Properties

Label 2646.2.h.t.667.3
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.t.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.03528 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.03528 q^{5} -1.00000 q^{8} +(0.517638 + 0.896575i) q^{10} +0.267949 q^{11} +(-0.896575 - 1.55291i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.41542 - 5.91567i) q^{17} +(-2.19067 + 3.79435i) q^{19} +(-0.517638 + 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} -5.46410 q^{23} -3.92820 q^{25} +(0.896575 - 1.55291i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(-3.34607 + 5.79555i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.41542 - 5.91567i) q^{34} +(-3.73205 + 6.46410i) q^{37} -4.38134 q^{38} -1.03528 q^{40} +(-4.31199 - 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} +(-0.133975 + 0.232051i) q^{44} +(-2.73205 - 4.73205i) q^{46} +(0.378937 + 0.656339i) q^{47} +(-1.96410 - 3.40192i) q^{50} +1.79315 q^{52} +(5.46410 + 9.46410i) q^{53} +0.277401 q^{55} -4.00000 q^{58} +(-0.637756 + 1.10463i) q^{59} +(6.31319 + 10.9348i) q^{61} -6.69213 q^{62} +1.00000 q^{64} +(-0.928203 - 1.60770i) q^{65} +(-6.23205 + 10.7942i) q^{67} +6.83083 q^{68} -9.46410 q^{71} +(-2.70831 - 4.69093i) q^{73} -7.46410 q^{74} +(-2.19067 - 3.79435i) q^{76} +(-4.46410 - 7.73205i) q^{79} +(-0.517638 - 0.896575i) q^{80} +(4.31199 - 7.46859i) q^{82} +(3.29530 - 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} -0.267949 q^{86} -0.267949 q^{88} +(3.53553 - 6.12372i) q^{89} +(2.73205 - 4.73205i) q^{92} +(-0.378937 + 0.656339i) q^{94} +(-2.26795 + 3.92820i) q^{95} +(9.07227 - 15.7136i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + O(q^{10}) \) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} - 16 q^{23} + 24 q^{25} - 16 q^{29} + 4 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} - 32 q^{58} + 8 q^{64} + 48 q^{65} - 36 q^{67} - 48 q^{71} - 32 q^{74} - 8 q^{79} - 56 q^{85} - 16 q^{86} - 16 q^{88} + 8 q^{92} - 32 q^{95} + O(q^{100}) \)

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
\(5\) 1.03528 0.462990 0.231495 0.972836i \(-0.425638\pi\)
0.231495 + 0.972836i \(0.425638\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.517638 + 0.896575i 0.163692 + 0.283522i
\(11\) 0.267949 0.0807897 0.0403949 0.999184i \(-0.487138\pi\)
0.0403949 + 0.999184i \(0.487138\pi\)
\(12\) 0 0
\(13\) −0.896575 1.55291i −0.248665 0.430701i 0.714490 0.699645i \(-0.246659\pi\)
−0.963156 + 0.268944i \(0.913325\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.41542 5.91567i −0.828360 1.43476i −0.899324 0.437283i \(-0.855941\pi\)
0.0709642 0.997479i \(-0.477392\pi\)
\(18\) 0 0
\(19\) −2.19067 + 3.79435i −0.502574 + 0.870484i 0.497421 + 0.867509i \(0.334280\pi\)
−0.999996 + 0.00297513i \(0.999053\pi\)
\(20\) −0.517638 + 0.896575i −0.115747 + 0.200480i
\(21\) 0 0
\(22\) 0.133975 + 0.232051i 0.0285635 + 0.0494734i
\(23\) −5.46410 −1.13934 −0.569672 0.821872i \(-0.692930\pi\)
−0.569672 + 0.821872i \(0.692930\pi\)
\(24\) 0 0
\(25\) −3.92820 −0.785641
\(26\) 0.896575 1.55291i 0.175833 0.304552i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) −3.34607 + 5.79555i −0.600971 + 1.04091i 0.391703 + 0.920092i \(0.371886\pi\)
−0.992674 + 0.120821i \(0.961447\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.41542 5.91567i 0.585739 1.01453i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.73205 + 6.46410i −0.613545 + 1.06269i 0.377092 + 0.926176i \(0.376924\pi\)
−0.990638 + 0.136516i \(0.956409\pi\)
\(38\) −4.38134 −0.710747
\(39\) 0 0
\(40\) −1.03528 −0.163692
\(41\) −4.31199 7.46859i −0.673420 1.16640i −0.976928 0.213569i \(-0.931491\pi\)
0.303508 0.952829i \(-0.401842\pi\)
\(42\) 0 0
\(43\) −0.133975 + 0.232051i −0.0204309 + 0.0353874i −0.876060 0.482202i \(-0.839837\pi\)
0.855629 + 0.517589i \(0.173170\pi\)
\(44\) −0.133975 + 0.232051i −0.0201974 + 0.0349830i
\(45\) 0 0
\(46\) −2.73205 4.73205i −0.402819 0.697703i
\(47\) 0.378937 + 0.656339i 0.0552737 + 0.0957369i 0.892338 0.451367i \(-0.149064\pi\)
−0.837065 + 0.547104i \(0.815730\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.96410 3.40192i −0.277766 0.481105i
\(51\) 0 0
\(52\) 1.79315 0.248665
\(53\) 5.46410 + 9.46410i 0.750552 + 1.29999i 0.947555 + 0.319592i \(0.103546\pi\)
−0.197003 + 0.980403i \(0.563121\pi\)
\(54\) 0 0
\(55\) 0.277401 0.0374048
