Properties

Label 1520.2.q.o.961.3
Level $1520$
Weight $2$
Character 1520.961
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 961.3
Root \(-0.245959 + 0.426014i\) of defining polynomial
Character \(\chi\) \(=\) 1520.961
Dual form 1520.2.q.o.881.3

$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.566252 0.824232i \(-0.691607\pi\)
0.996932 + 0.0782728i \(0.0249405\pi\)
\(4\) 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 0.817969 0.575262i \(-0.195100\pi\)
−0.907176 + 0.420751i \(0.861767\pi\)
\(14\) 0 0
\(15\) 0.745959 + 1.29204i 0.192606 + 0.333603i
\(16\) 0 0
\(17\) −1.87093 + 3.24054i −0.453766 + 0.785946i −0.998616 0.0525872i \(-0.983253\pi\)
0.544850 + 0.838534i \(0.316587\pi\)
\(18\) 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 0.886966 0.461834i \(-0.152808\pi\)
−0.843443 + 0.537218i \(0.819475\pi\)
\(24\) 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 0.826059 + 0.563584i \(0.190578\pi\)
0.0750490 + 0.997180i \(0.476089\pi\)
\(30\) 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 −0.665681 0.746236i \(-0.731859\pi\)
0.979100 + 0.203379i \(0.0651924\pi\)
\(42\) 0 0
\(43\) −1.02915 + 1.78254i −0.156944 + 0.271834i −0.933765 0.357887i \(-0.883497\pi\)
0.776821 + 0.629721i \(0.216831\pi\)
\(44\) 0 0
\(45\) −0.774179 −0.115408
\(46\) 0 0
\(47\) −1.97698 3.42423i −0.288372 0.499475i 0.685049 0.728497i \(-0.259781\pi\)
−0.973421 + 0.229022i \(0.926447\pi\)
\(48\) 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 0.945561 + 0.325444i \(0.105514\pi\)
−0.190937 + 0.981602i \(0.561153\pi\)
\(54\) 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 −0.774801 0.632206i \(-0.782150\pi\)
0.934906 + 0.354894i \(0.115483\pi\)
\(60\) 0 0
\(61\) −3.16740 5.48609i −0.405543 0.702422i 0.588841 0.808249i \(-0.299584\pi\)
−0.994385 + 0.105827i \(0.966251\pi\)
\(62\) 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 0.778263 0.627938i \(-0.216101\pi\)
−0.932942 + 0.360027i \(0.882767\pi\)
\(68\) 0 0
\(69\) 0.622817 0.0749783
\(70\) 0 0
\(71\) −0.891065 + 1.54337i −0.105750 + 0.183164i −0.914044 0.405614i \(-0.867058\pi\)
0.808294 + 0.588779i \(0.200391\pi\)
\(72\) 0 0
\(73\) 3.56545 6.17554i 0.417304 0.722792i −0.578363 0.815780i \(-0.696308\pi\)
0.995667 + 0.0929873i \(0.0296416\pi\)
\(74\) 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 −0.810133 0.586246i \(-0.800605\pi\)
0.912771 + 0.408473i \(0.133939\pi\)
\(80\) 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 0.723825 0.689984i \(-0.242382\pi\)
−0.959456 + 0.281859i \(0.909049\pi\)
\(90\) 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 −0.447165 0.894452i \(-0.647566\pi\)
0.998200 0.0599699i \(-0.0191005\pi\)
\(98\) 0 0
\(99\) 0.334755 + 0.579813i 0.0336442 + 0.0582734i
\(100\) 0 0
\(101\) 2.64799 + 4.58645i 0.263485 + 0.456369i 0.967166 0.254147i \(-0.0817948\pi\)
−0.703681 + 0.710516i \(0.748461\pi\)
\(102\) 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 −0.979350 0.202171i \(-0.935200\pi\)
0.664761 + 0.747056i \(0.268534\pi\)
\(110\) 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 0.992711 0.120516i \(-0.0384548\pi\)
−0.600725 + 0.799456i \(0.705121\pi\)
\(128\) 0 0
\(129\) 1.53540 + 2.65940i 0.135185 + 0.234147i
\(130\) 0 0
