Properties

Label 539.2.e.c.177.1
Level $539$
Weight $2$
Character 539.177
Analytic conductor $4.304$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 539.177
Dual form 539.2.e.c.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.00000 + 5.19615i) q^{9} +(0.500000 + 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{12} +4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{19} -2.00000 q^{20} +(2.50000 - 4.33013i) q^{23} +(2.00000 + 3.46410i) q^{25} +9.00000 q^{27} +10.0000 q^{29} +(0.500000 + 0.866025i) q^{31} +(1.50000 - 2.59808i) q^{33} -12.0000 q^{36} +(2.50000 - 4.33013i) q^{37} +(-6.00000 - 10.3923i) q^{39} +2.00000 q^{41} -8.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(4.00000 - 6.92820i) q^{47} +12.0000 q^{48} +(3.00000 - 5.19615i) q^{51} +(4.00000 + 6.92820i) q^{52} +(3.00000 + 5.19615i) q^{53} -1.00000 q^{55} +18.0000 q^{57} +(1.50000 + 2.59808i) q^{59} +(3.00000 + 5.19615i) q^{60} +(-1.00000 + 1.73205i) q^{61} -8.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.50000 + 2.59808i) q^{67} +(-2.00000 + 3.46410i) q^{68} -15.0000 q^{69} +1.00000 q^{71} +(5.00000 + 8.66025i) q^{73} +(6.00000 - 10.3923i) q^{75} -12.0000 q^{76} +(-3.00000 + 5.19615i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{83} -2.00000 q^{85} +(-15.0000 - 25.9808i) q^{87} +(-7.50000 + 12.9904i) q^{89} +10.0000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-3.00000 - 5.19615i) q^{95} +5.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} + 2 q^{4} - q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} + 2 q^{4} - q^{5} - 6 q^{9} + q^{11} + 6 q^{12} + 8 q^{13} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 6 q^{19} - 4 q^{20} + 5 q^{23} + 4 q^{25} + 18 q^{27} + 20 q^{29} + q^{31} + 3 q^{33} - 24 q^{36} + 5 q^{37} - 12 q^{39} + 4 q^{41} - 16 q^{43} - 2 q^{44} - 6 q^{45} + 8 q^{47} + 24 q^{48} + 6 q^{51} + 8 q^{52} + 6 q^{53} - 2 q^{55} + 36 q^{57} + 3 q^{59} + 6 q^{60} - 2 q^{61} - 16 q^{64} - 4 q^{65} + 3 q^{67} - 4 q^{68} - 30 q^{69} + 2 q^{71} + 10 q^{73} + 12 q^{75} - 24 q^{76} - 6 q^{79} - 4 q^{80} - 9 q^{81} - 24 q^{83} - 4 q^{85} - 30 q^{87} - 15 q^{89} + 20 q^{92} + 3 q^{93} - 6 q^{95} + 10 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 3.00000 5.19615i 0.866025 1.50000i
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 0 0
\(23\) 2.50000 4.33013i 0.521286 0.902894i −0.478407 0.878138i \(-0.658786\pi\)
0.999694 0.0247559i \(-0.00788087\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) −12.0000 −2.00000
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) −6.00000 10.3923i −0.960769 1.66410i
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 0 0
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) 12.0000 1.73205
\(49\) 0 0
\(50\) 0 0
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 4.00000 + 6.92820i 0.554700 + 0.960769i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 18.0000 2.38416
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 3.00000 + 5.19615i 0.387298 + 0.670820i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i \(-0.108004\pi\)
−0.759733 + 0.650236i \(0.774670\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) −15.0000 −1.80579
\(70\) 0 0
\(71\) 1.00000 0.118678 0.0593391 0.998238i \(-0.481101\pi\)
0.0593391 + 0.998238i \(0.481101\pi\)
\(72\) 0 0
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) 6.00000 10.3923i 0.692820 1.20000i
\(76\) −12.0000 −1.37649
\(77\) 0 0
\(78\) 0 0
