(161\) −10.8694 −0.856627
\(162\) 0 0
\(163\) −16.4303 + 16.4303i −1.28692 + 1.28692i −0.350278 + 0.936646i \(0.613913\pi\)
−0.936646 + 0.350278i \(0.886087\pi\)
\(164\) 0 0
\(165\) −5.29137 2.73443i −0.411933 0.212875i
\(166\) 0 0
\(167\) −11.8153 6.82158i −0.914297 0.527870i −0.0324861 0.999472i \(-0.510342\pi\)
−0.881811 + 0.471602i \(0.843676\pi\)
\(168\) 0 0
\(169\) −15.1054 + 8.72112i −1.16196 + 0.670855i
\(170\) 0 0
\(171\) 19.7109 + 3.35410i 1.50733 + 0.256494i
\(172\) 0 0
\(173\) −4.31671 1.15666i −0.328193 0.0879391i 0.0909602 0.995855i \(-0.471006\pi\)
−0.419153 + 0.907915i \(0.637673\pi\)
\(174\) 0 0
\(175\) −2.03024 + 3.51648i −0.153472 + 0.265821i
\(176\) 0 0
\(177\) 0.846482 3.87303i 0.0636255 0.291114i
\(178\) 0 0
\(179\) 17.9090 17.9090i 1.33858 1.33858i 0.441146 0.897435i \(-0.354572\pi\)
0.897435 0.441146i \(-0.145428\pi\)
\(180\) 0 0
\(181\) 9.03811 + 9.03811i 0.671797 + 0.671797i 0.958130 0.286333i \(-0.0924363\pi\)
−0.286333 + 0.958130i \(0.592436\pi\)
\(182\) 0 0
\(183\) −2.77574 + 3.04744i −0.205188 + 0.225273i
\(184\) 0 0
\(185\) 17.9396 + 10.3574i 1.31894 + 0.761493i
\(186\) 0 0
\(187\) −1.91398 + 7.14305i −0.139964 + 0.522352i
\(188\) 0 0
\(189\) 13.3399 10.4276i 0.970334 0.758495i
\(190\) 0 0
\(191\) −5.50837 9.54078i −0.398572 0.690346i 0.594978 0.803742i \(-0.297161\pi\)
−0.993550 + 0.113395i \(0.963827\pi\)
\(192\) 0 0
\(193\) −8.22204 + 14.2410i −0.591836 + 1.02509i 0.402149 + 0.915574i \(0.368263\pi\)
−0.993985 + 0.109515i \(0.965070\pi\)
\(194\) 0 0
\(195\) −23.8579 + 1.11317i −1.70850 + 0.0797158i
\(196\) 0 0
\(197\) 2.20874 + 2.20874i 0.157366 + 0.157366i 0.781398 0.624033i \(-0.214507\pi\)
−0.624033 + 0.781398i \(0.714507\pi\)
\(198\) 0 0
\(199\) 11.9387i 0.846312i −0.906057 0.423156i \(-0.860922\pi\)
0.906057 0.423156i \(-0.139078\pi\)
\(200\) 0 0
\(201\) 0.196682 + 0.0429865i 0.0138729 + 0.00303203i
\(202\) 0 0
\(203\) 9.90212 2.65326i 0.694992 0.186223i
\(204\) 0 0
\(205\) 7.83594 + 2.09963i 0.547286 + 0.146645i
\(206\) 0 0
\(207\) −0.931794 9.96353i −0.0647642 0.692513i
\(208\) 0 0
\(209\) −4.58515 7.94172i −0.317162 0.549340i
\(210\) 0 0
\(211\) 1.55584 + 5.80646i 0.107108 + 0.399733i 0.998576 0.0533513i \(-0.0169903\pi\)
−0.891468 + 0.453084i \(0.850324\pi\)
\(212\) 0 0
\(213\) 4.94115 + 2.55344i 0.338562 + 0.174959i
\(214\) 0 0
\(215\) 15.6079i 1.06445i
\(216\) 0 0
\(217\) 4.05231i 0.275089i
\(218\) 0 0
\(219\) 15.0094 + 7.75644i 1.01424 + 0.524131i
\(220\) 0 0
\(221\) 7.67493 + 28.6432i 0.516271 + 1.92675i
\(222\) 0 0
\(223\) −4.14191 7.17400i −0.277363 0.480407i 0.693366 0.720586i \(-0.256127\pi\)
−0.970729 + 0.240179i \(0.922794\pi\)
\(224\) 0 0
\(225\) −3.39746 1.55958i −0.226497 0.103972i
\(226\) 0 0
\(227\) 17.3293 + 4.64336i 1.15018 + 0.308191i 0.783039 0.621973i \(-0.213669\pi\)
0.367145 + 0.930164i \(0.380335\pi\)
\(228\) 0 0
\(229\) −9.17552 + 2.45857i −0.606335 + 0.162467i −0.548908 0.835883i \(-0.684956\pi\)
−0.0574270 + 0.998350i \(0.518290\pi\)
\(230\) 0 0
\(231\) −7.58666 1.65813i −0.499166 0.109097i
\(232\) 0 0
\(233\) 6.39614i 0.419025i −0.977806 0.209512i \(-0.932812\pi\)
0.977806 0.209512i \(-0.0671877\pi\)
\(234\) 0 0
\(235\) 7.68686 + 7.68686i 0.501435 + 0.501435i
\(236\) 0 0
