Properties

Label 180.3.f.h.19.8
Level $180$
Weight $3$
Character 180.19
Analytic conductor $4.905$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.90464475849\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.389136420864.4
Defining polynomial: \(x^{8} + 5 x^{6} + 24 x^{4} + 80 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.8
Root \(1.52274 + 1.29664i\) of defining polynomial
Character \(\chi\) \(=\) 180.19
Dual form 180.3.f.h.19.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} +0.837253 q^{7} +(-4.14959 + 6.83966i) q^{8} +O(q^{10})\) \(q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} +0.837253 q^{7} +(-4.14959 + 6.83966i) q^{8} +(-9.87212 - 1.59414i) q^{10} +15.7955i q^{11} +5.18655i q^{13} +(1.27492 + 1.08561i) q^{14} +(-15.1873 + 5.03449i) q^{16} -27.3586i q^{17} +17.9667i q^{19} +(-12.9656 - 15.2280i) q^{20} +(-20.4811 + 24.0524i) q^{22} +19.1101 q^{23} +(11.5498 - 22.1721i) q^{25} +(-6.72508 + 7.89776i) q^{26} +(0.533714 + 3.30621i) q^{28} +45.6495 q^{29} +13.6243i q^{31} +(-29.6542 - 12.0262i) q^{32} +(35.4743 - 41.6600i) q^{34} +(-3.57919 + 2.17123i) q^{35} -15.5597i q^{37} +(-23.2964 + 27.3586i) q^{38} +(0.00200734 - 40.0000i) q^{40} -13.2990 q^{41} +27.9430 q^{43} +(-62.3746 + 10.0690i) q^{44} +(29.0997 + 24.7789i) q^{46} +55.6558 q^{47} -48.2990 q^{49} +(46.3365 - 18.7863i) q^{50} +(-20.4811 + 3.30621i) q^{52} +15.5597i q^{53} +(-40.9621 - 67.5245i) q^{55} +(-3.47425 + 5.72653i) q^{56} +(69.5122 + 59.1909i) q^{58} -87.6625i q^{59} +38.0000 q^{61} +(-17.6658 + 20.7462i) q^{62} +(-29.5619 - 56.7635i) q^{64} +(-13.4502 - 22.1721i) q^{65} +92.2015 q^{67} +(108.036 - 17.4400i) q^{68} +(-8.26547 - 1.33470i) q^{70} +130.707i q^{71} +54.7173i q^{73} +(20.1752 - 23.6933i) q^{74} +(-70.9485 + 11.4531i) q^{76} +13.2249i q^{77} -13.6243i q^{79} +(51.8686 - 60.9069i) q^{80} +(-20.2509 - 17.2440i) q^{82} -59.0048 q^{83} +(70.9485 + 116.956i) q^{85} +(42.5498 + 36.2319i) q^{86} +(-108.036 - 65.5448i) q^{88} -39.8007 q^{89} +4.34246i q^{91} +(12.1819 + 75.4635i) q^{92} +(84.7492 + 72.1654i) q^{94} +(-46.5927 - 76.8064i) q^{95} -168.821i q^{97} +(-73.5467 - 62.6263i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 10q^{4} - 4q^{5} + O(q^{10}) \) \( 8q - 10q^{4} - 4q^{5} - 42q^{10} - 20q^{14} - 46q^{16} - 52q^{20} + 32q^{25} - 84q^{26} + 184q^{29} + 12q^{34} - 6q^{40} + 256q^{41} - 348q^{44} + 112q^{46} - 24q^{49} - 72q^{50} + 244q^{56} + 304q^{61} - 10q^{64} - 168q^{65} - 104q^{70} + 252q^{74} - 24q^{76} + 308q^{80} + 24q^{85} + 280q^{86} - 560q^{89} + 376q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52274 + 1.29664i 0.761369 + 0.648319i
\(3\) 0 0
\(4\) 0.637459 + 3.94888i 0.159365 + 0.987220i
\(5\) −4.27492 + 2.59328i −0.854983 + 0.518655i
\(6\) 0 0
\(7\) 0.837253 0.119608 0.0598038 0.998210i \(-0.480952\pi\)
0.0598038 + 0.998210i \(0.480952\pi\)
\(8\) −4.14959 + 6.83966i −0.518698 + 0.854957i
\(9\) 0 0
\(10\) −9.87212 1.59414i −0.987212 0.159414i
\(11\) 15.7955i 1.43596i 0.696066 + 0.717978i \(0.254932\pi\)
−0.696066 + 0.717978i \(0.745068\pi\)
\(12\) 0 0
\(13\) 5.18655i 0.398966i 0.979901 + 0.199483i \(0.0639262\pi\)
−0.979901 + 0.199483i \(0.936074\pi\)
\(14\) 1.27492 + 1.08561i 0.0910655 + 0.0775439i
\(15\) 0 0
\(16\) −15.1873 + 5.03449i −0.949206 + 0.314656i
\(17\) 27.3586i 1.60933i −0.593728 0.804666i \(-0.702344\pi\)
0.593728 0.804666i \(-0.297656\pi\)
\(18\) 0 0
\(19\) 17.9667i 0.945618i 0.881165 + 0.472809i \(0.156760\pi\)
−0.881165 + 0.472809i \(0.843240\pi\)
\(20\) −12.9656 15.2280i −0.648281 0.761401i
\(21\) 0 0
\(22\) −20.4811 + 24.0524i −0.930958 + 1.09329i
\(23\) 19.1101 0.830874 0.415437 0.909622i \(-0.363629\pi\)
0.415437 + 0.909622i \(0.363629\pi\)
\(24\) 0 0
\(25\) 11.5498 22.1721i 0.461993 0.886883i
\(26\) −6.72508 + 7.89776i −0.258657 + 0.303760i
\(27\) 0 0
\(28\) 0.533714 + 3.30621i 0.0190612 + 0.118079i
\(29\) 45.6495 1.57412 0.787060 0.616876i \(-0.211602\pi\)
0.787060 + 0.616876i \(0.211602\pi\)
\(30\) 0 0
\(31\) 13.6243i 0.439493i 0.975557 + 0.219747i \(0.0705230\pi\)
−0.975557 + 0.219747i \(0.929477\pi\)
\(32\) −29.6542 12.0262i −0.926693 0.375819i
\(33\) 0 0
\(34\) 35.4743 41.6600i 1.04336 1.22529i
\(35\) −3.57919 + 2.17123i −0.102263 + 0.0620351i
\(36\) 0 0
\(37\) 15.5597i 0.420531i −0.977644 0.210266i \(-0.932567\pi\)
0.977644 0.210266i \(-0.0674329\pi\)
\(38\) −23.2964 + 27.3586i −0.613062 + 0.719964i
\(39\) 0 0
\(40\) 0.00200734 40.0000i 5.01834e−5 1.00000i
\(41\) −13.2990 −0.324366 −0.162183 0.986761i \(-0.551853\pi\)
−0.162183 + 0.986761i \(0.551853\pi\)