\(79\) −3.00000 + 5.19615i −0.337526 + 0.584613i −0.983967 0.178352i \(-0.942924\pi\)
0.646440 + 0.762964i \(0.276257\pi\)
\(80\) −2.00000 3.46410i −0.223607 0.387298i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) −15.0000 25.9808i −1.60817 2.78543i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.0000 1.04257
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) 0 0
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 0 0
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) −4.00000 + 6.92820i −0.400000 + 0.692820i
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i \(-0.672747\pi\)
0.999818 + 0.0190994i \(0.00607989\pi\)
\(108\) 9.00000 + 15.5885i 0.866025 + 1.50000i
\(109\) −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i \(-0.228023\pi\)
−0.945769 + 0.324840i \(0.894690\pi\)
\(110\) 0 0
\(111\) −15.0000 −1.42374
\(112\) 0 0
\(113\) −19.0000 −1.78737 −0.893685 0.448695i \(-0.851889\pi\)
−0.893685 + 0.448695i \(0.851889\pi\)
\(114\) 0 0
\(115\) 2.50000 + 4.33013i 0.233126 + 0.403786i
\(116\) 10.0000 + 17.3205i 0.928477 + 1.60817i
\(117\) −12.0000 + 20.7846i −1.10940 + 1.92154i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) 12.0000 + 20.7846i 1.05654 + 1.82998i
\(130\) 0 0
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) 0 0
\(135\) −4.50000 + 7.79423i −0.387298 + 0.670820i
\(136\) 0 0
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) −24.0000 −2.02116
\(142\) 0 0
\(143\) 2.00000 + 3.46410i 0.167248 + 0.289683i
\(144\) −12.0000 20.7846i −1.00000 1.73205i
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) 11.0000 19.0526i 0.901155 1.56085i 0.0751583 0.997172i \(-0.476054\pi\)
0.825997 0.563675i \(-0.190613\pi\)
\(150\) 0 0
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 12.0000 20.7846i 0.960769 1.66410i
\(157\) 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i \(-0.0765542\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(158\) 0 0
\(159\) 9.00000 15.5885i 0.713746 1.23625i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) 1.50000 + 2.59808i 0.116775 + 0.202260i
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −18.0000 31.1769i −1.37649 2.38416i
\(172\) −8.00000 13.8564i −0.609994 1.05654i
\(173\) 8.00000 13.8564i 0.608229 1.05348i −0.383304 0.923622i \(-0.625214\pi\)
0.991532 0.129861i \(-0.0414530\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) 6.00000 10.3923i 0.447214 0.774597i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 2.50000 + 4.33013i 0.183804 + 0.318357i
\(186\) 0 0
\(187\) −1.00000 + 1.73205i −0.0731272 + 0.126660i
\(188\) 16.0000 1.16692
\(189\) 0 0
\(190\) 0 0
\(191\) −2.50000 + 4.33013i −0.180894 + 0.313317i −0.942185 0.335093i \(-0.891232\pi\)
0.761291 + 0.648410i \(0.224566\pi\)
\(192\) 12.0000 + 20.7846i 0.866025 + 1.50000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 0 0
\(195\) 12.0000 0.859338
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 0 0
\(201\) 4.50000 7.79423i 0.317406 0.549762i
\(202\) 0 0
\(203\) 0 0
\(204\) 12.0000 0.840168
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 0 0
\(207\) 15.0000 + 25.9808i 1.04257 + 1.80579i
\(208\) −8.00000 + 13.8564i −0.554700 + 0.960769i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) −1.50000 2.59808i −0.102778 0.178017i
\(214\) 0 0
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 15.0000 25.9808i 1.01361 1.75562i
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 0 0
\(225\) −24.0000 −1.60000
\(226\) 0 0
