Properties

Label 1520.2.q.o.881.2
Level $1520$
Weight $2$
Character 1520.881
Analytic conductor $12.137$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 881.2
Root \(0.689667 + 1.19454i\) of defining polynomial
Character \(\chi\) \(=\) 1520.881
Dual form 1520.2.q.o.961.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.189667 - 0.328513i) q^{3} +(-0.500000 - 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 - 2.47346i) q^{9} +O(q^{10})\) \(q+(-0.189667 - 0.328513i) q^{3} +(-0.500000 - 0.866025i) q^{5} -1.89307 q^{7} +(1.42805 - 2.47346i) q^{9} -0.134400 q^{11} +(-1.75687 + 3.04298i) q^{13} +(-0.189667 + 0.328513i) q^{15} +(0.830615 + 1.43867i) q^{17} +(-2.10596 - 3.81640i) q^{19} +(0.359052 + 0.621897i) q^{21} +(2.68492 - 4.65042i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.22142 q^{27} +(-2.48530 + 4.30466i) q^{29} -6.56472 q^{31} +(0.0254912 + 0.0441521i) q^{33} +(0.946534 + 1.63944i) q^{35} -1.69819 q^{37} +1.33288 q^{39} +(-5.31637 - 9.20823i) q^{41} +(4.25392 + 7.36801i) q^{43} -2.85611 q^{45} +(-5.55771 + 9.62623i) q^{47} -3.41630 q^{49} +(0.315080 - 0.545735i) q^{51} +(0.132424 - 0.229365i) q^{53} +(0.0672000 + 0.116394i) q^{55} +(-0.854305 + 1.41568i) q^{57} +(-3.44833 - 5.97269i) q^{59} +(-4.58794 + 7.94655i) q^{61} +(-2.70340 + 4.68243i) q^{63} +3.51373 q^{65} +(-1.47677 + 2.55784i) q^{67} -2.03696 q^{69} +(0.664176 + 1.15039i) q^{71} +(3.17119 + 5.49266i) q^{73} +0.379334 q^{75} +0.254428 q^{77} +(-0.733639 - 1.27070i) q^{79} +(-3.86283 - 6.69062i) q^{81} -7.44736 q^{83} +(0.830615 - 1.43867i) q^{85} +1.88551 q^{87} +(-4.86804 + 8.43169i) q^{89} +(3.32587 - 5.76057i) q^{91} +(1.24511 + 2.15659i) q^{93} +(-2.25212 + 3.73202i) q^{95} +(-8.73447 - 15.1285i) q^{97} +(-0.191930 + 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(3\) −0.189667 0.328513i −0.109504 0.189667i 0.806065 0.591827i \(-0.201593\pi\)
−0.915570 + 0.402160i \(0.868260\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.89307 −0.715512 −0.357756 0.933815i \(-0.616458\pi\)
−0.357756 + 0.933815i \(0.616458\pi\)
\(8\) 0 0
\(9\) 1.42805 2.47346i 0.476018 0.824487i
\(10\) 0 0
\(11\) −0.134400 −0.0405231 −0.0202615 0.999795i \(-0.506450\pi\)
−0.0202615 + 0.999795i \(0.506450\pi\)
\(12\) 0 0
\(13\) −1.75687 + 3.04298i −0.487267 + 0.843972i −0.999893 0.0146407i \(-0.995340\pi\)
0.512626 + 0.858612i \(0.328673\pi\)
\(14\) 0 0
\(15\) −0.189667 + 0.328513i −0.0489718 + 0.0848216i
\(16\) 0 0
\(17\) 0.830615 + 1.43867i 0.201454 + 0.348928i 0.948997 0.315285i \(-0.102100\pi\)
−0.747543 + 0.664213i \(0.768767\pi\)
\(18\) 0 0
\(19\) −2.10596 3.81640i −0.483141 0.875543i
\(20\) 0 0
\(21\) 0.359052 + 0.621897i 0.0783516 + 0.135709i
\(22\) 0 0
\(23\) 2.68492 4.65042i 0.559844 0.969679i −0.437664 0.899138i \(-0.644194\pi\)
0.997509 0.0705407i \(-0.0224725\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −2.22142 −0.427512
\(28\) 0 0
\(29\) −2.48530 + 4.30466i −0.461508 + 0.799355i −0.999036 0.0438905i \(-0.986025\pi\)
0.537528 + 0.843246i \(0.319358\pi\)
\(30\) 0 0
\(31\) −6.56472 −1.17906 −0.589529 0.807747i \(-0.700687\pi\)
−0.589529 + 0.807747i \(0.700687\pi\)
\(32\) 0 0
\(33\) 0.0254912 + 0.0441521i 0.00443745 + 0.00768589i
\(34\) 0 0
\(35\) 0.946534 + 1.63944i 0.159993 + 0.277117i
\(36\) 0 0
\(37\) −1.69819 −0.279181 −0.139590 0.990209i \(-0.544579\pi\)
−0.139590 + 0.990209i \(0.544579\pi\)
\(38\) 0 0
\(39\) 1.33288 0.213431
\(40\) 0 0
\(41\) −5.31637 9.20823i −0.830278 1.43808i −0.897818 0.440367i \(-0.854848\pi\)
0.0675398 0.997717i \(-0.478485\pi\)
\(42\) 0 0
\(43\) 4.25392 + 7.36801i 0.648717 + 1.12361i 0.983430 + 0.181290i \(0.0580274\pi\)
−0.334713 + 0.942320i \(0.608639\pi\)
\(44\) 0 0
\(45\) −2.85611 −0.425763
\(46\) 0 0
\(47\) −5.55771 + 9.62623i −0.810675 + 1.40413i 0.101718 + 0.994813i \(0.467566\pi\)
−0.912392 + 0.409316i \(0.865767\pi\)
\(48\) 0 0
\(49\) −3.41630 −0.488042
\(50\) 0 0
\(51\) 0.315080 0.545735i 0.0441201 0.0764182i
\(52\) 0 0
\(53\) 0.132424 0.229365i 0.0181898 0.0315057i −0.856787 0.515670i \(-0.827543\pi\)
0.874977 + 0.484164i \(0.160876\pi\)
\(54\) 0 0
\(55\) 0.0672000 + 0.116394i 0.00906124 + 0.0156945i