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) −0.637756 + 1.10463i −0.0830288 + 0.143810i −0.904550 0.426369i \(-0.859793\pi\)
0.821521 + 0.570179i \(0.193126\pi\)
\(60\) 0 0
\(61\) 6.31319 + 10.9348i 0.808322 + 1.40005i 0.914026 + 0.405656i \(0.132957\pi\)
−0.105704 + 0.994398i \(0.533710\pi\)
\(62\) −6.69213 −0.849901
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.928203 1.60770i −0.115129 0.199410i
\(66\) 0 0
\(67\) −6.23205 + 10.7942i −0.761366 + 1.31872i 0.180780 + 0.983524i \(0.442138\pi\)
−0.942146 + 0.335201i \(0.891196\pi\)
\(68\) 6.83083 0.828360
\(69\) 0 0
\(70\) 0 0
\(71\) −9.46410 −1.12318 −0.561591 0.827415i \(-0.689811\pi\)
−0.561591 + 0.827415i \(0.689811\pi\)
\(72\) 0 0
\(73\) −2.70831 4.69093i −0.316984 0.549032i 0.662874 0.748731i \(-0.269337\pi\)
−0.979857 + 0.199700i \(0.936003\pi\)
\(74\) −7.46410 −0.867684
\(75\) 0 0
\(76\) −2.19067 3.79435i −0.251287 0.435242i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.46410 7.73205i −0.502251 0.869924i −0.999997 0.00260080i \(-0.999172\pi\)
0.497746 0.867323i \(-0.334161\pi\)
\(80\) −0.517638 0.896575i −0.0578737 0.100240i
\(81\) 0 0
\(82\) 4.31199 7.46859i 0.476180 0.824768i
\(83\) 3.29530 5.70762i 0.361706 0.626493i −0.626536 0.779393i \(-0.715528\pi\)
0.988242 + 0.152900i \(0.0488611\pi\)
\(84\) 0 0
\(85\) −3.53590 6.12436i −0.383522 0.664280i
\(86\) −0.267949 −0.0288937
\(87\) 0 0
\(88\) −0.267949 −0.0285635
\(89\) 3.53553 6.12372i 0.374766 0.649113i −0.615526 0.788116i \(-0.711056\pi\)
0.990292 + 0.139003i \(0.0443898\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.73205 4.73205i 0.284836 0.493350i
\(93\) 0 0
\(94\) −0.378937 + 0.656339i −0.0390844 + 0.0676962i
\(95\) −2.26795 + 3.92820i −0.232687 + 0.403025i
\(96\) 0 0
\(97\) 9.07227 15.7136i 0.921149 1.59548i 0.123510 0.992343i \(-0.460585\pi\)
0.797640 0.603134i \(-0.206082\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.96410 3.40192i 0.196410 0.340192i
\(101\) 4.89898 0.487467 0.243733 0.969842i \(-0.421628\pi\)
0.243733 + 0.969842i \(0.421628\pi\)
\(102\) 0 0
\(103\) 12.3490 1.21678 0.608391 0.793638i \(-0.291815\pi\)
0.608391 + 0.793638i \(0.291815\pi\)
\(104\) 0.896575 + 1.55291i 0.0879165 + 0.152276i
\(105\) 0 0
\(106\) −5.46410 + 9.46410i −0.530720 + 0.919235i
\(107\) −8.69615 + 15.0622i −0.840689 + 1.45612i 0.0486244 + 0.998817i \(0.484516\pi\)
−0.889313 + 0.457299i \(0.848817\pi\)
\(108\) 0 0
\(109\) −2.46410 4.26795i −0.236018 0.408795i 0.723550 0.690272i \(-0.242509\pi\)
−0.959568 + 0.281477i \(0.909176\pi\)
\(110\) 0.138701 + 0.240237i 0.0132246 + 0.0229057i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.46410 6.00000i −0.325875 0.564433i 0.655814 0.754923i \(-0.272326\pi\)
−0.981689 + 0.190490i \(0.938992\pi\)
\(114\) 0 0
\(115\) −5.65685 −0.527504
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) −1.27551 −0.117420
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9282 −0.993473
\(122\) −6.31319 + 10.9348i −0.571570 + 0.989988i
\(123\) 0 0
\(124\) −3.34607 5.79555i −0.300486 0.520456i
\(125\) −9.24316 −0.826733
\(126\) 0 0
\(127\) 13.4641 1.19475 0.597373 0.801964i \(-0.296211\pi\)
0.597373 + 0.801964i \(0.296211\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0.928203 1.60770i 0.0814088 0.141004i
\(131\) −10.9348 −0.955375 −0.477688 0.878530i \(-0.658525\pi\)
−0.477688 + 0.878530i \(0.658525\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.4641 −1.07673
\(135\) 0 0
\(136\) 3.41542 + 5.91567i 0.292869 + 0.507265i
\(137\) −8.66025 −0.739895 −0.369948 0.929053i \(-0.620624\pi\)
−0.369948 + 0.929053i \(0.620624\pi\)
\(138\) 0 0
\(139\) −0.397520 0.688524i −0.0337172 0.0583999i 0.848674 0.528916i \(-0.177401\pi\)
−0.882392 + 0.470516i \(0.844068\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.73205 8.19615i −0.397105 0.687806i
\(143\) −0.240237 0.416102i −0.0200896 0.0347962i
\(144\) 0 0
\(145\) −2.07055 + 3.58630i −0.171950 + 0.297826i
\(146\) 2.70831 4.69093i 0.224141 0.388224i
\(147\) 0 0
\(148\) −3.73205 6.46410i −0.306773 0.531346i
\(149\) −22.9282 −1.87835 −0.939176 0.343437i \(-0.888409\pi\)
−0.939176 + 0.343437i \(0.888409\pi\)
\(150\) 0 0
\(151\) 18.3923 1.49674 0.748372 0.663279i \(-0.230836\pi\)
0.748372 + 0.663279i \(0.230836\pi\)
\(152\) 2.19067 3.79435i 0.177687 0.307763i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.46410 + 6.00000i −0.278243 + 0.481932i
\(156\) 0 0
