Properties

Label 1520.2.q.o.881.3
Level $1520$
Weight $2$
Character 1520.881
Analytic conductor $12.137$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 881.3
Root \(-0.245959 - 0.426014i\) of defining polynomial
Character \(\chi\) \(=\) 1520.881
Dual form 1520.2.q.o.961.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.745959 + 1.29204i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.84864 q^{7} +(0.387090 - 0.670459i) q^{9} +O(q^{10})\) \(q+(0.745959 + 1.29204i) q^{3} +(-0.500000 - 0.866025i) q^{5} +2.84864 q^{7} +(0.387090 - 0.670459i) q^{9} +0.864801 q^{11} +(-0.321640 + 0.557098i) q^{13} +(0.745959 - 1.29204i) q^{15} +(-1.87093 - 3.24054i) q^{17} +(3.36069 + 2.77592i) q^{19} +(2.12497 + 3.68055i) q^{21} +(0.208730 - 0.361531i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.63077 q^{27} +(4.85261 - 8.40497i) q^{29} -4.93349 q^{31} +(0.645106 + 1.11736i) q^{33} +(-1.42432 - 2.46699i) q^{35} +6.36467 q^{37} -0.959723 q^{39} +(2.00686 + 3.47598i) q^{41} +(-1.02915 - 1.78254i) q^{43} -0.774179 q^{45} +(-1.97698 + 3.42423i) q^{47} +1.11474 q^{49} +(2.79127 - 4.83462i) q^{51} +(5.49374 - 9.51544i) q^{53} +(-0.432400 - 0.748939i) q^{55} +(-1.07966 + 6.41287i) q^{57} +(1.22980 + 2.13007i) q^{59} +(-3.16740 + 5.48609i) q^{61} +(1.10268 - 1.90989i) q^{63} +0.643281 q^{65} +(-1.26610 + 2.19295i) q^{67} +0.622817 q^{69} +(-0.891065 - 1.54337i) q^{71} +(3.56545 + 6.17554i) q^{73} -1.49192 q^{75} +2.46350 q^{77} +(0.912262 + 1.58008i) q^{79} +(3.03905 + 5.26380i) q^{81} +7.43913 q^{83} +(-1.87093 + 3.24054i) q^{85} +14.4794 q^{87} +(-2.22294 + 3.85024i) q^{89} +(-0.916237 + 1.58697i) q^{91} +(-3.68018 - 6.37427i) q^{93} +(0.723670 - 4.29841i) q^{95} +(5.42707 + 9.39996i) q^{97} +(0.334755 - 0.579813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) 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
\(3\) 0.745959 + 1.29204i 0.430680 + 0.745959i 0.996932 0.0782728i \(-0.0249405\pi\)
−0.566252 + 0.824232i \(0.691607\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 2.84864 1.07668 0.538342 0.842727i \(-0.319051\pi\)
0.538342 + 0.842727i \(0.319051\pi\)
\(8\) 0 0
\(9\) 0.387090 0.670459i 0.129030 0.223486i
\(10\) 0 0
\(11\) 0.864801 0.260747 0.130374 0.991465i \(-0.458382\pi\)
0.130374 + 0.991465i \(0.458382\pi\)
\(12\) 0 0
\(13\) −0.321640 + 0.557098i −0.0892070 + 0.154511i −0.907176 0.420751i \(-0.861767\pi\)
0.817969 + 0.575262i \(0.195100\pi\)
\(14\) 0 0
\(15\) 0.745959 1.29204i 0.192606 0.333603i
\(16\) 0 0
\(17\) −1.87093 3.24054i −0.453766 0.785946i 0.544850 0.838534i \(-0.316587\pi\)
−0.998616 + 0.0525872i \(0.983253\pi\)
\(18\) 0 0
\(19\) 3.36069 + 2.77592i 0.770996 + 0.636840i
\(20\) 0 0
\(21\) 2.12497 + 3.68055i 0.463706 + 0.803162i
\(22\) 0 0
\(23\) 0.208730 0.361531i 0.0435233 0.0753845i −0.843443 0.537218i \(-0.819475\pi\)
0.886966 + 0.461834i \(0.152808\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.63077 1.08364
\(28\) 0 0
\(29\) 4.85261 8.40497i 0.901108 1.56076i 0.0750490 0.997180i \(-0.476089\pi\)
0.826059 0.563584i \(-0.190578\pi\)
\(30\) 0 0
\(31\) −4.93349 −0.886081 −0.443041 0.896501i \(-0.646100\pi\)
−0.443041 + 0.896501i \(0.646100\pi\)
\(32\) 0 0
\(33\) 0.645106 + 1.11736i 0.112299 + 0.194507i
\(34\) 0 0
\(35\) −1.42432 2.46699i −0.240754 0.416998i
\(36\) 0 0
\(37\) 6.36467 1.04635 0.523173 0.852227i \(-0.324748\pi\)
0.523173 + 0.852227i \(0.324748\pi\)
\(38\) 0 0
\(39\) −0.959723 −0.153679
\(40\) 0 0
\(41\) 2.00686 + 3.47598i 0.313419 + 0.542857i 0.979100 0.203379i \(-0.0651924\pi\)
−0.665681 + 0.746236i \(0.731859\pi\)
\(42\) 0 0
\(43\) −1.02915 1.78254i −0.156944 0.271834i 0.776821 0.629721i \(-0.216831\pi\)
−0.933765 + 0.357887i \(0.883497\pi\)
\(44\) 0 0
\(45\) −0.774179 −0.115408
\(46\) 0 0
\(47\) −1.97698 + 3.42423i −0.288372 + 0.499475i −0.973421 0.229022i \(-0.926447\pi\)
0.685049 + 0.728497i \(0.259781\pi\)
\(48\) 0 0
\(49\) 1.11474 0.159248
\(50\) 0 0
\(51\) 2.79127 4.83462i 0.390856 0.676982i
\(52\) 0 0
\(53\) 5.49374 9.51544i 0.754624 1.30705i −0.190937 0.981602i \(-0.561153\pi\)
0.945561 0.325444i \(-0.105514\pi\)
\(54\) 0 0
