Properties

Label 180.3.f.h.19.1
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 19.1
Root \(-1.52274 - 1.29664i\) of defining polynomial
Character \(\chi\) \(=\) 180.19
Dual form 180.3.f.h.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.52274 - 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} +(-4.27492 - 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 - 6.83966i) q^{8} +O(q^{10})\) \(q+(-1.52274 - 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} +(-4.27492 - 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 - 6.83966i) q^{8} +(3.14704 + 9.49190i) q^{10} +15.7955i q^{11} -5.18655i q^{13} +(1.27492 + 1.08561i) q^{14} +(-15.1873 + 5.03449i) q^{16} +27.3586i q^{17} +17.9667i q^{19} +(7.51545 - 18.5342i) q^{20} +(20.4811 - 24.0524i) q^{22} -19.1101 q^{23} +(11.5498 + 22.1721i) q^{25} +(-6.72508 + 7.89776i) q^{26} +(-0.533714 - 3.30621i) q^{28} +45.6495 q^{29} +13.6243i q^{31} +(29.6542 + 12.0262i) q^{32} +(35.4743 - 41.6600i) q^{34} +(3.57919 + 2.17123i) q^{35} +15.5597i q^{37} +(23.2964 - 27.3586i) q^{38} +(-35.4763 + 18.4780i) q^{40} -13.2990 q^{41} -27.9430 q^{43} +(-62.3746 + 10.0690i) q^{44} +(29.0997 + 24.7789i) q^{46} -55.6558 q^{47} -48.2990 q^{49} +(11.1618 - 48.7382i) q^{50} +(20.4811 - 3.30621i) q^{52} -15.5597i q^{53} +(40.9621 - 67.5245i) q^{55} +(-3.47425 + 5.72653i) q^{56} +(-69.5122 - 59.1909i) q^{58} -87.6625i q^{59} +38.0000 q^{61} +(17.6658 - 20.7462i) q^{62} +(-29.5619 - 56.7635i) q^{64} +(-13.4502 + 22.1721i) q^{65} -92.2015 q^{67} +(-108.036 + 17.4400i) q^{68} +(-2.63487 - 7.94713i) q^{70} +130.707i q^{71} -54.7173i q^{73} +(20.1752 - 23.6933i) q^{74} +(-70.9485 + 11.4531i) q^{76} -13.2249i q^{77} -13.6243i q^{79} +(77.9803 + 17.8628i) q^{80} +(20.2509 + 17.2440i) q^{82} +59.0048 q^{83} +(70.9485 - 116.956i) q^{85} +(42.5498 + 36.2319i) q^{86} +(108.036 + 65.5448i) q^{88} -39.8007 q^{89} +4.34246i q^{91} +(-12.1819 - 75.4635i) q^{92} +(84.7492 + 72.1654i) q^{94} +(46.5927 - 76.8064i) q^{95} +168.821i q^{97} +(73.5467 + 62.6263i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 10q^{4} - 4q^{5} + O(q^{10}) \) \( 8q - 10q^{4} - 4q^{5} - 42q^{10} - 20q^{14} - 46q^{16} - 52q^{20} + 32q^{25} - 84q^{26} + 184q^{29} + 12q^{34} - 6q^{40} + 256q^{41} - 348q^{44} + 112q^{46} - 24q^{49} - 72q^{50} + 244q^{56} + 304q^{61} - 10q^{64} - 168q^{65} - 104q^{70} + 252q^{74} - 24q^{76} + 308q^{80} + 24q^{85} + 280q^{86} - 560q^{89} + 376q^{94} + O(q^{100}) \)

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 \(-0.519048\pi\)
−0.0598038 + 0.998210i \(0.519048\pi\)
\(8\) 4.14959 6.83966i 0.518698 0.854957i
\(9\) 0 0
\(10\) 3.14704 + 9.49190i 0.314704 + 0.949190i
\(11\) 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 \(-0.936074\pi\)
0.979901 0.199483i \(-0.0639262\pi\)
\(14\) 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 \(0.297656\pi\)
−0.593728 + 0.804666i \(0.702344\pi\)
\(18\) 0 0
\(19\) 17.9667i 0.945618i 0.881165 + 0.472809i \(0.156760\pi\)
−0.881165 + 0.472809i \(0.843240\pi\)
\(20\) 7.51545 18.5342i 0.375773 0.926712i
\(21\) 0 0
\(22\) 20.4811 24.0524i 0.930958 1.09329i
\(23\) −19.1101 −0.830874 −0.415437 0.909622i \(-0.636371\pi\)
−0.415437 + 0.909622i \(0.636371\pi\)
\(24\) 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 \(0.0674329\pi\)
−0.977644 + 0.210266i \(0.932567\pi\)
\(38\) 23.2964 27.3586i 0.613062 0.719964i
\(39\) 0 0
\(40\) −35.4763 + 18.4780i −0.886907 + 0.461949i
