Properties

Label 690.3.f.a.229.7
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.7
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-3.10921 + 3.91571i) q^{5} -2.44949 q^{6} +3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-3.10921 + 3.91571i) q^{5} -2.44949 q^{6} +3.09410 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-5.53765 - 4.39709i) q^{10} +15.9443i q^{11} -3.46410i q^{12} +24.8732i q^{13} +4.37572i q^{14} +(-6.78221 - 5.38531i) q^{15} +4.00000 q^{16} +12.6980 q^{17} -4.24264i q^{18} -10.4874i q^{19} +(6.21842 - 7.83142i) q^{20} +5.35914i q^{21} -22.5487 q^{22} +(22.9821 + 0.906621i) q^{23} +4.89898 q^{24} +(-5.66561 - 24.3496i) q^{25} -35.1760 q^{26} -5.19615i q^{27} -6.18820 q^{28} -44.7809 q^{29} +(7.61598 - 9.59150i) q^{30} -50.0174 q^{31} +5.65685i q^{32} -27.6164 q^{33} +17.9577i q^{34} +(-9.62022 + 12.1156i) q^{35} +6.00000 q^{36} +39.1282 q^{37} +14.8314 q^{38} -43.0816 q^{39} +(11.0753 + 8.79418i) q^{40} +41.3571 q^{41} -7.57897 q^{42} -71.6357 q^{43} -31.8887i q^{44} +(9.32763 - 11.7471i) q^{45} +(-1.28216 + 32.5016i) q^{46} -17.3085i q^{47} +6.92820i q^{48} -39.4265 q^{49} +(34.4355 - 8.01238i) q^{50} +21.9936i q^{51} -49.7463i q^{52} +39.6184 q^{53} +7.34847 q^{54} +(-62.4335 - 49.5744i) q^{55} -8.75144i q^{56} +18.1647 q^{57} -63.3298i q^{58} +24.0107 q^{59} +(13.5644 + 10.7706i) q^{60} -76.0777i q^{61} -70.7353i q^{62} -9.28230 q^{63} -8.00000 q^{64} +(-97.3961 - 77.3359i) q^{65} -39.0555i q^{66} +76.7774 q^{67} -25.3960 q^{68} +(-1.57031 + 39.8062i) q^{69} +(-17.1341 - 13.6050i) q^{70} +22.9757 q^{71} +8.48528i q^{72} -51.8874i q^{73} +55.3356i q^{74} +(42.1747 - 9.81312i) q^{75} +20.9748i q^{76} +49.3334i q^{77} -60.9265i q^{78} -25.5241i q^{79} +(-12.4368 + 15.6628i) q^{80} +9.00000 q^{81} +58.4877i q^{82} +21.6791 q^{83} -10.7183i q^{84} +(-39.4807 + 49.7217i) q^{85} -101.308i q^{86} -77.5628i q^{87} +45.0974 q^{88} +165.958i q^{89} +(16.6130 + 13.1913i) q^{90} +76.9601i q^{91} +(-45.9642 - 1.81324i) q^{92} -86.6327i q^{93} +24.4779 q^{94} +(41.0657 + 32.6076i) q^{95} -9.79796 q^{96} +0.580105 q^{97} -55.7575i q^{98} -47.8330i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 96q^{4} - 144q^{9} + O(q^{10}) \) \( 48q - 96q^{4} - 144q^{9} + 192q^{16} + 96q^{25} + 64q^{26} - 152q^{29} - 8q^{31} + 56q^{35} + 288q^{36} - 48q^{39} + 40q^{41} - 160q^{46} + 424q^{49} + 96q^{50} + 32q^{55} + 360q^{59} - 384q^{64} + 192q^{69} - 496q^{70} - 152q^{71} + 144q^{75} + 432q^{81} - 136q^{85} + 256q^{94} + 496q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) −3.10921 + 3.91571i −0.621842 + 0.783142i
\(6\) −2.44949 −0.408248
\(7\) 3.09410 0.442015 0.221007 0.975272i \(-0.429066\pi\)
0.221007 + 0.975272i \(0.429066\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) −5.53765 4.39709i −0.553765 0.439709i
\(11\) 15.9443i 1.44949i 0.689019 + 0.724743i \(0.258042\pi\)
−0.689019 + 0.724743i \(0.741958\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 24.8732i 1.91332i 0.291208 + 0.956660i \(0.405943\pi\)
−0.291208 + 0.956660i \(0.594057\pi\)
\(14\) 4.37572i 0.312551i
\(15\) −6.78221 5.38531i −0.452148 0.359021i
\(16\) 4.00000 0.250000
\(17\) 12.6980 0.746940 0.373470 0.927642i \(-0.378168\pi\)
0.373470 + 0.927642i \(0.378168\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 10.4874i 0.551969i −0.961162 0.275984i \(-0.910996\pi\)
0.961162 0.275984i \(-0.0890038\pi\)
\(20\) 6.21842 7.83142i 0.310921 0.391571i
\(21\) 5.35914i 0.255197i
\(22\) −22.5487 −1.02494
\(23\) 22.9821 + 0.906621i 0.999223 + 0.0394183i
\(24\) 4.89898 0.204124
\(25\) −5.66561 24.3496i −0.226624 0.973982i
\(26\) −35.1760 −1.35292
\(27\) 5.19615i 0.192450i
\(28\) −6.18820 −0.221007
\(29\) −44.7809 −1.54417 −0.772084 0.635520i \(-0.780786\pi\)
−0.772084 + 0.635520i \(0.780786\pi\)
\(30\) 7.61598 9.59150i 0.253866 0.319717i
\(31\) −50.0174 −1.61346 −0.806732 0.590917i \(-0.798766\pi\)
−0.806732 + 0.590917i \(0.798766\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −27.6164 −0.836861
\(34\) 17.9577i 0.528167i
\(35\) −9.62022 + 12.1156i −0.274863 + 0.346160i
\(36\) 6.00000 0.166667
\(37\) 39.1282 1.05752 0.528759 0.848772i \(-0.322657\pi\)
0.528759 + 0.848772i \(0.322657\pi\)
\(38\) 14.8314 0.390301
\(39\) −43.0816 −1.10466
\(40\) 11.0753 + 8.79418i 0.276883 + 0.219854i
\(41\) 41.3571 1.00871 0.504355 0.863497i \(-0.331730\pi\)
0.504355 + 0.863497i \(0.331730\pi\)
\(42\) −7.57897 −0.180452
\(43\) −71.6357 −1.66595 −0.832973 0.553313i \(-0.813363\pi\)
−0.832973 + 0.553313i \(0.813363\pi\)
\(44\) 31.8887i 0.724743i
\(45\) 9.32763 11.7471i 0.207281 0.261047i
\(46\) −1.28216 + 32.5016i −0.0278730 + 0.706557i
\(47\) 17.3085i 0.368266i −0.982901 0.184133i \(-0.941052\pi\)
