Properties

Label 1323.2.o.e.881.12
Level $1323$
Weight $2$
Character 1323.881
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.12
Character \(\chi\) \(=\) 1323.881
Dual form 1323.2.o.e.440.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.105953 + 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} +(0.264715 - 0.458500i) q^{5} -0.487547i q^{8} +O(q^{10})\) \(q+(-0.105953 + 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} +(0.264715 - 0.458500i) q^{5} -0.487547i q^{8} +0.0647728i q^{10} +(3.64120 - 2.10225i) q^{11} +(-1.74714 - 1.00871i) q^{13} +(-1.95521 - 3.38652i) q^{16} -4.38762 q^{17} -5.24685i q^{19} +(0.525467 + 0.910136i) q^{20} +(-0.257198 + 0.445480i) q^{22} +(-5.43444 - 3.13757i) q^{23} +(2.35985 + 4.08738i) q^{25} +0.246821 q^{26} +(7.27689 - 4.20131i) q^{29} +(1.03204 + 0.595849i) q^{31} +(1.25878 + 0.726755i) q^{32} +(0.464883 - 0.268400i) q^{34} -3.23252 q^{37} +(0.320962 + 0.555922i) q^{38} +(-0.223540 - 0.129061i) q^{40} +(0.0994958 - 0.172332i) q^{41} +(3.96309 + 6.86427i) q^{43} +8.34605i q^{44} +0.767730 q^{46} +(-4.98595 - 8.63591i) q^{47} +(-0.500069 - 0.288715i) q^{50} +(3.46814 - 2.00233i) q^{52} -4.21753i q^{53} -2.22598i q^{55} +(-0.514008 + 0.890287i) q^{58} +(6.71960 - 11.6387i) q^{59} +(11.3564 - 6.55662i) q^{61} -0.145798 q^{62} +7.64300 q^{64} +(-0.924990 + 0.534043i) q^{65} +(3.29001 - 5.69847i) q^{67} +(4.35478 - 7.54270i) q^{68} +8.50587i q^{71} -5.61202i q^{73} +(0.342497 - 0.197741i) q^{74} +(9.01980 + 5.20758i) q^{76} +(-0.286342 - 0.495959i) q^{79} -2.07029 q^{80} +0.0243455i q^{82} +(-5.42692 - 9.39971i) q^{83} +(-1.16147 + 2.01172i) q^{85} +(-0.839806 - 0.484862i) q^{86} +(-1.02494 - 1.77525i) q^{88} -12.8738 q^{89} +(10.7875 - 6.22819i) q^{92} +(1.05656 + 0.610003i) q^{94} +(-2.40568 - 1.38892i) q^{95} +(0.493773 - 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.105953 + 0.0611722i −0.0749204 + 0.0432553i −0.536992 0.843587i \(-0.680440\pi\)
0.462072 + 0.886842i \(0.347106\pi\)
\(3\) 0 0
\(4\) −0.992516 + 1.71909i −0.496258 + 0.859544i
\(5\) 0.264715 0.458500i 0.118384 0.205047i −0.800743 0.599008i \(-0.795562\pi\)
0.919127 + 0.393960i \(0.128895\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.487547i 0.172374i
\(9\) 0 0
\(10\) 0.0647728i 0.0204830i
\(11\) 3.64120 2.10225i 1.09786 0.633851i 0.162204 0.986757i \(-0.448140\pi\)
0.935659 + 0.352906i \(0.114807\pi\)
\(12\) 0 0
\(13\) −1.74714 1.00871i −0.484570 0.279767i 0.237749 0.971327i \(-0.423590\pi\)
−0.722319 + 0.691560i \(0.756924\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.95521 3.38652i −0.488802 0.846630i
\(17\) −4.38762 −1.06415 −0.532077 0.846696i \(-0.678588\pi\)
−0.532077 + 0.846696i \(0.678588\pi\)
\(18\) 0 0
\(19\) 5.24685i 1.20371i −0.798605 0.601855i \(-0.794428\pi\)
0.798605 0.601855i \(-0.205572\pi\)
\(20\) 0.525467 + 0.910136i 0.117498 + 0.203513i
\(21\) 0 0
\(22\) −0.257198 + 0.445480i −0.0548348 + 0.0949767i
\(23\) −5.43444 3.13757i −1.13316 0.654230i −0.188431 0.982086i \(-0.560340\pi\)
−0.944727 + 0.327857i \(0.893674\pi\)
\(24\) 0 0
\(25\) 2.35985 + 4.08738i 0.471970 + 0.817477i
\(26\) 0.246821 0.0484056
\(27\) 0 0
\(28\) 0 0
\(29\) 7.27689 4.20131i 1.35128 0.780164i 0.362855 0.931846i \(-0.381802\pi\)
0.988429 + 0.151681i \(0.0484687\pi\)
\(30\) 0 0
\(31\) 1.03204 + 0.595849i 0.185360 + 0.107018i 0.589809 0.807543i \(-0.299203\pi\)
−0.404449 + 0.914561i \(0.632537\pi\)
\(32\) 1.25878 + 0.726755i 0.222522 + 0.128473i
\(33\) 0 0
\(34\) 0.464883 0.268400i 0.0797268 0.0460303i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.23252 −0.531424 −0.265712 0.964053i \(-0.585607\pi\)
−0.265712 + 0.964053i \(0.585607\pi\)
\(38\) 0.320962 + 0.555922i 0.0520668 + 0.0901824i
\(39\) 0 0
\(40\) −0.223540 0.129061i −0.0353448 0.0204063i
\(41\) 0.0994958 0.172332i 0.0155386 0.0269137i −0.858152 0.513396i \(-0.828387\pi\)
0.873690 + 0.486483i \(0.161720\pi\)
\(42\) 0 0
\(43\) 3.96309 + 6.86427i 0.604366 + 1.04679i 0.992151 + 0.125042i \(0.0399067\pi\)
−0.387786 + 0.921750i \(0.626760\pi\)
\(44\) 8.34605i 1.25821i
\(45\) 0 0
\(46\) 0.767730 0.113196
\(47\) −4.98595 8.63591i −0.727275 1.25968i −0.958031 0.286665i \(-0.907453\pi\)
0.230756 0.973012i \(-0.425880\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.500069 0.288715i −0.0707204 0.0408304i
\(51\) 0 0
\(52\) 3.46814 2.00233i 0.480944 0.277673i
\(53\) 4.21753i 0.579323i −0.957129 0.289661i \(-0.906457\pi\)
0.957129 0.289661i \(-0.0935427\pi\)