\(131\) 10.4564 18.1110i 0.913578 1.58236i 0.104609 0.994513i \(-0.466641\pi\)
0.808969 0.587851i \(-0.200026\pi\)
\(132\) 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 0.732882 0.680356i \(-0.238175\pi\)
−0.955646 + 0.294517i \(0.904841\pi\)
\(138\) 0 0
\(139\) −5.36192 9.28711i −0.454792 0.787723i 0.543884 0.839160i \(-0.316953\pi\)
−0.998676 + 0.0514375i \(0.983620\pi\)
\(140\) 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 −0.380304 0.924861i \(-0.624181\pi\)
0.991106 0.133078i \(-0.0424860\pi\)
\(150\) 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 −0.813433 0.581659i \(-0.802404\pi\)
0.910448 + 0.413624i \(0.135737\pi\)
\(158\) 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 0.858072 0.513529i \(-0.171662\pi\)
−0.873765 + 0.486348i \(0.838329\pi\)
\(168\) 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 0.288363 + 0.957521i \(0.406889\pi\)
−0.973419 + 0.229031i \(0.926444\pi\)
\(174\) 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 0.986320 + 0.164844i \(0.0527120\pi\)
−0.350401 + 0.936600i \(0.613955\pi\)
\(182\) 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 0.335642 + 0.941989i \(0.391047\pi\)
−0.983608 + 0.180320i \(0.942287\pi\)
\(194\) 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 0.889830 0.456292i \(-0.150823\pi\)
−0.840076 + 0.542469i \(0.817489\pi\)
\(200\) 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 −0.331722 0.943377i \(-0.607630\pi\)
0.982850 0.184409i \(-0.0590370\pi\)
\(212\) 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 0.458190 + 0.888854i \(0.348498\pi\)
−0.998865 + 0.0476227i \(0.984835\pi\)
\(224\) 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 0.0697556 + 0.997564i \(0.477778\pi\)
−0.898794 + 0.438372i \(0.855555\pi\)
\(234\) 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 0.698835 0.715283i \(-0.253702\pi\)
−0.968871 + 0.247568i \(0.920369\pi\)
\(242\) 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 0.995944 + 0.0899792i \(0.0286800\pi\)
−0.420048 + 0.907502i \(0.637987\pi\)
\(252\) 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 0.557911 0.829901i \(-0.311603\pi\)
−0.997671 + 0.0682144i \(0.978270\pi\)
\(258\) 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 −0.947766 0.318966i \(-0.896665\pi\)
0.750116 + 0.661307i \(0.229998\pi\)
\(264\) 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 0.449910 + 0.893074i \(0.351456\pi\)
−0.998380 + 0.0569032i \(0.981877\pi\)
\(270\) 0 0
\(271\) 5.94095 10.2900i 0.360887 0.625075i −0.627220 0.778842i \(-0.715807\pi\)
0.988107 + 0.153767i \(0.0491406\pi\)
\(272\) 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 0.583200 0.812328i \(-0.301800\pi\)
−0.995097 + 0.0989020i \(0.968467\pi\)
\(282\) 0 0
\(283\) −5.87868 + 10.1822i −0.349451 + 0.605268i −0.986152 0.165843i \(-0.946965\pi\)
0.636701 + 0.771111i \(0.280299\pi\)
\(284\) 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 −0.711922 0.702258i \(-0.752175\pi\)
0.964135 + 0.265414i \(0.0855085\pi\)
\(308\) 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 0.904884 0.425658i \(-0.139957\pi\)
−0.821073 + 0.570824i \(0.806624\pi\)
\(314\) 0 0
\(315\) −2.20536 −0.124258
\(316\) 0 0
\(317\) 5.18993 + 8.98921i 0.291495 + 0.504885i 0.974164 0.225844i \(-0.0725139\pi\)