\(227\) 2.00000 + 3.46410i 0.132745 + 0.229920i 0.924734 0.380615i \(-0.124288\pi\)
−0.791989 + 0.610535i \(0.790954\pi\)
\(228\) 18.0000 + 31.1769i 1.19208 + 2.06474i
\(229\) −3.50000 + 6.06218i −0.231287 + 0.400600i −0.958187 0.286143i \(-0.907627\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 18.0000 1.16923
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) −6.00000 + 10.3923i −0.387298 + 0.670820i
\(241\) −6.00000 10.3923i −0.386494 0.669427i 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) −12.0000 + 20.7846i −0.763542 + 1.32249i
\(248\) 0 0
\(249\) 18.0000 + 31.1769i 1.14070 + 1.97576i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 0 0
\(255\) 3.00000 + 5.19615i 0.187867 + 0.325396i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −8.00000 −0.496139
\(261\) −30.0000 + 51.9615i −1.85695 + 3.21634i
\(262\) 0 0
\(263\) −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 45.0000 2.75396
\(268\) −3.00000 + 5.19615i −0.183254 + 0.317406i
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) −15.0000 25.9808i −0.902894 1.56386i
\(277\) −12.0000 20.7846i −0.721010 1.24883i −0.960595 0.277951i \(-0.910345\pi\)
0.239585 0.970875i \(-0.422989\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 0 0
\(283\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) −9.00000 + 15.5885i −0.533114 + 0.923381i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) −10.0000 + 17.3205i −0.585206 + 1.01361i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −3.00000 −0.174667
\(296\) 0 0
\(297\) 4.50000 + 7.79423i 0.261116 + 0.452267i
\(298\) 0 0
\(299\) 10.0000 17.3205i 0.578315 1.00167i
\(300\) 24.0000 1.38564
\(301\) 0 0
\(302\) 0 0
\(303\) −18.0000 + 31.1769i −1.03407 + 1.79107i
\(304\) −12.0000 20.7846i −0.688247 1.19208i
\(305\) −1.00000 1.73205i −0.0572598 0.0991769i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 36.0000 2.04797
\(310\) 0 0
\(311\) 4.00000 + 6.92820i 0.226819 + 0.392862i 0.956864 0.290537i \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 0 0
\(313\) −11.5000 + 19.9186i −0.650018 + 1.12586i 0.333099 + 0.942892i \(0.391906\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) 0 0
\(319\) 5.00000 + 8.66025i 0.279946 + 0.484881i
\(320\) 4.00000 6.92820i 0.223607 0.387298i
\(321\) −30.0000 −1.67444
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 9.00000 15.5885i 0.500000 0.866025i
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 0 0
\(327\) −6.00000 + 10.3923i −0.331801 + 0.574696i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.50000 14.7224i 0.467202 0.809218i −0.532096 0.846684i \(-0.678595\pi\)
0.999298 + 0.0374662i \(0.0119287\pi\)
\(332\) −12.0000 20.7846i −0.658586 1.14070i
\(333\) 15.0000 + 25.9808i 0.821995 + 1.42374i
\(334\) 0 0
\(335\) −3.00000 −0.163908
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 28.5000 + 49.3634i 1.54791 + 2.68105i
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) −0.500000 + 0.866025i −0.0270765 + 0.0468979i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 7.50000 12.9904i 0.403786 0.699379i
\(346\) 0 0
\(347\) −7.00000 12.1244i −0.375780 0.650870i 0.614664 0.788789i \(-0.289292\pi\)
−0.990443 + 0.137920i \(0.955958\pi\)
\(348\) 30.0000 51.9615i 1.60817 2.78543i
\(349\) 34.0000 1.81998 0.909989 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) 0 0
\(351\) 36.0000 1.92154
\(352\) 0 0
\(353\) 4.50000 + 7.79423i 0.239511 + 0.414845i 0.960574 0.278024i \(-0.0896796\pi\)