\(42\) 0 0
\(43\) 27.9430 0.649837 0.324918 0.945742i \(-0.394663\pi\)
0.324918 + 0.945742i \(0.394663\pi\)
\(44\) −62.3746 + 10.0690i −1.41760 + 0.228841i
\(45\) 0 0
\(46\) 29.0997 + 24.7789i 0.632601 + 0.538672i
\(47\) 55.6558 1.18417 0.592083 0.805877i \(-0.298306\pi\)
0.592083 + 0.805877i \(0.298306\pi\)
\(48\) 0 0
\(49\) −48.2990 −0.985694
\(50\) 46.3365 18.7863i 0.926731 0.375726i
\(51\) 0 0
\(52\) −20.4811 + 3.30621i −0.393867 + 0.0635810i
\(53\) 15.5597i 0.293578i 0.989168 + 0.146789i \(0.0468939\pi\)
−0.989168 + 0.146789i \(0.953106\pi\)
\(54\) 0 0
\(55\) −40.9621 67.5245i −0.744766 1.22772i
\(56\) −3.47425 + 5.72653i −0.0620403 + 0.102259i
\(57\) 0 0
\(58\) 69.5122 + 59.1909i 1.19849 + 1.02053i
\(59\) 87.6625i 1.48581i −0.669400 0.742903i \(-0.733449\pi\)
0.669400 0.742903i \(-0.266551\pi\)
\(60\) 0 0
\(61\) 38.0000 0.622951 0.311475 0.950254i \(-0.399177\pi\)
0.311475 + 0.950254i \(0.399177\pi\)
\(62\) −17.6658 + 20.7462i −0.284932 + 0.334616i
\(63\) 0 0
\(64\) −29.5619 56.7635i −0.461904 0.886930i
\(65\) −13.4502 22.1721i −0.206926 0.341109i
\(66\) 0 0
\(67\) 92.2015 1.37614 0.688071 0.725643i \(-0.258458\pi\)
0.688071 + 0.725643i \(0.258458\pi\)
\(68\) 108.036 17.4400i 1.58876 0.256471i
\(69\) 0 0
\(70\) −8.26547 1.33470i −0.118078 0.0190672i
\(71\) 130.707i 1.84094i 0.390816 + 0.920469i \(0.372193\pi\)
−0.390816 + 0.920469i \(0.627807\pi\)
\(72\) 0 0
\(73\) 54.7173i 0.749552i 0.927115 + 0.374776i \(0.122280\pi\)
−0.927115 + 0.374776i \(0.877720\pi\)
\(74\) 20.1752 23.6933i 0.272638 0.320179i
\(75\) 0 0
\(76\) −70.9485 + 11.4531i −0.933533 + 0.150698i
\(77\) 13.2249i 0.171751i
\(78\) 0 0
\(79\) 13.6243i 0.172459i −0.996275 0.0862297i \(-0.972518\pi\)
0.996275 0.0862297i \(-0.0274819\pi\)
\(80\) 51.8686 60.9069i 0.648357 0.761336i
\(81\) 0 0
\(82\) −20.2509 17.2440i −0.246962 0.210293i
\(83\) −59.0048 −0.710901 −0.355451 0.934695i \(-0.615673\pi\)
−0.355451 + 0.934695i \(0.615673\pi\)
\(84\) 0 0
\(85\) 70.9485 + 116.956i 0.834688 + 1.37595i
\(86\) 42.5498 + 36.2319i 0.494766 + 0.421302i
\(87\) 0 0
\(88\) −108.036 65.5448i −1.22768 0.744828i
\(89\) −39.8007 −0.447198 −0.223599 0.974681i \(-0.571781\pi\)
−0.223599 + 0.974681i \(0.571781\pi\)
\(90\) 0 0
\(91\) 4.34246i 0.0477193i
\(92\) 12.1819 + 75.4635i 0.132412 + 0.820255i
\(93\) 0 0
\(94\) 84.7492 + 72.1654i 0.901587 + 0.767717i
\(95\) −46.5927 76.8064i −0.490450 0.808488i
\(96\) 0 0
\(97\) 168.821i 1.74043i −0.492675 0.870214i \(-0.663981\pi\)
0.492675 0.870214i \(-0.336019\pi\)
\(98\) −73.5467 62.6263i −0.750477 0.639044i
\(99\) 0 0
\(100\) 94.9174 + 31.4751i 0.949174 + 0.314751i
\(101\) −44.5498 −0.441087 −0.220544 0.975377i \(-0.570783\pi\)
−0.220544 + 0.975377i \(0.570783\pi\)
\(102\) 0 0
\(103\) −126.466 −1.22782 −0.613911 0.789375i \(-0.710405\pi\)
−0.613911 + 0.789375i \(0.710405\pi\)
\(104\) −35.4743 21.5220i −0.341099 0.206943i
\(105\) 0 0
\(106\) −20.1752 + 23.6933i −0.190333 + 0.223521i
\(107\) −104.383 −0.975546 −0.487773 0.872971i \(-0.662191\pi\)
−0.487773 + 0.872971i \(0.662191\pi\)
\(108\) 0 0
\(109\) −0.501656 −0.00460235 −0.00230117 0.999997i \(-0.500732\pi\)
−0.00230117 + 0.999997i \(0.500732\pi\)
\(110\) 25.1803 155.935i 0.228912 1.41759i
\(111\) 0 0
\(112\) −12.7156 + 4.21515i −0.113532 + 0.0376352i
\(113\) 16.9855i 0.150314i 0.997172 + 0.0751572i \(0.0239459\pi\)
−0.997172 + 0.0751572i \(0.976054\pi\)
\(114\) 0 0
\(115\) −81.6941 + 49.5578i −0.710384 + 0.430937i
\(116\) 29.0997 + 180.264i 0.250859 + 1.55400i
\(117\) 0 0
\(118\) 113.667 133.487i 0.963276 1.13125i
\(119\) 22.9061i 0.192488i
\(120\) 0 0
\(121\) −128.498 −1.06197
\(122\) 57.8640 + 49.2723i 0.474295 + 0.403871i
\(123\) 0 0
\(124\) −53.8007 + 8.68492i −0.433876 + 0.0700397i
\(125\) 8.12376 + 124.736i 0.0649901 + 0.997886i
\(126\) 0 0
\(127\) 8.45598 0.0665825 0.0332913 0.999446i \(-0.489401\pi\)
0.0332913 + 0.999446i \(0.489401\pi\)
\(128\) 28.5867 124.767i 0.223334 0.974742i
\(129\) 0 0
\(130\) 8.26810 51.2023i 0.0636008 0.393864i
\(131\) 51.7290i 0.394878i −0.980315 0.197439i \(-0.936738\pi\)
0.980315 0.197439i \(-0.0632624\pi\)
\(132\) 0 0
\(133\) 15.0427i 0.113103i
\(134\) 140.399 + 119.552i 1.04775 + 0.892179i
\(135\) 0 0
\(136\) 187.124 + 113.527i 1.37591 + 0.834757i
\(137\) 53.8083i 0.392762i 0.980528 + 0.196381i \(0.0629189\pi\)
−0.980528 + 0.196381i \(0.937081\pi\)
\(138\) 0 0
\(139\) 13.6243i 0.0980165i 0.998798 + 0.0490082i \(0.0156061\pi\)
−0.998798 + 0.0490082i \(0.984394\pi\)
\(140\) −10.8555 12.7497i −0.0775393 0.0910694i
\(141\) 0 0
\(142\) −169.479 + 199.032i −1.19352 + 1.40163i