\(157\) −4.76028 + 8.24504i −0.379912 + 0.658026i −0.991049 0.133498i \(-0.957379\pi\)
0.611137 + 0.791524i \(0.290712\pi\)
\(158\) 4.46410 7.73205i 0.355145 0.615129i
\(159\) 0 0
\(160\) 0.517638 0.896575i 0.0409229 0.0708805i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.66025 11.5359i 0.521671 0.903561i −0.478011 0.878354i \(-0.658642\pi\)
0.999682 0.0252074i \(-0.00802461\pi\)
\(164\) 8.62398 0.673420
\(165\) 0 0
\(166\) 6.59059 0.511529
\(167\) 0.757875 + 1.31268i 0.0586461 + 0.101578i 0.893858 0.448350i \(-0.147988\pi\)
−0.835212 + 0.549928i \(0.814655\pi\)
\(168\) 0 0
\(169\) 4.89230 8.47372i 0.376331 0.651825i
\(170\) 3.53590 6.12436i 0.271191 0.469717i
\(171\) 0 0
\(172\) −0.133975 0.232051i −0.0102155 0.0176937i
\(173\) 3.34607 + 5.79555i 0.254397 + 0.440628i 0.964731 0.263236i \(-0.0847898\pi\)
−0.710335 + 0.703864i \(0.751456\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.133975 0.232051i −0.0100987 0.0174915i
\(177\) 0 0
\(178\) 7.07107 0.529999
\(179\) 2.53590 + 4.39230i 0.189542 + 0.328296i 0.945098 0.326788i \(-0.105966\pi\)
−0.755556 + 0.655084i \(0.772633\pi\)
\(180\) 0 0
\(181\) −16.9706 −1.26141 −0.630706 0.776022i \(-0.717235\pi\)
−0.630706 + 0.776022i \(0.717235\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 5.46410 0.402819
\(185\) −3.86370 + 6.69213i −0.284065 + 0.492015i
\(186\) 0 0
\(187\) −0.915158 1.58510i −0.0669230 0.115914i
\(188\) −0.757875 −0.0552737
\(189\) 0 0
\(190\) −4.53590 −0.329069
\(191\) 7.46410 + 12.9282i 0.540083 + 0.935452i 0.998899 + 0.0469202i \(0.0149407\pi\)
−0.458815 + 0.888532i \(0.651726\pi\)
\(192\) 0 0
\(193\) −7.52628 + 13.0359i −0.541753 + 0.938344i 0.457050 + 0.889441i \(0.348906\pi\)
−0.998804 + 0.0489035i \(0.984427\pi\)
\(194\) 18.1445 1.30270
\(195\) 0 0
\(196\) 0 0
\(197\) 16.9282 1.20608 0.603042 0.797709i \(-0.293955\pi\)
0.603042 + 0.797709i \(0.293955\pi\)
\(198\) 0 0
\(199\) −13.1440 22.7661i −0.931755 1.61385i −0.780320 0.625380i \(-0.784944\pi\)
−0.151435 0.988467i \(-0.548389\pi\)
\(200\) 3.92820 0.277766
\(201\) 0 0
\(202\) 2.44949 + 4.24264i 0.172345 + 0.298511i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.46410 7.73205i −0.311786 0.540030i
\(206\) 6.17449 + 10.6945i 0.430197 + 0.745124i
\(207\) 0 0
\(208\) −0.896575 + 1.55291i −0.0621663 + 0.107675i
\(209\) −0.586988 + 1.01669i −0.0406028 + 0.0703262i
\(210\) 0 0
\(211\) −9.46410 16.3923i −0.651536 1.12849i −0.982750 0.184937i \(-0.940792\pi\)
0.331215 0.943555i \(-0.392542\pi\)
\(212\) −10.9282 −0.750552
\(213\) 0 0
\(214\) −17.3923 −1.18891
\(215\) −0.138701 + 0.240237i −0.00945931 + 0.0163840i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.46410 4.26795i 0.166890 0.289062i
\(219\) 0 0
\(220\) −0.138701 + 0.240237i −0.00935120 + 0.0161968i
\(221\) −6.12436 + 10.6077i −0.411969 + 0.713551i
\(222\) 0 0
\(223\) 3.58630 6.21166i 0.240157 0.415963i −0.720602 0.693349i \(-0.756135\pi\)
0.960759 + 0.277385i \(0.0894679\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.46410 6.00000i 0.230429 0.399114i
\(227\) 27.6651 1.83620 0.918098 0.396352i \(-0.129724\pi\)
0.918098 + 0.396352i \(0.129724\pi\)
\(228\) 0 0
\(229\) 0.480473 0.0317506 0.0158753 0.999874i \(-0.494947\pi\)
0.0158753 + 0.999874i \(0.494947\pi\)
\(230\) −2.82843 4.89898i −0.186501 0.323029i
\(231\) 0 0
\(232\) 2.00000 3.46410i 0.131306 0.227429i
\(233\) 0.0621778 0.107695i 0.00407340 0.00705534i −0.863982 0.503524i \(-0.832037\pi\)
0.868055 + 0.496468i \(0.165370\pi\)
\(234\) 0 0
\(235\) 0.392305 + 0.679492i 0.0255911 + 0.0443252i
\(236\) −0.637756 1.10463i −0.0415144 0.0719051i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.464102 + 0.803848i 0.0300202 + 0.0519966i 0.880645 0.473776i \(-0.157109\pi\)
−0.850625 + 0.525773i \(0.823776\pi\)
\(240\) 0 0
\(241\) 6.27603 0.404275 0.202137 0.979357i \(-0.435211\pi\)
0.202137 + 0.979357i \(0.435211\pi\)
\(242\) −5.46410 9.46410i −0.351246 0.608375i
\(243\) 0 0
\(244\) −12.6264 −0.808322
\(245\) 0 0
\(246\) 0 0
\(247\) 7.85641 0.499891
\(248\) 3.34607 5.79555i 0.212475 0.368018i
\(249\) 0 0
\(250\) −4.62158 8.00481i −0.292294 0.506269i
\(251\) −0.795040 −0.0501824 −0.0250912 0.999685i \(-0.507988\pi\)
−0.0250912 + 0.999685i \(0.507988\pi\)
\(252\) 0 0
\(253\) −1.46410 −0.0920473
\(254\) 6.73205 + 11.6603i 0.422406 + 0.731629i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −10.0382 −0.626165 −0.313083 0.949726i \(-0.601362\pi\)