\(56\) 0 0
\(57\) −0.854305 + 1.41568i −0.113155 + 0.187511i
\(58\) 0 0
\(59\) −3.44833 5.97269i −0.448935 0.777578i 0.549382 0.835571i \(-0.314863\pi\)
−0.998317 + 0.0579932i \(0.981530\pi\)
\(60\) 0 0
\(61\) −4.58794 + 7.94655i −0.587426 + 1.01745i 0.407142 + 0.913365i \(0.366525\pi\)
−0.994568 + 0.104087i \(0.966808\pi\)
\(62\) 0 0
\(63\) −2.70340 + 4.68243i −0.340596 + 0.589930i
\(64\) 0 0
\(65\) 3.51373 0.435825
\(66\) 0 0
\(67\) −1.47677 + 2.55784i −0.180416 + 0.312490i −0.942022 0.335550i \(-0.891078\pi\)
0.761606 + 0.648040i \(0.224411\pi\)
\(68\) 0 0
\(69\) −2.03696 −0.245221
\(70\) 0 0
\(71\) 0.664176 + 1.15039i 0.0788232 + 0.136526i 0.902742 0.430181i \(-0.141550\pi\)
−0.823919 + 0.566707i \(0.808217\pi\)
\(72\) 0 0
\(73\) 3.17119 + 5.49266i 0.371159 + 0.642867i 0.989744 0.142851i \(-0.0456271\pi\)
−0.618585 + 0.785718i \(0.712294\pi\)
\(74\) 0 0
\(75\) 0.379334 0.0438017
\(76\) 0 0
\(77\) 0.254428 0.0289948
\(78\) 0 0
\(79\) −0.733639 1.27070i −0.0825408 0.142965i 0.821800 0.569776i \(-0.192970\pi\)
−0.904341 + 0.426811i \(0.859637\pi\)
\(80\) 0 0
\(81\) −3.86283 6.69062i −0.429203 0.743402i
\(82\) 0 0
\(83\) −7.44736 −0.817454 −0.408727 0.912657i \(-0.634027\pi\)
−0.408727 + 0.912657i \(0.634027\pi\)
\(84\) 0 0
\(85\) 0.830615 1.43867i 0.0900928 0.156045i
\(86\) 0 0
\(87\) 1.88551 0.202148
\(88\) 0 0
\(89\) −4.86804 + 8.43169i −0.516011 + 0.893757i 0.483816 + 0.875170i \(0.339250\pi\)
−0.999827 + 0.0185878i \(0.994083\pi\)
\(90\) 0 0
\(91\) 3.32587 5.76057i 0.348646 0.603872i
\(92\) 0 0
\(93\) 1.24511 + 2.15659i 0.129112 + 0.223628i
\(94\) 0 0
\(95\) −2.25212 + 3.73202i −0.231063 + 0.382897i
\(96\) 0 0
\(97\) −8.73447 15.1285i −0.886851 1.53607i −0.843577 0.537008i \(-0.819555\pi\)
−0.0432737 0.999063i \(-0.513779\pi\)
\(98\) 0 0
\(99\) −0.191930 + 0.332433i −0.0192897 + 0.0334108i
\(100\) 0 0
\(101\) −2.69865 + 4.67420i −0.268526 + 0.465101i −0.968481 0.249086i \(-0.919870\pi\)
0.699955 + 0.714187i \(0.253203\pi\)
\(102\) 0 0
\(103\) −2.14750 −0.211599 −0.105800 0.994387i \(-0.533740\pi\)
−0.105800 + 0.994387i \(0.533740\pi\)
\(104\) 0 0
\(105\) 0.359052 0.621897i 0.0350399 0.0606909i
\(106\) 0 0
\(107\) 1.00093 0.0967631 0.0483815 0.998829i \(-0.484594\pi\)
0.0483815 + 0.998829i \(0.484594\pi\)
\(108\) 0 0
\(109\) −8.13145 14.0841i −0.778852 1.34901i −0.932604 0.360902i \(-0.882469\pi\)
0.153752 0.988109i \(-0.450864\pi\)
\(110\) 0 0
\(111\) 0.322091 + 0.557877i 0.0305715 + 0.0529514i
\(112\) 0 0
\(113\) 0.843010 0.0793037 0.0396519 0.999214i \(-0.487375\pi\)
0.0396519 + 0.999214i \(0.487375\pi\)
\(114\) 0 0
\(115\) −5.36984 −0.500740
\(116\) 0 0
\(117\) 5.01780 + 8.69108i 0.463896 + 0.803491i
\(118\) 0 0
\(119\) −1.57241 2.72349i −0.144143 0.249662i
\(120\) 0 0
\(121\) −10.9819 −0.998358
\(122\) 0 0
\(123\) −2.01668 + 3.49299i −0.181838 + 0.314953i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 9.36984 16.2290i 0.831439 1.44009i −0.0654584 0.997855i \(-0.520851\pi\)
0.896897 0.442239i \(-0.145816\pi\)
\(128\) 0 0
\(129\) 1.61366 2.79493i 0.142074 0.246080i
\(130\) 0 0
\(131\) 1.44322 + 2.49973i 0.126095 + 0.218402i 0.922160 0.386808i \(-0.126422\pi\)
−0.796066 + 0.605210i \(0.793089\pi\)
\(132\) 0 0
\(133\) 3.98673 + 7.22471i 0.345693 + 0.626461i
\(134\) 0 0
\(135\) 1.11071 + 1.92381i 0.0955946 + 0.165575i
\(136\) 0 0
\(137\) 9.41579 16.3086i 0.804445 1.39334i −0.112220 0.993683i \(-0.535796\pi\)
0.916665 0.399656i \(-0.130871\pi\)
\(138\) 0 0
\(139\) −9.08974 + 15.7439i −0.770982 + 1.33538i 0.166043 + 0.986118i \(0.446901\pi\)
−0.937025 + 0.349262i \(0.886432\pi\)
\(140\) 0 0
\(141\) 4.21645 0.355089
\(142\) 0 0
\(143\) 0.236123 0.408977i 0.0197456 0.0342003i
\(144\) 0 0
\(145\) 4.97059 0.412785
\(146\) 0 0
\(147\) 0.647958 + 1.12230i 0.0534427 + 0.0925655i
\(148\) 0 0
\(149\) 11.1272 + 19.2728i 0.911573 + 1.57889i 0.811842 + 0.583877i \(0.198465\pi\)
0.0997308 + 0.995014i \(0.468202\pi\)
\(150\) 0 0
\(151\) −3.33482 −0.271384 −0.135692 0.990751i \(-0.543326\pi\)
−0.135692 + 0.990751i \(0.543326\pi\)
\(152\) 0 0
\(153\) 4.74465 0.383582
\(154\) 0 0
\(155\) 3.28236 + 5.68521i 0.263645 + 0.456647i
