Properties

Label 585.2.j.i.451.2
Level $585$
Weight $2$
Character 585.451
Analytic conductor $4.671$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(-0.473183 - 0.819577i\) of defining polynomial
Character \(\chi\) \(=\) 585.451
Dual form 585.2.j.i.406.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.473183 + 0.819577i) q^{2} +(0.552196 + 0.956432i) q^{4} -1.00000 q^{5} +(0.781529 + 1.35365i) q^{7} -2.93789 q^{8} +O(q^{10})\) \(q+(-0.473183 + 0.819577i) q^{2} +(0.552196 + 0.956432i) q^{4} -1.00000 q^{5} +(0.781529 + 1.35365i) q^{7} -2.93789 q^{8} +(0.473183 - 0.819577i) q^{10} +(-0.754712 + 1.30720i) q^{11} +(-3.46327 + 1.00288i) q^{13} -1.47922 q^{14} +(0.285767 - 0.494963i) q^{16} +(-1.63121 - 2.82534i) q^{17} +(1.55220 + 2.68848i) q^{19} +(-0.552196 - 0.956432i) q^{20} +(-0.714233 - 1.23709i) q^{22} +(-1.46894 + 2.54429i) q^{23} +1.00000 q^{25} +(0.816822 - 3.31296i) q^{26} +(-0.863114 + 1.49496i) q^{28} +(-1.30267 + 2.25629i) q^{29} -2.65897 q^{31} +(-2.66745 - 4.62016i) q^{32} +3.08744 q^{34} +(-0.781529 - 1.35365i) q^{35} +(-0.285767 + 0.494963i) q^{37} -2.93789 q^{38} +2.93789 q^{40} +(-2.84400 + 4.92596i) q^{41} +(-0.632648 - 1.09578i) q^{43} -1.66700 q^{44} +(-1.39016 - 2.40783i) q^{46} -5.13459 q^{47} +(2.27843 - 3.94635i) q^{49} +(-0.473183 + 0.819577i) q^{50} +(-2.87159 - 2.75859i) q^{52} +2.91733 q^{53} +(0.754712 - 1.30720i) q^{55} +(-2.29605 - 3.97687i) q^{56} +(-1.23280 - 2.13528i) q^{58} +(6.40706 + 11.0974i) q^{59} +(-3.32949 - 5.76684i) q^{61} +(1.25818 - 2.17923i) q^{62} +6.19183 q^{64} +(3.46327 - 1.00288i) q^{65} +(-4.74904 + 8.22557i) q^{67} +(1.80149 - 3.12028i) q^{68} +1.47922 q^{70} +(0.610068 + 1.05667i) q^{71} -12.8785 q^{73} +(-0.270440 - 0.468416i) q^{74} +(-1.71423 + 2.96914i) q^{76} -2.35932 q^{77} +7.76563 q^{79} +(-0.285767 + 0.494963i) q^{80} +(-2.69147 - 4.66176i) q^{82} +11.2312 q^{83} +(1.63121 + 2.82534i) q^{85} +1.19743 q^{86} +(2.21726 - 3.84041i) q^{88} +(0.398407 - 0.690062i) q^{89} +(-4.06419 - 3.90427i) q^{91} -3.24458 q^{92} +(2.42960 - 4.20819i) q^{94} +(-1.55220 - 2.68848i) q^{95} +(2.90021 + 5.02331i) q^{97} +(2.15622 + 3.73469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29} + 18 q^{31} + 14 q^{32} + q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 6 q^{41} - 15 q^{43} - 28 q^{44} + 16 q^{46} - 20 q^{47} - 10 q^{49} + 2 q^{50} - 22 q^{52} + 40 q^{53} - 8 q^{55} - 2 q^{56} + 4 q^{58} + 12 q^{59} - 11 q^{61} - 22 q^{62} + 8 q^{64} - q^{65} - 5 q^{67} + 50 q^{68} - 8 q^{70} + 10 q^{71} + 2 q^{73} - 26 q^{74} - 24 q^{76} - 84 q^{77} - 34 q^{79} + 4 q^{80} - 16 q^{82} - 32 q^{83} - 88 q^{86} - 20 q^{88} + 4 q^{89} - q^{91} + 68 q^{92} + 16 q^{94} - 4 q^{95} + 11 q^{97} + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.473183 + 0.819577i −0.334591 + 0.579528i −0.983406 0.181418i \(-0.941931\pi\)
0.648815 + 0.760946i \(0.275265\pi\)
\(3\) 0 0
\(4\) 0.552196 + 0.956432i 0.276098 + 0.478216i
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.781529 + 1.35365i 0.295390 + 0.511631i 0.975076 0.221873i \(-0.0712170\pi\)
−0.679685 + 0.733504i \(0.737884\pi\)
\(8\) −2.93789 −1.03870
\(9\) 0 0
\(10\) 0.473183 0.819577i 0.149634 0.259173i
\(11\) −0.754712 + 1.30720i −0.227554 + 0.394135i −0.957083 0.289815i \(-0.906406\pi\)
0.729529 + 0.683950i \(0.239740\pi\)
\(12\) 0 0
\(13\) −3.46327 + 1.00288i −0.960538 + 0.278149i
\(14\) −1.47922 −0.395339
\(15\) 0 0
\(16\) 0.285767 0.494963i 0.0714417 0.123741i
\(17\) −1.63121 2.82534i −0.395626 0.685245i 0.597555 0.801828i \(-0.296139\pi\)
−0.993181 + 0.116583i \(0.962806\pi\)
\(18\) 0 0
\(19\) 1.55220 + 2.68848i 0.356098 + 0.616780i 0.987305 0.158834i \(-0.0507735\pi\)
−0.631207 + 0.775614i \(0.717440\pi\)
\(20\) −0.552196 0.956432i −0.123475 0.213865i
\(21\) 0 0
\(22\) −0.714233 1.23709i −0.152275 0.263748i
\(23\) −1.46894 + 2.54429i −0.306296 + 0.530521i −0.977549 0.210708i \(-0.932423\pi\)
0.671253 + 0.741228i \(0.265756\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.816822 3.31296i 0.160192 0.649725i
\(27\) 0 0
\(28\) −0.863114 + 1.49496i −0.163113 + 0.282521i
\(29\) −1.30267 + 2.25629i −0.241900 + 0.418983i −0.961255 0.275659i \(-0.911104\pi\)
0.719356 + 0.694642i \(0.244437\pi\)
\(30\) 0 0
\(31\) −2.65897 −0.477566 −0.238783 0.971073i \(-0.576748\pi\)
−0.238783 + 0.971073i \(0.576748\pi\)
\(32\) −2.66745 4.62016i −0.471543 0.816736i
\(33\) 0 0
\(34\) 3.08744 0.529492
\(35\) −0.781529 1.35365i −0.132103 0.228808i
\(36\) 0 0
\(37\) −0.285767 + 0.494963i −0.0469798 + 0.0813713i −0.888559 0.458762i \(-0.848293\pi\)
0.841579 + 0.540134i \(0.181626\pi\)
\(38\) −2.93789 −0.476589
\(39\) 0 0
\(40\) 2.93789 0.464521
\(41\) −2.84400 + 4.92596i −0.444159 + 0.769306i −0.997993 0.0633212i \(-0.979831\pi\)
