Properties

Label 690.3.f.a.229.6
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 229.6
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.8

$q$-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 \(-0.570934\pi\)
−0.221007 + 0.975272i \(0.570934\pi\)
\(8\) 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 \(-0.594057\pi\)
0.291208 0.956660i \(-0.405943\pi\)
\(14\) 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 \(-0.621832\pi\)
−0.373470 + 0.927642i \(0.621832\pi\)
\(18\) 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 \(-0.677343\pi\)
−0.528759 + 0.848772i \(0.677343\pi\)
\(38\) −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 \(-0.186637\pi\)
0.832973 + 0.553313i \(0.186637\pi\)
\(44\) 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 \(0.0589477\pi\)
−0.982901 + 0.184133i \(0.941052\pi\)
\(48\) 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 \(-0.621931\pi\)
−0.373758 + 0.927526i \(0.621931\pi\)
\(54\) 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 \(-0.694207\pi\)
−0.572966 + 0.819579i \(0.694207\pi\)
\(68\) 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 \(0.115653\pi\)
−0.934717 + 0.355393i \(0.884347\pi\)
\(74\) 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 \(-0.541689\pi\)
−0.130597 + 0.991436i \(0.541689\pi\)
\(84\) 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 \(-0.500952\pi\)
−0.00299023 + 0.999996i \(0.500952\pi\)
\(98\) 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 \(-0.214546\pi\)
0.781322 + 0.624128i \(0.214546\pi\)
\(104\) 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 \(-0.419361\pi\)
0.250633 + 0.968082i \(0.419361\pi\)
\(108\) 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 \(-0.587239\pi\)
−0.270652 + 0.962677i \(0.587239\pi\)
\(114\) 25.6888i 0.225340i
\(115\) −67.9062 92.8103i −0.590489 0.807046i
\(116\) 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 \(0.0213858\pi\)
−0.997744 + 0.0671350i \(0.978614\pi\)
\(128\) 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 \(-0.499548\pi\)
0.00141962 + 0.999999i \(0.499548\pi\)
\(138\) 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 \(-0.690136\pi\)
−0.562438 + 0.826840i \(0.690136\pi\)
\(158\) −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 \(-0.665442\pi\)
0.496664 0.867943i \(-0.334558\pi\)
\(164\) −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 \(-0.817365\pi\)
0.839864 0.542797i \(-0.182635\pi\)
\(168\) −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 \(0.104237\pi\)
−0.946859 + 0.321650i \(0.895763\pi\)
\(174\) 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 \(-0.861853\pi\)
0.907290 0.420506i \(-0.138147\pi\)
\(194\) 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 \(-0.650066\pi\)
0.454174 0.890913i \(-0.349934\pi\)
\(198\) −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 \(0.0380004\pi\)
−0.992882 + 0.119098i \(0.962000\pi\)
\(224\) 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 \(-0.805410\pi\)
−0.818889 + 0.573951i \(0.805410\pi\)
\(228\) 36.3294 0.159340
\(229\) 297.261i 1.29808i 0.760752 + 0.649042i \(0.224830\pi\)
−0.760752 + 0.649042i \(0.775170\pi\)
\(230\) −131.254 + 96.0339i −0.570668 + 0.417539i
\(231\) −85.4480 −0.369905
\(232\) 126.660i 0.545946i
\(233\) 180.942i 0.776575i −0.921538 0.388287i \(-0.873067\pi\)
0.921538 0.388287i \(-0.126933\pi\)
\(234\) 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 \(0.254600\pi\)
−0.696815 + 0.717251i \(0.745400\pi\)
\(258\) −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 \(-0.387002\pi\)
0.347584 + 0.937649i \(0.387002\pi\)
\(264\) 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 \(-0.871829\pi\)
0.920021 0.391869i \(-0.128171\pi\)
\(278\) 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 \(-0.540042\pi\)
−0.125464 + 0.992098i \(0.540042\pi\)
\(284\) −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 \(-0.183324\pi\)
0.838687 + 0.544614i \(0.183324\pi\)
\(294\) 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 \(0.197560\pi\)
−0.813498 + 0.581567i \(0.802440\pi\)
\(308\) 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 \(-0.224836\pi\)
0.760740 + 0.649056i \(0.224836\pi\)
\(314\) 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 \(-0.848656\pi\)
0.889082 0.457748i \(-0.151344\pi\)
\(318\) 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 \(-0.362691\pi\)
0.418114 + 0.908395i \(0.362691\pi\)
\(338\) 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