\(156\) 0 0
\(157\) −3.63145 6.28986i −0.289822 0.501986i 0.683945 0.729533i \(-0.260263\pi\)
−0.973767 + 0.227548i \(0.926929\pi\)
\(158\) 0 0
\(159\) −0.100466 −0.00796744
\(160\) 0 0
\(161\) −5.08273 + 8.80355i −0.400576 + 0.693817i
\(162\) 0 0
\(163\) 19.7783 1.54916 0.774578 0.632478i \(-0.217962\pi\)
0.774578 + 0.632478i \(0.217962\pi\)
\(164\) 0 0
\(165\) 0.0254912 0.0441521i 0.00198449 0.00343723i
\(166\) 0 0
\(167\) −1.70160 + 2.94726i −0.131674 + 0.228066i −0.924322 0.381614i \(-0.875368\pi\)
0.792648 + 0.609679i \(0.208702\pi\)
\(168\) 0 0
\(169\) 0.326838 + 0.566100i 0.0251414 + 0.0435461i
\(170\) 0 0
\(171\) −12.4471 0.241010i −0.951857 0.0184305i
\(172\) 0 0
\(173\) 5.29286 + 9.16750i 0.402409 + 0.696992i 0.994016 0.109234i \(-0.0348398\pi\)
−0.591607 + 0.806226i \(0.701506\pi\)
\(174\) 0 0
\(175\) 0.946534 1.63944i 0.0715512 0.123930i
\(176\) 0 0
\(177\) −1.30807 + 2.26564i −0.0983205 + 0.170296i
\(178\) 0 0
\(179\) 14.6024 1.09144 0.545718 0.837969i \(-0.316257\pi\)
0.545718 + 0.837969i \(0.316257\pi\)
\(180\) 0 0
\(181\) 2.71630 4.70478i 0.201901 0.349703i −0.747240 0.664555i \(-0.768621\pi\)
0.949141 + 0.314851i \(0.101955\pi\)
\(182\) 0 0
\(183\) 3.48072 0.257303
\(184\) 0 0
\(185\) 0.849095 + 1.47068i 0.0624267 + 0.108126i
\(186\) 0 0
\(187\) −0.111635 0.193357i −0.00816353 0.0141396i
\(188\) 0 0
\(189\) 4.20530 0.305890
\(190\) 0 0
\(191\) −20.4758 −1.48157 −0.740787 0.671740i \(-0.765547\pi\)
−0.740787 + 0.671740i \(0.765547\pi\)
\(192\) 0 0
\(193\) −5.51176 9.54664i −0.396745 0.687182i 0.596577 0.802556i \(-0.296527\pi\)
−0.993322 + 0.115373i \(0.963194\pi\)
\(194\) 0 0
\(195\) −0.666439 1.15431i −0.0477247 0.0826616i
\(196\) 0 0
\(197\) −19.8532 −1.41448 −0.707242 0.706971i \(-0.750061\pi\)
−0.707242 + 0.706971i \(0.750061\pi\)
\(198\) 0 0
\(199\) 10.5013 18.1888i 0.744417 1.28937i −0.206050 0.978542i \(-0.566061\pi\)
0.950467 0.310826i \(-0.100606\pi\)
\(200\) 0 0
\(201\) 1.12038 0.0790254
\(202\) 0 0
\(203\) 4.70483 8.14901i 0.330215 0.571948i
\(204\) 0 0
\(205\) −5.31637 + 9.20823i −0.371312 + 0.643131i
\(206\) 0 0
\(207\) −7.66842 13.2821i −0.532992 0.923169i
\(208\) 0 0
\(209\) 0.283041 + 0.512924i 0.0195784 + 0.0354797i
\(210\) 0 0
\(211\) −6.41284 11.1074i −0.441478 0.764663i 0.556321 0.830967i \(-0.312212\pi\)
−0.997799 + 0.0663046i \(0.978879\pi\)
\(212\) 0 0
\(213\) 0.251944 0.436380i 0.0172629 0.0299003i
\(214\) 0 0
\(215\) 4.25392 7.36801i 0.290115 0.502494i
\(216\) 0 0
\(217\) 12.4275 0.843630
\(218\) 0 0
\(219\) 1.20294 2.08355i 0.0812870 0.140793i
\(220\) 0 0
\(221\) −5.83712 −0.392647
\(222\) 0 0
\(223\) 10.1972 + 17.6621i 0.682856 + 1.18274i 0.974105 + 0.226095i \(0.0725959\pi\)
−0.291249 + 0.956647i \(0.594071\pi\)
\(224\) 0 0
\(225\) 1.42805 + 2.47346i 0.0952035 + 0.164897i
\(226\) 0 0
\(227\) −25.4172 −1.68700 −0.843500 0.537129i \(-0.819509\pi\)
−0.843500 + 0.537129i \(0.819509\pi\)
\(228\) 0 0
\(229\) 2.21553 0.146406 0.0732030 0.997317i \(-0.476678\pi\)
0.0732030 + 0.997317i \(0.476678\pi\)
\(230\) 0 0
\(231\) −0.0482566 0.0835829i −0.00317505 0.00549935i
\(232\) 0 0
\(233\) 7.07882 + 12.2609i 0.463749 + 0.803236i 0.999144 0.0413652i \(-0.0131707\pi\)
−0.535395 + 0.844602i \(0.679837\pi\)
\(234\) 0 0
\(235\) 11.1154 0.725089
\(236\) 0 0
\(237\) −0.278294 + 0.482019i −0.0180771 + 0.0313105i
\(238\) 0 0
\(239\) −3.01476 −0.195008 −0.0975042 0.995235i \(-0.531086\pi\)
−0.0975042 + 0.995235i \(0.531086\pi\)
\(240\) 0 0
\(241\) 11.8896 20.5934i 0.765877 1.32654i −0.173904 0.984763i \(-0.555638\pi\)
0.939781 0.341776i \(-0.111028\pi\)
\(242\) 0 0
\(243\) −4.79743 + 8.30939i −0.307755 + 0.533048i
\(244\) 0 0
\(245\) 1.70815 + 2.95860i 0.109130 + 0.189018i
\(246\) 0 0
\(247\) 15.3131 + 0.296503i 0.974352 + 0.0188660i
\(248\) 0 0
\(249\) 1.41252 + 2.44655i 0.0895147 + 0.155044i
\(250\) 0 0
\(251\) 8.59495 14.8869i 0.542509 0.939653i −0.456250 0.889851i \(-0.650808\pi\)
0.998759 0.0498012i \(-0.0158588\pi\)
\(252\) 0 0
\(253\) −0.360853 + 0.625016i −0.0226866 + 0.0392944i
\(254\) 0 0
\(255\) −0.630160 −0.0394622
\(256\) 0 0
\(257\) 9.77143 16.9246i 0.609525 1.05573i −0.381794 0.924248i \(-0.624693\pi\)
