Properties

Label 49.6.c.h.30.1
Level $49$
Weight $6$
Character 49.30
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 30.1
Root \(-4.10797 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 49.30
Dual form 49.6.c.h.18.1

$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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 −0.963199 0.268791i \(-0.913376\pi\)
0.714379 + 0.699759i \(0.246709\pi\)
\(3\) −3.27401 5.67075i −0.210028 0.363779i 0.741695 0.670737i \(-0.234022\pi\)
−0.951723 + 0.306958i \(0.900689\pi\)
\(4\) 12.0377 + 20.8499i 0.376178 + 0.651559i
\(5\) 22.9955 39.8294i 0.411356 0.712490i −0.583682 0.811982i \(-0.698388\pi\)
0.995038 + 0.0994921i \(0.0317218\pi\)
\(6\) 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 0.972653 + 0.232263i \(0.0746129\pi\)
−0.285181 + 0.958474i \(0.592054\pi\)
\(12\) 78.8229 136.525i 0.158015 0.273691i
\(13\) 1094.10 1.79555 0.897776 0.440453i \(-0.145182\pi\)
0.897776 + 0.440453i \(0.145182\pi\)
\(14\) 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 \(-0.00167290\pi\)
−0.504545 + 0.863386i \(0.668340\pi\)
\(18\) 281.681 + 487.886i 0.204916 + 0.354925i
\(19\) 583.063 1009.89i 0.370537 0.641789i −0.619111 0.785303i \(-0.712507\pi\)
0.989648 + 0.143514i \(0.0458404\pi\)
\(20\) 1107.25 0.618972
\(21\) 0 0
\(22\) −1553.30 −0.684226
\(23\) −22.1925 + 38.4386i −0.00874757 + 0.0151512i −0.870366 0.492405i \(-0.836118\pi\)
0.861618 + 0.507556i \(0.169451\pi\)
\(24\) 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 −0.905057 0.425290i \(-0.860172\pi\)
0.0842165 0.996447i \(-0.473161\pi\)
\(32\) −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 −0.778987 0.627040i \(-0.784266\pi\)
0.932526 + 0.361103i \(0.117600\pi\)
\(38\) 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 \(-0.701975\pi\)
−0.592794 + 0.805354i \(0.701975\pi\)
\(42\) 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 \(-0.914927\pi\)
0.710961 + 0.703231i \(0.248260\pi\)
\(48\) 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 0.974344 0.225065i \(-0.0722594\pi\)
−0.682084 + 0.731274i \(0.738926\pi\)
\(54\) 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 \(-0.225678\pi\)
−0.943350 + 0.331798i \(0.892345\pi\)
\(60\) −3625.15 6278.94i −0.130001 0.225169i
\(61\) 19258.9 33357.5i 0.662686 1.14781i −0.317221 0.948352i \(-0.602750\pi\)
0.979907 0.199454i \(-0.0639169\pi\)
\(62\) 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 0.800661 + 0.599118i \(0.204482\pi\)
0.118521 + 0.992952i \(0.462185\pi\)
\(68\) −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 \(-0.173135\pi\)
−0.876007 + 0.482299i \(0.839802\pi\)
\(74\) 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 −0.865987 0.500067i \(-0.833309\pi\)
0.866064 + 0.499933i \(0.166642\pi\)
\(80\) 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 \(-0.773405\pi\)
−0.757143 + 0.653249i \(0.773405\pi\)
\(84\) 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 \(-0.950106\pi\)
0.629062 + 0.777355i \(0.283439\pi\)
\(90\) 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 \(-0.494657\pi\)
0.0167846 + 0.999859i \(0.494657\pi\)
\(98\) 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 \(-0.200630\pi\)
−0.914349 + 0.404927i \(0.867297\pi\)
\(102\) 10882.1 + 18848.4i 0.103565 + 0.179380i
\(103\) −32670.7 + 56587.3i −0.303435 + 0.525565i −0.976912 0.213644i \(-0.931467\pi\)
0.673477 + 0.739208i \(0.264800\pi\)
\(104\) −172710. −1.56579
\(105\) 0 0
\(106\) −33649.5 −0.290880
\(107\) 54478.7 94359.8i 0.460010 0.796760i −0.538951 0.842337i \(-0.681179\pi\)
0.998961 + 0.0455767i \(0.0145125\pi\)
\(108\) −34928.3 60497.6i −0.288150 0.499090i
\(109\) −43364.3 75109.2i −0.349596 0.605518i 0.636582 0.771209i \(-0.280348\pi\)
−0.986178 + 0.165691i \(0.947014\pi\)
\(110\) −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 0.339134 + 0.940738i \(0.389866\pi\)
−0.984270 + 0.176671i \(0.943467\pi\)
\(132\) 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 0.955148 0.296130i \(-0.0956960\pi\)
−0.734030 + 0.679117i \(0.762363\pi\)
\(138\) −409.078 + 708.544i −0.00182856 + 0.00316715i
\(139\) 210308. 0.923249 0.461624 0.887076i \(-0.347267\pi\)
