Properties

Label 1456.2.r.p.625.4
Level $1456$
Weight $2$
Character 1456.625
Analytic conductor $11.626$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.4
Root \(1.50426 - 2.60546i\) of defining polynomial
Character \(\chi\) \(=\) 1456.625
Dual form 1456.2.r.p.417.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.879528 + 1.52339i) q^{3} +(-0.452861 + 0.784378i) q^{5} +(-0.237709 - 2.63505i) q^{7} +(-0.0471392 + 0.0816475i) q^{9} +O(q^{10})\) \(q+(0.879528 + 1.52339i) q^{3} +(-0.452861 + 0.784378i) q^{5} +(-0.237709 - 2.63505i) q^{7} +(-0.0471392 + 0.0816475i) q^{9} +(0.358181 + 0.620387i) q^{11} +1.00000 q^{13} -1.59322 q^{15} +(-1.17614 - 2.03713i) q^{17} +(3.31796 - 5.74687i) q^{19} +(3.80513 - 2.67972i) q^{21} +(1.87953 - 3.25544i) q^{23} +(2.08983 + 3.61970i) q^{25} +5.11133 q^{27} +3.25799 q^{29} +(0.785250 + 1.36009i) q^{31} +(-0.630060 + 1.09130i) q^{33} +(2.17452 + 1.00686i) q^{35} +(-2.60441 + 4.51098i) q^{37} +(0.879528 + 1.52339i) q^{39} +4.92168 q^{41} +9.43766 q^{43} +(-0.0426950 - 0.0739499i) q^{45} +(-4.15993 + 7.20521i) q^{47} +(-6.88699 + 1.25275i) q^{49} +(2.06889 - 3.58342i) q^{51} +(-7.04163 - 12.1965i) q^{53} -0.648824 q^{55} +11.6729 q^{57} +(0.358181 + 0.620387i) q^{59} +(5.82633 - 10.0915i) q^{61} +(0.226351 + 0.104806i) q^{63} +(-0.452861 + 0.784378i) q^{65} +(4.69587 + 8.13349i) q^{67} +6.61239 q^{69} -10.9914 q^{71} +(1.73650 + 3.00771i) q^{73} +(-3.67614 + 6.36725i) q^{75} +(1.54961 - 1.09130i) q^{77} +(6.50408 - 11.2654i) q^{79} +(4.63697 + 8.03147i) q^{81} -3.54083 q^{83} +2.13050 q^{85} +(2.86550 + 4.96318i) q^{87} +(-6.02503 + 10.4357i) q^{89} +(-0.237709 - 2.63505i) q^{91} +(-1.38130 + 2.39248i) q^{93} +(3.00514 + 5.20506i) q^{95} +7.43766 q^{97} -0.0675374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 0.879528 + 1.52339i 0.507796 + 0.879528i 0.999959 + 0.00902528i \(0.00287288\pi\)
−0.492164 + 0.870503i \(0.663794\pi\)
\(4\) 0 0
\(5\) −0.452861 + 0.784378i −0.202526 + 0.350784i −0.949342 0.314246i \(-0.898248\pi\)
0.746816 + 0.665031i \(0.231582\pi\)
\(6\) 0 0
\(7\) −0.237709 2.63505i −0.0898454 0.995956i
\(8\) 0 0
\(9\) −0.0471392 + 0.0816475i −0.0157131 + 0.0272158i
\(10\) 0 0
\(11\) 0.358181 + 0.620387i 0.107996 + 0.187054i 0.914958 0.403549i \(-0.132223\pi\)
−0.806963 + 0.590603i \(0.798890\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.59322 −0.411366
\(16\) 0 0
\(17\) −1.17614 2.03713i −0.285255 0.494076i 0.687416 0.726264i \(-0.258745\pi\)
−0.972671 + 0.232188i \(0.925412\pi\)
\(18\) 0 0
\(19\) 3.31796 5.74687i 0.761191 1.31842i −0.181046 0.983475i \(-0.557948\pi\)
0.942237 0.334947i \(-0.108718\pi\)
\(20\) 0 0
\(21\) 3.80513 2.67972i 0.830348 0.584764i
\(22\) 0 0
\(23\) 1.87953 3.25544i 0.391909 0.678806i −0.600793 0.799405i \(-0.705148\pi\)
0.992701 + 0.120599i \(0.0384816\pi\)
\(24\) 0 0
\(25\) 2.08983 + 3.61970i 0.417967 + 0.723940i
\(26\) 0 0
\(27\) 5.11133 0.983675
\(28\) 0 0
\(29\) 3.25799 0.604994 0.302497 0.953150i \(-0.402180\pi\)
0.302497 + 0.953150i \(0.402180\pi\)
\(30\) 0 0
\(31\) 0.785250 + 1.36009i 0.141035 + 0.244280i 0.927887 0.372862i \(-0.121624\pi\)
−0.786852 + 0.617142i \(0.788290\pi\)
\(32\) 0 0
\(33\) −0.630060 + 1.09130i −0.109679 + 0.189970i
\(34\) 0 0
\(35\) 2.17452 + 1.00686i 0.367562 + 0.170190i
\(36\) 0 0
\(37\) −2.60441 + 4.51098i −0.428163 + 0.741600i −0.996710 0.0810508i \(-0.974172\pi\)
0.568547 + 0.822651i \(0.307506\pi\)
\(38\) 0 0
\(39\) 0.879528 + 1.52339i 0.140837 + 0.243937i
\(40\) 0 0
\(41\) 4.92168 0.768637 0.384318 0.923201i \(-0.374437\pi\)
0.384318 + 0.923201i \(0.374437\pi\)
\(42\) 0 0
\(43\) 9.43766 1.43923 0.719615 0.694373i \(-0.244318\pi\)
0.719615 + 0.694373i \(0.244318\pi\)
\(44\) 0 0
\(45\) −0.0426950 0.0739499i −0.00636459 0.0110238i
\(46\) 0 0
\(47\) −4.15993 + 7.20521i −0.606788 + 1.05099i 0.384978 + 0.922926i \(0.374209\pi\)
−0.991766 + 0.128062i \(0.959124\pi\)
\(48\) 0 0
\(49\) −6.88699 + 1.25275i −0.983856 + 0.178964i
\(50\) 0 0
\(51\) 2.06889 3.58342i 0.289702 0.501779i
\(52\) 0 0
\(53\) −7.04163 12.1965i −0.967243 1.67531i −0.703465 0.710729i \(-0.748365\pi\)
−0.263777 0.964584i \(-0.584968\pi\)
\(54\) 0 0