\(237\) −3.84733 + 0.179511i −0.249911 + 0.0116605i
\(238\) 0 0
\(239\) −12.4015 + 21.4800i −0.802187 + 1.38943i 0.115987 + 0.993251i \(0.462997\pi\)
−0.918174 + 0.396178i \(0.870336\pi\)
\(240\) 0 0
\(241\) 4.32533 + 7.49168i 0.278619 + 0.482582i 0.971042 0.238910i \(-0.0767901\pi\)
−0.692423 + 0.721492i \(0.743457\pi\)
\(242\) 0 0
\(243\) 10.7021 + 11.3342i 0.686542 + 0.727090i
\(244\) 0 0
\(245\) −2.34031 + 8.73415i −0.149517 + 0.558005i
\(246\) 0 0
\(247\) −31.8458 18.3862i −2.02630 1.16989i
\(248\) 0 0
\(249\) −6.94023 + 7.61957i −0.439819 + 0.482871i
\(250\) 0 0
\(251\) 1.34312 + 1.34312i 0.0847772 + 0.0847772i 0.748224 0.663446i \(-0.230907\pi\)
−0.663446 + 0.748224i \(0.730907\pi\)
\(252\) 0 0
\(253\) −3.24540 + 3.24540i −0.204037 + 0.204037i
\(254\) 0 0
\(255\) −4.96752 + 22.7286i −0.311078 + 1.42332i
\(256\) 0 0
\(257\) −13.0905 + 22.6734i −0.816563 + 1.41433i 0.0916380 + 0.995792i \(0.470790\pi\)
−0.908201 + 0.418535i \(0.862544\pi\)
\(258\) 0 0
\(259\) 26.0881 + 6.99029i 1.62104 + 0.434356i
\(260\) 0 0
\(261\) 3.28102 + 8.84942i 0.203090 + 0.547765i
\(262\) 0 0
\(263\) −6.75594 + 3.90054i −0.416589 + 0.240518i −0.693617 0.720344i \(-0.743984\pi\)
0.277028 + 0.960862i \(0.410651\pi\)
\(264\) 0 0
\(265\) 0.411185 + 0.237398i 0.0252589 + 0.0145832i
\(266\) 0 0
\(267\) −9.42284 4.86945i −0.576668 0.298005i
\(268\) 0 0
\(269\) 4.79063 4.79063i 0.292090 0.292090i −0.545815 0.837905i \(-0.683780\pi\)
0.837905 + 0.545815i \(0.183780\pi\)
\(270\) 0 0
\(271\) 24.8625 1.51029 0.755144 0.655559i \(-0.227567\pi\)
0.755144 + 0.655559i \(0.227567\pi\)
\(272\) 0 0
\(273\) −29.6708 + 9.45283i −1.79576 + 0.572111i
\(274\) 0 0
\(275\) 0.443764 + 1.65615i 0.0267599 + 0.0998695i
\(276\) 0 0
\(277\) −0.238901 + 0.891589i −0.0143541 + 0.0535704i −0.972731 0.231934i \(-0.925495\pi\)
0.958377 + 0.285505i \(0.0921612\pi\)
\(278\) 0 0
\(279\) 3.71459 0.347390i 0.222387 0.0207977i
\(280\) 0 0
\(281\) −24.6632 + 14.2393i −1.47128 + 0.849446i −0.999480 0.0322571i \(-0.989730\pi\)
−0.471804 + 0.881703i \(0.656397\pi\)
\(282\) 0 0
\(283\) −6.41436 + 1.71872i −0.381294 + 0.102167i −0.444375 0.895841i \(-0.646574\pi\)
0.0630806 + 0.998008i \(0.479907\pi\)
\(284\) 0 0
\(285\) −15.5739 24.2855i −0.922519 1.43855i
\(286\) 0 0
\(287\) 10.5771 0.624344
\(288\) 0 0
\(289\) 11.8855 0.699145
\(290\) 0 0
\(291\) −7.66447 + 0.357612i −0.449299 + 0.0209636i
\(292\) 0 0
\(293\) −9.42116 + 2.52439i −0.550390 + 0.147477i −0.523288 0.852156i \(-0.675295\pi\)
−0.0271023 + 0.999633i \(0.508628\pi\)
\(294\) 0 0
\(295\) −4.95402 + 2.86020i −0.288434 + 0.166527i
\(296\) 0 0
\(297\) 0.869562 7.09653i 0.0504571 0.411783i
\(298\) 0 0
\(299\) −4.76340 + 17.7773i −0.275475 + 1.02809i
\(300\) 0 0
\(301\) −5.26694 19.6565i −0.303582 1.13298i
\(302\) 0 0
\(303\) 22.8736 + 20.8342i 1.31405 + 1.19690i
\(304\) 0 0
\(305\) 5.94786 0.340574
\(306\) 0 0
\(307\) 4.55233 4.55233i 0.259815 0.259815i −0.565164 0.824979i \(-0.691187\pi\)
0.824979 + 0.565164i \(0.191187\pi\)
\(308\) 0 0
\(309\) 14.7050 9.43010i 0.836540 0.536459i
\(310\) 0 0
\(311\) 5.56997 + 3.21582i 0.315844 + 0.182353i 0.649539 0.760329i \(-0.274962\pi\)
−0.333695 + 0.942681i \(0.608295\pi\)
\(312\) 0 0