\(55\) −0.432400 0.748939i −0.0583048 0.100987i
\(56\) 0 0
\(57\) −1.07966 + 6.41287i −0.143004 + 0.849406i
\(58\) 0 0
\(59\) 1.22980 + 2.13007i 0.160106 + 0.277311i 0.934906 0.354894i \(-0.115483\pi\)
−0.774801 + 0.632206i \(0.782150\pi\)
\(60\) 0 0
\(61\) −3.16740 + 5.48609i −0.405543 + 0.702422i −0.994385 0.105827i \(-0.966251\pi\)
0.588841 + 0.808249i \(0.299584\pi\)
\(62\) 0 0
\(63\) 1.10268 1.90989i 0.138924 0.240624i
\(64\) 0 0
\(65\) 0.643281 0.0797892
\(66\) 0 0
\(67\) −1.26610 + 2.19295i −0.154678 + 0.267911i −0.932942 0.360027i \(-0.882767\pi\)
0.778263 + 0.627938i \(0.216101\pi\)
\(68\) 0 0
\(69\) 0.622817 0.0749783
\(70\) 0 0
\(71\) −0.891065 1.54337i −0.105750 0.183164i 0.808294 0.588779i \(-0.200391\pi\)
−0.914044 + 0.405614i \(0.867058\pi\)
\(72\) 0 0
\(73\) 3.56545 + 6.17554i 0.417304 + 0.722792i 0.995667 0.0929873i \(-0.0296416\pi\)
−0.578363 + 0.815780i \(0.696308\pi\)
\(74\) 0 0
\(75\) −1.49192 −0.172272
\(76\) 0 0
\(77\) 2.46350 0.280742
\(78\) 0 0
\(79\) 0.912262 + 1.58008i 0.102637 + 0.177773i 0.912771 0.408473i \(-0.133939\pi\)
−0.810133 + 0.586246i \(0.800605\pi\)
\(80\) 0 0
\(81\) 3.03905 + 5.26380i 0.337673 + 0.584866i
\(82\) 0 0
\(83\) 7.43913 0.816550 0.408275 0.912859i \(-0.366130\pi\)
0.408275 + 0.912859i \(0.366130\pi\)
\(84\) 0 0
\(85\) −1.87093 + 3.24054i −0.202930 + 0.351486i
\(86\) 0 0
\(87\) 14.4794 1.55236
\(88\) 0 0
\(89\) −2.22294 + 3.85024i −0.235631 + 0.408125i −0.959456 0.281859i \(-0.909049\pi\)
0.723825 + 0.689984i \(0.242382\pi\)
\(90\) 0 0
\(91\) −0.916237 + 1.58697i −0.0960478 + 0.166360i
\(92\) 0 0
\(93\) −3.68018 6.37427i −0.381617 0.660981i
\(94\) 0 0
\(95\) 0.723670 4.29841i 0.0742470 0.441007i
\(96\) 0 0
\(97\) 5.42707 + 9.39996i 0.551036 + 0.954422i 0.998200 + 0.0599699i \(0.0191005\pi\)
−0.447165 + 0.894452i \(0.647566\pi\)
\(98\) 0 0
\(99\) 0.334755 0.579813i 0.0336442 0.0582734i
\(100\) 0 0
\(101\) 2.64799 4.58645i 0.263485 0.456369i −0.703681 0.710516i \(-0.748461\pi\)
0.967166 + 0.254147i \(0.0817948\pi\)
\(102\) 0 0
\(103\) 0.385134 0.0379484 0.0189742 0.999820i \(-0.493960\pi\)
0.0189742 + 0.999820i \(0.493960\pi\)
\(104\) 0 0
\(105\) 2.12497 3.68055i 0.207376 0.359185i
\(106\) 0 0
\(107\) 6.43336 0.621937 0.310968 0.950420i \(-0.399347\pi\)
0.310968 + 0.950420i \(0.399347\pi\)
\(108\) 0 0
\(109\) −3.28441 5.68877i −0.314590 0.544885i 0.664761 0.747056i \(-0.268534\pi\)
−0.979350 + 0.202171i \(0.935200\pi\)
\(110\) 0 0
\(111\) 4.74778 + 8.22340i 0.450640 + 0.780531i
\(112\) 0 0
\(113\) 0.294513 0.0277054 0.0138527 0.999904i \(-0.495590\pi\)
0.0138527 + 0.999904i \(0.495590\pi\)
\(114\) 0 0
\(115\) −0.417460 −0.0389284
\(116\) 0 0
\(117\) 0.249007 + 0.431294i 0.0230207 + 0.0398731i
\(118\) 0 0
\(119\) −5.32959 9.23112i −0.488563 0.846216i
\(120\) 0 0
\(121\) −10.2521 −0.932011
\(122\) 0 0
\(123\) −2.99407 + 5.18588i −0.269966 + 0.467595i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.41746 7.65127i 0.391986 0.678940i −0.600725 0.799456i \(-0.705121\pi\)
0.992711 + 0.120516i \(0.0384548\pi\)
\(128\) 0 0
\(129\) 1.53540 2.65940i 0.135185 0.234147i
\(130\) 0 0
\(131\) 10.4564 + 18.1110i 0.913578 + 1.58236i 0.808969 + 0.587851i \(0.200026\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(132\) 0 0
\(133\) 9.57340 + 7.90759i 0.830119 + 0.685675i
\(134\) 0 0
\(135\) −2.81538 4.87639i −0.242310 0.419693i
\(136\) 0 0
\(137\) −2.60739 + 4.51613i −0.222764 + 0.385839i −0.955646 0.294517i \(-0.904841\pi\)
0.732882 + 0.680356i \(0.238175\pi\)
\(138\) 0 0
\(139\) −5.36192 + 9.28711i −0.454792 + 0.787723i −0.998676 0.0514375i \(-0.983620\pi\)
0.543884 + 0.839160i \(0.316953\pi\)
\(140\) 0 0
\(141\) −5.89898 −0.496784
\(142\) 0 0
\(143\) −0.278155 + 0.481778i −0.0232605 + 0.0402883i
\(144\) 0 0
\(145\) −9.70523 −0.805975
\(146\) 0 0
\(147\) 0.831547 + 1.44028i 0.0685848 + 0.118792i
\(148\) 0 0
\(149\) 7.45578 + 12.9138i 0.610801 + 1.05794i 0.991106 + 0.133078i \(0.0424860\pi\)
−0.380304 + 0.924861i \(0.624181\pi\)
\(150\) 0 0
\(151\) −21.4589 −1.74630 −0.873152 0.487448i \(-0.837928\pi\)
−0.873152 + 0.487448i \(0.837928\pi\)
\(152\) 0 0
\(153\) −2.89687 −0.234198
\(154\) 0 0
