Properties

Label 1078.2.e.b.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.b.177.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{40} +10.0000 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.00000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} +16.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} + q^{11} + 4 q^{13} - q^{16} - 2 q^{17} + 3 q^{18} + 4 q^{20} - 2 q^{22} + 8 q^{23} + q^{25} - 2 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 4 q^{34} - 6 q^{36} + 2 q^{37} - 2 q^{40} + 20 q^{41} + 8 q^{43} + q^{44} + 6 q^{45} + 8 q^{46} - 8 q^{47} - 2 q^{50} - 2 q^{52} - 6 q^{53} - 4 q^{55} + 2 q^{58} - 10 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{65} + 12 q^{67} - 2 q^{68} + 32 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 2 q^{80} - 9 q^{81} - 10 q^{82} + 8 q^{85} - 4 q^{86} + q^{88} + 6 q^{89} - 12 q^{90} - 16 q^{92} - 8 q^{94} + 20 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.00000 1.73205i −0.158114 0.273861i
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 1.00000 + 1.73205i 0.131306 + 0.227429i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −5.00000 8.66025i −0.552158 0.956365i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) −6.00000 −0.632456
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) 0 0
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 0 0
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −5.00000 + 8.66025i −0.452679 + 0.784063i
\(123\) 0 0
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −2.00000 + 3.46410i −0.175412 + 0.303822i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 13.8564i −0.671345 1.16280i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 2.00000 + 3.46410i 0.166091 + 0.287678i
\(146\) −14.0000 −1.15865
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i \(-0.972267\pi\)
0.422744 0.906249i \(-0.361067\pi\)
\(150\) 0 0
\(151\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) −16.0000 −1.28515
\(156\) 0 0
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i \(0.119778\pi\)
−0.146772 + 0.989170i \(0.546888\pi\)
\(164\) −5.00000 + 8.66025i −0.390434 + 0.676252i
\(165\) 0 0
\(166\) 0 0
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −2.00000 3.46410i −0.153393 0.265684i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 7.00000 + 12.1244i 0.532200 + 0.921798i 0.999293 + 0.0375896i \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 3.00000 + 5.19615i 0.223607 + 0.387298i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.00000 + 6.92820i 0.294884 + 0.510754i
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 0 0
\(205\) −10.0000 17.3205i −0.698430 1.20972i
\(206\) 0 0
\(207\) −12.0000 + 20.7846i −0.834058 + 1.44463i
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) −2.00000 + 3.46410i −0.134535 + 0.233021i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) −1.00000 1.73205i −0.0665190 0.115214i
\(227\) −8.00000 + 13.8564i −0.530979 + 0.919682i 0.468368 + 0.883534i \(0.344842\pi\)
−0.999346 + 0.0361484i \(0.988491\pi\)
\(228\) 0 0
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) −16.0000 −1.05501
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) −8.00000 + 13.8564i −0.521862 + 0.903892i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 6.92820i 0.254000 0.439941i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0 0
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 + 10.3923i 0.366508 + 0.634811i
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) 0 0
\(277\) −15.0000 + 25.9808i −0.901263 + 1.56103i −0.0754058 + 0.997153i \(0.524025\pi\)
−0.825857 + 0.563880i \(0.809308\pi\)
\(278\) 8.00000 + 13.8564i 0.479808 + 0.831052i
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) 12.0000 20.7846i 0.713326 1.23552i −0.250276 0.968175i \(-0.580521\pi\)
0.963602 0.267342i \(-0.0861454\pi\)
\(284\) −8.00000 + 13.8564i −0.474713 + 0.822226i
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) 0 0
\(288\) −3.00000 −0.176777
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) 7.00000 + 12.1244i 0.409644 + 0.709524i
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 0 0
\(298\) −7.00000 + 12.1244i −0.405499 + 0.702345i
\(299\) 8.00000 + 13.8564i 0.462652 + 0.801337i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.0000 + 17.3205i −0.572598 + 0.991769i
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 8.00000 + 13.8564i 0.454369 + 0.786991i
\(311\) −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i \(-0.906166\pi\)
0.730044 + 0.683400i \(0.239499\pi\)
\(312\) 0 0
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) 10.0000 17.3205i 0.553849 0.959294i
\(327\) 0 0
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 0 0
\(333\) −3.00000 + 5.19615i −0.164399 + 0.284747i