0.553834 + 0.832627i \(0.313164\pi\)
\(42\) 0 0
\(43\) −0.632648 1.09578i −0.0964779 0.167105i 0.813747 0.581220i \(-0.197424\pi\)
−0.910224 + 0.414115i \(0.864091\pi\)
\(44\) −1.66700 −0.251309
\(45\) 0 0
\(46\) −1.39016 2.40783i −0.204968 0.355015i
\(47\) −5.13459 −0.748957 −0.374479 0.927236i \(-0.622178\pi\)
−0.374479 + 0.927236i \(0.622178\pi\)
\(48\) 0 0
\(49\) 2.27843 3.94635i 0.325489 0.563764i
\(50\) −0.473183 + 0.819577i −0.0669182 + 0.115906i
\(51\) 0 0
\(52\) −2.87159 2.75859i −0.398218 0.382548i
\(53\) 2.91733 0.400726 0.200363 0.979722i \(-0.435788\pi\)
0.200363 + 0.979722i \(0.435788\pi\)
\(54\) 0 0
\(55\) 0.754712 1.30720i 0.101765 0.176263i
\(56\) −2.29605 3.97687i −0.306822 0.531431i
\(57\) 0 0
\(58\) −1.23280 2.13528i −0.161875 0.280375i
\(59\) 6.40706 + 11.0974i 0.834128 + 1.44475i 0.894738 + 0.446591i \(0.147362\pi\)
−0.0606096 + 0.998162i \(0.519304\pi\)
\(60\) 0 0
\(61\) −3.32949 5.76684i −0.426297 0.738368i 0.570243 0.821476i \(-0.306849\pi\)
−0.996541 + 0.0831074i \(0.973516\pi\)
\(62\) 1.25818 2.17923i 0.159789 0.276763i
\(63\) 0 0
\(64\) 6.19183 0.773979
\(65\) 3.46327 1.00288i 0.429566 0.124392i
\(66\) 0 0
\(67\) −4.74904 + 8.22557i −0.580187 + 1.00491i 0.415270 + 0.909698i \(0.363687\pi\)
−0.995457 + 0.0952151i \(0.969646\pi\)
\(68\) 1.80149 3.12028i 0.218463 0.378390i
\(69\) 0 0
\(70\) 1.47922 0.176801
\(71\) 0.610068 + 1.05667i 0.0724018 + 0.125404i 0.899953 0.435986i \(-0.143600\pi\)
−0.827552 + 0.561390i \(0.810267\pi\)
\(72\) 0 0
\(73\) −12.8785 −1.50731 −0.753657 0.657268i \(-0.771712\pi\)
−0.753657 + 0.657268i \(0.771712\pi\)
\(74\) −0.270440 0.468416i −0.0314380 0.0544522i
\(75\) 0 0
\(76\) −1.71423 + 2.96914i −0.196636 + 0.340584i
\(77\) −2.35932 −0.268869
\(78\) 0 0
\(79\) 7.76563 0.873702 0.436851 0.899534i \(-0.356094\pi\)
0.436851 + 0.899534i \(0.356094\pi\)
\(80\) −0.285767 + 0.494963i −0.0319497 + 0.0553385i
\(81\) 0 0
\(82\) −2.69147 4.66176i −0.297223 0.514805i
\(83\) 11.2312 1.23279 0.616394 0.787438i \(-0.288593\pi\)
0.616394 + 0.787438i \(0.288593\pi\)
\(84\) 0 0
\(85\) 1.63121 + 2.82534i 0.176929 + 0.306451i
\(86\) 1.19743 0.129122
\(87\) 0 0
\(88\) 2.21726 3.84041i 0.236361 0.409389i
\(89\) 0.398407 0.690062i 0.0422311 0.0731464i −0.844137 0.536127i \(-0.819887\pi\)
0.886368 + 0.462981i \(0.153220\pi\)
\(90\) 0 0
\(91\) −4.06419 3.90427i −0.426043 0.409278i
\(92\) −3.24458 −0.338271
\(93\) 0 0
\(94\) 2.42960 4.20819i 0.250594 0.434042i
\(95\) −1.55220 2.68848i −0.159252 0.275832i
\(96\) 0 0
\(97\) 2.90021 + 5.02331i 0.294472 + 0.510040i 0.974862 0.222810i \(-0.0715230\pi\)
−0.680390 + 0.732850i \(0.738190\pi\)
\(98\) 2.15622 + 3.73469i 0.217811 + 0.377260i
\(99\) 0 0
\(100\) 0.552196 + 0.956432i 0.0552196 + 0.0956432i
\(101\) −3.02001 + 5.23081i −0.300502 + 0.520485i −0.976250 0.216648i \(-0.930488\pi\)
0.675748 + 0.737133i \(0.263821\pi\)
\(102\) 0 0
\(103\) −9.34411 −0.920702 −0.460351 0.887737i \(-0.652276\pi\)
−0.460351 + 0.887737i \(0.652276\pi\)
\(104\) 10.1747 2.94635i 0.997712 0.288914i
\(105\) 0 0
\(106\) −1.38043 + 2.39098i −0.134079 + 0.232232i
\(107\) 5.50519 9.53526i 0.532206 0.921808i −0.467087 0.884212i \(-0.654696\pi\)
0.999293 0.0375969i \(-0.0119703\pi\)
\(108\) 0 0
\(109\) 18.5677 1.77846 0.889230 0.457460i \(-0.151241\pi\)
0.889230 + 0.457460i \(0.151241\pi\)
\(110\) 0.714233 + 1.23709i 0.0680995 + 0.117952i
\(111\) 0 0
\(112\) 0.893340 0.0844127
\(113\) 6.52151 + 11.2956i 0.613492 + 1.06260i 0.990647 + 0.136449i \(0.0435689\pi\)
−0.377155 + 0.926150i \(0.623098\pi\)
\(114\) 0 0
\(115\) 1.46894 2.54429i 0.136980 0.237256i
\(116\) −2.87732 −0.267152
\(117\) 0 0
\(118\) −12.1268 −1.11637
\(119\) 2.54967 4.41617i 0.233728 0.404829i
\(120\) 0 0
\(121\) 4.36082 + 7.55316i 0.396438 + 0.686651i
\(122\) 6.30182 0.570540
\(123\) 0 0
\(124\) −1.46828 2.54313i −0.131855 0.228380i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 3.80200 6.58526i 0.337373 0.584347i −0.646565 0.762859i \(-0.723795\pi\)
0.983938 + 0.178512i \(0.0571283\pi\)
\(128\) 2.40503 4.16564i 0.212577 0.368194i
\(129\) 0 0
\(130\) −0.816822 + 3.31296i −0.0716400 + 0.290566i
\(131\) 19.0332 1.66294 0.831469 0.555571i \(-0.187500\pi\)
0.831469 + 0.555571i \(0.187500\pi\)
\(132\) 0 0
\(133\) −2.42617 + 4.20225i −0.210376 + 0.364382i
\(134\) −4.49432 7.78440i −0.388250 0.672469i
\(135\) 0 0
\(136\) 4.79231 + 8.30053i 0.410938 + 0.711765i
\(137\) 9.53422 + 16.5138i 0.814563 + 1.41087i 0.909641 + 0.415395i \(0.136357\pi\)
−0.0950776 + 0.995470i \(0.530310\pi\)
\(138\) 0 0
\(139\) 7.41454 + 12.8424i 0.628893 + 1.08928i 0.987774 + 0.155892i \(0.0498251\pi\)
−0.358881 + 0.933383i \(0.616842\pi\)