0.982901 0.184133i \(-0.0589477\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −39.4265 −0.804623
\(50\) 34.4355 8.01238i 0.688709 0.160248i
\(51\) 21.9936i 0.431246i
\(52\) 49.7463i 0.956660i
\(53\) 39.6184 0.747517 0.373758 0.927526i \(-0.378069\pi\)
0.373758 + 0.927526i \(0.378069\pi\)
\(54\) 7.34847 0.136083
\(55\) −62.4335 49.5744i −1.13515 0.901352i
\(56\) 8.75144i 0.156276i
\(57\) 18.1647 0.318679
\(58\) 63.3298i 1.09189i
\(59\) 24.0107 0.406961 0.203481 0.979079i \(-0.434775\pi\)
0.203481 + 0.979079i \(0.434775\pi\)
\(60\) 13.5644 + 10.7706i 0.226074 + 0.179510i
\(61\) 76.0777i 1.24717i −0.781754 0.623587i \(-0.785675\pi\)
0.781754 0.623587i \(-0.214325\pi\)
\(62\) 70.7353i 1.14089i
\(63\) −9.28230 −0.147338
\(64\) −8.00000 −0.125000
\(65\) −97.3961 77.3359i −1.49840 1.18978i
\(66\) 39.0555i 0.591750i
\(67\) 76.7774 1.14593 0.572966 0.819579i \(-0.305793\pi\)
0.572966 + 0.819579i \(0.305793\pi\)
\(68\) −25.3960 −0.373470
\(69\) −1.57031 + 39.8062i −0.0227582 + 0.576902i
\(70\) −17.1341 13.6050i −0.244772 0.194358i
\(71\) 22.9757 0.323602 0.161801 0.986823i \(-0.448270\pi\)
0.161801 + 0.986823i \(0.448270\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 51.8874i 0.710786i −0.934717 0.355393i \(-0.884347\pi\)
0.934717 0.355393i \(-0.115653\pi\)
\(74\) 55.3356i 0.747779i
\(75\) 42.1747 9.81312i 0.562329 0.130842i
\(76\) 20.9748i 0.275984i
\(77\) 49.3334i 0.640694i
\(78\) 60.9265i 0.781110i
\(79\) 25.5241i 0.323090i −0.986865 0.161545i \(-0.948352\pi\)
0.986865 0.161545i \(-0.0516478\pi\)
\(80\) −12.4368 + 15.6628i −0.155461 + 0.195786i
\(81\) 9.00000 0.111111
\(82\) 58.4877i 0.713265i
\(83\) 21.6791 0.261194 0.130597 0.991436i \(-0.458311\pi\)
0.130597 + 0.991436i \(0.458311\pi\)
\(84\) 10.7183i 0.127599i
\(85\) −39.4807 + 49.7217i −0.464479 + 0.584961i
\(86\) 101.308i 1.17800i
\(87\) 77.5628i 0.891526i
\(88\) 45.0974 0.512471
\(89\) 165.958i 1.86469i 0.361566 + 0.932346i \(0.382242\pi\)
−0.361566 + 0.932346i \(0.617758\pi\)
\(90\) 16.6130 + 13.1913i 0.184588 + 0.146570i
\(91\) 76.9601i 0.845715i
\(92\) −45.9642 1.81324i −0.499611 0.0197092i
\(93\) 86.6327i 0.931534i
\(94\) 24.4779 0.260403
\(95\) 41.0657 + 32.6076i 0.432270 + 0.343237i
\(96\) −9.79796 −0.102062
\(97\) 0.580105 0.00598047 0.00299023 0.999996i \(-0.499048\pi\)
0.00299023 + 0.999996i \(0.499048\pi\)
\(98\) 55.7575i 0.568955i
\(99\) 47.8330i 0.483162i
\(100\) 11.3312 + 48.6991i 0.113312 + 0.486991i
\(101\) −164.285 −1.62658 −0.813290 0.581859i \(-0.802326\pi\)
−0.813290 + 0.581859i \(0.802326\pi\)
\(102\) −31.1036 −0.304937
\(103\) −160.952 −1.56264 −0.781322 0.624128i \(-0.785454\pi\)
−0.781322 + 0.624128i \(0.785454\pi\)
\(104\) 70.3519 0.676461
\(105\) −20.9849 16.6627i −0.199856 0.158692i
\(106\) 56.0288i 0.528574i
\(107\) −53.6355 −0.501266 −0.250633 0.968082i \(-0.580639\pi\)
−0.250633 + 0.968082i \(0.580639\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 77.5961i 0.711890i 0.934507 + 0.355945i \(0.115841\pi\)
−0.934507 + 0.355945i \(0.884159\pi\)
\(110\) 70.1087 88.2943i 0.637352 0.802675i
\(111\) 67.7720i 0.610559i
\(112\) 12.3764 0.110504
\(113\) 61.1674 0.541305 0.270652 0.962677i \(-0.412761\pi\)
0.270652 + 0.962677i \(0.412761\pi\)
\(114\) 25.6888i 0.225340i
\(115\) −75.0064 + 87.1725i −0.652229 + 0.758022i
\(116\) 89.5618 0.772084
\(117\) 74.6195i 0.637773i
\(118\) 33.9563i 0.287765i
\(119\) 39.2889 0.330159
\(120\) −15.2320 + 19.1830i −0.126933 + 0.159858i
\(121\) −133.222 −1.10101
\(122\) 107.590 0.881886
\(123\) 71.6326i 0.582379i
\(124\) 100.035 0.806732
\(125\) 112.961 + 53.5230i 0.903691 + 0.428184i
\(126\) 13.1272i 0.104184i
\(127\) 17.0523i 0.134270i −0.997744 0.0671350i \(-0.978614\pi\)
0.997744 0.0671350i \(-0.0213858\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 124.077i 0.961835i
\(130\) 109.369 137.739i 0.841304 1.05953i
\(131\) 210.657 1.60807 0.804034 0.594583i \(-0.202683\pi\)
0.804034 + 0.594583i \(0.202683\pi\)
\(132\) 55.2328 0.418431
\(133\) 32.4491i 0.243978i
\(134\) 108.580i 0.810296i
\(135\) 20.3466 + 16.1559i 0.150716 + 0.119674i
\(136\) 35.9153i 0.264083i
\(137\) −0.388976 −0.00283924 −0.00141962 0.999999i \(-0.500452\pi\)
−0.00141962 + 0.999999i \(0.500452\pi\)
\(138\) −56.2945 2.22076i −0.407931 0.0160925i
\(139\) 113.401 0.815837 0.407918 0.913018i \(-0.366255\pi\)
0.407918 + 0.913018i \(0.366255\pi\)
\(140\) 19.2404 24.2312i 0.137432 0.173080i
\(141\) 29.9792 0.212618
\(142\) 32.4926i 0.228821i
\(143\) −396.586 −2.77333
\(144\) −12.0000 −0.0833333
\(145\) 139.233 175.349i 0.960230 1.20930i
\(146\) 73.3799 0.502602
\(147\) 68.2888i 0.464549i
\(148\) −78.2564 −0.528759
\(149\) 92.8418i 0.623099i −0.950230 0.311550i \(-0.899152\pi\)