\(143\) −81.9243 −0.572897
\(144\) 0 0
\(145\) −195.148 + 118.382i −1.34585 + 0.816426i
\(146\) −70.9485 + 83.3200i −0.485949 + 0.570685i
\(147\) 0 0
\(148\) 61.4432 9.91864i 0.415157 0.0670178i
\(149\) 33.6495 0.225836 0.112918 0.993604i \(-0.463980\pi\)
0.112918 + 0.993604i \(0.463980\pi\)
\(150\) 0 0
\(151\) 139.988i 0.927076i 0.886077 + 0.463538i \(0.153420\pi\)
−0.886077 + 0.463538i \(0.846580\pi\)
\(152\) −122.886 74.5546i −0.808463 0.490490i
\(153\) 0 0
\(154\) −17.1478 + 20.1380i −0.111350 + 0.130766i
\(155\) −35.3315 58.2427i −0.227945 0.375759i
\(156\) 0 0
\(157\) 21.2631i 0.135434i 0.997705 + 0.0677170i \(0.0215715\pi\)
−0.997705 + 0.0677170i \(0.978428\pi\)
\(158\) 17.6658 20.7462i 0.111809 0.131305i
\(159\) 0 0
\(160\) 157.956 25.4904i 0.987228 0.159315i
\(161\) 16.0000 0.0993789
\(162\) 0 0
\(163\) −210.211 −1.28964 −0.644819 0.764335i \(-0.723067\pi\)
−0.644819 + 0.764335i \(0.723067\pi\)
\(164\) −8.47757 52.5162i −0.0516925 0.320221i
\(165\) 0 0
\(166\) −89.8488 76.5079i −0.541258 0.460891i
\(167\) 238.384 1.42745 0.713725 0.700426i \(-0.247006\pi\)
0.713725 + 0.700426i \(0.247006\pi\)
\(168\) 0 0
\(169\) 142.100 0.840826
\(170\) −43.6136 + 270.088i −0.256550 + 1.58875i
\(171\) 0 0
\(172\) 17.8125 + 110.343i 0.103561 + 0.641532i
\(173\) 2.33481i 0.0134960i 0.999977 + 0.00674800i \(0.00214797\pi\)
−0.999977 + 0.00674800i \(0.997852\pi\)
\(174\) 0 0
\(175\) 9.67014 18.5637i 0.0552579 0.106078i
\(176\) −79.5224 239.891i −0.451832 1.36302i
\(177\) 0 0
\(178\) −60.6060 51.6071i −0.340483 0.289927i
\(179\) 227.054i 1.26846i 0.773145 + 0.634229i \(0.218682\pi\)
−0.773145 + 0.634229i \(0.781318\pi\)
\(180\) 0 0
\(181\) 114.096 0.630367 0.315183 0.949031i \(-0.397934\pi\)
0.315183 + 0.949031i \(0.397934\pi\)
\(182\) −5.63060 + 6.61243i −0.0309374 + 0.0363320i
\(183\) 0 0
\(184\) −79.2990 + 130.707i −0.430973 + 0.710362i
\(185\) 40.3505 + 66.5163i 0.218111 + 0.359547i
\(186\) 0 0
\(187\) 432.144 2.31093
\(188\) 35.4783 + 219.778i 0.188714 + 1.16903i
\(189\) 0 0
\(190\) 28.6415 177.370i 0.150745 0.933525i
\(191\) 139.392i 0.729798i −0.931047 0.364899i \(-0.881103\pi\)
0.931047 0.364899i \(-0.118897\pi\)
\(192\) 0 0
\(193\) 182.046i 0.943245i −0.881801 0.471623i \(-0.843669\pi\)
0.881801 0.471623i \(-0.156331\pi\)
\(194\) 218.900 257.071i 1.12835 1.32511i
\(195\) 0 0
\(196\) −30.7886 190.727i −0.157085 0.973097i
\(197\) 258.027i 1.30978i −0.755724 0.654890i \(-0.772715\pi\)
0.755724 0.654890i \(-0.227285\pi\)
\(198\) 0 0
\(199\) 256.474i 1.28881i −0.764683 0.644407i \(-0.777104\pi\)
0.764683 0.644407i \(-0.222896\pi\)
\(200\) 103.722 + 171.002i 0.518612 + 0.855009i
\(201\) 0 0
\(202\) −67.8377 57.7650i −0.335830 0.285965i
\(203\) 38.2202 0.188277
\(204\) 0 0
\(205\) 56.8522 34.4880i 0.277328 0.168234i
\(206\) −192.574 163.980i −0.934825 0.796020i
\(207\) 0 0
\(208\) −26.1117 78.7697i −0.125537 0.378700i
\(209\) −283.794 −1.35787
\(210\) 0 0
\(211\) 211.855i 1.00405i −0.864852 0.502027i \(-0.832588\pi\)
0.864852 0.502027i \(-0.167412\pi\)
\(212\) −61.4432 + 9.91864i −0.289826 + 0.0467860i
\(213\) 0 0
\(214\) −158.949 135.348i −0.742750 0.632465i
\(215\) −119.454 + 72.4639i −0.555600 + 0.337041i
\(216\) 0 0
\(217\) 11.4070i 0.0525667i
\(218\) −0.763890 0.650466i −0.00350408 0.00298379i
\(219\) 0 0
\(220\) 240.535 204.799i 1.09334 0.930903i
\(221\) 141.897 0.642068
\(222\) 0 0
\(223\) 349.843 1.56880 0.784401 0.620255i \(-0.212971\pi\)
0.784401 + 0.620255i \(0.212971\pi\)
\(224\) −24.8281 10.0690i −0.110840 0.0449508i
\(225\) 0 0
\(226\) −22.0241 + 25.8645i −0.0974517 + 0.114445i
\(227\) 185.554 0.817418 0.408709 0.912665i \(-0.365979\pi\)
0.408709 + 0.912665i \(0.365979\pi\)
\(228\) 0 0
\(229\) 263.897 1.15239 0.576194 0.817313i \(-0.304537\pi\)
0.576194 + 0.817313i \(0.304537\pi\)
\(230\) −188.657 30.4642i −0.820249 0.132453i
\(231\) 0 0
\(232\) −189.427 + 312.227i −0.816494 + 1.34581i
\(233\) 58.4780i 0.250978i −0.992095 0.125489i \(-0.959950\pi\)
0.992095 0.125489i \(-0.0400500\pi\)
\(234\) 0 0
\(235\) −237.924 + 144.331i −1.01244 + 0.614174i
\(236\) 346.169 55.8812i 1.46682 0.236785i
\(237\) 0 0
\(238\) 29.7009 34.8800i 0.124794 0.146555i
\(239\) 113.337i 0.474212i 0.971484 + 0.237106i \(0.0761989\pi\)
−0.971484 + 0.237106i \(0.923801\pi\)
\(240\) 0 0
\(241\) −77.7940 −0.322797 −0.161398 0.986889i \(-0.551600\pi\)
−0.161398 + 0.986889i \(0.551600\pi\)
\(242\) −195.669 166.616i −0.808551 0.688495i
\(243\) 0 0
\(244\) 24.2234 + 150.057i 0.0992763 + 0.614989i
\(245\) 206.474 125.253i 0.842752 0.511235i