\(55\) −0.648824 −0.0874874
\(56\) 0 0
\(57\) 11.6729 1.54612
\(58\) 0 0
\(59\) 0.358181 + 0.620387i 0.0466311 + 0.0807675i 0.888399 0.459072i \(-0.151818\pi\)
−0.841768 + 0.539840i \(0.818485\pi\)
\(60\) 0 0
\(61\) 5.82633 10.0915i 0.745986 1.29208i −0.203747 0.979024i \(-0.565312\pi\)
0.949733 0.313061i \(-0.101355\pi\)
\(62\) 0 0
\(63\) 0.226351 + 0.104806i 0.0285175 + 0.0132043i
\(64\) 0 0
\(65\) −0.452861 + 0.784378i −0.0561705 + 0.0972901i
\(66\) 0 0
\(67\) 4.69587 + 8.13349i 0.573692 + 0.993664i 0.996182 + 0.0872964i \(0.0278227\pi\)
−0.422490 + 0.906367i \(0.638844\pi\)
\(68\) 0 0
\(69\) 6.61239 0.796038
\(70\) 0 0
\(71\) −10.9914 −1.30444 −0.652220 0.758030i \(-0.726162\pi\)
−0.652220 + 0.758030i \(0.726162\pi\)
\(72\) 0 0
\(73\) 1.73650 + 3.00771i 0.203242 + 0.352025i 0.949571 0.313552i \(-0.101519\pi\)
−0.746329 + 0.665577i \(0.768186\pi\)
\(74\) 0 0
\(75\) −3.67614 + 6.36725i −0.424484 + 0.735227i
\(76\) 0 0
\(77\) 1.54961 1.09130i 0.176594 0.124365i
\(78\) 0 0
\(79\) 6.50408 11.2654i 0.731766 1.26746i −0.224361 0.974506i \(-0.572030\pi\)
0.956128 0.292950i \(-0.0946370\pi\)
\(80\) 0 0
\(81\) 4.63697 + 8.03147i 0.515219 + 0.892386i
\(82\) 0 0
\(83\) −3.54083 −0.388656 −0.194328 0.980937i \(-0.562253\pi\)
−0.194328 + 0.980937i \(0.562253\pi\)
\(84\) 0 0
\(85\) 2.13050 0.231085
\(86\) 0 0
\(87\) 2.86550 + 4.96318i 0.307213 + 0.532109i
\(88\) 0 0
\(89\) −6.02503 + 10.4357i −0.638651 + 1.10618i 0.347077 + 0.937836i \(0.387174\pi\)
−0.985729 + 0.168340i \(0.946159\pi\)
\(90\) 0 0
\(91\) −0.237709 2.63505i −0.0249186 0.276228i
\(92\) 0 0
\(93\) −1.38130 + 2.39248i −0.143234 + 0.248088i
\(94\) 0 0
\(95\) 3.00514 + 5.20506i 0.308321 + 0.534028i
\(96\) 0 0
\(97\) 7.43766 0.755180 0.377590 0.925973i \(-0.376753\pi\)
0.377590 + 0.925973i \(0.376753\pi\)
\(98\) 0 0
\(99\) −0.0675374 −0.00678776
\(100\) 0 0
\(101\) 0.599526 + 1.03841i 0.0596551 + 0.103326i 0.894311 0.447447i \(-0.147667\pi\)
−0.834656 + 0.550772i \(0.814333\pi\)
\(102\) 0 0
\(103\) −7.20615 + 12.4814i −0.710043 + 1.22983i 0.254797 + 0.966995i \(0.417991\pi\)
−0.964840 + 0.262837i \(0.915342\pi\)
\(104\) 0 0
\(105\) 0.378721 + 4.19820i 0.0369594 + 0.409703i
\(106\) 0 0
\(107\) 6.79661 11.7721i 0.657053 1.13805i −0.324322 0.945947i \(-0.605136\pi\)
0.981375 0.192102i \(-0.0615305\pi\)
\(108\) 0 0
\(109\) 6.86241 + 11.8860i 0.657299 + 1.13848i 0.981312 + 0.192423i \(0.0616346\pi\)
−0.324013 + 0.946053i \(0.605032\pi\)
\(110\) 0 0
\(111\) −9.16262 −0.869677
\(112\) 0 0
\(113\) −3.25799 −0.306486 −0.153243 0.988189i \(-0.548972\pi\)
−0.153243 + 0.988189i \(0.548972\pi\)
\(114\) 0 0
\(115\) 1.70233 + 2.94852i 0.158743 + 0.274951i
\(116\) 0 0
\(117\) −0.0471392 + 0.0816475i −0.00435802 + 0.00754831i
\(118\) 0 0
\(119\) −5.08836 + 3.58342i −0.466449 + 0.328492i
\(120\) 0 0
\(121\) 5.24341 9.08186i 0.476674 0.825623i
\(122\) 0 0
\(123\) 4.32875 + 7.49762i 0.390310 + 0.676037i
\(124\) 0 0
\(125\) −8.31422 −0.743647
\(126\) 0 0
\(127\) 0.950834 0.0843729 0.0421865 0.999110i \(-0.486568\pi\)
0.0421865 + 0.999110i \(0.486568\pi\)
\(128\) 0 0
\(129\) 8.30069 + 14.3772i 0.730835 + 1.26584i
\(130\) 0 0
\(131\) −9.40980 + 16.2983i −0.822138 + 1.42399i 0.0819487 + 0.996637i \(0.473886\pi\)
−0.904087 + 0.427349i \(0.859448\pi\)
\(132\) 0 0
\(133\) −15.9320 7.37690i −1.38148 0.639658i
\(134\) 0 0
\(135\) −2.31472 + 4.00921i −0.199219 + 0.345058i
\(136\) 0 0
\(137\) −3.09090 5.35359i −0.264073 0.457388i 0.703247 0.710945i \(-0.251733\pi\)
−0.967320 + 0.253557i \(0.918399\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −14.6351 −1.23250
\(142\) 0 0
\(143\) 0.358181 + 0.620387i 0.0299526 + 0.0518794i
\(144\) 0 0
\(145\) −1.47542 + 2.55550i −0.122527 + 0.212223i
\(146\) 0 0
\(147\) −7.96572 9.38972i −0.657002 0.774451i
\(148\) 0 0
\(149\) 10.5385 18.2533i 0.863351 1.49537i −0.00532425 0.999986i \(-0.501695\pi\)
0.868675 0.495382i \(-0.164972\pi\)
\(150\) 0 0
\(151\) −7.86171 13.6169i −0.639777 1.10813i −0.985481 0.169783i \(-0.945693\pi\)
0.345704 0.938344i \(-0.387640\pi\)
\(152\) 0 0
\(153\) 0.221768 0.0179289
\(154\) 0 0
\(155\) −1.42244 −0.114253
\(156\) 0 0