\(345\) −160.752 + 117.617i −0.465948 + 0.340919i
\(346\) 157.389 0.454882
\(347\) 31.0131i 0.0893749i −0.999001 0.0446874i \(-0.985771\pi\)
0.999001 0.0446874i \(-0.0142292\pi\)
\(348\) 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 \(-0.894100\pi\)
0.945166 0.326590i \(-0.105900\pi\)
\(354\) −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 \(-0.913964\pi\)
−0.963693 + 0.267012i \(0.913964\pi\)
\(368\) −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 \(-0.720394\pi\)
−0.638378 + 0.769723i \(0.720394\pi\)
\(374\) −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 \(-0.489219\pi\)
0.0338619 + 0.999427i \(0.489219\pi\)
\(384\) 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 \(-0.925512\pi\)
0.972744 0.231880i \(-0.0744876\pi\)
\(398\) 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 \(-0.269062\pi\)
0.663520 + 0.748159i \(0.269062\pi\)
\(434\) 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 \(-0.995277\pi\)
0.999890 0.0148382i \(-0.00472332\pi\)
\(444\) 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 \(-0.744905\pi\)
−0.695698 + 0.718334i \(0.744905\pi\)
\(458\) 420.391 0.917885
\(459\) 65.9807i 0.143749i
\(460\) 135.812 + 185.621i 0.295244 + 0.403523i
\(461\) −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 \(0.221564\pi\)
−0.767371 + 0.641203i \(0.778436\pi\)
\(464\) −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 \(-0.279599\pi\)
0.638395 + 0.769709i \(0.279599\pi\)
\(468\) 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 \(0.131489\pi\)
−0.915887 + 0.401436i \(0.868511\pi\)
\(488\) 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 \(-0.559144\pi\)
−0.184740 + 0.982787i \(0.559144\pi\)
\(504\) 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 \(-0.588844\pi\)
−0.275501 + 0.961301i \(0.588844\pi\)
\(524\) −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 \(0.242953\pi\)
−0.722588 + 0.691279i \(0.757047\pi\)
\(548\) −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 \(-0.420144\pi\)
0.248253 + 0.968695i \(0.420144\pi\)
\(558\) 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 \(-0.657624\pi\)
−0.475201 + 0.879878i \(0.657624\pi\)
\(564\) −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
\(575\) 152.284 554.468i 0.264841 0.964292i
\(576\) 24.0000 0.0416667
\(577\) 511.175i 0.885919i −0.896542 0.442960i \(-0.853929\pi\)
0.896542 0.442960i \(-0.146071\pi\)
\(578\) 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 \(-0.862185\pi\)
0.907728 0.419560i \(-0.137815\pi\)
\(588\) 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 \(-0.850890\pi\)
0.892272 0.451498i \(-0.149110\pi\)
\(594\) 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 \(-0.938679\pi\)
0.981501 0.191457i \(-0.0613214\pi\)
\(608\) −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 \(-0.320782\pi\)
0.533751 + 0.845642i \(0.320782\pi\)
\(614\) 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 \(-0.684507\pi\)
−0.547728 + 0.836657i \(0.684507\pi\)
\(618\) −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 \(-0.868366\pi\)
−0.915703 + 0.401855i \(0.868366\pi\)
\(644\) −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 \(0.141503\pi\)
−0.902806 + 0.430048i \(0.858497\pi\)
\(648\) 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 \(-0.691588\pi\)
0.566204 0.824265i \(-0.308412\pi\)
\(654\) 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 \(0.116558\pi\)
−0.933702 + 0.358050i \(0.883442\pi\)
\(674\) 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 \(-0.542641\pi\)
−0.133560 + 0.991041i \(0.542641\pi\)
\(678\) 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 \(0.00432250\pi\)
−0.999908 + 0.0135791i \(0.995678\pi\)
\(684\) 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
\(690\) 166.336 + 227.338i 0.241066 + 0.329475i
\(691\) −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 \(-0.731331\pi\)
−0.664443 + 0.747339i \(0.731331\pi\)
\(728\) −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 \(-0.487275\pi\)
0.0399659 + 0.999201i \(0.487275\pi\)
\(734\) 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 \(-0.603341\pi\)
−0.318981 + 0.947761i \(0.603341\pi\)
\(744\) −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 \(-0.406279\pi\)
0.290197 + 0.956967i \(0.406279\pi\)
\(758\) −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 \(-0.487509\pi\)
0.0392327 + 0.999230i \(0.487509\pi\)
\(774\) 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 \(-0.303608\pi\)
0.578578 + 0.815627i \(0.303608\pi\)