−0.721063 + 0.692869i \(0.756346\pi\)
\(354\) 0 0
\(355\) −0.500000 + 0.866025i −0.0265372 + 0.0459639i
\(356\) −30.0000 −1.59000
\(357\) 0 0
\(358\) 0 0
\(359\) −4.00000 + 6.92820i −0.211112 + 0.365657i −0.952063 0.305903i \(-0.901042\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 0 0
\(363\) 3.00000 0.157459
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) −5.50000 9.52628i −0.287098 0.497268i 0.686018 0.727585i \(-0.259357\pi\)
−0.973116 + 0.230317i \(0.926024\pi\)
\(368\) 10.0000 + 17.3205i 0.521286 + 0.902894i
\(369\) −6.00000 + 10.3923i −0.312348 + 0.541002i
\(370\) 0 0
\(371\) 0 0
\(372\) 6.00000 0.311086
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 0 0
\(375\) 13.5000 + 23.3827i 0.697137 + 1.20748i
\(376\) 0 0
\(377\) 40.0000 2.06010
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) −3.00000 5.19615i −0.153695 0.266207i
\(382\) 0 0
\(383\) 8.50000 14.7224i 0.434330 0.752281i −0.562911 0.826518i \(-0.690319\pi\)
0.997241 + 0.0742364i \(0.0236519\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 24.0000 41.5692i 1.21999 2.11308i
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) −4.50000 7.79423i −0.228159 0.395183i 0.729103 0.684403i \(-0.239937\pi\)
−0.957263 + 0.289220i \(0.906604\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 0 0
\(393\) −54.0000 −2.72394
\(394\) 0 0
\(395\) −3.00000 5.19615i −0.150946 0.261447i
\(396\) −6.00000 10.3923i −0.301511 0.522233i
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) 12.0000 20.7846i 0.597022 1.03407i
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) 5.00000 0.247841
\(408\) 0 0
\(409\) −13.0000 22.5167i −0.642809 1.11338i −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −24.0000 −1.18240
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) −15.0000 25.9808i −0.734553 1.27228i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) 24.0000 + 41.5692i 1.16692 + 2.02116i
\(424\) 0 0
\(425\) −4.00000 + 6.92820i −0.194029 + 0.336067i
\(426\) 0 0
\(427\) 0 0
\(428\) 20.0000 0.966736
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) 0 0
\(431\) 10.0000 + 17.3205i 0.481683 + 0.834300i 0.999779 0.0210230i \(-0.00669232\pi\)
−0.518096 + 0.855323i \(0.673359\pi\)
\(432\) −18.0000 + 31.1769i −0.866025 + 1.50000i
\(433\) 25.0000 1.20142 0.600712 0.799466i \(-0.294884\pi\)
0.600712 + 0.799466i \(0.294884\pi\)
\(434\) 0 0
\(435\) 30.0000 1.43839
\(436\) 4.00000 6.92820i 0.191565 0.331801i
\(437\) 15.0000 + 25.9808i 0.717547 + 1.24283i
\(438\) 0 0
\(439\) −7.00000 + 12.1244i −0.334092 + 0.578664i −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.5000 33.7750i 0.926473 1.60470i 0.137298 0.990530i \(-0.456158\pi\)
0.789175 0.614168i \(-0.210508\pi\)
\(444\) −15.0000 25.9808i −0.711868 1.23299i
\(445\) −7.50000 12.9904i −0.355534 0.615803i
\(446\) 0 0
\(447\) −66.0000 −3.12169
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) 1.00000 + 1.73205i 0.0470882 + 0.0815591i
\(452\) −19.0000 32.9090i −0.893685 1.54791i
\(453\) −9.00000 + 15.5885i −0.422857 + 0.732410i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.00000 + 6.92820i −0.187112 + 0.324088i −0.944286 0.329125i \(-0.893246\pi\)
0.757174 + 0.653213i \(0.226579\pi\)
\(458\) 0 0
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) −5.00000 + 8.66025i −0.233126 + 0.403786i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) −20.0000 + 34.6410i −0.928477 + 1.60817i
\(465\) 1.50000 + 2.59808i 0.0695608 + 0.120483i
