Properties

Label 2646.2.h.g.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
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 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.g.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +2.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -3.00000 q^{23} -4.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 + 6.92820i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{37} +7.00000 q^{38} +1.00000 q^{40} +(-6.00000 - 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} +2.00000 q^{52} +(2.00000 + 3.46410i) q^{53} -2.00000 q^{55} -8.00000 q^{58} +(2.00000 - 3.46410i) q^{59} +(-6.50000 - 11.2583i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +5.00000 q^{71} +(7.00000 + 12.1244i) q^{73} +6.00000 q^{74} +(3.50000 + 6.06218i) q^{76} +(5.50000 + 9.52628i) q^{79} +(0.500000 + 0.866025i) q^{80} +(6.00000 - 10.3923i) q^{82} +(6.00000 - 10.3923i) q^{83} +8.00000 q^{86} -2.00000 q^{88} +(7.00000 - 12.1244i) q^{89} +(1.50000 - 2.59808i) q^{92} +(4.00000 - 6.92820i) q^{94} +(-3.50000 + 6.06218i) q^{95} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 2 q^{5} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 2 q^{5} - 2 q^{8} - q^{10} + 4 q^{11} - 2 q^{13} - q^{16} + 7 q^{19} + q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} + 2 q^{26} - 8 q^{29} - 4 q^{31} + q^{32} + 6 q^{37} + 14 q^{38} + 2 q^{40} - 12 q^{41} + 8 q^{43} - 2 q^{44} - 3 q^{46} - 8 q^{47} - 4 q^{50} + 4 q^{52} + 4 q^{53} - 4 q^{55} - 16 q^{58} + 4 q^{59} - 13 q^{61} - 8 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 10 q^{71} + 14 q^{73} + 12 q^{74} + 7 q^{76} + 11 q^{79} + q^{80} + 12 q^{82} + 12 q^{83} + 16 q^{86} - 4 q^{88} + 14 q^{89} + 3 q^{92} + 8 q^{94} - 7 q^{95} + 2 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) 1.00000 + 1.73205i 0.213201 + 0.369274i
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 + 6.92820i −0.742781 + 1.28654i 0.208443 + 0.978035i \(0.433160\pi\)
−0.951224 + 0.308500i \(0.900173\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 7.00000 1.13555
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −6.00000 10.3923i −0.937043 1.62301i −0.770950 0.636895i \(-0.780218\pi\)
−0.166092 0.986110i \(-0.553115\pi\)
\(42\) 0 0
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 0 0
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) −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
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) −8.00000 −1.05045
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −6.50000 11.2583i −0.832240 1.44148i −0.896258 0.443533i \(-0.853725\pi\)
0.0640184 0.997949i \(-0.479608\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 6.00000 10.3923i 0.662589 1.14764i
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) −3.50000 + 6.06218i −0.359092 + 0.621966i
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 11.0000 1.09454 0.547270 0.836956i \(-0.315667\pi\)
0.547270 + 0.836956i \(0.315667\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 0 0
\(109\) −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i \(-0.228023\pi\)
−0.945769 + 0.324840i \(0.894690\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 0.866025i −0.0470360 0.0814688i 0.841549 0.540181i \(-0.181644\pi\)
−0.888585 + 0.458712i \(0.848311\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 6.50000 11.2583i 0.588482 1.01928i
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i \(-0.291323\pi\)
−0.991303 + 0.131597i \(0.957989\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.50000 + 4.33013i 0.209795 + 0.363376i
\(143\) −2.00000 3.46410i −0.167248 0.289683i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) −7.00000 + 12.1244i −0.579324 + 1.00342i
\(147\) 0 0
\(148\) 3.00000 + 5.19615i 0.246598 + 0.427121i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 3.46410i 0.160644 0.278243i
\(156\) 0 0
\(157\) −5.50000 + 9.52628i −0.438948 + 0.760280i −0.997609 0.0691164i \(-0.977982\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −5.50000 + 9.52628i −0.437557 + 0.757870i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 3.00000 5.19615i 0.234978 0.406994i −0.724288 0.689497i \(-0.757831\pi\)