0.991319 0.131481i \(-0.0419732\pi\)
\(258\) 0 0
\(259\) 3.21479 0.199757
\(260\) 0 0
\(261\) 7.09827 + 12.2946i 0.439372 + 0.761014i
\(262\) 0 0
\(263\) 4.40680 + 7.63280i 0.271735 + 0.470659i 0.969306 0.245857i \(-0.0790692\pi\)
−0.697571 + 0.716515i \(0.745736\pi\)
\(264\) 0 0
\(265\) −0.264847 −0.0162694
\(266\) 0 0
\(267\) 3.69322 0.226022
\(268\) 0 0
\(269\) −0.144181 0.249729i −0.00879088 0.0152263i 0.861596 0.507594i \(-0.169465\pi\)
−0.870387 + 0.492368i \(0.836132\pi\)
\(270\) 0 0
\(271\) −12.4356 21.5391i −0.755409 1.30841i −0.945171 0.326577i \(-0.894105\pi\)
0.189761 0.981830i \(-0.439229\pi\)
\(272\) 0 0
\(273\) −2.52323 −0.152713
\(274\) 0 0
\(275\) 0.0672000 0.116394i 0.00405231 0.00701881i
\(276\) 0 0
\(277\) −4.40486 −0.264662 −0.132331 0.991206i \(-0.542246\pi\)
−0.132331 + 0.991206i \(0.542246\pi\)
\(278\) 0 0
\(279\) −9.37476 + 16.2376i −0.561252 + 0.972118i
\(280\) 0 0
\(281\) 16.3607 28.3376i 0.975998 1.69048i 0.299398 0.954128i \(-0.403214\pi\)
0.676600 0.736350i \(-0.263452\pi\)
\(282\) 0 0
\(283\) −0.664463 1.15088i −0.0394982 0.0684129i 0.845600 0.533816i \(-0.179243\pi\)
−0.885099 + 0.465403i \(0.845909\pi\)
\(284\) 0 0
\(285\) 1.65317 + 0.0320097i 0.0979252 + 0.00189609i
\(286\) 0 0
\(287\) 10.0643 + 17.4318i 0.594074 + 1.02897i
\(288\) 0 0
\(289\) 7.12016 12.3325i 0.418833 0.725440i
\(290\) 0 0
\(291\) −3.31328 + 5.73877i −0.194228 + 0.336413i
\(292\) 0 0
\(293\) −7.72365 −0.451220 −0.225610 0.974218i \(-0.572438\pi\)
−0.225610 + 0.974218i \(0.572438\pi\)
\(294\) 0 0
\(295\) −3.44833 + 5.97269i −0.200770 + 0.347743i
\(296\) 0 0
\(297\) 0.298558 0.0173241
\(298\) 0 0
\(299\) 9.43409 + 16.3403i 0.545588 + 0.944986i
\(300\) 0 0
\(301\) −8.05296 13.9481i −0.464165 0.803957i
\(302\) 0 0
\(303\) 2.04738 0.117619
\(304\) 0 0
\(305\) 9.17589 0.525410
\(306\) 0 0
\(307\) −4.55001 7.88085i −0.259683 0.449784i 0.706474 0.707739i \(-0.250285\pi\)
−0.966157 + 0.257955i \(0.916951\pi\)
\(308\) 0 0
\(309\) 0.407309 + 0.705480i 0.0231710 + 0.0401333i
\(310\) 0 0
\(311\) 12.4569 0.706364 0.353182 0.935555i \(-0.385100\pi\)
0.353182 + 0.935555i \(0.385100\pi\)
\(312\) 0 0
\(313\) −1.02277 + 1.77148i −0.0578101 + 0.100130i −0.893482 0.449099i \(-0.851745\pi\)
0.835672 + 0.549229i \(0.185078\pi\)
\(314\) 0 0
\(315\) 5.40680 0.304639
\(316\) 0 0
\(317\) −11.7856 + 20.4133i −0.661947 + 1.14653i 0.318157 + 0.948038i \(0.396936\pi\)
−0.980103 + 0.198487i \(0.936397\pi\)
\(318\) 0 0
\(319\) 0.334024 0.578546i 0.0187017 0.0323923i
\(320\) 0 0
\(321\) −0.189842 0.328817i −0.0105960 0.0183528i
\(322\) 0 0
\(323\) 3.74129 6.19974i 0.208171 0.344963i
\(324\) 0 0
\(325\) −1.75687 3.04298i −0.0974534 0.168794i
\(326\) 0 0
\(327\) −3.08454 + 5.34257i −0.170575 + 0.295445i
\(328\) 0 0
\(329\) 10.5211 18.2231i 0.580048 1.00467i
\(330\) 0 0
\(331\) 18.7175 1.02881 0.514403 0.857549i \(-0.328014\pi\)
0.514403 + 0.857549i \(0.328014\pi\)
\(332\) 0 0
\(333\) −2.42511 + 4.20041i −0.132895 + 0.230181i
\(334\) 0 0
\(335\) 2.95354 0.161369
\(336\) 0 0
\(337\) 16.3440 + 28.3087i 0.890316 + 1.54207i 0.839497 + 0.543365i \(0.182850\pi\)
0.0508197 + 0.998708i \(0.483817\pi\)
\(338\) 0 0
\(339\) −0.159891 0.276940i −0.00868409 0.0150413i
\(340\) 0 0
\(341\) 0.882297 0.0477791
\(342\) 0 0
\(343\) 19.7188 1.06471
\(344\) 0 0
\(345\) 1.01848 + 1.76406i 0.0548332 + 0.0949738i
\(346\) 0 0
\(347\) −1.28333 2.22279i −0.0688927 0.119326i 0.829521 0.558475i \(-0.188613\pi\)
−0.898414 + 0.439149i \(0.855280\pi\)
\(348\) 0 0
\(349\) 16.6195 0.889619 0.444810 0.895625i \(-0.353271\pi\)
0.444810 + 0.895625i \(0.353271\pi\)
\(350\) 0 0
\(351\) 3.90274 6.75974i 0.208313 0.360808i
\(352\) 0 0
\(353\) 28.3629 1.50961 0.754803 0.655951i \(-0.227732\pi\)
0.754803 + 0.655951i \(0.227732\pi\)
\(354\) 0 0
\(355\) 0.664176 1.15039i 0.0352508 0.0610562i
\(356\) 0 0
\(357\) −0.596468 + 1.03311i −0.0315684 + 0.0546781i
\(358\) 0 0
\(359\) 8.69427 + 15.0589i 0.458866 + 0.794780i 0.998901 0.0468628i \(-0.0149224\pi\)
−0.540035 + 0.841643i \(0.681589\pi\)
\(360\) 0 0
\(361\) −10.1298 + 16.0744i −0.533150 + 0.846021i
\(362\) 0 0