\(157\) 3.89250 + 6.74200i 0.310655 + 0.538070i 0.978504 0.206226i \(-0.0661183\pi\)
−0.667849 + 0.744297i \(0.732785\pi\)
\(158\) 0 0
\(159\) 12.3866 21.4543i 0.982323 1.70143i
\(160\) 0 0
\(161\) −9.02503 4.17881i −0.711272 0.329336i
\(162\) 0 0
\(163\) 0.844956 1.46351i 0.0661820 0.114631i −0.831036 0.556219i \(-0.812252\pi\)
0.897218 + 0.441588i \(0.145585\pi\)
\(164\) 0 0
\(165\) −0.570659 0.988410i −0.0444257 0.0769476i
\(166\) 0 0
\(167\) 21.8667 1.69210 0.846049 0.533105i \(-0.178975\pi\)
0.846049 + 0.533105i \(0.178975\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.312812 + 0.541805i 0.0239213 + 0.0414329i
\(172\) 0 0
\(173\) −2.92061 + 5.05865i −0.222050 + 0.384602i −0.955430 0.295217i \(-0.904608\pi\)
0.733380 + 0.679819i \(0.237942\pi\)
\(174\) 0 0
\(175\) 9.04132 6.36725i 0.683460 0.481319i
\(176\) 0 0
\(177\) −0.630060 + 1.09130i −0.0473582 + 0.0820268i
\(178\) 0 0
\(179\) 1.26714 + 2.19475i 0.0947103 + 0.164043i 0.909488 0.415731i \(-0.136474\pi\)
−0.814777 + 0.579774i \(0.803141\pi\)
\(180\) 0 0
\(181\) −10.7248 −0.797169 −0.398585 0.917132i \(-0.630498\pi\)
−0.398585 + 0.917132i \(0.630498\pi\)
\(182\) 0 0
\(183\) 20.4977 1.51523
\(184\) 0 0
\(185\) −2.35887 4.08569i −0.173428 0.300386i
\(186\) 0 0
\(187\) 0.842538 1.45932i 0.0616125 0.106716i
\(188\) 0 0
\(189\) −1.21501 13.4686i −0.0883787 0.979697i
\(190\) 0 0
\(191\) −0.839303 + 1.45371i −0.0607298 + 0.105187i −0.894792 0.446484i \(-0.852676\pi\)
0.834062 + 0.551671i \(0.186009\pi\)
\(192\) 0 0
\(193\) 3.22408 + 5.58427i 0.232074 + 0.401964i 0.958418 0.285367i \(-0.0921154\pi\)
−0.726344 + 0.687331i \(0.758782\pi\)
\(194\) 0 0
\(195\) −1.59322 −0.114093
\(196\) 0 0
\(197\) 1.87251 0.133411 0.0667054 0.997773i \(-0.478751\pi\)
0.0667054 + 0.997773i \(0.478751\pi\)
\(198\) 0 0
\(199\) −5.69833 9.86979i −0.403944 0.699651i 0.590254 0.807217i \(-0.299028\pi\)
−0.994198 + 0.107566i \(0.965694\pi\)
\(200\) 0 0
\(201\) −8.26030 + 14.3073i −0.582637 + 1.00916i
\(202\) 0 0
\(203\) −0.774453 8.58498i −0.0543559 0.602547i
\(204\) 0 0
\(205\) −2.22883 + 3.86045i −0.155669 + 0.269626i
\(206\) 0 0
\(207\) 0.177199 + 0.306918i 0.0123162 + 0.0213322i
\(208\) 0 0
\(209\) 4.75371 0.328821
\(210\) 0 0
\(211\) −7.53599 −0.518799 −0.259400 0.965770i \(-0.583525\pi\)
−0.259400 + 0.965770i \(0.583525\pi\)
\(212\) 0 0
\(213\) −9.66725 16.7442i −0.662389 1.14729i
\(214\) 0 0
\(215\) −4.27395 + 7.40269i −0.291481 + 0.504859i
\(216\) 0 0
\(217\) 3.39725 2.39248i 0.230621 0.162412i
\(218\) 0 0
\(219\) −3.05460 + 5.29072i −0.206411 + 0.357514i
\(220\) 0 0
\(221\) −1.17614 2.03713i −0.0791154 0.137032i
\(222\) 0 0
\(223\) −17.6349 −1.18092 −0.590459 0.807067i \(-0.701053\pi\)
−0.590459 + 0.807067i \(0.701053\pi\)
\(224\) 0 0
\(225\) −0.394052 −0.0262702
\(226\) 0 0
\(227\) −2.66452 4.61509i −0.176851 0.306314i 0.763950 0.645276i \(-0.223258\pi\)
−0.940800 + 0.338962i \(0.889924\pi\)
\(228\) 0 0
\(229\) 4.25950 7.37767i 0.281476 0.487530i −0.690273 0.723549i \(-0.742509\pi\)
0.971748 + 0.236019i \(0.0758428\pi\)
\(230\) 0 0
\(231\) 3.02539 + 1.40083i 0.199056 + 0.0921678i
\(232\) 0 0
\(233\) −2.37685 + 4.11683i −0.155713 + 0.269703i −0.933318 0.359050i \(-0.883101\pi\)
0.777605 + 0.628752i \(0.216434\pi\)
\(234\) 0 0
\(235\) −3.76774 6.52592i −0.245780 0.425704i
\(236\) 0 0
\(237\) 22.8821 1.48635
\(238\) 0 0
\(239\) −14.8314 −0.959365 −0.479682 0.877442i \(-0.659248\pi\)
−0.479682 + 0.877442i \(0.659248\pi\)
\(240\) 0 0
\(241\) 3.06066 + 5.30121i 0.197154 + 0.341481i 0.947605 0.319446i \(-0.103497\pi\)
−0.750450 + 0.660927i \(0.770163\pi\)
\(242\) 0 0
\(243\) −0.489705 + 0.848195i −0.0314146 + 0.0544117i
\(244\) 0 0
\(245\) 2.13622 5.96932i 0.136478 0.381366i
\(246\) 0 0
\(247\) 3.31796 5.74687i 0.211116 0.365664i
\(248\) 0 0
\(249\) −3.11426 5.39405i −0.197358 0.341834i
\(250\) 0 0
\(251\) 13.9708 0.881832 0.440916 0.897548i \(-0.354654\pi\)
0.440916 + 0.897548i \(0.354654\pi\)
\(252\) 0 0
\(253\) 2.69284 0.169298
\(254\) 0 0
\(255\) 1.87384 + 3.24558i 0.117344 + 0.203246i
\(256\) 0 0
\(257\) −8.63253 + 14.9520i −0.538482 + 0.932679i 0.460504 + 0.887658i \(0.347669\pi\)
−0.998986 + 0.0450210i \(0.985665\pi\)