\(313\) −2.90181 + 1.67536i −0.164020 + 0.0946969i −0.579763 0.814785i \(-0.696855\pi\)
0.415743 + 0.909482i \(0.363522\pi\)
\(314\) 0 0
\(315\) −24.0852 4.09844i −1.35705 0.230921i
\(316\) 0 0
\(317\) −14.6346 3.92134i −0.821963 0.220244i −0.176758 0.984254i \(-0.556561\pi\)
−0.645204 + 0.764010i \(0.723228\pi\)
\(318\) 0 0
\(319\) 2.16438 3.74881i 0.121182 0.209893i
\(320\) 0 0
\(321\) −8.39917 + 2.67590i −0.468796 + 0.149354i
\(322\) 0 0
\(323\) −25.3284 + 25.3284i −1.40931 + 1.40931i
\(324\) 0 0
\(325\) 4.86159 + 4.86159i 0.269672 + 0.269672i
\(326\) 0 0
\(327\) 5.40577 + 16.9678i 0.298940 + 0.938319i
\(328\) 0 0
\(329\) 12.2747 + 7.08682i 0.676728 + 0.390709i
\(330\) 0 0
\(331\) 2.68206 10.0096i 0.147420 0.550177i −0.852216 0.523190i \(-0.824742\pi\)
0.999636 0.0269876i \(-0.00859146\pi\)
\(332\) 0 0
\(333\) −4.17128 + 24.5132i −0.228585 + 1.34331i
\(334\) 0 0
\(335\) −0.145248 0.251578i −0.00793577 0.0137452i
\(336\) 0 0
\(337\) 6.52225 11.2969i 0.355289 0.615379i −0.631878 0.775068i \(-0.717716\pi\)
0.987167 + 0.159689i \(0.0510490\pi\)
\(338\) 0 0
\(339\) −10.8665 16.9449i −0.590187 0.920321i
\(340\) 0 0
\(341\) −1.20995 1.20995i −0.0655223 0.0655223i
\(342\) 0 0
\(343\) 11.0203i 0.595038i
\(344\) 0 0
\(345\) −9.72320 + 10.6750i −0.523480 + 0.574720i
\(346\) 0 0
\(347\) −23.5314 + 6.30523i −1.26323 + 0.338482i −0.827435 0.561562i \(-0.810201\pi\)
−0.435798 + 0.900044i \(0.643534\pi\)
\(348\) 0 0
\(349\) 27.7772 + 7.44289i 1.48688 + 0.398409i 0.908683 0.417487i \(-0.137089\pi\)
0.578199 + 0.815896i \(0.303756\pi\)
\(350\) 0 0
\(351\) −11.2086 26.3876i −0.598271 1.40847i
\(352\) 0 0
\(353\) 17.6048 + 30.4924i 0.937010 + 1.62295i 0.771011 + 0.636822i \(0.219752\pi\)
0.165999 + 0.986126i \(0.446915\pi\)
\(354\) 0 0
\(355\) −2.07714 7.75199i −0.110243 0.411433i
\(356\) 0 0
\(357\) 1.41378 + 30.3005i 0.0748249 + 1.60367i
\(358\) 0 0
\(359\) 17.6127i 0.929564i 0.885425 + 0.464782i \(0.153867\pi\)
−0.885425 + 0.464782i \(0.846133\pi\)
\(360\) 0 0
\(361\) 25.4188i 1.33783i
\(362\) 0 0
\(363\) 13.2777 8.51480i 0.696901 0.446911i
\(364\) 0 0
\(365\) −6.30960 23.5477i −0.330259 1.23255i
\(366\) 0 0
\(367\) 8.31959 + 14.4100i 0.434279 + 0.752193i 0.997236 0.0742925i \(-0.0236698\pi\)
−0.562957 + 0.826486i \(0.690337\pi\)
\(368\) 0 0
\(369\) 0.906734 + 9.69556i 0.0472027 + 0.504731i
\(370\) 0 0
\(371\) 0.597954 + 0.160221i 0.0310442 + 0.00831828i
\(372\) 0 0
\(373\) −3.22714 + 0.864710i −0.167095 + 0.0447730i −0.341397 0.939919i \(-0.610900\pi\)
0.174302 + 0.984692i \(0.444233\pi\)
\(374\) 0 0
\(375\) −4.93274 15.4830i −0.254726 0.799539i
\(376\) 0 0
\(377\) 17.3580i 0.893984i
\(378\) 0 0
\(379\) 10.2384 + 10.2384i 0.525910 + 0.525910i 0.919350 0.393440i \(-0.128715\pi\)
−0.393440 + 0.919350i \(0.628715\pi\)
\(380\) 0 0
\(381\) 5.86656 11.3523i 0.300553 0.581598i
\(382\) 0 0
\(383\) −5.44755 + 9.43544i −0.278357 + 0.482128i −0.970977 0.239175i \(-0.923123\pi\)
0.692620 + 0.721303i \(0.256456\pi\)
\(384\) 0 0
\(385\) 5.60270 + 9.70416i 0.285540 + 0.494570i
\(386\) 0 0
\(387\) 17.5668 6.51308i 0.892971 0.331079i
\(388\) 0 0
\(389\) 3.72849 13.9149i 0.189042 0.705513i −0.804687 0.593699i \(-0.797667\pi\)
0.993729 0.111815i \(-0.0356663\pi\)
\(390\) 0 0
\(391\) 15.5258 + 8.96381i 0.785172 + 0.453319i