\(246\) 0 0
\(247\) −93.1855 −0.377269
\(248\) −93.1855 56.5351i −0.375748 0.227964i
\(249\) 0 0
\(250\) −149.367 + 200.473i −0.597467 + 0.801893i
\(251\) 106.226i 0.423212i −0.977355 0.211606i \(-0.932131\pi\)
0.977355 0.211606i \(-0.0678693\pi\)
\(252\) 0 0
\(253\) 301.854i 1.19310i
\(254\) 12.8762 + 10.9644i 0.0506939 + 0.0431667i
\(255\) 0 0
\(256\) 205.308 152.921i 0.801983 0.597346i
\(257\) 381.078i 1.48279i −0.671067 0.741397i \(-0.734164\pi\)
0.671067 0.741397i \(-0.265836\pi\)
\(258\) 0 0
\(259\) 13.0274i 0.0502988i
\(260\) 78.9810 67.2469i 0.303773 0.258642i
\(261\) 0 0
\(262\) 67.0738 78.7697i 0.256007 0.300648i
\(263\) 11.4914 0.0436934 0.0218467 0.999761i \(-0.493045\pi\)
0.0218467 + 0.999761i \(0.493045\pi\)
\(264\) 0 0
\(265\) −40.3505 66.5163i −0.152266 0.251005i
\(266\) −19.5050 + 22.9061i −0.0733269 + 0.0861132i
\(267\) 0 0
\(268\) 58.7746 + 364.093i 0.219308 + 1.35855i
\(269\) 77.9518 0.289784 0.144892 0.989447i \(-0.453717\pi\)
0.144892 + 0.989447i \(0.453717\pi\)
\(270\) 0 0
\(271\) 86.6851i 0.319871i −0.987127 0.159936i \(-0.948871\pi\)
0.987127 0.159936i \(-0.0511287\pi\)
\(272\) 137.737 + 415.504i 0.506386 + 1.52759i
\(273\) 0 0
\(274\) −69.7700 + 81.9360i −0.254635 + 0.299036i
\(275\) 350.220 + 182.436i 1.27353 + 0.663402i
\(276\) 0 0
\(277\) 287.328i 1.03729i −0.854991 0.518643i \(-0.826437\pi\)
0.854991 0.518643i \(-0.173563\pi\)
\(278\) −17.6658 + 20.7462i −0.0635459 + 0.0746267i
\(279\) 0 0
\(280\) 0.00168065 33.4901i 6.00232e−6 0.119608i
\(281\) 224.598 0.799281 0.399641 0.916672i \(-0.369135\pi\)
0.399641 + 0.916672i \(0.369135\pi\)
\(282\) 0 0
\(283\) −84.1224 −0.297252 −0.148626 0.988893i \(-0.547485\pi\)
−0.148626 + 0.988893i \(0.547485\pi\)
\(284\) −516.145 + 83.3200i −1.81741 + 0.293380i
\(285\) 0 0
\(286\) −124.749 106.226i −0.436186 0.371420i
\(287\) −11.1346 −0.0387967
\(288\) 0 0
\(289\) −459.495 −1.58995
\(290\) −450.657 72.7718i −1.55399 0.250937i
\(291\) 0 0
\(292\) −216.072 + 34.8800i −0.739972 + 0.119452i
\(293\) 246.620i 0.841706i 0.907129 + 0.420853i \(0.138269\pi\)
−0.907129 + 0.420853i \(0.861731\pi\)
\(294\) 0 0
\(295\) 227.333 + 374.750i 0.770621 + 1.27034i
\(296\) 106.423 + 64.5661i 0.359536 + 0.218129i
\(297\) 0 0
\(298\) 51.2394 + 43.6312i 0.171944 + 0.146414i
\(299\) 99.1156i 0.331490i
\(300\) 0 0
\(301\) 23.3954 0.0777255
\(302\) −181.514 + 213.166i −0.601041 + 0.705846i
\(303\) 0 0
\(304\) −90.4535 272.866i −0.297544 0.897586i
\(305\) −162.447 + 98.5445i −0.532613 + 0.323097i
\(306\) 0 0
\(307\) −115.811 −0.377236 −0.188618 0.982051i \(-0.560401\pi\)
−0.188618 + 0.982051i \(0.560401\pi\)
\(308\) −52.2233 + 8.43030i −0.169556 + 0.0273711i
\(309\) 0 0
\(310\) 21.7190 134.501i 0.0700614 0.433873i
\(311\) 203.767i 0.655201i −0.944816 0.327600i \(-0.893760\pi\)
0.944816 0.327600i \(-0.106240\pi\)
\(312\) 0 0
\(313\) 99.0614i 0.316490i −0.987400 0.158245i \(-0.949416\pi\)
0.987400 0.158245i \(-0.0505836\pi\)
\(314\) −27.5706 + 32.3782i −0.0878045 + 0.103115i
\(315\) 0 0
\(316\) 53.8007 8.68492i 0.170255 0.0274839i
\(317\) 471.192i 1.48641i 0.669063 + 0.743206i \(0.266696\pi\)
−0.669063 + 0.743206i \(0.733304\pi\)
\(318\) 0 0
\(319\) 721.057i 2.26037i
\(320\) 273.578 + 165.997i 0.854931 + 0.518741i
\(321\) 0 0
\(322\) 24.3638 + 20.7462i 0.0756640 + 0.0644292i
\(323\) 491.546 1.52181
\(324\) 0 0
\(325\) 114.997 + 59.9038i 0.353836 + 0.184319i
\(326\) −320.096 272.568i −0.981891 0.836098i
\(327\) 0 0
\(328\) 55.1854 90.9607i 0.168248 0.277319i
\(329\) 46.5980 0.141635
\(330\) 0 0
\(331\) 270.695i 0.817810i 0.912577 + 0.408905i \(0.134089\pi\)
−0.912577 + 0.408905i \(0.865911\pi\)
\(332\) −37.6131 233.003i −0.113293 0.701816i
\(333\) 0 0
\(334\) 362.997 + 309.098i 1.08682 + 0.925444i
\(335\) −394.154 + 239.104i −1.17658 + 0.713743i
\(336\) 0 0
\(337\) 377.317i 1.11964i −0.828615 0.559818i \(-0.810871\pi\)
0.828615 0.559818i \(-0.189129\pi\)
\(338\) 216.380 + 184.252i 0.640179 + 0.545124i
\(339\) 0 0
\(340\) −416.618 + 354.722i −1.22535 + 1.04330i
\(341\) −215.203 −0.631093
\(342\) 0 0
\(343\) −81.4639 −0.237504
\(344\) −115.952 + 191.121i −0.337069 + 0.555583i
\(345\) 0 0
\(346\) −3.02740 + 3.55530i −0.00874971 + 0.0102754i
\(347\) −462.222 −1.33205 −0.666025 0.745929i \(-0.732006\pi\)
−0.666025 + 0.745929i \(0.732006\pi\)
\(348\) 0 0
\(349\) 200.598 0.574779 0.287390 0.957814i \(-0.407213\pi\)
0.287390 + 0.957814i \(0.407213\pi\)
\(350\) 38.7954 15.7289i 0.110844 0.0449397i
\(351\) 0 0
\(352\) 189.960 468.403i 0.539660 1.33069i
\(353\) 250.897i 0.710757i −0.934722 0.355379i \(-0.884352\pi\)
