Properties

Label 1386.2.k.d.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.d.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} -1.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +9.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(3.50000 + 6.06218i) q^{37} +(0.500000 - 0.866025i) q^{38} +6.00000 q^{41} +11.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -5.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-2.00000 + 1.73205i) q^{56} +(-4.50000 - 7.79423i) q^{58} +(4.50000 - 7.79423i) q^{59} +(5.00000 + 8.66025i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} -3.00000 q^{71} +(2.00000 - 3.46410i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{76} +(0.500000 + 2.59808i) q^{77} +(8.00000 + 13.8564i) q^{79} +(-3.00000 - 5.19615i) q^{82} +(-5.50000 - 9.52628i) q^{86} +(0.500000 - 0.866025i) q^{88} +(8.00000 - 6.92820i) q^{91} +3.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} -1.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 4q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 4q^{7} + 2q^{8} + q^{11} - 8q^{13} + 5q^{14} - q^{16} + 3q^{17} + q^{19} - 2q^{22} - 3q^{23} + 5q^{25} + 4q^{26} - q^{28} + 18q^{29} - 2q^{31} - q^{32} - 6q^{34} + 7q^{37} + q^{38} + 12q^{41} + 22q^{43} + q^{44} - 3q^{46} - 3q^{47} + 2q^{49} - 10q^{50} + 4q^{52} - 4q^{56} - 9q^{58} + 9q^{59} + 10q^{61} + 4q^{62} + 2q^{64} + 4q^{67} + 3q^{68} - 6q^{71} + 4q^{73} + 7q^{74} - 2q^{76} + q^{77} + 16q^{79} - 6q^{82} - 11q^{86} + q^{88} + 16q^{91} + 6q^{92} - 3q^{94} - 2q^{97} - 13q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 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
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 0 0
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) 0 0
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 0 0
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 0.500000 + 2.59808i 0.0569803 + 0.296078i
\(78\) 0 0
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 5.19615i −0.331295 0.573819i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.50000 9.52628i −0.593080 1.02725i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 8.00000 6.92820i 0.838628 0.726273i
\(92\) 3.00000 0.312772
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) 0 0
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 15.5885i −0.870063 1.50699i −0.861931 0.507026i \(-0.830745\pi\)
−0.00813215 0.999967i \(-0.502589\pi\)
\(108\) 0 0
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 0 0
\(118\) −9.00000 −0.828517
\(119\) 1.50000 + 7.79423i 0.137505 + 0.714496i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 0 0
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) −19.0000 −1.61156 −0.805779 0.592216i \(-0.798253\pi\)
−0.805779 + 0.592216i \(0.798253\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.50000 + 2.59808i 0.125877 + 0.218026i
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) 0 0
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 0 0
\(151\) 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i \(-0.552039\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) 2.00000 1.73205i 0.161165 0.139573i
\(155\) 0 0
\(156\) 0 0
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) 0 0
\(160\) 0 0
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) −3.00000 + 5.19615i −0.234261 + 0.405751i
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) −5.50000 + 9.52628i −0.419371 + 0.726372i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 2.50000 + 12.9904i 0.188982 + 0.981981i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 0 0
\(179\) −7.50000 + 12.9904i −0.560576 + 0.970947i 0.436870 + 0.899525i \(0.356087\pi\)
−0.997446 + 0.0714220i \(0.977246\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −10.0000 3.46410i −0.741249 0.256776i