\(140\) 0.863114 1.49496i 0.0729465 0.126347i
\(141\) 0 0
\(142\) −1.15470 −0.0968999
\(143\) 1.30281 5.28407i 0.108946 0.441876i
\(144\) 0 0
\(145\) 1.30267 2.25629i 0.108181 0.187375i
\(146\) 6.09389 10.5549i 0.504334 0.873531i
\(147\) 0 0
\(148\) −0.631197 −0.0518841
\(149\) 11.1399 + 19.2949i 0.912617 + 1.58070i 0.810353 + 0.585942i \(0.199276\pi\)
0.102265 + 0.994757i \(0.467391\pi\)
\(150\) 0 0
\(151\) −16.7896 −1.36632 −0.683160 0.730269i \(-0.739395\pi\)
−0.683160 + 0.730269i \(0.739395\pi\)
\(152\) −4.56018 7.89847i −0.369880 0.640650i
\(153\) 0 0
\(154\) 1.11639 1.93364i 0.0899611 0.155817i
\(155\) 2.65897 0.213574
\(156\) 0 0
\(157\) 3.26279 0.260399 0.130200 0.991488i \(-0.458438\pi\)
0.130200 + 0.991488i \(0.458438\pi\)
\(158\) −3.67456 + 6.36453i −0.292333 + 0.506335i
\(159\) 0 0
\(160\) 2.66745 + 4.62016i 0.210880 + 0.365256i
\(161\) −4.59209 −0.361908
\(162\) 0 0
\(163\) −1.57274 2.72407i −0.123187 0.213366i 0.797836 0.602875i \(-0.205978\pi\)
−0.921023 + 0.389509i \(0.872645\pi\)
\(164\) −6.28179 −0.490526
\(165\) 0 0
\(166\) −5.31443 + 9.20486i −0.412480 + 0.714436i
\(167\) 5.21393 9.03079i 0.403466 0.698823i −0.590676 0.806909i \(-0.701139\pi\)
0.994142 + 0.108086i \(0.0344721\pi\)
\(168\) 0 0
\(169\) 10.9885 6.94649i 0.845266 0.534345i
\(170\) −3.08744 −0.236796
\(171\) 0 0
\(172\) 0.698691 1.21017i 0.0532747 0.0922745i
\(173\) −6.20274 10.7435i −0.471586 0.816811i 0.527886 0.849315i \(-0.322985\pi\)
−0.999472 + 0.0325048i \(0.989652\pi\)
\(174\) 0 0
\(175\) 0.781529 + 1.35365i 0.0590780 + 0.102326i
\(176\) 0.431343 + 0.747108i 0.0325137 + 0.0563154i
\(177\) 0 0
\(178\) 0.377039 + 0.653051i 0.0282603 + 0.0489482i
\(179\) 4.58176 7.93585i 0.342457 0.593153i −0.642431 0.766343i \(-0.722074\pi\)
0.984888 + 0.173190i \(0.0554075\pi\)
\(180\) 0 0
\(181\) −4.71081 −0.350152 −0.175076 0.984555i \(-0.556017\pi\)
−0.175076 + 0.984555i \(0.556017\pi\)
\(182\) 5.12295 1.48349i 0.379738 0.109963i
\(183\) 0 0
\(184\) 4.31560 7.47484i 0.318150 0.551052i
\(185\) 0.285767 0.494963i 0.0210100 0.0363904i
\(186\) 0 0
\(187\) 4.92437 0.360106
\(188\) −2.83530 4.91089i −0.206786 0.358163i
\(189\) 0 0
\(190\) 2.93789 0.213137
\(191\) 7.57528 + 13.1208i 0.548128 + 0.949386i 0.998403 + 0.0564956i \(0.0179927\pi\)
−0.450275 + 0.892890i \(0.648674\pi\)
\(192\) 0 0
\(193\) −5.14501 + 8.91142i −0.370346 + 0.641458i −0.989619 0.143718i \(-0.954094\pi\)
0.619273 + 0.785176i \(0.287427\pi\)
\(194\) −5.48932 −0.394110
\(195\) 0 0
\(196\) 5.03255 0.359468
\(197\) −2.59506 + 4.49478i −0.184890 + 0.320240i −0.943540 0.331260i \(-0.892526\pi\)
0.758649 + 0.651499i \(0.225860\pi\)
\(198\) 0 0
\(199\) 6.30890 + 10.9273i 0.447226 + 0.774618i 0.998204 0.0599015i \(-0.0190787\pi\)
−0.550978 + 0.834520i \(0.685745\pi\)
\(200\) −2.93789 −0.207740
\(201\) 0 0
\(202\) −2.85803 4.95025i −0.201090 0.348299i
\(203\) −4.07230 −0.285819
\(204\) 0 0
\(205\) 2.84400 4.92596i 0.198634 0.344044i
\(206\) 4.42147 7.65821i 0.308058 0.533573i
\(207\) 0 0
\(208\) −0.493299 + 2.00078i −0.0342041 + 0.138729i
\(209\) −4.68584 −0.324127
\(210\) 0 0
\(211\) 3.05458 5.29069i 0.210286 0.364226i −0.741518 0.670933i \(-0.765894\pi\)
0.951804 + 0.306707i \(0.0992271\pi\)
\(212\) 1.61094 + 2.79023i 0.110640 + 0.191634i
\(213\) 0 0
\(214\) 5.20992 + 9.02384i 0.356143 + 0.616857i
\(215\) 0.632648 + 1.09578i 0.0431462 + 0.0747314i
\(216\) 0 0
\(217\) −2.07807 3.59931i −0.141068 0.244337i
\(218\) −8.78590 + 15.2176i −0.595057 + 1.03067i
\(219\) 0 0
\(220\) 1.66700 0.112389
\(221\) 8.48279 + 8.14900i 0.570614 + 0.548161i
\(222\) 0 0
\(223\) 3.18831 5.52232i 0.213505 0.369802i −0.739304 0.673372i \(-0.764845\pi\)
0.952809 + 0.303570i \(0.0981786\pi\)
\(224\) 4.16938 7.22158i 0.278578 0.482512i
\(225\) 0 0
\(226\) −12.3435 −0.821075
\(227\) 6.72532 + 11.6486i 0.446375 + 0.773145i 0.998147 0.0608506i \(-0.0193813\pi\)
−0.551772 + 0.833995i \(0.686048\pi\)
\(228\) 0 0
\(229\) −9.14533 −0.604341 −0.302170 0.953254i \(-0.597711\pi\)
−0.302170 + 0.953254i \(0.597711\pi\)
\(230\) 1.39016 + 2.40783i 0.0916644 + 0.158767i
\(231\) 0 0
\(232\) 3.82710 6.62873i 0.251261 0.435198i
\(233\) −22.1655 −1.45211 −0.726056 0.687636i \(-0.758649\pi\)
−0.726056 + 0.687636i \(0.758649\pi\)
\(234\) 0 0
\(235\) 5.13459 0.334944
\(236\) −7.07591 + 12.2558i −0.460602 + 0.797787i
\(237\) 0 0
\(238\) 2.41292 + 4.17931i 0.156407 + 0.270904i
\(239\) −17.5940 −1.13806 −0.569030 0.822317i \(-0.692681\pi\)
−0.569030 + 0.822317i \(0.692681\pi\)
\(240\) 0 0
\(241\) −14.0692 24.3686i −0.906277 1.56972i −0.819194 0.573517i \(-0.805579\pi\)
−0.0870830 0.996201i \(-0.527755\pi\)
\(242\) −8.25386 −0.530578
\(243\) 0 0
\(244\) 3.67706 6.36885i 0.235400 0.407724i
\(245\) −2.27843 + 3.94635i −0.145563 + 0.252123i