0.934722 0.355379i \(-0.115648\pi\)
\(354\) 0 0
\(355\) −338.958 558.760i −0.954812 1.57397i
\(356\) −25.3713 157.168i −0.0712676 0.441483i
\(357\) 0 0
\(358\) −294.407 + 345.744i −0.822366 + 0.965764i
\(359\) 215.601i 0.600560i −0.953851 0.300280i \(-0.902920\pi\)
0.953851 0.300280i \(-0.0970801\pi\)
\(360\) 0 0
\(361\) 38.1960 0.105806
\(362\) 173.739 + 147.942i 0.479941 + 0.408679i
\(363\) 0 0
\(364\) −17.1478 + 2.76814i −0.0471095 + 0.00760478i
\(365\) −141.897 233.912i −0.388759 0.640854i
\(366\) 0 0
\(367\) −67.0637 −0.182735 −0.0913675 0.995817i \(-0.529124\pi\)
−0.0913675 + 0.995817i \(0.529124\pi\)
\(368\) −290.231 + 96.2097i −0.788670 + 0.261439i
\(369\) 0 0
\(370\) −24.8043 + 153.607i −0.0670387 + 0.415153i
\(371\) 13.0274i 0.0351142i
\(372\) 0 0
\(373\) 567.402i 1.52119i 0.649230 + 0.760593i \(0.275091\pi\)
−0.649230 + 0.760593i \(0.724909\pi\)
\(374\) 658.042 + 560.334i 1.75947 + 1.49822i
\(375\) 0 0
\(376\) −230.949 + 380.667i −0.614225 + 1.01241i
\(377\) 236.764i 0.628020i
\(378\) 0 0
\(379\) 240.298i 0.634031i −0.948420 0.317016i \(-0.897319\pi\)
0.948420 0.317016i \(-0.102681\pi\)
\(380\) 273.598 232.950i 0.719995 0.613026i
\(381\) 0 0
\(382\) 180.740 212.257i 0.473142 0.555646i
\(383\) −670.068 −1.74952 −0.874762 0.484553i \(-0.838982\pi\)
−0.874762 + 0.484553i \(0.838982\pi\)
\(384\) 0 0
\(385\) −34.2957 56.5351i −0.0890797 0.146845i
\(386\) 236.048 277.209i 0.611524 0.718157i
\(387\) 0 0
\(388\) 666.655 107.617i 1.71818 0.277363i
\(389\) 474.640 1.22015 0.610077 0.792342i \(-0.291139\pi\)
0.610077 + 0.792342i \(0.291139\pi\)
\(390\) 0 0
\(391\) 522.826i 1.33715i
\(392\) 200.421 330.349i 0.511278 0.842726i
\(393\) 0 0
\(394\) 334.567 392.907i 0.849156 0.997226i
\(395\) 35.3315 + 58.2427i 0.0894469 + 0.147450i
\(396\) 0 0
\(397\) 499.460i 1.25809i 0.777371 + 0.629043i \(0.216553\pi\)
−0.777371 + 0.629043i \(0.783447\pi\)
\(398\) 332.554 390.542i 0.835562 0.981262i
\(399\) 0 0
\(400\) −63.7855 + 394.882i −0.159464 + 0.987204i
\(401\) −344.694 −0.859587 −0.429793 0.902927i \(-0.641414\pi\)
−0.429793 + 0.902927i \(0.641414\pi\)
\(402\) 0 0
\(403\) −70.6631 −0.175343
\(404\) −28.3987 175.922i −0.0702938 0.435450i
\(405\) 0 0
\(406\) 58.1993 + 49.5578i 0.143348 + 0.122063i
\(407\) 245.773 0.603864
\(408\) 0 0
\(409\) −501.890 −1.22712 −0.613558 0.789650i \(-0.710262\pi\)
−0.613558 + 0.789650i \(0.710262\pi\)
\(410\) 131.289 + 21.2005i 0.320218 + 0.0517085i
\(411\) 0 0
\(412\) −80.6166 499.397i −0.195671 1.21213i
\(413\) 73.3957i 0.177714i
\(414\) 0 0
\(415\) 252.241 153.016i 0.607809 0.368713i
\(416\) 62.3746 153.803i 0.149939 0.369719i
\(417\) 0 0
\(418\) −432.144 367.978i −1.03384 0.880331i
\(419\) 218.369i 0.521167i −0.965451 0.260584i \(-0.916085\pi\)
0.965451 0.260584i \(-0.0839150\pi\)
\(420\) 0 0
\(421\) 281.698 0.669116 0.334558 0.942375i \(-0.391413\pi\)
0.334558 + 0.942375i \(0.391413\pi\)
\(422\) 274.700 322.600i 0.650947 0.764455i
\(423\) 0 0
\(424\) −106.423 64.5661i −0.250997 0.152279i
\(425\) −606.598 315.988i −1.42729 0.743501i
\(426\) 0 0
\(427\) 31.8156 0.0745097
\(428\) −66.5401 412.197i −0.155468 0.963078i
\(429\) 0 0
\(430\) −275.856 44.5451i −0.641527 0.103593i
\(431\) 441.081i 1.02339i −0.859167 0.511694i \(-0.829018\pi\)
0.859167 0.511694i \(-0.170982\pi\)
\(432\) 0 0
\(433\) 123.443i 0.285089i −0.989788 0.142544i \(-0.954472\pi\)
0.989788 0.142544i \(-0.0455283\pi\)
\(434\) −14.7907 + 17.3698i −0.0340800 + 0.0400227i
\(435\) 0 0
\(436\) −0.319785 1.98098i −0.000733451 0.00454353i
\(437\) 343.346i 0.785690i
\(438\) 0 0
\(439\) 330.728i 0.753368i −0.926342 0.376684i \(-0.877064\pi\)
0.926342 0.376684i \(-0.122936\pi\)
\(440\) 631.821 + 0.0317069i 1.43596 + 7.20612e-5i
\(441\) 0 0
\(442\) 216.072 + 183.989i 0.488850 + 0.416265i
\(443\) −154.952 −0.349780 −0.174890 0.984588i \(-0.555957\pi\)
−0.174890 + 0.984588i \(0.555957\pi\)
\(444\) 0 0
\(445\) 170.145 103.214i 0.382347 0.231942i
\(446\) 532.718 + 453.619i 1.19444 + 1.01708i
\(447\) 0 0
\(448\) −24.7508 47.5254i −0.0552473 0.106084i
\(449\) 95.8970 0.213579 0.106790 0.994282i \(-0.465943\pi\)
0.106790 + 0.994282i \(0.465943\pi\)
\(450\) 0 0
\(451\) 210.065i 0.465775i
\(452\) −67.0738 + 10.8276i −0.148393 + 0.0239548i
\(453\) 0 0
\(454\) 282.550 + 240.596i 0.622356 + 0.529948i
\(455\) −11.2612 18.5637i −0.0247499 0.0407992i
\(456\) 0 0
\(457\) 485.718i 1.06284i 0.847108 + 0.531420i \(0.178341\pi\)
−0.847108 + 0.531420i \(0.821659\pi\)
\(458\) 401.846 + 342.179i 0.877393 + 0.747116i
\(459\) 0 0
\(460\) −247.774 291.009i −0.538640 0.632629i