\(466\) 0 0
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) −48.0000 −2.21880
\(469\) 0 0
\(470\) 0 0
\(471\) 10.5000 18.1865i 0.483814 0.837991i
\(472\) 0 0
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −24.0000 −1.10120
\(476\) 0 0
\(477\) −36.0000 −1.64833
\(478\) 0 0
\(479\) −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i \(-0.945735\pi\)
0.345827 0.938298i \(-0.387598\pi\)
\(480\) 0 0
\(481\) 10.0000 17.3205i 0.455961 0.789747i
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −2.50000 + 4.33013i −0.113519 + 0.196621i
\(486\) 0 0
\(487\) 6.50000 + 11.2583i 0.294543 + 0.510164i 0.974879 0.222737i \(-0.0714992\pi\)
−0.680335 + 0.732901i \(0.738166\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 10.0000 + 17.3205i 0.450377 + 0.780076i
\(494\) 0 0
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) −22.0000 + 38.1051i −0.984855 + 1.70582i −0.342277 + 0.939599i \(0.611198\pi\)
−0.642578 + 0.766220i \(0.722135\pi\)
\(500\) −9.00000 15.5885i −0.402492 0.697137i
\(501\) −3.00000 5.19615i −0.134030 0.232147i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) −4.50000 7.79423i −0.199852 0.346154i
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) −15.5000 + 26.8468i −0.687025 + 1.18996i 0.285770 + 0.958298i \(0.407751\pi\)
−0.972796 + 0.231665i \(0.925583\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −27.0000 + 46.7654i −1.19208 + 2.06474i
\(514\) 0 0
\(515\) −6.00000 10.3923i −0.264392 0.457940i
\(516\) −24.0000 + 41.5692i −1.05654 + 1.82998i
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) −48.0000 −2.10697
\(520\) 0 0
\(521\) 3.50000 + 6.06218i 0.153338 + 0.265589i 0.932453 0.361293i \(-0.117664\pi\)
−0.779115 + 0.626881i \(0.784331\pi\)
\(522\) 0 0
\(523\) 16.0000 27.7128i 0.699631 1.21180i −0.268963 0.963150i \(-0.586681\pi\)
0.968594 0.248646i \(-0.0799857\pi\)
\(524\) 36.0000 1.57267
\(525\) 0 0
\(526\) 0 0
\(527\) −1.00000 + 1.73205i −0.0435607 + 0.0754493i
\(528\) 6.00000 + 10.3923i 0.261116 + 0.452267i
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 5.00000 + 8.66025i 0.216169 + 0.374415i
\(536\) 0 0
\(537\) −1.50000 + 2.59808i −0.0647298 + 0.112115i
\(538\) 0 0
\(539\) 0 0
\(540\) −18.0000 −0.774597
\(541\) −16.0000 + 27.7128i −0.687894 + 1.19147i 0.284624 + 0.958639i \(0.408131\pi\)
−0.972518 + 0.232828i \(0.925202\pi\)
\(542\) 0 0
\(543\) 7.50000 + 12.9904i 0.321856 + 0.557471i
\(544\) 0 0
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −24.0000 −1.02617 −0.513083 0.858339i \(-0.671497\pi\)
−0.513083 + 0.858339i \(0.671497\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) −6.00000 10.3923i −0.256074 0.443533i
\(550\) 0 0
\(551\) −30.0000 + 51.9615i −1.27804 + 2.21364i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 7.50000 12.9904i 0.318357 0.551411i
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) −7.00000 12.1244i −0.296600 0.513725i 0.678756 0.734364i \(-0.262519\pi\)
−0.975356 + 0.220638i \(0.929186\pi\)
\(558\) 0 0
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 0 0
\(563\) 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) −24.0000 41.5692i −1.01058 1.75038i
\(565\) 9.50000 16.4545i 0.399668 0.692245i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) −4.00000 + 6.92820i −0.167248 + 0.289683i
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) 20.0000 0.834058
\(576\) 24.0000 41.5692i 1.00000 1.73205i
\(577\) −12.5000 21.6506i −0.520382 0.901328i −0.999719 0.0236970i \(-0.992456\pi\)
