Properties

Label 49.6.c.h.18.2
Level $49$
Weight $6$
Character 49.18
Analytic conductor $7.859$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85880717084\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.54095201243136.19
Defining polynomial: \( x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 18.2
Root \(-5.52218 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.6.c.h.30.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40754 - 2.43792i) q^{2} +(3.27401 - 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(-22.9955 - 39.8294i) q^{5} -18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +O(q^{10})\) \(q+(-1.40754 - 2.43792i) q^{2} +(3.27401 - 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(-22.9955 - 39.8294i) q^{5} -18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +(-64.7341 + 112.123i) q^{10} +(275.890 - 477.856i) q^{11} +(-78.8229 - 136.525i) q^{12} -1094.10 q^{13} -301.150 q^{15} +(-163.017 - 282.354i) q^{16} +(-590.357 + 1022.53i) q^{17} +(281.681 - 487.886i) q^{18} +(-583.063 - 1009.89i) q^{19} -1107.25 q^{20} -1553.30 q^{22} +(-22.1925 - 38.4386i) q^{23} +(-516.823 + 895.163i) q^{24} +(504.912 - 874.533i) q^{25} +(1539.98 + 2667.33i) q^{26} +2901.58 q^{27} +3329.02 q^{29} +(423.880 + 734.181i) q^{30} +(4392.01 - 7607.18i) q^{31} +(-2984.61 + 5169.49i) q^{32} +(-1806.53 - 3129.01i) q^{33} +3323.80 q^{34} +4818.05 q^{36} +(1278.56 + 2214.53i) q^{37} +(-1641.37 + 2842.93i) q^{38} +(-3582.08 + 6204.35i) q^{39} +(3629.99 + 6287.32i) q^{40} +12761.3 q^{41} -96.7714 q^{43} +(-6642.16 - 11504.6i) q^{44} +(4601.94 - 7970.80i) q^{45} +(-62.4736 + 108.207i) q^{46} +(3839.58 + 6650.34i) q^{47} -2134.88 q^{48} -2842.73 q^{50} +(3865.67 + 6695.53i) q^{51} +(-13170.4 + 22811.8i) q^{52} +(5976.67 - 10351.9i) q^{53} +(-4084.08 - 7073.83i) q^{54} -25377.0 q^{55} -7635.81 q^{57} +(-4685.71 - 8115.89i) q^{58} +(4928.62 - 8536.62i) q^{59} +(-3625.15 + 6278.94i) q^{60} +(-19258.9 - 33357.5i) q^{61} -24727.6 q^{62} +6370.65 q^{64} +(25159.4 + 43577.3i) q^{65} +(-5085.53 + 8808.39i) q^{66} +(33774.5 - 58499.1i) q^{67} +(14213.1 + 24617.7i) q^{68} -290.634 q^{69} -61374.6 q^{71} +(-15795.4 - 27358.4i) q^{72} +(925.199 - 1602.49i) q^{73} +(3599.24 - 6234.07i) q^{74} +(-3306.17 - 5726.45i) q^{75} -28074.9 q^{76} +20167.7 q^{78} +(4.26456 + 7.38644i) q^{79} +(-7497.34 + 12985.8i) q^{80} +(-14815.2 + 25660.7i) q^{81} +(-17961.9 - 31111.0i) q^{82} +95039.3 q^{83} +54302.3 q^{85} +(136.209 + 235.921i) q^{86} +(10899.2 - 18878.0i) q^{87} +(-43551.0 + 75432.6i) q^{88} +(26802.8 + 46423.8i) q^{89} -25909.6 q^{90} -1068.59 q^{92} +(-28758.9 - 49811.9i) q^{93} +(10808.7 - 18721.2i) q^{94} +(-26815.7 + 46446.1i) q^{95} +(19543.2 + 33849.9i) q^{96} -3110.79 q^{97} +110424. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40754 2.43792i −0.248820 0.430968i 0.714379 0.699759i \(-0.246709\pi\)
−0.963199 + 0.268791i \(0.913376\pi\)
\(3\) 3.27401 5.67075i 0.210028 0.363779i −0.741695 0.670737i \(-0.765978\pi\)
0.951723 + 0.306958i \(0.0993113\pi\)
\(4\) 12.0377 20.8499i 0.376178 0.651559i
\(5\) −22.9955 39.8294i −0.411356 0.712490i 0.583682 0.811982i \(-0.301612\pi\)
−0.995038 + 0.0994921i \(0.968278\pi\)
\(6\) −18.4331 −0.209036
\(7\) 0 0
\(8\) −157.856 −0.872041
\(9\) 100.062 + 173.312i 0.411777 + 0.713218i
\(10\) −64.7341 + 112.123i −0.204707 + 0.354563i
\(11\) 275.890 477.856i 0.687472 1.19074i −0.285181 0.958474i \(-0.592054\pi\)
0.972653 0.232263i \(-0.0746129\pi\)
\(12\) −78.8229 136.525i −0.158015 0.273691i
\(13\) −1094.10 −1.79555 −0.897776 0.440453i \(-0.854818\pi\)
−0.897776 + 0.440453i \(0.854818\pi\)
\(14\) 0 0
\(15\) −301.150 −0.345585
\(16\) −163.017 282.354i −0.159197 0.275737i
\(17\) −590.357 + 1022.53i −0.495442 + 0.858130i −0.999986 0.00525555i \(-0.998327\pi\)
0.504545 + 0.863386i \(0.331660\pi\)
\(18\) 281.681 487.886i 0.204916 0.354925i
\(19\) −583.063 1009.89i −0.370537 0.641789i 0.619111 0.785303i \(-0.287493\pi\)
−0.989648 + 0.143514i \(0.954160\pi\)
\(20\) −1107.25 −0.618972
\(21\) 0 0
\(22\) −1553.30 −0.684226
\(23\) −22.1925 38.4386i −0.00874757 0.0151512i 0.861618 0.507556i \(-0.169451\pi\)
−0.870366 + 0.492405i \(0.836118\pi\)
\(24\) −516.823 + 895.163i −0.183153 + 0.317230i
\(25\) 504.912 874.533i 0.161572 0.279850i
\(26\) 1539.98 + 2667.33i 0.446768 + 0.773826i
\(27\) 2901.58 0.765993
\(28\) 0 0
\(29\) 3329.02 0.735057 0.367529 0.930012i \(-0.380204\pi\)
0.367529 + 0.930012i \(0.380204\pi\)
\(30\) 423.880 + 734.181i 0.0859883 + 0.148936i
\(31\) 4392.01 7607.18i 0.820841 1.42174i −0.0842165 0.996447i \(-0.526839\pi\)
0.905057 0.425290i \(-0.139828\pi\)
\(32\) −2984.61 + 5169.49i −0.515243 + 0.892427i
\(33\) −1806.53 3129.01i −0.288776 0.500175i
\(34\) 3323.80 0.493102
\(35\) 0 0
\(36\) 4818.05 0.619605
\(37\) 1278.56 + 2214.53i 0.153539 + 0.265937i 0.932526 0.361103i \(-0.117600\pi\)
−0.778987 + 0.627040i \(0.784266\pi\)
\(38\) −1641.37 + 2842.93i −0.184394 + 0.319379i
\(39\) −3582.08 + 6204.35i −0.377115 + 0.653183i
\(40\) 3629.99 + 6287.32i 0.358720 + 0.621321i
\(41\) 12761.3 1.18559 0.592794 0.805354i \(-0.298025\pi\)
0.592794 + 0.805354i \(0.298025\pi\)
\(42\) 0 0
\(43\) −96.7714 −0.00798135 −0.00399067 0.999992i \(-0.501270\pi\)
−0.00399067 + 0.999992i \(0.501270\pi\)