\(461\) −353.650 −0.767136 −0.383568 0.923513i \(-0.625305\pi\)
−0.383568 + 0.923513i \(0.625305\pi\)
\(462\) 0 0
\(463\) 421.720 0.910842 0.455421 0.890276i \(-0.349489\pi\)
0.455421 + 0.890276i \(0.349489\pi\)
\(464\) −693.292 + 229.822i −1.49416 + 0.495306i
\(465\) 0 0
\(466\) 75.8248 89.0466i 0.162714 0.191087i
\(467\) −640.974 −1.37254 −0.686268 0.727349i \(-0.740752\pi\)
−0.686268 + 0.727349i \(0.740752\pi\)
\(468\) 0 0
\(469\) 77.1960 0.164597
\(470\) −549.441 88.7232i −1.16902 0.188773i
\(471\) 0 0
\(472\) 599.582 + 363.763i 1.27030 + 0.770684i
\(473\) 441.374i 0.933137i
\(474\) 0 0
\(475\) 398.360 + 207.513i 0.838653 + 0.436869i
\(476\) 90.4535 14.6017i 0.190028 0.0306758i
\(477\) 0 0
\(478\) −146.957 + 172.582i −0.307441 + 0.361050i
\(479\) 221.137i 0.461664i −0.972994 0.230832i \(-0.925855\pi\)
0.972994 0.230832i \(-0.0741448\pi\)
\(480\) 0 0
\(481\) 80.7010 0.167778
\(482\) −118.460 100.871i −0.245767 0.209275i
\(483\) 0 0
\(484\) −81.9124 507.424i −0.169240 1.04840i
\(485\) 437.801 + 721.698i 0.902682 + 1.48804i
\(486\) 0 0
\(487\) −889.949 −1.82741 −0.913705 0.406377i \(-0.866792\pi\)
−0.913705 + 0.406377i \(0.866792\pi\)
\(488\) −157.684 + 259.907i −0.323123 + 0.532596i
\(489\) 0 0
\(490\) 476.813 + 76.9955i 0.973089 + 0.157134i
\(491\) 552.843i 1.12595i 0.826473 + 0.562977i \(0.190344\pi\)
−0.826473 + 0.562977i \(0.809656\pi\)
\(492\) 0 0
\(493\) 1248.91i 2.53328i
\(494\) −141.897 120.828i −0.287241 0.244591i
\(495\) 0 0
\(496\) −68.5914 206.916i −0.138289 0.417169i
\(497\) 109.435i 0.220190i
\(498\) 0 0
\(499\) 533.302i 1.06874i 0.845250 + 0.534371i \(0.179451\pi\)
−0.845250 + 0.534371i \(0.820549\pi\)
\(500\) −487.388 + 111.594i −0.974776 + 0.223187i
\(501\) 0 0
\(502\) 137.737 161.755i 0.274376 0.322220i
\(503\) 574.914 1.14297 0.571485 0.820612i \(-0.306367\pi\)
0.571485 + 0.820612i \(0.306367\pi\)
\(504\) 0 0
\(505\) 190.447 115.530i 0.377122 0.228772i
\(506\) −391.395 + 459.644i −0.773509 + 0.908388i
\(507\) 0 0
\(508\) 5.39034 + 33.3917i 0.0106109 + 0.0657316i
\(509\) −207.547 −0.407753 −0.203877 0.978997i \(-0.565354\pi\)
−0.203877 + 0.978997i \(0.565354\pi\)
\(510\) 0 0
\(511\) 45.8122i 0.0896521i
\(512\) 510.913 + 33.3518i 0.997876 + 0.0651403i
\(513\) 0 0
\(514\) 494.120 580.282i 0.961324 1.12895i
\(515\) 540.630 327.960i 1.04977 0.636816i
\(516\) 0 0
\(517\) 879.112i 1.70041i
\(518\) 16.8918 19.8373i 0.0326096 0.0382959i
\(519\) 0 0
\(520\) 207.462 + 0.0104112i 0.398966 + 2.00214e-5i
\(521\) 712.900 1.36833 0.684165 0.729327i \(-0.260167\pi\)
0.684165 + 0.729327i \(0.260167\pi\)
\(522\) 0 0
\(523\) −139.548 −0.266822 −0.133411 0.991061i \(-0.542593\pi\)
−0.133411 + 0.991061i \(0.542593\pi\)
\(524\) 204.272 32.9751i 0.389831 0.0629296i
\(525\) 0 0
\(526\) 17.4983 + 14.9002i 0.0332668 + 0.0283273i
\(527\) 372.742 0.707290
\(528\) 0 0
\(529\) −163.804 −0.309648
\(530\) 24.8043 153.607i 0.0468006 0.289824i
\(531\) 0 0
\(532\) −59.4019 + 9.58911i −0.111658 + 0.0180246i
\(533\) 68.9760i 0.129411i
\(534\) 0 0
\(535\) 446.230 270.695i 0.834075 0.505972i
\(536\) −382.598 + 630.627i −0.713802 + 1.17654i
\(537\) 0 0
\(538\) 118.700 + 101.075i 0.220632 + 0.187872i
\(539\) 762.908i 1.41541i
\(540\) 0 0
\(541\) −946.688 −1.74988 −0.874942 0.484227i \(-0.839101\pi\)
−0.874942 + 0.484227i \(0.839101\pi\)
\(542\) 112.399 131.999i 0.207379 0.243540i
\(543\) 0 0
\(544\) −329.021 + 811.298i −0.604818 + 1.49136i
\(545\) 2.14454 1.30093i 0.00393493 0.00238703i
\(546\) 0 0
\(547\) −50.3388 −0.0920271 −0.0460136 0.998941i \(-0.514652\pi\)
−0.0460136 + 0.998941i \(0.514652\pi\)
\(548\) −212.483 + 34.3006i −0.387742 + 0.0625923i
\(549\) 0 0
\(550\) 296.739 + 731.910i 0.539526 + 1.33074i
\(551\) 820.173i 1.48852i
\(552\) 0 0
\(553\) 11.4070i 0.0206275i
\(554\) 372.561 437.525i 0.672492 0.789757i
\(555\) 0 0
\(556\) −53.8007 + 8.68492i −0.0967638 + 0.0156204i
\(557\) 790.157i 1.41859i −0.704910 0.709297i \(-0.749013\pi\)
0.704910 0.709297i \(-0.250987\pi\)
\(558\) 0 0
\(559\) 144.928i 0.259263i
\(560\) 43.4272 50.9945i 0.0775485 0.0910616i
\(561\) 0 0
\(562\) 342.004 + 291.222i 0.608548 + 0.518189i
\(563\) −354.133 −0.629010 −0.314505 0.949256i \(-0.601838\pi\)
−0.314505 + 0.949256i \(0.601838\pi\)
\(564\) 0 0
\(565\) −44.0482 72.6117i −0.0779614 0.128516i
\(566\) −128.096 109.076i −0.226319 0.192714i
\(567\) 0 0
\(568\) −893.989 542.378i −1.57392 0.954891i
\(569\) −55.4983 −0.0975366 −0.0487683 0.998810i \(-0.515530\pi\)
−0.0487683 + 0.998810i \(0.515530\pi\)
\(570\) 0 0
\(571\) 791.134i 1.38552i 0.721167 + 0.692762i \(0.243606\pi\)