\(183\) 0 0
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.50000 2.59808i −0.109691 0.189990i
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 21.0000 1.49619 0.748094 0.663593i \(-0.230969\pi\)
0.748094 + 0.663593i \(0.230969\pi\)
\(198\) 0 0
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 0 0
\(202\) −15.0000 −1.05540
\(203\) −18.0000 + 15.5885i −1.26335 + 1.09410i
\(204\) 0 0
\(205\) 0 0
\(206\) 2.00000 3.46410i 0.139347 0.241355i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −9.00000 + 15.5885i −0.615227 + 1.06561i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.00000 5.19615i −0.0678844 0.352738i
\(218\) −10.0000 −0.677285
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) 0 0
\(229\) −13.0000 22.5167i −0.859064 1.48794i −0.872823 0.488037i \(-0.837713\pi\)
0.0137585 0.999905i \(-0.495620\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) 4.50000 + 7.79423i 0.294805 + 0.510617i 0.974939 0.222470i \(-0.0714120\pi\)
−0.680135 + 0.733087i \(0.738079\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 0 0
\(238\) 6.00000 5.19615i 0.388922 0.336817i
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 14.0000 24.2487i 0.901819 1.56200i 0.0766885 0.997055i \(-0.475565\pi\)
0.825131 0.564942i \(-0.191101\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 0.500000 + 0.866025i 0.0313728 + 0.0543393i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) 0 0
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.00000 15.5885i 0.556022 0.963058i
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.500000 + 2.59808i 0.0306570 + 0.159298i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) −2.50000 4.33013i −0.150756 0.261116i
\(276\) 0 0
\(277\) −16.0000 + 27.7128i −0.961347 + 1.66510i −0.242222 + 0.970221i \(0.577876\pi\)
−0.719125 + 0.694881i \(0.755457\pi\)
\(278\) 9.50000 + 16.4545i 0.569772 + 0.986874i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.0000 0.894825 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 0 0
\(283\) −10.0000 + 17.3205i −0.594438 + 1.02960i 0.399188 + 0.916869i \(0.369292\pi\)
−0.993626 + 0.112728i \(0.964041\pi\)
\(284\) 1.50000 2.59808i 0.0890086 0.154167i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) −12.0000 + 10.3923i −0.708338 + 0.613438i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.50000 + 6.06218i 0.203433 + 0.352357i
\(297\) 0 0
\(298\) 4.50000 7.79423i 0.260678 0.451508i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) −22.0000 + 19.0526i −1.26806 + 1.09817i
\(302\) −19.0000 −1.09333
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 0 0
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) −2.50000 0.866025i −0.142451 0.0493464i
\(309\) 0 0
\(310\) 0 0
\(311\) −10.5000 + 18.1865i −0.595400 + 1.03126i 0.398090 + 0.917346i \(0.369673\pi\)
−0.993490 + 0.113917i \(0.963660\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.50000 7.79423i −0.0835917 0.434355i
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −10.0000 + 17.3205i −0.554700 + 0.960769i
\(326\) −1.00000 + 1.73205i −0.0553849 + 0.0959294i
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) 7.50000 + 2.59808i 0.413488 + 0.143237i
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 0 0
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.00000 + 1.73205i 0.0541530 + 0.0937958i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 11.0000 0.593080
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 10.0000 8.66025i 0.534522 0.462910i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) 2.00000 + 10.3923i 0.104828 + 0.544705i
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) −1.50000 + 2.59808i −0.0775632 + 0.134343i
\(375\) 0 0
\(376\) −1.50000 2.59808i −0.0773566 0.133986i