−0.313083 + 0.949726i \(0.601362\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.85641 0.115129
\(261\) 0 0
\(262\) −5.46739 9.46979i −0.337776 0.585046i
\(263\) 8.53590 0.526346 0.263173 0.964749i \(-0.415231\pi\)
0.263173 + 0.964749i \(0.415231\pi\)
\(264\) 0 0
\(265\) 5.65685 + 9.79796i 0.347498 + 0.601884i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.23205 10.7942i −0.380683 0.659362i
\(269\) −2.82843 4.89898i −0.172452 0.298696i 0.766824 0.641857i \(-0.221836\pi\)
−0.939277 + 0.343161i \(0.888502\pi\)
\(270\) 0 0
\(271\) −6.55343 + 11.3509i −0.398093 + 0.689516i −0.993491 0.113914i \(-0.963661\pi\)
0.595398 + 0.803431i \(0.296994\pi\)
\(272\) −3.41542 + 5.91567i −0.207090 + 0.358690i
\(273\) 0 0
\(274\) −4.33013 7.50000i −0.261593 0.453092i
\(275\) −1.05256 −0.0634717
\(276\) 0 0
\(277\) 31.4641 1.89049 0.945247 0.326355i \(-0.105820\pi\)
0.945247 + 0.326355i \(0.105820\pi\)
\(278\) 0.397520 0.688524i 0.0238417 0.0412949i
\(279\) 0 0
\(280\) 0 0
\(281\) 8.92820 15.4641i 0.532612 0.922511i −0.466663 0.884435i \(-0.654544\pi\)
0.999275 0.0380757i \(-0.0121228\pi\)
\(282\) 0 0
\(283\) 7.53794 13.0561i 0.448084 0.776104i −0.550177 0.835048i \(-0.685440\pi\)
0.998261 + 0.0589437i \(0.0187732\pi\)
\(284\) 4.73205 8.19615i 0.280796 0.486352i
\(285\) 0 0
\(286\) 0.240237 0.416102i 0.0142055 0.0246046i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.8301 + 25.6865i −0.872360 + 1.51097i
\(290\) −4.14110 −0.243174
\(291\) 0 0
\(292\) 5.41662 0.316984
\(293\) −4.62158 8.00481i −0.269995 0.467646i 0.698865 0.715254i \(-0.253689\pi\)
−0.968860 + 0.247608i \(0.920356\pi\)
\(294\) 0 0
\(295\) −0.660254 + 1.14359i −0.0384415 + 0.0665826i
\(296\) 3.73205 6.46410i 0.216921 0.375718i
\(297\) 0 0
\(298\) −11.4641 19.8564i −0.664098 1.15025i
\(299\) 4.89898 + 8.48528i 0.283315 + 0.490716i
\(300\) 0 0
\(301\) 0 0
\(302\) 9.19615 + 15.9282i 0.529179 + 0.916565i
\(303\) 0 0
\(304\) 4.38134 0.251287
\(305\) 6.53590 + 11.3205i 0.374244 + 0.648210i
\(306\) 0 0
\(307\) 1.17398 0.0670024 0.0335012 0.999439i \(-0.489334\pi\)
0.0335012 + 0.999439i \(0.489334\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6.92820 −0.393496
\(311\) −3.72500 + 6.45189i −0.211226 + 0.365853i −0.952098 0.305792i \(-0.901079\pi\)
0.740873 + 0.671645i \(0.234412\pi\)
\(312\) 0 0
\(313\) −3.13801 5.43520i −0.177371 0.307216i 0.763608 0.645680i \(-0.223426\pi\)
−0.940979 + 0.338464i \(0.890093\pi\)
\(314\) −9.52056 −0.537276
\(315\) 0 0
\(316\) 8.92820 0.502251
\(317\) −13.0000 22.5167i −0.730153 1.26466i −0.956818 0.290689i \(-0.906116\pi\)
0.226665 0.973973i \(-0.427218\pi\)
\(318\) 0 0
\(319\) −0.535898 + 0.928203i −0.0300045 + 0.0519694i
\(320\) 1.03528 0.0578737
\(321\) 0 0
\(322\) 0 0
\(323\) 29.9282 1.66525
\(324\) 0 0
\(325\) 3.52193 + 6.10016i 0.195362 + 0.338376i
\(326\) 13.3205 0.737755
\(327\) 0 0
\(328\) 4.31199 + 7.46859i 0.238090 + 0.412384i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.73205 + 9.92820i 0.315062 + 0.545703i 0.979451 0.201684i \(-0.0646413\pi\)
−0.664389 + 0.747387i \(0.731308\pi\)
\(332\) 3.29530 + 5.70762i 0.180853 + 0.313246i
\(333\) 0 0
\(334\) −0.757875 + 1.31268i −0.0414691 + 0.0718265i
\(335\) −6.45189 + 11.1750i −0.352505 + 0.610556i
\(336\) 0 0
\(337\) 3.50000 + 6.06218i 0.190657 + 0.330228i 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) 9.78461 0.532213
\(339\) 0 0
\(340\) 7.07180 0.383522
\(341\) −0.896575 + 1.55291i −0.0485523 + 0.0840950i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.133975 0.232051i 0.00722343 0.0125113i
\(345\) 0 0
\(346\) −3.34607 + 5.79555i −0.179886 + 0.311571i
\(347\) −4.79423 + 8.30385i −0.257368 + 0.445774i −0.965536 0.260270i \(-0.916188\pi\)
0.708168 + 0.706044i \(0.249522\pi\)
\(348\) 0 0
\(349\) 4.00240 6.93237i 0.214244 0.371081i −0.738795 0.673931i \(-0.764605\pi\)
0.953038 + 0.302850i \(0.0979380\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.133975 0.232051i 0.00714087 0.0123683i
\(353\) −25.0125 −1.33128 −0.665641 0.746272i \(-0.731842\pi\)
−0.665641 + 0.746272i \(0.731842\pi\)
\(354\) 0 0
\(355\) −9.79796 −0.520022
\(356\) 3.53553 + 6.12372i 0.187383 + 0.324557i
\(357\) 0 0
\(358\) −2.53590 + 4.39230i −0.134026 + 0.232141i
\(359\) 3.73205 6.46410i 0.196970 0.341162i −0.750574 0.660786i \(-0.770223\pi\)
0.947545 + 0.319624i \(0.103556\pi\)
\(360\) 0 0