−0.682668 + 0.730728i \(0.739181\pi\)
\(318\) 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 −0.996896 0.0787246i \(-0.974915\pi\)
0.566626 + 0.823975i \(0.308249\pi\)
\(338\) 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 0.423121 + 0.906073i \(0.360935\pi\)
−0.996243 + 0.0866031i \(0.972399\pi\)
\(348\) 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 0.256868 + 0.966447i \(0.417309\pi\)
−0.965401 + 0.260769i \(0.916024\pi\)
\(360\) 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 −0.992915 0.118826i \(-0.962087\pi\)
0.393551 0.919303i \(-0.371246\pi\)
\(368\) 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 −0.743692 0.668523i \(-0.766927\pi\)
0.950804 + 0.309794i \(0.100260\pi\)
\(384\) 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 0.558824 0.829286i \(-0.311253\pi\)
−0.997595 + 0.0693125i \(0.977919\pi\)
\(390\) 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 −0.686996 0.726662i \(-0.741071\pi\)
0.972805 + 0.231625i \(0.0744041\pi\)
\(398\) 0 0
\(399\) −3.07555 18.2679i −0.153970 0.914541i
\(400\) 0 0
\(401\) 4.46930 7.74106i 0.223186 0.386570i −0.732587 0.680673i \(-0.761687\pi\)
0.955774 + 0.294103i \(0.0950208\pi\)
\(402\) 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 0.935517 0.353282i \(-0.114934\pi\)
−0.773709 + 0.633541i \(0.781601\pi\)
\(410\) 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 −0.247885 0.968789i \(-0.579736\pi\)
0.962939 0.269720i \(-0.0869311\pi\)
\(422\) 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 0.668076 0.744093i \(-0.267118\pi\)
−0.978442 + 0.206524i \(0.933785\pi\)
\(432\) 0 0
\(433\) 6.92144 + 11.9883i 0.332623 + 0.576120i 0.983025 0.183470i \(-0.0587330\pi\)
−0.650402 + 0.759590i \(0.725400\pi\)
\(434\) 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 −0.866869 0.498536i \(-0.833871\pi\)
0.865179 + 0.501463i \(0.167205\pi\)
\(440\) 0 0
\(441\) 0.431503 + 0.747384i 0.0205477 + 0.0355897i
\(442\) 0 0
\(443\) −1.89457 3.28149i −0.0900137 0.155908i 0.817503 0.575924i \(-0.195358\pi\)
−0.907517 + 0.420016i \(0.862024\pi\)
\(444\) 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 −0.549915 0.835220i \(-0.685340\pi\)
0.998280 + 0.0586304i \(0.0186734\pi\)
\(462\) 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 −0.996999 0.0774158i \(-0.975333\pi\)
0.431455 0.902134i \(-0.358000\pi\)
\(480\) 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 −0.740335 0.672238i \(-0.765333\pi\)
0.952343 + 0.305030i \(0.0986666\pi\)
\(492\) 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 −0.440100 0.897949i \(-0.645057\pi\)
0.997696 0.0678367i \(-0.0216097\pi\)
\(500\) 0 0
\(501\) −0.605119 −0.0270347
\(502\) 0 0
\(503\) −15.6590 27.1222i −0.698200 1.20932i −0.969090 0.246707i \(-0.920651\pi\)
0.270890 0.962610i \(-0.412682\pi\)
\(504\) 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 0.953032 0.302870i \(-0.0979447\pi\)
−0.738809 + 0.673915i \(0.764611\pi\)
\(510\) 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 0.863594 + 0.504187i \(0.168208\pi\)
0.00484172 + 0.999988i \(0.498459\pi\)
\(524\) 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 −0.980191 0.198052i \(-0.936538\pi\)