\(44\) −6642.16 11504.6i −0.517223 0.895857i
\(45\) 4601.94 7970.80i 0.338774 0.586774i
\(46\) −62.4736 + 108.207i −0.00435313 + 0.00753985i
\(47\) 3839.58 + 6650.34i 0.253535 + 0.439136i 0.964497 0.264095i \(-0.0850732\pi\)
−0.710961 + 0.703231i \(0.751740\pi\)
\(48\) −2134.88 −0.133743
\(49\) 0 0
\(50\) −2842.73 −0.160809
\(51\) 3865.67 + 6695.53i 0.208113 + 0.360462i
\(52\) −13170.4 + 22811.8i −0.675446 + 1.16991i
\(53\) 5976.67 10351.9i 0.292260 0.506209i −0.682084 0.731274i \(-0.738926\pi\)
0.974344 + 0.225065i \(0.0722594\pi\)
\(54\) −4084.08 7073.83i −0.190594 0.330119i
\(55\) −25377.0 −1.13118
\(56\) 0 0
\(57\) −7635.81 −0.311292
\(58\) −4685.71 8115.89i −0.182897 0.316786i
\(59\) 4928.62 8536.62i 0.184330 0.319268i −0.759021 0.651066i \(-0.774322\pi\)
0.943350 + 0.331798i \(0.107655\pi\)
\(60\) −3625.15 + 6278.94i −0.130001 + 0.225169i
\(61\) −19258.9 33357.5i −0.662686 1.14781i −0.979907 0.199454i \(-0.936083\pi\)
0.317221 0.948352i \(-0.397250\pi\)
\(62\) −24727.6 −0.816965
\(63\) 0 0
\(64\) 6370.65 0.194417
\(65\) 25159.4 + 43577.3i 0.738612 + 1.27931i
\(66\) −5085.53 + 8808.39i −0.143706 + 0.248907i
\(67\) 33774.5 58499.1i 0.919182 1.59207i 0.118521 0.992952i \(-0.462185\pi\)
0.800661 0.599118i \(-0.204482\pi\)
\(68\) 14213.1 + 24617.7i 0.372748 + 0.645619i
\(69\) −290.634 −0.00734893
\(70\) 0 0
\(71\) −61374.6 −1.44492 −0.722458 0.691415i \(-0.756988\pi\)
−0.722458 + 0.691415i \(0.756988\pi\)
\(72\) −15795.4 27358.4i −0.359086 0.621955i
\(73\) 925.199 1602.49i 0.0203202 0.0351956i −0.855686 0.517495i \(-0.826865\pi\)
0.876007 + 0.482299i \(0.160198\pi\)
\(74\) 3599.24 6234.07i 0.0764068 0.132340i
\(75\) −3306.17 5726.45i −0.0678691 0.117553i
\(76\) −28074.9 −0.557551
\(77\) 0 0
\(78\) 20167.7 0.375335
\(79\) 4.26456 + 7.38644i 7.68788e−5 + 0.000133158i 0.866064 0.499933i \(-0.166642\pi\)
−0.865987 + 0.500067i \(0.833309\pi\)
\(80\) −7497.34 + 12985.8i −0.130973 + 0.226852i
\(81\) −14815.2 + 25660.7i −0.250897 + 0.434566i
\(82\) −17961.9 31111.0i −0.294998 0.510951i
\(83\) 95039.3 1.51429 0.757143 0.653249i \(-0.226595\pi\)
0.757143 + 0.653249i \(0.226595\pi\)
\(84\) 0 0
\(85\) 54302.3 0.815212
\(86\) 136.209 + 235.921i 0.00198592 + 0.00343971i
\(87\) 10899.2 18878.0i 0.154382 0.267398i
\(88\) −43551.0 + 75432.6i −0.599503 + 1.03837i
\(89\) 26802.8 + 46423.8i 0.358678 + 0.621249i 0.987740 0.156106i \(-0.0498942\pi\)
−0.629062 + 0.777355i \(0.716561\pi\)
\(90\) −25909.6 −0.337175
\(91\) 0 0
\(92\) −1068.59 −0.0131626
\(93\) −28758.9 49811.9i −0.344798 0.597208i
\(94\) 10808.7 18721.2i 0.126169 0.218531i
\(95\) −26815.7 + 46446.1i −0.304846 + 0.528008i
\(96\) 19543.2 + 33849.9i 0.216431 + 0.374869i
\(97\) −3110.79 −0.0335693 −0.0167846 0.999859i \(-0.505343\pi\)
−0.0167846 + 0.999859i \(0.505343\pi\)
\(98\) 0 0
\(99\) 110424. 1.13234
\(100\) −12155.9 21054.7i −0.121559 0.210547i
\(101\) 10918.0 18910.4i 0.106497 0.184458i −0.807852 0.589386i \(-0.799370\pi\)
0.914349 + 0.404927i \(0.132703\pi\)
\(102\) 10882.1 18848.4i 0.103565 0.179380i
\(103\) 32670.7 + 56587.3i 0.303435 + 0.525565i 0.976912 0.213644i \(-0.0685332\pi\)
−0.673477 + 0.739208i \(0.735200\pi\)
\(104\) 172710. 1.56579
\(105\) 0 0
\(106\) −33649.5 −0.290880
\(107\) 54478.7 + 94359.8i 0.460010 + 0.796760i 0.998961 0.0455767i \(-0.0145125\pi\)
−0.538951 + 0.842337i \(0.681179\pi\)
\(108\) 34928.3 60497.6i 0.288150 0.499090i
\(109\) −43364.3 + 75109.2i −0.349596 + 0.605518i −0.986178 0.165691i \(-0.947014\pi\)
0.636582 + 0.771209i \(0.280348\pi\)
\(110\) 35719.0 + 61867.2i 0.281461 + 0.487504i
\(111\) 16744.1 0.128989
\(112\) 0 0
\(113\) −101496. −0.747746 −0.373873 0.927480i \(-0.621970\pi\)
−0.373873 + 0.927480i \(0.621970\pi\)
\(114\) 10747.7 + 18615.5i 0.0774556 + 0.134157i
\(115\) −1020.66 + 1767.83i −0.00719674 + 0.0124651i
\(116\) 40073.7 69409.6i 0.276512 0.478933i
\(117\) −109477. 189620.i −0.739366 1.28062i
\(118\) −27748.9 −0.183459
\(119\) 0 0
\(120\) 47538.4 0.301364
\(121\) −71705.6 124198.i −0.445235 0.771170i
\(122\) −54215.3 + 93903.7i −0.329779 + 0.571193i
\(123\) 41780.5 72365.9i 0.249006 0.431292i
\(124\) −105739. 183146.i −0.617564 1.06965i
\(125\) −190165. −1.08857
\(126\) 0 0
\(127\) −3094.61 −0.0170253 −0.00851267 0.999964i \(-0.502710\pi\)
−0.00851267 + 0.999964i \(0.502710\pi\)
\(128\) 86540.5 + 149892.i 0.466868 + 0.808639i
\(129\) −316.830 + 548.766i −0.00167630 + 0.00290344i
\(130\) 70825.4 122673.i 0.367562 0.636636i
\(131\) 126715. + 219478.i 0.645136 + 1.11741i 0.984270 + 0.176671i \(0.0565328\pi\)
−0.339134 + 0.940738i \(0.610134\pi\)
\(132\) −86986.0 −0.434525
\(133\) 0 0
\(134\) −190155. −0.914842
\(135\) −66723.3 115568.i −0.315096 0.545763i
\(136\) 93191.6 161413.i 0.432045 0.748324i
\(137\) 48576.4 84136.9i 0.221118 0.382988i −0.734030 0.679117i \(-0.762363\pi\)
0.955148 + 0.296130i \(0.0956960\pi\)
\(138\) 409.078 + 708.544i 0.00182856 + 0.00316715i
\(139\) −210308. −0.923249 −0.461624 0.887076i \(-0.652733\pi\)
−0.461624 + 0.887076i \(0.652733\pi\)
\(140\) 0 0
\(141\) 50283.2 0.212998
\(142\) 86387.0 + 149627.i 0.359524 + 0.622713i
\(143\) −301851. + 522822.i −1.23439 + 2.13803i
\(144\) 32623.6 56505.8i 0.131107 0.227084i
\(145\) −76552.5 132593.i −0.302370 0.523721i
\(146\) −5209.01 −0.0202243
\(147\) 0 0
\(148\) 61563.7 0.231031