\(54\) 0 0
\(55\) 2.22598i 0.300152i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.514008 + 0.890287i −0.0674925 + 0.116900i
\(59\) 6.71960 11.6387i 0.874817 1.51523i 0.0178590 0.999841i \(-0.494315\pi\)
0.856958 0.515387i \(-0.172352\pi\)
\(60\) 0 0
\(61\) 11.3564 6.55662i 1.45404 0.839489i 0.455330 0.890323i \(-0.349521\pi\)
0.998707 + 0.0508335i \(0.0161878\pi\)
\(62\) −0.145798 −0.0185163
\(63\) 0 0
\(64\) 7.64300 0.955375
\(65\) −0.924990 + 0.534043i −0.114731 + 0.0662399i
\(66\) 0 0
\(67\) 3.29001 5.69847i 0.401939 0.696179i −0.592021 0.805923i \(-0.701670\pi\)
0.993960 + 0.109744i \(0.0350030\pi\)
\(68\) 4.35478 7.54270i 0.528095 0.914687i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.50587i 1.00946i 0.863277 + 0.504730i \(0.168408\pi\)
−0.863277 + 0.504730i \(0.831592\pi\)
\(72\) 0 0
\(73\) 5.61202i 0.656837i −0.944532 0.328419i \(-0.893484\pi\)
0.944532 0.328419i \(-0.106516\pi\)
\(74\) 0.342497 0.197741i 0.0398145 0.0229869i
\(75\) 0 0
\(76\) 9.01980 + 5.20758i 1.03464 + 0.597351i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.286342 0.495959i −0.0322160 0.0557997i 0.849468 0.527640i \(-0.176923\pi\)
−0.881684 + 0.471841i \(0.843590\pi\)
\(80\) −2.07029 −0.231465
\(81\) 0 0
\(82\) 0.0243455i 0.00268851i
\(83\) −5.42692 9.39971i −0.595682 1.03175i −0.993450 0.114266i \(-0.963548\pi\)
0.397768 0.917486i \(-0.369785\pi\)
\(84\) 0 0
\(85\) −1.16147 + 2.01172i −0.125979 + 0.218202i
\(86\) −0.839806 0.484862i −0.0905586 0.0522840i
\(87\) 0 0
\(88\) −1.02494 1.77525i −0.109259 0.189243i
\(89\) −12.8738 −1.36461 −0.682307 0.731065i \(-0.739023\pi\)
−0.682307 + 0.731065i \(0.739023\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.7875 6.22819i 1.12468 0.649333i
\(93\) 0 0
\(94\) 1.05656 + 0.610003i 0.108975 + 0.0629170i
\(95\) −2.40568 1.38892i −0.246817 0.142500i
\(96\) 0 0
\(97\) 0.493773 0.285080i 0.0501351 0.0289455i −0.474723 0.880135i \(-0.657452\pi\)
0.524858 + 0.851190i \(0.324118\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −9.36876 −0.936876
\(101\) 5.81552 + 10.0728i 0.578666 + 1.00228i 0.995633 + 0.0933576i \(0.0297600\pi\)
−0.416966 + 0.908922i \(0.636907\pi\)
\(102\) 0 0
\(103\) 5.54001 + 3.19853i 0.545874 + 0.315160i 0.747456 0.664311i \(-0.231275\pi\)
−0.201582 + 0.979472i \(0.564608\pi\)
\(104\) −0.491795 + 0.851814i −0.0482245 + 0.0835272i
\(105\) 0 0
\(106\) 0.257996 + 0.446862i 0.0250588 + 0.0434031i
\(107\) 0.253263i 0.0244839i 0.999925 + 0.0122419i \(0.00389683\pi\)
−0.999925 + 0.0122419i \(0.996103\pi\)
\(108\) 0 0
\(109\) 11.9720 1.14671 0.573357 0.819306i \(-0.305641\pi\)
0.573357 + 0.819306i \(0.305641\pi\)
\(110\) 0.136168 + 0.235851i 0.0129831 + 0.0224875i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.28636 2.47473i −0.403227 0.232803i 0.284648 0.958632i \(-0.408123\pi\)
−0.687875 + 0.725829i \(0.741456\pi\)
\(114\) 0 0
\(115\) −2.87715 + 1.66113i −0.268296 + 0.154901i
\(116\) 16.6795i 1.54865i
\(117\) 0 0
\(118\) 1.64421i 0.151362i
\(119\) 0 0
\(120\) 0 0
\(121\) 3.33888 5.78311i 0.303535 0.525737i
\(122\) −0.802166 + 1.38939i −0.0726247 + 0.125790i
\(123\) 0 0
\(124\) −2.04863 + 1.18278i −0.183973 + 0.106217i
\(125\) 5.14590 0.460263
\(126\) 0 0
\(127\) −3.68446 −0.326943 −0.163472 0.986548i \(-0.552269\pi\)
−0.163472 + 0.986548i \(0.552269\pi\)
\(128\) −3.32736 + 1.92105i −0.294100 + 0.169798i
\(129\) 0 0
\(130\) 0.0653372 0.113167i 0.00573045 0.00992543i
\(131\) 2.72837 4.72567i 0.238379 0.412884i −0.721871 0.692028i \(-0.756717\pi\)
0.960249 + 0.279144i \(0.0900508\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.805030i 0.0695440i
\(135\) 0 0
\(136\) 2.13917i 0.183432i
\(137\) 1.39996 0.808270i 0.119607 0.0690551i −0.439003 0.898486i \(-0.644668\pi\)
0.558610 + 0.829431i \(0.311335\pi\)
\(138\) 0 0
\(139\) −9.79085 5.65275i −0.830449 0.479460i 0.0235572 0.999722i \(-0.492501\pi\)
−0.854006 + 0.520262i \(0.825834\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.520323 0.901226i −0.0436645 0.0756292i
\(143\) −8.48226 −0.709322
\(144\) 0 0
\(145\) 4.44860i 0.369436i
\(146\) 0.343300 + 0.594613i 0.0284117 + 0.0492105i
\(147\) 0 0
\(148\) 3.20833 5.55699i 0.263723 0.456782i
\(149\) −4.61426 2.66404i −0.378015 0.218247i 0.298939 0.954272i \(-0.403367\pi\)
−0.676954 + 0.736025i \(0.736700\pi\)
\(150\) 0 0
\(151\) 1.32132 + 2.28859i 0.107527 + 0.186243i 0.914768 0.403980i \(-0.132373\pi\)
−0.807241 + 0.590222i \(0.799040\pi\)
\(152\) −2.55808 −0.207488