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) 14.0000 0.719132 0.359566 0.933120i \(-0.382925\pi\)
0.359566 + 0.933120i \(0.382925\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 0.500000 0.866025i 0.0253837 0.0439658i
\(389\) 6.00000 10.3923i 0.304212 0.526911i −0.672874 0.739758i \(-0.734940\pi\)
0.977086 + 0.212847i \(0.0682735\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 0 0
\(394\) −10.5000 18.1865i −0.528982 0.916224i
\(395\) 0 0
\(396\) 0 0
\(397\) 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −3.00000 5.19615i −0.149813 0.259483i 0.781345 0.624099i \(-0.214534\pi\)
−0.931158 + 0.364615i \(0.881200\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 7.50000 + 12.9904i 0.373139 + 0.646296i
\(405\) 0 0
\(406\) 22.5000 + 7.79423i 1.11666 + 0.386821i
\(407\) 7.00000 0.346977
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 4.50000 + 23.3827i 0.221431 + 1.15059i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) −0.500000 0.866025i −0.0244558 0.0423587i
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 0 0
\(424\) 0 0
\(425\) −7.50000 12.9904i −0.363803 0.630126i
\(426\) 0 0
\(427\) −25.0000 8.66025i −1.20983 0.419099i
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0 0
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) −4.00000 + 3.46410i −0.192006 + 0.166282i
\(435\) 0 0
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 1.50000 2.59808i 0.0717547 0.124283i
\(438\) 0 0
\(439\) 18.5000 + 32.0429i 0.882957 + 1.52933i 0.848038 + 0.529936i \(0.177784\pi\)
0.0349192 + 0.999390i \(0.488883\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) 1.50000 + 2.59808i 0.0712672 + 0.123438i 0.899457 0.437009i \(-0.143962\pi\)
−0.828190 + 0.560448i \(0.810629\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 0 0
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) −13.0000 + 22.5167i −0.607450 + 1.05213i
\(459\) 0 0
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) 0 0
\(466\) 4.50000 7.79423i 0.208458 0.361061i
\(467\) −16.5000 28.5788i −0.763529 1.32247i −0.941021 0.338349i \(-0.890132\pi\)
0.177492 0.984122i \(-0.443202\pi\)
\(468\) 0 0
\(469\) 2.00000 + 10.3923i 0.0923514 + 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 4.50000 7.79423i 0.207129 0.358758i
\(473\) 5.50000 9.52628i 0.252890 0.438019i
\(474\) 0 0
\(475\) 5.00000 0.229416
\(476\) −7.50000 2.59808i −0.343762 0.119083i
\(477\) 0 0
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 0 0
\(481\) −14.0000 24.2487i −0.638345 1.10565i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0 0
\(487\) 2.00000 3.46410i 0.0906287 0.156973i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 0 0
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 13.5000 23.3827i 0.608009 1.05310i
\(494\) −2.00000 + 3.46410i −0.0899843 + 0.155857i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 6.00000 5.19615i 0.269137 0.233079i
\(498\) 0 0
\(499\) 5.00000 + 8.66025i 0.223831 + 0.387686i 0.955968 0.293471i \(-0.0948104\pi\)
−0.732137 + 0.681157i \(0.761477\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 7.50000 + 12.9904i 0.334741 + 0.579789i
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1.50000 + 2.59808i 0.0666831 + 0.115499i
\(507\) 0 0
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) −18.0000 31.1769i −0.797836 1.38189i −0.921023 0.389509i \(-0.872645\pi\)
0.123187 0.992384i \(-0.460689\pi\)
\(510\) 0 0
\(511\) 2.00000 + 10.3923i 0.0884748 + 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.00000 10.3923i 0.264649 0.458385i
\(515\) 0 0
\(516\) 0 0
\(517\) −3.00000 −0.131940
\(518\) 3.50000 + 18.1865i 0.153781 + 0.799070i
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i \(0.394910\pi\)
−0.981347 + 0.192244i \(0.938423\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000 1.73205i 0.0867110 0.0750939i