\(363\) 2.08291 + 3.60771i 0.109324 + 0.189355i
\(364\) 0 0
\(365\) 3.17119 5.49266i 0.165987 0.287499i
\(366\) 0 0
\(367\) 12.9024 22.3477i 0.673501 1.16654i −0.303404 0.952862i \(-0.598123\pi\)
0.976905 0.213676i \(-0.0685436\pi\)
\(368\) 0 0
\(369\) −30.3683 −1.58091
\(370\) 0 0
\(371\) −0.250687 + 0.434203i −0.0130150 + 0.0225427i
\(372\) 0 0
\(373\) 27.0663 1.40144 0.700719 0.713437i \(-0.252862\pi\)
0.700719 + 0.713437i \(0.252862\pi\)
\(374\) 0 0
\(375\) −0.189667 0.328513i −0.00979436 0.0169643i
\(376\) 0 0
\(377\) −8.73267 15.1254i −0.449755 0.778999i
\(378\) 0 0
\(379\) −12.4028 −0.637092 −0.318546 0.947907i \(-0.603194\pi\)
−0.318546 + 0.947907i \(0.603194\pi\)
\(380\) 0 0
\(381\) −7.10859 −0.364184
\(382\) 0 0
\(383\) −2.67971 4.64139i −0.136927 0.237164i 0.789405 0.613873i \(-0.210389\pi\)
−0.926332 + 0.376709i \(0.877056\pi\)
\(384\) 0 0
\(385\) −0.127214 0.220341i −0.00648343 0.0112296i
\(386\) 0 0
\(387\) 24.2993 1.23520
\(388\) 0 0
\(389\) −4.28467 + 7.42126i −0.217241 + 0.376273i −0.953964 0.299923i \(-0.903039\pi\)
0.736722 + 0.676195i \(0.236372\pi\)
\(390\) 0 0
\(391\) 8.92053 0.451131
\(392\) 0 0
\(393\) 0.547462 0.948232i 0.0276158 0.0478320i
\(394\) 0 0
\(395\) −0.733639 + 1.27070i −0.0369134 + 0.0639359i
\(396\) 0 0
\(397\) 5.32227 + 9.21844i 0.267117 + 0.462660i 0.968116 0.250502i \(-0.0805957\pi\)
−0.700999 + 0.713162i \(0.747262\pi\)
\(398\) 0 0
\(399\) 1.61726 2.67998i 0.0809641 0.134167i
\(400\) 0 0
\(401\) −3.82604 6.62690i −0.191063 0.330932i 0.754539 0.656255i \(-0.227860\pi\)
−0.945603 + 0.325323i \(0.894527\pi\)
\(402\) 0 0
\(403\) 11.5333 19.9763i 0.574516 0.995091i
\(404\) 0 0
\(405\) −3.86283 + 6.69062i −0.191946 + 0.332459i
\(406\) 0 0
\(407\) 0.228237 0.0113133
\(408\) 0 0
\(409\) 8.84435 15.3189i 0.437325 0.757469i −0.560157 0.828386i \(-0.689259\pi\)
0.997482 + 0.0709173i \(0.0225927\pi\)
\(410\) 0 0
\(411\) −7.14345 −0.352361
\(412\) 0 0
\(413\) 6.52793 + 11.3067i 0.321218 + 0.556367i
\(414\) 0 0
\(415\) 3.72368 + 6.44961i 0.182788 + 0.316599i
\(416\) 0 0
\(417\) 6.89609 0.337703
\(418\) 0 0
\(419\) −1.18732 −0.0580045 −0.0290023 0.999579i \(-0.509233\pi\)
−0.0290023 + 0.999579i \(0.509233\pi\)
\(420\) 0 0
\(421\) −16.6836 28.8969i −0.813111 1.40835i −0.910677 0.413120i \(-0.864439\pi\)
0.0975661 0.995229i \(-0.468894\pi\)
\(422\) 0 0
\(423\) 15.8734 + 27.4935i 0.771791 + 1.33678i
\(424\) 0 0
\(425\) −1.66123 −0.0805815
\(426\) 0 0
\(427\) 8.68529 15.0434i 0.420311 0.727999i
\(428\) 0 0
\(429\) −0.179139 −0.00864890
\(430\) 0 0
\(431\) −3.08799 + 5.34855i −0.148743 + 0.257631i −0.930763 0.365623i \(-0.880856\pi\)
0.782020 + 0.623253i \(0.214189\pi\)
\(432\) 0 0
\(433\) 9.27761 16.0693i 0.445854 0.772241i −0.552258 0.833673i \(-0.686234\pi\)
0.998111 + 0.0614325i \(0.0195669\pi\)
\(434\) 0 0
\(435\) −0.942757 1.63290i −0.0452017 0.0782917i
\(436\) 0 0
\(437\) −23.4022 0.453129i −1.11948 0.0216761i
\(438\) 0 0
\(439\) −0.113656 0.196858i −0.00542450 0.00939550i 0.863300 0.504690i \(-0.168393\pi\)
−0.868725 + 0.495295i \(0.835060\pi\)
\(440\) 0 0
\(441\) −4.87865 + 8.45007i −0.232317 + 0.402384i
\(442\) 0 0
\(443\) −17.4913 + 30.2959i −0.831038 + 1.43940i 0.0661770 + 0.997808i \(0.478920\pi\)
−0.897216 + 0.441593i \(0.854414\pi\)
\(444\) 0 0
\(445\) 9.73608 0.461534
\(446\) 0 0
\(447\) 4.22091 7.31083i 0.199642 0.345791i
\(448\) 0 0
\(449\) −16.9509 −0.799961 −0.399980 0.916524i \(-0.630983\pi\)
−0.399980 + 0.916524i \(0.630983\pi\)
\(450\) 0 0
\(451\) 0.714520 + 1.23759i 0.0336454 + 0.0582756i
\(452\) 0 0
\(453\) 0.632505 + 1.09553i 0.0297177 + 0.0514725i
\(454\) 0 0
\(455\) −6.65174 −0.311838
\(456\) 0 0
\(457\) 1.60241 0.0749578 0.0374789 0.999297i \(-0.488067\pi\)
0.0374789 + 0.999297i \(0.488067\pi\)
\(458\) 0 0
\(459\) −1.84514 3.19588i −0.0861239 0.149171i
\(460\) 0 0
\(461\) 4.37081 + 7.57046i 0.203569 + 0.352592i 0.949676 0.313234i \(-0.101413\pi\)
−0.746107 + 0.665826i \(0.768079\pi\)
\(462\) 0 0
\(463\) −21.1886 −0.984718 −0.492359 0.870392i \(-0.663865\pi\)
−0.492359 + 0.870392i \(0.663865\pi\)
\(464\) 0 0
\(465\) 1.24511 2.15659i 0.0577406 0.100010i
\(466\) 0 0