\(149\) −70203.2 121595.i −0.259055 0.448696i 0.706934 0.707279i \(-0.250078\pi\)
−0.965989 + 0.258584i \(0.916744\pi\)
\(150\) −9307.11 + 16120.4i −0.0337743 + 0.0584988i
\(151\) −59847.9 + 103660.i −0.213603 + 0.369971i −0.952839 0.303475i \(-0.901853\pi\)
0.739237 + 0.673446i \(0.235186\pi\)
\(152\) 92040.1 + 159418.i 0.323123 + 0.559666i
\(153\) −236289. −0.816045
\(154\) 0 0
\(155\) −403986. −1.35063
\(156\) 86240.0 + 149372.i 0.283725 + 0.491426i
\(157\) 48808.4 84538.7i 0.158032 0.273720i −0.776127 0.630577i \(-0.782818\pi\)
0.934159 + 0.356857i \(0.116152\pi\)
\(158\) 12.0051 20.7934i 3.82579e−5 6.62647e-5i
\(159\) −39135.3 67784.3i −0.122765 0.212636i
\(160\) 274530. 0.847794
\(161\) 0 0
\(162\) 83411.8 0.249712
\(163\) −91339.0 158204.i −0.269270 0.466389i 0.699404 0.714727i \(-0.253449\pi\)
−0.968673 + 0.248338i \(0.920116\pi\)
\(164\) 153616. 266071.i 0.445992 0.772481i
\(165\) −83084.4 + 143906.i −0.237580 + 0.411501i
\(166\) −133771. 231699.i −0.376784 0.652609i
\(167\) 451674. 1.25324 0.626619 0.779326i \(-0.284438\pi\)
0.626619 + 0.779326i \(0.284438\pi\)
\(168\) 0 0
\(169\) 825757. 2.22400
\(170\) −76432.5 132385.i −0.202841 0.351331i
\(171\) 116685. 202104.i 0.305157 0.528547i
\(172\) −1164.90 + 2017.67i −0.00300240 + 0.00520031i
\(173\) 185824. + 321856.i 0.472047 + 0.817610i 0.999488 0.0319815i \(-0.0101818\pi\)
−0.527441 + 0.849592i \(0.676848\pi\)
\(174\) −61364.2 −0.153653
\(175\) 0 0
\(176\) −179900. −0.437773
\(177\) −32272.7 55897.9i −0.0774287 0.134110i
\(178\) 75451.8 130686.i 0.178492 0.309158i
\(179\) −42501.7 + 73615.1i −0.0991457 + 0.171725i −0.911331 0.411674i \(-0.864944\pi\)
0.812186 + 0.583399i \(0.198278\pi\)
\(180\) −110794. 191900.i −0.254878 0.441462i
\(181\) 379442. 0.860892 0.430446 0.902616i \(-0.358356\pi\)
0.430446 + 0.902616i \(0.358356\pi\)
\(182\) 0 0
\(183\) −252216. −0.556730
\(184\) 3503.23 + 6067.77i 0.00762824 + 0.0132125i
\(185\) 58802.4 101849.i 0.126318 0.218789i
\(186\) −80958.5 + 140224.i −0.171585 + 0.297194i
\(187\) 325748. + 564212.i 0.681204 + 1.17988i
\(188\) 184878. 0.381497
\(189\) 0 0
\(190\) 150976. 0.303406
\(191\) 461098. + 798645.i 0.914555 + 1.58406i 0.807552 + 0.589796i \(0.200792\pi\)
0.107003 + 0.994259i \(0.465875\pi\)
\(192\) 20857.6 36126.4i 0.0408329 0.0707247i
\(193\) −252553. + 437435.i −0.488045 + 0.845319i −0.999905 0.0137498i \(-0.995623\pi\)
0.511860 + 0.859069i \(0.328956\pi\)
\(194\) 4378.55 + 7583.88i 0.00835269 + 0.0144673i
\(195\) 329488. 0.620516
\(196\) 0 0
\(197\) 251505. 0.461723 0.230861 0.972987i \(-0.425846\pi\)
0.230861 + 0.972987i \(0.425846\pi\)
\(198\) −155426. 269206.i −0.281748 0.488002i
\(199\) −104017. + 180162.i −0.186196 + 0.322501i −0.943979 0.330006i \(-0.892949\pi\)
0.757783 + 0.652507i \(0.226283\pi\)
\(200\) −79703.5 + 138050.i −0.140897 + 0.244041i
\(201\) −221156. 383053.i −0.386107 0.668757i
\(202\) −61469.7 −0.105994
\(203\) 0 0
\(204\) 186135. 0.313150
\(205\) −293452. 508274.i −0.487700 0.844720i
\(206\) 91970.5 159297.i 0.151001 0.261542i
\(207\) 4441.25 7692.47i 0.00720409 0.0124779i
\(208\) 178357. + 308923.i 0.285846 + 0.495100i
\(209\) −643446. −1.01893
\(210\) 0 0
\(211\) −640577. −0.990525 −0.495262 0.868744i \(-0.664928\pi\)
−0.495262 + 0.868744i \(0.664928\pi\)
\(212\) −143890. 249225.i −0.219883 0.380849i
\(213\) −200941. + 348040.i −0.303472 + 0.525630i
\(214\) 153361. 265630.i 0.228919 0.396499i
\(215\) 2225.31 + 3854.35i 0.00328318 + 0.00568663i
\(216\) −458032. −0.667977
\(217\) 0 0
\(218\) 244148. 0.347945
\(219\) −6058.22 10493.1i −0.00853561 0.0147841i
\(220\) −305480. + 529107.i −0.425526 + 0.737033i
\(221\) 645909. 1.11875e6i 0.889591 1.54082i
\(222\) −23567.9 40820.8i −0.0320951 0.0555903i
\(223\) −390135. −0.525354 −0.262677 0.964884i \(-0.584605\pi\)
−0.262677 + 0.964884i \(0.584605\pi\)
\(224\) 0 0
\(225\) 202089. 0.266126
\(226\) 142860. + 247440.i 0.186054 + 0.322255i
\(227\) 145676. 252319.i 0.187639 0.325001i −0.756823 0.653620i \(-0.773250\pi\)
0.944463 + 0.328618i \(0.106583\pi\)
\(228\) −91917.5 + 159206.i −0.117101 + 0.202825i
\(229\) −615202. 1.06556e6i −0.775227 1.34273i −0.934667 0.355526i \(-0.884302\pi\)
0.159439 0.987208i \(-0.449031\pi\)
\(230\) 5746.45 0.00716276
\(231\) 0 0
\(232\) −525506. −0.641000
\(233\) −57139.3 98968.1i −0.0689517 0.119428i 0.829488 0.558524i \(-0.188632\pi\)
−0.898440 + 0.439096i \(0.855299\pi\)
\(234\) −308187. + 533795.i −0.367938 + 0.637287i
\(235\) 176586. 305856.i 0.208587 0.361283i
\(236\) −118658. 205522.i −0.138681 0.240203i
\(237\) 55.8489 6.45867e−5
\(238\) 0 0
\(239\) −1.14782e6 −1.29981 −0.649906 0.760014i \(-0.725192\pi\)
−0.649906 + 0.760014i \(0.725192\pi\)
\(240\) 49092.7 + 85031.1i 0.0550160 + 0.0952905i
\(241\) 406354. 703825.i 0.450673 0.780589i −0.547755 0.836639i \(-0.684517\pi\)
0.998428 + 0.0560501i \(0.0178507\pi\)
\(242\) −201856. + 349626.i −0.221567 + 0.383764i
\(243\) 449552. + 778647.i 0.488387 + 0.845912i
\(244\) −927332. −0.997150
\(245\) 0 0
\(246\) −235230. −0.247831
\(247\) 637928. + 1.10492e6i 0.665318 + 1.15236i
\(248\) −693306. + 1.20084e6i −0.715806 + 1.23981i
\(249\) 311159. 538944.i 0.318042 0.550865i
\(250\) 267664. + 463608.i 0.270857 + 0.469138i
\(251\) 406772. 0.407537 0.203768 0.979019i \(-0.434681\pi\)