\(258\) 0 0
\(259\) 12.5057 + 5.79047i 0.777069 + 0.359802i
\(260\) 0 0
\(261\) −0.153579 + 0.266007i −0.00950631 + 0.0164654i
\(262\) 0 0
\(263\) −1.30336 2.25749i −0.0803687 0.139203i 0.823040 0.567984i \(-0.192276\pi\)
−0.903408 + 0.428781i \(0.858943\pi\)
\(264\) 0 0
\(265\) 12.7555 0.783565
\(266\) 0 0
\(267\) −21.1967 −1.29722
\(268\) 0 0
\(269\) 7.24477 + 12.5483i 0.441721 + 0.765084i 0.997817 0.0660343i \(-0.0210347\pi\)
−0.556096 + 0.831118i \(0.687701\pi\)
\(270\) 0 0
\(271\) −4.31796 + 7.47892i −0.262297 + 0.454312i −0.966852 0.255338i \(-0.917813\pi\)
0.704555 + 0.709650i \(0.251147\pi\)
\(272\) 0 0
\(273\) 3.80513 2.67972i 0.230297 0.162184i
\(274\) 0 0
\(275\) −1.49708 + 2.59301i −0.0902771 + 0.156364i
\(276\) 0 0
\(277\) −6.11349 10.5889i −0.367324 0.636223i 0.621822 0.783158i \(-0.286393\pi\)
−0.989146 + 0.146935i \(0.953059\pi\)
\(278\) 0 0
\(279\) −0.148064 −0.00886437
\(280\) 0 0
\(281\) −24.1822 −1.44259 −0.721293 0.692630i \(-0.756452\pi\)
−0.721293 + 0.692630i \(0.756452\pi\)
\(282\) 0 0
\(283\) −15.3842 26.6461i −0.914493 1.58395i −0.807642 0.589674i \(-0.799256\pi\)
−0.106851 0.994275i \(-0.534077\pi\)
\(284\) 0 0
\(285\) −5.28622 + 9.15599i −0.313128 + 0.542354i
\(286\) 0 0
\(287\) −1.16992 12.9689i −0.0690585 0.765528i
\(288\) 0 0
\(289\) 5.73341 9.93056i 0.337259 0.584150i
\(290\) 0 0
\(291\) 6.54163 + 11.3304i 0.383477 + 0.664202i
\(292\) 0 0
\(293\) −31.8295 −1.85950 −0.929749 0.368193i \(-0.879976\pi\)
−0.929749 + 0.368193i \(0.879976\pi\)
\(294\) 0 0
\(295\) −0.648824 −0.0377760
\(296\) 0 0
\(297\) 1.83078 + 3.17100i 0.106233 + 0.184000i
\(298\) 0 0
\(299\) 1.87953 3.25544i 0.108696 0.188267i
\(300\) 0 0
\(301\) −2.24341 24.8687i −0.129308 1.43341i
\(302\) 0 0
\(303\) −1.05460 + 1.82662i −0.0605852 + 0.104937i
\(304\) 0 0
\(305\) 5.27704 + 9.14010i 0.302162 + 0.523360i
\(306\) 0 0
\(307\) −28.7884 −1.64304 −0.821520 0.570179i \(-0.806874\pi\)
−0.821520 + 0.570179i \(0.806874\pi\)
\(308\) 0 0
\(309\) −25.3521 −1.44223
\(310\) 0 0
\(311\) 2.75931 + 4.77927i 0.156466 + 0.271007i 0.933592 0.358338i \(-0.116656\pi\)
−0.777126 + 0.629345i \(0.783323\pi\)
\(312\) 0 0
\(313\) 2.42399 4.19848i 0.137012 0.237312i −0.789352 0.613941i \(-0.789583\pi\)
0.926364 + 0.376629i \(0.122917\pi\)
\(314\) 0 0
\(315\) −0.184713 + 0.130082i −0.0104074 + 0.00732929i
\(316\) 0 0
\(317\) 3.82756 6.62952i 0.214977 0.372351i −0.738288 0.674485i \(-0.764366\pi\)
0.953265 + 0.302134i \(0.0976990\pi\)
\(318\) 0 0
\(319\) 1.16695 + 2.02122i 0.0653366 + 0.113166i
\(320\) 0 0
\(321\) 23.9112 1.33459
\(322\) 0 0
\(323\) −15.6095 −0.868534
\(324\) 0 0
\(325\) 2.08983 + 3.61970i 0.115923 + 0.200785i
\(326\) 0 0
\(327\) −12.0714 + 20.9082i −0.667548 + 1.15623i
\(328\) 0 0
\(329\) 19.9750 + 9.24889i 1.10125 + 0.509908i
\(330\) 0 0
\(331\) 5.67159 9.82348i 0.311739 0.539947i −0.667000 0.745058i \(-0.732422\pi\)
0.978739 + 0.205110i \(0.0657553\pi\)
\(332\) 0 0
\(333\) −0.245540 0.425288i −0.0134555 0.0233056i
\(334\) 0 0
\(335\) −8.50631 −0.464749
\(336\) 0 0
\(337\) 1.74149 0.0948649 0.0474324 0.998874i \(-0.484896\pi\)
0.0474324 + 0.998874i \(0.484896\pi\)
\(338\) 0 0
\(339\) −2.86550 4.96318i −0.155632 0.269563i
\(340\) 0 0
\(341\) −0.562522 + 0.974317i −0.0304623 + 0.0527622i
\(342\) 0 0
\(343\) 4.93815 + 17.8498i 0.266635 + 0.963798i
\(344\) 0 0
\(345\) −2.99449 + 5.18661i −0.161218 + 0.279238i
\(346\) 0 0
\(347\) 10.5251 + 18.2301i 0.565019 + 0.978641i 0.997048 + 0.0767814i \(0.0244643\pi\)
−0.432029 + 0.901860i \(0.642202\pi\)
\(348\) 0 0
\(349\) −8.35601 −0.447287 −0.223643 0.974671i \(-0.571795\pi\)
−0.223643 + 0.974671i \(0.571795\pi\)
\(350\) 0 0
\(351\) 5.11133 0.272822
\(352\) 0 0
\(353\) 4.26677 + 7.39027i 0.227097 + 0.393344i 0.956947 0.290264i \(-0.0937431\pi\)
−0.729849 + 0.683608i \(0.760410\pi\)
\(354\) 0 0
\(355\) 4.97758 8.62141i 0.264182 0.457577i
\(356\) 0 0
\(357\) −9.93429 4.59982i −0.525778 0.243448i
\(358\) 0 0
\(359\) −8.08565 + 14.0047i −0.426744 + 0.739142i −0.996582 0.0826150i \(-0.973673\pi\)
0.569837 + 0.821757i \(0.307006\pi\)
\(360\) 0 0
\(361\) −12.5177 21.6812i −0.658824 1.14112i
\(362\) 0 0
\(363\) 18.4469 0.968212