\(467\) −20.4516 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(468\) 0 0
\(469\) 2.79563 4.84217i 0.129090 0.223591i
\(470\) 0 0
\(471\) −1.37753 + 2.38596i −0.0634734 + 0.109939i
\(472\) 0 0
\(473\) −0.571727 0.990259i −0.0262880 0.0455322i
\(474\) 0 0
\(475\) 4.35808 + 0.0843840i 0.199963 + 0.00387180i
\(476\) 0 0
\(477\) −0.378216 0.655090i −0.0173173 0.0299945i
\(478\) 0 0
\(479\) 11.7746 20.3942i 0.537994 0.931833i −0.461018 0.887391i \(-0.652516\pi\)
0.999012 0.0444419i \(-0.0141510\pi\)
\(480\) 0 0
\(481\) 2.98350 5.16757i 0.136036 0.235621i
\(482\) 0 0
\(483\) 3.85611 0.175459
\(484\) 0 0
\(485\) −8.73447 + 15.1285i −0.396612 + 0.686952i
\(486\) 0 0
\(487\) −36.0392 −1.63309 −0.816546 0.577280i \(-0.804114\pi\)
−0.816546 + 0.577280i \(0.804114\pi\)
\(488\) 0 0
\(489\) −3.75129 6.49742i −0.169639 0.293824i
\(490\) 0 0
\(491\) 10.0297 + 17.3720i 0.452635 + 0.783988i 0.998549 0.0538541i \(-0.0171506\pi\)
−0.545913 + 0.837842i \(0.683817\pi\)
\(492\) 0 0
\(493\) −8.25729 −0.371890
\(494\) 0 0
\(495\) 0.383860 0.0172532
\(496\) 0 0
\(497\) −1.25733 2.17776i −0.0563989 0.0976858i
\(498\) 0 0
\(499\) −18.4364 31.9328i −0.825328 1.42951i −0.901668 0.432429i \(-0.857657\pi\)
0.0763399 0.997082i \(-0.475677\pi\)
\(500\) 0 0
\(501\) 1.29095 0.0576753
\(502\) 0 0
\(503\) −10.8244 + 18.7483i −0.482634 + 0.835947i −0.999801 0.0199377i \(-0.993653\pi\)
0.517167 + 0.855884i \(0.326987\pi\)
\(504\) 0 0
\(505\) 5.39731 0.240177
\(506\) 0 0
\(507\) 0.123981 0.214741i 0.00550617 0.00953697i
\(508\) 0 0
\(509\) 18.2279 31.5717i 0.807938 1.39939i −0.106351 0.994329i \(-0.533917\pi\)
0.914289 0.405062i \(-0.132750\pi\)
\(510\) 0 0
\(511\) −6.00327 10.3980i −0.265569 0.459979i
\(512\) 0 0
\(513\) 4.67822 + 8.47783i 0.206549 + 0.374305i
\(514\) 0 0
\(515\) 1.07375 + 1.85979i 0.0473150 + 0.0819520i
\(516\) 0 0
\(517\) 0.746955 1.29376i 0.0328511 0.0568997i
\(518\) 0 0
\(519\) 2.00776 3.47754i 0.0881309 0.152647i
\(520\) 0 0
\(521\) −22.6092 −0.990528 −0.495264 0.868742i \(-0.664929\pi\)
−0.495264 + 0.868742i \(0.664929\pi\)
\(522\) 0 0
\(523\) 0.266456 0.461515i 0.0116513 0.0201806i −0.860141 0.510056i \(-0.829625\pi\)
0.871792 + 0.489876i \(0.162958\pi\)
\(524\) 0 0
\(525\) −0.718104 −0.0313406
\(526\) 0 0
\(527\) −5.45275 9.44444i −0.237525 0.411406i
\(528\) 0 0
\(529\) −2.91759 5.05341i −0.126852 0.219714i
\(530\) 0 0
\(531\) −19.6976 −0.854804
\(532\) 0 0
\(533\) 37.3606 1.61827
\(534\) 0 0
\(535\) −0.500463 0.866827i −0.0216369 0.0374762i
\(536\) 0 0
\(537\) −2.76959 4.79708i −0.119517 0.207009i
\(538\) 0 0
\(539\) 0.459150 0.0197770
\(540\) 0 0
\(541\) −2.50820 + 4.34433i −0.107836 + 0.186777i −0.914893 0.403696i \(-0.867725\pi\)
0.807057 + 0.590473i \(0.201059\pi\)
\(542\) 0 0
\(543\) −2.06077 −0.0884362
\(544\) 0 0
\(545\) −8.13145 + 14.0841i −0.348313 + 0.603296i
\(546\) 0 0
\(547\) 11.3149 19.5981i 0.483792 0.837952i −0.516035 0.856568i \(-0.672592\pi\)
0.999827 + 0.0186154i \(0.00592582\pi\)
\(548\) 0 0
\(549\) 13.1037 + 22.6962i 0.559250 + 0.968650i
\(550\) 0 0
\(551\) 21.6622 + 0.419439i 0.922843 + 0.0178687i
\(552\) 0 0
\(553\) 1.38883 + 2.40552i 0.0590590 + 0.102293i
\(554\) 0 0
\(555\) 0.322091 0.557877i 0.0136720 0.0236806i
\(556\) 0 0
\(557\) −17.6277 + 30.5321i −0.746910 + 1.29369i 0.202387 + 0.979306i \(0.435130\pi\)
−0.949297 + 0.314381i \(0.898203\pi\)
\(558\) 0 0
\(559\) −29.8943 −1.26439
\(560\) 0 0
\(561\) −0.0423468 + 0.0733467i −0.00178788 + 0.00309670i
\(562\) 0 0
\(563\) 24.6295 1.03801 0.519005 0.854771i \(-0.326302\pi\)
0.519005 + 0.854771i \(0.326302\pi\)
\(564\) 0 0
\(565\) −0.421505 0.730068i −0.0177329 0.0307142i
\(566\) 0 0
\(567\) 7.31260 + 12.6658i 0.307100 + 0.531913i
\(568\) 0 0
\(569\) −20.0193 −0.839252 −0.419626 0.907697i \(-0.637839\pi\)
−0.419626 + 0.907697i \(0.637839\pi\)
\(570\) 0 0
\(571\) 16.6121 0.695195 0.347597 0.937644i \(-0.386998\pi\)
0.347597 + 0.937644i \(0.386998\pi\)
\(572\) 0 0
\(573\) 3.88357 + 6.72655i 0.162239 + 0.281006i
\(574\) 0 0
\(575\) 2.68492 + 4.65042i 0.111969 + 0.193936i
\(576\) 0 0
\(577\) 12.4486 0.518244 0.259122 0.965845i \(-0.416567\pi\)