0.203768 + 0.979019i \(0.434681\pi\)
\(252\) 0 0
\(253\) −24490.8 −0.0240548
\(254\) 4355.77 + 7544.41i 0.00423624 + 0.00733738i
\(255\) 177786. 307935.i 0.171217 0.296557i
\(256\) 345548. 598507.i 0.329540 0.570781i
\(257\) −848562. 1.46975e6i −0.801403 1.38807i −0.918693 0.394973i \(-0.870754\pi\)
0.117290 0.993098i \(-0.462579\pi\)
\(258\) 1783.80 0.00166839
\(259\) 0 0
\(260\) 1.21144e6 1.11140
\(261\) 333107. + 576959.i 0.302679 + 0.524256i
\(262\) 356713. 617846.i 0.321045 0.556067i
\(263\) −102847. + 178136.i −0.0916859 + 0.158805i −0.908221 0.418492i \(-0.862559\pi\)
0.816535 + 0.577296i \(0.195892\pi\)
\(264\) 285173. + 493934.i 0.251825 + 0.436173i
\(265\) −549746. −0.480892
\(266\) 0 0
\(267\) 351010. 0.301330
\(268\) −813133. 1.40839e6i −0.691551 1.19780i
\(269\) 867123. 1.50190e6i 0.730635 1.26550i −0.225978 0.974132i \(-0.572558\pi\)
0.956612 0.291364i \(-0.0941090\pi\)
\(270\) −187831. + 325333.i −0.156804 + 0.271593i
\(271\) 184521. + 319600.i 0.152624 + 0.264352i 0.932191 0.361966i \(-0.117894\pi\)
−0.779567 + 0.626318i \(0.784561\pi\)
\(272\) 384954. 0.315491
\(273\) 0 0
\(274\) −273492. −0.220074
\(275\) −278601. 482550.i −0.222152 0.384779i
\(276\) −3498.56 + 6059.69i −0.00276450 + 0.00478826i
\(277\) −613835. + 1.06319e6i −0.480676 + 0.832554i −0.999754 0.0221720i \(-0.992942\pi\)
0.519079 + 0.854727i \(0.326275\pi\)
\(278\) 296016. + 512715.i 0.229722 + 0.397891i
\(279\) 1.75789e6 1.35201
\(280\) 0 0
\(281\) 2.00671e6 1.51607 0.758035 0.652214i \(-0.226159\pi\)
0.758035 + 0.652214i \(0.226159\pi\)
\(282\) −70775.4 122587.i −0.0529980 0.0917953i
\(283\) −892905. + 1.54656e6i −0.662734 + 1.14789i 0.317160 + 0.948372i \(0.397271\pi\)
−0.979894 + 0.199517i \(0.936063\pi\)
\(284\) −738808. + 1.27965e6i −0.543545 + 0.941448i
\(285\) 175589. + 304130.i 0.128052 + 0.221793i
\(286\) 1.69947e6 1.22856
\(287\) 0 0
\(288\) −1.19458e6 −0.848660
\(289\) 12885.4 + 22318.1i 0.00907513 + 0.0157186i
\(290\) −215501. + 373258.i −0.150471 + 0.260624i
\(291\) −10184.8 + 17640.5i −0.00705047 + 0.0122118i
\(292\) −22274.5 38580.6i −0.0152880 0.0264796i
\(293\) −853248. −0.580639 −0.290319 0.956930i \(-0.593762\pi\)
−0.290319 + 0.956930i \(0.593762\pi\)
\(294\) 0 0
\(295\) −453345. −0.303301
\(296\) −201829. 349578.i −0.133892 0.231908i
\(297\) 800518. 1.38654e6i 0.526599 0.912096i
\(298\) −197627. + 342300.i −0.128916 + 0.223289i
\(299\) 24280.8 + 42055.6i 0.0157067 + 0.0272048i
\(300\) −159194. −0.102123
\(301\) 0 0
\(302\) 336952. 0.212594
\(303\) −71490.9 123826.i −0.0447347 0.0774827i
\(304\) −190099. + 329261.i −0.117977 + 0.204341i
\(305\) −885739. + 1.53414e6i −0.545200 + 0.944315i
\(306\) 332585. + 576054.i 0.203048 + 0.351690i
\(307\) 1.96068e6 1.18730 0.593652 0.804722i \(-0.297686\pi\)
0.593652 + 0.804722i \(0.297686\pi\)
\(308\) 0 0
\(309\) 427857. 0.254919
\(310\) 568625. + 984888.i 0.336064 + 0.582080i
\(311\) 431802. 747903.i 0.253153 0.438474i −0.711239 0.702950i \(-0.751866\pi\)
0.964392 + 0.264476i \(0.0851990\pi\)
\(312\) 565454. 979396.i 0.328860 0.569602i
\(313\) 550235. + 953035.i 0.317459 + 0.549855i 0.979957 0.199209i \(-0.0638372\pi\)
−0.662498 + 0.749063i \(0.730504\pi\)
\(314\) −274799. −0.157286
\(315\) 0 0
\(316\) 205.342 0.000115680
\(317\) −747954. 1.29549e6i −0.418048 0.724081i 0.577695 0.816253i \(-0.303952\pi\)
−0.995743 + 0.0921719i \(0.970619\pi\)
\(318\) −110169. + 190818.i −0.0610929 + 0.105816i
\(319\) 918444. 1.59079e6i 0.505331 0.875259i
\(320\) −146496. 253739.i −0.0799746 0.138520i
\(321\) 713454. 0.386459
\(322\) 0 0
\(323\) 1.37686e6 0.734318
\(324\) 356682. + 617791.i 0.188764 + 0.326948i
\(325\) −552423. + 956824.i −0.290110 + 0.502486i
\(326\) −257126. + 445355.i −0.133999 + 0.232093i
\(327\) 283950. + 491816.i 0.146850 + 0.254351i
\(328\) −2.01445e6 −1.03388
\(329\) 0 0
\(330\) 467777. 0.236458
\(331\) 1.37008e6 + 2.37304e6i 0.687345 + 1.19052i 0.972694 + 0.232093i \(0.0745573\pi\)
−0.285348 + 0.958424i \(0.592109\pi\)
\(332\) 1.14405e6 1.98156e6i 0.569640 0.986646i
\(333\) −255870. + 443180.i −0.126447 + 0.219013i
\(334\) −635747. 1.10115e6i −0.311830 0.540106i
\(335\) −3.10665e6 −1.51245
\(336\) 0 0
\(337\) −2.31353e6 −1.10968 −0.554842 0.831956i \(-0.687221\pi\)
−0.554842 + 0.831956i \(0.687221\pi\)
\(338\) −1.16228e6 2.01313e6i −0.553376 0.958475i
\(339\) −332300. + 575560.i −0.157047 + 0.272014i
\(340\) 653674. 1.13220e6i 0.306665 0.531159i
\(341\) −2.42343e6 4.19750e6i −1.12861 1.95481i
\(342\) −656951. −0.303716
\(343\) 0 0
\(344\) 15276.0 0.00696006
\(345\) 6683.29 + 11575.8i 0.00302303 + 0.00523604i
\(346\) 523107. 906048.i 0.234909 0.406875i
\(347\) 1.52963e6 2.64940e6i 0.681966 1.18120i −0.292414 0.956292i \(-0.594459\pi\)
0.974380 0.224908i \(-0.0722081\pi\)
\(348\) −262403. 454495.i −0.116150 0.201178i
\(349\) 210232. 0.0923921 0.0461961 0.998932i \(-0.485290\pi\)
0.0461961 + 0.998932i \(0.485290\pi\)
\(350\) 0 0
\(351\) −3.17461e6 −1.37538
\(352\) 1.64685e6 + 2.85243e6i 0.708430 + 1.22704i
\(353\) −1.88395e6 + 3.26310e6i −0.804697 + 1.39378i 0.111798 + 0.993731i \(0.464339\pi\)
−0.916495 + 0.400045i \(0.868994\pi\)
\(354\) −90850.0 + 157357.i −0.0385316 + 0.0667386i
\(355\) 1.41134e6 + 2.44451e6i 0.594376 + 1.02949i
\(356\) 1.29057e6 0.539707
\(357\) 0 0
\(358\) 239291. 0.0986776