\(41\) −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 \(-0.605337\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(44\) −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 \(-0.701694\pi\)
−0.592083 + 0.805877i \(0.701694\pi\)
\(48\) 0 0
\(49\) −48.2990 −0.985694
\(50\) 11.1618 48.7382i 0.223236 0.974764i
\(51\) 0 0
\(52\) 20.4811 3.30621i 0.393867 0.0635810i
\(53\) 15.5597i 0.293578i −0.989168 0.146789i \(-0.953106\pi\)
0.989168 0.146789i \(-0.0468939\pi\)
\(54\) 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 \(-0.741542\pi\)
−0.688071 + 0.725643i \(0.741542\pi\)
\(68\) −108.036 + 17.4400i −1.58876 + 0.256471i
\(69\) 0 0
\(70\) −2.63487 7.94713i −0.0376409 0.113530i
\(71\) 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 \(-0.877720\pi\)
0.927115 0.374776i \(-0.122280\pi\)
\(74\) 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 \(-0.0274819\pi\)
\(80\) 77.9803 + 17.8628i 0.974753 + 0.223285i
\(81\) 0 0
\(82\) 20.2509 + 17.2440i 0.246962 + 0.210293i
\(83\) 59.0048 0.710901 0.355451 0.934695i \(-0.384327\pi\)
0.355451 + 0.934695i \(0.384327\pi\)
\(84\) 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 \(0.336019\pi\)
−0.492675 + 0.870214i \(0.663981\pi\)
\(98\) 73.5467 + 62.6263i 0.750477 + 0.639044i
\(99\) 0 0
\(100\) −80.1923 + 59.7427i −0.801923 + 0.597427i
\(101\) −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 \(-0.289595\pi\)
0.613911 + 0.789375i \(0.289595\pi\)
\(104\) −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 \(-0.337809\pi\)
0.487773 + 0.872971i \(0.337809\pi\)
\(108\) 0 0
\(109\) −0.501656 −0.00460235 −0.00230117 0.999997i \(-0.500732\pi\)
−0.00230117 + 0.999997i \(0.500732\pi\)
\(110\) −149.929 + 49.7090i −1.36300 + 0.451900i
\(111\) 0 0
\(112\) 12.7156 4.21515i 0.113532 0.0376352i
\(113\) 16.9855i 0.150314i −0.997172 0.0751572i \(-0.976054\pi\)
0.997172 0.0751572i \(-0.0239459\pi\)
\(114\) 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 \(-0.510599\pi\)
−0.0332913 + 0.999446i \(0.510599\pi\)
\(128\) −28.5867 + 124.767i −0.223334 + 0.974742i
\(129\) 0 0
\(130\) 49.2302 16.3223i 0.378694 0.125556i
\(131\) 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 \(-0.937081\pi\)
0.980528 0.196381i \(-0.0629189\pi\)
\(138\) 0 0
\(139\) 13.6243i 0.0980165i 0.998798 + 0.0490082i \(0.0156061\pi\)
−0.998798 + 0.0490082i \(0.984394\pi\)
\(140\) −6.29234 + 15.5179i −0.0449453 + 0.110842i
\(141\) 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 \(-0.978428\pi\)
0.997705 0.0677170i \(-0.0215715\pi\)
\(158\) −17.6658 + 20.7462i −0.111809 + 0.131305i
\(159\) 0 0
\(160\) −95.5819 128.313i −0.597387 0.801953i
\(161\) 16.0000 0.0993789
\(162\) 0 0
\(163\) 210.211 1.28964 0.644819 0.764335i \(-0.276933\pi\)
0.644819 + 0.764335i \(0.276933\pi\)
\(164\) −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 \(-0.752994\pi\)
−0.713725 + 0.700426i \(0.752994\pi\)
\(168\) 0 0
\(169\) 142.100 0.840826
\(170\) −259.685 + 86.0986i −1.52756 + 0.506462i
\(171\) 0 0
\(172\) −17.8125 110.343i −0.103561 0.641532i
\(173\) 2.33481i 0.0134960i −0.999977 0.00674800i \(-0.997852\pi\)
0.999977 0.00674800i \(-0.00214797\pi\)
\(174\) 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
\(190\) −170.539 + 56.5420i −0.897571 + 0.297589i
\(191\) 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 \(0.156331\pi\)
−0.881801 + 0.471623i \(0.843669\pi\)
\(194\) 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 \(0.227285\pi\)
−0.755724 + 0.654890i \(0.772715\pi\)
\(198\) 0 0
\(199\) 256.474i 1.28881i −0.764683 0.644407i \(-0.777104\pi\)
0.764683 0.644407i \(-0.222896\pi\)