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) 0 0
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) −10.0000 17.3205i −0.429934 0.744667i 0.566933 0.823764i \(-0.308130\pi\)
−0.996867 + 0.0790969i \(0.974796\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 0 0
\(546\) 0 0
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 0 0
\(550\) −2.50000 + 4.33013i −0.106600 + 0.184637i
\(551\) 4.50000 + 7.79423i 0.191706 + 0.332045i
\(552\) 0 0
\(553\) −40.0000 13.8564i −1.70097 0.589234i
\(554\) 32.0000 1.35955
\(555\) 0 0
\(556\) 9.50000 16.4545i 0.402890 0.697826i
\(557\) 22.5000 38.9711i 0.953356 1.65126i 0.215268 0.976555i \(-0.430937\pi\)
0.738087 0.674705i \(-0.235729\pi\)
\(558\) 0 0
\(559\) −44.0000 −1.86100
\(560\) 0 0
\(561\) 0 0
\(562\) −7.50000 12.9904i −0.316368 0.547966i
\(563\) −18.0000 + 31.1769i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331202i \(0.892546\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) −10.5000 18.1865i −0.440183 0.762419i 0.557520 0.830164i \(-0.311753\pi\)
−0.997703 + 0.0677445i \(0.978420\pi\)
\(570\) 0 0
\(571\) −14.5000 + 25.1147i −0.606806 + 1.05102i 0.384957 + 0.922934i \(0.374216\pi\)
−0.991763 + 0.128085i \(0.959117\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) 0 0
\(574\) 15.0000 + 5.19615i 0.626088 + 0.216883i
\(575\) −15.0000 −0.625543
\(576\) 0 0
\(577\) 11.0000 19.0526i 0.457936 0.793168i −0.540916 0.841077i \(-0.681922\pi\)
0.998852 + 0.0479084i \(0.0152556\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 4.50000 + 7.79423i 0.184793 + 0.320071i 0.943507 0.331353i \(-0.107505\pi\)
−0.758714 + 0.651424i \(0.774172\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.00000 −0.368654
\(597\) 0 0
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) 24.0000 41.5692i 0.980613 1.69847i 0.320607 0.947212i \(-0.396113\pi\)
0.660006 0.751260i \(-0.270554\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 27.5000 + 9.52628i 1.12082 + 0.388262i
\(603\) 0 0
\(604\) 9.50000 + 16.4545i 0.386550 + 0.669523i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 + 10.3923i 0.242734 + 0.420428i
\(612\) 0 0
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) 2.00000 + 3.46410i 0.0807134 + 0.139800i
\(615\) 0 0
\(616\) 0.500000 + 2.59808i 0.0201456 + 0.104679i
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 21.0000 0.842023
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 0.500000 0.866025i 0.0199840 0.0346133i
\(627\) 0 0
\(628\) 6.50000 + 11.2583i 0.259378 + 0.449256i
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) 0 0
\(634\) −6.00000 + 10.3923i −0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 + 27.7128i −0.158486 + 1.09802i
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) 0 0
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 0 0
\(643\) −46.0000 −1.81406 −0.907031 0.421063i \(-0.861657\pi\)
−0.907031 + 0.421063i \(0.861657\pi\)
\(644\) −6.00000 + 5.19615i −0.236433 + 0.204757i
\(645\) 0 0
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) 24.0000 41.5692i 0.943537 1.63425i 0.184884 0.982760i \(-0.440809\pi\)
0.758654 0.651494i \(-0.225858\pi\)
\(648\) 0 0
\(649\) −4.50000 7.79423i −0.176640 0.305950i
\(650\) 20.0000 0.784465
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) 12.0000 + 20.7846i 0.469596 + 0.813365i 0.999396 0.0347583i \(-0.0110661\pi\)
−0.529799 + 0.848123i \(0.677733\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) 0 0
\(658\) −1.50000 7.79423i −0.0584761 0.303851i
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) 0 0
\(661\) −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i \(0.404978\pi\)
−0.974776 + 0.223184i \(0.928355\pi\)
