Properties

Label 1782.2.e.f.1189.1
Level $1782$
Weight $2$
Character 1782.1189
Analytic conductor $14.229$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1782 = 2 \cdot 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1782.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.2293416402\)
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 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1189.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1782.1189
Dual form 1782.2.e.f.595.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{11} +(2.00000 + 3.46410i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{22} +(3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} -4.00000 q^{26} +2.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -10.0000 q^{37} +(2.00000 - 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} +1.00000 q^{44} -6.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(1.50000 + 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{50} +(2.00000 - 3.46410i) q^{52} +(-1.00000 + 1.73205i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} -6.00000 q^{71} +2.00000 q^{73} +(5.00000 - 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(-7.00000 + 12.1244i) q^{79} -6.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} +6.00000 q^{89} -8.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-7.00000 + 12.1244i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 2 q^{7} + 2 q^{8} - q^{11} + 4 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{19} - q^{22} + 6 q^{23} + 5 q^{25} - 8 q^{26} + 4 q^{28} + 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 20 q^{37} + 4 q^{38} + 6 q^{41} - 8 q^{43} + 2 q^{44} - 12 q^{46} - 6 q^{47} + 3 q^{49} + 5 q^{50} + 4 q^{52} - 2 q^{56} + 6 q^{58} - 8 q^{61} + 16 q^{62} + 2 q^{64} + 4 q^{67} - 6 q^{68} - 12 q^{71} + 4 q^{73} + 10 q^{74} + 4 q^{76} - 2 q^{77} - 14 q^{79} - 12 q^{82} - 12 q^{83} - 8 q^{86} - q^{88} + 12 q^{89} - 16 q^{91} + 6 q^{92} - 6 q^{94} - 14 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1782\mathbb{Z}\right)^\times\).

\(n\) \(1135\) \(1541\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −1.00000 1.73205i −0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 2.50000 + 4.33013i 0.353553 + 0.612372i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 0 0
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 5.00000 8.66025i 0.581238 1.00673i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) −1.00000 1.73205i −0.113961 0.197386i
\(78\) 0 0
\(79\) −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 3.00000 5.19615i 0.312772 0.541736i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 2.00000 + 3.46410i 0.196116 + 0.339683i
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 1.73205i −0.0944911 0.163663i
\(113\) 9.00000 + 15.5885i 0.846649 + 1.46644i 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 0 0
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 0 0
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) −4.00000 −0.334497
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 5.00000 + 8.66025i 0.410997 + 0.711868i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) −4.00000 −0.324443
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) −7.00000 12.1244i −0.556890 0.964562i
\(159\) 0 0
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 5.00000 + 8.66025i 0.377964 + 0.654654i
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 4.00000 6.92820i 0.296500 0.513553i
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −7.00000 12.1244i −0.502571 0.870478i
\(195\) 0 0
\(196\) 1.50000 2.59808i 0.107143 0.185577i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 0 0
\(202\) 3.00000 + 5.19615i 0.211079 + 0.365600i
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 2.00000 3.46410i 0.138343 0.239617i
\(210\) 0 0
\(211\) −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i \(-0.255467\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 0 0
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 2.00000 3.46410i 0.135457 0.234619i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) 8.00000 13.8564i 0.535720 0.927894i −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) −18.0000 −1.19734
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i \(-0.293538\pi\)
−0.992195 + 0.124696i \(0.960204\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 1.00000 0.0642824
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) −8.00000 13.8564i −0.509028 0.881662i
\(248\) −4.00000 6.92820i −0.254000 0.439941i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −7.00000 + 12.1244i −0.439219 + 0.760750i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −15.0000 25.9808i −0.935674 1.62064i −0.773427 0.633885i \(-0.781459\pi\)
−0.162247 0.986750i \(-0.551874\pi\)
\(258\) 0 0
\(259\) 10.0000 17.3205i 0.621370 1.07624i
\(260\) 0 0
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 + 6.92820i 0.245256 + 0.424795i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) −9.00000 15.5885i −0.543710 0.941733i
\(275\) 2.50000 + 4.33013i 0.150756 + 0.261116i
\(276\) 0 0