0.959266 + 0.282503i \(0.0911648\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 1.00000 + 1.73205i 0.0773823 + 0.134030i 0.902120 0.431486i \(-0.142010\pi\)
−0.824737 + 0.565516i \(0.808677\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i \(-0.851372\pi\)
0.0566411 0.998395i \(-0.481961\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) 0 0
\(178\) 14.0000 1.04934
\(179\) −12.0000 20.7846i −0.896922 1.55351i −0.831408 0.555663i \(-0.812464\pi\)
−0.0655145 0.997852i \(-0.520869\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −7.00000 −0.507833
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) 5.50000 + 9.52628i 0.386979 + 0.670267i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 7.00000 12.1244i 0.484200 0.838659i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 3.46410i 0.135457 0.234619i
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 0 0
\(222\) 0 0
\(223\) 1.00000 1.73205i 0.0669650 0.115987i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440884i \(0.145335\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) −17.0000 −1.12833 −0.564165 0.825662i \(-0.690802\pi\)
−0.564165 + 0.825662i \(0.690802\pi\)
\(228\) 0 0
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) 1.50000 + 2.59808i 0.0989071 + 0.171312i
\(231\) 0 0
\(232\) 4.00000 6.92820i 0.262613 0.454859i
\(233\) 0.500000 0.866025i 0.0327561 0.0567352i −0.849183 0.528099i \(-0.822905\pi\)
0.881939 + 0.471364i \(0.156238\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) −14.0000 −0.890799
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 0 0
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −7.00000 −0.441836 −0.220918 0.975292i \(-0.570905\pi\)
−0.220918 + 0.975292i \(0.570905\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −7.50000 12.9904i −0.463352 0.802548i
\(263\) −19.0000 −1.17159 −0.585795 0.810459i \(-0.699218\pi\)
−0.585795 + 0.810459i \(0.699218\pi\)
\(264\) 0 0
\(265\) −2.00000 3.46410i −0.122859 0.212798i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 3.50000 + 6.06218i 0.213399 + 0.369618i 0.952776 0.303674i \(-0.0982133\pi\)
−0.739377 + 0.673291i \(0.764880\pi\)
\(270\) 0 0
\(271\) −7.00000 + 12.1244i −0.425220 + 0.736502i −0.996441 0.0842940i \(-0.973137\pi\)
0.571221 + 0.820796i \(0.306470\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.00000 + 1.73205i 0.0604122 + 0.104637i
\(275\) −8.00000 −0.482418
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 4.50000 7.79423i 0.269892 0.467467i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) −12.5000 + 21.6506i −0.743048 + 1.28700i 0.208053 + 0.978117i \(0.433287\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) −2.50000 + 4.33013i −0.148348 + 0.256946i
\(285\) 0 0
\(286\) 2.00000 3.46410i 0.118262 0.204837i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 8.00000 0.469776
\(291\) 0 0
\(292\) −14.0000 −0.819288
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) −2.00000 + 3.46410i −0.116445 + 0.201688i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 9.50000 + 16.4545i 0.546664 + 0.946849i
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) 6.50000 + 11.2583i 0.372189 + 0.644650i
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 0.227185
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) −8.00000 + 13.8564i −0.447914 + 0.775810i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 4.00000 + 6.92820i 0.221880 + 0.384308i
\(326\) 6.00000 0.332309
\(327\) 0 0
\(328\) 6.00000 + 10.3923i 0.331295 + 0.573819i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) 0 0
\(334\) −1.00000 + 1.73205i −0.0547176 + 0.0947736i
\(335\) −1.00000 + 1.73205i −0.0546358 + 0.0946320i
\(336\) 0 0
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 0 0
\(341\) −4.00000 + 6.92820i −0.216612 + 0.375183i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) 11.0000 19.0526i 0.591364 1.02427i
\(347\) 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
\(349\) 15.0000 25.9808i 0.802932 1.39072i −0.114747 0.993395i \(-0.536606\pi\)
0.917679 0.397324i \(-0.130061\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) −5.00000 −0.265372
\(356\) 7.00000 + 12.1244i 0.370999 + 0.642590i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 14.5000 25.1147i 0.765281 1.32551i −0.174817 0.984601i \(-0.555933\pi\)