\(662\) 5.00000 8.66025i 0.194331 0.336590i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −13.5000 23.3827i −0.522722 0.905381i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 44.0000 1.69608 0.848038 0.529936i \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) 5.00000 + 8.66025i 0.192593 + 0.333581i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −16.5000 28.5788i −0.634147 1.09837i −0.986695 0.162581i \(-0.948018\pi\)
0.352549 0.935793i \(-0.385315\pi\)
\(678\) 0 0
\(679\) 2.00000 1.73205i 0.0767530 0.0664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 1.00000 1.73205i 0.0382920 0.0663237i
\(683\) 16.5000 28.5788i 0.631355 1.09354i −0.355920 0.934516i \(-0.615832\pi\)
0.987275 0.159022i \(-0.0508342\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −5.50000 9.52628i −0.209686 0.363186i
\(689\) 0 0
\(690\) 0 0
\(691\) −25.0000 43.3013i −0.951045 1.64726i −0.743170 0.669102i \(-0.766679\pi\)
−0.207875 0.978155i \(-0.566655\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) −4.00000 6.92820i −0.151402 0.262236i
\(699\) 0 0
\(700\) −12.5000 4.33013i −0.472456 0.163663i
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 0 0
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 7.50000 + 38.9711i 0.282067 + 1.46566i
\(708\) 0 0
\(709\) −17.5000 30.3109i −0.657226 1.13835i −0.981331 0.192328i \(-0.938396\pi\)
0.324104 0.946021i \(-0.394937\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) −7.50000 12.9904i −0.280288 0.485473i
\(717\) 0 0
\(718\) −9.00000 + 15.5885i −0.335877 + 0.581756i
\(719\) 4.50000 + 7.79423i 0.167822 + 0.290676i 0.937654 0.347571i \(-0.112993\pi\)
−0.769832 + 0.638247i \(0.779660\pi\)
\(720\) 0 0
\(721\) −10.0000 3.46410i −0.372419 0.129010i
\(722\) −18.0000 −0.669891
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 22.5000 38.9711i 0.835629 1.44735i
\(726\) 0 0
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) 8.00000 6.92820i 0.296500 0.256776i
\(729\) 0 0
\(730\) 0 0
\(731\) 16.5000 28.5788i 0.610275 1.05703i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −2.00000 3.46410i −0.0736709 0.127602i
\(738\) 0 0
\(739\) 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i \(-0.809894\pi\)
0.900464 + 0.434930i \(0.143227\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) 0 0
\(748\) 3.00000 0.109691
\(749\) 45.0000 + 15.5885i 1.64426 + 0.569590i
\(750\) 0 0
\(751\) −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i \(-0.178285\pi\)
−0.883694 + 0.468065i \(0.844951\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 18.0000 + 31.1769i 0.655521 + 1.13540i
\(755\) 0 0
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) −7.00000 12.1244i −0.254251 0.440376i
\(759\) 0 0
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 0 0
\(763\) 5.00000 + 25.9808i 0.181012 + 0.940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 7.50000 12.9904i 0.270986 0.469362i
\(767\) −18.0000 + 31.1769i −0.649942 + 1.12573i
\(768\) 0 0
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) 27.0000 46.7654i 0.971123 1.68203i 0.278944 0.960307i \(-0.410016\pi\)
0.692179 0.721726i \(-0.256651\pi\)
\(774\) 0 0
\(775\) 5.00000 + 8.66025i 0.179605 + 0.311086i
\(776\) −1.00000 −0.0358979
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) 3.00000 + 5.19615i 0.107486 + 0.186171i
\(780\) 0 0
\(781\) −1.50000 + 2.59808i −0.0536742 + 0.0929665i
\(782\) 4.50000 + 7.79423i 0.160920 + 0.278721i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 0 0
\(786\) 0 0
\(787\) −11.5000 + 19.9186i −0.409931 + 0.710021i −0.994882 0.101048i \(-0.967780\pi\)
0.584951 + 0.811069i \(0.301114\pi\)
\(788\) −10.5000 + 18.1865i −0.374047 + 0.647868i
\(789\) 0 0
\(790\) 0 0
\(791\) 24.0000 20.7846i 0.853342 0.739016i
\(792\) 0 0
\(793\) −20.0000 34.6410i −0.710221 1.23014i
\(794\) 6.50000 11.2583i 0.230676 0.399543i
\(795\) 0