0.950230 0.311550i \(-0.100848\pi\)
\(150\) 13.8778 + 59.6440i 0.0925190 + 0.397627i
\(151\) −184.936 −1.22474 −0.612372 0.790570i \(-0.709784\pi\)
−0.612372 + 0.790570i \(0.709784\pi\)
\(152\) −29.6629 −0.195150
\(153\) −38.0940 −0.248980
\(154\) −69.7680 −0.453039
\(155\) 155.515 195.854i 1.00332 1.26357i
\(156\) 86.1631 0.552328
\(157\) 176.605 1.12488 0.562438 0.826840i \(-0.309864\pi\)
0.562438 + 0.826840i \(0.309864\pi\)
\(158\) 36.0966 0.228459
\(159\) 68.6210i 0.431579i
\(160\) −22.1506 17.5884i −0.138441 0.109927i
\(161\) 71.1090 + 2.80518i 0.441671 + 0.0174235i
\(162\) 12.7279i 0.0785674i
\(163\) 282.949i 1.73589i 0.496664 + 0.867943i \(0.334558\pi\)
−0.496664 + 0.867943i \(0.665442\pi\)
\(164\) −82.7142 −0.504355
\(165\) 85.8653 108.138i 0.520396 0.655382i
\(166\) 30.6588i 0.184692i
\(167\) 181.294i 1.08559i 0.839864 + 0.542797i \(0.182635\pi\)
−0.839864 + 0.542797i \(0.817365\pi\)
\(168\) 15.1579 0.0902258
\(169\) −449.674 −2.66079
\(170\) −70.3171 55.8342i −0.413630 0.328436i
\(171\) 31.4622i 0.183990i
\(172\) 143.271 0.832973
\(173\) 111.291i 0.643300i −0.946859 0.321650i \(-0.895763\pi\)
0.946859 0.321650i \(-0.104237\pi\)
\(174\) 109.690 0.630404
\(175\) −17.5300 75.3400i −0.100171 0.430514i
\(176\) 63.7774i 0.362372i
\(177\) 41.5878i 0.234959i
\(178\) −234.700 −1.31854
\(179\) 81.4644 0.455108 0.227554 0.973765i \(-0.426927\pi\)
0.227554 + 0.973765i \(0.426927\pi\)
\(180\) −18.6553 + 23.4943i −0.103640 + 0.130524i
\(181\) 126.722i 0.700121i 0.936727 + 0.350061i \(0.113839\pi\)
−0.936727 + 0.350061i \(0.886161\pi\)
\(182\) −108.838 −0.598011
\(183\) 131.770 0.720057
\(184\) 2.56431 65.0033i 0.0139365 0.353279i
\(185\) −121.658 + 153.215i −0.657610 + 0.828188i
\(186\) 122.517 0.658694
\(187\) 202.461i 1.08268i
\(188\) 34.6170i 0.184133i
\(189\) 16.0774i 0.0850657i
\(190\) −46.1141 + 58.0756i −0.242706 + 0.305661i
\(191\) 111.905i 0.585888i −0.956130 0.292944i \(-0.905365\pi\)
0.956130 0.292944i \(-0.0946350\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 162.315i 0.841011i 0.907290 + 0.420506i \(0.138147\pi\)
−0.907290 + 0.420506i \(0.861853\pi\)
\(194\) 0.820393i 0.00422883i
\(195\) 133.950 168.695i 0.686922 0.865103i
\(196\) 78.8531 0.402312
\(197\) 351.020i 1.78183i 0.454174 + 0.890913i \(0.349934\pi\)
−0.454174 + 0.890913i \(0.650066\pi\)
\(198\) 67.6461 0.341647
\(199\) 17.0849i 0.0858540i 0.999078 + 0.0429270i \(0.0136683\pi\)
−0.999078 + 0.0429270i \(0.986332\pi\)
\(200\) −68.8709 + 16.0248i −0.344355 + 0.0801238i
\(201\) 132.982i 0.661604i
\(202\) 232.333i 1.15017i
\(203\) −138.557 −0.682545
\(204\) 43.9871i 0.215623i
\(205\) −128.588 + 161.942i −0.627258 + 0.789963i
\(206\) 227.621i 1.10496i
\(207\) −68.9464 2.71986i −0.333074 0.0131394i
\(208\) 99.4926i 0.478330i
\(209\) 167.215 0.800071
\(210\) 23.5646 29.6771i 0.112212 0.141319i
\(211\) −167.474 −0.793717 −0.396858 0.917880i \(-0.629900\pi\)
−0.396858 + 0.917880i \(0.629900\pi\)
\(212\) −79.2368 −0.373758
\(213\) 39.7951i 0.186832i
\(214\) 75.8520i 0.354449i
\(215\) 222.731 280.505i 1.03596 1.30467i
\(216\) −14.6969 −0.0680414
\(217\) −154.759 −0.713175
\(218\) −109.737 −0.503383
\(219\) 89.8716 0.410373
\(220\) 124.867 + 99.1487i 0.567577 + 0.450676i
\(221\) 315.839i 1.42914i
\(222\) −95.8441 −0.431730
\(223\) 53.1179i 0.238197i −0.992882 0.119098i \(-0.962000\pi\)
0.992882 0.119098i \(-0.0380004\pi\)
\(224\) 17.5029i 0.0781379i
\(225\) 16.9968 + 73.0487i 0.0755414 + 0.324661i
\(226\) 86.5038i 0.382760i
\(227\) 371.776 1.63778 0.818889 0.573951i \(-0.194590\pi\)
0.818889 + 0.573951i \(0.194590\pi\)
\(228\) −36.3294 −0.159340
\(229\) 297.261i 1.29808i 0.760752 + 0.649042i \(0.224830\pi\)
−0.760752 + 0.649042i \(0.775170\pi\)
\(230\) −123.281 106.075i −0.536002 0.461196i
\(231\) −85.4480 −0.369905
\(232\) 126.660i 0.545946i
\(233\) 180.942i 0.776575i 0.921538 + 0.388287i \(0.126933\pi\)
−0.921538 + 0.388287i \(0.873067\pi\)
\(234\) 105.528 0.450974
\(235\) 67.7751 + 53.8158i 0.288405 + 0.229003i
\(236\) −48.0214 −0.203481
\(237\) 44.2091 0.186536
\(238\) 55.5628i 0.233457i
\(239\) 339.522 1.42059 0.710296 0.703903i \(-0.248561\pi\)
0.710296 + 0.703903i \(0.248561\pi\)
\(240\) −27.1289 21.5412i −0.113037 0.0897552i
\(241\) 33.1123i 0.137395i −0.997638 0.0686977i \(-0.978116\pi\)
0.997638 0.0686977i \(-0.0218844\pi\)
\(242\) 188.405i 0.778532i
\(243\) 15.5885i 0.0641500i
\(244\) 152.155i 0.623587i
\(245\) 122.585 154.383i 0.500349 0.630135i
\(246\) −101.304 −0.411804
\(247\) 260.855 1.05609
\(248\) 141.471i 0.570446i
\(249\) 37.5492i 0.150800i
\(250\) −75.6930 + 159.752i −0.302772 + 0.639006i
\(251\) 21.2171i 0.0845304i −0.999106 0.0422652i \(-0.986543\pi\)