\(364\) 0 0
\(365\) −3.14557 −0.164647
\(366\) 0 0
\(367\) 14.0770 + 24.3821i 0.734813 + 1.27273i 0.954805 + 0.297232i \(0.0960636\pi\)
−0.219992 + 0.975502i \(0.570603\pi\)
\(368\) 0 0
\(369\) −0.232004 + 0.401842i −0.0120776 + 0.0209191i
\(370\) 0 0
\(371\) −30.4644 + 21.4543i −1.58164 + 1.11385i
\(372\) 0 0
\(373\) 14.2518 24.6849i 0.737932 1.27814i −0.215493 0.976505i \(-0.569136\pi\)
0.953425 0.301630i \(-0.0975308\pi\)
\(374\) 0 0
\(375\) −7.31259 12.6658i −0.377621 0.654058i
\(376\) 0 0
\(377\) 3.25799 0.167795
\(378\) 0 0
\(379\) 7.26263 0.373056 0.186528 0.982450i \(-0.440276\pi\)
0.186528 + 0.982450i \(0.440276\pi\)
\(380\) 0 0
\(381\) 0.836286 + 1.44849i 0.0428442 + 0.0742083i
\(382\) 0 0
\(383\) 6.46627 11.1999i 0.330411 0.572289i −0.652181 0.758063i \(-0.726146\pi\)
0.982592 + 0.185774i \(0.0594793\pi\)
\(384\) 0 0
\(385\) 0.154231 + 1.70968i 0.00786034 + 0.0871336i
\(386\) 0 0
\(387\) −0.444884 + 0.770561i −0.0226147 + 0.0391698i
\(388\) 0 0
\(389\) 10.5679 + 18.3041i 0.535811 + 0.928053i 0.999124 + 0.0418574i \(0.0133275\pi\)
−0.463312 + 0.886195i \(0.653339\pi\)
\(390\) 0 0
\(391\) −8.84232 −0.447175
\(392\) 0 0
\(393\) −33.1047 −1.66991
\(394\) 0 0
\(395\) 5.89089 + 10.2033i 0.296403 + 0.513384i
\(396\) 0 0
\(397\) −9.60366 + 16.6340i −0.481994 + 0.834838i −0.999786 0.0206683i \(-0.993421\pi\)
0.517792 + 0.855506i \(0.326754\pi\)
\(398\) 0 0
\(399\) −2.77476 30.7588i −0.138912 1.53987i
\(400\) 0 0
\(401\) −8.33460 + 14.4360i −0.416210 + 0.720897i −0.995555 0.0941856i \(-0.969975\pi\)
0.579344 + 0.815083i \(0.303309\pi\)
\(402\) 0 0
\(403\) 0.785250 + 1.36009i 0.0391161 + 0.0677510i
\(404\) 0 0
\(405\) −8.39961 −0.417380
\(406\) 0 0
\(407\) −3.73140 −0.184959
\(408\) 0 0
\(409\) −6.17416 10.6940i −0.305293 0.528782i 0.672034 0.740520i \(-0.265421\pi\)
−0.977326 + 0.211738i \(0.932088\pi\)
\(410\) 0 0
\(411\) 5.43706 9.41727i 0.268190 0.464520i
\(412\) 0 0
\(413\) 1.54961 1.09130i 0.0762513 0.0536991i
\(414\) 0 0
\(415\) 1.60350 2.77735i 0.0787128 0.136335i
\(416\) 0 0
\(417\) 3.51811 + 6.09355i 0.172283 + 0.298402i
\(418\) 0 0
\(419\) −4.35934 −0.212968 −0.106484 0.994314i \(-0.533959\pi\)
−0.106484 + 0.994314i \(0.533959\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) −0.392192 0.679296i −0.0190690 0.0330285i
\(424\) 0 0
\(425\) 4.91586 8.51451i 0.238454 0.413015i
\(426\) 0 0
\(427\) −27.9766 12.9538i −1.35388 0.626881i
\(428\) 0 0
\(429\) −0.630060 + 1.09130i −0.0304196 + 0.0526882i
\(430\) 0 0
\(431\) −11.6813 20.2326i −0.562667 0.974569i −0.997262 0.0739426i \(-0.976442\pi\)
0.434595 0.900626i \(-0.356891\pi\)
\(432\) 0 0
\(433\) −2.71285 −0.130371 −0.0651856 0.997873i \(-0.520764\pi\)
−0.0651856 + 0.997873i \(0.520764\pi\)
\(434\) 0 0
\(435\) −5.19068 −0.248874
\(436\) 0 0
\(437\) −12.4724 21.6028i −0.596635 1.03340i
\(438\) 0 0
\(439\) −4.41760 + 7.65150i −0.210840 + 0.365186i −0.951978 0.306167i \(-0.900953\pi\)
0.741137 + 0.671353i \(0.234287\pi\)
\(440\) 0 0
\(441\) 0.222363 0.621359i 0.0105887 0.0295885i
\(442\) 0 0
\(443\) −1.45279 + 2.51630i −0.0690240 + 0.119553i −0.898472 0.439031i \(-0.855322\pi\)
0.829448 + 0.558584i \(0.188655\pi\)
\(444\) 0 0
\(445\) −5.45700 9.45179i −0.258686 0.448058i
\(446\) 0 0
\(447\) 37.0758 1.75362
\(448\) 0 0
\(449\) −15.2777 −0.720998 −0.360499 0.932760i \(-0.617394\pi\)
−0.360499 + 0.932760i \(0.617394\pi\)
\(450\) 0 0
\(451\) 1.76285 + 3.05334i 0.0830093 + 0.143776i
\(452\) 0 0
\(453\) 13.8292 23.9529i 0.649752 1.12540i
\(454\) 0 0
\(455\) 2.17452 + 1.00686i 0.101943 + 0.0472022i
\(456\) 0 0
\(457\) −11.8300 + 20.4902i −0.553384 + 0.958489i 0.444643 + 0.895708i \(0.353330\pi\)
−0.998027 + 0.0627815i \(0.980003\pi\)
\(458\) 0 0
\(459\) −6.01161 10.4124i −0.280598 0.486010i
\(460\) 0 0
\(461\) −26.6170 −1.23968 −0.619839 0.784729i \(-0.712802\pi\)
−0.619839 + 0.784729i \(0.712802\pi\)
\(462\) 0 0
\(463\) 1.44250 0.0670385 0.0335193 0.999438i \(-0.489328\pi\)
0.0335193 + 0.999438i \(0.489328\pi\)
\(464\) 0 0
\(465\) −1.25107 2.16692i −0.0580171 0.100488i
\(466\) 0 0
\(467\) −4.19480 + 7.26560i −0.194112 + 0.336212i −0.946609 0.322384i \(-0.895516\pi\)