\(153\) 0 0
\(154\) 0 0
\(155\) 0.546393 0.315460i 0.0438873 0.0253384i
\(156\) 0 0
\(157\) −11.3181 6.53448i −0.903279 0.521508i −0.0250163 0.999687i \(-0.507964\pi\)
−0.878263 + 0.478179i \(0.841297\pi\)
\(158\) 0.0606778 + 0.0350324i 0.00482727 + 0.00278703i
\(159\) 0 0
\(160\) 0.666434 0.384766i 0.0526862 0.0304184i
\(161\) 0 0
\(162\) 0 0
\(163\) 17.0269 1.33365 0.666825 0.745214i \(-0.267653\pi\)
0.666825 + 0.745214i \(0.267653\pi\)
\(164\) 0.197502 + 0.342084i 0.0154223 + 0.0267123i
\(165\) 0 0
\(166\) 1.15000 + 0.663954i 0.0892575 + 0.0515328i
\(167\) −10.6605 + 18.4645i −0.824932 + 1.42882i 0.0770396 + 0.997028i \(0.475453\pi\)
−0.901971 + 0.431796i \(0.857880\pi\)
\(168\) 0 0
\(169\) −4.46499 7.73360i −0.343461 0.594892i
\(170\) 0.284198i 0.0217970i
\(171\) 0 0
\(172\) −15.7337 −1.19968
\(173\) 10.2433 + 17.7418i 0.778781 + 1.34889i 0.932645 + 0.360796i \(0.117495\pi\)
−0.153864 + 0.988092i \(0.549172\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −14.2386 8.22066i −1.07327 0.619655i
\(177\) 0 0
\(178\) 1.36402 0.787516i 0.102237 0.0590268i
\(179\) 14.4071i 1.07684i −0.842676 0.538420i \(-0.819021\pi\)
0.842676 0.538420i \(-0.180979\pi\)
\(180\) 0 0
\(181\) 6.97309i 0.518306i −0.965836 0.259153i \(-0.916557\pi\)
0.965836 0.259153i \(-0.0834434\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.52971 + 2.64954i −0.112772 + 0.195327i
\(185\) −0.855697 + 1.48211i −0.0629121 + 0.108967i
\(186\) 0 0
\(187\) −15.9762 + 9.22386i −1.16829 + 0.674515i
\(188\) 19.7945 1.44366
\(189\) 0 0
\(190\) 0.339853 0.0246555
\(191\) 9.38310 5.41734i 0.678937 0.391985i −0.120517 0.992711i \(-0.538455\pi\)
0.799455 + 0.600727i \(0.205122\pi\)
\(192\) 0 0
\(193\) −5.26223 + 9.11444i −0.378783 + 0.656072i −0.990886 0.134707i \(-0.956991\pi\)
0.612102 + 0.790779i \(0.290324\pi\)
\(194\) −0.0348780 + 0.0604104i −0.00250409 + 0.00433722i
\(195\) 0 0
\(196\) 0 0
\(197\) 15.5156i 1.10544i 0.833366 + 0.552721i \(0.186410\pi\)
−0.833366 + 0.552721i \(0.813590\pi\)
\(198\) 0 0
\(199\) 12.5479i 0.889495i 0.895656 + 0.444748i \(0.146707\pi\)
−0.895656 + 0.444748i \(0.853293\pi\)
\(200\) 1.99279 1.15054i 0.140912 0.0813553i
\(201\) 0 0
\(202\) −1.23235 0.711497i −0.0867078 0.0500608i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0526760 0.0912375i −0.00367905 0.00637231i
\(206\) −0.782644 −0.0545294
\(207\) 0 0
\(208\) 7.88898i 0.547002i
\(209\) −11.0302 19.1048i −0.762973 1.32151i
\(210\) 0 0
\(211\) −1.19765 + 2.07438i −0.0824494 + 0.142807i −0.904302 0.426894i \(-0.859608\pi\)
0.821852 + 0.569701i \(0.192941\pi\)
\(212\) 7.25031 + 4.18597i 0.497953 + 0.287493i
\(213\) 0 0
\(214\) −0.0154927 0.0268341i −0.00105906 0.00183434i
\(215\) 4.19636 0.286189
\(216\) 0 0
\(217\) 0 0
\(218\) −1.26848 + 0.732357i −0.0859123 + 0.0496015i
\(219\) 0 0
\(220\) 3.82666 + 2.20932i 0.257993 + 0.148953i
\(221\) 7.66580 + 4.42585i 0.515657 + 0.297715i
\(222\) 0 0
\(223\) −2.42193 + 1.39830i −0.162184 + 0.0936370i −0.578895 0.815402i \(-0.696516\pi\)
0.416711 + 0.909039i \(0.363183\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.605540 0.0402799
\(227\) 1.42300 + 2.46471i 0.0944480 + 0.163589i 0.909378 0.415970i \(-0.136558\pi\)
−0.814930 + 0.579559i \(0.803225\pi\)
\(228\) 0 0
\(229\) −20.5460 11.8623i −1.35772 0.783880i −0.368404 0.929666i \(-0.620096\pi\)
−0.989316 + 0.145786i \(0.953429\pi\)
\(230\) 0.203229 0.352004i 0.0134006 0.0232104i
\(231\) 0 0
\(232\) −2.04834 3.54782i −0.134480 0.232926i
\(233\) 18.7298i 1.22703i −0.789684 0.613514i \(-0.789755\pi\)
0.789684 0.613514i \(-0.210245\pi\)
\(234\) 0 0
\(235\) −5.27942 −0.344391
\(236\) 13.3386 + 23.1032i 0.868270 + 1.50389i
\(237\) 0 0
\(238\) 0 0
\(239\) −11.1421 6.43288i −0.720721 0.416109i 0.0942969 0.995544i \(-0.469940\pi\)
−0.815018 + 0.579436i \(0.803273\pi\)
\(240\) 0 0
\(241\) 3.64082 2.10203i 0.234526 0.135403i −0.378132 0.925752i \(-0.623434\pi\)
0.612658 + 0.790348i \(0.290100\pi\)
\(242\) 0.816987i 0.0525179i
\(243\) 0 0
\(244\) 26.0302i 1.66641i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.29257 + 9.16700i −0.336758 + 0.583282i
\(248\) 0.290504 0.503168i 0.0184470 0.0319512i
\(249\) 0 0
\(250\) −0.545226 + 0.314786i −0.0344831 + 0.0199088i
\(251\) 7.50592 0.473770 0.236885 0.971538i \(-0.423874\pi\)
0.236885 + 0.971538i \(0.423874\pi\)
\(252\) 0 0
\(253\) −26.3838 −1.65874
\(254\) 0.390381 0.225387i 0.0244947 0.0141420i
\(255\) 0 0
\(256\) −7.40797 + 12.8310i −0.462998 + 0.801936i