\(246\) 0 0
\(247\) −8.07190 7.75427i −0.513603 0.493392i
\(248\) 7.81177 0.496048
\(249\) 0 0
\(250\) 0.473183 0.819577i 0.0299267 0.0518346i
\(251\) −14.0411 24.3199i −0.886268 1.53506i −0.844254 0.535944i \(-0.819956\pi\)
−0.0420141 0.999117i \(-0.513377\pi\)
\(252\) 0 0
\(253\) −2.21726 3.84041i −0.139398 0.241444i
\(254\) 3.59808 + 6.23206i 0.225764 + 0.391034i
\(255\) 0 0
\(256\) 8.46787 + 14.6668i 0.529242 + 0.916674i
\(257\) −15.1282 + 26.2028i −0.943672 + 1.63449i −0.185282 + 0.982685i \(0.559320\pi\)
−0.758389 + 0.651802i \(0.774013\pi\)
\(258\) 0 0
\(259\) −0.893340 −0.0555094
\(260\) 2.87159 + 2.75859i 0.178088 + 0.171081i
\(261\) 0 0
\(262\) −9.00618 + 15.5992i −0.556404 + 0.963720i
\(263\) 14.0620 24.3561i 0.867102 1.50186i 0.00215657 0.999998i \(-0.499314\pi\)
0.864945 0.501866i \(-0.167353\pi\)
\(264\) 0 0
\(265\) −2.91733 −0.179210
\(266\) −2.29605 3.97687i −0.140780 0.243837i
\(267\) 0 0
\(268\) −10.4896 −0.640754
\(269\) −10.3621 17.9477i −0.631787 1.09429i −0.987186 0.159573i \(-0.948988\pi\)
0.355399 0.934715i \(-0.384345\pi\)
\(270\) 0 0
\(271\) 3.97408 6.88331i 0.241408 0.418131i −0.719707 0.694277i \(-0.755724\pi\)
0.961116 + 0.276146i \(0.0890574\pi\)
\(272\) −1.86458 −0.113057
\(273\) 0 0
\(274\) −18.0457 −1.09018
\(275\) −0.754712 + 1.30720i −0.0455108 + 0.0788271i
\(276\) 0 0
\(277\) 3.08619 + 5.34544i 0.185431 + 0.321176i 0.943722 0.330741i \(-0.107299\pi\)
−0.758291 + 0.651917i \(0.773965\pi\)
\(278\) −14.0337 −0.841687
\(279\) 0 0
\(280\) 2.29605 + 3.97687i 0.137215 + 0.237663i
\(281\) −18.5723 −1.10793 −0.553967 0.832539i \(-0.686886\pi\)
−0.553967 + 0.832539i \(0.686886\pi\)
\(282\) 0 0
\(283\) 3.63956 6.30390i 0.216349 0.374728i −0.737340 0.675522i \(-0.763918\pi\)
0.953689 + 0.300794i \(0.0972516\pi\)
\(284\) −0.673755 + 1.16698i −0.0399800 + 0.0692474i
\(285\) 0 0
\(286\) 3.71423 + 3.56808i 0.219627 + 0.210985i
\(287\) −8.89069 −0.524801
\(288\) 0 0
\(289\) 3.17831 5.50500i 0.186960 0.323823i
\(290\) 1.23280 + 2.13528i 0.0723926 + 0.125388i
\(291\) 0 0
\(292\) −7.11146 12.3174i −0.416167 0.720822i
\(293\) 3.22104 + 5.57901i 0.188175 + 0.325929i 0.944642 0.328103i \(-0.106409\pi\)
−0.756467 + 0.654032i \(0.773076\pi\)
\(294\) 0 0
\(295\) −6.40706 11.0974i −0.373034 0.646113i
\(296\) 0.839551 1.45415i 0.0487979 0.0845205i
\(297\) 0 0
\(298\) −21.0849 −1.22141
\(299\) 2.53574 10.2847i 0.146645 0.594781i
\(300\) 0 0
\(301\) 0.988865 1.71276i 0.0569972 0.0987221i
\(302\) 7.94456 13.7604i 0.457158 0.791821i
\(303\) 0 0
\(304\) 1.77426 0.101761
\(305\) 3.32949 + 5.76684i 0.190646 + 0.330208i
\(306\) 0 0
\(307\) 4.94599 0.282283 0.141141 0.989989i \(-0.454923\pi\)
0.141141 + 0.989989i \(0.454923\pi\)
\(308\) −1.30281 2.25652i −0.0742342 0.128577i
\(309\) 0 0
\(310\) −1.25818 + 2.17923i −0.0714599 + 0.123772i
\(311\) −30.0486 −1.70390 −0.851950 0.523623i \(-0.824580\pi\)
−0.851950 + 0.523623i \(0.824580\pi\)
\(312\) 0 0
\(313\) −4.57620 −0.258662 −0.129331 0.991601i \(-0.541283\pi\)
−0.129331 + 0.991601i \(0.541283\pi\)
\(314\) −1.54390 + 2.67411i −0.0871271 + 0.150909i
\(315\) 0 0
\(316\) 4.28815 + 7.42730i 0.241227 + 0.417818i
\(317\) −1.50960 −0.0847875 −0.0423937 0.999101i \(-0.513498\pi\)
−0.0423937 + 0.999101i \(0.513498\pi\)
\(318\) 0 0
\(319\) −1.96628 3.40570i −0.110091 0.190682i
\(320\) −6.19183 −0.346134
\(321\) 0 0
\(322\) 2.17290 3.76357i 0.121091 0.209736i
\(323\) 5.06391 8.77096i 0.281764 0.488029i
\(324\) 0 0
\(325\) −3.46327 + 1.00288i −0.192108 + 0.0556298i
\(326\) 2.97678 0.164869
\(327\) 0 0
\(328\) 8.35537 14.4719i 0.461348 0.799079i
\(329\) −4.01283 6.95043i −0.221235 0.383190i
\(330\) 0 0
\(331\) −4.17945 7.23901i −0.229723 0.397892i 0.728003 0.685574i \(-0.240449\pi\)
−0.957726 + 0.287682i \(0.907115\pi\)
\(332\) 6.20185 + 10.7419i 0.340371 + 0.589539i
\(333\) 0 0
\(334\) 4.93428 + 8.54643i 0.269992 + 0.467640i
\(335\) 4.74904 8.22557i 0.259468 0.449411i
\(336\) 0 0
\(337\) 15.5359 0.846297 0.423148 0.906060i \(-0.360925\pi\)
0.423148 + 0.906060i \(0.360925\pi\)
\(338\) 0.493629 + 12.2928i 0.0268499 + 0.668643i
\(339\) 0 0
\(340\) −1.80149 + 3.12028i −0.0976998 + 0.169221i
\(341\) 2.00676 3.47581i 0.108672 0.188226i
\(342\) 0 0
\(343\) 18.0640 0.975366
\(344\) 1.85865 + 3.21928i 0.100212 + 0.173572i
\(345\) 0 0
\(346\) 11.7401 0.631153
\(347\) 2.89046 + 5.00643i 0.155168 + 0.268759i 0.933120 0.359564i \(-0.117075\pi\)
−0.777952 + 0.628324i \(0.783741\pi\)
\(348\) 0 0
\(349\) −2.72812 + 4.72525i −0.146033 + 0.252937i −0.929758 0.368172i \(-0.879984\pi\)
0.783725 + 0.621108i \(0.213317\pi\)
\(350\) −1.47922 −0.0790679
\(351\) 0 0
\(352\) 8.05262 0.429206
\(353\) 6.13125 10.6196i 0.326334 0.565226i −0.655448 0.755240i \(-0.727520\pi\)