\(200\) 199.577 + 13.0080i 0.997883 + 0.0650401i
\(201\) 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
\(220\) 292.758 + 118.710i 1.33072 + 0.539593i
\(221\) 141.897 0.642068
\(222\) 0 0
\(223\) −349.843 −1.56880 −0.784401 0.620255i \(-0.787029\pi\)
−0.784401 + 0.620255i \(0.787029\pi\)
\(224\) −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 \(-0.634021\pi\)
−0.408709 + 0.912665i \(0.634021\pi\)
\(228\) 0 0
\(229\) 263.897 1.15239 0.576194 0.817313i \(-0.304537\pi\)
0.576194 + 0.817313i \(0.304537\pi\)
\(230\) −60.1402 181.391i −0.261479 0.788657i
\(231\) 0 0
\(232\) 189.427 312.227i 0.816494 1.34581i
\(233\) 58.4780i 0.250978i 0.992095 + 0.125489i \(0.0400500\pi\)
−0.992095 + 0.125489i \(0.959950\pi\)
\(234\) 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
\(250\) −174.107 + 179.406i −0.696430 + 0.717625i
\(251\) 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 \(0.265836\pi\)
−0.671067 + 0.741397i \(0.734164\pi\)
\(258\) 0 0
\(259\) 13.0274i 0.0502988i
\(260\) −96.1288 38.9793i −0.369726 0.149920i
\(261\) 0 0
\(262\) −67.0738 + 78.7697i −0.256007 + 0.300648i
\(263\) −11.4914 −0.0436934 −0.0218467 0.999761i \(-0.506955\pi\)
−0.0218467 + 0.999761i \(0.506955\pi\)
\(264\) 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 \(0.173563\pi\)
−0.854991 + 0.518643i \(0.826437\pi\)
\(278\) 17.6658 20.7462i 0.0635459 0.0746267i
\(279\) 0 0
\(280\) 29.7026 15.4707i 0.106081 0.0552526i
\(281\) 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 \(-0.452515\pi\)
0.148626 + 0.988893i \(0.452515\pi\)
\(284\) −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
\(290\) 143.661 + 433.301i 0.495381 + 1.49414i
\(291\) 0 0
\(292\) 216.072 34.8800i 0.739972 0.119452i
\(293\) 246.620i 0.841706i −0.907129 0.420853i \(-0.861731\pi\)
0.907129 0.420853i \(-0.138269\pi\)
\(294\) 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 \(-0.439599\pi\)
0.188618 + 0.982051i \(0.439599\pi\)
\(308\) 52.2233 8.43030i 0.169556 0.0273711i
\(309\) 0 0
\(310\) −129.320 + 42.8761i −0.417162 + 0.138310i
\(311\) 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 \(0.0505836\pi\)
−0.987400 + 0.158245i \(0.949416\pi\)
\(314\) −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 \(-0.733304\pi\)
0.669063 0.743206i \(-0.266696\pi\)
\(318\) 0 0
\(319\) 721.057i 2.26037i
\(320\) −20.8289 + 319.321i −0.0650902 + 0.997879i
\(321\) 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 \(0.189129\pi\)
−0.828615 + 0.559818i \(0.810871\pi\)
\(338\) −216.380 184.252i −0.640179 0.545124i
\(339\) 0 0
\(340\) 507.071 + 205.613i 1.49139 + 0.604743i
\(341\) −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 \(-0.267994\pi\)
0.666025 + 0.745929i \(0.267994\pi\)
\(348\) 0 0
\(349\) 200.598 0.574779 0.287390 0.957814i \(-0.407213\pi\)
0.287390 + 0.957814i \(0.407213\pi\)
\(350\) −9.34526 + 40.8062i −0.0267007 + 0.116589i
\(351\) 0 0
\(352\) −189.960 + 468.403i −0.539660 + 1.33069i
\(353\) 250.897i 0.710757i 0.934722 + 0.355379i \(0.115648\pi\)
−0.934722 + 0.355379i \(0.884352\pi\)
\(354\) 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 \(-0.470876\pi\)
0.0913675 + 0.995817i \(0.470876\pi\)
\(368\) 290.231 96.2097i 0.788670 0.261439i
\(369\) 0 0
\(370\) −147.691 + 48.9668i −0.399164 + 0.132343i
\(371\) 13.0274i 0.0351142i
\(372\) 0 0
\(373\) 567.402i 1.52119i −0.649230 0.760593i \(-0.724909\pi\)
0.649230 0.760593i \(-0.275091\pi\)
\(374\) 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 \(-0.102681\pi\)
\(380\) 333.000 + 135.028i 0.876316 + 0.355337i