\(392\) 0 0
\(393\) 25.7271 + 5.62287i 1.29776 + 0.283636i
\(394\) 0 0
\(395\) 3.92972 + 3.92972i 0.197725 + 0.197725i
\(396\) 0 0
\(397\) 15.4247 15.4247i 0.774145 0.774145i −0.204683 0.978828i \(-0.565616\pi\)
0.978828 + 0.204683i \(0.0656165\pi\)
\(398\) 0 0
\(399\) −27.8089 25.3295i −1.39219 1.26806i
\(400\) 0 0
\(401\) −3.21720 + 5.57235i −0.160659 + 0.278270i −0.935105 0.354370i \(-0.884695\pi\)
0.774446 + 0.632640i \(0.218029\pi\)
\(402\) 0 0
\(403\) −6.62770 1.77589i −0.330149 0.0884633i
\(404\) 0 0
\(405\) 1.69214 22.4292i 0.0840832 1.11452i
\(406\) 0 0
\(407\) 9.87661 5.70227i 0.489566 0.282651i
\(408\) 0 0
\(409\) 31.8642 + 18.3968i 1.57558 + 0.909663i 0.995465 + 0.0951294i \(0.0303265\pi\)
0.580117 + 0.814533i \(0.303007\pi\)
\(410\) 0 0
\(411\) −1.07568 23.0544i −0.0530594 1.13719i
\(412\) 0 0
\(413\) −5.27387 + 5.27387i −0.259510 + 0.259510i
\(414\) 0 0
\(415\) 14.8716 0.730017
\(416\) 0 0
\(417\) 6.20735 28.4013i 0.303975 1.39082i
\(418\) 0 0
\(419\) 5.78093 + 21.5747i 0.282417 + 1.05399i 0.950706 + 0.310093i \(0.100360\pi\)
−0.668290 + 0.743901i \(0.732973\pi\)
\(420\) 0 0
\(421\) 2.33477 8.71347i 0.113790 0.424669i −0.885404 0.464822i \(-0.846118\pi\)
0.999194 + 0.0401539i \(0.0127848\pi\)
\(422\) 0 0
\(423\) −5.44393 + 11.8593i −0.264693 + 0.576618i
\(424\) 0 0
\(425\) 5.79996 3.34861i 0.281340 0.162431i
\(426\) 0 0
\(427\) 7.49070 2.00713i 0.362500 0.0971316i
\(428\) 0 0
\(429\) −6.03671 + 11.6816i −0.291455 + 0.563993i
\(430\) 0 0
\(431\) 2.82883 0.136260 0.0681299 0.997676i \(-0.478297\pi\)
0.0681299 + 0.997676i \(0.478297\pi\)
\(432\) 0 0
\(433\) −9.90919 −0.476205 −0.238103 0.971240i \(-0.576525\pi\)
−0.238103 + 0.971240i \(0.576525\pi\)
\(434\) 0 0
\(435\) 6.25214 12.0985i 0.299767 0.580077i
\(436\) 0 0
\(437\) −21.4739 + 5.75390i −1.02723 + 0.275246i
\(438\) 0 0
\(439\) −5.53112 + 3.19339i −0.263986 + 0.152412i −0.626151 0.779701i \(-0.715371\pi\)
0.362166 + 0.932114i \(0.382037\pi\)
\(440\) 0 0
\(441\) −10.8069 + 1.01067i −0.514616 + 0.0481272i
\(442\) 0 0
\(443\) 4.33005 16.1600i 0.205727 0.767783i −0.783500 0.621392i \(-0.786568\pi\)
0.989227 0.146391i \(-0.0467658\pi\)
\(444\) 0 0
\(445\) 3.96113 + 14.7831i 0.187776 + 0.700788i
\(446\) 0 0
\(447\) 4.89198 22.3830i 0.231383 1.05868i
\(448\) 0 0
\(449\) −23.7209 −1.11946 −0.559729 0.828676i \(-0.689095\pi\)
−0.559729 + 0.828676i \(0.689095\pi\)
\(450\) 0 0
\(451\) 3.15812 3.15812i 0.148710 0.148710i
\(452\) 0 0
\(453\) −0.964205 20.6652i −0.0453023 0.970935i
\(454\) 0 0
\(455\) 38.9131 + 22.4665i 1.82427 + 1.05324i
\(456\) 0 0
\(457\) −25.8782 + 14.9408i −1.21053 + 0.698901i −0.962875 0.269946i \(-0.912994\pi\)
−0.247657 + 0.968848i \(0.579661\pi\)
\(458\) 0 0
\(459\) −27.6541 + 3.89351i −1.29078 + 0.181733i
\(460\) 0 0
\(461\) 26.9785 + 7.22887i 1.25651 + 0.336682i 0.824850 0.565352i \(-0.191260\pi\)
0.431665 + 0.902034i \(0.357926\pi\)
\(462\) 0 0
\(463\) −9.00954 + 15.6050i −0.418709 + 0.725225i −0.995810 0.0914480i \(-0.970850\pi\)
0.577101 + 0.816673i \(0.304184\pi\)
\(464\) 0 0
\(465\) −3.97982 3.62500i −0.184560 0.168105i
\(466\) 0 0
\(467\) −3.24566 + 3.24566i −0.150191 + 0.150191i −0.778204 0.628012i \(-0.783869\pi\)
0.628012 + 0.778204i \(0.283869\pi\)
