Properties

Label 483.2.i.b.277.1
Level $483$
Weight $2$
Character 483.277
Analytic conductor $3.857$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 277.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 483.277
Dual form 483.2.i.b.415.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(1.00000 + 1.73205i) q^{12} +5.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-2.50000 + 4.33013i) q^{39} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(5.00000 - 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -1.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.50000 + 4.33013i) q^{67} +(-6.00000 - 10.3923i) q^{68} -1.00000 q^{69} -6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(2.50000 + 4.33013i) q^{75} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(12.5000 + 4.33013i) q^{91} +2.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9} - 6 q^{11} + 2 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + q^{19} - 4 q^{21} + q^{23} + 5 q^{25} + 2 q^{27} + 8 q^{28} + 12 q^{29} - 5 q^{31} - 6 q^{33} - 4 q^{36} + 7 q^{37} - 5 q^{39} - 2 q^{43} + 12 q^{44} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 6 q^{51} + 10 q^{52} - 12 q^{53} - 2 q^{57} + 6 q^{59} - 14 q^{61} - q^{63} - 16 q^{64} - 5 q^{67} - 12 q^{68} - 2 q^{69} - 12 q^{71} + 7 q^{73} + 5 q^{75} + 4 q^{76} - 24 q^{77} - 5 q^{79} - q^{81} - 24 q^{83} + 2 q^{84} - 6 q^{87} + 6 q^{89} + 25 q^{91} + 4 q^{92} - 5 q^{93} - 20 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 4.00000 3.46410i 0.755929 0.654654i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 0 0
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0 0
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 6.00000 + 10.3923i 0.904534 + 1.56670i
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 4.00000 0.577350
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 5.00000 8.66025i 0.693375 1.20096i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i \(-0.812942\pi\)
−0.0640184 0.997949i \(-0.520392\pi\)
\(62\) 0 0
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) −6.00000 10.3923i −0.727607 1.26025i
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) 0 0
\(75\) 2.50000 + 4.33013i 0.288675 + 0.500000i
\(76\) 2.00000 0.229416
\(77\) −12.0000 + 10.3923i −1.36753 + 1.18431i
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 1.00000 + 5.19615i 0.109109 + 0.566947i
\(85\) 0 0
\(86\) 0 0
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 12.5000 + 4.33013i 1.31036 + 0.453921i
\(92\) 2.00000 0.208514
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) −5.00000 8.66025i −0.500000 0.866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −5.50000 9.52628i −0.541931 0.938652i −0.998793 0.0491146i \(-0.984360\pi\)
0.456862 0.889538i \(-0.348973\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 1.00000 1.73205i 0.0962250 0.166667i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) −2.00000 10.3923i −0.188982 0.981981i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.00000 10.3923i 0.557086 0.964901i
\(117\) −2.50000 4.33013i −0.231125 0.400320i
\(118\) 0 0
\(119\) 12.0000 10.3923i 1.10004 0.952661i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 0 0
\(123\) 0 0
\(124\) 5.00000 + 8.66025i 0.449013 + 0.777714i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0 0
\(129\) 0.500000 0.866025i 0.0440225 0.0762493i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) −12.0000 −1.04447
\(133\) 0.500000 + 2.59808i 0.0433555 + 0.225282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −15.0000 + 25.9808i −1.25436 + 2.17262i
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) 0 0
\(146\) 0 0
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) 14.0000 1.15079
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i \(0.469265\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 + 8.66025i 0.400320 + 0.693375i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 0 0
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) 0.500000 + 2.59808i 0.0394055 + 0.204757i
\(162\) 0 0