\(155\) 2.46675 + 4.27253i 0.198134 + 0.343178i
\(156\) 0 0
\(157\) 1.21559 + 2.10546i 0.0970145 + 0.168034i 0.910448 0.413624i \(-0.135737\pi\)
−0.813433 + 0.581659i \(0.802404\pi\)
\(158\) 0 0
\(159\) 16.3924 1.30000
\(160\) 0 0
\(161\) 0.594597 1.02987i 0.0468608 0.0811653i
\(162\) 0 0
\(163\) −17.8175 −1.39558 −0.697788 0.716305i \(-0.745832\pi\)
−0.697788 + 0.716305i \(0.745832\pi\)
\(164\) 0 0
\(165\) 0.645106 1.11736i 0.0502214 0.0869861i
\(166\) 0 0
\(167\) −0.202799 + 0.351258i −0.0156931 + 0.0271812i −0.873765 0.486348i \(-0.838329\pi\)
0.858072 + 0.513529i \(0.171662\pi\)
\(168\) 0 0
\(169\) 6.29309 + 10.9000i 0.484084 + 0.838458i
\(170\) 0 0
\(171\) 3.16203 1.17868i 0.241807 0.0901358i
\(172\) 0 0
\(173\) −9.01051 15.6067i −0.685056 1.18655i −0.973419 0.229031i \(-0.926444\pi\)
0.288363 0.957521i \(-0.406889\pi\)
\(174\) 0 0
\(175\) −1.42432 + 2.46699i −0.107668 + 0.186487i
\(176\) 0 0
\(177\) −1.83476 + 3.17789i −0.137909 + 0.238865i
\(178\) 0 0
\(179\) −20.1523 −1.50625 −0.753127 0.657875i \(-0.771455\pi\)
−0.753127 + 0.657875i \(0.771455\pi\)
\(180\) 0 0
\(181\) 8.55541 14.8184i 0.635919 1.10144i −0.350401 0.936600i \(-0.613955\pi\)
0.986320 0.164844i \(-0.0527120\pi\)
\(182\) 0 0
\(183\) −9.45099 −0.698637
\(184\) 0 0
\(185\) −3.18233 5.51197i −0.233970 0.405248i
\(186\) 0 0
\(187\) −1.61798 2.80242i −0.118318 0.204933i
\(188\) 0 0
\(189\) 16.0400 1.16674
\(190\) 0 0
\(191\) −5.28080 −0.382105 −0.191053 0.981580i \(-0.561190\pi\)
−0.191053 + 0.981580i \(0.561190\pi\)
\(192\) 0 0
\(193\) −9.00182 15.5916i −0.647966 1.12231i −0.983608 0.180320i \(-0.942287\pi\)
0.335642 0.941989i \(-0.391047\pi\)
\(194\) 0 0
\(195\) 0.479861 + 0.831144i 0.0343636 + 0.0595195i
\(196\) 0 0
\(197\) 8.07785 0.575523 0.287761 0.957702i \(-0.407089\pi\)
0.287761 + 0.957702i \(0.407089\pi\)
\(198\) 0 0
\(199\) 0.701872 1.21568i 0.0497544 0.0861771i −0.840076 0.542469i \(-0.817489\pi\)
0.889830 + 0.456292i \(0.150823\pi\)
\(200\) 0 0
\(201\) −3.77783 −0.266468
\(202\) 0 0
\(203\) 13.8233 23.9427i 0.970208 1.68045i
\(204\) 0 0
\(205\) 2.00686 3.47598i 0.140165 0.242773i
\(206\) 0 0
\(207\) −0.161595 0.279890i −0.0112316 0.0194537i
\(208\) 0 0
\(209\) 2.90633 + 2.40062i 0.201035 + 0.166054i
\(210\) 0 0
\(211\) 9.45817 + 16.3820i 0.651128 + 1.12779i 0.982850 + 0.184409i \(0.0590370\pi\)
−0.331722 + 0.943377i \(0.607630\pi\)
\(212\) 0 0
\(213\) 1.32940 2.30258i 0.0910888 0.157770i
\(214\) 0 0
\(215\) −1.02915 + 1.78254i −0.0701873 + 0.121568i
\(216\) 0 0
\(217\) −14.0537 −0.954030
\(218\) 0 0
\(219\) −5.31936 + 9.21340i −0.359449 + 0.622584i
\(220\) 0 0
\(221\) 2.40706 0.161917
\(222\) 0 0
\(223\) −8.07400 13.9846i −0.540675 0.936477i −0.998865 0.0476227i \(-0.984835\pi\)
0.458190 0.888854i \(-0.348498\pi\)
\(224\) 0 0
\(225\) 0.387090 + 0.670459i 0.0258060 + 0.0446973i
\(226\) 0 0
\(227\) −26.3186 −1.74683 −0.873414 0.486978i \(-0.838099\pi\)
−0.873414 + 0.486978i \(0.838099\pi\)
\(228\) 0 0
\(229\) −13.3323 −0.881026 −0.440513 0.897746i \(-0.645203\pi\)
−0.440513 + 0.897746i \(0.645203\pi\)
\(230\) 0 0
\(231\) 1.83767 + 3.18294i 0.120910 + 0.209422i
\(232\) 0 0
\(233\) −12.6547 21.9186i −0.829038 1.43594i −0.898794 0.438372i \(-0.855555\pi\)
0.0697556 0.997564i \(-0.477778\pi\)
\(234\) 0 0
\(235\) 3.95396 0.257928
\(236\) 0 0
\(237\) −1.36102 + 2.35736i −0.0884077 + 0.153127i
\(238\) 0 0
\(239\) 23.5500 1.52332 0.761660 0.647977i \(-0.224385\pi\)
0.761660 + 0.647977i \(0.224385\pi\)
\(240\) 0 0
\(241\) −4.19208 + 7.26089i −0.270035 + 0.467715i −0.968871 0.247568i \(-0.920369\pi\)
0.698835 + 0.715283i \(0.253702\pi\)
\(242\) 0 0
\(243\) 3.91213 6.77601i 0.250963 0.434681i
\(244\) 0 0
\(245\) −0.557368 0.965389i −0.0356089 0.0616764i
\(246\) 0 0
\(247\) −2.62739 + 0.979387i −0.167177 + 0.0623169i
\(248\) 0 0
\(249\) 5.54929 + 9.61165i 0.351672 + 0.609113i
\(250\) 0 0
\(251\) 9.12391 15.8031i 0.575896 0.997481i −0.420048 0.907502i \(-0.637987\pi\)
0.995944 0.0899792i \(-0.0286800\pi\)
\(252\) 0 0
\(253\) 0.180510 0.312652i 0.0113486 0.0196563i
\(254\) 0 0
\(255\) −5.58254 −0.349592
\(256\) 0 0