0.999106 0.0422652i \(-0.0134574\pi\)
\(252\) 18.5646 0.0736691
\(253\) −14.4555 + 366.435i −0.0571363 + 1.44836i
\(254\) 24.1156 0.0949432
\(255\) −86.1205 68.3826i −0.337727 0.268167i
\(256\) 16.0000 0.0625000
\(257\) 368.667i 1.43450i −0.696815 0.717251i \(-0.745400\pi\)
0.696815 0.717251i \(-0.254600\pi\)
\(258\) 175.471 0.680120
\(259\) 121.067 0.467439
\(260\) 194.792 + 154.672i 0.749201 + 0.594892i
\(261\) 134.343 0.514723
\(262\) 297.914i 1.13708i
\(263\) −182.829 −0.695169 −0.347584 0.937649i \(-0.612998\pi\)
−0.347584 + 0.937649i \(0.612998\pi\)
\(264\) 78.1110i 0.295875i
\(265\) −123.182 + 155.134i −0.464837 + 0.585412i
\(266\) 45.8900 0.172519
\(267\) −287.447 −1.07658
\(268\) −153.555 −0.572966
\(269\) −231.329 −0.859958 −0.429979 0.902839i \(-0.641479\pi\)
−0.429979 + 0.902839i \(0.641479\pi\)
\(270\) −22.8479 + 28.7745i −0.0846220 + 0.106572i
\(271\) 241.547 0.891318 0.445659 0.895203i \(-0.352969\pi\)
0.445659 + 0.895203i \(0.352969\pi\)
\(272\) 50.7919 0.186735
\(273\) −133.299 −0.488274
\(274\) 0.550095i 0.00200765i
\(275\) 388.238 90.3344i 1.41177 0.328489i
\(276\) 3.14063 79.6124i 0.0113791 0.288451i
\(277\) 217.095i 0.783737i 0.920021 + 0.391869i \(0.128171\pi\)
−0.920021 + 0.391869i \(0.871829\pi\)
\(278\) 160.374i 0.576884i
\(279\) 150.052 0.537821
\(280\) 34.2681 + 27.2101i 0.122386 + 0.0971789i
\(281\) 262.796i 0.935218i −0.883935 0.467609i \(-0.845115\pi\)
0.883935 0.467609i \(-0.154885\pi\)
\(282\) 42.3970i 0.150344i
\(283\) 71.0126 0.250928 0.125464 0.992098i \(-0.459958\pi\)
0.125464 + 0.992098i \(0.459958\pi\)
\(284\) −45.9514 −0.161801
\(285\) −56.4780 + 71.1278i −0.198168 + 0.249571i
\(286\) 560.858i 1.96104i
\(287\) 127.963 0.445864
\(288\) 16.9706i 0.0589256i
\(289\) −127.761 −0.442080
\(290\) 247.981 + 196.906i 0.855107 + 0.678985i
\(291\) 1.00477i 0.00345282i
\(292\) 103.775i 0.355393i
\(293\) −491.470 −1.67737 −0.838687 0.544614i \(-0.816676\pi\)
−0.838687 + 0.544614i \(0.816676\pi\)
\(294\) 96.5749 0.328486
\(295\) −74.6544 + 94.0190i −0.253066 + 0.318708i
\(296\) 110.671i 0.373889i
\(297\) 82.8493 0.278954
\(298\) 131.298 0.440598
\(299\) −22.5505 + 571.638i −0.0754198 + 1.91183i
\(300\) −84.3493 + 19.6262i −0.281164 + 0.0654208i
\(301\) −221.648 −0.736372
\(302\) 261.539i 0.866025i
\(303\) 284.549i 0.939106i
\(304\) 41.9496i 0.137992i
\(305\) 297.898 + 236.542i 0.976715 + 0.775546i
\(306\) 53.8730i 0.176056i
\(307\) 357.082i 1.16313i −0.813498 0.581567i \(-0.802440\pi\)
0.813498 0.581567i \(-0.197560\pi\)
\(308\) 98.6669i 0.320347i
\(309\) 278.778i 0.902193i
\(310\) 276.979 + 219.931i 0.893481 + 0.709455i
\(311\) 137.819 0.443149 0.221575 0.975143i \(-0.428880\pi\)
0.221575 + 0.975143i \(0.428880\pi\)
\(312\) 121.853i 0.390555i
\(313\) −476.224 −1.52148 −0.760740 0.649056i \(-0.775164\pi\)
−0.760740 + 0.649056i \(0.775164\pi\)
\(314\) 249.758i 0.795407i
\(315\) 28.8606 36.3468i 0.0916211 0.115387i
\(316\) 51.0483i 0.161545i
\(317\) 290.212i 0.915495i 0.889082 + 0.457748i \(0.151344\pi\)
−0.889082 + 0.457748i \(0.848656\pi\)
\(318\) −97.0448 −0.305172
\(319\) 714.002i 2.23825i
\(320\) 24.8737 31.3257i 0.0777303 0.0978928i
\(321\) 92.8994i 0.289406i
\(322\) −3.96712 + 100.563i −0.0123202 + 0.312309i
\(323\) 133.169i 0.412288i
\(324\) −18.0000 −0.0555556
\(325\) 605.650 140.922i 1.86354 0.433605i
\(326\) −400.151 −1.22746
\(327\) −134.400 −0.411010
\(328\) 116.975i 0.356633i
\(329\) 53.5542i 0.162779i
\(330\) 152.930 + 121.432i 0.463425 + 0.367975i
\(331\) 124.642 0.376561 0.188280 0.982115i \(-0.439709\pi\)
0.188280 + 0.982115i \(0.439709\pi\)
\(332\) −43.3581 −0.130597
\(333\) −117.385 −0.352506
\(334\) −256.389 −0.767631
\(335\) −238.717 + 300.638i −0.712589 + 0.897428i
\(336\) 21.4366i 0.0637993i
\(337\) −281.809 −0.836228 −0.418114 0.908395i \(-0.637309\pi\)
−0.418114 + 0.908395i \(0.637309\pi\)
\(338\) 635.935i 1.88146i
\(339\) 105.945i 0.312522i
\(340\) 78.9615 99.4433i 0.232240 0.292480i
\(341\) 797.495i 2.33869i
\(342\) −44.4943 −0.130100
\(343\) −273.601 −0.797670
\(344\) 202.616i 0.589001i
\(345\) −150.987 129.915i −0.437644 0.376565i
\(346\) 157.389 0.454882
\(347\) 31.0131i 0.0893749i 0.999001 + 0.0446874i \(0.0142292\pi\)
−0.999001 + 0.0446874i \(0.985771\pi\)
\(348\) 155.126i 0.445763i
\(349\) 226.092 0.647828 0.323914 0.946087i \(-0.395001\pi\)
0.323914 + 0.946087i \(0.395001\pi\)
\(350\) 106.547 24.7911i 0.304420 0.0708318i
\(351\) 129.245 0.368219
\(352\) −90.1949 −0.256235
\(353\) 230.573i 0.653180i 0.945166 + 0.326590i \(0.105900\pi\)
−0.945166 + 0.326590i \(0.894100\pi\)
\(354\) −58.8140 −0.166141
\(355\) −71.4364 + 89.9663i −0.201229 + 0.253426i
\(356\) 331.915i 0.932346i
\(357\) 68.0503i 0.190617i