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0.500000 0.866025i 0.0382360 0.0662266i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 10.0000 8.66025i 0.755929 0.654654i
\(176\) 24.0000 1.80907
\(177\) 3.00000 + 5.19615i 0.225494 + 0.390567i
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) 23.0000 1.70958 0.854788 0.518977i \(-0.173687\pi\)
0.854788 + 0.518977i \(0.173687\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 18.0000 + 31.1769i 1.31629 + 2.27988i
\(188\) −12.0000 −0.875190
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 4.00000 6.92820i 0.288675 0.500000i
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 13.0000 5.19615i 0.928571 0.371154i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0 0
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) 0 0
\(203\) 15.0000 + 5.19615i 1.05279 + 0.364698i
\(204\) 12.0000 0.840168
\(205\) 0 0
\(206\) 0 0
\(207\) 0.500000 0.866025i 0.0347524 0.0601929i
\(208\) −10.0000 17.3205i −0.693375 1.20096i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 12.0000 + 20.7846i 0.824163 + 1.42749i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −10.0000 + 8.66025i −0.678844 + 0.587896i
\(218\) 0 0
\(219\) 3.50000 + 6.06218i 0.236508 + 0.409644i
\(220\) 0 0
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 0 0
\(227\) 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) 0 0
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −28.0000 −1.79252
\(245\) 0 0
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) 30.0000 1.89358 0.946792 0.321847i \(-0.104304\pi\)
0.946792 + 0.321847i \(0.104304\pi\)
\(252\) −5.00000 1.73205i −0.314970 0.109109i
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 0 0
\(259\) 3.50000 + 18.1865i 0.217479 + 1.13006i
\(260\) 0 0
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 12.0000 20.7846i 0.731653 1.26726i −0.224523 0.974469i \(-0.572083\pi\)
0.956176 0.292791i \(-0.0945841\pi\)
\(270\) 0 0
\(271\) 14.0000 + 24.2487i 0.850439 + 1.47300i 0.880812 + 0.473466i \(0.156997\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) −24.0000 −1.45521
\(273\) −10.0000 + 8.66025i −0.605228 + 0.524142i
\(274\) 0 0
\(275\) 15.0000 + 25.9808i 0.904534 + 1.56670i
\(276\) −1.00000 + 1.73205i −0.0601929 + 0.104257i
\(277\) 15.5000 26.8468i 0.931305 1.61307i 0.150210 0.988654i \(-0.452005\pi\)
0.781094 0.624413i \(-0.214662\pi\)
\(278\) 0 0
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 6.50000 11.2583i 0.386385 0.669238i −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 5.00000 8.66025i 0.293105 0.507673i
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.00000 + 5.19615i −0.174078 + 0.301511i
\(298\) 0 0
\(299\) 2.50000 + 4.33013i 0.144579 + 0.250418i
\(300\) 10.0000 0.577350
\(301\) −2.50000 0.866025i −0.144098 0.0499169i
\(302\) 0 0
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 6.00000 + 31.1769i 0.341882 + 1.77647i
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 0 0
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 12.5000 21.6506i 0.693375 1.20096i
\(326\) 0 0
\(327\) −5.50000 9.52628i −0.304151 0.526804i
\(328\) 0 0
\(329\) −3.00000 15.5885i −0.165395 0.859419i
\(330\) 0 0
\(331\) −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i \(-0.264424\pi\)
−0.976658 + 0.214799i \(0.931090\pi\)
\(332\) −12.0000 + 20.7846i −0.658586 + 1.14070i
\(333\) 3.50000 6.06218i 0.191799 0.332205i
\(334\) 0 0
\(335\) 0 0
\(336\) 10.0000 + 3.46410i 0.545545 + 0.188982i
\(337\) −25.0000 −1.36184 −0.680918 0.732359i \(-0.738419\pi\)
−0.680918 + 0.732359i \(0.738419\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 6.00000 + 10.3923i 0.321634 + 0.557086i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 12.0000 0.635999
\(357\) 3.00000 + 15.5885i 0.158777 + 0.825029i
\(358\) 0 0
\(359\) 9.00000 + 15.5885i 0.475002 + 0.822727i 0.999590 0.0286287i \(-0.00911406\pi\)
−0.524588 + 0.851356i \(0.675781\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) 25.0000 1.31216
\(364\) 20.0000 17.3205i 1.04828 0.907841i
\(365\) 0 0