\(361\) −0.0980762 0.169873i −0.00516191 0.00894068i
\(362\) −8.48528 14.6969i −0.445976 0.772454i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.80385 4.85641i −0.146760 0.254196i
\(366\) 0 0
\(367\) 18.5606 0.968858 0.484429 0.874831i \(-0.339027\pi\)
0.484429 + 0.874831i \(0.339027\pi\)
\(368\) 2.73205 + 4.73205i 0.142418 + 0.246675i
\(369\) 0 0
\(370\) −7.72741 −0.401729
\(371\) 0 0
\(372\) 0 0
\(373\) −10.7846 −0.558406 −0.279203 0.960232i \(-0.590070\pi\)
−0.279203 + 0.960232i \(0.590070\pi\)
\(374\) 0.915158 1.58510i 0.0473217 0.0819636i
\(375\) 0 0
\(376\) −0.378937 0.656339i −0.0195422 0.0338481i
\(377\) 7.17260 0.369408
\(378\) 0 0
\(379\) 13.5885 0.697992 0.348996 0.937124i \(-0.386523\pi\)
0.348996 + 0.937124i \(0.386523\pi\)
\(380\) −2.26795 3.92820i −0.116343 0.201513i
\(381\) 0 0
\(382\) −7.46410 + 12.9282i −0.381897 + 0.661464i
\(383\) −27.3233 −1.39616 −0.698078 0.716021i \(-0.745961\pi\)
−0.698078 + 0.716021i \(0.745961\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −15.0526 −0.766155
\(387\) 0 0
\(388\) 9.07227 + 15.7136i 0.460575 + 0.797739i
\(389\) −8.00000 −0.405616 −0.202808 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) 18.6622 + 32.3238i 0.943787 + 1.63469i
\(392\) 0 0
\(393\) 0 0
\(394\) 8.46410 + 14.6603i 0.426415 + 0.738573i
\(395\) −4.62158 8.00481i −0.232537 0.402766i
\(396\) 0 0
\(397\) −6.55343 + 11.3509i −0.328907 + 0.569684i −0.982295 0.187339i \(-0.940014\pi\)
0.653388 + 0.757023i \(0.273347\pi\)
\(398\) 13.1440 22.7661i 0.658850 1.14116i
\(399\) 0 0
\(400\) 1.96410 + 3.40192i 0.0982051 + 0.170096i
\(401\) 23.7846 1.18775 0.593873 0.804559i \(-0.297598\pi\)
0.593873 + 0.804559i \(0.297598\pi\)
\(402\) 0 0
\(403\) 12.0000 0.597763
\(404\) −2.44949 + 4.24264i −0.121867 + 0.211079i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.00000 + 1.73205i −0.0495682 + 0.0858546i
\(408\) 0 0
\(409\) −2.24144 + 3.88229i −0.110832 + 0.191967i −0.916106 0.400936i \(-0.868685\pi\)
0.805274 + 0.592903i \(0.202018\pi\)
\(410\) 4.46410 7.73205i 0.220466 0.381859i
\(411\) 0 0
\(412\) −6.17449 + 10.6945i −0.304195 + 0.526882i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.41154 5.90897i 0.167466 0.290060i
\(416\) −1.79315 −0.0879165
\(417\) 0 0
\(418\) −1.17398 −0.0574211
\(419\) 18.0938 + 31.3393i 0.883939 + 1.53103i 0.846925 + 0.531712i \(0.178451\pi\)
0.0370132 + 0.999315i \(0.488216\pi\)
\(420\) 0 0
\(421\) −3.80385 + 6.58846i −0.185388 + 0.321102i −0.943707 0.330782i \(-0.892688\pi\)
0.758319 + 0.651884i \(0.226021\pi\)
\(422\) 9.46410 16.3923i 0.460705 0.797965i
\(423\) 0 0
\(424\) −5.46410 9.46410i −0.265360 0.459617i
\(425\) 13.4164 + 23.2380i 0.650793 + 1.12721i
\(426\) 0 0
\(427\) 0 0
\(428\) −8.69615 15.0622i −0.420344 0.728058i
\(429\) 0 0
\(430\) −0.277401 −0.0133775
\(431\) −5.07180 8.78461i −0.244300 0.423140i 0.717635 0.696420i \(-0.245225\pi\)
−0.961935 + 0.273280i \(0.911891\pi\)
\(432\) 0 0
\(433\) −19.8362 −0.953265 −0.476632 0.879103i \(-0.658143\pi\)
−0.476632 + 0.879103i \(0.658143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.92820 0.236018
\(437\) 11.9700 20.7327i 0.572605 0.991781i
\(438\) 0 0
\(439\) −9.79796 16.9706i −0.467631 0.809961i 0.531685 0.846942i \(-0.321559\pi\)
−0.999316 + 0.0369815i \(0.988226\pi\)
\(440\) −0.277401 −0.0132246
\(441\) 0 0
\(442\) −12.2487 −0.582612
\(443\) 8.16025 + 14.1340i 0.387705 + 0.671525i 0.992140 0.125129i \(-0.0399345\pi\)
−0.604435 + 0.796654i \(0.706601\pi\)
\(444\) 0 0
\(445\) 3.66025 6.33975i 0.173513 0.300533i
\(446\) 7.17260 0.339633
\(447\) 0 0
\(448\) 0 0
\(449\) −23.7846 −1.12247 −0.561233 0.827658i \(-0.689673\pi\)
−0.561233 + 0.827658i \(0.689673\pi\)
\(450\) 0 0
\(451\) −1.15539 2.00120i −0.0544054 0.0942329i
\(452\) 6.92820 0.325875
\(453\) 0 0
\(454\) 13.8325 + 23.9587i 0.649194 + 1.12444i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.5263 + 26.8923i 0.726289 + 1.25797i 0.958441 + 0.285290i \(0.0920898\pi\)
−0.232153 + 0.972679i \(0.574577\pi\)
\(458\) 0.240237 + 0.416102i 0.0112255 + 0.0194432i
\(459\) 0 0
\(460\) 2.82843 4.89898i 0.131876 0.228416i
\(461\) −5.51815 + 9.55772i −0.257006 + 0.445148i −0.965438 0.260631i \(-0.916069\pi\)
0.708432 + 0.705779i \(0.249403\pi\)
\(462\) 0 0
\(463\) 15.3205 + 26.5359i 0.712004 + 1.23323i 0.964104 + 0.265526i \(0.0855457\pi\)
−0.252099 + 0.967701i \(0.581121\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) 0.124356 0.00576066