0.940098 0.340904i \(-0.110733\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 3.50000 + 6.06218i 0.183956 + 0.318621i
\(363\) 0 0
\(364\) 0 0
\(365\) −7.00000 12.1244i −0.366397 0.634618i
\(366\) 0 0
\(367\) −32.0000 −1.67039 −0.835193 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 0 0
\(370\) −6.00000 −0.311925
\(371\) 0 0
\(372\) 0 0
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) 16.0000 0.824042
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −3.50000 6.06218i −0.179546 0.310983i
\(381\) 0 0
\(382\) −1.50000 + 2.59808i −0.0767467 + 0.132929i
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) −5.50000 9.52628i −0.276735 0.479319i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −7.00000 + 12.1244i −0.350878 + 0.607739i
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) −5.50000 + 9.52628i −0.273635 + 0.473950i
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 0 0
\(409\) 12.0000 20.7846i 0.593362 1.02773i −0.400414 0.916334i \(-0.631134\pi\)
0.993776 0.111398i \(-0.0355330\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 0 0
\(412\) −4.00000 + 6.92820i −0.197066 + 0.341328i
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) −2.00000 −0.0980581
\(417\) 0 0
\(418\) 14.0000 0.684762
\(419\) −2.50000 4.33013i −0.122133 0.211541i 0.798476 0.602027i \(-0.205640\pi\)
−0.920609 + 0.390487i \(0.872307\pi\)
\(420\) 0 0
\(421\) 18.0000 31.1769i 0.877266 1.51947i 0.0229375 0.999737i \(-0.492698\pi\)
0.854329 0.519733i \(-0.173969\pi\)
\(422\) −11.0000 + 19.0526i −0.535472 + 0.927464i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 + 6.92820i 0.193347 + 0.334887i
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 16.0000 + 27.7128i 0.770693 + 1.33488i 0.937184 + 0.348836i \(0.113423\pi\)
−0.166491 + 0.986043i \(0.553244\pi\)
\(432\) 0 0
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) −10.5000 + 18.1865i −0.502283 + 0.869980i
\(438\) 0 0
\(439\) 18.0000 + 31.1769i 0.859093 + 1.48799i 0.872795 + 0.488087i \(0.162305\pi\)
−0.0137020 + 0.999906i \(0.504362\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) 0 0
\(445\) −7.00000 + 12.1244i −0.331832 + 0.574750i
\(446\) 2.00000 0.0947027
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) −12.0000 20.7846i −0.565058 0.978709i
\(452\) 1.00000 0.0470360
\(453\) 0 0
\(454\) −8.50000 14.7224i −0.398925 0.690958i
\(455\) 0 0
\(456\) 0 0
\(457\) −8.50000 14.7224i −0.397613 0.688686i 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) −6.50000 11.2583i −0.303725 0.526067i
\(459\) 0 0
\(460\) −1.50000 + 2.59808i −0.0699379 + 0.121136i
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) 0.500000 + 0.866025i 0.0232370 + 0.0402476i 0.877410 0.479741i \(-0.159269\pi\)
−0.854173 + 0.519989i \(0.825936\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 1.00000 0.0463241
\(467\) −14.0000 + 24.2487i −0.647843 + 1.12210i 0.335794 + 0.941935i \(0.390995\pi\)
−0.983637 + 0.180161i \(0.942338\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −4.00000 + 6.92820i −0.184506 + 0.319574i
\(471\) 0 0
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) −14.0000 + 24.2487i −0.642364 + 1.11261i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 5.00000 + 8.66025i 0.227744 + 0.394464i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) −12.5000 21.6506i −0.566429 0.981084i −0.996915 0.0784867i \(-0.974991\pi\)
0.430486 0.902597i \(-0.358342\pi\)
\(488\) 6.50000 + 11.2583i 0.294241 + 0.509641i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.00000 + 5.19615i 0.135388 + 0.234499i 0.925746 0.378147i \(-0.123439\pi\)
−0.790358 + 0.612646i \(0.790105\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −7.00000 12.1244i −0.314945 0.545501i
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 24.0000 1.07439 0.537194 0.843459i \(-0.319484\pi\)
0.537194 + 0.843459i \(0.319484\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 0 0
\(502\) −3.50000 6.06218i −0.156213 0.270568i
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) 0 0
\(505\) −11.0000 −0.489494
\(506\) −3.00000 5.19615i −0.133366 0.230997i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −4.00000 6.92820i −0.176432 0.305590i
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) −8.00000 13.8564i −0.351840 0.609404i