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279741i \(0.909752\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) 2.00000 3.46410i 0.118262 0.204837i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −3.00000 5.19615i −0.175262 0.303562i 0.764990 0.644042i \(-0.222744\pi\)
−0.940252 + 0.340480i \(0.889411\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −1.00000 + 1.73205i −0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) 0 0
\(311\) −9.00000 15.5885i −0.510343 0.883940i −0.999928 0.0119847i \(-0.996185\pi\)
0.489585 0.871956i \(-0.337148\pi\)
\(312\) 0 0
\(313\) −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i \(0.429392\pi\)
−0.954810 + 0.297218i \(0.903941\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) 6.00000 10.3923i 0.334367 0.579141i
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 20.0000 1.10940
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 0 0
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) −6.00000 10.3923i −0.330791 0.572946i
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) 0 0
\(341\) 8.00000 0.433224
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 18.0000 + 31.1769i 0.966291 + 1.67366i 0.706107 + 0.708105i \(0.250450\pi\)
0.260184 + 0.965559i \(0.416217\pi\)
\(348\) 0 0
\(349\) 2.00000 3.46410i 0.107058 0.185429i −0.807519 0.589841i \(-0.799190\pi\)
0.914577 + 0.404412i \(0.132524\pi\)
\(350\) −10.0000 −0.534522
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) 0 0
\(364\) 4.00000 + 6.92820i 0.209657 + 0.363137i
\(365\) 0 0
\(366\) 0 0
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 17.3205i −0.517780 0.896822i −0.999787 0.0206542i \(-0.993425\pi\)
0.482006 0.876168i \(-0.339908\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) 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
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) 18.0000 + 31.1769i 0.910299 + 1.57668i
\(392\) 1.50000 + 2.59808i 0.0757614 + 0.131223i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 2.00000 3.46410i 0.100251 0.173640i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 0 0
\(403\) 16.0000 27.7128i 0.797017 1.38047i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 5.00000 8.66025i 0.247841 0.429273i
\(408\) 0 0
\(409\) 17.0000 + 29.4449i 0.840596 + 1.45595i 0.889392 + 0.457146i \(0.151128\pi\)
−0.0487958 + 0.998809i \(0.515538\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) 2.00000 + 3.46410i 0.0978232 + 0.169435i
\(419\) 12.0000 + 20.7846i 0.586238 + 1.01539i 0.994720 + 0.102628i \(0.0327251\pi\)
−0.408481 + 0.912767i \(0.633942\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) 8.00000 0.389434
\(423\) 0 0
\(424\) 0 0
\(425\) 15.0000 25.9808i 0.727607 1.26025i
\(426\) 0 0
\(427\) −8.00000 13.8564i −0.387147 0.670559i
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −8.00000 + 13.8564i −0.384012 + 0.665129i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) −12.0000 20.7846i −0.574038 0.994263i
\(438\) 0 0
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 0 0
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 0 0
\(454\) −6.00000 10.3923i −0.281594 0.487735i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) 0 0
\(461\) 21.0000 36.3731i 0.978068 1.69406i 0.308651 0.951175i \(-0.400123\pi\)
0.669417 0.742887i \(-0.266544\pi\)
\(462\) 0 0
\(463\) 2.00000 + 3.46410i 0.0929479 + 0.160990i 0.908750 0.417340i \(-0.137038\pi\)
−0.815802 + 0.578331i \(0.803704\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −10.0000 + 17.3205i −0.458831 + 0.794719i
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) −20.0000 34.6410i −0.911922 1.57949i
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 0 0
\(508\) −7.00000 12.1244i −0.310575 0.537931i
\(509\) 12.0000 + 20.7846i 0.531891 + 0.921262i 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 0 0
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 0 0
\(517\) −3.00000 5.19615i −0.131940 0.228527i
\(518\) 10.0000 + 17.3205i 0.439375 + 0.761019i
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −6.00000 + 10.3923i −0.262111 + 0.453990i
\(525\) 0 0
\(526\) 0 0
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) −12.0000 + 20.7846i −0.519778 + 0.900281i
\(534\) 0 0
\(535\) 0 0
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −12.0000 + 20.7846i −0.517357 + 0.896088i
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.0000 24.2487i 0.598597 1.03680i −0.394432 0.918925i \(-0.629059\pi\)
0.993028 0.117875i \(-0.0376081\pi\)
\(548\) 18.0000 0.768922
\(549\) 0 0
\(550\) −5.00000 −0.213201
\(551\) −12.0000 + 20.7846i −0.511217 + 0.885454i
\(552\) 0 0
\(553\) −14.0000 24.2487i −0.595341 1.03116i
\(554\) 8.00000 + 13.8564i 0.339887 + 0.588702i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 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
\(571\) 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i \(0.0325850\pi\)
−0.408883 + 0.912587i \(0.634082\pi\)
\(572\) 2.00000 + 3.46410i 0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 6.00000 10.3923i 0.250435 0.433766i
\(575\) 30.0000 1.25109
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 20.7846i −0.497844 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 12.0000 20.7846i 0.495293 0.857873i −0.504692 0.863299i \(-0.668394\pi\)
0.999985 + 0.00542667i \(0.00172737\pi\)
\(588\) 0 0