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 2.00000 3.46410i 0.104257 0.180579i
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) −10.0000 −0.518476
\(373\) 15.5000 + 26.8468i 0.802560 + 1.39007i 0.917926 + 0.396751i \(0.129862\pi\)
−0.115367 + 0.993323i \(0.536804\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30.0000 1.54508
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 3.50000 6.06218i 0.179310 0.310575i
\(382\) 0 0
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.500000 + 0.866025i 0.0254164 + 0.0440225i
\(388\) −10.0000 + 17.3205i −0.507673 + 0.879316i
\(389\) −18.0000 + 31.1769i −0.912636 + 1.58073i −0.102311 + 0.994753i \(0.532624\pi\)
−0.810326 + 0.585980i \(0.800710\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) 12.5000 + 21.6506i 0.627357 + 1.08661i 0.988080 + 0.153941i \(0.0491966\pi\)
−0.360723 + 0.932673i \(0.617470\pi\)
\(398\) 0 0
\(399\) −2.50000 0.866025i −0.125157 0.0433555i
\(400\) −20.0000 −1.00000
\(401\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) −12.5000 + 21.6506i −0.622669 + 1.07849i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −42.0000 −2.08186
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 0 0
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) −22.0000 −1.08386
\(413\) 12.0000 10.3923i 0.590481 0.511372i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.50000 + 4.33013i −0.122426 + 0.212047i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) −15.0000 25.9808i −0.727607 1.26025i
\(426\) 0 0
\(427\) −7.00000 36.3731i −0.338754 1.76022i
\(428\) 0 0
\(429\) −15.0000 25.9808i −0.724207 1.25436i
\(430\) 0 0
\(431\) 18.0000 31.1769i 0.867029 1.50174i 0.00201168 0.999998i \(-0.499360\pi\)
0.865018 0.501741i \(-0.167307\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11.0000 + 19.0526i 0.526804 + 0.912452i
\(437\) −0.500000 + 0.866025i −0.0239182 + 0.0414276i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) −9.00000 15.5885i −0.427603 0.740630i 0.569057 0.822298i \(-0.307309\pi\)
−0.996660 + 0.0816684i \(0.973975\pi\)
\(444\) −7.00000 + 12.1244i −0.332205 + 0.575396i
\(445\) 0 0
\(446\) 0 0
\(447\) 18.0000 0.851371
\(448\) −20.0000 6.92820i −0.944911 0.327327i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) 0 0
\(459\) 3.00000 5.19615i 0.140028 0.242536i
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) −12.0000 20.7846i −0.557086 0.964901i
\(465\) 0 0
\(466\) 0 0
\(467\) 9.00000 + 15.5885i 0.416470 + 0.721348i 0.995582 0.0939008i \(-0.0299336\pi\)
−0.579111 + 0.815249i \(0.696600\pi\)
\(468\) −10.0000 −0.462250
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) 0 0
\(475\) 5.00000 0.229416
\(476\) −6.00000 31.1769i −0.275010 1.42899i
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 0 0
\(481\) 17.5000 + 30.3109i 0.797931 + 1.38206i
\(482\) 0 0
\(483\) −2.50000 0.866025i −0.113754 0.0394055i
\(484\) −50.0000 −2.27273
\(485\) 0 0
\(486\) 0 0
\(487\) 6.50000 11.2583i 0.294543 0.510164i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714992\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) −15.0000 5.19615i −0.672842 0.233079i
\(498\) 0 0
\(499\) −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i \(-0.202365\pi\)
−0.916542 + 0.399937i \(0.869032\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) −7.00000 + 12.1244i −0.310575 + 0.537931i
\(509\) 6.00000 + 10.3923i 0.265945 + 0.460631i 0.967811 0.251679i \(-0.0809826\pi\)
−0.701866 + 0.712309i \(0.747649\pi\)
\(510\) 0 0
\(511\) 14.0000 12.1244i 0.619324 0.536350i
\(512\) 0 0
\(513\) 0.500000 + 0.866025i 0.0220755 + 0.0382360i
\(514\) 0 0
\(515\) 0 0
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 36.0000 1.58328
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i \(0.394910\pi\)
−0.981347 + 0.192244i \(0.938423\pi\)
\(522\) 0 0
\(523\) −20.5000 35.5070i −0.896402 1.55261i −0.832059 0.554687i \(-0.812838\pi\)
−0.0643431 0.997928i \(-0.520495\pi\)
\(524\) 0 0
\(525\) 2.50000 + 12.9904i 0.109109 + 0.566947i
\(526\) 0 0