0.752497 + 0.658596i \(0.228849\pi\)
\(468\) 0 0
\(469\) 20.3159 14.3073i 0.938102 0.660648i
\(470\) 0 0
\(471\) −6.84712 + 11.8596i −0.315499 + 0.546460i
\(472\) 0 0
\(473\) 3.38039 + 5.85500i 0.155430 + 0.269213i
\(474\) 0 0
\(475\) 27.7359 1.27261
\(476\) 0 0
\(477\) 1.32775 0.0607934
\(478\) 0 0
\(479\) 6.30608 + 10.9225i 0.288132 + 0.499060i 0.973364 0.229265i \(-0.0736324\pi\)
−0.685232 + 0.728325i \(0.740299\pi\)
\(480\) 0 0
\(481\) −2.60441 + 4.51098i −0.118751 + 0.205683i
\(482\) 0 0
\(483\) −1.57182 17.4240i −0.0715204 0.792819i
\(484\) 0 0
\(485\) −3.36823 + 5.83394i −0.152943 + 0.264905i
\(486\) 0 0
\(487\) 10.7840 + 18.6785i 0.488671 + 0.846403i 0.999915 0.0130329i \(-0.00414861\pi\)
−0.511244 + 0.859435i \(0.670815\pi\)
\(488\) 0 0
\(489\) 2.97265 0.134428
\(490\) 0 0
\(491\) −39.2347 −1.77064 −0.885318 0.464987i \(-0.846059\pi\)
−0.885318 + 0.464987i \(0.846059\pi\)
\(492\) 0 0
\(493\) −3.83184 6.63694i −0.172577 0.298913i
\(494\) 0 0
\(495\) 0.0305850 0.0529748i 0.00137469 0.00238104i
\(496\) 0 0
\(497\) 2.61275 + 28.9629i 0.117198 + 1.29916i
\(498\) 0 0
\(499\) 4.58407 7.93984i 0.205211 0.355436i −0.744989 0.667077i \(-0.767545\pi\)
0.950200 + 0.311641i \(0.100879\pi\)
\(500\) 0 0
\(501\) 19.2324 + 33.3115i 0.859240 + 1.48825i
\(502\) 0 0
\(503\) −24.9370 −1.11188 −0.555942 0.831221i \(-0.687642\pi\)
−0.555942 + 0.831221i \(0.687642\pi\)
\(504\) 0 0
\(505\) −1.08601 −0.0483267
\(506\) 0 0
\(507\) 0.879528 + 1.52339i 0.0390612 + 0.0676560i
\(508\) 0 0
\(509\) −2.94904 + 5.10788i −0.130714 + 0.226403i −0.923952 0.382509i \(-0.875060\pi\)
0.793238 + 0.608912i \(0.208394\pi\)
\(510\) 0 0
\(511\) 7.51268 5.29072i 0.332341 0.234048i
\(512\) 0 0
\(513\) 16.9592 29.3741i 0.748765 1.29690i
\(514\) 0 0
\(515\) −6.52677 11.3047i −0.287604 0.498144i
\(516\) 0 0
\(517\) −5.96003 −0.262122
\(518\) 0 0
\(519\) −10.2750 −0.451024
\(520\) 0 0
\(521\) 18.5948 + 32.2071i 0.814652 + 1.41102i 0.909578 + 0.415534i \(0.136405\pi\)
−0.0949259 + 0.995484i \(0.530261\pi\)
\(522\) 0 0
\(523\) −2.54540 + 4.40876i −0.111303 + 0.192782i −0.916296 0.400502i \(-0.868836\pi\)
0.804993 + 0.593284i \(0.202169\pi\)
\(524\) 0 0
\(525\) 17.6519 + 8.17325i 0.770392 + 0.356710i
\(526\) 0 0
\(527\) 1.84712 3.19931i 0.0804618 0.139364i
\(528\) 0 0
\(529\) 4.43475 + 7.68121i 0.192815 + 0.333966i
\(530\) 0 0
\(531\) −0.0675374 −0.00293087
\(532\) 0 0
\(533\) 4.92168 0.213181
\(534\) 0 0
\(535\) 6.15583 + 10.6622i 0.266140 + 0.460968i
\(536\) 0 0
\(537\) −2.22897 + 3.86068i −0.0961870 + 0.166601i
\(538\) 0 0
\(539\) −3.24397 3.82389i −0.139728 0.164707i
\(540\) 0 0
\(541\) 0.383425 0.664111i 0.0164847 0.0285524i −0.857665 0.514208i \(-0.828086\pi\)
0.874150 + 0.485656i \(0.161419\pi\)
\(542\) 0 0
\(543\) −9.43277 16.3380i −0.404799 0.701133i
\(544\) 0 0
\(545\) −12.4309 −0.532480
\(546\) 0 0
\(547\) −14.1428 −0.604702 −0.302351 0.953197i \(-0.597771\pi\)
−0.302351 + 0.953197i \(0.597771\pi\)
\(548\) 0 0
\(549\) 0.549297 + 0.951411i 0.0234434 + 0.0406052i
\(550\) 0 0
\(551\) 10.8099 18.7233i 0.460516 0.797637i
\(552\) 0 0
\(553\) −31.2310 14.4607i −1.32808 0.614932i
\(554\) 0 0
\(555\) 4.14939 7.18696i 0.176132 0.305069i
\(556\) 0 0
\(557\) 12.4314 + 21.5317i 0.526733 + 0.912329i 0.999515 + 0.0311490i \(0.00991664\pi\)
−0.472782 + 0.881180i \(0.656750\pi\)
\(558\) 0 0
\(559\) 9.43766 0.399171
\(560\) 0 0
\(561\) 2.96414 0.125146
\(562\) 0 0
\(563\) 22.0047 + 38.1133i 0.927388 + 1.60628i 0.787675 + 0.616091i \(0.211285\pi\)
0.139713 + 0.990192i \(0.455382\pi\)
\(564\) 0 0
\(565\) 1.47542 2.55550i 0.0620713 0.107511i
\(566\) 0 0
\(567\) 20.0611 14.1278i 0.842487 0.593312i
\(568\) 0 0
\(569\) 16.6308 28.8054i 0.697199 1.20758i −0.272235 0.962231i \(-0.587763\pi\)
0.969434 0.245353i \(-0.0789040\pi\)
\(570\) 0 0
\(571\) −6.17699 10.6989i −0.258499 0.447734i 0.707341 0.706873i \(-0.249895\pi\)
−0.965840 + 0.259139i \(0.916561\pi\)
\(572\) 0 0
\(573\) −2.95276 −0.123353
\(574\) 0 0
\(575\) 15.7116 0.655219
\(576\) 0 0
\(577\) 12.9829 + 22.4871i 0.540486 + 0.936150i 0.998876 + 0.0473984i \(0.0150930\pi\)
−0.458390 + 0.888751i \(0.651574\pi\)
\(578\) 0 0
\(579\) −5.67133 + 9.82304i −0.235693 + 0.408232i