\(518\) 0 0
\(519\) 0 0
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) 7.00000 + 12.1244i 0.306676 + 0.531178i 0.977633 0.210318i \(-0.0674500\pi\)
−0.670957 + 0.741496i \(0.734117\pi\)
\(522\) 0 0
\(523\) −17.5000 + 30.3109i −0.765222 + 1.32540i 0.174908 + 0.984585i \(0.444037\pi\)
−0.940129 + 0.340818i \(0.889296\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 0 0
\(526\) −9.50000 16.4545i −0.414220 0.717450i
\(527\) 0 0
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 2.00000 3.46410i 0.0868744 0.150471i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 + 20.7846i −0.519778 + 0.900281i
\(534\) 0 0
\(535\) −4.00000 + 6.92820i −0.172935 + 0.299532i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) −3.50000 + 6.06218i −0.150896 + 0.261359i
\(539\) 0 0
\(540\) 0 0
\(541\) 10.0000 17.3205i 0.429934 0.744667i −0.566933 0.823764i \(-0.691870\pi\)
0.996867 + 0.0790969i \(0.0252036\pi\)
\(542\) −14.0000 −0.601351
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 + 3.46410i 0.0856706 + 0.148386i
\(546\) 0 0
\(547\) 4.00000 6.92820i 0.171028 0.296229i −0.767752 0.640747i \(-0.778625\pi\)
0.938779 + 0.344519i \(0.111958\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) −4.00000 6.92820i −0.170561 0.295420i
\(551\) 28.0000 + 48.4974i 1.19284 + 2.06606i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 1.73205i −0.0424859 0.0735878i
\(555\) 0 0
\(556\) 9.00000 0.381685
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −15.0000 −0.632737
\(563\) 5.50000 9.52628i 0.231797 0.401485i −0.726540 0.687124i \(-0.758873\pi\)
0.958337 + 0.285640i \(0.0922060\pi\)
\(564\) 0 0
\(565\) 0.500000 + 0.866025i 0.0210352 + 0.0364340i
\(566\) −25.0000 −1.05083
\(567\) 0 0
\(568\) −5.00000 −0.209795
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) 4.00000 0.167248
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −14.0000 24.2487i −0.582828 1.00949i −0.995142 0.0984456i \(-0.968613\pi\)
0.412315 0.911041i \(-0.364720\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) 4.00000 + 6.92820i 0.166091 + 0.287678i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) −11.5000 + 19.9186i −0.474656 + 0.822128i −0.999579 0.0290218i \(-0.990761\pi\)
0.524923 + 0.851150i \(0.324094\pi\)
\(588\) 0 0
\(589\) 14.0000 + 24.2487i 0.576860 + 0.999151i
\(590\) −4.00000 −0.164677
\(591\) 0 0
\(592\) −6.00000 −0.246598
\(593\) 21.0000 36.3731i 0.862367 1.49366i −0.00727173 0.999974i \(-0.502315\pi\)
0.869638 0.493689i \(-0.164352\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.00000 8.66025i 0.204808 0.354738i
\(597\) 0 0
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i \(0.344580\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) −6.00000 −0.243532 −0.121766 0.992559i \(-0.538856\pi\)
−0.121766 + 0.992559i \(0.538856\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 0 0
\(610\) −6.50000 + 11.2583i −0.263177 + 0.455836i
\(611\) −8.00000 + 13.8564i −0.323645 + 0.560570i
\(612\) 0 0
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 0 0
\(617\) −11.0000 19.0526i −0.442843 0.767027i 0.555056 0.831813i \(-0.312697\pi\)
−0.997899 + 0.0647859i \(0.979364\pi\)
\(618\) 0 0
\(619\) −11.0000 −0.442127 −0.221064 0.975259i \(-0.570953\pi\)
−0.221064 + 0.975259i \(0.570953\pi\)
\(620\) 2.00000 + 3.46410i 0.0803219 + 0.139122i
\(621\) 0 0
\(622\) −10.0000 −0.400963
\(623\) 0 0
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) 0 0
\(628\) −5.50000 9.52628i −0.219474 0.380140i
\(629\) 0 0
\(630\) 0 0
\(631\) 9.00000 0.358284 0.179142 0.983823i \(-0.442668\pi\)
0.179142 + 0.983823i \(0.442668\pi\)
\(632\) −5.50000 9.52628i −0.218778 0.378935i
\(633\) 0 0
\(634\) −12.0000 + 20.7846i −0.476581 + 0.825462i
\(635\) 19.0000 0.753992
\(636\) 0 0
\(637\) 0 0
\(638\) −16.0000 −0.633446
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −47.0000 −1.85639 −0.928194 0.372096i \(-0.878639\pi\)
−0.928194 + 0.372096i \(0.878639\pi\)
\(642\) 0 0
\(643\) 6.00000 + 10.3923i 0.236617 + 0.409832i 0.959741 0.280885i \(-0.0906280\pi\)
−0.723124 + 0.690718i \(0.757295\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21.0000 36.3731i −0.825595 1.42997i −0.901464 0.432855i \(-0.857506\pi\)
0.0758684 0.997118i \(-0.475827\pi\)