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) −12.0000 + 20.7846i −0.522233 + 0.904534i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 5.00000 + 1.73205i 0.216777 + 0.0750939i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 0 0
\(539\) −39.0000 + 15.5885i −1.67985 + 0.671442i
\(540\) 0 0
\(541\) 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i \(0.0654977\pi\)
−0.312507 + 0.949915i \(0.601169\pi\)
\(542\) 0 0
\(543\) −11.5000 + 19.9186i −0.493512 + 0.854788i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 12.0000 + 20.7846i 0.512615 + 0.887875i
\(549\) −7.00000 + 12.1244i −0.298753 + 0.517455i
\(550\) 0 0
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) −2.50000 12.9904i −0.106311 0.552407i
\(554\) 0 0
\(555\) 0 0
\(556\) 5.00000 8.66025i 0.212047 0.367277i
\(557\) 3.00000 5.19615i 0.127114 0.220168i −0.795443 0.606028i \(-0.792762\pi\)
0.922557 + 0.385860i \(0.126095\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) −36.0000 −1.51992
\(562\) 0 0
\(563\) 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(564\) 6.00000 10.3923i 0.252646 0.437595i
\(565\) 0 0
\(566\) 0 0
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) 12.0000 + 20.7846i 0.503066 + 0.871336i 0.999994 + 0.00354413i \(0.00112814\pi\)
−0.496928 + 0.867792i \(0.665539\pi\)
\(570\) 0 0
\(571\) 6.50000 11.2583i 0.272017 0.471146i −0.697362 0.716720i \(-0.745643\pi\)
0.969378 + 0.245573i \(0.0789761\pi\)
\(572\) 30.0000 + 51.9615i 1.25436 + 2.17262i
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 5.00000 0.208514
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) 6.50000 11.2583i 0.270599 0.468690i −0.698417 0.715691i \(-0.746112\pi\)
0.969015 + 0.247001i \(0.0794451\pi\)
\(578\) 0 0
\(579\) −5.50000 9.52628i −0.228572 0.395899i
\(580\) 0 0
\(581\) −30.0000 10.3923i −1.24461 0.431145i
\(582\) 0 0
\(583\) −36.0000 62.3538i −1.49097 2.58243i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) −2.00000 + 13.8564i −0.0824786 + 0.571429i
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 14.0000 24.2487i 0.575396 0.996616i
\(593\) −15.0000 25.9808i −0.615976 1.06690i −0.990212 0.139569i \(-0.955428\pi\)
0.374236 0.927333i \(-0.377905\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36.0000 −1.47462
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) 0 0
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) 0 0
\(603\) 5.00000 0.203616
\(604\) 20.0000 + 34.6410i 0.813788 + 1.40952i
\(605\) 0 0
\(606\) 0 0
\(607\) 12.5000 + 21.6506i 0.507359 + 0.878772i 0.999964 + 0.00851879i \(0.00271165\pi\)
−0.492604 + 0.870253i \(0.663955\pi\)
\(608\) 0 0
\(609\) −12.0000 + 10.3923i −0.486265 + 0.421117i
\(610\) 0 0
\(611\) −15.0000 25.9808i −0.606835 1.05107i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i \(0.342626\pi\)
−0.999574 + 0.0291886i \(0.990708\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) 9.50000 16.4545i 0.381837 0.661361i −0.609488 0.792796i \(-0.708625\pi\)
0.991325 + 0.131434i \(0.0419582\pi\)
\(620\) 0 0
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) 0 0
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) 20.0000 0.800641
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 0 0
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 14.0000 + 24.2487i 0.558661 + 0.967629i
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 2.00000 3.46410i 0.0794929 0.137686i
\(634\) 0 0
\(635\) 0 0
\(636\) −24.0000 −0.951662
\(637\) 27.5000 + 21.6506i 1.08959 + 0.857829i
\(638\) 0 0
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) −13.0000 −0.512670 −0.256335 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 5.00000 + 1.73205i 0.197028 + 0.0682524i
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) 0 0
\(649\) 18.0000 + 31.1769i 0.706562 + 1.22380i
\(650\) 0 0
\(651\) −2.50000 12.9904i −0.0979827 0.509133i
\(652\) 8.00000 0.313304
\(653\) 21.0000 + 36.3731i 0.821794 + 1.42339i 0.904345 + 0.426801i \(0.140360\pi\)
−0.0825519 + 0.996587i \(0.526307\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.00000 −0.273096