\(580\) 0 0
\(581\) 0.841685 + 9.33026i 0.0349190 + 0.387085i
\(582\) 0 0
\(583\) 5.04435 8.73707i 0.208916 0.361853i
\(584\) 0 0
\(585\) −0.0426950 0.0739499i −0.00176522 0.00305745i
\(586\) 0 0
\(587\) 23.9747 0.989543 0.494771 0.869023i \(-0.335252\pi\)
0.494771 + 0.869023i \(0.335252\pi\)
\(588\) 0 0
\(589\) 10.4217 0.429418
\(590\) 0 0
\(591\) 1.64693 + 2.85256i 0.0677454 + 0.117339i
\(592\) 0 0
\(593\) −23.5240 + 40.7448i −0.966015 + 1.67319i −0.259154 + 0.965836i \(0.583444\pi\)
−0.706862 + 0.707352i \(0.749890\pi\)
\(594\) 0 0
\(595\) −0.506439 5.61398i −0.0207620 0.230151i
\(596\) 0 0
\(597\) 10.0237 17.3615i 0.410242 0.710560i
\(598\) 0 0
\(599\) 10.0868 + 17.4708i 0.412135 + 0.713840i 0.995123 0.0986415i \(-0.0314497\pi\)
−0.582988 + 0.812481i \(0.698116\pi\)
\(600\) 0 0
\(601\) 29.5773 1.20648 0.603242 0.797558i \(-0.293875\pi\)
0.603242 + 0.797558i \(0.293875\pi\)
\(602\) 0 0
\(603\) −0.885439 −0.0360579
\(604\) 0 0
\(605\) 4.74907 + 8.22564i 0.193077 + 0.334420i
\(606\) 0 0
\(607\) −7.72099 + 13.3732i −0.313385 + 0.542799i −0.979093 0.203413i \(-0.934796\pi\)
0.665708 + 0.746213i \(0.268130\pi\)
\(608\) 0 0
\(609\) 12.3971 8.73052i 0.502356 0.353779i
\(610\) 0 0
\(611\) −4.15993 + 7.20521i −0.168293 + 0.291492i
\(612\) 0 0
\(613\) −0.997423 1.72759i −0.0402855 0.0697766i 0.845180 0.534482i \(-0.179493\pi\)
−0.885465 + 0.464706i \(0.846160\pi\)
\(614\) 0 0
\(615\) −7.84129 −0.316191
\(616\) 0 0
\(617\) −2.85584 −0.114972 −0.0574858 0.998346i \(-0.518308\pi\)
−0.0574858 + 0.998346i \(0.518308\pi\)
\(618\) 0 0
\(619\) 15.9911 + 27.6975i 0.642738 + 1.11326i 0.984819 + 0.173585i \(0.0555351\pi\)
−0.342080 + 0.939671i \(0.611132\pi\)
\(620\) 0 0
\(621\) 9.60688 16.6396i 0.385511 0.667725i
\(622\) 0 0
\(623\) 28.9307 + 13.3956i 1.15908 + 0.536684i
\(624\) 0 0
\(625\) −6.68398 + 11.5770i −0.267359 + 0.463080i
\(626\) 0 0
\(627\) 4.18102 + 7.24174i 0.166974 + 0.289207i
\(628\) 0 0
\(629\) 12.2526 0.488542
\(630\) 0 0
\(631\) −32.1115 −1.27834 −0.639169 0.769066i \(-0.720722\pi\)
−0.639169 + 0.769066i \(0.720722\pi\)
\(632\) 0 0
\(633\) −6.62812 11.4802i −0.263444 0.456298i
\(634\) 0 0
\(635\) −0.430596 + 0.745814i −0.0170877 + 0.0295967i
\(636\) 0 0
\(637\) −6.88699 + 1.25275i −0.272872 + 0.0496357i
\(638\) 0 0
\(639\) 0.518126 0.897420i 0.0204967 0.0355014i
\(640\) 0 0
\(641\) −16.5124 28.6003i −0.652200 1.12964i −0.982588 0.185799i \(-0.940513\pi\)
0.330387 0.943845i \(-0.392821\pi\)
\(642\) 0 0
\(643\) −15.7942 −0.622863 −0.311432 0.950269i \(-0.600808\pi\)
−0.311432 + 0.950269i \(0.600808\pi\)
\(644\) 0 0
\(645\) −15.0362 −0.592051
\(646\) 0 0
\(647\) −2.32036 4.01898i −0.0912227 0.158002i 0.816803 0.576916i \(-0.195744\pi\)
−0.908026 + 0.418914i \(0.862411\pi\)
\(648\) 0 0
\(649\) −0.256587 + 0.444421i −0.0100719 + 0.0174451i
\(650\) 0 0
\(651\) 6.63265 + 3.07108i 0.259954 + 0.120365i
\(652\) 0 0
\(653\) −13.4143 + 23.2342i −0.524941 + 0.909225i 0.474637 + 0.880182i \(0.342579\pi\)
−0.999578 + 0.0290430i \(0.990754\pi\)
\(654\) 0 0
\(655\) −8.52266 14.7617i −0.333008 0.576787i
\(656\) 0 0
\(657\) −0.327429 −0.0127742
\(658\) 0 0
\(659\) 42.9889 1.67461 0.837306 0.546735i \(-0.184129\pi\)
0.837306 + 0.546735i \(0.184129\pi\)
\(660\) 0 0
\(661\) 14.7349 + 25.5216i 0.573122 + 0.992676i 0.996243 + 0.0866030i \(0.0276012\pi\)
−0.423121 + 0.906073i \(0.639066\pi\)
\(662\) 0 0
\(663\) 2.06889 3.58342i 0.0803490 0.139169i
\(664\) 0 0
\(665\) 13.0013 9.15599i 0.504167 0.355054i
\(666\) 0 0
\(667\) 6.12349 10.6062i 0.237102 0.410673i
\(668\) 0 0
\(669\) −15.5104 26.8647i −0.599666 1.03865i
\(670\) 0 0
\(671\) 8.34752 0.322252
\(672\) 0 0
\(673\) −20.1702 −0.777504 −0.388752 0.921342i \(-0.627094\pi\)
−0.388752 + 0.921342i \(0.627094\pi\)
\(674\) 0 0
\(675\) 10.6818 + 18.5015i 0.411144 + 0.712122i
\(676\) 0 0
\(677\) 3.10241 5.37353i 0.119235 0.206521i −0.800230 0.599694i \(-0.795289\pi\)
0.919465 + 0.393172i \(0.128622\pi\)
\(678\) 0 0
\(679\) −1.76800 19.5986i −0.0678495 0.752126i
\(680\) 0 0
\(681\) 4.68704 8.11820i 0.179608 0.311090i
\(682\) 0 0
\(683\) −0.884758 1.53245i −0.0338543 0.0586374i 0.848602 0.529032i \(-0.177445\pi\)