\(257\) −2.51960 + 4.36408i −0.157169 + 0.272224i −0.933847 0.357674i \(-0.883570\pi\)
0.776678 + 0.629898i \(0.216903\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.12018i 0.131488i
\(261\) 0 0
\(262\) 0.667601i 0.0412445i
\(263\) −12.2494 + 7.07220i −0.755331 + 0.436091i −0.827617 0.561293i \(-0.810304\pi\)
0.0722856 + 0.997384i \(0.476971\pi\)
\(264\) 0 0
\(265\) −1.93374 1.11644i −0.118789 0.0685826i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.53078 + 11.3116i 0.398931 + 0.690969i
\(269\) −15.7771 −0.961948 −0.480974 0.876735i \(-0.659717\pi\)
−0.480974 + 0.876735i \(0.659717\pi\)
\(270\) 0 0
\(271\) 16.8078i 1.02100i 0.859877 + 0.510501i \(0.170540\pi\)
−0.859877 + 0.510501i \(0.829460\pi\)
\(272\) 8.57871 + 14.8588i 0.520160 + 0.900944i
\(273\) 0 0
\(274\) −0.0988873 + 0.171278i −0.00597400 + 0.0103473i
\(275\) 17.1854 + 9.92198i 1.03632 + 0.598318i
\(276\) 0 0
\(277\) −8.91066 15.4337i −0.535390 0.927322i −0.999144 0.0413586i \(-0.986831\pi\)
0.463755 0.885964i \(-0.346502\pi\)
\(278\) 1.38317 0.0829568
\(279\) 0 0
\(280\) 0 0
\(281\) −7.59774 + 4.38656i −0.453243 + 0.261680i −0.709199 0.705008i \(-0.750943\pi\)
0.255956 + 0.966688i \(0.417610\pi\)
\(282\) 0 0
\(283\) 18.7047 + 10.7991i 1.11188 + 0.641942i 0.939315 0.343056i \(-0.111462\pi\)
0.172562 + 0.984999i \(0.444796\pi\)
\(284\) −14.6223 8.44221i −0.867676 0.500953i
\(285\) 0 0
\(286\) 0.898724 0.518879i 0.0531427 0.0306819i
\(287\) 0 0
\(288\) 0 0
\(289\) 2.25120 0.132424
\(290\) 0.272131 + 0.471344i 0.0159801 + 0.0276783i
\(291\) 0 0
\(292\) 9.64756 + 5.57002i 0.564581 + 0.325961i
\(293\) −9.79756 + 16.9699i −0.572379 + 0.991390i 0.423942 + 0.905690i \(0.360646\pi\)
−0.996321 + 0.0857006i \(0.972687\pi\)
\(294\) 0 0
\(295\) −3.55755 6.16186i −0.207129 0.358758i
\(296\) 1.57601i 0.0916035i
\(297\) 0 0
\(298\) 0.651862 0.0377613
\(299\) 6.32983 + 10.9636i 0.366063 + 0.634040i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.279996 0.161656i −0.0161120 0.00930224i
\(303\) 0 0
\(304\) −17.7686 + 10.2587i −1.01910 + 0.588376i
\(305\) 6.94254i 0.397529i
\(306\) 0 0
\(307\) 27.7677i 1.58478i −0.610012 0.792392i \(-0.708835\pi\)
0.610012 0.792392i \(-0.291165\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.0385948 + 0.0668482i −0.00219204 + 0.00379672i
\(311\) 10.0080 17.3344i 0.567501 0.982941i −0.429311 0.903157i \(-0.641244\pi\)
0.996812 0.0797841i \(-0.0254231\pi\)
\(312\) 0 0
\(313\) −15.9654 + 9.21765i −0.902420 + 0.521012i −0.877984 0.478689i \(-0.841112\pi\)
−0.0244352 + 0.999701i \(0.507779\pi\)
\(314\) 1.59891 0.0902320
\(315\) 0 0
\(316\) 1.13680 0.0639498
\(317\) 12.5992 7.27416i 0.707642 0.408558i −0.102545 0.994728i \(-0.532699\pi\)
0.810187 + 0.586171i \(0.199365\pi\)
\(318\) 0 0
\(319\) 17.6644 30.5956i 0.989016 1.71303i
\(320\) 2.02322 3.50431i 0.113101 0.195897i
\(321\) 0 0
\(322\) 0 0
\(323\) 23.0212i 1.28093i
\(324\) 0 0
\(325\) 9.52166i 0.528167i
\(326\) −1.80406 + 1.04157i −0.0999176 + 0.0576874i
\(327\) 0 0
\(328\) −0.0840197 0.0485088i −0.00463921 0.00267845i
\(329\) 0 0
\(330\) 0 0
\(331\) 14.8446 + 25.7115i 0.815930 + 1.41323i 0.908658 + 0.417541i \(0.137108\pi\)
−0.0927274 + 0.995692i \(0.529559\pi\)
\(332\) 21.5452 1.18245
\(333\) 0 0
\(334\) 2.60850i 0.142731i
\(335\) −1.74183 3.01694i −0.0951664 0.164833i
\(336\) 0 0
\(337\) −4.60606 + 7.97793i −0.250908 + 0.434586i −0.963776 0.266713i \(-0.914063\pi\)
0.712868 + 0.701298i \(0.247396\pi\)
\(338\) 0.946163 + 0.546267i 0.0514645 + 0.0297130i
\(339\) 0 0
\(340\) −2.30555 3.99333i −0.125036 0.216569i
\(341\) 5.01049 0.271333
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34665 1.93219i 0.180439 0.104177i
\(345\) 0 0
\(346\) −2.17062 1.25321i −0.116693 0.0673728i
\(347\) −15.7313 9.08247i −0.844501 0.487573i 0.0142910 0.999898i \(-0.495451\pi\)
−0.858791 + 0.512325i \(0.828784\pi\)
\(348\) 0 0
\(349\) −5.70494 + 3.29375i −0.305378 + 0.176310i −0.644856 0.764304i \(-0.723083\pi\)
0.339478 + 0.940614i \(0.389750\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.11128 0.325732
\(353\) 10.4692 + 18.1332i 0.557221 + 0.965135i 0.997727 + 0.0673857i \(0.0214658\pi\)
−0.440506 + 0.897750i \(0.645201\pi\)
\(354\) 0 0
\(355\) 3.89994 + 2.25163i 0.206987 + 0.119504i
\(356\) 12.7774 22.1311i 0.677201 1.17295i
\(357\) 0 0
\(358\) 0.881317 + 1.52649i 0.0465791 + 0.0806773i
\(359\) 14.2265i 0.750845i 0.926854 + 0.375422i \(0.122502\pi\)
−0.926854 + 0.375422i \(0.877498\pi\)
\(360\) 0 0