\(358\) 115.208i 0.321810i
\(359\) 569.575i 1.58656i 0.608858 + 0.793279i \(0.291628\pi\)
−0.608858 + 0.793279i \(0.708372\pi\)
\(360\) −33.2259 26.3825i −0.0922942 0.0732848i
\(361\) 251.014 0.695331
\(362\) −179.212 −0.495061
\(363\) 230.748i 0.635669i
\(364\) 153.920i 0.422858i
\(365\) 203.176 + 161.329i 0.556647 + 0.441997i
\(366\) 186.351i 0.509157i
\(367\) 707.351 1.92739 0.963693 0.267012i \(-0.0860364\pi\)
0.963693 + 0.267012i \(0.0860364\pi\)
\(368\) 91.9285 + 3.62648i 0.249806 + 0.00985458i
\(369\) −124.071 −0.336236
\(370\) −216.678 172.050i −0.585617 0.465000i
\(371\) 122.583 0.330413
\(372\) 173.265i 0.465767i
\(373\) 476.230 1.27676 0.638378 0.769723i \(-0.279606\pi\)
0.638378 + 0.769723i \(0.279606\pi\)
\(374\) −286.323 −0.765570
\(375\) −92.7046 + 195.655i −0.247212 + 0.521747i
\(376\) −48.9558 −0.130202
\(377\) 1113.84i 2.95449i
\(378\) 22.7369 0.0601506
\(379\) 218.771i 0.577232i −0.957445 0.288616i \(-0.906805\pi\)
0.957445 0.288616i \(-0.0931950\pi\)
\(380\) −82.1313 65.2151i −0.216135 0.171619i
\(381\) 29.5354 0.0775208
\(382\) 158.257 0.414286
\(383\) −25.9382 −0.0677238 −0.0338619 0.999427i \(-0.510781\pi\)
−0.0338619 + 0.999427i \(0.510781\pi\)
\(384\) 19.5959 0.0510310
\(385\) −193.176 153.388i −0.501755 0.398411i
\(386\) −229.548 −0.594685
\(387\) 214.907 0.555315
\(388\) −1.16021 −0.00299023
\(389\) 117.093i 0.301011i 0.988609 + 0.150505i \(0.0480901\pi\)
−0.988609 + 0.150505i \(0.951910\pi\)
\(390\) 238.571 + 189.434i 0.611720 + 0.485727i
\(391\) 291.827 + 11.5123i 0.746360 + 0.0294431i
\(392\) 111.515i 0.284477i
\(393\) 364.869i 0.928419i
\(394\) −496.417 −1.25994
\(395\) 99.9452 + 79.3600i 0.253026 + 0.200911i
\(396\) 95.6661i 0.241581i
\(397\) 184.113i 0.463760i 0.972744 + 0.231880i \(0.0744876\pi\)
−0.972744 + 0.231880i \(0.925512\pi\)
\(398\) −24.1618 −0.0607079
\(399\) 56.2035 0.140861
\(400\) −22.6624 97.3982i −0.0566561 0.243496i
\(401\) 483.910i 1.20676i 0.797454 + 0.603379i \(0.206179\pi\)
−0.797454 + 0.603379i \(0.793821\pi\)
\(402\) −188.066 −0.467825
\(403\) 1244.09i 3.08707i
\(404\) 328.569 0.813290
\(405\) −27.9829 + 35.2414i −0.0690936 + 0.0870158i
\(406\) 195.949i 0.482632i
\(407\) 623.873i 1.53286i
\(408\) 62.2072 0.152469
\(409\) −587.697 −1.43691 −0.718457 0.695572i \(-0.755151\pi\)
−0.718457 + 0.695572i \(0.755151\pi\)
\(410\) −229.021 181.851i −0.558588 0.443538i
\(411\) 0.673726i 0.00163924i
\(412\) 321.905 0.781322
\(413\) 74.2915 0.179883
\(414\) 3.84647 97.5049i 0.00929098 0.235519i
\(415\) −67.4048 + 84.8890i −0.162421 + 0.204552i
\(416\) −140.704 −0.338230
\(417\) 196.417i 0.471024i
\(418\) 236.477i 0.565736i
\(419\) 249.476i 0.595408i −0.954658 0.297704i \(-0.903779\pi\)
0.954658 0.297704i \(-0.0962208\pi\)
\(420\) 41.9697 + 33.3254i 0.0999279 + 0.0793462i
\(421\) 297.570i 0.706816i 0.935469 + 0.353408i \(0.114977\pi\)
−0.935469 + 0.353408i \(0.885023\pi\)
\(422\) 236.844i 0.561243i
\(423\) 51.9255i 0.122755i
\(424\) 112.058i 0.264287i
\(425\) −71.9418 309.190i −0.169275 0.727507i
\(426\) −56.2788 −0.132110
\(427\) 235.392i 0.551269i
\(428\) 107.271 0.250633
\(429\) 686.908i 1.60118i
\(430\) 396.694 + 314.989i 0.922543 + 0.732531i
\(431\) 83.3118i 0.193299i 0.995318 + 0.0966495i \(0.0308126\pi\)
−0.995318 + 0.0966495i \(0.969187\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) −574.608 −1.32704 −0.663520 0.748159i \(-0.730938\pi\)
−0.663520 + 0.748159i \(0.730938\pi\)
\(434\) 218.862i 0.504291i
\(435\) 303.714 + 241.159i 0.698192 + 0.554389i
\(436\) 155.192i 0.355945i
\(437\) 9.50810 241.023i 0.0217577 0.551540i
\(438\) 127.098i 0.290177i
\(439\) −196.774 −0.448231 −0.224116 0.974563i \(-0.571949\pi\)
−0.224116 + 0.974563i \(0.571949\pi\)
\(440\) −140.217 + 176.589i −0.318676 + 0.401338i
\(441\) 118.280 0.268208
\(442\) −446.664 −1.01055
\(443\) 13.1466i 0.0296764i 0.999890 + 0.0148382i \(0.00472332\pi\)
−0.999890 + 0.0148382i \(0.995277\pi\)
\(444\) 135.544i 0.305279i
\(445\) −649.842 515.997i −1.46032 1.15954i
\(446\) 75.1201 0.168431
\(447\) 160.807 0.359747
\(448\) −24.7528 −0.0552518
\(449\) 7.26549 0.0161815 0.00809074 0.999967i \(-0.497425\pi\)
0.00809074 + 0.999967i \(0.497425\pi\)
\(450\) −103.306 + 24.0371i −0.229570 + 0.0534159i
\(451\) 659.412i 1.46211i
\(452\) −122.335 −0.270652
\(453\) 320.319i 0.707106i
\(454\) 525.770i 1.15808i
\(455\) −301.354 239.285i −0.662315 0.525901i
\(456\) 51.3776i 0.112670i
\(457\) 635.868 1.39140 0.695698 0.718334i \(-0.255095\pi\)
0.695698 + 0.718334i \(0.255095\pi\)
\(458\) −420.391 −0.917885
\(459\) 65.9807i 0.143749i
\(460\) 150.013 174.345i 0.326115 0.379011i
\(461\) −638.029 −1.38401 −0.692006 0.721892i \(-0.743273\pi\)
−0.692006 + 0.721892i \(0.743273\pi\)