0.318577 0.947897i \(-0.396795\pi\)
\(542\) 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 0.609398 0.792865i \(-0.291411\pi\)
−0.991340 + 0.131322i \(0.958078\pi\)
\(548\) 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 0.956555 0.291551i \(-0.0941712\pi\)
−0.730768 + 0.682626i \(0.760838\pi\)
\(558\) 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 −0.954864 0.297045i \(-0.903999\pi\)
0.734680 + 0.678414i \(0.237332\pi\)
\(588\) 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 0.986091 0.166205i \(-0.0531513\pi\)
−0.636983 + 0.770878i \(0.719818\pi\)
\(594\) 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 0.994773 + 0.102110i \(0.0325592\pi\)
−0.408957 + 0.912554i \(0.634107\pi\)
\(600\) 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 0.269099 + 0.963112i \(0.413274\pi\)
−0.968629 + 0.248509i \(0.920059\pi\)
\(614\) 0 0
\(615\) 5.98814 0.241465
\(616\) 0 0
\(617\) −2.23284 3.86740i −0.0898909 0.155696i 0.817574 0.575824i \(-0.195319\pi\)
−0.907465 + 0.420128i \(0.861985\pi\)
\(618\) 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 0.911231 0.411896i \(-0.135133\pi\)
−0.812328 + 0.583201i \(0.801800\pi\)
\(632\) 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 −0.198550 0.980091i \(-0.563623\pi\)
0.948059 0.318096i \(-0.103043\pi\)
\(642\) 0 0
\(643\) 17.6251 30.5276i 0.695067 1.20389i −0.275092 0.961418i \(-0.588708\pi\)
0.970158 0.242473i \(-0.0779585\pi\)
\(644\) 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 −0.799861 0.600185i \(-0.795094\pi\)
−0.119844 0.992793i \(-0.538240\pi\)
\(660\) 0 0
\(661\) 13.0580 + 22.6171i 0.507896 + 0.879702i 0.999958 + 0.00914181i \(0.00290997\pi\)
−0.492062 + 0.870560i \(0.663757\pi\)
\(662\) 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 −0.784244 0.620453i \(-0.786949\pi\)
0.929450 + 0.368949i \(0.120282\pi\)
\(702\) 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 0.540018 0.841654i \(-0.318418\pi\)
−0.998902 + 0.0468421i \(0.985084\pi\)
\(710\) 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 −0.995144 0.0984282i \(-0.968619\pi\)
0.582813 + 0.812606i \(0.301952\pi\)
\(720\) 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 0.460283 + 0.887772i \(0.347748\pi\)
−0.998975 + 0.0452694i \(0.985585\pi\)
\(728\) 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 −0.906443 0.422327i \(-0.861213\pi\)
0.818968 + 0.573839i \(0.194547\pi\)
\(740\) 0 0
\(741\) −3.22533 + 2.66411i −0.118486 + 0.0978687i
\(742\) 0 0
\(743\) 2.93853 5.08968i 0.107804 0.186722i −0.807076 0.590447i \(-0.798951\pi\)
0.914880 + 0.403725i \(0.132285\pi\)
\(744\) 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 0.880434 0.474169i \(-0.157251\pi\)
−0.850859 + 0.525394i \(0.823918\pi\)
\(752\) 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 −0.489019 0.872273i \(-0.662645\pi\)
0.999920 0.0126336i \(-0.00402151\pi\)
\(758\) 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 −0.907981 0.419011i \(-0.862377\pi\)
0.0911160 0.995840i \(-0.470957\pi\)
\(770\) 0 0
\(771\) −21.0357 −0.757583
\(772\) 0 0
\(773\) 10.0881 + 17.4731i 0.362843 + 0.628462i 0.988428 0.151694i \(-0.0484728\pi\)
−0.625585 + 0.780156i \(0.715139\pi\)
\(774\) 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