\(361\) −8.52944 −0.448918
\(362\) 0.426560 + 0.738823i 0.0224195 + 0.0388317i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.57311 1.48559i −0.134683 0.0777591i
\(366\) 0 0
\(367\) 10.7237 6.19136i 0.559775 0.323186i −0.193280 0.981144i \(-0.561913\pi\)
0.753055 + 0.657957i \(0.228579\pi\)
\(368\) 24.5384i 1.27915i
\(369\) 0 0
\(370\) 0.209380i 0.0108851i
\(371\) 0 0
\(372\) 0 0
\(373\) 10.6559 18.4565i 0.551740 0.955642i −0.446409 0.894829i \(-0.647297\pi\)
0.998149 0.0608130i \(-0.0193693\pi\)
\(374\) 1.12849 1.95460i 0.0583527 0.101070i
\(375\) 0 0
\(376\) −4.21041 + 2.43088i −0.217135 + 0.125363i
\(377\) −16.9517 −0.873057
\(378\) 0 0
\(379\) 10.6001 0.544489 0.272244 0.962228i \(-0.412234\pi\)
0.272244 + 0.962228i \(0.412234\pi\)
\(380\) 4.77535 2.75705i 0.244970 0.141434i
\(381\) 0 0
\(382\) −0.662781 + 1.14797i −0.0339108 + 0.0587353i
\(383\) −6.32174 + 10.9496i −0.323026 + 0.559497i −0.981111 0.193446i \(-0.938033\pi\)
0.658085 + 0.752944i \(0.271367\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.28761i 0.0655375i
\(387\) 0 0
\(388\) 1.13179i 0.0574578i
\(389\) −11.4538 + 6.61286i −0.580732 + 0.335286i −0.761424 0.648254i \(-0.775499\pi\)
0.180692 + 0.983540i \(0.442166\pi\)
\(390\) 0 0
\(391\) 23.8442 + 13.7665i 1.20586 + 0.696201i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.949125 1.64393i −0.0478162 0.0828201i
\(395\) −0.303196 −0.0152554
\(396\) 0 0
\(397\) 24.7882i 1.24409i 0.782983 + 0.622043i \(0.213697\pi\)
−0.782983 + 0.622043i \(0.786303\pi\)
\(398\) −0.767582 1.32949i −0.0384754 0.0666413i
\(399\) 0 0
\(400\) 9.22800 15.9834i 0.461400 0.799168i
\(401\) −3.19615 1.84530i −0.159608 0.0921499i 0.418068 0.908416i \(-0.362707\pi\)
−0.577677 + 0.816266i \(0.696041\pi\)
\(402\) 0 0
\(403\) −1.20208 2.08207i −0.0598800 0.103715i
\(404\) −23.0880 −1.14867
\(405\) 0 0
\(406\) 0 0
\(407\) −11.7703 + 6.79556i −0.583430 + 0.336843i
\(408\) 0 0
\(409\) −16.0535 9.26852i −0.793797 0.458299i 0.0475008 0.998871i \(-0.484874\pi\)
−0.841297 + 0.540573i \(0.818208\pi\)
\(410\) 0.0111624 + 0.00644462i 0.000551272 + 0.000318277i
\(411\) 0 0
\(412\) −10.9971 + 6.34918i −0.541788 + 0.312802i
\(413\) 0 0
\(414\) 0 0
\(415\) −5.74635 −0.282077
\(416\) −1.46618 2.53949i −0.0718852 0.124509i
\(417\) 0 0
\(418\) 2.33737 + 1.34948i 0.114324 + 0.0660053i
\(419\) −1.46994 + 2.54600i −0.0718111 + 0.124380i −0.899695 0.436519i \(-0.856211\pi\)
0.827884 + 0.560899i \(0.189545\pi\)
\(420\) 0 0
\(421\) −14.1081 24.4359i −0.687585 1.19093i −0.972617 0.232415i \(-0.925337\pi\)
0.285031 0.958518i \(-0.407996\pi\)
\(422\) 0.293051i 0.0142655i
\(423\) 0 0
\(424\) −2.05624 −0.0998600
\(425\) −10.3541 17.9339i −0.502249 0.869921i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.435382 0.251368i −0.0210450 0.0121503i
\(429\) 0 0
\(430\) −0.444618 + 0.256700i −0.0214414 + 0.0123792i
\(431\) 6.76465i 0.325842i 0.986639 + 0.162921i \(0.0520915\pi\)
−0.986639 + 0.162921i \(0.947908\pi\)
\(432\) 0 0
\(433\) 28.3475i 1.36229i 0.732146 + 0.681147i \(0.238519\pi\)
−0.732146 + 0.681147i \(0.761481\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.8824 + 20.5810i −0.569066 + 0.985651i
\(437\) −16.4624 + 28.5137i −0.787503 + 1.36399i
\(438\) 0 0
\(439\) 22.8208 13.1756i 1.08918 0.628837i 0.155821 0.987785i \(-0.450198\pi\)
0.933358 + 0.358948i \(0.116864\pi\)
\(440\) −1.08527 −0.0517382
\(441\) 0 0
\(442\) −1.08296 −0.0515110
\(443\) 4.75958 2.74795i 0.226135 0.130559i −0.382653 0.923892i \(-0.624989\pi\)
0.608788 + 0.793333i \(0.291656\pi\)
\(444\) 0 0
\(445\) −3.40787 + 5.90261i −0.161549 + 0.279810i
\(446\) 0.171074 0.296309i 0.00810060 0.0140306i
\(447\) 0 0
\(448\) 0 0
\(449\) 7.38342i 0.348445i −0.984706 0.174223i \(-0.944259\pi\)
0.984706 0.174223i \(-0.0557412\pi\)
\(450\) 0 0
\(451\) 0.836659i 0.0393967i
\(452\) 8.50857 4.91242i 0.400209 0.231061i
\(453\) 0 0
\(454\) −0.301544 0.174097i −0.0141522 0.00817076i
\(455\) 0 0
\(456\) 0 0
\(457\) −20.7109 35.8724i −0.968817 1.67804i −0.698991 0.715130i \(-0.746367\pi\)
−0.269826 0.962909i \(-0.586966\pi\)
\(458\) 2.90256 0.135628
\(459\) 0 0
\(460\) 6.59477i 0.307483i
\(461\) −5.44638 9.43341i −0.253663 0.439357i 0.710868 0.703325i \(-0.248302\pi\)
−0.964532 + 0.263968i \(0.914969\pi\)
\(462\) 0 0
\(463\) −2.87980 + 4.98796i −0.133836 + 0.231810i −0.925152 0.379597i \(-0.876063\pi\)
0.791316 + 0.611407i \(0.209396\pi\)
\(464\) −28.4557 16.4289i −1.32102 0.762692i
\(465\) 0 0