0.259122 + 0.965845i \(0.416567\pi\)
\(578\) 0 0
\(579\) −2.09080 + 3.62136i −0.0868905 + 0.150499i
\(580\) 0 0
\(581\) 14.0984 0.584899
\(582\) 0 0
\(583\) −0.0177977 + 0.0308266i −0.000737107 + 0.00127671i
\(584\) 0 0
\(585\) 5.01780 8.69108i 0.207460 0.359332i
\(586\) 0 0
\(587\) 2.25572 + 3.90702i 0.0931036 + 0.161260i 0.908816 0.417198i \(-0.136988\pi\)
−0.815712 + 0.578458i \(0.803655\pi\)
\(588\) 0 0
\(589\) 13.8250 + 25.0536i 0.569651 + 1.03232i
\(590\) 0 0
\(591\) 3.76550 + 6.52204i 0.154892 + 0.268281i
\(592\) 0 0
\(593\) −9.80411 + 16.9812i −0.402606 + 0.697335i −0.994040 0.109019i \(-0.965229\pi\)
0.591433 + 0.806354i \(0.298562\pi\)
\(594\) 0 0
\(595\) −1.57241 + 2.72349i −0.0644625 + 0.111652i
\(596\) 0 0
\(597\) −7.96699 −0.326067
\(598\) 0 0
\(599\) 5.38795 9.33221i 0.220146 0.381304i −0.734706 0.678385i \(-0.762680\pi\)
0.954852 + 0.297082i \(0.0960134\pi\)
\(600\) 0 0
\(601\) 15.0244 0.612860 0.306430 0.951893i \(-0.400866\pi\)
0.306430 + 0.951893i \(0.400866\pi\)
\(602\) 0 0
\(603\) 4.21782 + 7.30547i 0.171763 + 0.297502i
\(604\) 0 0
\(605\) 5.49097 + 9.51064i 0.223240 + 0.386662i
\(606\) 0 0
\(607\) −25.1901 −1.02243 −0.511217 0.859452i \(-0.670805\pi\)
−0.511217 + 0.859452i \(0.670805\pi\)
\(608\) 0 0
\(609\) −3.56940 −0.144640
\(610\) 0 0
\(611\) −19.5283 33.8240i −0.790030 1.36837i
\(612\) 0 0
\(613\) −8.11753 14.0600i −0.327864 0.567877i 0.654224 0.756301i \(-0.272995\pi\)
−0.982088 + 0.188424i \(0.939662\pi\)
\(614\) 0 0
\(615\) 4.03336 0.162641
\(616\) 0 0
\(617\) −3.25913 + 5.64498i −0.131208 + 0.227258i −0.924142 0.382048i \(-0.875219\pi\)
0.792935 + 0.609307i \(0.208552\pi\)
\(618\) 0 0
\(619\) 4.39112 0.176494 0.0882470 0.996099i \(-0.471874\pi\)
0.0882470 + 0.996099i \(0.471874\pi\)
\(620\) 0 0
\(621\) −5.96433 + 10.3305i −0.239340 + 0.414550i
\(622\) 0 0
\(623\) 9.21553 15.9618i 0.369212 0.639494i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0.114819 0.190267i 0.00458541 0.00759855i
\(628\) 0 0
\(629\) −1.41054 2.44313i −0.0562420 0.0974140i
\(630\) 0 0
\(631\) −17.3104 + 29.9826i −0.689118 + 1.19359i 0.283006 + 0.959118i \(0.408668\pi\)
−0.972124 + 0.234469i \(0.924665\pi\)
\(632\) 0 0
\(633\) −2.43261 + 4.21340i −0.0966875 + 0.167468i
\(634\) 0 0
\(635\) −18.7397 −0.743661
\(636\) 0 0
\(637\) 6.00198 10.3957i 0.237807 0.411894i
\(638\) 0 0
\(639\) 3.79391 0.150085
\(640\) 0 0
\(641\) −3.70621 6.41934i −0.146386 0.253549i 0.783503 0.621388i \(-0.213431\pi\)
−0.929889 + 0.367839i \(0.880098\pi\)
\(642\) 0 0
\(643\) −8.27294 14.3292i −0.326253 0.565087i 0.655512 0.755185i \(-0.272453\pi\)
−0.981765 + 0.190098i \(0.939120\pi\)
\(644\) 0 0
\(645\) −3.22731 −0.127075
\(646\) 0 0
\(647\) −29.4822 −1.15907 −0.579533 0.814949i \(-0.696765\pi\)
−0.579533 + 0.814949i \(0.696765\pi\)
\(648\) 0 0
\(649\) 0.463456 + 0.802729i 0.0181922 + 0.0315099i
\(650\) 0 0
\(651\) −2.35708 4.08258i −0.0923811 0.160009i
\(652\) 0 0
\(653\) 6.57421 0.257269 0.128634 0.991692i \(-0.458941\pi\)
0.128634 + 0.991692i \(0.458941\pi\)
\(654\) 0 0
\(655\) 1.44322 2.49973i 0.0563912 0.0976725i
\(656\) 0 0
\(657\) 18.1145 0.706713
\(658\) 0 0
\(659\) −13.1685 + 22.8085i −0.512972 + 0.888494i 0.486915 + 0.873450i \(0.338122\pi\)
−0.999887 + 0.0150445i \(0.995211\pi\)
\(660\) 0 0
\(661\) −1.89210 + 3.27721i −0.0735941 + 0.127469i −0.900474 0.434910i \(-0.856780\pi\)
0.826880 + 0.562378i \(0.190114\pi\)
\(662\) 0 0
\(663\) 1.10711 + 1.91757i 0.0429965 + 0.0744721i
\(664\) 0 0
\(665\) 4.26341 7.06496i 0.165328 0.273967i
\(666\) 0 0
\(667\) 13.3456 + 23.1153i 0.516745 + 0.895029i
\(668\) 0 0
\(669\) 3.86815 6.69983i 0.149551 0.259031i
\(670\) 0 0
\(671\) 0.616619 1.06802i 0.0238043 0.0412303i
\(672\) 0 0
\(673\) −21.0431 −0.811150 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(674\) 0 0
\(675\) 1.11071 1.92381i 0.0427512 0.0740473i
\(676\) 0 0
\(677\) −15.2744 −0.587043 −0.293522 0.955952i \(-0.594827\pi\)
−0.293522 + 0.955952i \(0.594827\pi\)
\(678\) 0 0
\(679\) 16.5349 + 28.6394i 0.634553 + 1.09908i
\(680\) 0 0
\(681\) 4.82081 + 8.34988i 0.184734 + 0.319968i
\(682\) 0 0
\(683\) 8.60225 0.329156 0.164578 0.986364i \(-0.447374\pi\)