0.479337 0.877631i \(-0.340877\pi\)
\(578\) 0 0
\(579\) −21.0000 + 36.3731i −0.872730 + 1.51161i
\(580\) −20.0000 −0.830455
\(581\) 0 0
\(582\) 0 0
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) 0 0
\(585\) −12.0000 20.7846i −0.496139 0.859338i
\(586\) 0 0
\(587\) −36.0000 −1.48588 −0.742940 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 0 0
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) −27.0000 46.7654i −1.11063 1.92367i
\(592\) 10.0000 + 17.3205i 0.410997 + 0.711868i
\(593\) 15.0000 25.9808i 0.615976 1.06690i −0.374236 0.927333i \(-0.622095\pi\)
0.990212 0.139569i \(-0.0445716\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 44.0000 1.80231
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) 0 0
\(599\) 24.0000 + 41.5692i 0.980613 + 1.69847i 0.660006 + 0.751260i \(0.270554\pi\)
0.320607 + 0.947212i \(0.396113\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) −18.0000 −0.733017
\(604\) 6.00000 10.3923i 0.244137 0.422857i
\(605\) −0.500000 0.866025i −0.0203279 0.0352089i
\(606\) 0 0
\(607\) −5.00000 + 8.66025i −0.202944 + 0.351509i −0.949476 0.313841i \(-0.898384\pi\)
0.746532 + 0.665350i \(0.231718\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.0000 27.7128i 0.647291 1.12114i
\(612\) −12.0000 20.7846i −0.485071 0.840168i
\(613\) −8.00000 13.8564i −0.323117 0.559655i 0.658012 0.753007i \(-0.271397\pi\)
−0.981129 + 0.193352i \(0.938064\pi\)
\(614\) 0 0
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i \(-0.0556830\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) −1.00000 1.73205i −0.0401610 0.0695608i
\(621\) 22.5000 38.9711i 0.902894 1.56386i
\(622\) 0 0
\(623\) 0 0
\(624\) 48.0000 1.92154
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) 9.00000 + 15.5885i 0.359425 + 0.622543i
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 27.0000 1.07485 0.537427 0.843311i \(-0.319397\pi\)
0.537427 + 0.843311i \(0.319397\pi\)
\(632\) 0 0
\(633\) 3.00000 + 5.19615i 0.119239 + 0.206529i
\(634\) 0 0
\(635\) −1.00000 + 1.73205i −0.0396838 + 0.0687343i
\(636\) 36.0000 1.42749
\(637\) 0 0
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i \(-0.262397\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(642\) 0 0
\(643\) 29.0000 1.14365 0.571824 0.820376i \(-0.306236\pi\)
0.571824 + 0.820376i \(0.306236\pi\)
\(644\) 0 0
\(645\) −24.0000 −0.944999
\(646\) 0 0
\(647\) −10.5000 18.1865i −0.412798 0.714986i 0.582397 0.812905i \(-0.302115\pi\)
−0.995194 + 0.0979182i \(0.968782\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) 8.50000 14.7224i 0.332631 0.576133i −0.650396 0.759595i \(-0.725397\pi\)
0.983027 + 0.183462i \(0.0587304\pi\)
\(654\) 0 0
\(655\) 9.00000 + 15.5885i 0.351659 + 0.609091i
\(656\) −4.00000 + 6.92820i −0.156174 + 0.270501i
\(657\) −60.0000 −2.34082
\(658\) 0 0
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) 17.5000 + 30.3109i 0.680671 + 1.17896i 0.974776 + 0.223184i \(0.0716450\pi\)
−0.294105 + 0.955773i \(0.595022\pi\)
\(662\) 0 0
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.0000 43.3013i 0.968004 1.67663i
\(668\) 2.00000 + 3.46410i 0.0773823 + 0.134030i
\(669\) 1.50000 + 2.59808i 0.0579934 + 0.100447i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) 0 0
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) 0 0
\(675\) 18.0000 + 31.1769i 0.692820 + 1.20000i
\(676\) 3.00000 + 5.19615i 0.115385 + 0.199852i
\(677\) 19.0000 32.9090i 0.730229 1.26479i −0.226556 0.973998i \(-0.572747\pi\)