0.461624 + 0.887076i \(0.347267\pi\)
\(140\) 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 −0.965989 0.258584i \(-0.916744\pi\)
0.706934 + 0.707279i \(0.250078\pi\)
\(150\) 9307.11 + 16120.4i 0.0337743 + 0.0584988i
\(151\) −59847.9 103660.i −0.213603 0.369971i 0.739237 0.673446i \(-0.235186\pi\)
−0.952839 + 0.303475i \(0.901853\pi\)
\(152\) −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 \(-0.217182\pi\)
−0.934159 + 0.356857i \(0.883848\pi\)
\(158\) 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 −0.968673 0.248338i \(-0.920116\pi\)
0.699404 + 0.714727i \(0.253449\pi\)
\(164\) −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 \(-0.715562\pi\)
−0.626619 + 0.779326i \(0.715562\pi\)
\(168\) 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 \(-0.989818\pi\)
0.527441 + 0.849592i \(0.323152\pi\)
\(174\) 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 0.812186 0.583399i \(-0.198278\pi\)
−0.911331 + 0.411674i \(0.864944\pi\)
\(180\) 110794. 191900.i 0.254878 0.441462i
\(181\) −379442. −0.860892 −0.430446 0.902616i \(-0.641644\pi\)
−0.430446 + 0.902616i \(0.641644\pi\)
\(182\) 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 0.107003 0.994259i \(-0.465875\pi\)
0.807552 0.589796i \(-0.200792\pi\)
\(192\) −20857.6 36126.4i −0.0408329 0.0707247i
\(193\) −252553. 437435.i −0.488045 0.845319i 0.511860 0.859069i \(-0.328956\pi\)
−0.999905 + 0.0137498i \(0.995623\pi\)
\(194\) −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 \(-0.107051\pi\)
−0.757783 + 0.652507i \(0.773717\pi\)
\(200\) −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 \(-0.415395\pi\)
0.262677 + 0.964884i \(0.415395\pi\)
\(224\) 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 \(-0.226750\pi\)
−0.944463 + 0.328618i \(0.893417\pi\)
\(228\) −91917.5 159206.i −0.117101 0.202825i
\(229\) 615202. 1.06556e6i 0.775227 1.34273i −0.159439 0.987208i \(-0.550969\pi\)
0.934667 0.355526i \(-0.115698\pi\)
\(230\) −5746.45 −0.00716276
\(231\) 0 0
\(232\) −525506. −0.641000
\(233\) −57139.3 + 98968.1i −0.0689517 + 0.119428i −0.898440 0.439096i \(-0.855299\pi\)
0.829488 + 0.558524i \(0.188632\pi\)
\(234\) 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 \(-0.315483\pi\)
−0.998428 + 0.0560501i \(0.982149\pi\)
\(242\) −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 \(-0.565319\pi\)
−0.203768 + 0.979019i \(0.565319\pi\)
\(252\) 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 −0.117290 0.993098i \(-0.537421\pi\)
0.918693 0.394973i \(-0.129246\pi\)
\(258\) −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 0.816535 0.577296i \(-0.195892\pi\)
−0.908221 + 0.418492i \(0.862559\pi\)
\(264\) −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 −0.956612 0.291364i \(-0.905891\pi\)
0.225978 0.974132i \(-0.427442\pi\)
\(270\) −187831. 325333.i −0.156804 0.271593i
\(271\) −184521. + 319600.i −0.152624 + 0.264352i −0.932191 0.361966i \(-0.882106\pi\)
0.779567 + 0.626318i \(0.215439\pi\)
\(272\) −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 0.519079 0.854727i \(-0.326275\pi\)
−0.999754 + 0.0221720i \(0.992942\pi\)
\(278\) −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 0.979894 + 0.199517i \(0.0639374\pi\)
−0.317160 + 0.948372i \(0.602729\pi\)
\(284\) −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 \(-0.406238\pi\)
0.290319 + 0.956930i \(0.406238\pi\)
\(294\) 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 \(-0.702314\pi\)
−0.593652 + 0.804722i \(0.702314\pi\)
\(308\) 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 \(-0.248134\pi\)
−0.964392 + 0.264476i \(0.914801\pi\)
\(312\) 565454. + 979396.i 0.328860 + 0.569602i
\(313\) −550235. + 953035.i −0.317459 + 0.549855i −0.979957 0.199209i \(-0.936163\pi\)
0.662498 + 0.749063i \(0.269496\pi\)
\(314\) 274799. 0.157286
\(315\) 0 0
\(316\) 205.342 0.000115680
\(317\) −747954. + 1.29549e6i −0.418048 + 0.724081i −0.995743 0.0921719i \(-0.970619\pi\)
0.577695 + 0.816253i \(0.303952\pi\)
\(318\) 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 −0.285348 0.958424i \(-0.592109\pi\)
0.972694 0.232093i \(-0.0745573\pi\)