−0.882456 + 0.470395i \(0.844112\pi\)
\(684\) 0 0
\(685\) 5.59899 0.213926
\(686\) 0 0
\(687\) 14.9854 0.571729
\(688\) 0 0
\(689\) −7.04163 12.1965i −0.268265 0.464648i
\(690\) 0 0
\(691\) 22.4658 38.9120i 0.854641 1.48028i −0.0223363 0.999751i \(-0.507110\pi\)
0.876977 0.480531i \(-0.159556\pi\)
\(692\) 0 0
\(693\) 0.0160542 + 0.177964i 0.000609849 + 0.00676031i
\(694\) 0 0
\(695\) −1.81144 + 3.13751i −0.0687120 + 0.119013i
\(696\) 0 0
\(697\) −5.78856 10.0261i −0.219257 0.379765i
\(698\) 0 0
\(699\) −8.36204 −0.316281
\(700\) 0 0
\(701\) 38.5707 1.45679 0.728397 0.685156i \(-0.240266\pi\)
0.728397 + 0.685156i \(0.240266\pi\)
\(702\) 0 0
\(703\) 17.2827 + 29.9344i 0.651828 + 1.12900i
\(704\) 0 0
\(705\) 6.62767 11.4795i 0.249612 0.432341i
\(706\) 0 0
\(707\) 2.59375 1.82662i 0.0975480 0.0686972i
\(708\) 0 0
\(709\) −4.38866 + 7.60137i −0.164819 + 0.285476i −0.936591 0.350424i \(-0.886037\pi\)
0.771772 + 0.635900i \(0.219371\pi\)
\(710\) 0 0
\(711\) 0.613194 + 1.06208i 0.0229966 + 0.0398312i
\(712\) 0 0
\(713\) 5.90360 0.221091
\(714\) 0 0
\(715\) −0.648824 −0.0242646
\(716\) 0 0
\(717\) −13.0447 22.5940i −0.487161 0.843788i
\(718\) 0 0
\(719\) 2.10218 3.64109i 0.0783982 0.135790i −0.824161 0.566356i \(-0.808353\pi\)
0.902559 + 0.430566i \(0.141686\pi\)
\(720\) 0 0
\(721\) 34.6022 + 16.0216i 1.28865 + 0.596677i
\(722\) 0 0
\(723\) −5.38386 + 9.32513i −0.200228 + 0.346805i
\(724\) 0 0
\(725\) 6.80866 + 11.7930i 0.252867 + 0.437979i
\(726\) 0 0
\(727\) 28.9856 1.07502 0.537509 0.843258i \(-0.319366\pi\)
0.537509 + 0.843258i \(0.319366\pi\)
\(728\) 0 0
\(729\) 26.0990 0.966630
\(730\) 0 0
\(731\) −11.1000 19.2257i −0.410547 0.711089i
\(732\) 0 0
\(733\) 12.0172 20.8145i 0.443867 0.768800i −0.554106 0.832446i \(-0.686940\pi\)
0.997972 + 0.0636467i \(0.0202731\pi\)
\(734\) 0 0
\(735\) 10.9725 1.99590i 0.404725 0.0736198i
\(736\) 0 0
\(737\) −3.36394 + 5.82652i −0.123912 + 0.214622i
\(738\) 0 0
\(739\) 5.90276 + 10.2239i 0.217136 + 0.376091i 0.953931 0.300025i \(-0.0969950\pi\)
−0.736795 + 0.676116i \(0.763662\pi\)
\(740\) 0 0
\(741\) 11.6729 0.428816
\(742\) 0 0
\(743\) −47.2786 −1.73448 −0.867241 0.497888i \(-0.834109\pi\)
−0.867241 + 0.497888i \(0.834109\pi\)
\(744\) 0 0
\(745\) 9.54499 + 16.5324i 0.349701 + 0.605700i
\(746\) 0 0
\(747\) 0.166912 0.289100i 0.00610698 0.0105776i
\(748\) 0 0
\(749\) −32.6356 15.1111i −1.19248 0.552147i
\(750\) 0 0
\(751\) 2.73850 4.74322i 0.0999294 0.173083i −0.811726 0.584039i \(-0.801472\pi\)
0.911655 + 0.410956i \(0.134805\pi\)
\(752\) 0 0
\(753\) 12.2877 + 21.2830i 0.447790 + 0.775596i
\(754\) 0 0
\(755\) 14.2410 0.518285
\(756\) 0 0
\(757\) 10.7453 0.390546 0.195273 0.980749i \(-0.437441\pi\)
0.195273 + 0.980749i \(0.437441\pi\)
\(758\) 0 0
\(759\) 2.36843 + 4.10224i 0.0859686 + 0.148902i
\(760\) 0 0
\(761\) 16.5200 28.6134i 0.598848 1.03724i −0.394143 0.919049i \(-0.628959\pi\)
0.992991 0.118186i \(-0.0377080\pi\)
\(762\) 0 0
\(763\) 29.6891 20.9082i 1.07482 0.756928i
\(764\) 0 0
\(765\) −0.100430 + 0.173950i −0.00363106 + 0.00628918i
\(766\) 0 0
\(767\) 0.358181 + 0.620387i 0.0129332 + 0.0224009i
\(768\) 0 0
\(769\) 2.98332 0.107581 0.0537907 0.998552i \(-0.482870\pi\)
0.0537907 + 0.998552i \(0.482870\pi\)
\(770\) 0 0
\(771\) −30.3702 −1.09376
\(772\) 0 0
\(773\) 10.9543 + 18.9733i 0.393998 + 0.682424i 0.992973 0.118344i \(-0.0377585\pi\)
−0.598975 + 0.800768i \(0.704425\pi\)
\(774\) 0 0
\(775\) −3.28208 + 5.68473i −0.117896 + 0.204202i
\(776\) 0 0
\(777\) 2.17803 + 24.1440i 0.0781365 + 0.866160i
\(778\) 0 0
\(779\) 16.3299 28.2842i 0.585079 1.01339i
\(780\) 0 0
\(781\) −3.93691 6.81892i −0.140874 0.244000i
\(782\) 0 0
\(783\) 16.6527 0.595118
\(784\) 0 0
\(785\) −7.05104 −0.251662
\(786\) 0 0
\(787\) −6.68161 11.5729i −0.238174 0.412529i 0.722017 0.691876i \(-0.243215\pi\)
−0.960190 + 0.279347i \(0.909882\pi\)
\(788\) 0 0
\(789\) 2.29269 3.97105i 0.0816218 0.141373i
\(790\) 0 0
\(791\) 0.774453 + 8.58498i 0.0275364 + 0.305247i
\(792\) 0 0
\(793\) 5.82633 10.0915i 0.206899 0.358360i
\(794\) 0 0
\(795\) 11.2188 + 19.4316i 0.397891 + 0.689167i
\(796\) 0 0
\(797\) 32.5388 1.15258