\(468\) 0 0
\(469\) −0.267820 0.267820i −0.0123668 0.0123668i
\(470\) 0 0
\(471\) −25.3936 5.54998i −1.17008 0.255730i
\(472\) 0 0
\(473\) −7.44169 4.29646i −0.342169 0.197552i
\(474\) 0 0
\(475\) −2.14949 + 8.02199i −0.0986252 + 0.368074i
\(476\) 0 0
\(477\) −0.0956080 + 0.561856i −0.00437759 + 0.0257256i
\(478\) 0 0
\(479\) 1.27156 + 2.20241i 0.0580991 + 0.100631i 0.893612 0.448840i \(-0.148163\pi\)
−0.835513 + 0.549471i \(0.814829\pi\)
\(480\) 0 0
\(481\) 22.8657 39.6046i 1.04259 1.80582i
\(482\) 0 0
\(483\) −8.64304 + 16.7251i −0.393272 + 0.761018i
\(484\) 0 0
\(485\) 7.82859 + 7.82859i 0.355478 + 0.355478i
\(486\) 0 0
\(487\) 26.4554i 1.19881i 0.800447 + 0.599404i \(0.204596\pi\)
−0.800447 + 0.599404i \(0.795404\pi\)
\(488\) 0 0
\(489\) 12.2170 + 38.3469i 0.552470 + 1.73411i
\(490\) 0 0
\(491\) 21.9322 5.87672i 0.989787 0.265213i 0.272626 0.962120i \(-0.412108\pi\)
0.717161 + 0.696907i \(0.245441\pi\)
\(492\) 0 0
\(493\) −16.3322 4.37621i −0.735567 0.197095i
\(494\) 0 0
\(495\) −8.41511 + 5.96767i −0.378231 + 0.268227i
\(496\) 0 0
\(497\) −5.23187 9.06186i −0.234681 0.406480i
\(498\) 0 0
\(499\) −7.34516 27.4125i −0.328815 1.22715i −0.910421 0.413683i \(-0.864242\pi\)
0.581606 0.813470i \(-0.302424\pi\)
\(500\) 0 0
\(501\) −19.8918 + 12.7563i −0.888701 + 0.569910i
\(502\) 0 0
\(503\) 32.0583i 1.42941i −0.699427 0.714704i \(-0.746561\pi\)
0.699427 0.714704i \(-0.253439\pi\)
\(504\) 0 0
\(505\) 44.6437i 1.98662i
\(506\) 0 0
\(507\) 1.40806 + 30.1780i 0.0625341 + 1.34025i
\(508\) 0 0
\(509\) 7.15242 + 26.6932i 0.317025 + 1.18316i 0.922089 + 0.386978i \(0.126481\pi\)
−0.605064 + 0.796177i \(0.706852\pi\)
\(510\) 0 0
\(511\) −15.8925 27.5267i −0.703044 1.21771i
\(512\) 0 0
\(513\) 20.8346 27.6627i 0.919871 1.22134i
\(514\) 0 0
\(515\) −24.3475 6.52390i −1.07288 0.287477i
\(516\) 0 0
\(517\) 5.78101 1.54902i 0.254248 0.0681256i
\(518\) 0 0
\(519\) −5.21232 + 5.72252i −0.228795 + 0.251191i
\(520\) 0 0
\(521\) 6.90291i 0.302422i −0.988502 0.151211i \(-0.951683\pi\)
0.988502 0.151211i \(-0.0483173\pi\)
\(522\) 0 0
\(523\) −14.2754 14.2754i −0.624219 0.624219i 0.322389 0.946607i \(-0.395514\pi\)
−0.946607 + 0.322389i \(0.895514\pi\)
\(524\) 0 0
\(525\) 3.79653 + 5.92020i 0.165694 + 0.258379i
\(526\) 0 0
\(527\) −3.34188 + 5.78830i −0.145574 + 0.252142i
\(528\) 0 0
\(529\) −5.93666 10.2826i −0.258116 0.447069i
\(530\) 0 0
\(531\) −5.28645 4.38223i −0.229413 0.190173i
\(532\) 0 0
\(533\) 4.63529 17.2992i 0.200777 0.749310i
\(534\) 0 0
\(535\) 11.0155 + 6.35979i 0.476241 + 0.274958i
\(536\) 0 0
\(537\) −13.3164 41.7979i −0.574646 1.80371i
\(538\) 0 0
\(539\) 3.52012 + 3.52012i 0.151622 + 0.151622i
\(540\) 0 0
\(541\) −15.3215 + 15.3215i −0.658723 + 0.658723i −0.955078 0.296355i \(-0.904229\pi\)
0.296355 + 0.955078i \(0.404229\pi\)
\(542\) 0 0
\(543\) 21.0941 6.72038i 0.905234 0.288399i
\(544\) 0 0
\(545\) 12.8479 22.2532i 0.550342 0.953220i
\(546\) 0 0
\(547\) −4.09038 1.09601i −0.174892 0.0468622i 0.170310 0.985390i \(-0.445523\pi\)
−0.345202 + 0.938528i \(0.612190\pi\)
\(548\) 0 0
\(549\) 2.48200 + 6.69436i 0.105929 + 0.285708i
\(550\) 0 0
\(551\) 18.1584 10.4837i 0.773572 0.446622i
\(552\) 0 0
\(553\) 6.27515 + 3.62296i 0.266847 + 0.154064i
\(554\) 0 0