\(257\) −7.04989 + 12.2108i −0.439760 + 0.761687i −0.997671 0.0682144i \(-0.978270\pi\)
0.557911 + 0.829901i \(0.311603\pi\)
\(258\) 0 0
\(259\) 18.1306 1.12658
\(260\) 0 0
\(261\) −3.75679 6.50696i −0.232540 0.402770i
\(262\) 0 0
\(263\) −3.20536 5.55184i −0.197651 0.342341i 0.750116 0.661307i \(-0.229998\pi\)
−0.947766 + 0.318966i \(0.896665\pi\)
\(264\) 0 0
\(265\) −10.9875 −0.674956
\(266\) 0 0
\(267\) −6.63288 −0.405926
\(268\) 0 0
\(269\) −8.99557 15.5808i −0.548469 0.949977i −0.998380 0.0569032i \(-0.981877\pi\)
0.449910 0.893074i \(-0.351456\pi\)
\(270\) 0 0
\(271\) 5.94095 + 10.2900i 0.360887 + 0.625075i 0.988107 0.153767i \(-0.0491406\pi\)
−0.627220 + 0.778842i \(0.715807\pi\)
\(272\) 0 0
\(273\) −2.73390 −0.165463
\(274\) 0 0
\(275\) −0.432400 + 0.748939i −0.0260747 + 0.0451627i
\(276\) 0 0
\(277\) 23.6240 1.41943 0.709715 0.704489i \(-0.248824\pi\)
0.709715 + 0.704489i \(0.248824\pi\)
\(278\) 0 0
\(279\) −1.90970 + 3.30770i −0.114331 + 0.198027i
\(280\) 0 0
\(281\) −6.90465 + 11.9592i −0.411897 + 0.713426i −0.995097 0.0989020i \(-0.968467\pi\)
0.583200 + 0.812328i \(0.301800\pi\)
\(282\) 0 0
\(283\) −5.87868 10.1822i −0.349451 0.605268i 0.636701 0.771111i \(-0.280299\pi\)
−0.986152 + 0.165843i \(0.946965\pi\)
\(284\) 0 0
\(285\) 6.09354 2.27143i 0.360950 0.134548i
\(286\) 0 0
\(287\) 5.71681 + 9.90181i 0.337453 + 0.584485i
\(288\) 0 0
\(289\) 1.49927 2.59681i 0.0881922 0.152753i
\(290\) 0 0
\(291\) −8.09675 + 14.0240i −0.474640 + 0.822100i
\(292\) 0 0
\(293\) −27.0576 −1.58072 −0.790362 0.612640i \(-0.790108\pi\)
−0.790362 + 0.612640i \(0.790108\pi\)
\(294\) 0 0
\(295\) 1.22980 2.13007i 0.0716015 0.124017i
\(296\) 0 0
\(297\) 4.86949 0.282557
\(298\) 0 0
\(299\) 0.134272 + 0.232566i 0.00776516 + 0.0134497i
\(300\) 0 0
\(301\) −2.93167 5.07780i −0.168979 0.292679i
\(302\) 0 0
\(303\) 7.90117 0.453910
\(304\) 0 0
\(305\) 6.33479 0.362729
\(306\) 0 0
\(307\) 4.41912 + 7.65414i 0.252212 + 0.436845i 0.964135 0.265414i \(-0.0855085\pi\)
−0.711922 + 0.702258i \(0.752175\pi\)
\(308\) 0 0
\(309\) 0.287294 + 0.497608i 0.0163436 + 0.0283080i
\(310\) 0 0
\(311\) 0.651493 0.0369428 0.0184714 0.999829i \(-0.494120\pi\)
0.0184714 + 0.999829i \(0.494120\pi\)
\(312\) 0 0
\(313\) 1.48278 2.56825i 0.0838116 0.145166i −0.821073 0.570824i \(-0.806624\pi\)
0.904884 + 0.425658i \(0.139957\pi\)
\(314\) 0 0
\(315\) −2.20536 −0.124258
\(316\) 0 0
\(317\) 5.18993 8.98921i 0.291495 0.504885i −0.682668 0.730728i \(-0.739181\pi\)
0.974164 + 0.225844i \(0.0725139\pi\)
\(318\) 0 0
\(319\) 4.19654 7.26862i 0.234961 0.406965i
\(320\) 0 0
\(321\) 4.79903 + 8.31216i 0.267856 + 0.463939i
\(322\) 0 0
\(323\) 2.70787 16.0840i 0.150670 0.894938i
\(324\) 0 0
\(325\) −0.321640 0.557098i −0.0178414 0.0309022i
\(326\) 0 0
\(327\) 4.90007 8.48718i 0.270975 0.469342i
\(328\) 0 0
\(329\) −5.63170 + 9.75438i −0.310485 + 0.537776i
\(330\) 0 0
\(331\) −15.0922 −0.829543 −0.414772 0.909926i \(-0.636139\pi\)
−0.414772 + 0.909926i \(0.636139\pi\)
\(332\) 0 0
\(333\) 2.46370 4.26725i 0.135010 0.233844i
\(334\) 0 0
\(335\) 2.53220 0.138349
\(336\) 0 0
\(337\) −7.89872 13.6810i −0.430271 0.745251i 0.566626 0.823975i \(-0.308249\pi\)
−0.996896 + 0.0787246i \(0.974915\pi\)
\(338\) 0 0
\(339\) 0.219695 + 0.380522i 0.0119322 + 0.0206671i
\(340\) 0 0
\(341\) −4.26649 −0.231043
\(342\) 0 0
\(343\) −16.7650 −0.905224
\(344\) 0 0
\(345\) −0.311408 0.539375i −0.0167657 0.0290390i
\(346\) 0 0
\(347\) −10.6761 18.4915i −0.573122 0.992676i −0.996243 0.0866031i \(-0.972399\pi\)
0.423121 0.906073i \(-0.360935\pi\)
\(348\) 0 0
\(349\) −32.3897 −1.73378 −0.866891 0.498497i \(-0.833885\pi\)
−0.866891 + 0.498497i \(0.833885\pi\)
\(350\) 0 0
\(351\) −1.81108 + 3.13689i −0.0966685 + 0.167435i
\(352\) 0 0
\(353\) 0.730583 0.0388850 0.0194425 0.999811i \(-0.493811\pi\)
0.0194425 + 0.999811i \(0.493811\pi\)
\(354\) 0 0
\(355\) −0.891065 + 1.54337i −0.0472928 + 0.0819136i
\(356\) 0 0
\(357\) 7.95132 13.7721i 0.420828 0.728896i
\(358\) 0 0
\(359\) −13.4248 23.2524i −0.708533 1.22722i −0.965401 0.260769i \(-0.916024\pi\)
0.256868 0.966447i \(-0.417309\pi\)
\(360\) 0 0
\(361\) 3.58853 + 18.6580i 0.188870 + 0.982002i