\(589\) 16.0000 + 27.7128i 0.659269 + 1.14189i
\(590\) 0 0
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) −12.0000 20.7846i −0.490716 0.849946i
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0 0
\(601\) 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i \(-0.685221\pi\)
0.998302 + 0.0582563i \(0.0185541\pi\)
\(602\) 16.0000 0.652111
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −7.00000 12.1244i −0.284121 0.492112i 0.688274 0.725450i \(-0.258368\pi\)
−0.972396 + 0.233338i \(0.925035\pi\)
\(608\) 2.00000 + 3.46410i 0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −10.0000 + 17.3205i −0.403567 + 0.698999i
\(615\) 0 0
\(616\) −1.00000 1.73205i −0.0402911 0.0697863i
\(617\) −15.0000 25.9808i −0.603877 1.04595i −0.992228 0.124434i \(-0.960288\pi\)
0.388351 0.921512i \(-0.373045\pi\)
\(618\) 0 0
\(619\) −22.0000 + 38.1051i −0.884255 + 1.53157i −0.0376891 + 0.999290i \(0.512000\pi\)
−0.846566 + 0.532284i \(0.821334\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) −6.00000 + 10.3923i −0.240385 + 0.416359i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −13.0000 22.5167i −0.519584 0.899947i
\(627\) 0 0
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −7.00000 + 12.1244i −0.278445 + 0.482281i
\(633\) 0 0
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) −6.00000 + 10.3923i −0.237729 + 0.411758i
\(638\) −6.00000 −0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) 3.00000 5.19615i 0.118493 0.205236i −0.800678 0.599095i \(-0.795527\pi\)
0.919171 + 0.393860i \(0.128860\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 6.00000 + 10.3923i 0.236433 + 0.409514i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −10.0000 + 17.3205i −0.392232 + 0.679366i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) −18.0000 31.1769i −0.704394 1.22005i −0.966910 0.255119i \(-0.917885\pi\)
0.262515 0.964928i \(-0.415448\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) 12.0000 0.467809
\(659\) 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i \(-0.585990\pi\)
0.968052 0.250748i \(-0.0806766\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 2.00000 + 3.46410i 0.0777322 + 0.134636i
\(663\) 0 0
\(664\) −6.00000 + 10.3923i −0.232845 + 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 36.0000 1.39393
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 6.92820i −0.154418 0.267460i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 15.0000 25.9808i 0.576497 0.998522i −0.419380 0.907811i \(-0.637753\pi\)
0.995877 0.0907112i \(-0.0289140\pi\)
\(678\) 0 0
\(679\) −14.0000 24.2487i −0.537271 0.930580i
\(680\) 0 0
\(681\) 0 0
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 0 0
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 0 0
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 2.00000 + 3.46410i 0.0757011 + 0.131118i
\(699\) 0 0
\(700\) 5.00000 8.66025i 0.188982 0.327327i
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 40.0000 1.50863
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −3.00000 5.19615i −0.112906 0.195560i
\(707\) 6.00000 + 10.3923i 0.225653 + 0.390843i
\(708\) 0 0
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 24.0000 41.5692i 0.898807 1.55678i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 + 20.7846i 0.448461 + 0.776757i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 1.50000 2.59808i 0.0558242 0.0966904i
\(723\) 0 0
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) −15.0000 25.9808i −0.557086 0.964901i
\(726\) 0 0
\(727\) 14.0000 24.2487i 0.519231 0.899335i −0.480519 0.876984i \(-0.659552\pi\)
0.999750 0.0223506i \(-0.00711500\pi\)
\(728\) −8.00000 −0.296500
\(729\) 0 0
\(730\) 0 0
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 0 0
\(733\) 2.00000 + 3.46410i 0.0738717 + 0.127950i 0.900595 0.434659i \(-0.143131\pi\)
−0.826723 + 0.562609i \(0.809798\pi\)
\(734\) −4.00000 6.92820i −0.147643 0.255725i
\(735\) 0 0
\(736\) 3.00000 5.19615i 0.110581 0.191533i
\(737\) −4.00000 −0.147342
\(738\) 0 0
\(739\) 8.00000 0.294285 0.147142 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 20.0000 0.732252
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) −12.0000 + 20.7846i −0.438470 + 0.759453i
\(750\) 0 0
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) −12.0000 + 20.7846i −0.437014 + 0.756931i
\(755\) 0 0
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) 0 0
\(761\) 9.00000 + 15.5885i 0.326250 + 0.565081i 0.981764 0.190101i \(-0.0608816\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(762\) 0 0
\(763\) 4.00000 6.92820i 0.144810 0.250818i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) 0 0
\(769\) 17.0000 + 29.4449i 0.613036 + 1.06181i 0.990726 + 0.135877i \(0.0433852\pi\)
−0.377690 + 0.925932i \(0.623282\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) −7.00000 + 12.1244i −0.251285 + 0.435239i
\(777\) 0 0
\(778\) 0 0
\(779\) −12.0000 20.7846i −0.429945 0.744686i
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) −36.0000 −1.28736
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 3.00000 + 5.19615i 0.106871 + 0.185105i
\(789\) 0 0
\(790\) 0 0
\(791\) −36.0000 −1.28001
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) −13.0000 + 22.5167i −0.461353 + 0.799086i