\(381\) 0 0
\(382\) −180.740 + 212.257i −0.473142 + 0.555646i
\(383\) 670.068 1.74952 0.874762 0.484553i \(-0.161018\pi\)
0.874762 + 0.484553i \(0.161018\pi\)
\(384\) 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 \(-0.783447\pi\)
0.777371 0.629043i \(-0.216553\pi\)
\(398\) −332.554 + 390.542i −0.835562 + 0.981262i
\(399\) 0 0
\(400\) −287.036 278.586i −0.717590 0.696466i
\(401\) −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 \(0.710262\pi\)
\(410\) −41.8524 126.233i −0.102079 0.307885i
\(411\) 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
\(430\) −87.9376 265.232i −0.204506 0.616819i
\(431\) 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 \(0.0455283\pi\)
−0.989788 + 0.142544i \(0.954472\pi\)
\(434\) −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 \(-0.122936\pi\)
\(440\) −291.869 560.366i −0.663338 1.27356i
\(441\) 0 0
\(442\) −216.072 183.989i −0.488850 0.416265i
\(443\) 154.952 0.349780 0.174890 0.984588i \(-0.444043\pi\)
0.174890 + 0.984588i \(0.444043\pi\)
\(444\) 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 \(-0.821659\pi\)
0.847108 0.531420i \(-0.178341\pi\)
\(458\) −401.846 342.179i −0.877393 0.747116i
\(459\) 0 0
\(460\) −143.621 + 354.191i −0.312220 + 0.769981i
\(461\) −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 \(-0.650511\pi\)
−0.455421 + 0.890276i \(0.650511\pi\)
\(464\) −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 \(-0.259248\pi\)
0.686268 + 0.727349i \(0.259248\pi\)
\(468\) 0 0
\(469\) 77.1960 0.164597
\(470\) −175.151 528.279i −0.372661 1.12400i
\(471\) 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 \(-0.133208\pi\)
0.913705 + 0.406377i \(0.133208\pi\)
\(488\) 157.684 259.907i 0.323123 0.532596i
\(489\) 0 0
\(490\) −151.999 458.449i −0.310201 0.935611i
\(491\) 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 \(0.820549\pi\)
\(500\) 497.745 47.4341i 0.995490 0.0948683i
\(501\) 0 0
\(502\) −137.737 + 161.755i −0.274376 + 0.322220i
\(503\) −574.914 −1.14297 −0.571485 0.820612i \(-0.693633\pi\)
−0.571485 + 0.820612i \(0.693633\pi\)
\(504\) 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
\(520\) 95.8369 + 184.000i 0.184302 + 0.353845i
\(521\) 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 \(-0.457407\pi\)
0.133411 + 0.991061i \(0.457407\pi\)
\(524\) 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
\(530\) 147.691 48.9668i 0.278662 0.0923902i
\(531\) 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 \(-0.485348\pi\)
0.0460136 + 0.998941i \(0.485348\pi\)
\(548\) 212.483 34.3006i 0.387742 0.0625923i
\(549\) 0 0
\(550\) 769.845 + 176.307i 1.39972 + 0.320557i
\(551\) 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 \(0.250987\pi\)
−0.704910 + 0.709297i \(0.749013\pi\)
\(558\) 0 0
\(559\) 144.928i 0.259263i
\(560\) −65.2892 14.9557i −0.116588 0.0267066i
\(561\) 0 0
\(562\) −342.004 291.222i −0.608548 0.518189i
\(563\) 354.133 0.629010 0.314505 0.949256i \(-0.398162\pi\)
0.314505 + 0.949256i \(0.398162\pi\)
\(564\) 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 \(-0.944061\pi\)
0.984598 0.174834i \(-0.0559389\pi\)
\(578\) 699.690 + 595.799i 1.21054 + 1.03079i
\(579\) 0 0
\(580\) 343.077 846.079i 0.591512 1.45876i
\(581\) −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 \(-0.376382\pi\)
0.378668 + 0.925533i \(0.376382\pi\)
\(588\) 0 0
\(589\) −244.784 −0.415593
\(590\) 832.084 275.877i 1.41031 0.467588i
\(591\) 0 0
\(592\) −78.3350 236.309i −0.132323 0.399171i