\(359\) −503608. 872275.i −0.206232 0.357205i 0.744292 0.667854i \(-0.232787\pi\)
−0.950525 + 0.310649i \(0.899454\pi\)
\(360\) −726446. + 1.25824e6i −0.295425 + 0.511691i
\(361\) 558124. 966700.i 0.225405 0.390412i
\(362\) −534078. 925050.i −0.214207 0.371017i
\(363\) −939058. −0.374047
\(364\) 0 0
\(365\) −85101.8 −0.0334354
\(366\) 355003. + 614883.i 0.138525 + 0.239933i
\(367\) −763248. + 1.32198e6i −0.295802 + 0.512343i −0.975171 0.221453i \(-0.928920\pi\)
0.679369 + 0.733796i \(0.262253\pi\)
\(368\) −7235.54 + 12532.3i −0.00278517 + 0.00482405i
\(369\) 1.27691e6 + 2.21168e6i 0.488198 + 0.845583i
\(370\) −331066. −0.125722
\(371\) 0 0
\(372\) −1.38476e6 −0.518822
\(373\) −2.43149e6 4.21146e6i −0.904898 1.56733i −0.821054 0.570850i \(-0.806614\pi\)
−0.0838438 0.996479i \(-0.526720\pi\)
\(374\) 917004. 1.58830e6i 0.338994 0.587155i
\(375\) −622601. + 1.07838e6i −0.228629 + 0.395997i
\(376\) −606101. 1.04980e6i −0.221093 0.382945i
\(377\) −3.64227e6 −1.31983
\(378\) 0 0
\(379\) 630878. 0.225604 0.112802 0.993617i \(-0.464017\pi\)
0.112802 + 0.993617i \(0.464017\pi\)
\(380\) 645597. + 1.11821e6i 0.229352 + 0.397249i
\(381\) −10131.8 + 17548.7i −0.00357579 + 0.00619346i
\(382\) 1.29802e6 2.24824e6i 0.455118 0.788288i
\(383\) 282822. + 489862.i 0.0985182 + 0.170639i 0.911072 0.412248i \(-0.135256\pi\)
−0.812553 + 0.582887i \(0.801923\pi\)
\(384\) 1.13334e6 0.392221
\(385\) 0 0
\(386\) 1.42191e6 0.485741
\(387\) −9683.12 16771.7i −0.00328653 0.00569244i
\(388\) −37446.7 + 64859.7i −0.0126280 + 0.0218723i
\(389\) −296106. + 512870.i −0.0992140 + 0.171844i −0.911360 0.411611i \(-0.864966\pi\)
0.812146 + 0.583455i \(0.198300\pi\)
\(390\) −463766. 803266.i −0.154396 0.267423i
\(391\) 52406.1 0.0173356
\(392\) 0 0
\(393\) 1.65947e6 0.541986
\(394\) −354003. 613151.i −0.114886 0.198988i
\(395\) 196.132 339.710i 6.32492e−5 0.000109551i
\(396\) 1.32925e6 2.30233e6i 0.425961 0.737786i
\(397\) 671558. + 1.16317e6i 0.213849 + 0.370397i 0.952916 0.303235i \(-0.0980666\pi\)
−0.739067 + 0.673632i \(0.764733\pi\)
\(398\) 585629. 0.185317
\(399\) 0 0
\(400\) −329238. −0.102887
\(401\) 1.84358e6 + 3.19318e6i 0.572534 + 0.991658i 0.996305 + 0.0858884i \(0.0273729\pi\)
−0.423771 + 0.905769i \(0.639294\pi\)
\(402\) −622569. + 1.07832e6i −0.192142 + 0.332800i
\(403\) −4.80529e6 + 8.32300e6i −1.47386 + 2.55280i
\(404\) −262854. 455276.i −0.0801236 0.138778i
\(405\) 1.36273e6 0.412832
\(406\) 0 0
\(407\) 1.41097e6 0.422214
\(408\) −610220. 1.05693e6i −0.181483 0.314338i
\(409\) 728151. 1.26119e6i 0.215235 0.372798i −0.738110 0.674680i \(-0.764282\pi\)
0.953345 + 0.301882i \(0.0976149\pi\)
\(410\) −826089. + 1.43083e6i −0.242698 + 0.420366i
\(411\) −318079. 550929.i −0.0928818 0.160876i
\(412\) 1.57312e6 0.456582
\(413\) 0 0
\(414\) −25004.9 −0.00717008
\(415\) −2.18548e6 3.78536e6i −0.622911 1.07891i
\(416\) 3.26545e6 5.65593e6i 0.925145 1.60240i
\(417\) −688550. + 1.19260e6i −0.193908 + 0.335858i
\(418\) 905674. + 1.56867e6i 0.253531 + 0.439129i
\(419\) 2.92192e6 0.813080 0.406540 0.913633i \(-0.366735\pi\)
0.406540 + 0.913633i \(0.366735\pi\)
\(420\) 0 0
\(421\) 2.01999e6 0.555450 0.277725 0.960661i \(-0.410420\pi\)
0.277725 + 0.960661i \(0.410420\pi\)
\(422\) 901636. + 1.56168e6i 0.246462 + 0.426885i
\(423\) −768389. + 1.33089e6i −0.208800 + 0.361652i
\(424\) −943454. + 1.63411e6i −0.254863 + 0.441435i
\(425\) 596156. + 1.03257e6i 0.160099 + 0.277299i
\(426\) 1.13133e6 0.302040
\(427\) 0 0
\(428\) 2.62319e6 0.692182
\(429\) 1.97653e6 + 3.42344e6i 0.518513 + 0.898090i
\(430\) 6264.41 10850.3i 0.00163384 0.00282989i
\(431\) 2.71900e6 4.70944e6i 0.705043 1.22117i −0.261633 0.965167i \(-0.584261\pi\)
0.966676 0.256003i \(-0.0824057\pi\)
\(432\) −473008. 819274.i −0.121944 0.211213i
\(433\) 3.77335e6 0.967179 0.483590 0.875295i \(-0.339333\pi\)
0.483590 + 0.875295i \(0.339333\pi\)
\(434\) 0 0
\(435\) −1.00253e6 −0.254025
\(436\) 1.04401e6 + 1.80828e6i 0.263020 + 0.455565i
\(437\) −25879.3 + 44824.3i −0.00648260 + 0.0112282i
\(438\) −17054.3 + 29539.0i −0.00424766 + 0.00735716i
\(439\) 1.17575e6 + 2.03646e6i 0.291175 + 0.504330i 0.974088 0.226170i \(-0.0726205\pi\)
−0.682913 + 0.730500i \(0.739287\pi\)
\(440\) 4.00591e6 0.986439
\(441\) 0 0
\(442\) −3.63656e6 −0.885391
\(443\) −2.40188e6 4.16019e6i −0.581491 1.00717i −0.995303 0.0968092i \(-0.969136\pi\)
0.413812 0.910362i \(-0.364197\pi\)
\(444\) 201560. 349112.i 0.0485229 0.0840441i
\(445\) 1.23269e6 2.13508e6i 0.295089 0.511110i
\(446\) 549129. + 951119.i 0.130718 + 0.226411i
\(447\) −919383. −0.217634
\(448\) 0 0
\(449\) −2.76805e6 −0.647975 −0.323987 0.946061i \(-0.605024\pi\)
−0.323987 + 0.946061i \(0.605024\pi\)
\(450\) −284448. 492679.i −0.0662174 0.114692i
\(451\) 3.52071e6 6.09805e6i 0.815059 1.41172i
\(452\) −1.22178e6 + 2.11619e6i −0.281285 + 0.487201i
\(453\) 391885. + 678765.i 0.0897249 + 0.155408i
\(454\) −820179. −0.186754
\(455\) 0 0
\(456\) 1.20536e6 0.271459
\(457\) −120783. 209203.i −0.0270530 0.0468573i 0.852182 0.523246i \(-0.175279\pi\)
−0.879235 + 0.476388i \(0.841946\pi\)
\(458\) −1.73184e6 + 2.99963e6i −0.385784 + 0.668197i
\(459\) −1.71297e6 + 2.96695e6i −0.379505 + 0.657322i
\(460\) 24572.7 + 42561.2i 0.00541450 + 0.00937819i
\(461\) −990579. −0.217088 −0.108544 0.994092i \(-0.534619\pi\)