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 15.5000 26.8468i 0.602880 1.04422i −0.389503 0.921025i \(-0.627353\pi\)
0.992383 0.123194i \(-0.0393136\pi\)
\(662\) 0 0
\(663\) 15.0000 + 25.9808i 0.582552 + 1.00901i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.00000 + 5.19615i 0.116160 + 0.201196i
\(668\) 0 0
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) 84.0000 3.24278
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 0 0
\(675\) 2.50000 4.33013i 0.0962250 0.166667i
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) 0 0
\(679\) −25.0000 8.66025i −0.959412 0.332350i
\(680\) 0 0
\(681\) 3.00000 + 5.19615i 0.114960 + 0.199117i
\(682\) 0 0
\(683\) 18.0000 31.1769i 0.688751 1.19295i −0.283491 0.958975i \(-0.591493\pi\)
0.972242 0.233977i \(-0.0751739\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) 0 0
\(686\) 0 0
\(687\) −13.0000 −0.495981
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −30.0000 + 51.9615i −1.14291 + 1.97958i
\(690\) 0 0
\(691\) 6.50000 + 11.2583i 0.247272 + 0.428287i 0.962768 0.270330i \(-0.0871327\pi\)
−0.715496 + 0.698617i \(0.753799\pi\)
\(692\) −12.0000 −0.456172
\(693\) 15.0000 + 5.19615i 0.569803 + 0.197386i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 18.0000 0.680823
\(700\) −5.00000 25.9808i −0.188982 0.981981i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) 24.0000 41.5692i 0.904534 1.56670i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −2.50000 + 4.33013i −0.0937573 + 0.162392i
\(712\) 0 0
\(713\) −5.00000 −0.187251
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 + 20.7846i 0.448461 + 0.776757i
\(717\) −12.0000 + 20.7846i −0.448148 + 0.776215i
\(718\) 0 0
\(719\) −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i \(-0.880269\pi\)
0.146920 0.989148i \(-0.453064\pi\)
\(720\) 0 0
\(721\) −5.50000 28.5788i −0.204831 1.06433i
\(722\) 0 0
\(723\) −1.00000 1.73205i −0.0371904 0.0644157i
\(724\) 23.0000 39.8372i 0.854788 1.48054i
\(725\) 15.0000 25.9808i 0.557086 0.964901i
\(726\) 0 0
\(727\) 5.00000 0.185440 0.0927199 0.995692i \(-0.470444\pi\)
0.0927199 + 0.995692i \(0.470444\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) 14.0000 24.2487i 0.517455 0.896258i
\(733\) −11.5000 19.9186i −0.424762 0.735710i 0.571636 0.820507i \(-0.306309\pi\)
−0.996398 + 0.0847976i \(0.972976\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 0 0
\(739\) −14.5000 + 25.1147i −0.533391 + 0.923861i 0.465848 + 0.884865i \(0.345749\pi\)
−0.999239 + 0.0389959i \(0.987584\pi\)
\(740\) 0 0
\(741\) −5.00000 −0.183680
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.00000 + 10.3923i 0.219529 + 0.380235i
\(748\) 72.0000 2.63258
\(749\) 0 0
\(750\) 0 0
\(751\) 0.500000 + 0.866025i 0.0182453 + 0.0316017i 0.875004 0.484116i \(-0.160859\pi\)
−0.856759 + 0.515718i \(0.827525\pi\)
\(752\) −12.0000 + 20.7846i −0.437595 + 0.757937i
\(753\) −15.0000 + 25.9808i −0.546630 + 0.946792i
\(754\) 0 0
\(755\) 0 0
\(756\) 4.00000 3.46410i 0.145479 0.125988i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 3.00000 5.19615i 0.108893 0.188608i
\(760\) 0 0
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) 0 0
\(763\) −22.0000 + 19.0526i −0.796453 + 0.689749i
\(764\) −36.0000 −1.30243
\(765\) 0 0
\(766\) 0 0
\(767\) 15.0000 25.9808i 0.541619 0.938111i
\(768\) −8.00000 13.8564i −0.288675 0.500000i
\(769\) 17.0000 0.613036 0.306518 0.951865i \(-0.400836\pi\)
0.306518 + 0.951865i \(0.400836\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) 11.0000 + 19.0526i 0.395899 + 0.685717i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 0 0
\(775\) 12.5000 + 21.6506i 0.449013 + 0.777714i
\(776\) 0 0
\(777\) −17.5000 6.06218i −0.627809 0.217479i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 4.00000 27.7128i 0.142857 0.989743i
\(785\) 0 0
\(786\) 0 0
\(787\) −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i \(0.359855\pi\)
−0.996531 + 0.0832226i \(0.973479\pi\)
\(788\) −12.0000 + 20.7846i −0.427482 + 0.740421i
\(789\) 0 0
\(790\) 0 0
\(791\) 15.0000 + 5.19615i 0.533339 + 0.184754i
\(792\) 0 0
\(793\)