\(466\) 1.14574 + 1.98448i 0.0530755 + 0.0919294i
\(467\) 23.8882 1.10541 0.552707 0.833376i \(-0.313595\pi\)
0.552707 + 0.833376i \(0.313595\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.559372 0.322954i 0.0258019 0.0148967i
\(471\) 0 0
\(472\) −5.67440 3.27612i −0.261185 0.150795i
\(473\) 28.8608 + 16.6628i 1.32702 + 0.766156i
\(474\) 0 0
\(475\) 21.4459 12.3818i 0.984005 0.568116i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.57406 0.0719956
\(479\) −0.947645 1.64137i −0.0432990 0.0749961i 0.843564 0.537029i \(-0.180453\pi\)
−0.886863 + 0.462033i \(0.847120\pi\)
\(480\) 0 0
\(481\) 5.64768 + 3.26069i 0.257512 + 0.148675i
\(482\) −0.257171 + 0.445434i −0.0117138 + 0.0202890i
\(483\) 0 0
\(484\) 6.62778 + 11.4797i 0.301263 + 0.521803i
\(485\) 0.301860i 0.0137067i
\(486\) 0 0
\(487\) 28.2248 1.27899 0.639494 0.768796i \(-0.279144\pi\)
0.639494 + 0.768796i \(0.279144\pi\)
\(488\) −3.19666 5.53677i −0.144706 0.250638i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.30250 + 1.32935i 0.103910 + 0.0599927i 0.551055 0.834469i \(-0.314226\pi\)
−0.447144 + 0.894462i \(0.647559\pi\)
\(492\) 0 0
\(493\) −31.9282 + 18.4338i −1.43797 + 0.830215i
\(494\) 1.29503i 0.0582663i
\(495\) 0 0
\(496\) 4.66003i 0.209242i
\(497\) 0 0
\(498\) 0 0
\(499\) 6.27844 10.8746i 0.281062 0.486813i −0.690585 0.723251i \(-0.742647\pi\)
0.971646 + 0.236438i \(0.0759801\pi\)
\(500\) −5.10739 + 8.84625i −0.228409 + 0.395617i
\(501\) 0 0
\(502\) −0.795278 + 0.459154i −0.0354950 + 0.0204930i
\(503\) −18.1502 −0.809278 −0.404639 0.914476i \(-0.632603\pi\)
−0.404639 + 0.914476i \(0.632603\pi\)
\(504\) 0 0
\(505\) 6.15782 0.274020
\(506\) 2.79546 1.61396i 0.124273 0.0717491i
\(507\) 0 0
\(508\) 3.65689 6.33391i 0.162248 0.281022i
\(509\) −9.33827 + 16.1744i −0.413912 + 0.716916i −0.995314 0.0967005i \(-0.969171\pi\)
0.581402 + 0.813617i \(0.302504\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 9.49685i 0.419705i
\(513\) 0 0
\(514\) 0.616519i 0.0271935i
\(515\) 2.93305 1.69340i 0.129245 0.0746199i
\(516\) 0 0
\(517\) −36.3096 20.9634i −1.59690 0.921968i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.260371 + 0.450975i 0.0114180 + 0.0197766i
\(521\) −18.0665 −0.791508 −0.395754 0.918357i \(-0.629517\pi\)
−0.395754 + 0.918357i \(0.629517\pi\)
\(522\) 0 0
\(523\) 21.1338i 0.924116i −0.886850 0.462058i \(-0.847111\pi\)
0.886850 0.462058i \(-0.152889\pi\)
\(524\) 5.41590 + 9.38061i 0.236595 + 0.409794i
\(525\) 0 0
\(526\) 0.865245 1.49865i 0.0377265 0.0653442i
\(527\) −4.52820 2.61436i −0.197252 0.113883i
\(528\) 0 0
\(529\) 8.18875 + 14.1833i 0.356033 + 0.616666i
\(530\) 0.273181 0.0118662
\(531\) 0 0
\(532\) 0 0
\(533\) −0.347667 + 0.200725i −0.0150591 + 0.00869439i
\(534\) 0 0
\(535\) 0.116121 + 0.0670425i 0.00502035 + 0.00289850i
\(536\) −2.77827 1.60403i −0.120003 0.0692837i
\(537\) 0 0
\(538\) 1.67164 0.965122i 0.0720695 0.0416093i
\(539\) 0 0
\(540\) 0 0
\(541\) 17.7732 0.764131 0.382065 0.924135i \(-0.375213\pi\)
0.382065 + 0.924135i \(0.375213\pi\)
\(542\) −1.02817 1.78084i −0.0441637 0.0764938i
\(543\) 0 0
\(544\) −5.52304 3.18873i −0.236798 0.136715i
\(545\) 3.16918 5.48918i 0.135753 0.235131i
\(546\) 0 0
\(547\) 14.1560 + 24.5190i 0.605268 + 1.04835i 0.992009 + 0.126166i \(0.0402673\pi\)
−0.386741 + 0.922188i \(0.626399\pi\)
\(548\) 3.20888i 0.137077i
\(549\) 0 0
\(550\) −2.42780 −0.103522
\(551\) −22.0437 38.1808i −0.939092 1.62655i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.88823 + 1.09017i 0.0802232 + 0.0463169i
\(555\) 0 0
\(556\) 19.4352 11.2209i 0.824234 0.475872i
\(557\) 11.7214i 0.496651i −0.968677 0.248326i \(-0.920120\pi\)
0.968677 0.248326i \(-0.0798803\pi\)
\(558\) 0 0
\(559\) 15.9905i 0.676326i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.536671 0.929541i 0.0226381 0.0392103i
\(563\) 18.3014 31.6990i 0.771314 1.33595i −0.165529 0.986205i \(-0.552933\pi\)
0.936843 0.349750i \(-0.113733\pi\)
\(564\) 0 0
\(565\) −2.26933 + 1.31020i −0.0954713 + 0.0551204i
\(566\) −2.64243 −0.111070
\(567\) 0 0
\(568\) 4.14701 0.174005
\(569\) −32.6468 + 18.8486i −1.36862 + 0.790176i −0.990752 0.135682i \(-0.956677\pi\)
−0.377872 + 0.925858i \(0.623344\pi\)
\(570\) 0 0
\(571\) −14.1123 + 24.4432i −0.590581 + 1.02292i 0.403574 + 0.914947i \(0.367768\pi\)
−0.994154 + 0.107968i \(0.965565\pi\)
\(572\) 8.41878 14.5817i 0.352007 0.609694i
\(573\) 0 0
\(574\) 0 0
\(575\) 29.6168i 1.23511i
\(576\) 0 0
\(577\) 9.38512i 0.390708i −0.980733 0.195354i \(-0.937414\pi\)