−0.108544 + 0.994092i \(0.534619\pi\)
\(462\) 0 0
\(463\) 6.20488e6 1.34518 0.672591 0.740014i \(-0.265181\pi\)
0.672591 + 0.740014i \(0.265181\pi\)
\(464\) −542688. 939963.i −0.117019 0.202682i
\(465\) −1.32265e6 + 2.29090e6i −0.283670 + 0.491331i
\(466\) −160851. + 278602.i −0.0343131 + 0.0594320i
\(467\) −3.44249e6 5.96256e6i −0.730432 1.26515i −0.956699 0.291080i \(-0.905985\pi\)
0.226266 0.974066i \(-0.427348\pi\)
\(468\) −5.27141e6 −1.11253
\(469\) 0 0
\(470\) −994206. −0.207602
\(471\) −319598. 553561.i −0.0663823 0.114978i
\(472\) −778014. + 1.34756e6i −0.160743 + 0.278415i
\(473\) −26698.3 + 46242.8i −0.00548695 + 0.00950368i
\(474\) −78.6093 136.155i −1.60705e−5 2.78348e-5i
\(475\) −1.17758e6 −0.239473
\(476\) 0 0
\(477\) 2.39214e6 0.481383
\(478\) 1.61561e6 + 2.79831e6i 0.323419 + 0.560178i
\(479\) −2.70644e6 + 4.68769e6i −0.538963 + 0.933512i 0.459997 + 0.887921i \(0.347851\pi\)
−0.998960 + 0.0455914i \(0.985483\pi\)
\(480\) 898814. 1.55679e6i 0.178060 0.308409i
\(481\) −1.39887e6 2.42292e6i −0.275686 0.477503i
\(482\) −2.28783e6 −0.448545
\(483\) 0 0
\(484\) −3.45268e6 −0.669950
\(485\) 71534.3 + 123901.i 0.0138089 + 0.0239178i
\(486\) 1.26552e6 2.19195e6i 0.243041 0.420959i
\(487\) 1.50521e6 2.60711e6i 0.287591 0.498122i −0.685643 0.727938i \(-0.740479\pi\)
0.973234 + 0.229815i \(0.0738122\pi\)
\(488\) 3.04014e6 + 5.26568e6i 0.577889 + 1.00093i
\(489\) −1.19618e6 −0.226216
\(490\) 0 0
\(491\) −7.24498e6 −1.35623 −0.678115 0.734956i \(-0.737203\pi\)
−0.678115 + 0.734956i \(0.737203\pi\)
\(492\) −1.00588e6 1.74224e6i −0.187341 0.324485i
\(493\) −1.96531e6 + 3.40402e6i −0.364178 + 0.630775i
\(494\) 1.79581e6 3.11044e6i 0.331088 0.573462i
\(495\) −2.53927e6 4.39814e6i −0.465795 0.806781i
\(496\) −2.86389e6 −0.522700
\(497\) 0 0
\(498\) −1.75187e6 −0.316540
\(499\) 2.56394e6 + 4.44088e6i 0.460953 + 0.798394i 0.999009 0.0445152i \(-0.0141743\pi\)
−0.538056 + 0.842909i \(0.680841\pi\)
\(500\) −2.28914e6 + 3.96491e6i −0.409495 + 0.709265i
\(501\) 1.47878e6 2.56133e6i 0.263215 0.455901i
\(502\) −572546. 991679.i −0.101403 0.175635i
\(503\) −1.05978e7 −1.86766 −0.933830 0.357718i \(-0.883555\pi\)
−0.933830 + 0.357718i \(0.883555\pi\)
\(504\) 0 0
\(505\) −1.00426e6 −0.175233
\(506\) 34471.7 + 59706.8i 0.00598531 + 0.0103669i
\(507\) 2.70354e6 4.68266e6i 0.467103 0.809045i
\(508\) −37251.9 + 64522.1i −0.00640455 + 0.0110930i
\(509\) 4.39420e6 + 7.61097e6i 0.751770 + 1.30210i 0.946964 + 0.321340i \(0.104133\pi\)
−0.195194 + 0.980765i \(0.562534\pi\)
\(510\) −1.00096e6 −0.170409
\(511\) 0 0
\(512\) 3.59310e6 0.605752
\(513\) −1.69180e6 2.93029e6i −0.283829 0.491606i
\(514\) −2.38877e6 + 4.13746e6i −0.398810 + 0.690759i
\(515\) 1.50256e6 2.60251e6i 0.249640 0.432389i
\(516\) 7627.81 + 13211.8i 0.00126118 + 0.00218442i
\(517\) 4.23721e6 0.697194
\(518\) 0 0
\(519\) 2.43355e6 0.396572
\(520\) −3.97156e6 6.87895e6i −0.644099 1.11561i
\(521\) 81066.4 140411.i 0.0130842 0.0226625i −0.859409 0.511288i \(-0.829168\pi\)
0.872493 + 0.488626i \(0.162502\pi\)
\(522\) 937721. 1.62418e6i 0.150625 0.260890i
\(523\) −3.57422e6 6.19073e6i −0.571383 0.989664i −0.996424 0.0844904i \(-0.973074\pi\)
0.425041 0.905174i \(-0.360260\pi\)
\(524\) 6.10144e6 0.970743
\(525\) 0 0
\(526\) 579044. 0.0912530
\(527\) 5.18571e6 + 8.98191e6i 0.813357 + 1.40878i
\(528\) −588993. + 1.02017e6i −0.0919445 + 0.159252i
\(529\) 3.21719e6 5.57233e6i 0.499847 0.865760i
\(530\) 773788. + 1.34024e6i 0.119655 + 0.207249i
\(531\) 1.97267e6 0.303611
\(532\) 0 0
\(533\) −1.39621e7 −2.12879
\(534\) −494060. 855737.i −0.0749767 0.129863i
\(535\) 2.50553e6 4.33971e6i 0.378456 0.655505i
\(536\) −5.33151e6 + 9.23445e6i −0.801564 + 1.38835i
\(537\) 278302. + 482033.i 0.0416467 + 0.0721342i
\(538\) −4.88203e6 −0.727185
\(539\) 0 0
\(540\) −3.21278e6 −0.474129
\(541\) 2.41802e6 + 4.18813e6i 0.355195 + 0.615216i 0.987151 0.159788i \(-0.0510811\pi\)
−0.631956 + 0.775004i \(0.717748\pi\)
\(542\) 519440. 899696.i 0.0759516 0.131552i
\(543\) 1.24230e6 2.15172e6i 0.180811 0.313174i
\(544\) −3.52397e6 6.10369e6i −0.510546 0.884291i
\(545\) 3.98874e6 0.575234
\(546\) 0 0
\(547\) 9.98777e6 1.42725 0.713626 0.700527i \(-0.247052\pi\)
0.713626 + 0.700527i \(0.247052\pi\)
\(548\) −1.16950e6 2.02563e6i −0.166359 0.288143i
\(549\) 3.85417e6 6.67561e6i 0.545757 0.945279i
\(550\) −784281. + 1.35841e6i −0.110552 + 0.191481i
\(551\) −1.94103e6 3.36196e6i −0.272366 0.471751i
\(552\) 45878.4 0.00640856
\(553\) 0 0
\(554\) 3.45598e6 0.478406
\(555\) −385039. 666907.i −0.0530606 0.0919037i
\(556\) −2.53162e6 + 4.38490e6i −0.347305 + 0.601551i
\(557\) −873096. + 1.51225e6i −0.119241 + 0.206531i −0.919467 0.393167i \(-0.871379\pi\)
0.800226 + 0.599698i \(0.204713\pi\)
\(558\) −2.47429e6 4.28560e6i −0.336407 0.582674i
\(559\) 105877. 0.0143309
\(560\) 0 0
\(561\) 4.26600e6 0.572287
\(562\) −2.82452e6 4.89221e6i −0.377228 0.653378i
\(563\) −377609. + 654038.i −0.0502078 + 0.0869625i −0.890037 0.455888i \(-0.849322\pi\)
0.839829 + 0.542851i \(0.182655\pi\)
\(564\) 605293. 1.04840e6i 0.0801250 0.138781i
\(565\) 2.33396e6 + 4.04254e6i 0.307590 + 0.532762i
\(566\) 5.02719e6 0.659605
\(567\) 0 0
\(568\) 9.68836e6 1.26003
\(569\) 2.19767e6 + 3.80648e6i 0.284565 + 0.492882i 0.972504 0.232888i \(-0.0748174\pi\)