0.956785 0.290796i \(-0.0939201\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) 0 0
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 36.0000 62.3538i 1.37649 2.38416i
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) 21.0000 0.801200
\(688\) 16.0000 27.7128i 0.609994 1.05654i
\(689\) 12.0000 + 20.7846i 0.457164 + 0.791831i
\(690\) 0 0
\(691\) 7.50000 12.9904i 0.285313 0.494177i −0.687372 0.726306i \(-0.741236\pi\)
0.972685 + 0.232128i \(0.0745690\pi\)
\(692\) 32.0000 1.21646
\(693\) 0 0
\(694\) 0 0
\(695\) −5.00000 + 8.66025i −0.189661 + 0.328502i
\(696\) 0 0
\(697\) 2.00000 + 3.46410i 0.0757554 + 0.131212i
\(698\) 0 0
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 15.0000 + 25.9808i 0.565736 + 0.979883i
\(704\) −4.00000 6.92820i −0.150756 0.261116i
\(705\) 12.0000 20.7846i 0.451946 0.782794i
\(706\) 0 0
\(707\) 0 0
\(708\) 18.0000 0.676481
\(709\) −19.5000 + 33.7750i −0.732338 + 1.26845i 0.223544 + 0.974694i \(0.428237\pi\)
−0.955882 + 0.293752i \(0.905096\pi\)
\(710\) 0 0
\(711\) −18.0000 31.1769i −0.675053 1.16923i
\(712\) 0 0
\(713\) 5.00000 0.187251
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 0 0
\(719\) −5.50000 + 9.52628i −0.205115 + 0.355270i −0.950169 0.311734i \(-0.899090\pi\)
0.745054 + 0.667004i \(0.232424\pi\)
\(720\) 24.0000 0.894427
\(721\) 0 0
\(722\) 0 0
\(723\) −18.0000 + 31.1769i −0.669427 + 1.15948i
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) 20.0000 + 34.6410i 0.742781 + 1.28654i
\(726\) 0 0
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 6.00000 + 10.3923i 0.221766 + 0.384111i
\(733\) −2.00000 + 3.46410i −0.0738717 + 0.127950i −0.900595 0.434659i \(-0.856869\pi\)
0.826723 + 0.562609i \(0.190202\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.50000 + 2.59808i −0.0552532 + 0.0957014i
\(738\) 0 0
\(739\) 9.00000 + 15.5885i 0.331070 + 0.573431i 0.982722 0.185088i \(-0.0592569\pi\)
−0.651652 + 0.758518i \(0.725924\pi\)
\(740\) −5.00000 + 8.66025i −0.183804 + 0.318357i
\(741\) 72.0000 2.64499
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 11.0000 + 19.0526i 0.403009 + 0.698032i
\(746\) 0 0
\(747\) 36.0000 62.3538i 1.31717 2.28141i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) 11.5000 19.9186i 0.419641 0.726839i −0.576262 0.817265i \(-0.695489\pi\)
0.995903 + 0.0904254i \(0.0288227\pi\)
\(752\) 16.0000 + 27.7128i 0.583460 + 1.01058i
\(753\) −31.5000 54.5596i −1.14792 1.98826i
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) −7.50000 12.9904i −0.272233 0.471521i
\(760\) 0 0
\(761\) −24.0000 + 41.5692i −0.869999 + 1.50688i −0.00800331 + 0.999968i \(0.502548\pi\)
−0.861996 + 0.506915i \(0.830786\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −10.0000 −0.361787
\(765\) 6.00000 10.3923i 0.216930 0.375735i
\(766\) 0 0
\(767\) 6.00000 + 10.3923i 0.216647 + 0.375244i
\(768\) −24.0000 + 41.5692i −0.866025 + 1.50000i
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 14.0000 24.2487i 0.503871 0.872730i
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) 0 0
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 12.0000 + 20.7846i 0.429669 + 0.744208i
\(781\) 0.500000 + 0.866025i 0.0178914 + 0.0309888i
\(782\) 0 0
\(783\) 90.0000 3.21634
\(784\) 0 0
\(785\) −7.00000 −0.249841
\(786\) 0 0
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) 18.0000 + 31.1769i 0.641223 + 1.11063i
\(789\) −27.0000 + 46.7654i −0.961225 + 1.66489i
\(790\) 0 0
\(791\) 0 0