\(462\) 120.842i 0.261562i
\(463\) 593.754i 1.28241i −0.767371 0.641203i \(-0.778436\pi\)
0.767371 0.641203i \(-0.221564\pi\)
\(464\) −179.124 −0.386042
\(465\) 339.229 + 269.359i 0.729524 + 0.579267i
\(466\) −255.891 −0.549121
\(467\) −596.261 −1.27679 −0.638395 0.769709i \(-0.720401\pi\)
−0.638395 + 0.769709i \(0.720401\pi\)
\(468\) 149.239i 0.318887i
\(469\) 237.557 0.506519
\(470\) −76.1070 + 95.8484i −0.161930 + 0.203933i
\(471\) 305.890i 0.649447i
\(472\) 67.9125i 0.143882i
\(473\) 1142.18i 2.41477i
\(474\) 62.5211i 0.131901i
\(475\) −255.364 + 59.4175i −0.537608 + 0.125090i
\(476\) −78.5777 −0.165079
\(477\) −118.855 −0.249172
\(478\) 480.156i 1.00451i
\(479\) 203.911i 0.425702i −0.977085 0.212851i \(-0.931725\pi\)
0.977085 0.212851i \(-0.0682750\pi\)
\(480\) 30.4639 38.3660i 0.0634665 0.0799291i
\(481\) 973.242i 2.02337i
\(482\) 46.8279 0.0971533
\(483\) −4.85871 + 123.164i −0.0100594 + 0.254999i
\(484\) 266.444 0.550505
\(485\) −1.80367 + 2.27153i −0.00371891 + 0.00468356i
\(486\) −22.0454 −0.0453609
\(487\) 390.999i 0.802873i −0.915887 0.401436i \(-0.868511\pi\)
0.915887 0.401436i \(-0.131489\pi\)
\(488\) −215.180 −0.440943
\(489\) −490.083 −1.00221
\(490\) 218.330 + 173.362i 0.445572 + 0.353800i
\(491\) 449.372 0.915217 0.457609 0.889154i \(-0.348706\pi\)
0.457609 + 0.889154i \(0.348706\pi\)
\(492\) 143.265i 0.291189i
\(493\) −568.627 −1.15340
\(494\) 368.905i 0.746770i
\(495\) 187.300 + 148.723i 0.378385 + 0.300451i
\(496\) −200.070 −0.403366
\(497\) 71.0892 0.143037
\(498\) −53.1027 −0.106632
\(499\) 770.506 1.54410 0.772050 0.635561i \(-0.219231\pi\)
0.772050 + 0.635561i \(0.219231\pi\)
\(500\) −225.923 107.046i −0.451846 0.214092i
\(501\) −314.011 −0.626768
\(502\) 30.0055 0.0597720
\(503\) 185.848 0.369480 0.184740 0.982787i \(-0.440856\pi\)
0.184740 + 0.982787i \(0.440856\pi\)
\(504\) 26.2543i 0.0520919i
\(505\) 510.795 643.291i 1.01148 1.27384i
\(506\) −518.217 20.4431i −1.02414 0.0404015i
\(507\) 778.858i 1.53621i
\(508\) 34.1046i 0.0671350i
\(509\) −110.051 −0.216210 −0.108105 0.994139i \(-0.534478\pi\)
−0.108105 + 0.994139i \(0.534478\pi\)
\(510\) 96.7076 121.793i 0.189623 0.238809i
\(511\) 160.545i 0.314178i
\(512\) 22.6274i 0.0441942i
\(513\) −54.4942 −0.106226
\(514\) 521.374 1.01435
\(515\) 500.435 630.243i 0.971718 1.22377i
\(516\) 248.153i 0.480917i
\(517\) 275.973 0.533796
\(518\) 171.214i 0.330529i
\(519\) 192.761 0.371409
\(520\) −218.739 + 275.478i −0.420652 + 0.529765i
\(521\) 39.4422i 0.0757049i 0.999283 + 0.0378524i \(0.0120517\pi\)
−0.999283 + 0.0378524i \(0.987948\pi\)
\(522\) 189.989i 0.363964i
\(523\) 288.174 0.551003 0.275501 0.961301i \(-0.411156\pi\)
0.275501 + 0.961301i \(0.411156\pi\)
\(524\) −421.314 −0.804034
\(525\) 130.493 30.3628i 0.248558 0.0578339i
\(526\) 258.560i 0.491558i
\(527\) −635.120 −1.20516
\(528\) −110.466 −0.209215
\(529\) 527.356 + 41.6722i 0.996892 + 0.0787753i
\(530\) −219.393 174.206i −0.413949 0.328690i
\(531\) −72.0321 −0.135654
\(532\) 64.8982i 0.121989i
\(533\) 1028.68i 1.92998i
\(534\) 406.512i 0.761258i
\(535\) 166.764 210.021i 0.311709 0.392563i
\(536\) 217.159i 0.405148i
\(537\) 141.100i 0.262757i
\(538\) 327.148i 0.608082i
\(539\) 628.630i 1.16629i
\(540\) −40.6933 32.3119i −0.0753579 0.0598368i
\(541\) −153.598 −0.283915 −0.141958 0.989873i \(-0.545340\pi\)
−0.141958 + 0.989873i \(0.545340\pi\)
\(542\) 341.599i 0.630257i
\(543\) −219.489 −0.404215
\(544\) 71.8307i 0.132042i
\(545\) −303.844 241.263i −0.557512 0.442684i
\(546\) 188.513i 0.345262i
\(547\) 756.260i 1.38256i −0.722588 0.691279i \(-0.757047\pi\)
0.722588 0.691279i \(-0.242953\pi\)
\(548\) 0.777952 0.00141962
\(549\) 228.233i 0.415725i
\(550\) 127.752 + 549.051i 0.232277 + 0.998275i
\(551\) 469.635i 0.852333i
\(552\) 112.589 + 4.44152i 0.203965 + 0.00804623i
\(553\) 78.9743i 0.142811i
\(554\) −307.019 −0.554186
\(555\) −265.376 210.718i −0.478154 0.379671i
\(556\) −226.803 −0.407918
\(557\) −276.554 −0.496506 −0.248253 0.968695i \(-0.579856\pi\)
−0.248253 + 0.968695i \(0.579856\pi\)
\(558\) 212.206i 0.380297i
\(559\) 1781.81i 3.18749i
\(560\) −38.4809 + 48.4624i −0.0687158 + 0.0865401i
\(561\) −350.673 −0.625086
\(562\) 371.650 0.661299
\(563\) 535.076 0.950401 0.475201 0.879878i \(-0.342376\pi\)
0.475201 + 0.879878i \(0.342376\pi\)
\(564\) −59.9584 −0.106309
\(565\) −190.183 + 239.514i −0.336606 + 0.423919i
\(566\) 100.427i 0.177433i
\(567\) 27.8469 0.0491127
\(568\) 64.9851i 0.114410i
\(569\) 94.4406i 0.165976i 0.996551 + 0.0829882i \(0.0264464\pi\)
−0.996551 + 0.0829882i \(0.973554\pi\)
\(570\) −100.590 79.8719i −0.176474 0.140126i
\(571\) 594.892i 1.04184i 0.853605 + 0.520921i \(0.174411\pi\)
−0.853605 + 0.520921i \(0.825589\pi\)