\(467\) 4.58939 7.94906i 0.212372 0.367839i −0.740085 0.672514i \(-0.765215\pi\)
0.952456 + 0.304675i \(0.0985479\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.392305 + 0.679492i −0.0180957 + 0.0313426i
\(471\) 0 0
\(472\) 0.637756 1.10463i 0.0293551 0.0508446i
\(473\) −0.0358984 + 0.0621778i −0.00165061 + 0.00285894i
\(474\) 0 0
\(475\) 8.60540 14.9050i 0.394843 0.683888i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.464102 + 0.803848i −0.0212275 + 0.0367671i
\(479\) 4.14110 0.189212 0.0946060 0.995515i \(-0.469841\pi\)
0.0946060 + 0.995515i \(0.469841\pi\)
\(480\) 0 0
\(481\) 13.3843 0.610270
\(482\) 3.13801 + 5.43520i 0.142933 + 0.247567i
\(483\) 0 0
\(484\) 5.46410 9.46410i 0.248368 0.430186i
\(485\) 9.39230 16.2679i 0.426483 0.738690i
\(486\) 0 0
\(487\) 1.39230 + 2.41154i 0.0630914 + 0.109277i 0.895846 0.444365i \(-0.146571\pi\)
−0.832754 + 0.553643i \(0.813237\pi\)
\(488\) −6.31319 10.9348i −0.285785 0.494994i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.69615 + 16.7942i 0.437581 + 0.757913i 0.997502 0.0706330i \(-0.0225019\pi\)
−0.559921 + 0.828546i \(0.689169\pi\)
\(492\) 0 0
\(493\) 27.3233 1.23058
\(494\) 3.92820 + 6.80385i 0.176738 + 0.306120i
\(495\) 0 0
\(496\) 6.69213 0.300486
\(497\) 0 0
\(498\) 0 0
\(499\) 33.3923 1.49484 0.747422 0.664349i \(-0.231291\pi\)
0.747422 + 0.664349i \(0.231291\pi\)
\(500\) 4.62158 8.00481i 0.206683 0.357986i
\(501\) 0 0
\(502\) −0.397520 0.688524i −0.0177422 0.0307303i
\(503\) 12.3490 0.550614 0.275307 0.961356i \(-0.411220\pi\)
0.275307 + 0.961356i \(0.411220\pi\)
\(504\) 0 0
\(505\) 5.07180 0.225692
\(506\) −0.732051 1.26795i −0.0325436 0.0563672i
\(507\) 0 0
\(508\) −6.73205 + 11.6603i −0.298686 + 0.517340i
\(509\) −21.5921 −0.957055 −0.478527 0.878073i \(-0.658829\pi\)
−0.478527 + 0.878073i \(0.658829\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −5.01910 8.69333i −0.221383 0.383446i
\(515\) 12.7846 0.563357
\(516\) 0 0
\(517\) 0.101536 + 0.175865i 0.00446555 + 0.00773455i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.928203 + 1.60770i 0.0407044 + 0.0705021i
\(521\) −16.8876 29.2502i −0.739860 1.28147i −0.952558 0.304357i \(-0.901559\pi\)
0.212699 0.977118i \(-0.431775\pi\)
\(522\) 0 0
\(523\) −10.3664 + 17.9551i −0.453289 + 0.785120i −0.998588 0.0531215i \(-0.983083\pi\)
0.545299 + 0.838242i \(0.316416\pi\)
\(524\) 5.46739 9.46979i 0.238844 0.413690i
\(525\) 0 0
\(526\) 4.26795 + 7.39230i 0.186091 + 0.322320i
\(527\) 45.7128 1.99128
\(528\) 0 0
\(529\) 6.85641 0.298105
\(530\) −5.65685 + 9.79796i −0.245718 + 0.425596i
\(531\) 0 0
\(532\) 0 0
\(533\) −7.73205 + 13.3923i −0.334912 + 0.580085i
\(534\) 0 0
\(535\) −9.00292 + 15.5935i −0.389230 + 0.674166i
\(536\) 6.23205 10.7942i 0.269184 0.466240i
\(537\) 0 0
\(538\) 2.82843 4.89898i 0.121942 0.211210i
\(539\) 0 0
\(540\) 0 0
\(541\) −7.66025 + 13.2679i −0.329340 + 0.570434i −0.982381 0.186889i \(-0.940160\pi\)
0.653041 + 0.757323i \(0.273493\pi\)
\(542\) −13.1069 −0.562988
\(543\) 0 0
\(544\) −6.83083 −0.292869
\(545\) −2.55103 4.41851i −0.109274 0.189268i
\(546\) 0 0
\(547\) −17.1865 + 29.7679i −0.734843 + 1.27279i 0.219949 + 0.975511i \(0.429411\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(548\) 4.33013 7.50000i 0.184974 0.320384i
\(549\) 0 0
\(550\) −0.526279 0.911543i −0.0224406 0.0388683i
\(551\) −8.76268 15.1774i −0.373303 0.646579i
\(552\) 0 0
\(553\) 0 0
\(554\) 15.7321 + 27.2487i 0.668391 + 1.15769i
\(555\) 0 0
\(556\) 0.795040 0.0337172
\(557\) −3.46410 6.00000i −0.146779 0.254228i 0.783256 0.621699i \(-0.213557\pi\)
−0.930035 + 0.367471i \(0.880224\pi\)
\(558\) 0 0
\(559\) 0.480473 0.0203219
\(560\) 0 0
\(561\) 0 0
\(562\) 17.8564 0.753227
\(563\) −9.12304 + 15.8016i −0.384490 + 0.665957i −0.991698 0.128586i \(-0.958956\pi\)
0.607208 + 0.794543i \(0.292289\pi\)
\(564\) 0 0
\(565\) −3.58630 6.21166i −0.150877 0.261326i
\(566\) 15.0759 0.633686
\(567\) 0 0
\(568\) 9.46410 0.397105
\(569\) −12.8923 22.3301i −0.540474 0.936128i −0.998877 0.0473833i \(-0.984912\pi\)
0.458403 0.888744i \(-0.348422\pi\)
\(570\) 0 0
\(571\) 16.5263 28.6244i 0.691603 1.19789i −0.279709 0.960085i \(-0.590238\pi\)
0.971312 0.237807i \(-0.0764286\pi\)
\(572\) 0.480473 0.0200896
\(573\) 0 0
\(574\) 0 0
\(575\) 21.4641 0.895115
\(576\) 0 0