\(362\) 0 0
\(363\) −7.64766 13.2461i −0.401398 0.695242i
\(364\) 0 0
\(365\) 3.56545 6.17554i 0.186624 0.323242i
\(366\) 0 0
\(367\) −11.4822 + 19.8877i −0.599364 + 1.03813i 0.393551 + 0.919303i \(0.371246\pi\)
−0.992915 + 0.118826i \(0.962087\pi\)
\(368\) 0 0
\(369\) 3.10734 0.161761
\(370\) 0 0
\(371\) 15.6497 27.1060i 0.812491 1.40728i
\(372\) 0 0
\(373\) 29.5305 1.52903 0.764515 0.644606i \(-0.222979\pi\)
0.764515 + 0.644606i \(0.222979\pi\)
\(374\) 0 0
\(375\) 0.745959 + 1.29204i 0.0385212 + 0.0667206i
\(376\) 0 0
\(377\) 3.12159 + 5.40676i 0.160770 + 0.278462i
\(378\) 0 0
\(379\) −17.5117 −0.899517 −0.449759 0.893150i \(-0.648490\pi\)
−0.449759 + 0.893150i \(0.648490\pi\)
\(380\) 0 0
\(381\) 13.1810 0.675282
\(382\) 0 0
\(383\) 4.05326 + 7.02045i 0.207112 + 0.358728i 0.950804 0.309794i \(-0.100260\pi\)
−0.743692 + 0.668523i \(0.766927\pi\)
\(384\) 0 0
\(385\) −1.23175 2.13346i −0.0627759 0.108731i
\(386\) 0 0
\(387\) −1.59349 −0.0810016
\(388\) 0 0
\(389\) −8.65392 + 14.9890i −0.438771 + 0.759974i −0.997595 0.0693125i \(-0.977919\pi\)
0.558824 + 0.829286i \(0.311253\pi\)
\(390\) 0 0
\(391\) −1.56208 −0.0789976
\(392\) 0 0
\(393\) −15.6001 + 27.0201i −0.786920 + 1.36298i
\(394\) 0 0
\(395\) 0.912262 1.58008i 0.0459009 0.0795026i
\(396\) 0 0
\(397\) 5.69472 + 9.86354i 0.285810 + 0.495037i 0.972805 0.231625i \(-0.0744041\pi\)
−0.686996 + 0.726662i \(0.741071\pi\)
\(398\) 0 0
\(399\) −3.07555 + 18.2679i −0.153970 + 0.914541i
\(400\) 0 0
\(401\) 4.46930 + 7.74106i 0.223186 + 0.386570i 0.955774 0.294103i \(-0.0950208\pi\)
−0.732587 + 0.680673i \(0.761687\pi\)
\(402\) 0 0
\(403\) 1.58681 2.74844i 0.0790447 0.136909i
\(404\) 0 0
\(405\) 3.03905 5.26380i 0.151012 0.261560i
\(406\) 0 0
\(407\) 5.50417 0.272832
\(408\) 0 0
\(409\) 3.27235 5.66788i 0.161808 0.280259i −0.773709 0.633541i \(-0.781601\pi\)
0.935517 + 0.353282i \(0.114934\pi\)
\(410\) 0 0
\(411\) −7.78001 −0.383760
\(412\) 0 0
\(413\) 3.50324 + 6.06780i 0.172383 + 0.298577i
\(414\) 0 0
\(415\) −3.71956 6.44247i −0.182586 0.316249i
\(416\) 0 0
\(417\) −15.9991 −0.783479
\(418\) 0 0
\(419\) −21.8441 −1.06715 −0.533576 0.845752i \(-0.679152\pi\)
−0.533576 + 0.845752i \(0.679152\pi\)
\(420\) 0 0
\(421\) 14.6717 + 25.4121i 0.715054 + 1.23851i 0.962939 + 0.269720i \(0.0869311\pi\)
−0.247885 + 0.968789i \(0.579736\pi\)
\(422\) 0 0
\(423\) 1.53054 + 2.65097i 0.0744172 + 0.128894i
\(424\) 0 0
\(425\) 3.74185 0.181507
\(426\) 0 0
\(427\) −9.02276 + 15.6279i −0.436642 + 0.756286i
\(428\) 0 0
\(429\) −0.829969 −0.0400713
\(430\) 0 0
\(431\) −6.44336 + 11.1602i −0.310366 + 0.537570i −0.978442 0.206524i \(-0.933785\pi\)
0.668076 + 0.744093i \(0.267118\pi\)
\(432\) 0 0
\(433\) 6.92144 11.9883i 0.332623 0.576120i −0.650402 0.759590i \(-0.725400\pi\)
0.983025 + 0.183470i \(0.0587330\pi\)
\(434\) 0 0
\(435\) −7.23970 12.5395i −0.347117 0.601225i
\(436\) 0 0
\(437\) 1.70506 0.635578i 0.0815641 0.0304038i
\(438\) 0 0
\(439\) −0.0354040 0.0613216i −0.00168974 0.00292672i 0.865179 0.501463i \(-0.167205\pi\)
−0.866869 + 0.498536i \(0.833871\pi\)
\(440\) 0 0
\(441\) 0.431503 0.747384i 0.0205477 0.0355897i
\(442\) 0 0
\(443\) −1.89457 + 3.28149i −0.0900137 + 0.155908i −0.907517 0.420016i \(-0.862024\pi\)
0.817503 + 0.575924i \(0.195358\pi\)
\(444\) 0 0
\(445\) 4.44588 0.210755
\(446\) 0 0
\(447\) −11.1234 + 19.2663i −0.526120 + 0.911266i
\(448\) 0 0
\(449\) −26.5765 −1.25422 −0.627112 0.778929i \(-0.715763\pi\)
−0.627112 + 0.778929i \(0.715763\pi\)
\(450\) 0 0
\(451\) 1.73553 + 3.00603i 0.0817230 + 0.141548i
\(452\) 0 0
\(453\) −16.0075 27.7258i −0.752098 1.30267i
\(454\) 0 0
\(455\) 1.83247 0.0859077
\(456\) 0 0
\(457\) −33.1523 −1.55080 −0.775400 0.631471i \(-0.782452\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(458\) 0 0
\(459\) −10.5348 18.2467i −0.491720 0.851684i
\(460\) 0 0
\(461\) 9.62679 + 16.6741i 0.448364 + 0.776590i 0.998280 0.0586304i \(-0.0186734\pi\)
−0.549915 + 0.835220i \(0.685340\pi\)
\(462\) 0 0
\(463\) −39.1713 −1.82044 −0.910222 0.414120i \(-0.864089\pi\)
−0.910222 + 0.414120i \(0.864089\pi\)
\(464\) 0 0
\(465\) −3.68018 + 6.37427i −0.170664 + 0.295600i