\(572\) 793.173 1.38667
\(573\) 193.825 0.338263
\(574\) 180.967i 0.315274i
\(575\) −108.132 564.741i −0.188055 0.982158i
\(576\) 24.0000 0.0416667
\(577\) 511.175i 0.885919i 0.896542 + 0.442960i \(0.146071\pi\)
−0.896542 + 0.442960i \(0.853929\pi\)
\(578\) 180.682i 0.312598i
\(579\) −281.138 −0.485558
\(580\) −278.467 + 350.698i −0.480115 + 0.604652i
\(581\) 67.0772 0.115451
\(582\) −1.42096 −0.00244152
\(583\) 631.689i 1.08351i
\(584\) −146.760 −0.251301
\(585\) 292.188 + 232.008i 0.499467 + 0.396594i
\(586\) 695.044i 1.18608i
\(587\) 492.563i 0.839119i 0.907728 + 0.419560i \(0.137815\pi\)
−0.907728 + 0.419560i \(0.862185\pi\)
\(588\) 136.578i 0.232275i
\(589\) 524.553i 0.890582i
\(590\) −132.963 105.577i −0.225361 0.178944i
\(591\) −607.984 −1.02874
\(592\) 156.513 0.264380
\(593\) 535.477i 0.902996i 0.892272 + 0.451498i \(0.149110\pi\)
−0.892272 + 0.451498i \(0.850890\pi\)
\(594\) 117.167i 0.197250i
\(595\) −122.157 + 153.844i −0.205307 + 0.258561i
\(596\) 185.684i 0.311550i
\(597\) −29.5920 −0.0495678
\(598\) −808.418 31.8913i −1.35187 0.0533299i
\(599\) −522.025 −0.871495 −0.435747 0.900069i \(-0.643516\pi\)
−0.435747 + 0.900069i \(0.643516\pi\)
\(600\) −27.7557 119.288i −0.0462595 0.198813i
\(601\) 500.049 0.832028 0.416014 0.909358i \(-0.363427\pi\)
0.416014 + 0.909358i \(0.363427\pi\)
\(602\) 313.458i 0.520694i
\(603\) −230.332 −0.381977
\(604\) 369.873 0.612372
\(605\) 414.216 521.660i 0.684655 0.862248i
\(606\) 402.413 0.664048
\(607\) 232.429i 0.382915i 0.981501 + 0.191457i \(0.0613214\pi\)
−0.981501 + 0.191457i \(0.938679\pi\)
\(608\) 59.3257 0.0975752
\(609\) 239.987i 0.394068i
\(610\) −334.520 + 421.292i −0.548394 + 0.690642i
\(611\) 430.517 0.704610
\(612\) 76.1879 0.124490
\(613\) −654.378 −1.06750 −0.533751 0.845642i \(-0.679218\pi\)
−0.533751 + 0.845642i \(0.679218\pi\)
\(614\) 504.991 0.822460
\(615\) −280.493 222.721i −0.456085 0.362148i
\(616\) 139.536 0.226520
\(617\) 675.896 1.09546 0.547728 0.836657i \(-0.315493\pi\)
0.547728 + 0.836657i \(0.315493\pi\)
\(618\) 394.251 0.637947
\(619\) 1153.52i 1.86352i −0.363075 0.931760i \(-0.618273\pi\)
0.363075 0.931760i \(-0.381727\pi\)
\(620\) −311.029 + 391.707i −0.501660 + 0.631786i
\(621\) 4.71094 119.419i 0.00758606 0.192301i
\(622\) 194.906i 0.313354i
\(623\) 513.490i 0.824221i
\(624\) −172.326 −0.276164
\(625\) −560.802 + 275.910i −0.897283 + 0.441456i
\(626\) 673.482i 1.07585i
\(627\) 289.625i 0.461921i
\(628\) −353.211 −0.562438
\(629\) 496.849 0.789903
\(630\) 51.4022 + 40.8151i 0.0815908 + 0.0647859i
\(631\) 210.863i 0.334173i −0.985942 0.167086i \(-0.946564\pi\)
0.985942 0.167086i \(-0.0534359\pi\)
\(632\) −72.1932 −0.114230
\(633\) 290.074i 0.458253i
\(634\) −410.422 −0.647353
\(635\) 66.7719 + 53.0192i 0.105153 + 0.0834947i
\(636\) 137.242i 0.215789i
\(637\) 980.662i 1.53950i
\(638\) 1009.75 1.58268
\(639\) −68.9272 −0.107867
\(640\) 44.3012 + 35.1767i 0.0692207 + 0.0549636i
\(641\) 358.037i 0.558560i 0.960210 + 0.279280i \(0.0900958\pi\)
−0.960210 + 0.279280i \(0.909904\pi\)
\(642\) 131.380 0.204641
\(643\) 1177.59 1.83141 0.915703 0.401855i \(-0.131634\pi\)
0.915703 + 0.401855i \(0.131634\pi\)
\(644\) −142.218 5.61036i −0.220835 0.00871173i
\(645\) 485.848 + 385.781i 0.753253 + 0.598109i
\(646\) 188.329 0.291531
\(647\) 556.482i 0.860096i −0.902806 0.430048i \(-0.858497\pi\)
0.902806 0.430048i \(-0.141503\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 382.835i 0.589884i
\(650\) 199.293 + 856.519i 0.306605 + 1.31772i
\(651\) 268.050i 0.411752i
\(652\) 565.899i 0.867943i
\(653\) 1076.49i 1.64853i 0.566204 + 0.824265i \(0.308412\pi\)
−0.566204 + 0.824265i \(0.691588\pi\)
\(654\) 190.071i 0.290628i
\(655\) −654.977 + 824.872i −0.999965 + 1.25935i
\(656\) 165.428 0.252177
\(657\) 155.662i 0.236929i
\(658\) 75.7371 0.115102
\(659\) 1142.54i 1.73375i 0.498526 + 0.866875i \(0.333875\pi\)
−0.498526 + 0.866875i \(0.666125\pi\)
\(660\) −171.731 + 216.276i −0.260198 + 0.327691i
\(661\) 1194.32i 1.80684i −0.428754 0.903421i \(-0.641047\pi\)
0.428754 0.903421i \(-0.358953\pi\)
\(662\) 176.270i 0.266269i
\(663\) −547.049 −0.825112
\(664\) 61.3177i 0.0923459i
\(665\) 127.061 + 100.891i 0.191070 + 0.151716i
\(666\) 166.007i 0.249260i
\(667\) −1029.16 40.5993i −1.54297 0.0608685i
\(668\) 362.588i 0.542797i
\(669\) 92.0029 0.137523
\(670\) −425.167 337.597i −0.634577 0.503877i
\(671\) 1213.01 1.80776
\(672\) −30.3159 −0.0451129
\(673\) 481.936i 0.716100i −0.933702 0.358050i \(-0.883442\pi\)
0.933702 0.358050i \(-0.116558\pi\)
\(674\) 398.538i 0.591302i
\(675\) −126.524 + 29.4394i −0.187443 + 0.0436139i
\(676\) 899.348 1.33040
\(677\) 180.841 0.267121 0.133560 0.991041i \(-0.457359\pi\)