\(577\) 13.7446 + 23.8064i 0.572196 + 0.991072i 0.996340 + 0.0854776i \(0.0272416\pi\)
−0.424144 + 0.905595i \(0.639425\pi\)
\(578\) −29.6603 −1.23370
\(579\) 0 0
\(580\) −2.07055 3.58630i −0.0859750 0.148913i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.46410 + 2.53590i 0.0606369 + 0.105026i
\(584\) 2.70831 + 4.69093i 0.112071 + 0.194112i
\(585\) 0 0
\(586\) 4.62158 8.00481i 0.190916 0.330676i
\(587\) −20.9408 + 36.2705i −0.864319 + 1.49704i 0.00340370 + 0.999994i \(0.498917\pi\)
−0.867722 + 0.497049i \(0.834417\pi\)
\(588\) 0 0
\(589\) −14.6603 25.3923i −0.604065 1.04627i
\(590\) −1.32051 −0.0543645
\(591\) 0 0
\(592\) 7.46410 0.306773
\(593\) 8.43451 14.6090i 0.346364 0.599920i −0.639237 0.769010i \(-0.720750\pi\)
0.985601 + 0.169090i \(0.0540829\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.4641 19.8564i 0.469588 0.813350i
\(597\) 0 0
\(598\) −4.89898 + 8.48528i −0.200334 + 0.346989i
\(599\) 2.39230 4.14359i 0.0977469 0.169303i −0.813005 0.582257i \(-0.802170\pi\)
0.910752 + 0.412954i \(0.135503\pi\)
\(600\) 0 0
\(601\) 1.67303 2.89778i 0.0682444 0.118203i −0.829884 0.557936i \(-0.811594\pi\)
0.898129 + 0.439733i \(0.144927\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9.19615 + 15.9282i −0.374186 + 0.648109i
\(605\) −11.3137 −0.459968
\(606\) 0 0
\(607\) −2.27362 −0.0922836 −0.0461418 0.998935i \(-0.514693\pi\)
−0.0461418 + 0.998935i \(0.514693\pi\)
\(608\) 2.19067 + 3.79435i 0.0888434 + 0.153881i
\(609\) 0 0
\(610\) −6.53590 + 11.3205i −0.264631 + 0.458354i
\(611\) 0.679492 1.17691i 0.0274893 0.0476129i
\(612\) 0 0
\(613\) −12.4641 21.5885i −0.503420 0.871950i −0.999992 0.00395396i \(-0.998741\pi\)
0.496572 0.867996i \(-0.334592\pi\)
\(614\) 0.586988 + 1.01669i 0.0236889 + 0.0410304i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.57180 2.72243i −0.0632782 0.109601i 0.832651 0.553798i \(-0.186822\pi\)
−0.895929 + 0.444197i \(0.853489\pi\)
\(618\) 0 0
\(619\) −31.7047 −1.27432 −0.637159 0.770732i \(-0.719891\pi\)
−0.637159 + 0.770732i \(0.719891\pi\)
\(620\) −3.46410 6.00000i −0.139122 0.240966i
\(621\) 0 0
\(622\) −7.45001 −0.298718
\(623\) 0 0
\(624\) 0 0
\(625\) 10.0718 0.402872
\(626\) 3.13801 5.43520i 0.125420 0.217234i
\(627\) 0 0
\(628\) −4.76028 8.24504i −0.189956 0.329013i
\(629\) 50.9860 2.03295
\(630\) 0 0
\(631\) −19.7128 −0.784755 −0.392377 0.919804i \(-0.628347\pi\)
−0.392377 + 0.919804i \(0.628347\pi\)
\(632\) 4.46410 + 7.73205i 0.177572 + 0.307564i
\(633\) 0 0
\(634\) 13.0000 22.5167i 0.516296 0.894251i
\(635\) 13.9391 0.553155
\(636\) 0 0
\(637\) 0 0
\(638\) −1.07180 −0.0424328
\(639\) 0 0
\(640\) 0.517638 + 0.896575i 0.0204614 + 0.0354403i
\(641\) −4.07180 −0.160826 −0.0804132 0.996762i \(-0.525624\pi\)
−0.0804132 + 0.996762i \(0.525624\pi\)
\(642\) 0 0
\(643\) 22.4565 + 38.8959i 0.885599 + 1.53390i 0.845025 + 0.534726i \(0.179585\pi\)
0.0405737 + 0.999177i \(0.487081\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 14.9641 + 25.9186i 0.588755 + 1.01975i
\(647\) 10.9348 + 18.9396i 0.429890 + 0.744592i 0.996863 0.0791447i \(-0.0252189\pi\)
−0.566973 + 0.823736i \(0.691886\pi\)
\(648\) 0 0
\(649\) −0.170886 + 0.295984i −0.00670787 + 0.0116184i
\(650\) −3.52193 + 6.10016i −0.138141 + 0.239268i
\(651\) 0 0
\(652\) 6.66025 + 11.5359i 0.260836 + 0.451781i
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) −11.3205 −0.442329
\(656\) −4.31199 + 7.46859i −0.168355 + 0.291599i
\(657\) 0 0
\(658\) 0 0
\(659\) −24.1244 + 41.7846i −0.939751 + 1.62770i −0.173818 + 0.984778i \(0.555610\pi\)
−0.765934 + 0.642919i \(0.777723\pi\)
\(660\) 0 0
\(661\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(662\) −5.73205 + 9.92820i −0.222782 + 0.385871i
\(663\) 0 0
\(664\) −3.29530 + 5.70762i −0.127882 + 0.221499i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.9282 18.9282i 0.423142 0.732903i
\(668\) −1.51575 −0.0586461
\(669\) 0 0
\(670\) −12.9038 −0.498517
\(671\) 1.69161 + 2.92996i 0.0653041 + 0.113110i
\(672\) 0 0
\(673\) −20.7846 + 36.0000i −0.801188 + 1.38770i 0.117647 + 0.993055i \(0.462465\pi\)
−0.918835 + 0.394643i \(0.870868\pi\)
\(674\) −3.50000 + 6.06218i −0.134815 + 0.233506i
\(675\) 0 0
\(676\) 4.89230 + 8.47372i 0.188166 + 0.325912i
\(677\) −2.68973 4.65874i −0.103375 0.179050i 0.809698 0.586846i \(-0.199631\pi\)
−0.913073 + 0.407796i \(0.866297\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.53590 + 6.12436i 0.135596 + 0.234858i