\(555\) 30.2024 19.3683i 1.28202 0.822138i
\(556\) 0 0
\(557\) 3.77104 3.77104i 0.159784 0.159784i −0.622687 0.782471i \(-0.713959\pi\)
0.782471 + 0.622687i \(0.213959\pi\)
\(558\) 0 0
\(559\) −34.4571 −1.45738
\(560\) 0 0
\(561\) 9.46931 + 8.62506i 0.399795 + 0.364150i
\(562\) 0 0
\(563\) −4.72321 17.6273i −0.199060 0.742901i −0.991178 0.132534i \(-0.957689\pi\)
0.792119 0.610367i \(-0.208978\pi\)
\(564\) 0 0
\(565\) −7.51763 + 28.0562i −0.316269 + 1.18033i
\(566\) 0 0
\(567\) −5.43775 28.8182i −0.228364 1.21025i
\(568\) 0 0
\(569\) −10.5687 + 6.10184i −0.443062 + 0.255802i −0.704896 0.709311i \(-0.749006\pi\)
0.261833 + 0.965113i \(0.415673\pi\)
\(570\) 0 0
\(571\) −10.1445 + 2.71820i −0.424533 + 0.113753i −0.464759 0.885437i \(-0.653859\pi\)
0.0402258 + 0.999191i \(0.487192\pi\)
\(572\) 0 0
\(573\) −19.0608 + 0.889348i −0.796277 + 0.0371531i
\(574\) 0 0
\(575\) 4.15660 0.173342
\(576\) 0 0
\(577\) −11.0011 −0.457982 −0.228991 0.973429i \(-0.573543\pi\)
−0.228991 + 0.973429i \(0.573543\pi\)
\(578\) 0 0
\(579\) 15.3752 + 23.9756i 0.638970 + 0.996391i
\(580\) 0 0
\(581\) 18.7291 5.01846i 0.777016 0.208201i
\(582\) 0 0
\(583\) 0.226378 0.130699i 0.00937560 0.00541300i
\(584\) 0 0
\(585\) −17.2582 + 37.5960i −0.713540 + 1.55440i
\(586\) 0 0
\(587\) 4.43586 16.5549i 0.183088 0.683292i −0.811944 0.583735i \(-0.801591\pi\)
0.995032 0.0995570i \(-0.0317426\pi\)
\(588\) 0 0
\(589\) −2.14516 8.00586i −0.0883900 0.329876i
\(590\) 0 0
\(591\) 5.15498 1.64233i 0.212048 0.0675564i
\(592\) 0 0
\(593\) 38.5906 1.58472 0.792362 0.610051i \(-0.208851\pi\)
0.792362 + 0.610051i \(0.208851\pi\)
\(594\) 0 0
\(595\) 30.9493 30.9493i 1.26880 1.26880i
\(596\) 0 0
\(597\) −18.3705 9.49332i −0.751853 0.388536i
\(598\) 0 0
\(599\) 4.83678 + 2.79252i 0.197626 + 0.114099i 0.595547 0.803320i \(-0.296935\pi\)
−0.397922 + 0.917419i \(0.630268\pi\)
\(600\) 0 0
\(601\) 29.8602 17.2398i 1.21802 0.703227i 0.253529 0.967328i \(-0.418409\pi\)
0.964495 + 0.264101i \(0.0850753\pi\)
\(602\) 0 0
\(603\) 0.222541 0.268460i 0.00906257 0.0109325i
\(604\) 0 0
\(605\) −21.9843 5.89068i −0.893790 0.239490i
\(606\) 0 0
\(607\) −7.58467 + 13.1370i −0.307852 + 0.533216i −0.977892 0.209109i \(-0.932944\pi\)
0.670040 + 0.742325i \(0.266277\pi\)
\(608\) 0 0
\(609\) 3.79123 17.3465i 0.153628 0.702917i
\(610\) 0 0
\(611\) 16.9700 16.9700i 0.686534 0.686534i
\(612\) 0 0
\(613\) 7.90551 + 7.90551i 0.319301 + 0.319301i 0.848498 0.529198i \(-0.177507\pi\)
−0.529198 + 0.848498i \(0.677507\pi\)
\(614\) 0 0
\(615\) 9.46170 10.3879i 0.381533 0.418879i
\(616\) 0 0
\(617\) −25.0266 14.4491i −1.00753 0.581700i −0.0970648 0.995278i \(-0.530945\pi\)
−0.910468 + 0.413578i \(0.864279\pi\)
\(618\) 0 0
\(619\) −8.96627 + 33.4626i −0.360385 + 1.34497i 0.513186 + 0.858277i \(0.328465\pi\)
−0.873571 + 0.486697i \(0.838202\pi\)
\(620\) 0 0
\(621\) −16.0722 6.48894i −0.644953 0.260392i
\(622\) 0 0
\(623\) 9.97724 + 17.2811i 0.399730 + 0.692352i
\(624\) 0 0
\(625\) −14.8389 + 25.7017i −0.593555 + 1.02807i
\(626\) 0 0
\(627\) −15.8662 + 0.740291i −0.633634 + 0.0295644i
\(628\) 0 0
\(629\) −31.4994 31.4994i −1.25596 1.25596i
\(630\) 0 0
\(631\) 30.4132i 1.21073i 0.795948 + 0.605365i \(0.206973\pi\)
−0.795948 + 0.605365i \(0.793027\pi\)