0.981781 + 0.190014i \(0.0608534\pi\)
\(354\) 0 0
\(355\) −0.610068 1.05667i −0.0323791 0.0560822i
\(356\) 0.879996 0.0466397
\(357\) 0 0
\(358\) 4.33602 + 7.51021i 0.229166 + 0.396927i
\(359\) −27.4508 −1.44880 −0.724398 0.689382i \(-0.757882\pi\)
−0.724398 + 0.689382i \(0.757882\pi\)
\(360\) 0 0
\(361\) 4.68137 8.10838i 0.246388 0.426757i
\(362\) 2.22908 3.86087i 0.117158 0.202923i
\(363\) 0 0
\(364\) 1.48993 6.04304i 0.0780937 0.316741i
\(365\) 12.8785 0.674092
\(366\) 0 0
\(367\) −16.9110 + 29.2908i −0.882749 + 1.52897i −0.0344768 + 0.999405i \(0.510976\pi\)
−0.848272 + 0.529561i \(0.822357\pi\)
\(368\) 0.839551 + 1.45415i 0.0437646 + 0.0758026i
\(369\) 0 0
\(370\) 0.270440 + 0.468416i 0.0140595 + 0.0243518i
\(371\) 2.27998 + 3.94904i 0.118371 + 0.205024i
\(372\) 0 0
\(373\) 1.52596 + 2.64304i 0.0790113 + 0.136852i 0.902824 0.430011i \(-0.141490\pi\)
−0.823812 + 0.566863i \(0.808157\pi\)
\(374\) −2.33013 + 4.03590i −0.120488 + 0.208691i
\(375\) 0 0
\(376\) 15.0849 0.777942
\(377\) 2.24871 9.12056i 0.115814 0.469733i
\(378\) 0 0
\(379\) 1.50609 2.60862i 0.0773626 0.133996i −0.824749 0.565500i \(-0.808683\pi\)
0.902111 + 0.431504i \(0.142017\pi\)
\(380\) 1.71423 2.96914i 0.0879383 0.152314i
\(381\) 0 0
\(382\) −14.3380 −0.733594
\(383\) −1.60958 2.78787i −0.0822456 0.142454i 0.821969 0.569533i \(-0.192876\pi\)
−0.904214 + 0.427079i \(0.859543\pi\)
\(384\) 0 0
\(385\) 2.35932 0.120242
\(386\) −4.86906 8.43346i −0.247829 0.429252i
\(387\) 0 0
\(388\) −3.20297 + 5.54771i −0.162606 + 0.281642i
\(389\) −12.8066 −0.649322 −0.324661 0.945830i \(-0.605250\pi\)
−0.324661 + 0.945830i \(0.605250\pi\)
\(390\) 0 0
\(391\) 9.58463 0.484715
\(392\) −6.69376 + 11.5939i −0.338086 + 0.585582i
\(393\) 0 0
\(394\) −2.45588 4.25370i −0.123725 0.214298i
\(395\) −7.76563 −0.390731
\(396\) 0 0
\(397\) 17.1125 + 29.6397i 0.858853 + 1.48758i 0.873024 + 0.487677i \(0.162155\pi\)
−0.0141718 + 0.999900i \(0.504511\pi\)
\(398\) −11.9410 −0.598551
\(399\) 0 0
\(400\) 0.285767 0.494963i 0.0142883 0.0247481i
\(401\) −13.0953 + 22.6817i −0.653948 + 1.13267i 0.328208 + 0.944606i \(0.393555\pi\)
−0.982156 + 0.188066i \(0.939778\pi\)
\(402\) 0 0
\(403\) 9.20874 2.66663i 0.458720 0.132834i
\(404\) −6.67054 −0.331872
\(405\) 0 0
\(406\) 1.92694 3.33756i 0.0956325 0.165640i
\(407\) −0.431343 0.747108i −0.0213809 0.0370328i
\(408\) 0 0
\(409\) −7.14686 12.3787i −0.353390 0.612089i 0.633451 0.773782i \(-0.281638\pi\)
−0.986841 + 0.161694i \(0.948304\pi\)
\(410\) 2.69147 + 4.66176i 0.132922 + 0.230228i
\(411\) 0 0
\(412\) −5.15978 8.93700i −0.254204 0.440294i
\(413\) −10.0146 + 17.3458i −0.492787 + 0.853532i
\(414\) 0 0
\(415\) −11.2312 −0.551320
\(416\) 13.8716 + 13.3257i 0.680109 + 0.653347i
\(417\) 0 0
\(418\) 2.21726 3.84041i 0.108450 0.187840i
\(419\) 11.7425 20.3386i 0.573659 0.993607i −0.422527 0.906351i \(-0.638857\pi\)
0.996186 0.0872566i \(-0.0278100\pi\)
\(420\) 0 0
\(421\) −12.7618 −0.621971 −0.310985 0.950415i \(-0.600659\pi\)
−0.310985 + 0.950415i \(0.600659\pi\)
\(422\) 2.89075 + 5.00693i 0.140720 + 0.243733i
\(423\) 0 0
\(424\) −8.57080 −0.416235
\(425\) −1.63121 2.82534i −0.0791253 0.137049i
\(426\) 0 0
\(427\) 5.20418 9.01391i 0.251848 0.436214i
\(428\) 12.1598 0.587765
\(429\) 0 0
\(430\) −1.19743 −0.0577453
\(431\) 7.34814 12.7274i 0.353948 0.613055i −0.632990 0.774160i \(-0.718172\pi\)
0.986937 + 0.161105i \(0.0515058\pi\)
\(432\) 0 0
\(433\) 9.76216 + 16.9085i 0.469139 + 0.812573i 0.999378 0.0352756i \(-0.0112309\pi\)
−0.530238 + 0.847849i \(0.677898\pi\)
\(434\) 3.93322 0.188801
\(435\) 0 0
\(436\) 10.2530 + 17.7587i 0.491030 + 0.850488i
\(437\) −9.12036 −0.436286
\(438\) 0 0
\(439\) −15.2080 + 26.3410i −0.725838 + 1.25719i 0.232791 + 0.972527i \(0.425214\pi\)
−0.958628 + 0.284661i \(0.908119\pi\)
\(440\) −2.21726 + 3.84041i −0.105704 + 0.183084i
\(441\) 0 0
\(442\) −10.6926 + 3.09633i −0.508597 + 0.147278i
\(443\) 8.83602 0.419812 0.209906 0.977722i \(-0.432684\pi\)
0.209906 + 0.977722i \(0.432684\pi\)
\(444\) 0 0
\(445\) −0.398407 + 0.690062i −0.0188863 + 0.0327121i
\(446\) 3.01731 + 5.22613i 0.142874 + 0.247465i
\(447\) 0 0
\(448\) 4.83910 + 8.38156i 0.228626 + 0.395992i
\(449\) 10.5602 + 18.2908i 0.498366 + 0.863195i 0.999998 0.00188602i \(-0.000600341\pi\)
−0.501632 + 0.865081i \(0.667267\pi\)
\(450\) 0 0
\(451\) −4.29281 7.43536i −0.202140 0.350117i
\(452\) −7.20230 + 12.4748i −0.338768 + 0.586763i
\(453\) 0 0
\(454\) −12.7292 −0.597412
\(455\) 4.06419 + 3.90427i 0.190532 + 0.183035i
\(456\) 0 0
\(457\) −19.7092 + 34.1373i −0.921957 + 1.59688i −0.125574 + 0.992084i \(0.540077\pi\)
−0.796383 + 0.604792i \(0.793256\pi\)
\(458\) 4.32742 7.49530i 0.202207 0.350233i