\(466\) 0 0
\(467\) 39.0650 1.80771 0.903856 0.427836i \(-0.140724\pi\)
0.903856 + 0.427836i \(0.140724\pi\)
\(468\) 0 0
\(469\) −3.60665 + 6.24691i −0.166540 + 0.288455i
\(470\) 0 0
\(471\) −1.81356 + 3.14118i −0.0835644 + 0.144738i
\(472\) 0 0
\(473\) −0.890007 1.54154i −0.0409226 0.0708800i
\(474\) 0 0
\(475\) −4.08436 + 1.52249i −0.187404 + 0.0698565i
\(476\) 0 0
\(477\) −4.25314 7.36666i −0.194738 0.337296i
\(478\) 0 0
\(479\) −12.3775 + 21.4385i −0.565543 + 0.979550i 0.431455 + 0.902134i \(0.358000\pi\)
−0.996999 + 0.0774158i \(0.975333\pi\)
\(480\) 0 0
\(481\) −2.04714 + 3.54574i −0.0933413 + 0.161672i
\(482\) 0 0
\(483\) 1.77418 0.0807280
\(484\) 0 0
\(485\) 5.42707 9.39996i 0.246431 0.426830i
\(486\) 0 0
\(487\) −21.8871 −0.991797 −0.495899 0.868380i \(-0.665161\pi\)
−0.495899 + 0.868380i \(0.665161\pi\)
\(488\) 0 0
\(489\) −13.2911 23.0209i −0.601046 1.04104i
\(490\) 0 0
\(491\) 4.69777 + 8.13677i 0.212007 + 0.367207i 0.952343 0.305030i \(-0.0986666\pi\)
−0.740335 + 0.672238i \(0.765333\pi\)
\(492\) 0 0
\(493\) −36.3155 −1.63557
\(494\) 0 0
\(495\) −0.669511 −0.0300923
\(496\) 0 0
\(497\) −2.53832 4.39650i −0.113859 0.197210i
\(498\) 0 0
\(499\) 12.4558 + 21.5740i 0.557596 + 0.965785i 0.997696 + 0.0678367i \(0.0216097\pi\)
−0.440100 + 0.897949i \(0.645057\pi\)
\(500\) 0 0
\(501\) −0.605119 −0.0270347
\(502\) 0 0
\(503\) −15.6590 + 27.1222i −0.698200 + 1.20932i 0.270890 + 0.962610i \(0.412682\pi\)
−0.969090 + 0.246707i \(0.920651\pi\)
\(504\) 0 0
\(505\) −5.29598 −0.235668
\(506\) 0 0
\(507\) −9.38878 + 16.2619i −0.416971 + 0.722214i
\(508\) 0 0
\(509\) 4.83310 8.37117i 0.214223 0.371045i −0.738809 0.673915i \(-0.764611\pi\)
0.953032 + 0.302870i \(0.0979447\pi\)
\(510\) 0 0
\(511\) 10.1567 + 17.5919i 0.449305 + 0.778219i
\(512\) 0 0
\(513\) 18.9233 + 15.6306i 0.835484 + 0.690106i
\(514\) 0 0
\(515\) −0.192567 0.333536i −0.00848552 0.0146973i
\(516\) 0 0
\(517\) −1.70969 + 2.96127i −0.0751922 + 0.130237i
\(518\) 0 0
\(519\) 13.4429 23.2839i 0.590080 1.02205i
\(520\) 0 0
\(521\) −0.982633 −0.0430499 −0.0215250 0.999768i \(-0.506852\pi\)
−0.0215250 + 0.999768i \(0.506852\pi\)
\(522\) 0 0
\(523\) 19.8604 34.3993i 0.868436 1.50418i 0.00484172 0.999988i \(-0.498459\pi\)
0.863594 0.504187i \(-0.168208\pi\)
\(524\) 0 0
\(525\) −4.24993 −0.185482
\(526\) 0 0
\(527\) 9.23020 + 15.9872i 0.402074 + 0.696413i
\(528\) 0 0
\(529\) 11.4129 + 19.7677i 0.496211 + 0.859463i
\(530\) 0 0
\(531\) 1.90417 0.0826337
\(532\) 0 0
\(533\) −2.58195 −0.111837
\(534\) 0 0
\(535\) −3.21668 5.57146i −0.139069 0.240875i
\(536\) 0 0
\(537\) −15.0328 26.0376i −0.648713 1.12360i
\(538\) 0 0
\(539\) 0.964024 0.0415234
\(540\) 0 0
\(541\) −15.3887 + 26.6541i −0.661614 + 1.14595i 0.318577 + 0.947897i \(0.396795\pi\)
−0.980191 + 0.198052i \(0.936538\pi\)
\(542\) 0 0
\(543\) 25.5280 1.09551
\(544\) 0 0
\(545\) −3.28441 + 5.68877i −0.140689 + 0.243680i
\(546\) 0 0
\(547\) −8.93287 + 15.4722i −0.381942 + 0.661543i −0.991340 0.131322i \(-0.958078\pi\)
0.609398 + 0.792865i \(0.291411\pi\)
\(548\) 0 0
\(549\) 2.45213 + 4.24722i 0.104654 + 0.181267i
\(550\) 0 0
\(551\) 39.6397 14.7761i 1.68871 0.629482i
\(552\) 0 0
\(553\) 2.59870 + 4.50109i 0.110508 + 0.191406i
\(554\) 0 0
\(555\) 4.74778 8.22340i 0.201532 0.349064i
\(556\) 0 0
\(557\) 5.32878 9.22971i 0.225787 0.391075i −0.730768 0.682626i \(-0.760838\pi\)
0.956555 + 0.291551i \(0.0941712\pi\)
\(558\) 0 0
\(559\) 1.32406 0.0560019
\(560\) 0 0
\(561\) 2.41389 4.18098i 0.101915 0.176521i
\(562\) 0 0
\(563\) −7.75961 −0.327029 −0.163514 0.986541i \(-0.552283\pi\)
−0.163514 + 0.986541i \(0.552283\pi\)
\(564\) 0 0
\(565\) −0.147256 0.255056i −0.00619513 0.0107303i
\(566\) 0 0
\(567\) 8.65716 + 14.9946i 0.363567 + 0.629716i
\(568\) 0 0
\(569\) 5.72754 0.240111 0.120056 0.992767i \(-0.461693\pi\)
0.120056 + 0.992767i \(0.461693\pi\)
\(570\) 0 0
\(571\) 20.8347 0.871903 0.435952 0.899970i \(-0.356412\pi\)
0.435952 + 0.899970i \(0.356412\pi\)
\(572\) 0 0
\(573\) −3.93926 6.82300i −0.164565 0.285035i
\(574\) 0 0
\(575\) 0.208730 + 0.361531i 0.00870465 + 0.0150769i
\(576\) 0 0