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 7.00000 12.1244i 0.376322 0.651809i
\(347\) 14.0000 24.2487i 0.751559 1.30174i −0.195507 0.980702i \(-0.562635\pi\)
0.947067 0.321037i \(-0.104031\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) −16.0000 27.7128i −0.849192 1.47084i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) −16.0000 27.7128i −0.844448 1.46263i −0.886100 0.463494i \(-0.846596\pi\)
0.0416523 0.999132i \(-0.486738\pi\)
\(360\) 3.00000 5.19615i 0.158114 0.273861i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 11.0000 + 19.0526i 0.578147 + 1.00138i
\(363\) 0 0
\(364\) 0 0
\(365\) −28.0000 −1.46559
\(366\) 0 0
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 4.00000 6.92820i 0.208514 0.361158i
\(369\) 15.0000 + 25.9808i 0.780869 + 1.35250i
\(370\) −4.00000 −0.207950
\(371\) 0 0
\(372\) 0 0
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 0 0
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i \(-0.232188\pi\)
−0.949938 + 0.312437i \(0.898855\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 6.00000 + 10.3923i 0.304997 + 0.528271i
\(388\) −5.00000 + 8.66025i −0.253837 + 0.439658i
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 0 0
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i \(-0.315848\pi\)
−0.998492 + 0.0549046i \(0.982515\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 8.00000 13.8564i 0.398508 0.690237i
\(404\) −9.00000 15.5885i −0.447767 0.775555i
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) −10.0000 + 17.3205i −0.493865 + 0.855399i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 24.0000 1.17954
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) 12.0000 20.7846i 0.583460 1.01058i
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 4.00000 6.92820i 0.192673 0.333720i −0.753462 0.657491i \(-0.771618\pi\)
0.946135 + 0.323772i \(0.104951\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) −20.0000 34.6410i −0.954548 1.65333i −0.735399 0.677634i \(-0.763005\pi\)
−0.219149 0.975691i \(-0.570328\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 4.00000 0.190261
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −1.50000 2.59808i −0.0707107 0.122474i
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) −1.00000 + 1.73205i −0.0470360 + 0.0814688i
\(453\) 0 0
\(454\) 16.0000 0.750917
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) 11.0000 19.0526i 0.513996 0.890268i
\(459\) 0 0
\(460\) 8.00000 + 13.8564i 0.373002 + 0.646058i
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −12.0000 20.7846i −0.555294 0.961797i −0.997881 0.0650714i \(-0.979272\pi\)
0.442587 0.896726i \(-0.354061\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 16.0000 0.738025
\(471\) 0 0
\(472\) 0 0
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 4.00000 + 6.92820i 0.182956 + 0.316889i
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 18.0000 0.819878
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −10.0000 17.3205i −0.454077 0.786484i
\(486\) 0 0
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) −5.00000 8.66025i −0.226339 0.392031i
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) −4.00000 6.92820i −0.177822 0.307996i
\(507\) 0 0
\(508\) −4.00000 + 6.92820i −0.177471 + 0.307389i
\(509\) −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i \(-0.180780\pi\)
−0.887336 + 0.461123i \(0.847447\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 15.0000 25.9808i 0.661622 1.14596i
\(515\) 0 0
\(516\) 0 0
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 0 0
\(520\) −2.00000 3.46410i −0.0877058 0.151911i
\(521\) −17.0000 + 29.4449i −0.744784 + 1.29000i 0.205512 + 0.978655i \(0.434114\pi\)
−0.950296 + 0.311348i \(0.899219\pi\)
\(522\) −3.00000 + 5.19615i −0.131306 + 0.227429i
\(523\) −4.00000 6.92820i −0.174908 0.302949i 0.765222 0.643767i \(-0.222629\pi\)
−0.940129 + 0.340818i \(0.889296\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 8.00000 + 13.8564i 0.348485 + 0.603595i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 0 0
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) −19.0000 32.9090i −0.816874 1.41487i −0.907975 0.419025i \(-0.862372\pi\)
0.0911008 0.995842i \(-0.470961\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 0 0
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 15.0000 25.9808i 0.640184 1.10883i
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) 5.00000 8.66025i 0.211857 0.366947i −0.740439 0.672124i \(-0.765382\pi\)
0.952296 + 0.305177i \(0.0987156\pi\)
\(558\) −12.0000 20.7846i −0.508001 0.879883i
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 11.0000 + 19.0526i 0.464007 + 0.803684i
\(563\) −4.00000 + 6.92820i −0.168580 + 0.291989i −0.937921 0.346850i \(-0.887251\pi\)
0.769341 + 0.638838i \(0.220585\pi\)
\(564\) 0 0
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) −24.0000 −1.00880