0.164578 + 0.986364i \(0.447374\pi\)
\(684\) 0 0
\(685\) −18.8316 −0.719518
\(686\) 0 0
\(687\) −0.420212 0.727828i −0.0160321 0.0277684i
\(688\) 0 0
\(689\) 0.465302 + 0.805926i 0.0177266 + 0.0307033i
\(690\) 0 0
\(691\) −34.1079 −1.29753 −0.648763 0.760990i \(-0.724714\pi\)
−0.648763 + 0.760990i \(0.724714\pi\)
\(692\) 0 0
\(693\) 0.363337 0.629318i 0.0138020 0.0239058i
\(694\) 0 0
\(695\) 18.1795 0.689587
\(696\) 0 0
\(697\) 8.83172 15.2970i 0.334525 0.579414i
\(698\) 0 0
\(699\) 2.68523 4.65096i 0.101565 0.175916i
\(700\) 0 0
\(701\) −5.36463 9.29181i −0.202619 0.350947i 0.746752 0.665102i \(-0.231612\pi\)
−0.949372 + 0.314155i \(0.898279\pi\)
\(702\) 0 0
\(703\) 3.57633 + 6.48098i 0.134884 + 0.244435i
\(704\) 0 0
\(705\) −2.10823 3.65155i −0.0794004 0.137525i
\(706\) 0 0
\(707\) 5.10873 8.84859i 0.192134 0.332785i
\(708\) 0 0
\(709\) 14.4238 24.9828i 0.541697 0.938247i −0.457109 0.889410i \(-0.651115\pi\)
0.998807 0.0488369i \(-0.0155514\pi\)
\(710\) 0 0
\(711\) −4.19070 −0.157164
\(712\) 0 0
\(713\) −17.6257 + 30.5287i −0.660089 + 1.14331i
\(714\) 0 0
\(715\) −0.472245 −0.0176610
\(716\) 0 0
\(717\) 0.571800 + 0.990386i 0.0213542 + 0.0369866i
\(718\) 0 0
\(719\) −10.0278 17.3686i −0.373972 0.647739i 0.616200 0.787589i \(-0.288671\pi\)
−0.990173 + 0.139851i \(0.955338\pi\)
\(720\) 0 0
\(721\) 4.06535 0.151402
\(722\) 0 0
\(723\) −9.02026 −0.335467
\(724\) 0 0
\(725\) −2.48530 4.30466i −0.0923016 0.159871i
\(726\) 0 0
\(727\) −0.390261 0.675951i −0.0144740 0.0250697i 0.858698 0.512482i \(-0.171274\pi\)
−0.873172 + 0.487413i \(0.837941\pi\)
\(728\) 0 0
\(729\) −19.5373 −0.723604
\(730\) 0 0
\(731\) −7.06674 + 12.2399i −0.261373 + 0.452711i
\(732\) 0 0
\(733\) −26.8391 −0.991326 −0.495663 0.868515i \(-0.665075\pi\)
−0.495663 + 0.868515i \(0.665075\pi\)
\(734\) 0 0
\(735\) 0.647958 1.12230i 0.0239003 0.0413965i
\(736\) 0 0
\(737\) 0.198478 0.343774i 0.00731103 0.0126631i
\(738\) 0 0
\(739\) 10.3265 + 17.8861i 0.379867 + 0.657949i 0.991043 0.133546i \(-0.0426363\pi\)
−0.611175 + 0.791495i \(0.709303\pi\)
\(740\) 0 0
\(741\) −2.80699 5.08680i −0.103117 0.186868i
\(742\) 0 0
\(743\) 0.736585 + 1.27580i 0.0270227 + 0.0468047i 0.879220 0.476415i \(-0.158064\pi\)
−0.852198 + 0.523220i \(0.824731\pi\)
\(744\) 0 0
\(745\) 11.1272 19.2728i 0.407668 0.706102i
\(746\) 0 0
\(747\) −10.6352 + 18.4208i −0.389123 + 0.673980i
\(748\) 0 0
\(749\) −1.89482 −0.0692352
\(750\) 0 0
\(751\) 7.78121 13.4775i 0.283940 0.491799i −0.688411 0.725321i \(-0.741692\pi\)
0.972352 + 0.233521i \(0.0750249\pi\)
\(752\) 0 0
\(753\) −6.52071 −0.237628
\(754\) 0 0
\(755\) 1.66741 + 2.88804i 0.0606832 + 0.105106i
\(756\) 0 0
\(757\) −10.0878 17.4726i −0.366647 0.635052i 0.622392 0.782706i \(-0.286161\pi\)
−0.989039 + 0.147654i \(0.952828\pi\)
\(758\) 0 0
\(759\) 0.273767 0.00993713
\(760\) 0 0
\(761\) −15.1076 −0.547649 −0.273825 0.961780i \(-0.588289\pi\)
−0.273825 + 0.961780i \(0.588289\pi\)
\(762\) 0 0
\(763\) 15.3934 + 26.6621i 0.557278 + 0.965234i
\(764\) 0 0
\(765\) −2.37232 4.10898i −0.0857715 0.148561i
\(766\) 0 0
\(767\) 24.2331 0.875005
\(768\) 0 0
\(769\) −25.8290 + 44.7372i −0.931418 + 1.61326i −0.150518 + 0.988607i \(0.548094\pi\)
−0.780900 + 0.624656i \(0.785239\pi\)
\(770\) 0 0
\(771\) −7.41327 −0.266982
\(772\) 0 0
\(773\) −15.0779 + 26.1157i −0.542314 + 0.939316i 0.456457 + 0.889746i \(0.349118\pi\)
−0.998771 + 0.0495699i \(0.984215\pi\)
\(774\) 0 0
\(775\) 3.28236 5.68521i 0.117906 0.204219i
\(776\) 0 0
\(777\) −0.609739 1.05610i −0.0218743 0.0378874i
\(778\) 0 0
\(779\) −23.9462 + 39.6816i −0.857962 + 1.42174i
\(780\) 0 0
\(781\) −0.0892652 0.154612i −0.00319416 0.00553244i
\(782\) 0 0
\(783\) 5.52088 9.56245i 0.197300 0.341734i
\(784\) 0 0
\(785\) −3.63145 + 6.28986i −0.129612 + 0.224495i
\(786\) 0 0
\(787\) −43.0969 −1.53624 −0.768119 0.640307i \(-0.778807\pi\)
−0.768119 + 0.640307i \(0.778807\pi\)
\(788\) 0 0
\(789\) 1.67165 2.89538i 0.0595123 0.103078i
\(790\) 0 0
\(791\) −1.59588 −0.0567428
\(792\) 0 0
\(793\) −16.1208 27.9221i −0.572467 0.991542i
\(794\) 0 0
\(795\) 0.0502328 + 0.0870057i 0.00178157 + 0.00308578i