\(577\) −5.11190 −0.212811 −0.106406 0.994323i \(-0.533934\pi\)
−0.106406 + 0.994323i \(0.533934\pi\)
\(578\) 0 0
\(579\) 13.4300 23.2614i 0.558131 0.966712i
\(580\) 0 0
\(581\) 21.1914 0.879167
\(582\) 0 0
\(583\) 4.75099 8.22896i 0.196766 0.340809i
\(584\) 0 0
\(585\) 0.249007 0.431294i 0.0102952 0.0178318i
\(586\) 0 0
\(587\) −5.33462 9.23984i −0.220184 0.381369i 0.734680 0.678414i \(-0.237332\pi\)
−0.954864 + 0.297045i \(0.903999\pi\)
\(588\) 0 0
\(589\) −16.5800 13.6950i −0.683165 0.564292i
\(590\) 0 0
\(591\) 6.02574 + 10.4369i 0.247866 + 0.429316i
\(592\) 0 0
\(593\) 8.50133 14.7247i 0.349108 0.604673i −0.636983 0.770878i \(-0.719818\pi\)
0.986091 + 0.166205i \(0.0531513\pi\)
\(594\) 0 0
\(595\) −5.32959 + 9.23112i −0.218492 + 0.378439i
\(596\) 0 0
\(597\) 2.09427 0.0857128
\(598\) 0 0
\(599\) 14.3375 24.8334i 0.585816 1.01466i −0.408957 0.912554i \(-0.634107\pi\)
0.994773 0.102110i \(-0.0325592\pi\)
\(600\) 0 0
\(601\) 27.4370 1.11918 0.559590 0.828770i \(-0.310959\pi\)
0.559590 + 0.828770i \(0.310959\pi\)
\(602\) 0 0
\(603\) 0.980187 + 1.69773i 0.0399163 + 0.0691371i
\(604\) 0 0
\(605\) 5.12606 + 8.87860i 0.208404 + 0.360966i
\(606\) 0 0
\(607\) 17.7547 0.720639 0.360320 0.932829i \(-0.382668\pi\)
0.360320 + 0.932829i \(0.382668\pi\)
\(608\) 0 0
\(609\) 41.2466 1.67140
\(610\) 0 0
\(611\) −1.27175 2.20274i −0.0514496 0.0891133i
\(612\) 0 0
\(613\) −17.3196 29.9983i −0.699530 1.21162i −0.968629 0.248509i \(-0.920059\pi\)
0.269099 0.963112i \(-0.413274\pi\)
\(614\) 0 0
\(615\) 5.98814 0.241465
\(616\) 0 0
\(617\) −2.23284 + 3.86740i −0.0898909 + 0.155696i −0.907465 0.420128i \(-0.861985\pi\)
0.817574 + 0.575824i \(0.195319\pi\)
\(618\) 0 0
\(619\) 17.9112 0.719913 0.359957 0.932969i \(-0.382791\pi\)
0.359957 + 0.932969i \(0.382791\pi\)
\(620\) 0 0
\(621\) 1.17531 2.03570i 0.0471636 0.0816898i
\(622\) 0 0
\(623\) −6.33234 + 10.9679i −0.253700 + 0.439421i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −0.933688 + 5.54586i −0.0372879 + 0.221480i
\(628\) 0 0
\(629\) −11.9078 20.6250i −0.474796 0.822371i
\(630\) 0 0
\(631\) 2.48440 4.30311i 0.0989026 0.171304i −0.812328 0.583201i \(-0.801800\pi\)
0.911231 + 0.411896i \(0.135133\pi\)
\(632\) 0 0
\(633\) −14.1108 + 24.4407i −0.560855 + 0.971429i
\(634\) 0 0
\(635\) −8.83492 −0.350603
\(636\) 0 0
\(637\) −0.358544 + 0.621016i −0.0142060 + 0.0246056i
\(638\) 0 0
\(639\) −1.37969 −0.0545796
\(640\) 0 0
\(641\) 18.9760 + 32.8675i 0.749508 + 1.29819i 0.948059 + 0.318096i \(0.103043\pi\)
−0.198550 + 0.980091i \(0.563623\pi\)
\(642\) 0 0
\(643\) 17.6251 + 30.5276i 0.695067 + 1.20389i 0.970158 + 0.242473i \(0.0779585\pi\)
−0.275092 + 0.961418i \(0.588708\pi\)
\(644\) 0 0
\(645\) −3.07081 −0.120913
\(646\) 0 0
\(647\) −35.5219 −1.39651 −0.698254 0.715850i \(-0.746040\pi\)
−0.698254 + 0.715850i \(0.746040\pi\)
\(648\) 0 0
\(649\) 1.06353 + 1.84209i 0.0417471 + 0.0723082i
\(650\) 0 0
\(651\) −10.4835 18.1580i −0.410881 0.711667i
\(652\) 0 0
\(653\) 8.02411 0.314008 0.157004 0.987598i \(-0.449816\pi\)
0.157004 + 0.987598i \(0.449816\pi\)
\(654\) 0 0
\(655\) 10.4564 18.1110i 0.408565 0.707655i
\(656\) 0 0
\(657\) 5.52059 0.215379
\(658\) 0 0
\(659\) −23.6098 + 40.8933i −0.919706 + 1.59298i −0.119844 + 0.992793i \(0.538240\pi\)
−0.799861 + 0.600185i \(0.795094\pi\)
\(660\) 0 0
\(661\) 13.0580 22.6171i 0.507896 0.879702i −0.492062 0.870560i \(-0.663757\pi\)
0.999958 0.00914181i \(-0.00290997\pi\)
\(662\) 0 0
\(663\) 1.79557 + 3.11002i 0.0697342 + 0.120783i
\(664\) 0 0
\(665\) 2.06147 12.2446i 0.0799405 0.474825i
\(666\) 0 0
\(667\) −2.02577 3.50874i −0.0784383 0.135859i
\(668\) 0 0
\(669\) 12.0458 20.8639i 0.465716 0.806643i
\(670\) 0 0
\(671\) −2.73917 + 4.74437i −0.105744 + 0.183154i
\(672\) 0 0
\(673\) 15.3820 0.592931 0.296466 0.955044i \(-0.404192\pi\)
0.296466 + 0.955044i \(0.404192\pi\)
\(674\) 0 0
\(675\) −2.81538 + 4.87639i −0.108364 + 0.187692i
\(676\) 0 0
\(677\) 24.4763 0.940701 0.470350 0.882480i \(-0.344128\pi\)
0.470350 + 0.882480i \(0.344128\pi\)
\(678\) 0 0
\(679\) 15.4598 + 26.7771i 0.593291 + 1.02761i
\(680\) 0 0
\(681\) −19.6326 34.0047i −0.752324 1.30306i
\(682\) 0 0