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i \(-0.460975\pi\)
0.798379 0.602155i \(-0.205691\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) 0 0
\(580\) −4.00000 −0.166091
\(581\) 0 0
\(582\) 0 0
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) 7.00000 12.1244i 0.289662 0.501709i
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) 15.0000 + 25.9808i 0.619644 + 1.07326i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −21.0000 36.3731i −0.862367 1.49366i −0.869638 0.493689i \(-0.835648\pi\)
0.00727173 0.999974i \(-0.497685\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 14.0000 0.573462
\(597\) 0 0
\(598\) 8.00000 13.8564i 0.327144 0.566631i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) 36.0000 1.46603
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 20.0000 0.809776
\(611\) −8.00000 13.8564i −0.323645 0.560570i
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) −11.0000 + 19.0526i −0.444286 + 0.769526i −0.998002 0.0631797i \(-0.979876\pi\)
0.553716 + 0.832705i \(0.313209\pi\)
\(614\) 8.00000 + 13.8564i 0.322854 + 0.559199i
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) 8.00000 13.8564i 0.321547 0.556936i −0.659260 0.751915i \(-0.729130\pi\)
0.980807 + 0.194979i \(0.0624638\pi\)
\(620\) 8.00000 13.8564i 0.321288 0.556487i
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 0 0
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −8.00000 13.8564i −0.317470 0.549875i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.00000 0.0791808
\(639\) 24.0000 + 41.5692i 0.949425 + 1.64445i
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −20.0000 −0.783260
\(653\) 13.0000 + 22.5167i 0.508729 + 0.881145i 0.999949 + 0.0101092i \(0.00321793\pi\)
−0.491220 + 0.871036i \(0.663449\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −5.00000 8.66025i −0.195217 0.338126i
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) −2.00000 + 3.46410i −0.0777322 + 0.134636i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) −8.00000 + 13.8564i −0.309529 + 0.536120i
\(669\) 0 0
\(670\) 12.0000 + 20.7846i 0.463600 + 0.802980i
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −13.0000 22.5167i −0.499631 0.865386i 0.500369 0.865812i \(-0.333198\pi\)
−1.00000 0.000426509i \(0.999864\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) −12.0000 20.7846i −0.456502 0.790684i 0.542272 0.840203i \(-0.317564\pi\)
−0.998773 + 0.0495194i \(0.984231\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) −28.0000 −1.06287
\(695\) 16.0000 + 27.7128i 0.606915 + 1.05121i
\(696\) 0 0
\(697\) −10.0000 + 17.3205i −0.378777 + 0.656061i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) 0 0
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) 0 0
\(709\) −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i \(-0.976184\pi\)
0.433865 0.900978i \(-0.357149\pi\)
\(710\) −16.0000 + 27.7128i −0.600469 + 1.04004i
\(711\) 0 0
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 64.0000 2.39682
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 0 0
\(718\) −16.0000 + 27.7128i −0.597115 + 1.03423i
\(719\) 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i \(-0.119005\pi\)
−0.781748 + 0.623595i \(0.785672\pi\)
\(720\) −6.00000 −0.223607
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) −1.00000 + 1.73205i −0.0371391 + 0.0643268i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 14.0000 + 24.2487i 0.518163 + 0.897485i
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) 15.0000 25.9808i 0.552158 0.956365i
\(739\) −6.00000 + 10.3923i −0.220714 + 0.382287i −0.955025 0.296526i \(-0.904172\pi\)
0.734311 + 0.678813i \(0.237505\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −14.0000 + 24.2487i −0.512920 + 0.888404i
\(746\) −7.00000 + 12.1244i −0.256288 + 0.443904i
\(747\) 0 0
\(748\) −2.00000 −0.0731272
\(749\) 0 0
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) 0 0
\(754\) 2.00000 + 3.46410i 0.0728357 + 0.126155i
\(755\) 0 0
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) −2.00000 3.46410i −0.0726433 0.125822i
\(759\) 0 0
\(760\) 0 0
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 6.00000 + 10.3923i 0.216930 + 0.375735i
\(766\) −4.00000 + 6.92820i −0.144526 + 0.250326i
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 6.00000 10.3923i 0.215666 0.373544i
\(775\) −4.00000 6.92820i −0.143684 0.248868i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) 8.00000 13.8564i 0.286263 0.495821i
\(782\) 8.00000 + 13.8564i 0.286079 + 0.495504i
\(783\) 0 0
\(784\) 0 0
\(785\) −28.0000 −0.999363
\(786\) 0 0
\(787\) −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i \(0.359855\pi\)
−0.996531 + 0.0832226i \(0.973479\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 3.00000 0.106600
\(793\) −10.0000 17.3205i