\(648\) 0 0
\(649\) 4.00000 6.92820i 0.157014 0.271956i
\(650\) −4.00000 + 6.92820i −0.156893 + 0.271746i
\(651\) 0 0
\(652\) 3.00000 + 5.19615i 0.117489 + 0.203497i
\(653\) 32.0000 1.25226 0.626128 0.779720i \(-0.284639\pi\)
0.626128 + 0.779720i \(0.284639\pi\)
\(654\) 0 0
\(655\) 15.0000 0.586098
\(656\) −6.00000 + 10.3923i −0.234261 + 0.405751i
\(657\) 0 0
\(658\) 0 0
\(659\) 10.0000 17.3205i 0.389545 0.674711i −0.602844 0.797859i \(-0.705966\pi\)
0.992388 + 0.123148i \(0.0392990\pi\)
\(660\) 0 0
\(661\) 15.5000 26.8468i 0.602880 1.04422i −0.389503 0.921025i \(-0.627353\pi\)
0.992383 0.123194i \(-0.0393136\pi\)
\(662\) −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
\(667\) 12.0000 20.7846i 0.464642 0.804783i
\(668\) −2.00000 −0.0773823
\(669\) 0 0
\(670\) −2.00000 −0.0772667
\(671\) −13.0000 22.5167i −0.501859 0.869246i
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −8.00000 −0.306336
\(683\) −5.00000 8.66025i −0.191320 0.331375i 0.754368 0.656452i \(-0.227943\pi\)
−0.945688 + 0.325076i \(0.894610\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) 4.00000 6.92820i 0.152388 0.263944i
\(690\) 0 0
\(691\) 14.5000 + 25.1147i 0.551606 + 0.955410i 0.998159 + 0.0606524i \(0.0193181\pi\)
−0.446553 + 0.894757i \(0.647349\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 4.50000 + 7.79423i 0.170695 + 0.295652i
\(696\) 0 0
\(697\) 0 0
\(698\) 30.0000 1.13552
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −21.0000 36.3731i −0.792030 1.37184i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −12.0000 20.7846i −0.451626 0.782239i
\(707\) 0 0
\(708\) 0 0
\(709\) 16.0000 + 27.7128i 0.600893 + 1.04078i 0.992686 + 0.120723i \(0.0385214\pi\)
−0.391794 + 0.920053i \(0.628145\pi\)
\(710\) −2.50000 4.33013i −0.0938233 0.162507i
\(711\) 0 0
\(712\) −7.00000 + 12.1244i −0.262336 + 0.454379i
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) 2.00000 + 3.46410i 0.0747958 + 0.129550i
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 29.0000 1.08227
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 0 0
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) 16.0000 27.7128i 0.594225 1.02923i
\(726\) 0 0
\(727\) −13.0000 + 22.5167i −0.482143 + 0.835097i −0.999790 0.0204978i \(-0.993475\pi\)
0.517647 + 0.855595i \(0.326808\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) 0 0
\(732\) 0 0
\(733\) 1.00000 0.0369358 0.0184679 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) −16.0000 27.7128i −0.590571 1.02290i
\(735\) 0 0
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) 2.00000 3.46410i 0.0736709 0.127602i
\(738\) 0 0
\(739\) 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i \(0.0796718\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(740\) −3.00000 5.19615i −0.110282 0.191014i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 + 41.5692i 0.880475 + 1.52503i 0.850814 + 0.525467i \(0.176109\pi\)
0.0296605 + 0.999560i \(0.490557\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) −16.0000 27.7128i −0.585802 1.01464i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −39.0000 −1.42313 −0.711565 0.702620i \(-0.752013\pi\)
−0.711565 + 0.702620i \(0.752013\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) 0 0
\(754\) 8.00000 + 13.8564i 0.291343 + 0.504621i
\(755\) −19.0000 −0.691481
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −6.00000 10.3923i −0.217930 0.377466i
\(759\) 0 0
\(760\) 3.50000 6.06218i 0.126958 0.219898i
\(761\) 20.0000 0.724999 0.362500 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.00000 −0.108536
\(765\) 0 0
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i \(-0.0433959\pi\)
−0.613062 + 0.790034i \(0.710063\pi\)
\(774\) 0 0
\(775\) 8.00000 13.8564i 0.287368 0.497737i
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) 15.0000 + 25.9808i 0.537776 + 0.931455i
\(779\) −84.0000 −3.00961
\(780\) 0 0
\(781\) 10.0000 0.357828
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.50000 9.52628i 0.196303 0.340007i
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) −6.00000 + 10.3923i −0.213741 + 0.370211i
\(789\) 0 0
\(790\) 5.50000 9.52628i 0.195681 0.338930i
\(791\) 0 0
\(792\) 0 0
\(793\) −13.0000 + 22.5167i −0.461644 + 0.799590i
\(794\) −14.0000 −0.496841
\(795\) 0 0