\(683\) 17.8502 0.683018 0.341509 0.939879i \(-0.389062\pi\)
0.341509 + 0.939879i \(0.389062\pi\)
\(684\) 0 0
\(685\) 5.21477 0.199246
\(686\) 0 0
\(687\) −9.94538 17.2259i −0.379440 0.657210i
\(688\) 0 0
\(689\) 3.53402 + 6.12110i 0.134635 + 0.233195i
\(690\) 0 0
\(691\) 9.27242 0.352739 0.176370 0.984324i \(-0.443565\pi\)
0.176370 + 0.984324i \(0.443565\pi\)
\(692\) 0 0
\(693\) 0.953597 1.65168i 0.0362241 0.0627421i
\(694\) 0 0
\(695\) 10.7238 0.406778
\(696\) 0 0
\(697\) 7.50937 13.0066i 0.284438 0.492660i
\(698\) 0 0
\(699\) 18.8798 32.7008i 0.714100 1.23686i
\(700\) 0 0
\(701\) 3.84453 + 6.65892i 0.145206 + 0.251504i 0.929450 0.368949i \(-0.120282\pi\)
−0.784244 + 0.620453i \(0.786949\pi\)
\(702\) 0 0
\(703\) 21.3897 + 17.6678i 0.806728 + 0.666354i
\(704\) 0 0
\(705\) 2.94949 + 5.10867i 0.111084 + 0.192404i
\(706\) 0 0
\(707\) 7.54316 13.0651i 0.283690 0.491365i
\(708\) 0 0
\(709\) −12.2187 + 21.1635i −0.458885 + 0.794812i −0.998902 0.0468421i \(-0.985084\pi\)
0.540018 + 0.841654i \(0.318418\pi\)
\(710\) 0 0
\(711\) 1.41251 0.0529732
\(712\) 0 0
\(713\) −1.02977 + 1.78361i −0.0385652 + 0.0667968i
\(714\) 0 0
\(715\) 0.556310 0.0208048
\(716\) 0 0
\(717\) 17.5673 + 30.4275i 0.656063 + 1.13633i
\(718\) 0 0
\(719\) −11.0563 19.1501i −0.412331 0.714178i 0.582813 0.812606i \(-0.301952\pi\)
−0.995144 + 0.0984282i \(0.968619\pi\)
\(720\) 0 0
\(721\) 1.09711 0.0408584
\(722\) 0 0
\(723\) −12.5085 −0.465195
\(724\) 0 0
\(725\) 4.85261 + 8.40497i 0.180222 + 0.312153i
\(726\) 0 0
\(727\) −14.5247 25.1575i −0.538692 0.933042i −0.998975 0.0452694i \(-0.985585\pi\)
0.460283 0.887772i \(-0.347748\pi\)
\(728\) 0 0
\(729\) 29.9075 1.10768
\(730\) 0 0
\(731\) −3.85092 + 6.66999i −0.142431 + 0.246698i
\(732\) 0 0
\(733\) 14.5428 0.537151 0.268576 0.963259i \(-0.413447\pi\)
0.268576 + 0.963259i \(0.413447\pi\)
\(734\) 0 0
\(735\) 0.831547 1.44028i 0.0306721 0.0531256i
\(736\) 0 0
\(737\) −1.09492 + 1.89646i −0.0403320 + 0.0698570i
\(738\) 0 0
\(739\) −2.37798 4.11878i −0.0874754 0.151512i 0.818968 0.573839i \(-0.194547\pi\)
−0.906443 + 0.422327i \(0.861213\pi\)
\(740\) 0 0
\(741\) −3.22533 2.66411i −0.118486 0.0978687i
\(742\) 0 0
\(743\) 2.93853 + 5.08968i 0.107804 + 0.186722i 0.914880 0.403725i \(-0.132285\pi\)
−0.807076 + 0.590447i \(0.798951\pi\)
\(744\) 0 0
\(745\) 7.45578 12.9138i 0.273159 0.473125i
\(746\) 0 0
\(747\) 2.87961 4.98763i 0.105359 0.182488i
\(748\) 0 0
\(749\) 18.3263 0.669629
\(750\) 0 0
\(751\) 0.810481 1.40379i 0.0295749 0.0512252i −0.850859 0.525394i \(-0.823918\pi\)
0.880434 + 0.474169i \(0.157251\pi\)
\(752\) 0 0
\(753\) 27.2243 0.992107
\(754\) 0 0
\(755\) 10.7295 + 18.5840i 0.390485 + 0.676341i
\(756\) 0 0
\(757\) 14.0567 + 24.3470i 0.510901 + 0.884907i 0.999920 + 0.0126336i \(0.00402151\pi\)
−0.489019 + 0.872273i \(0.662645\pi\)
\(758\) 0 0
\(759\) 0.538612 0.0195504
\(760\) 0 0
\(761\) 20.1663 0.731027 0.365514 0.930806i \(-0.380893\pi\)
0.365514 + 0.930806i \(0.380893\pi\)
\(762\) 0 0
\(763\) −9.35610 16.2052i −0.338713 0.586669i
\(764\) 0 0
\(765\) 1.44843 + 2.50876i 0.0523682 + 0.0907044i
\(766\) 0 0
\(767\) −1.58221 −0.0571303
\(768\) 0 0
\(769\) −22.6524 + 39.2350i −0.816865 + 1.41485i 0.0911160 + 0.995840i \(0.470957\pi\)
−0.907981 + 0.419011i \(0.862377\pi\)
\(770\) 0 0
\(771\) −21.0357 −0.757583
\(772\) 0 0
\(773\) 10.0881 17.4731i 0.362843 0.628462i −0.625585 0.780156i \(-0.715139\pi\)
0.988428 + 0.151694i \(0.0484728\pi\)
\(774\) 0 0
\(775\) 2.46675 4.27253i 0.0886081 0.153474i
\(776\) 0 0
\(777\) 13.5247 + 23.4255i 0.485196 + 0.840385i
\(778\) 0 0
\(779\) −2.90461 + 17.2526i −0.104068 + 0.618138i
\(780\) 0 0
\(781\) −0.770594 1.33471i −0.0275740 0.0477596i
\(782\) 0 0
\(783\) 27.3239 47.3264i 0.976478 1.69131i
\(784\) 0 0
\(785\) 1.21559 2.10546i 0.0433862 0.0751471i
\(786\) 0 0
\(787\) 46.1385 1.64466 0.822331 0.569010i \(-0.192673\pi\)
0.822331 + 0.569010i \(0.192673\pi\)
\(788\) 0 0
\(789\) 4.78213 8.28289i 0.170248 0.294879i
\(790\) 0 0
\(791\) 0.838961 0.0298300
\(792\) 0 0
\(793\) −2.03753 3.52910i −0.0723546 0.125322i
\(794\) 0 0
\(795\) −8.19622 14.1963i −0.290690 0.503490i
\(796\) 0