0.980733 0.195354i \(-0.0625855\pi\)
\(578\) −0.238523 + 0.137711i −0.00992123 + 0.00572802i
\(579\) 0 0
\(580\) 7.64754 + 4.41531i 0.317547 + 0.183336i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.86629 15.3569i −0.367204 0.636017i
\(584\) −2.73612 −0.113222
\(585\) 0 0
\(586\) 2.39735i 0.0990338i
\(587\) 23.1819 + 40.1523i 0.956821 + 1.65726i 0.730146 + 0.683291i \(0.239452\pi\)
0.226675 + 0.973971i \(0.427215\pi\)
\(588\) 0 0
\(589\) 3.12633 5.41496i 0.128818 0.223120i
\(590\) 0.753870 + 0.435247i 0.0310363 + 0.0179188i
\(591\) 0 0
\(592\) 6.32025 + 10.9470i 0.259761 + 0.449919i
\(593\) 18.1416 0.744986 0.372493 0.928035i \(-0.378503\pi\)
0.372493 + 0.928035i \(0.378503\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.15945 5.28821i 0.375186 0.216613i
\(597\) 0 0
\(598\) −1.34133 0.774419i −0.0548512 0.0316684i
\(599\) −6.02771 3.48010i −0.246286 0.142193i 0.371777 0.928322i \(-0.378749\pi\)
−0.618062 + 0.786129i \(0.712082\pi\)
\(600\) 0 0
\(601\) 2.08865 1.20588i 0.0851976 0.0491889i −0.456796 0.889572i \(-0.651003\pi\)
0.541994 + 0.840383i \(0.317670\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.24571 −0.213445
\(605\) −1.76770 3.06175i −0.0718673 0.124478i
\(606\) 0 0
\(607\) −11.0306 6.36850i −0.447717 0.258489i 0.259149 0.965837i \(-0.416558\pi\)
−0.706865 + 0.707348i \(0.749891\pi\)
\(608\) 3.81318 6.60462i 0.154645 0.267853i
\(609\) 0 0
\(610\) 0.424690 + 0.735585i 0.0171952 + 0.0297830i
\(611\) 20.1176i 0.813870i
\(612\) 0 0
\(613\) −10.3352 −0.417436 −0.208718 0.977976i \(-0.566929\pi\)
−0.208718 + 0.977976i \(0.566929\pi\)
\(614\) 1.69861 + 2.94208i 0.0685503 + 0.118733i
\(615\) 0 0
\(616\) 0 0
\(617\) 41.3741 + 23.8873i 1.66566 + 0.961668i 0.969937 + 0.243355i \(0.0782481\pi\)
0.695721 + 0.718313i \(0.255085\pi\)
\(618\) 0 0
\(619\) 35.2626 20.3588i 1.41732 0.818291i 0.421259 0.906940i \(-0.361588\pi\)
0.996063 + 0.0886491i \(0.0282550\pi\)
\(620\) 1.25240i 0.0502975i
\(621\) 0 0
\(622\) 2.44884i 0.0981897i
\(623\) 0 0
\(624\) 0 0
\(625\) −10.4371 + 18.0775i −0.417483 + 0.723101i
\(626\) 1.12773 1.95328i 0.0450731 0.0780689i
\(627\) 0 0
\(628\) 22.4667 12.9711i 0.896519 0.517605i
\(629\) 14.1831 0.565517
\(630\) 0 0
\(631\) 11.4782 0.456942 0.228471 0.973551i \(-0.426627\pi\)
0.228471 + 0.973551i \(0.426627\pi\)
\(632\) −0.241803 + 0.139605i −0.00961841 + 0.00555319i
\(633\) 0 0
\(634\) −0.889953 + 1.54144i −0.0353446 + 0.0612186i
\(635\) −0.975332 + 1.68932i −0.0387049 + 0.0670388i
\(636\) 0 0
\(637\) 0 0
\(638\) 4.32228i 0.171121i
\(639\) 0 0
\(640\) 2.03412i 0.0804057i
\(641\) 30.5823 17.6567i 1.20793 0.697398i 0.245622 0.969366i \(-0.421008\pi\)
0.962306 + 0.271968i \(0.0876744\pi\)
\(642\) 0 0
\(643\) 6.09416 + 3.51846i 0.240330 + 0.138755i 0.615328 0.788271i \(-0.289023\pi\)
−0.374998 + 0.927025i \(0.622357\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.40826 2.43917i −0.0554071 0.0959680i
\(647\) 14.9942 0.589482 0.294741 0.955577i \(-0.404767\pi\)
0.294741 + 0.955577i \(0.404767\pi\)
\(648\) 0 0
\(649\) 56.5050i 2.21801i
\(650\) 0.582461 + 1.00885i 0.0228460 + 0.0395704i
\(651\) 0 0
\(652\) −16.8995 + 29.2708i −0.661835 + 1.14633i
\(653\) −4.15597 2.39945i −0.162636 0.0938977i 0.416473 0.909148i \(-0.363266\pi\)
−0.579109 + 0.815250i \(0.696599\pi\)
\(654\) 0 0
\(655\) −1.44448 2.50191i −0.0564405 0.0977577i
\(656\) −0.778140 −0.0303812
\(657\) 0 0
\(658\) 0 0
\(659\) 13.4562 7.76893i 0.524179 0.302635i −0.214464 0.976732i \(-0.568800\pi\)
0.738643 + 0.674097i \(0.235467\pi\)
\(660\) 0 0
\(661\) 18.2131 + 10.5154i 0.708409 + 0.409000i 0.810472 0.585778i \(-0.199211\pi\)
−0.102062 + 0.994778i \(0.532544\pi\)
\(662\) −3.14566 1.81615i −0.122260 0.0705866i
\(663\) 0 0
\(664\) −4.58280 + 2.64588i −0.177847 + 0.102680i
\(665\) 0 0
\(666\) 0 0
\(667\) −52.7277 −2.04163
\(668\) −21.1614 36.6526i −0.818758 1.41813i
\(669\) 0 0
\(670\) 0.369106 + 0.213103i 0.0142598 + 0.00823290i
\(671\) 27.5673 47.7479i 1.06422 1.84329i
\(672\) 0 0
\(673\) 10.7194 + 18.5665i 0.413201 + 0.715686i 0.995238 0.0974770i \(-0.0310772\pi\)
−0.582036 + 0.813163i \(0.697744\pi\)
\(674\) 1.12705i 0.0434124i
\(675\) 0 0
\(676\) 17.7263 0.681781
\(677\) −9.03150 15.6430i −0.347109 0.601210i 0.638626 0.769517i \(-0.279503\pi\)
−0.985735 + 0.168308i \(0.946170\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.980808 + 0.566270i 0.0376123 + 0.0217155i
\(681\) 0 0
\(682\) −0.530878 + 0.306503i −0.0203284 + 0.0117366i