−0.687938 + 0.725769i \(0.741484\pi\)
\(570\) 494297. 856148.i 0.0637237 0.110373i
\(571\) −5.80520e6 + 1.00549e7i −0.745121 + 1.29059i 0.205018 + 0.978758i \(0.434275\pi\)
−0.950138 + 0.311829i \(0.899059\pi\)
\(572\) 7.26718e6 + 1.25871e7i 0.928700 + 1.60856i
\(573\) 6.03855e6 0.768327
\(574\) 0 0
\(575\) −44821.1 −0.00565344
\(576\) 637458. + 1.10411e6i 0.0800563 + 0.138662i
\(577\) 5.33214e6 9.23554e6i 0.666748 1.15484i −0.312060 0.950062i \(-0.601019\pi\)
0.978808 0.204779i \(-0.0656477\pi\)
\(578\) 36273.3 62827.2i 0.00451614 0.00782218i
\(579\) 1.65372e6 + 2.86433e6i 0.205006 + 0.355081i
\(580\) −3.68606e6 −0.454980
\(581\) 0 0
\(582\) 57341.7 0.00701719
\(583\) −3.29781e6 5.71197e6i −0.401841 0.696009i
\(584\) −146049. + 252963.i −0.0177201 + 0.0306920i
\(585\) −5.03498e6 + 8.72084e6i −0.608286 + 1.05358i
\(586\) 1.20098e6 + 2.08015e6i 0.144474 + 0.250237i
\(587\) 1.39482e7 1.67079 0.835396 0.549648i \(-0.185238\pi\)
0.835396 + 0.549648i \(0.185238\pi\)
\(588\) 0 0
\(589\) −1.02433e7 −1.21661
\(590\) 638099. + 1.10522e6i 0.0754672 + 0.130713i
\(591\) 823430. 1.42622e6i 0.0969746 0.167965i
\(592\) 416856. 722015.i 0.0488857 0.0846724i
\(593\) 5.89663e6 + 1.02133e7i 0.688600 + 1.19269i 0.972291 + 0.233774i \(0.0751076\pi\)
−0.283691 + 0.958916i \(0.591559\pi\)
\(594\) −4.50703e6 −0.524113
\(595\) 0 0
\(596\) −3.38033e6 −0.389802
\(597\) 681102. + 1.17970e6i 0.0782125 + 0.135468i
\(598\) 68352.3 118390.i 0.00781628 0.0135382i
\(599\) 2.19029e6 3.79369e6i 0.249421 0.432011i −0.713944 0.700203i \(-0.753093\pi\)
0.963365 + 0.268192i \(0.0864262\pi\)
\(600\) 521899. + 903956.i 0.0591846 + 0.102511i
\(601\) −688570. −0.0777610 −0.0388805 0.999244i \(-0.512379\pi\)
−0.0388805 + 0.999244i \(0.512379\pi\)
\(602\) 0 0
\(603\) 1.35181e7 1.51399
\(604\) 1.44086e6 + 2.49564e6i 0.160705 + 0.278349i
\(605\) −3.29781e6 + 5.71198e6i −0.366301 + 0.634451i
\(606\) −201252. + 348579.i −0.0222617 + 0.0385584i
\(607\) −4.68660e6 8.11742e6i −0.516281 0.894224i −0.999821 0.0189023i \(-0.993983\pi\)
0.483541 0.875322i \(-0.339350\pi\)
\(608\) 6.96085e6 0.763666
\(609\) 0 0
\(610\) 4.98684e6 0.542626
\(611\) −4.20087e6 7.27612e6i −0.455236 0.788492i
\(612\) −2.84437e6 + 4.92659e6i −0.306978 + 0.531701i
\(613\) 1.08342e6 1.87655e6i 0.116452 0.201701i −0.801907 0.597449i \(-0.796181\pi\)
0.918359 + 0.395748i \(0.129515\pi\)
\(614\) −2.75974e6 4.78000e6i −0.295424 0.511690i
\(615\) −3.84306e6 −0.409722
\(616\) 0 0
\(617\) −5.07951e6 −0.537166 −0.268583 0.963256i \(-0.586555\pi\)
−0.268583 + 0.963256i \(0.586555\pi\)
\(618\) −602224. 1.04308e6i −0.0634288 0.109862i
\(619\) −1.09517e6 + 1.89689e6i −0.114883 + 0.198983i −0.917733 0.397198i \(-0.869983\pi\)
0.802850 + 0.596181i \(0.203316\pi\)
\(620\) −4.86306e6 + 8.42306e6i −0.508078 + 0.880016i
\(621\) −64393.4 111533.i −0.00670058 0.0116057i
\(622\) −2.43111e6 −0.251958
\(623\) 0 0
\(624\) 2.33577e6 0.240142
\(625\) 2.79509e6 + 4.84124e6i 0.286217 + 0.495743i
\(626\) 1.54895e6 2.68286e6i 0.157980 0.273629i
\(627\) −2.10665e6 + 3.64882e6i −0.214005 + 0.370667i
\(628\) −1.17508e6 2.03530e6i −0.118896 0.205935i
\(629\) −3.01923e6 −0.304278
\(630\) 0 0
\(631\) −7.18693e6 −0.718572 −0.359286 0.933228i \(-0.616980\pi\)
−0.359286 + 0.933228i \(0.616980\pi\)
\(632\) −673.188 1166.00i −6.70415e−5 0.000116119i
\(633\) −2.09725e6 + 3.63255e6i −0.208038 + 0.360332i
\(634\) −2.10554e6 + 3.64691e6i −0.208037 + 0.360331i
\(635\) 71162.1 + 123256.i 0.00700349 + 0.0121304i
\(636\) −1.88439e6 −0.184726
\(637\) 0 0
\(638\) −5.17097e6 −0.502945
\(639\) −6.14125e6 1.06370e7i −0.594983 1.03054i
\(640\) 3.98009e6 6.89371e6i 0.384098 0.665278i
\(641\) 8.82500e6 1.52854e7i 0.848340 1.46937i −0.0343490 0.999410i \(-0.510936\pi\)
0.882689 0.469958i \(-0.155731\pi\)
\(642\) −1.00421e6 1.73935e6i −0.0961586 0.166552i
\(643\) −898309. −0.0856837 −0.0428419 0.999082i \(-0.513641\pi\)
−0.0428419 + 0.999082i \(0.513641\pi\)
\(644\) 0 0
\(645\) 29142.7 0.00275823
\(646\) −1.93798e6 3.35669e6i −0.182713 0.316468i
\(647\) −693210. + 1.20068e6i −0.0651035 + 0.112763i −0.896740 0.442558i \(-0.854071\pi\)
0.831636 + 0.555321i \(0.187404\pi\)
\(648\) 2.33867e6 4.05070e6i 0.218792 0.378959i
\(649\) −2.71952e6 4.71034e6i −0.253443 0.438976i
\(650\) 3.11022e6 0.288741
\(651\) 0 0
\(652\) −4.39804e6 −0.405173
\(653\) 8.77125e6 + 1.51923e7i 0.804968 + 1.39425i 0.916313 + 0.400464i \(0.131151\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(654\) 799341. 1.38450e6i 0.0730782 0.126575i
\(655\) 5.82778e6 1.00940e7i 0.530762 0.919307i
\(656\) −2.08031e6 3.60320e6i −0.188742 0.326910i
\(657\) 370308. 0.0334696
\(658\) 0 0
\(659\) 9.87522e6 0.885795 0.442898 0.896572i \(-0.353950\pi\)
0.442898 + 0.896572i \(0.353950\pi\)
\(660\) 2.00029e6 + 3.46460e6i 0.178744 + 0.309595i
\(661\) −4.03396e6 + 6.98702e6i −0.359110 + 0.621997i −0.987812 0.155649i \(-0.950253\pi\)
0.628702 + 0.777646i \(0.283586\pi\)
\(662\) 3.85687e6 6.68029e6i 0.342050 0.592448i
\(663\) −4.22942e6 7.32557e6i −0.373677 0.647228i
\(664\) −1.50025e7 −1.32052
\(665\) 0 0
\(666\) 1.44059e6 0.125850
\(667\) −73879.3 127963.i −0.00642996 0.0111370i
\(668\) 5.43710e6 9.41734e6i 0.471440 0.816558i
\(669\) −1.27730e6 + 2.21236e6i −0.110339 + 0.191113i