−0.721167 + 0.692762i \(0.756394\pi\)
\(572\) −52.2233 323.509i −0.0912995 0.565575i
\(573\) 0 0
\(574\) −16.9551 14.4376i −0.0295386 0.0251526i
\(575\) 220.719 423.711i 0.383858 0.736888i
\(576\) 0 0
\(577\) 201.759i 0.349668i 0.984598 + 0.174834i \(0.0559389\pi\)
−0.984598 + 0.174834i \(0.944061\pi\)
\(578\) −699.690 595.799i −1.21054 1.03079i
\(579\) 0 0
\(580\) −591.874 695.152i −1.02047 1.19854i
\(581\) −49.4020 −0.0850292
\(582\) 0 0
\(583\) −245.773 −0.421566
\(584\) −374.248 227.054i −0.640835 0.388791i
\(585\) 0 0
\(586\) −319.777 + 375.537i −0.545694 + 0.640848i
\(587\) −444.556 −0.757335 −0.378668 0.925533i \(-0.623618\pi\)
−0.378668 + 0.925533i \(0.623618\pi\)
\(588\) 0 0
\(589\) −244.784 −0.415593
\(590\) −139.746 + 865.415i −0.236858 + 1.46680i
\(591\) 0 0
\(592\) 78.3350 + 236.309i 0.132323 + 0.399171i
\(593\) 563.908i 0.950942i −0.879731 0.475471i \(-0.842278\pi\)
0.879731 0.475471i \(-0.157722\pi\)
\(594\) 0 0
\(595\) 59.4019 + 97.9217i 0.0998351 + 0.164574i
\(596\) 21.4502 + 132.878i 0.0359902 + 0.222949i
\(597\) 0 0
\(598\) −128.517 + 150.927i −0.214911 + 0.252386i
\(599\) 845.034i 1.41074i 0.708839 + 0.705371i \(0.249219\pi\)
−0.708839 + 0.705371i \(0.750781\pi\)
\(600\) 0 0
\(601\) 672.296 1.11863 0.559314 0.828956i \(-0.311065\pi\)
0.559314 + 0.828956i \(0.311065\pi\)
\(602\) 35.6250 + 30.3353i 0.0591777 + 0.0503909i
\(603\) 0 0
\(604\) −552.797 + 89.2368i −0.915227 + 0.147743i
\(605\) 549.320 333.232i 0.907967 0.550796i
\(606\) 0 0
\(607\) −882.664 −1.45414 −0.727071 0.686562i \(-0.759119\pi\)
−0.727071 + 0.686562i \(0.759119\pi\)
\(608\) 216.072 532.789i 0.355381 0.876298i
\(609\) 0 0
\(610\) −375.140 60.5774i −0.614984 0.0993072i
\(611\) 288.662i 0.472442i
\(612\) 0 0
\(613\) 469.374i 0.765701i −0.923810 0.382850i \(-0.874943\pi\)
0.923810 0.382850i \(-0.125057\pi\)
\(614\) −176.350 150.166i −0.287216 0.244569i
\(615\) 0 0
\(616\) −90.4535 54.8777i −0.146840 0.0890871i
\(617\) 218.994i 0.354934i −0.984127 0.177467i \(-0.943210\pi\)
0.984127 0.177467i \(-0.0567902\pi\)
\(618\) 0 0
\(619\) 879.610i 1.42102i −0.703689 0.710509i \(-0.748465\pi\)
0.703689 0.710509i \(-0.251535\pi\)
\(620\) 207.471 176.647i 0.334631 0.284915i
\(621\) 0 0
\(622\) 264.213 310.284i 0.424779 0.498849i
\(623\) −33.3232 −0.0534884
\(624\) 0 0
\(625\) −358.203 512.168i −0.573124 0.819468i
\(626\) 128.447 150.845i 0.205187 0.240966i
\(627\) 0 0
\(628\) −83.9656 + 13.5544i −0.133703 + 0.0215834i
\(629\) −425.691 −0.676774
\(630\) 0 0
\(631\) 635.566i 1.00724i 0.863926 + 0.503618i \(0.167998\pi\)
−0.863926 + 0.503618i \(0.832002\pi\)
\(632\) 93.1855 + 56.5351i 0.147445 + 0.0894543i
\(633\) 0 0
\(634\) −610.966 + 717.502i −0.963669 + 1.13171i
\(635\) −36.1486 + 21.9287i −0.0569270 + 0.0345334i
\(636\) 0 0
\(637\) 250.505i 0.393258i
\(638\) −934.951 + 1097.98i −1.46544 + 1.72097i
\(639\) 0 0
\(640\) 201.349 + 607.502i 0.314608 + 0.949222i
\(641\) 296.309 0.462260 0.231130 0.972923i \(-0.425758\pi\)
0.231130 + 0.972923i \(0.425758\pi\)
\(642\) 0 0
\(643\) 591.032 0.919179 0.459590 0.888131i \(-0.347997\pi\)
0.459590 + 0.888131i \(0.347997\pi\)
\(644\) 10.1993 + 63.1821i 0.0158375 + 0.0981088i
\(645\) 0 0
\(646\) 748.495 + 637.357i 1.15866 + 0.986621i
\(647\) 166.507 0.257352 0.128676 0.991687i \(-0.458927\pi\)
0.128676 + 0.991687i \(0.458927\pi\)
\(648\) 0 0
\(649\) 1384.67 2.13355
\(650\) 97.4362 + 240.327i 0.149902 + 0.369734i
\(651\) 0 0
\(652\) −134.001 830.098i −0.205523 1.27316i
\(653\) 621.335i 0.951509i −0.879578 0.475754i \(-0.842175\pi\)
0.879578 0.475754i \(-0.157825\pi\)
\(654\) 0 0
\(655\) 134.148 + 221.137i 0.204806 + 0.337614i
\(656\) 201.976 66.9538i 0.307890 0.102064i
\(657\) 0 0
\(658\) 70.9565 + 60.4208i 0.107837 + 0.0918249i
\(659\) 702.113i 1.06542i 0.846297 + 0.532711i \(0.178827\pi\)
−0.846297 + 0.532711i \(0.821173\pi\)
\(660\) 0 0
\(661\) 358.193 0.541895 0.270948 0.962594i \(-0.412663\pi\)
0.270948 + 0.962594i \(0.412663\pi\)
\(662\) −350.994 + 412.197i −0.530202 + 0.622655i
\(663\) 0 0
\(664\) 244.846 403.573i 0.368743 0.607790i
\(665\) −39.0099 64.3064i −0.0586616 0.0967013i
\(666\) 0 0
\(667\) 872.367 1.30790
\(668\) 151.960 + 941.351i 0.227485 + 1.40921i
\(669\) 0 0
\(670\) −910.224 146.982i −1.35854 0.219377i
\(671\) 600.230i 0.894530i
\(672\) 0 0
\(673\) 714.176i 1.06118i 0.847628 + 0.530592i \(0.178030\pi\)
−0.847628 + 0.530592i \(0.821970\pi\)
\(674\) 489.244 574.555i 0.725882 0.852456i
\(675\) 0 0
\(676\) 90.5827 + 561.134i 0.133998 + 0.830081i
\(677\) 509.833i 0.753077i 0.926401 + 0.376538i \(0.122886\pi\)