\(459\) 0 0
\(460\) 3.24458 0.151279
\(461\) −0.212077 0.367328i −0.00987742 0.0171082i 0.861044 0.508530i \(-0.169811\pi\)
−0.870922 + 0.491422i \(0.836477\pi\)
\(462\) 0 0
\(463\) 30.1509 1.40123 0.700616 0.713538i \(-0.252909\pi\)
0.700616 + 0.713538i \(0.252909\pi\)
\(464\) 0.744520 + 1.28955i 0.0345635 + 0.0598657i
\(465\) 0 0
\(466\) 10.4883 18.1663i 0.485863 0.841540i
\(467\) 8.07034 0.373451 0.186725 0.982412i \(-0.440213\pi\)
0.186725 + 0.982412i \(0.440213\pi\)
\(468\) 0 0
\(469\) −14.8460 −0.685526
\(470\) −2.42960 + 4.20819i −0.112069 + 0.194109i
\(471\) 0 0
\(472\) −18.8232 32.6028i −0.866410 1.50067i
\(473\) 1.90987 0.0878158
\(474\) 0 0
\(475\) 1.55220 + 2.68848i 0.0712196 + 0.123356i
\(476\) 5.63168 0.258128
\(477\) 0 0
\(478\) 8.32517 14.4196i 0.380785 0.659538i
\(479\) 18.6079 32.2299i 0.850218 1.47262i −0.0307941 0.999526i \(-0.509804\pi\)
0.881012 0.473094i \(-0.156863\pi\)
\(480\) 0 0
\(481\) 0.493299 2.00078i 0.0224925 0.0912276i
\(482\) 26.6292 1.21293
\(483\) 0 0
\(484\) −4.81606 + 8.34165i −0.218912 + 0.379166i
\(485\) −2.90021 5.02331i −0.131692 0.228097i
\(486\) 0 0
\(487\) 5.72861 + 9.92224i 0.259588 + 0.449619i 0.966132 0.258050i \(-0.0830799\pi\)
−0.706544 + 0.707669i \(0.749747\pi\)
\(488\) 9.78167 + 16.9423i 0.442795 + 0.766944i
\(489\) 0 0
\(490\) −2.15622 3.73469i −0.0974082 0.168716i
\(491\) 10.5519 18.2765i 0.476202 0.824807i −0.523426 0.852071i \(-0.675346\pi\)
0.999628 + 0.0272644i \(0.00867959\pi\)
\(492\) 0 0
\(493\) 8.49971 0.382808
\(494\) 10.1747 2.94635i 0.457782 0.132563i
\(495\) 0 0
\(496\) −0.759847 + 1.31609i −0.0341181 + 0.0590943i
\(497\) −0.953572 + 1.65164i −0.0427736 + 0.0740860i
\(498\) 0 0
\(499\) −19.9900 −0.894876 −0.447438 0.894315i \(-0.647663\pi\)
−0.447438 + 0.894315i \(0.647663\pi\)
\(500\) −0.552196 0.956432i −0.0246950 0.0427729i
\(501\) 0 0
\(502\) 26.5761 1.18615
\(503\) −5.37097 9.30280i −0.239480 0.414791i 0.721085 0.692846i \(-0.243644\pi\)
−0.960565 + 0.278055i \(0.910310\pi\)
\(504\) 0 0
\(505\) 3.02001 5.23081i 0.134389 0.232768i
\(506\) 4.19668 0.186565
\(507\) 0 0
\(508\) 8.39780 0.372592
\(509\) −1.11592 + 1.93284i −0.0494624 + 0.0856715i −0.889697 0.456552i \(-0.849084\pi\)
0.840234 + 0.542224i \(0.182417\pi\)
\(510\) 0 0
\(511\) −10.0649 17.4330i −0.445246 0.771189i
\(512\) −6.40728 −0.283164
\(513\) 0 0
\(514\) −14.3168 24.7975i −0.631488 1.09377i
\(515\) 9.34411 0.411751
\(516\) 0 0
\(517\) 3.87514 6.71193i 0.170428 0.295190i
\(518\) 0.422713 0.732161i 0.0185729 0.0321693i
\(519\) 0 0
\(520\) −10.1747 + 2.94635i −0.446190 + 0.129206i
\(521\) 33.9482 1.48730 0.743649 0.668570i \(-0.233093\pi\)
0.743649 + 0.668570i \(0.233093\pi\)
\(522\) 0 0
\(523\) −2.60173 + 4.50633i −0.113766 + 0.197048i −0.917286 0.398230i \(-0.869625\pi\)
0.803520 + 0.595278i \(0.202958\pi\)
\(524\) 10.5101 + 18.2040i 0.459134 + 0.795243i
\(525\) 0 0
\(526\) 13.3078 + 23.0498i 0.580248 + 1.00502i
\(527\) 4.33734 + 7.51250i 0.188938 + 0.327250i
\(528\) 0 0
\(529\) 7.18440 + 12.4437i 0.312365 + 0.541033i
\(530\) 1.38043 2.39098i 0.0599621 0.103857i
\(531\) 0 0
\(532\) −5.35889 −0.232337
\(533\) 4.90940 19.9121i 0.212650 0.862490i
\(534\) 0 0
\(535\) −5.50519 + 9.53526i −0.238010 + 0.412245i
\(536\) 13.9521 24.1658i 0.602641 1.04380i
\(537\) 0 0
\(538\) 19.6126 0.845561
\(539\) 3.43911 + 5.95671i 0.148133 + 0.256574i
\(540\) 0 0
\(541\) −5.87388 −0.252538 −0.126269 0.991996i \(-0.540300\pi\)
−0.126269 + 0.991996i \(0.540300\pi\)
\(542\) 3.76093 + 6.51413i 0.161546 + 0.279806i
\(543\) 0 0
\(544\) −8.70234 + 15.0729i −0.373110 + 0.646245i
\(545\) −18.5677 −0.795352
\(546\) 0 0
\(547\) 43.6009 1.86424 0.932119 0.362151i \(-0.117958\pi\)
0.932119 + 0.362151i \(0.117958\pi\)
\(548\) −10.5295 + 18.2377i −0.449799 + 0.779074i
\(549\) 0 0
\(550\) −0.714233 1.23709i −0.0304550 0.0527496i
\(551\) −8.08800 −0.344560
\(552\) 0 0
\(553\) 6.06907 + 10.5119i 0.258083 + 0.447013i
\(554\) −5.84133 −0.248174
\(555\) 0 0
\(556\) −8.18856 + 14.1830i −0.347272 + 0.601493i
\(557\) 17.8250 30.8737i 0.755268 1.30816i −0.189973 0.981789i \(-0.560840\pi\)
0.945241 0.326373i \(-0.105827\pi\)
\(558\) 0 0
\(559\) 3.28996 + 3.16050i 0.139151 + 0.133675i
\(560\) −0.893340 −0.0377505
\(561\) 0 0
\(562\) 8.78811 15.2215i 0.370704 0.642079i
\(563\) −9.10954 15.7782i −0.383921 0.664971i 0.607698 0.794168i \(-0.292093\pi\)
−0.991619 + 0.129197i \(0.958760\pi\)
\(564\) 0 0
\(565\) −6.52151 11.2956i −0.274362 0.475209i
\(566\) 3.44435 + 5.96580i 0.144777 + 0.250761i
\(567\) 0 0
\(568\) −1.79231 3.10438i −0.0752038 0.130257i
\(569\) −13.2713 + 22.9866i −0.556362 + 0.963648i 0.441434 + 0.897294i \(0.354470\pi\)
−0.997796 + 0.0663539i \(0.978863\pi\)
\(570\) 0 0