0.133560 + 0.991041i \(0.457359\pi\)
\(678\) −149.829 −0.220987
\(679\) 1.79490 0.00264345
\(680\) 140.634 + 111.668i 0.206815 + 0.164218i
\(681\) 643.935i 0.945572i
\(682\) 1127.83 1.65371
\(683\) 18.5491i 0.0271582i −0.999908 0.0135791i \(-0.995678\pi\)
0.999908 0.0135791i \(-0.00432250\pi\)
\(684\) 62.9244i 0.0919948i
\(685\) 1.20941 1.52312i 0.00176556 0.00222353i
\(686\) 386.930i 0.564038i
\(687\) −514.872 −0.749450
\(688\) −286.543 −0.416487
\(689\) 985.434i 1.43024i
\(690\) 183.727 213.528i 0.266271 0.309461i
\(691\) −502.845 −0.727706 −0.363853 0.931456i \(-0.618539\pi\)
−0.363853 + 0.931456i \(0.618539\pi\)
\(692\) 222.582i 0.321650i
\(693\) 148.000i 0.213565i
\(694\) −43.8591 −0.0631976
\(695\) −352.589 + 444.047i −0.507322 + 0.638916i
\(696\) −219.381 −0.315202
\(697\) 525.152 0.753446
\(698\) 319.742i 0.458084i
\(699\) −313.401 −0.448356
\(700\) 35.0599 + 150.680i 0.0500856 + 0.215257i
\(701\) 183.664i 0.262002i 0.991382 + 0.131001i \(0.0418192\pi\)
−0.991382 + 0.131001i \(0.958181\pi\)
\(702\) 182.780i 0.260370i
\(703\) 410.353i 0.583717i
\(704\) 127.555i 0.181186i
\(705\) −93.2116 + 117.390i −0.132215 + 0.166510i
\(706\) −326.079 −0.461868
\(707\) −508.313 −0.718972
\(708\) 83.1755i 0.117480i
\(709\) 39.2008i 0.0552903i −0.999618 0.0276452i \(-0.991199\pi\)
0.999618 0.0276452i \(-0.00880085\pi\)
\(710\) −127.232 101.026i −0.179199 0.142291i
\(711\) 76.5724i 0.107697i
\(712\) 469.399 0.659268
\(713\) −1149.51 45.3468i −1.61221 0.0636000i
\(714\) −96.2377 −0.134787
\(715\) 1233.07 1552.92i 1.72457 2.17191i
\(716\) −162.929 −0.227554
\(717\) 588.069i 0.820179i
\(718\) −805.500 −1.12187
\(719\) −44.6052 −0.0620378 −0.0310189 0.999519i \(-0.509875\pi\)
−0.0310189 + 0.999519i \(0.509875\pi\)
\(720\) 37.3105 46.9885i 0.0518202 0.0652619i
\(721\) −498.003 −0.690711
\(722\) 354.988i 0.491673i
\(723\) 57.3522 0.0793253
\(724\) 253.444i 0.350061i
\(725\) 253.711 + 1090.39i 0.349946 + 1.50399i
\(726\) 326.327 0.449486
\(727\) 966.099 1.32889 0.664443 0.747339i \(-0.268669\pi\)
0.664443 + 0.747339i \(0.268669\pi\)
\(728\) 217.676 0.299005
\(729\) −27.0000 −0.0370370
\(730\) −228.153 + 287.334i −0.312539 + 0.393609i
\(731\) −909.629 −1.24436
\(732\) −263.541 −0.360028
\(733\) −58.5900 −0.0799317 −0.0399659 0.999201i \(-0.512725\pi\)
−0.0399659 + 0.999201i \(0.512725\pi\)
\(734\) 1000.35i 1.36287i
\(735\) 267.399 + 212.324i 0.363808 + 0.288876i
\(736\) −5.12862 + 130.007i −0.00696824 + 0.176639i
\(737\) 1224.17i 1.66101i
\(738\) 175.463i 0.237755i
\(739\) −513.758 −0.695207 −0.347603 0.937642i \(-0.613004\pi\)
−0.347603 + 0.937642i \(0.613004\pi\)
\(740\) 243.316 306.429i 0.328805 0.414094i
\(741\) 451.814i 0.609735i
\(742\) 173.359i 0.233637i
\(743\) 474.006 0.637962 0.318981 0.947761i \(-0.396659\pi\)
0.318981 + 0.947761i \(0.396659\pi\)
\(744\) −245.034 −0.329347
\(745\) 363.542 + 288.665i 0.487976 + 0.387470i
\(746\) 673.491i 0.902803i
\(747\) −65.0372 −0.0870645
\(748\) 404.922i 0.541340i
\(749\) −165.954 −0.221567
\(750\) −276.698 131.104i −0.368930 0.174805i
\(751\) 870.368i 1.15894i 0.814992 + 0.579472i \(0.196741\pi\)
−0.814992 + 0.579472i \(0.803259\pi\)
\(752\) 69.2340i 0.0920665i
\(753\) 36.7491 0.0488036
\(754\) 1575.21 2.08914
\(755\) 575.006 724.157i 0.761597 0.959149i
\(756\) 32.1548i 0.0425329i
\(757\) −439.359 −0.580395 −0.290197 0.956967i \(-0.593721\pi\)
−0.290197 + 0.956967i \(0.593721\pi\)
\(758\) 309.389 0.408164
\(759\) −634.684 25.0376i −0.836211 0.0329877i
\(760\) 92.2281 116.151i 0.121353 0.152831i
\(761\) −814.037 −1.06969 −0.534847 0.844949i \(-0.679631\pi\)
−0.534847 + 0.844949i \(0.679631\pi\)
\(762\) 41.7694i 0.0548155i
\(763\) 240.090i 0.314666i
\(764\) 223.809i 0.292944i
\(765\) 118.442 149.165i 0.154826 0.194987i
\(766\) 36.6822i 0.0478880i
\(767\) 597.222i 0.778647i
\(768\) 27.7128i 0.0360844i
\(769\) 1396.26i 1.81568i −0.419320 0.907838i \(-0.637731\pi\)
0.419320 0.907838i \(-0.362269\pi\)
\(770\) 216.923 273.191i 0.281719 0.354794i
\(771\) 638.550 0.828210
\(772\) 324.630i 0.420506i
\(773\) −60.6538 −0.0784654 −0.0392327 0.999230i \(-0.512491\pi\)
−0.0392327 + 0.999230i \(0.512491\pi\)
\(774\) 303.924i 0.392667i
\(775\) 283.379 + 1217.90i 0.365650 + 1.57149i
\(776\) 1.64079i 0.00211441i
\(777\) 209.693i 0.269876i
\(778\) −165.595 −0.212847
\(779\) 433.728i 0.556776i
\(780\) −267.899 + 337.390i −0.343461 + 0.432551i
\(781\) 366.333i 0.469056i
\(782\) −16.2808 + 412.705i −0.0208194 + 0.527756i
\(783\) 232.688i 0.297175i
\(784\) −157.706 −0.201156
\(785\) −549.104 + 691.536i −0.699495 + 0.880938i
\(786\) −516.002 −0.656491
\(787\) −910.682 −1.15716 −0.578578 0.815627i \(-0.696392\pi\)
−0.578578 + 0.815627i \(0.696392\pi\)
\(788\)