−0.926401 + 0.376538i \(0.877114\pi\)
\(678\) 0 0
\(679\) 141.346i 0.208168i
\(680\) −1094.35 0.0549180i −1.60933 8.07617e-5i
\(681\) 0 0
\(682\) −327.697 279.040i −0.480494 0.409150i
\(683\) 1263.93 1.85055 0.925275 0.379298i \(-0.123834\pi\)
0.925275 + 0.379298i \(0.123834\pi\)
\(684\) 0 0
\(685\) −139.540 230.026i −0.203708 0.335805i
\(686\) −124.048 105.629i −0.180828 0.153978i
\(687\) 0 0
\(688\) −424.378 + 140.679i −0.616829 + 0.204475i
\(689\) −80.7010 −0.117128
\(690\) 0 0
\(691\) 512.351i 0.741463i 0.928740 + 0.370731i \(0.120893\pi\)
−0.928740 + 0.370731i \(0.879107\pi\)
\(692\) −9.21987 + 1.48834i −0.0133235 + 0.00215078i
\(693\) 0 0
\(694\) −703.842 599.334i −1.01418 0.863594i
\(695\) −35.3315 58.2427i −0.0508368 0.0838024i
\(696\) 0 0
\(697\) 363.843i 0.522012i
\(698\) 305.458 + 260.103i 0.437619 + 0.372640i
\(699\) 0 0
\(700\) 79.4699 + 26.3526i 0.113528 + 0.0376466i
\(701\) −1092.03 −1.55781 −0.778907 0.627139i \(-0.784226\pi\)
−0.778907 + 0.627139i \(0.784226\pi\)
\(702\) 0 0
\(703\) 279.556 0.397662
\(704\) 896.609 466.945i 1.27359 0.663274i
\(705\) 0 0
\(706\) 325.323 382.051i 0.460798 0.541148i
\(707\) −37.2995 −0.0527574
\(708\) 0 0
\(709\) 416.887 0.587993 0.293997 0.955806i \(-0.405015\pi\)
0.293997 + 0.955806i \(0.405015\pi\)
\(710\) 208.365 1290.35i 0.293472 1.81740i
\(711\) 0 0
\(712\) 165.156 272.223i 0.231961 0.382336i
\(713\) 260.362i 0.365163i
\(714\) 0 0
\(715\) 350.220 212.452i 0.489818 0.297136i
\(716\) −896.609 + 144.738i −1.25225 + 0.202147i
\(717\) 0 0
\(718\) 279.556 328.304i 0.389354 0.457247i
\(719\) 395.268i 0.549747i 0.961480 + 0.274874i \(0.0886361\pi\)
−0.961480 + 0.274874i \(0.911364\pi\)
\(720\) 0 0
\(721\) −105.884 −0.146857
\(722\) 58.1625 + 49.5264i 0.0805575 + 0.0685962i
\(723\) 0 0
\(724\) 72.7317 + 450.553i 0.100458 + 0.622310i
\(725\) 527.244 1012.14i 0.727233 1.39606i
\(726\) 0 0
\(727\) −597.583 −0.821985 −0.410993 0.911639i \(-0.634818\pi\)
−0.410993 + 0.911639i \(0.634818\pi\)
\(728\) −29.7009 18.0194i −0.0407980 0.0247519i
\(729\) 0 0
\(730\) 87.2271 540.175i 0.119489 0.739966i
\(731\) 764.482i 1.04580i
\(732\) 0 0
\(733\) 23.8650i 0.0325580i −0.999867 0.0162790i \(-0.994818\pi\)
0.999867 0.0162790i \(-0.00518200\pi\)
\(734\) −102.120 86.9574i −0.139129 0.118471i
\(735\) 0 0
\(736\) −566.694 229.822i −0.769965 0.312258i
\(737\) 1456.37i 1.97608i
\(738\) 0 0
\(739\) 125.767i 0.170186i 0.996373 + 0.0850928i \(0.0271187\pi\)
−0.996373 + 0.0850928i \(0.972881\pi\)
\(740\) −236.943 + 201.741i −0.320193 + 0.272622i
\(741\) 0 0
\(742\) −16.8918 + 19.8373i −0.0227652 + 0.0267349i
\(743\) 148.841 0.200325 0.100162 0.994971i \(-0.468064\pi\)
0.100162 + 0.994971i \(0.468064\pi\)
\(744\) 0 0
\(745\) −143.849 + 87.2625i −0.193086 + 0.117131i
\(746\) −735.715 + 864.004i −0.986213 + 1.15818i
\(747\) 0 0
\(748\) 275.474 + 1706.48i 0.368280 + 2.28140i
\(749\) −87.3954 −0.116683
\(750\) 0 0
\(751\) 463.390i 0.617030i −0.951219 0.308515i \(-0.900168\pi\)
0.951219 0.308515i \(-0.0998321\pi\)
\(752\) −845.261 + 280.199i −1.12402 + 0.372605i
\(753\) 0 0
\(754\) −306.997 + 360.529i −0.407157 + 0.478155i
\(755\) −363.029 598.439i −0.480833 0.792634i
\(756\) 0 0
\(757\) 719.363i 0.950281i −0.879910 0.475141i \(-0.842397\pi\)
0.879910 0.475141i \(-0.157603\pi\)
\(758\) 311.579 365.910i 0.411054 0.482731i
\(759\) 0 0
\(760\) 718.670 + 0.0360653i 0.945618 + 4.74543e-5i
\(761\) 1107.49 1.45530 0.727651 0.685947i \(-0.240612\pi\)
0.727651 + 0.685947i \(0.240612\pi\)
\(762\) 0 0
\(763\) −0.420013 −0.000550476
\(764\) 550.440 88.8563i 0.720472 0.116304i
\(765\) 0 0
\(766\) −1020.34 868.835i −1.33203 1.13425i
\(767\) 454.666 0.592785
\(768\) 0 0
\(769\) −231.691 −0.301289 −0.150644 0.988588i \(-0.548135\pi\)
−0.150644 + 0.988588i \(0.548135\pi\)
\(770\) 21.0823 130.557i 0.0273796 0.169555i
\(771\) 0 0
\(772\) 718.879 116.047i 0.931190 0.150320i
\(773\) 519.956i 0.672647i −0.941746 0.336324i \(-0.890816\pi\)
0.941746 0.336324i \(-0.109184\pi\)
\(774\) 0 0
\(775\) 302.079 + 157.358i 0.389779 + 0.203043i
\(776\) 1154.68 + 700.539i 1.48799 + 0.902756i
\(777\) 0 0
\(778\) 722.751 + 615.436i 0.928986 + 0.791049i
\(779\) 238.940i 0.306726i
\(780\) 0 0
\(781\) −2064.58 −2.64351
\(782\) 677.917 796.127i 0.866901 1.01807i
\(783\) 0 0
\(784\) 733.531 243.161i 0.935626 0.310154i
\(785\) −55.1412 90.8982i −0.0702436 0.115794i
\(786\) 0 0
\(787\) −46.0288 −0.0584864 −0.0292432 0.999572i \(-0.509310\pi\)
−0.0292432 + 0.999572i \(0.509310\pi\)
\(788\) 1018.92 164.481i 1.29304 0.208733i
\(789\) 0 0