\(681\) 0 0
\(682\) −1.79315 −0.0686633
\(683\) −19.1603 33.1865i −0.733147 1.26985i −0.955532 0.294888i \(-0.904718\pi\)
0.222385 0.974959i \(-0.428616\pi\)
\(684\) 0 0
\(685\) −8.96575 −0.342564
\(686\) 0 0
\(687\) 0 0
\(688\) 0.267949 0.0102155
\(689\) 9.79796 16.9706i 0.373273 0.646527i
\(690\) 0 0
\(691\) −12.1595 21.0609i −0.462570 0.801194i 0.536518 0.843889i \(-0.319739\pi\)
−0.999088 + 0.0426942i \(0.986406\pi\)
\(692\) −6.69213 −0.254397
\(693\) 0 0
\(694\) −9.58846 −0.363973
\(695\) −0.411543 0.712813i −0.0156107 0.0270385i
\(696\) 0 0
\(697\) −29.4545 + 51.0167i −1.11567 + 1.93239i
\(698\) 8.00481 0.302986
\(699\) 0 0
\(700\) 0 0
\(701\) 20.7846 0.785024 0.392512 0.919747i \(-0.371606\pi\)
0.392512 + 0.919747i \(0.371606\pi\)
\(702\) 0 0
\(703\) −16.3514 28.3214i −0.616704 1.06816i
\(704\) 0.267949 0.0100987
\(705\) 0 0
\(706\) −12.5063 21.6615i −0.470680 0.815241i
\(707\) 0 0
\(708\) 0 0
\(709\) 6.19615 + 10.7321i 0.232701 + 0.403051i 0.958602 0.284749i \(-0.0919102\pi\)
−0.725901 + 0.687799i \(0.758577\pi\)
\(710\) −4.89898 8.48528i −0.183855 0.318447i
\(711\) 0 0
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) 18.2832 31.6675i 0.684713 1.18596i
\(714\) 0 0
\(715\) −0.248711 0.430781i −0.00930128 0.0161103i
\(716\) −5.07180 −0.189542
\(717\) 0 0
\(718\) 7.46410 0.278558
\(719\) −24.8367 + 43.0184i −0.926251 + 1.60431i −0.136716 + 0.990610i \(0.543655\pi\)
−0.789536 + 0.613704i \(0.789679\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.0980762 0.169873i 0.00365002 0.00632202i
\(723\) 0 0
\(724\) 8.48528 14.6969i 0.315353 0.546207i
\(725\) 7.85641 13.6077i 0.291780 0.505377i
\(726\) 0 0
\(727\) −16.3514 + 28.3214i −0.606439 + 1.05038i 0.385383 + 0.922757i \(0.374069\pi\)
−0.991822 + 0.127627i \(0.959264\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.80385 4.85641i 0.103775 0.179744i
\(731\) 1.83032 0.0676967
\(732\) 0 0
\(733\) 8.00481 0.295664 0.147832 0.989012i \(-0.452770\pi\)
0.147832 + 0.989012i \(0.452770\pi\)
\(734\) 9.28032 + 16.0740i 0.342543 + 0.593302i
\(735\) 0 0
\(736\) −2.73205 + 4.73205i −0.100705 + 0.174426i
\(737\) −1.66987 + 2.89230i −0.0615106 + 0.106539i
\(738\) 0 0
\(739\) −3.06218 5.30385i −0.112644 0.195105i 0.804191 0.594370i \(-0.202599\pi\)
−0.916836 + 0.399265i \(0.869265\pi\)
\(740\) −3.86370 6.69213i −0.142033 0.246008i
\(741\) 0 0
\(742\) 0 0
\(743\) −15.7846 27.3397i −0.579081 1.00300i −0.995585 0.0938641i \(-0.970078\pi\)
0.416504 0.909134i \(-0.363255\pi\)
\(744\) 0 0
\(745\) −23.7370 −0.869657
\(746\) −5.39230 9.33975i −0.197426 0.341952i
\(747\) 0 0
\(748\) 1.83032 0.0669230
\(749\) 0 0
\(750\) 0 0
\(751\) 34.7846 1.26931 0.634654 0.772796i \(-0.281143\pi\)
0.634654 + 0.772796i \(0.281143\pi\)
\(752\) 0.378937 0.656339i 0.0138184 0.0239342i
\(753\) 0 0
\(754\) 3.58630 + 6.21166i 0.130605 + 0.226215i
\(755\) 19.0411 0.692977
\(756\) 0 0
\(757\) 19.3205 0.702216 0.351108 0.936335i \(-0.385805\pi\)
0.351108 + 0.936335i \(0.385805\pi\)
\(758\) 6.79423 + 11.7679i 0.246777 + 0.427431i
\(759\) 0 0
\(760\) 2.26795 3.92820i 0.0822672 0.142491i
\(761\) 40.2543 1.45922 0.729609 0.683865i \(-0.239702\pi\)
0.729609 + 0.683865i \(0.239702\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −14.9282 −0.540083
\(765\) 0 0
\(766\) −13.6617 23.6627i −0.493616 0.854968i
\(767\) 2.28719 0.0825855
\(768\) 0 0
\(769\) −19.0919 33.0681i −0.688471 1.19247i −0.972332 0.233601i \(-0.924949\pi\)
0.283862 0.958865i \(-0.408384\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.52628 13.0359i −0.270877 0.469172i
\(773\) 19.6975 + 34.1170i 0.708468 + 1.22710i 0.965425 + 0.260680i \(0.0839468\pi\)
−0.256957 + 0.966423i \(0.582720\pi\)
\(774\) 0 0
\(775\) 13.1440 22.7661i 0.472147 0.817783i
\(776\) −9.07227 + 15.7136i −0.325676 + 0.564087i
\(777\) 0 0
\(778\) −4.00000 6.92820i −0.143407 0.248388i
\(779\) 37.7846 1.35377
\(780\) 0 0
\(781\) −2.53590 −0.0907416
\(782\) −18.6622 + 32.3238i −0.667358 + 1.15590i
\(783\) 0 0
\(784\) 0 0
\(785\) −4.92820 + 8.53590i −0.175895 + 0.304659i
\(786\) 0 0
\(787\) −3.57270 + 6.18810i −0.127353 + 0.220582i −0.922650 0.385638i \(-0.873981\pi\)
0.795297 + 0.606220i \(0.207315\pi\)
\(788\) −8.46410 + 14.6603i −0.301521 + 0.522250i
\(789\) 0 0
\(790\) 4.62158 8.00481i 0.164428 0.284798i
\(791\) 0 0
\(792\) 0 0
\(793\) 11.3205 19.6077i 0.402003 0.696290i
\(794\) −13.1069 −0.465145
\(795\)