\(593\) 563.908i 0.950942i 0.879731 + 0.475471i \(0.157722\pi\)
−0.879731 + 0.475471i \(0.842278\pi\)
\(594\) 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 \(-0.240881\pi\)
0.727071 + 0.686562i \(0.240881\pi\)
\(608\) −216.072 + 532.789i −0.355381 + 0.876298i
\(609\) 0 0
\(610\) 119.587 + 360.692i 0.196045 + 0.591299i
\(611\) 288.662i 0.472442i
\(612\) 0 0
\(613\) 469.374i 0.765701i 0.923810 + 0.382850i \(0.125057\pi\)
−0.923810 + 0.382850i \(0.874943\pi\)
\(614\) −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 \(0.0567902\pi\)
−0.984127 + 0.177467i \(0.943210\pi\)
\(618\) 0 0
\(619\) 879.610i 1.42102i −0.703689 0.710509i \(-0.748465\pi\)
0.703689 0.710509i \(-0.251535\pi\)
\(620\) 252.516 + 102.393i 0.407284 + 0.165149i
\(621\) 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
\(640\) 445.761 459.235i 0.696502 0.717555i
\(641\) 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 \(-0.652003\pi\)
−0.459590 + 0.888131i \(0.652003\pi\)
\(644\) 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 \(-0.541073\pi\)
−0.128676 + 0.991687i \(0.541073\pi\)
\(648\) 0 0
\(649\) 1384.67 2.13355
\(650\) −252.783 57.8913i −0.388897 0.0890635i
\(651\) 0 0
\(652\) 134.001 + 830.098i 0.205523 + 1.27316i
\(653\) 621.335i 0.951509i 0.879578 + 0.475754i \(0.157825\pi\)
−0.879578 + 0.475754i \(0.842175\pi\)
\(654\) 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
\(670\) −290.161 875.167i −0.433077 1.30622i
\(671\) 600.230i 0.894530i
\(672\) 0 0
\(673\) 714.176i 1.06118i −0.847628 0.530592i \(-0.821970\pi\)
0.847628 0.530592i \(-0.178030\pi\)
\(674\) 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 \(-0.877114\pi\)
0.926401 0.376538i \(-0.122886\pi\)
\(678\) 0 0
\(679\) 141.346i 0.208168i
\(680\) −505.532 970.582i −0.743429 1.42733i
\(681\) 0 0
\(682\) 327.697 + 279.040i 0.480494 + 0.409150i
\(683\) −1263.93 −1.85055 −0.925275 0.379298i \(-0.876166\pi\)
−0.925275 + 0.379298i \(0.876166\pi\)
\(684\) 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
\(700\) 67.1413 50.0198i 0.0959162 0.0714568i
\(701\) −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 \(0.405015\pi\)
\(710\) −1240.65 + 411.338i −1.74740 + 0.579350i
\(711\) 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 \(-0.365182\pi\)
0.410993 + 0.911639i \(0.365182\pi\)
\(728\) 29.7009 + 18.0194i 0.0407980 + 0.0247519i
\(729\) 0 0
\(730\) 519.371 172.197i 0.711467 0.235887i
\(731\) 764.482i 1.04580i
\(732\) 0 0
\(733\) 23.8650i 0.0325580i 0.999867 + 0.0162790i \(0.00518200\pi\)
−0.999867 + 0.0162790i \(0.994818\pi\)
\(734\) −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 \(0.972881\pi\)
\(740\) 288.386 + 116.938i 0.389711 + 0.158024i
\(741\) 0 0
\(742\) 16.8918 19.8373i 0.0227652 0.0267349i
\(743\) −148.841 −0.200325 −0.100162 0.994971i \(-0.531936\pi\)
−0.100162 + 0.994971i \(0.531936\pi\)
\(744\) 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 \(0.157603\pi\)
−0.879910 + 0.475141i \(0.842397\pi\)
\(758\) −311.579 + 365.910i −0.411054 + 0.482731i
\(759\) 0 0
\(760\) −331.989 637.393i −0.436827 0.838675i
\(761\) 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 \(0.548135\pi\)
\(770\) 125.529 41.6191i 0.163025 0.0540507i
\(771\) 0 0
\(772\) −718.879 + 116.047i −0.931190 + 0.150320i
\(773\) 519.956i 0.672647i 0.941746 + 0.336324i \(0.109184\pi\)
−0.941746 + 0.336324i \(0.890816\pi\)
\(774\) 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 \(-0.490690\pi\)
0.0292432 + 0.999572i \(0.490690\pi\)
\(788\) −1018.92 + 164.481i −1.29304 + 0.208733i
\(789\) 0 0