\(571\) 26.7099 1.11778 0.558888 0.829243i \(-0.311228\pi\)
0.558888 + 0.829243i \(0.311228\pi\)
\(572\) 5.77325 1.67180i 0.241392 0.0699014i
\(573\) 0 0
\(574\) 4.20692 7.28660i 0.175593 0.304137i
\(575\) −1.46894 + 2.54429i −0.0612592 + 0.106104i
\(576\) 0 0
\(577\) −12.0139 −0.500144 −0.250072 0.968227i \(-0.580454\pi\)
−0.250072 + 0.968227i \(0.580454\pi\)
\(578\) 3.00784 + 5.20974i 0.125110 + 0.216697i
\(579\) 0 0
\(580\) 2.87732 0.119474
\(581\) 8.77754 + 15.2031i 0.364154 + 0.630733i
\(582\) 0 0
\(583\) −2.20174 + 3.81353i −0.0911869 + 0.157940i
\(584\) 37.8356 1.56565
\(585\) 0 0
\(586\) −6.09657 −0.251847
\(587\) 21.6560 37.5093i 0.893840 1.54818i 0.0586057 0.998281i \(-0.481335\pi\)
0.835234 0.549895i \(-0.185332\pi\)
\(588\) 0 0
\(589\) −4.12725 7.14861i −0.170060 0.294553i
\(590\) 12.1268 0.499254
\(591\) 0 0
\(592\) 0.163325 + 0.282888i 0.00671263 + 0.0116266i
\(593\) −1.84854 −0.0759104 −0.0379552 0.999279i \(-0.512084\pi\)
−0.0379552 + 0.999279i \(0.512084\pi\)
\(594\) 0 0
\(595\) −2.54967 + 4.41617i −0.104526 + 0.181045i
\(596\) −12.3028 + 21.3091i −0.503944 + 0.872856i
\(597\) 0 0
\(598\) 7.22926 + 6.94479i 0.295626 + 0.283993i
\(599\) 25.2041 1.02981 0.514906 0.857247i \(-0.327827\pi\)
0.514906 + 0.857247i \(0.327827\pi\)
\(600\) 0 0
\(601\) −4.04333 + 7.00325i −0.164931 + 0.285669i −0.936631 0.350318i \(-0.886073\pi\)
0.771700 + 0.635987i \(0.219407\pi\)
\(602\) 0.935828 + 1.62090i 0.0381415 + 0.0660630i
\(603\) 0 0
\(604\) −9.27117 16.0581i −0.377238 0.653396i
\(605\) −4.36082 7.55316i −0.177293 0.307080i
\(606\) 0 0
\(607\) −22.5197 39.0052i −0.914045 1.58317i −0.808293 0.588780i \(-0.799608\pi\)
−0.105752 0.994393i \(-0.533725\pi\)
\(608\) 8.28081 14.3428i 0.335831 0.581677i
\(609\) 0 0
\(610\) −6.30182 −0.255153
\(611\) 17.7825 5.14938i 0.719402 0.208322i
\(612\) 0 0
\(613\) 20.6480 35.7634i 0.833965 1.44447i −0.0609049 0.998144i \(-0.519399\pi\)
0.894870 0.446327i \(-0.147268\pi\)
\(614\) −2.34036 + 4.05362i −0.0944492 + 0.163591i
\(615\) 0 0
\(616\) 6.93141 0.279275
\(617\) 3.43181 + 5.94406i 0.138159 + 0.239299i 0.926800 0.375555i \(-0.122548\pi\)
−0.788641 + 0.614855i \(0.789215\pi\)
\(618\) 0 0
\(619\) −37.3813 −1.50248 −0.751241 0.660028i \(-0.770544\pi\)
−0.751241 + 0.660028i \(0.770544\pi\)
\(620\) 1.46828 + 2.54313i 0.0589674 + 0.102134i
\(621\) 0 0
\(622\) 14.2185 24.6271i 0.570109 0.987458i
\(623\) 1.24547 0.0498986
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 2.16538 3.75055i 0.0865460 0.149902i
\(627\) 0 0
\(628\) 1.80170 + 3.12064i 0.0718957 + 0.124527i
\(629\) 1.86458 0.0743457
\(630\) 0 0
\(631\) −4.40493 7.62957i −0.175358 0.303728i 0.764927 0.644117i \(-0.222775\pi\)
−0.940285 + 0.340388i \(0.889441\pi\)
\(632\) −22.8146 −0.907515
\(633\) 0 0
\(634\) 0.714316 1.23723i 0.0283691 0.0491367i
\(635\) −3.80200 + 6.58526i −0.150878 + 0.261328i
\(636\) 0 0
\(637\) −3.93308 + 15.9523i −0.155834 + 0.632051i
\(638\) 3.72164 0.147341
\(639\) 0 0
\(640\) −2.40503 + 4.16564i −0.0950672 + 0.164661i
\(641\) −4.08665 7.07829i −0.161413 0.279576i 0.773963 0.633231i \(-0.218272\pi\)
−0.935376 + 0.353656i \(0.884938\pi\)
\(642\) 0 0
\(643\) −12.6636 21.9339i −0.499402 0.864989i 0.500598 0.865680i \(-0.333113\pi\)
−1.00000 0.000690710i \(0.999780\pi\)
\(644\) −2.53574 4.39202i −0.0999220 0.173070i
\(645\) 0 0
\(646\) 4.79231 + 8.30053i 0.188551 + 0.326580i
\(647\) −0.573255 + 0.992906i −0.0225370 + 0.0390352i −0.877074 0.480355i \(-0.840508\pi\)
0.854537 + 0.519391i \(0.173841\pi\)
\(648\) 0 0
\(649\) −19.3419 −0.759238
\(650\) 0.816822 3.31296i 0.0320384 0.129945i
\(651\) 0 0
\(652\) 1.73693 3.00845i 0.0680233 0.117820i
\(653\) −11.4214 + 19.7825i −0.446956 + 0.774150i −0.998186 0.0602031i \(-0.980825\pi\)
0.551231 + 0.834353i \(0.314158\pi\)
\(654\) 0 0
\(655\) −19.0332 −0.743689
\(656\) 1.62544 + 2.81535i 0.0634629 + 0.109921i
\(657\) 0 0
\(658\) 7.59521 0.296092
\(659\) 9.54096 + 16.5254i 0.371663 + 0.643739i 0.989822 0.142314i \(-0.0454543\pi\)
−0.618158 + 0.786054i \(0.712121\pi\)
\(660\) 0 0
\(661\) −5.79424 + 10.0359i −0.225370 + 0.390352i −0.956430 0.291961i \(-0.905692\pi\)
0.731060 + 0.682313i \(0.239026\pi\)
\(662\) 7.91057 0.307453
\(663\) 0 0
\(664\) −32.9961 −1.28050
\(665\) 2.42617 4.20225i 0.0940829 0.162956i
\(666\) 0 0
\(667\) −3.82710 6.62873i −0.148186 0.256666i
\(668\) 11.5164 0.445585
\(669\) 0 0
\(670\) 4.49432 + 7.78440i 0.173631 + 0.300738i
\(671\) 10.0512 0.388023
\(672\) 0 0
\(673\) −17.7188 + 30.6899i −0.683010 + 1.18301i 0.291048 + 0.956708i \(0.405996\pi\)
−0.974058 + 0.226299i \(0.927337\pi\)
\(674\) −7.35134 + 12.7329i −0.283163 + 0.490453i
\(675\) 0 0
\(676\) 12.7116 + 6.67389i 0.488909 + 0.256688i