\(632\) 0 0
\(633\) 10.1717 + 2.22312i 0.404291 + 0.0883611i
\(634\) 0 0
\(635\) −17.8103 + 4.77225i −0.706779 + 0.189381i
\(636\) 0 0
\(637\) 19.2821 + 5.16663i 0.763985 + 0.204709i
\(638\) 0 0
\(639\) 7.85814 5.57269i 0.310863 0.220452i
\(640\) 0 0
\(641\) −6.19753 10.7344i −0.244788 0.423985i 0.717284 0.696781i \(-0.245385\pi\)
−0.962072 + 0.272796i \(0.912052\pi\)
\(642\) 0 0
\(643\) −6.97693 26.0383i −0.275143 1.02685i −0.955745 0.294195i \(-0.904948\pi\)
0.680602 0.732653i \(-0.261718\pi\)
\(644\) 0 0
\(645\) −24.0164 12.4110i −0.945646 0.488682i
\(646\) 0 0
\(647\) 1.44109i 0.0566551i −0.999599 0.0283275i \(-0.990982\pi\)
0.999599 0.0283275i \(-0.00901814\pi\)
\(648\) 0 0
\(649\) 3.14936i 0.123623i
\(650\) 0 0
\(651\) −6.23543 3.22229i −0.244386 0.126291i
\(652\) 0 0
\(653\) 3.87857 + 14.4750i 0.151780 + 0.566451i 0.999360 + 0.0357824i \(0.0113923\pi\)
−0.847580 + 0.530668i \(0.821941\pi\)
\(654\) 0 0
\(655\) −18.9993 32.9077i −0.742363 1.28581i
\(656\) 0 0
\(657\) 23.8702 16.9278i 0.931264 0.660417i
\(658\) 0 0
\(659\) 5.05876 + 1.35549i 0.197061 + 0.0528024i 0.356000 0.934486i \(-0.384140\pi\)
−0.158938 + 0.987289i \(0.550807\pi\)
\(660\) 0 0
\(661\) 19.8188 5.31043i 0.770862 0.206552i 0.148110 0.988971i \(-0.452681\pi\)
0.622752 + 0.782419i \(0.286014\pi\)
\(662\) 0 0
\(663\) 50.1772 + 10.9666i 1.94872 + 0.425909i
\(664\) 0 0
\(665\) 54.2763i 2.10474i
\(666\) 0 0
\(667\) −7.42045 7.42045i −0.287321 0.287321i
\(668\) 0 0
\(669\) −14.3324 + 0.668728i −0.554123 + 0.0258545i
\(670\) 0 0
\(671\) 1.63729 2.83588i 0.0632071 0.109478i
\(672\) 0 0
\(673\) 7.01009 + 12.1418i 0.270219 + 0.468033i 0.968918 0.247383i \(-0.0795706\pi\)
−0.698699 + 0.715416i \(0.746237\pi\)
\(674\) 0 0
\(675\) −5.10135 + 3.98764i −0.196351 + 0.153484i
\(676\) 0 0
\(677\) 4.35650 16.2587i 0.167434 0.624872i −0.830283 0.557342i \(-0.811821\pi\)
0.997717 0.0675306i \(-0.0215120\pi\)
\(678\) 0 0
\(679\) 12.5010 + 7.21748i 0.479746 + 0.276982i
\(680\) 0 0
\(681\) 20.9247 22.9728i 0.801834 0.880321i
\(682\) 0 0
\(683\) −26.6987 26.6987i −1.02160 1.02160i −0.999762 0.0218370i \(-0.993049\pi\)
−0.0218370 0.999762i \(-0.506951\pi\)
\(684\) 0 0
\(685\) −23.5480 + 23.5480i −0.899724 + 0.899724i
\(686\) 0 0
\(687\) −3.51303 + 16.0737i −0.134031 + 0.613248i
\(688\) 0 0
\(689\) 0.524096 0.907760i 0.0199665 0.0345829i
\(690\) 0 0
\(691\) 28.2719 + 7.57544i 1.07551 + 0.288183i 0.752757 0.658299i \(-0.228724\pi\)
0.322757 + 0.946482i \(0.395390\pi\)
\(692\) 0 0
\(693\) −8.58412 + 10.3553i −0.326084 + 0.393367i
\(694\) 0 0
\(695\) −36.3284 + 20.9742i −1.37801 + 0.795597i
\(696\) 0 0
\(697\) −15.1082 8.72273i −0.572264 0.330397i
\(698\) 0 0
\(699\) −9.84195 5.08603i −0.372257 0.192371i
\(700\) 0 0
\(701\) −28.6250 + 28.6250i −1.08115 + 1.08115i −0.0847476 + 0.996402i \(0.527008\pi\)
−0.996402 + 0.0847476i \(0.972992\pi\)
\(702\) 0 0
\(703\) 55.2409 2.08345
\(704\) 0 0
\(705\) 17.9404 5.71565i 0.675675 0.215264i
\(706\) 0 0
\(707\) −15.0652 56.2240i −0.566584 2.11452i
\(708\) 0 0
\(709\) 6.98798 26.0795i 0.262439 0.979437i −0.701360 0.712807i \(-0.747423\pi\)
0.963799 0.266629i \(-0.0859099\pi\)
\(710\) 0 0
\(711\) −2.78308 + 6.06276i −0.104374 + 0.227371i
\(712\) 0 0