\(670\) 4.37272e6 + 7.57377e6i 0.376326 + 0.651816i
\(671\) −2.12534e7 −1.82231
\(672\) 0 0
\(673\) −1.12772e7 −0.959762 −0.479881 0.877334i \(-0.659320\pi\)
−0.479881 + 0.877334i \(0.659320\pi\)
\(674\) 3.25637e6 + 5.64020e6i 0.276111 + 0.478239i
\(675\) 1.46504e6 2.53753e6i 0.123763 0.214364i
\(676\) 9.94020e6 1.72169e7i 0.836621 1.44907i
\(677\) 2.60186e6 + 4.50655e6i 0.218179 + 0.377897i 0.954251 0.299006i \(-0.0966551\pi\)
−0.736073 + 0.676903i \(0.763322\pi\)
\(678\) 1.87090e6 0.156306
\(679\) 0 0
\(680\) −8.57196e6 −0.710899
\(681\) −953891. 1.65219e6i −0.0788190 0.136518i
\(682\) −6.82212e6 + 1.18163e7i −0.561640 + 0.972790i
\(683\) −3.02957e6 + 5.24737e6i −0.248502 + 0.430418i −0.963110 0.269107i \(-0.913272\pi\)
0.714608 + 0.699525i \(0.246605\pi\)
\(684\) −2.80922e6 4.86572e6i −0.229586 0.397655i
\(685\) −4.46816e6 −0.363833
\(686\) 0 0
\(687\) −8.05671e6 −0.651277
\(688\) 15775.4 + 27323.8i 0.00127060 + 0.00220075i
\(689\) −6.53906e6 + 1.13260e7i −0.524768 + 0.908924i
\(690\) 18813.9 32586.7i 0.00150438 0.00260566i
\(691\) 3.68249e6 + 6.37826e6i 0.293391 + 0.508168i 0.974609 0.223912i \(-0.0718830\pi\)
−0.681219 + 0.732080i \(0.738550\pi\)
\(692\) 8.94754e6 0.710295
\(693\) 0 0
\(694\) −8.61204e6 −0.678746
\(695\) 4.83614e6 + 8.37644e6i 0.379784 + 0.657806i
\(696\) −1.72051e6 + 2.98001e6i −0.134628 + 0.233182i
\(697\) −7.53370e6 + 1.30488e7i −0.587390 + 1.01739i
\(698\) −295909. 512529.i −0.0229890 0.0398181i
\(699\) −748298. −0.0579271
\(700\) 0 0
\(701\) 7.80919e6 0.600221 0.300110 0.953904i \(-0.402977\pi\)
0.300110 + 0.953904i \(0.402977\pi\)
\(702\) 4.46838e6 + 7.73946e6i 0.342222 + 0.592745i
\(703\) 1.49096e6 2.58243e6i 0.113783 0.197079i
\(704\) 1.75760e6 3.04426e6i 0.133656 0.231499i
\(705\) −1.15629e6 2.00275e6i −0.0876180 0.151759i
\(706\) 1.06069e7 0.800898
\(707\) 0 0
\(708\) −1.55395e6 −0.116508
\(709\) −8.78251e6 1.52118e7i −0.656150 1.13649i −0.981604 0.190927i \(-0.938851\pi\)
0.325454 0.945558i \(-0.394483\pi\)
\(710\) 3.97303e6 6.88149e6i 0.295785 0.512314i
\(711\) −853.439 + 1478.20i −6.33138e−5 + 0.000109663i
\(712\) −4.23099e6 7.32829e6i −0.312782 0.541755i
\(713\) −389879. −0.0287214
\(714\) 0 0
\(715\) 2.77649e7 2.03110
\(716\) 1.02324e6 + 1.77231e6i 0.0745928 + 0.129198i
\(717\) −3.75799e6 + 6.50902e6i −0.272997 + 0.472844i
\(718\) −1.41769e6 + 2.45552e6i −0.102629 + 0.177759i
\(719\) −4.04610e6 7.00805e6i −0.291887 0.505563i 0.682369 0.731008i \(-0.260950\pi\)
−0.974256 + 0.225445i \(0.927616\pi\)
\(720\) −3.00079e6 −0.215727
\(721\) 0 0
\(722\) −3.14232e6 −0.224341
\(723\) −2.66081e6 4.60866e6i −0.189308 0.327890i
\(724\) 4.56760e6 7.91131e6i 0.323848 0.560922i
\(725\) 1.68086e6 2.91133e6i 0.118764 0.205706i
\(726\) 1.32176e6 + 2.28935e6i 0.0930702 + 0.161202i
\(727\) −1.51986e7 −1.06652 −0.533258 0.845952i \(-0.679033\pi\)
−0.533258 + 0.845952i \(0.679033\pi\)
\(728\) 0 0
\(729\) −1.31285e6 −0.0914944
\(730\) 119784. + 207472.i 0.00831938 + 0.0144096i
\(731\) 57129.7 98951.6i 0.00395429 0.00684903i
\(732\) −3.03609e6 + 5.25866e6i −0.209429 + 0.362742i
\(733\) 2.91701e6 + 5.05241e6i 0.200530 + 0.347327i 0.948699 0.316180i \(-0.102400\pi\)
−0.748170 + 0.663507i \(0.769067\pi\)
\(734\) 4.29720e6 0.294405
\(735\) 0 0
\(736\) 264944. 0.0180285
\(737\) −1.86361e7 3.22787e7i −1.26382 2.18901i
\(738\) 3.59461e6 6.22604e6i 0.242946 0.420796i
\(739\) −3.23860e6 + 5.60941e6i −0.218145 + 0.377838i −0.954241 0.299039i \(-0.903334\pi\)
0.736096 + 0.676877i \(0.236667\pi\)
\(740\) −1.41569e6 2.45205e6i −0.0950361 0.164607i
\(741\) 8.35433e6 0.558941
\(742\) 0 0
\(743\) −1.50899e7 −1.00280 −0.501401 0.865215i \(-0.667182\pi\)
−0.501401 + 0.865215i \(0.667182\pi\)
\(744\) 4.53978e6 + 7.86312e6i 0.300678 + 0.520790i
\(745\) −3.22872e6 + 5.59230e6i −0.213127 + 0.369148i
\(746\) −6.84481e6 + 1.18556e7i −0.450313 + 0.779965i
\(747\) 9.50979e6 + 1.64714e7i 0.623548 + 1.08002i
\(748\) 1.56850e7 1.02502
\(749\) 0 0
\(750\) 3.50534e6 0.227550
\(751\) 1.06998e6 + 1.85327e6i 0.0692273 + 0.119905i 0.898561 0.438848i \(-0.144613\pi\)
−0.829334 + 0.558753i \(0.811280\pi\)
\(752\) 1.25184e6 2.16824e6i 0.0807240 0.139818i
\(753\) 1.33177e6 2.30670e6i 0.0855940 0.148253i
\(754\) 5.12663e6 + 8.87958e6i 0.328400 + 0.568806i
\(755\) 5.50494e6 0.351467
\(756\) 0 0
\(757\) 2.10943e7 1.33791 0.668954 0.743304i \(-0.266742\pi\)
0.668954 + 0.743304i \(0.266742\pi\)
\(758\) −887984. 1.53803e6i −0.0561348 0.0972283i
\(759\) −80183.2 + 138881.i −0.00505218 + 0.00875063i
\(760\) 4.23302e6 7.33181e6i 0.265838 0.460444i
\(761\) 4.89979e6 + 8.48669e6i 0.306701 + 0.531222i 0.977639 0.210292i \(-0.0674414\pi\)
−0.670937 + 0.741514i \(0.734108\pi\)
\(762\) 57043.3 0.00355891
\(763\) 0 0
\(764\) 2.22022e7 1.37614
\(765\) 5.43358e6 + 9.41124e6i 0.335686 + 0.581424i
\(766\) 796165. 1.37900e6i 0.0490265 0.0849164i
\(767\) −5.39239e6 + 9.33990e6i −0.330973 + 0.573263i
\(768\) −2.26265e6 3.91903e6i −0.138425 0.239759i
\(769\) 3.23493e7 1.97265 0.986323 0.164825i \(-0.0527060\pi\)
0.986323 + 0.164825i \(0.0527060\pi\)
\(770\) 0 0
\(771\) −1.11128e7 −0.673267
\(772\) 6.08031e6 + 1.05314e7i 0.367183 + 0.635980i
\(773\) 4.59856e6 7.96495e6i 0.276805 0.479440i −0.693784 0.720183i \(-0.744058\pi\)
0.970589 + 0.240743i \(0.0773912\pi\)
\(774\) −27258.7 + 47213.4i −0.00163551