\(683\) 45.5647i 1.74349i −0.489963 0.871743i \(-0.662990\pi\)
0.489963 0.871743i \(-0.337010\pi\)
\(684\) 0 0
\(685\) 0.855844i 0.0327001i
\(686\) 0 0
\(687\) 0 0
\(688\) 15.4973 26.8422i 0.590830 1.02335i
\(689\) −4.25428 + 7.36863i −0.162075 + 0.280723i
\(690\) 0 0
\(691\) 3.33627 1.92620i 0.126918 0.0732760i −0.435197 0.900335i \(-0.643321\pi\)
0.562115 + 0.827059i \(0.309988\pi\)
\(692\) −40.6664 −1.54590
\(693\) 0 0
\(694\) 2.22238 0.0843604
\(695\) −5.18357 + 2.99273i −0.196624 + 0.113521i
\(696\) 0 0
\(697\) −0.436550 + 0.756126i −0.0165355 + 0.0286403i
\(698\) 0.402972 0.697967i 0.0152527 0.0264185i
\(699\) 0 0
\(700\) 0 0
\(701\) 46.5216i 1.75710i −0.477653 0.878549i \(-0.658512\pi\)
0.477653 0.878549i \(-0.341488\pi\)
\(702\) 0 0
\(703\) 16.9606i 0.639680i
\(704\) 27.8297 16.0675i 1.04887 0.605566i
\(705\) 0 0
\(706\) −2.21850 1.28085i −0.0834944 0.0482055i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.6187 + 25.3203i 0.549017 + 0.950925i 0.998342 + 0.0575566i \(0.0183310\pi\)
−0.449326 + 0.893368i \(0.648336\pi\)
\(710\) −0.550949 −0.0206767
\(711\) 0 0
\(712\) 6.27655i 0.235224i
\(713\) −3.73904 6.47621i −0.140028 0.242536i
\(714\) 0 0
\(715\) −2.24538 + 3.88911i −0.0839724 + 0.145445i
\(716\) 24.7672 + 14.2993i 0.925592 + 0.534391i
\(717\) 0 0
\(718\) −0.870265 1.50734i −0.0324780 0.0562536i
\(719\) −3.37122 −0.125725 −0.0628627 0.998022i \(-0.520023\pi\)
−0.0628627 + 0.998022i \(0.520023\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.903723 0.521765i 0.0336331 0.0194181i
\(723\) 0 0
\(724\) 11.9874 + 6.92091i 0.445507 + 0.257214i
\(725\) 34.3448 + 19.8290i 1.27553 + 0.736429i
\(726\) 0 0
\(727\) −4.34397 + 2.50799i −0.161109 + 0.0930164i −0.578387 0.815763i \(-0.696318\pi\)
0.417278 + 0.908779i \(0.362984\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.363506 0.0134540
\(731\) −17.3885 30.1178i −0.643138 1.11395i
\(732\) 0 0
\(733\) 19.6875 + 11.3666i 0.727175 + 0.419835i 0.817388 0.576088i \(-0.195421\pi\)
−0.0902126 + 0.995923i \(0.528755\pi\)
\(734\) −0.757478 + 1.31199i −0.0279590 + 0.0484265i
\(735\) 0 0
\(736\) −4.56050 7.89901i −0.168102 0.291162i
\(737\) 27.6657i 1.01908i
\(738\) 0 0
\(739\) −2.39022 −0.0879256 −0.0439628 0.999033i \(-0.513998\pi\)
−0.0439628 + 0.999033i \(0.513998\pi\)
\(740\) −1.69859 2.94204i −0.0624413 0.108151i
\(741\) 0 0
\(742\) 0 0
\(743\) 36.1039 + 20.8446i 1.32453 + 0.764715i 0.984447 0.175682i \(-0.0562131\pi\)
0.340078 + 0.940397i \(0.389546\pi\)
\(744\) 0 0
\(745\) −2.44292 + 1.41042i −0.0895018 + 0.0516739i
\(746\) 2.60737i 0.0954627i
\(747\) 0 0
\(748\) 36.6193i 1.33893i
\(749\) 0 0
\(750\) 0 0
\(751\) −13.2710 + 22.9861i −0.484267 + 0.838775i −0.999837 0.0180728i \(-0.994247\pi\)
0.515570 + 0.856848i \(0.327580\pi\)
\(752\) −19.4971 + 33.7700i −0.710987 + 1.23147i
\(753\) 0 0
\(754\) 1.79609 1.03697i 0.0654097 0.0377643i
\(755\) 1.39909 0.0509180
\(756\) 0 0
\(757\) 20.3580 0.739923 0.369961 0.929047i \(-0.379371\pi\)
0.369961 + 0.929047i \(0.379371\pi\)
\(758\) −1.12311 + 0.648430i −0.0407933 + 0.0235520i
\(759\) 0 0
\(760\) −0.677163 + 1.17288i −0.0245633 + 0.0425448i
\(761\) 12.9578 22.4436i 0.469720 0.813578i −0.529681 0.848197i \(-0.677688\pi\)
0.999401 + 0.0346186i \(0.0110217\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.5072i 0.778102i
\(765\) 0 0
\(766\) 1.54686i 0.0558903i
\(767\) −23.4802 + 13.5563i −0.847821 + 0.489489i
\(768\) 0 0
\(769\) 18.8269 + 10.8697i 0.678914 + 0.391971i 0.799446 0.600738i \(-0.205127\pi\)
−0.120532 + 0.992709i \(0.538460\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.4457 18.0925i −0.375948 0.651162i
\(773\) 20.3213 0.730905 0.365453 0.930830i \(-0.380914\pi\)
0.365453 + 0.930830i \(0.380914\pi\)
\(774\) 0 0
\(775\) 5.62446i 0.202037i
\(776\) −0.138990 0.240738i −0.00498945 0.00864197i
\(777\) 0 0
\(778\) 0.809047 1.40131i 0.0290058 0.0502394i
\(779\) −0.904199 0.522039i −0.0323963 0.0187040i
\(780\) 0 0
\(781\) 17.8814 + 30.9715i 0.639848 + 1.10825i
\(782\) −3.36851 −0.120458
\(783\) 0 0
\(784\) 0 0
\(785\) −5.99211 + 3.45955i −0.213868 + 0.123477i
\(786\) 0 0
\(787\) 16.4065 + 9.47232i 0.584830 + 0.337652i 0.763051 0.646339i \(-0.223701\pi\)
−0.178221 + 0.983991i \(0.557034\pi\)
\(788\) −26.6727 15.3995i −0.950176 0.548584i
\(789\) 0 0
\(790\) 0.0321246 0.0185472i 0.00114294 0.000659879i
\(791\) 0 0
\(792\) 0 0
\(793\) −26.4550 −0.939445
\(794\) −1.51635 2.62640i −0.0538133 0.0932074i
\(795\) 0 0