\(713\) −3.59248 + 2.07412i −0.134539 + 0.0776764i
\(714\) 0 0
\(715\) 18.3268 4.91066i 0.685384 0.183648i
\(716\) 0 0
\(717\) 23.1907 + 36.1630i 0.866073 + 1.35053i
\(718\) 0 0
\(719\) −3.06518 −0.114312 −0.0571560 0.998365i \(-0.518203\pi\)
−0.0571560 + 0.998365i \(0.518203\pi\)
\(720\) 0 0
\(721\) −32.8646 −1.22394
\(722\) 0 0
\(723\) 14.9671 0.698341i 0.556632 0.0259716i
\(724\) 0 0
\(725\) −3.78670 + 1.01464i −0.140635 + 0.0376829i
\(726\) 0 0
\(727\) 12.5849 7.26589i 0.466748 0.269477i −0.248130 0.968727i \(-0.579816\pi\)
0.714877 + 0.699250i \(0.246483\pi\)
\(728\) 0 0
\(729\) 25.9504 7.45506i 0.961125 0.276113i
\(730\) 0 0
\(731\) −8.68713 + 32.4208i −0.321305 + 1.19913i
\(732\) 0 0
\(733\) −1.26777 4.73140i −0.0468263 0.174758i 0.938552 0.345137i \(-0.112168\pi\)
−0.985379 + 0.170379i \(0.945501\pi\)
\(734\) 0 0
\(735\) 11.5786 + 10.5463i 0.427083 + 0.389005i
\(736\) 0 0
\(737\) −0.159933 −0.00589119
\(738\) 0 0
\(739\) −27.6544 + 27.6544i −1.01728 + 1.01728i −0.0174359 + 0.999848i \(0.505550\pi\)
−0.999848 + 0.0174359i \(0.994450\pi\)
\(740\) 0 0
\(741\) −53.6144 + 34.3820i −1.96957 + 1.26306i
\(742\) 0 0
\(743\) −16.0882 9.28853i −0.590219 0.340763i 0.174965 0.984575i \(-0.444019\pi\)
−0.765184 + 0.643812i \(0.777352\pi\)
\(744\) 0 0
\(745\) −28.6302 + 16.5297i −1.04893 + 0.605600i
\(746\) 0 0
\(747\) 6.20580 + 16.7380i 0.227059 + 0.612413i
\(748\) 0 0
\(749\) 16.0189 + 4.29226i 0.585320 + 0.156836i
\(750\) 0 0
\(751\) −17.4576 + 30.2374i −0.637037 + 1.10338i 0.349043 + 0.937107i \(0.386507\pi\)
−0.986080 + 0.166273i \(0.946827\pi\)
\(752\) 0 0
\(753\) 3.13473 0.998694i 0.114236 0.0363944i
\(754\) 0 0
\(755\) −21.1077 + 21.1077i −0.768187 + 0.768187i
\(756\) 0 0
\(757\) 15.4255 + 15.4255i 0.560649 + 0.560649i 0.929492 0.368843i \(-0.120246\pi\)
−0.368843 + 0.929492i \(0.620246\pi\)
\(758\) 0 0
\(759\) 2.41315 + 7.57446i 0.0875919 + 0.274935i
\(760\) 0 0
\(761\) 14.7108 + 8.49331i 0.533268 + 0.307882i 0.742346 0.670017i \(-0.233713\pi\)
−0.209078 + 0.977899i \(0.567046\pi\)
\(762\) 0 0
\(763\) 8.67111 32.3610i 0.313915 1.17155i
\(764\) 0 0
\(765\) 31.0232 + 25.7168i 1.12165 + 0.929795i
\(766\) 0 0
\(767\) 6.31438 + 10.9368i 0.227999 + 0.394906i
\(768\) 0 0
\(769\) −21.5351 + 37.2999i −0.776575 + 1.34507i 0.157330 + 0.987546i \(0.449712\pi\)
−0.933905 + 0.357522i \(0.883622\pi\)
\(770\) 0 0
\(771\) 24.4791 + 38.1720i 0.881594 + 1.37473i
\(772\) 0 0
\(773\) 32.8660 + 32.8660i 1.18211 + 1.18211i 0.979198 + 0.202909i \(0.0650394\pi\)
0.202909 + 0.979198i \(0.434961\pi\)
\(774\) 0 0
\(775\) 1.54966i 0.0556653i
\(776\) 0 0
\(777\) 31.5008 34.5842i 1.13008 1.24070i
\(778\) 0 0
\(779\) 20.8963 5.59915i 0.748689 0.200611i
\(780\) 0 0
\(781\) −4.26785 1.14357i −0.152716 0.0409200i
\(782\) 0 0
\(783\) 16.2259 + 1.98821i 0.579865 + 0.0710528i
\(784\) 0 0
\(785\) 18.7530 + 32.4812i 0.669324 + 1.15930i
\(786\) 0 0
\(787\) −1.55972 5.82094i −0.0555978 0.207494i 0.932539 0.361069i \(-0.117588\pi\)
−0.988137 + 0.153575i \(0.950921\pi\)
\(788\) 0 0
\(789\) 0.629758 + 13.4972i 0.0224200 + 0.480513i
\(790\) 0 0
\(791\) 37.8706i 1.34652i
\(792\) 0 0
\(793\) 13.1309i 0.466292i
\(794\) 0 0
\(795\) 0.692255 0.443932i 0.0245518 0.0157447i
\(796\) 0 0
\(797\) −13.4797 50.3069i