\(677\) −30.5442 −1.17391 −0.586954 0.809620i \(-0.699673\pi\)
−0.586954 + 0.809620i \(0.699673\pi\)
\(678\) 0 0
\(679\) −4.53320 + 7.85173i −0.173968 + 0.301322i
\(680\) −4.79231 8.30053i −0.183777 0.318311i
\(681\) 0 0
\(682\) 1.89913 + 3.28939i 0.0727214 + 0.125957i
\(683\) 9.78636 + 16.9505i 0.374465 + 0.648592i 0.990247 0.139325i \(-0.0444932\pi\)
−0.615782 + 0.787916i \(0.711160\pi\)
\(684\) 0 0
\(685\) −9.53422 16.5138i −0.364284 0.630958i
\(686\) −8.54759 + 14.8049i −0.326348 + 0.565252i
\(687\) 0 0
\(688\) −0.723159 −0.0275702
\(689\) −10.1035 + 2.92573i −0.384913 + 0.111462i
\(690\) 0 0
\(691\) 8.38548 14.5241i 0.318999 0.552522i −0.661281 0.750138i \(-0.729987\pi\)
0.980279 + 0.197617i \(0.0633202\pi\)
\(692\) 6.85026 11.8650i 0.260408 0.451040i
\(693\) 0 0
\(694\) −5.47087 −0.207671
\(695\) −7.41454 12.8424i −0.281250 0.487139i
\(696\) 0 0
\(697\) 18.5567 0.702884
\(698\) −2.58180 4.47181i −0.0977226 0.169260i
\(699\) 0 0
\(700\) −0.863114 + 1.49496i −0.0326227 + 0.0565041i
\(701\) −40.4052 −1.52608 −0.763041 0.646350i \(-0.776294\pi\)
−0.763041 + 0.646350i \(0.776294\pi\)
\(702\) 0 0
\(703\) −1.77426 −0.0669176
\(704\) −4.67305 + 8.09396i −0.176122 + 0.305053i
\(705\) 0 0
\(706\) 5.80240 + 10.0501i 0.218376 + 0.378239i
\(707\) −9.44089 −0.355061
\(708\) 0 0
\(709\) −8.69058 15.0525i −0.326382 0.565310i 0.655409 0.755274i \(-0.272496\pi\)
−0.981791 + 0.189964i \(0.939163\pi\)
\(710\) 1.15470 0.0433349
\(711\) 0 0
\(712\) −1.17048 + 2.02733i −0.0438655 + 0.0759772i
\(713\) 3.90589 6.76519i 0.146277 0.253359i
\(714\) 0 0
\(715\) −1.30281 + 5.28407i −0.0487222 + 0.197613i
\(716\) 10.1201 0.378207
\(717\) 0 0
\(718\) 12.9892 22.4980i 0.484754 0.839618i
\(719\) 1.23074 + 2.13171i 0.0458990 + 0.0794995i 0.888062 0.459723i \(-0.152051\pi\)
−0.842163 + 0.539223i \(0.818718\pi\)
\(720\) 0 0
\(721\) −7.30269 12.6486i −0.271966 0.471060i
\(722\) 4.43029 + 7.67349i 0.164878 + 0.285578i
\(723\) 0 0
\(724\) −2.60129 4.50557i −0.0966763 0.167448i
\(725\) −1.30267 + 2.25629i −0.0483799 + 0.0837965i
\(726\) 0 0
\(727\) 30.0547 1.11467 0.557333 0.830289i \(-0.311825\pi\)
0.557333 + 0.830289i \(0.311825\pi\)
\(728\) 11.9401 + 11.4703i 0.442531 + 0.425118i
\(729\) 0 0
\(730\) −6.09389 + 10.5549i −0.225545 + 0.390655i
\(731\) −2.06396 + 3.57489i −0.0763384 + 0.132222i
\(732\) 0 0
\(733\) 18.4533 0.681587 0.340794 0.940138i \(-0.389304\pi\)
0.340794 + 0.940138i \(0.389304\pi\)
\(734\) −16.0040 27.7198i −0.590719 1.02316i
\(735\) 0 0
\(736\) 15.6733 0.577727
\(737\) −7.16831 12.4159i −0.264048 0.457344i
\(738\) 0 0
\(739\) −17.8603 + 30.9349i −0.657002 + 1.13796i 0.324386 + 0.945925i \(0.394842\pi\)
−0.981388 + 0.192036i \(0.938491\pi\)
\(740\) 0.631197 0.0232033
\(741\) 0 0
\(742\) −4.31539 −0.158423
\(743\) −5.57372 + 9.65396i −0.204480 + 0.354170i −0.949967 0.312351i \(-0.898884\pi\)
0.745487 + 0.666520i \(0.232217\pi\)
\(744\) 0 0
\(745\) −11.1399 19.2949i −0.408135 0.706910i
\(746\) −2.88823 −0.105746
\(747\) 0 0
\(748\) 2.71922 + 4.70982i 0.0994245 + 0.172208i
\(749\) 17.2098 0.628834
\(750\) 0 0
\(751\) −6.32279 + 10.9514i −0.230722 + 0.399622i −0.958021 0.286699i \(-0.907442\pi\)
0.727299 + 0.686321i \(0.240775\pi\)
\(752\) −1.46730 + 2.54143i −0.0535068 + 0.0926764i
\(753\) 0 0
\(754\) 6.41095 + 6.15868i 0.233473 + 0.224286i
\(755\) 16.7896 0.611037
\(756\) 0 0
\(757\) −2.77640 + 4.80887i −0.100910 + 0.174781i −0.912060 0.410057i \(-0.865509\pi\)
0.811150 + 0.584839i \(0.198842\pi\)
\(758\) 1.42531 + 2.46871i 0.0517696 + 0.0896676i
\(759\) 0 0
\(760\) 4.56018 + 7.89847i 0.165415 + 0.286507i
\(761\) −15.1323 26.2099i −0.548544 0.950106i −0.998375 0.0569925i \(-0.981849\pi\)
0.449830 0.893114i \(-0.351484\pi\)
\(762\) 0 0
\(763\) 14.5112 + 25.1341i 0.525340 + 0.909915i
\(764\) −8.36608 + 14.4905i −0.302674 + 0.524247i
\(765\) 0 0
\(766\) 3.04650 0.110074
\(767\) −33.3187 32.0076i −1.20307 1.15573i
\(768\) 0 0
\(769\) 26.1245 45.2489i 0.942072 1.63172i 0.180562 0.983564i \(-0.442208\pi\)
0.761510 0.648153i \(-0.224458\pi\)
\(770\) −1.11639 + 1.93364i −0.0402318 + 0.0696836i
\(771\) 0 0
\(772\) −11.3642 −0.409007
\(773\) 19.7389 + 34.1887i 0.709957 + 1.22968i 0.964872 + 0.262719i \(0.0846192\pi\)
−0.254915 + 0.966963i \(0.582048\pi\)
\(774\) 0 0
\(775\) −2.65897 −0.0955132
\(776\) −8.52050 14.7579i −0.305868 0.529779i
\(777\) 0 0
\(778\) 6.05988 10.4960i 0.217257 0.376300i
\(779\) −17.6578 −0.632657
\(780\) 0 0
\(781\) −1.84170 −0.0659013
\(782\) −4.53528 + 7.85534i −0.162181 + 0.280906i
\(783\) 0 0
\(784\) −1.30220 2.25547i −0.0465070 0.0805525i
\(785\) −3.26279 −0.116454
\(786\) 0 0
\(787\) 15.6650 + 27.1326i 0.558396 + 0.967171i 0.997631 + 0.0687984i \(0.0219165\pi\)
−0.439234 + 0.898373i \(0.644750\pi\)