\(332\) −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 0.974380 + 0.224908i \(0.0722081\pi\)
−0.292414 + 0.956292i \(0.594459\pi\)
\(348\) 262403. 454495.i 0.116150 0.201178i
\(349\) −210232. −0.0923921 −0.0461961 0.998932i \(-0.514710\pi\)
−0.0461961 + 0.998932i \(0.514710\pi\)
\(350\) 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 0.916495 + 0.400045i \(0.131006\pi\)
−0.111798 + 0.993731i \(0.535661\pi\)
\(354\) −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 −0.950525 0.310649i \(-0.899454\pi\)
0.744292 + 0.667854i \(0.232787\pi\)
\(360\) 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 \(-0.0710799\pi\)
−0.679369 + 0.733796i \(0.737747\pi\)
\(368\) −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 −0.0838438 + 0.996479i \(0.526720\pi\)
−0.821054 + 0.570850i \(0.806614\pi\)
\(374\) −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 \(-0.864744\pi\)
0.812553 + 0.582887i \(0.198077\pi\)
\(384\) −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 0.812146 0.583455i \(-0.198300\pi\)
−0.911360 + 0.411611i \(0.864966\pi\)
\(390\) 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 \(-0.901933\pi\)
0.739067 + 0.673632i \(0.235267\pi\)
\(398\) −585629. −0.185317
\(399\) 0 0
\(400\) −329238. −0.102887
\(401\) 1.84358e6 3.19318e6i 0.572534 0.991658i −0.423771 0.905769i \(-0.639294\pi\)
0.996305 0.0858884i \(-0.0273729\pi\)
\(402\) 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 \(-0.235718\pi\)
−0.953345 + 0.301882i \(0.902385\pi\)
\(410\) −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 \(-0.633265\pi\)
−0.406540 + 0.913633i \(0.633265\pi\)
\(420\) 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 0.966676 + 0.256003i \(0.0824057\pi\)
−0.261633 + 0.965167i \(0.584261\pi\)
\(432\) 473008. 819274.i 0.121944 0.211213i
\(433\) −3.77335e6 −0.967179 −0.483590 0.875295i \(-0.660667\pi\)
−0.483590 + 0.875295i \(0.660667\pi\)
\(434\) 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 \(-0.927379\pi\)
0.682913 + 0.730500i \(0.260713\pi\)
\(440\) −4.00591e6 −0.986439
\(441\) 0 0
\(442\) −3.63656e6 −0.885391
\(443\) −2.40188e6 + 4.16019e6i −0.581491 + 1.00717i 0.413812 + 0.910362i \(0.364197\pi\)
−0.995303 + 0.0968092i \(0.969136\pi\)
\(444\) −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 −0.879235 0.476388i \(-0.841946\pi\)
0.852182 + 0.523246i \(0.175279\pi\)
\(458\) 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 \(-0.465381\pi\)
0.108544 + 0.994092i \(0.465381\pi\)
\(462\) 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 −0.226266 0.974066i \(-0.572652\pi\)
0.956699 0.291080i \(-0.0940147\pi\)
\(468\) 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 0.998960 + 0.0455914i \(0.0145172\pi\)
−0.459997 + 0.887921i \(0.652149\pi\)
\(480\) 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 0.973234 0.229815i \(-0.0738122\pi\)
−0.685643 + 0.727938i \(0.740479\pi\)
\(488\) −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 −0.538056 0.842909i \(-0.680841\pi\)
0.999009 + 0.0445152i \(0.0141743\pi\)
\(500\) 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 \(-0.116445\pi\)
0.933830 + 0.357718i \(0.116445\pi\)
\(504\) 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 0.195194 + 0.980765i \(0.437466\pi\)
−0.946964 + 0.321340i \(0.895867\pi\)
\(510\) 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 \(-0.170832\pi\)
−0.872493 + 0.488626i \(0.837498\pi\)
\(522\) 937721. + 1.62418e6i 0.150625 + 0.260890i
\(523\) 3.57422e6 6.19073e6i 0.571383 0.989664i −0.425041 0.905174i \(-0.639740\pi\)
0.996424 0.0844904i \(-0.0269262\pi\)
\(524\) −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 −0.631956 0.775004i \(-0.717748\pi\)
0.987151 + 0.159788i \(0.0510811\pi\)
\(542\) −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 0.800226 0.599698i \(-0.204713\pi\)
−0.919467 + 0.393167i \(0.871379\pi\)
\(558\) 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 \(-0.150678\pi\)
−0.839829 + 0.542851i \(0.817345\pi\)
\(564\) 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 −0.687938 0.725769i \(-0.741484\pi\)
0.972504 + 0.232888i \(0.0748174\pi\)
\(570\) −494297. 856148.i −0.0637237 0.110373i
\(571\) −5.80520e6 1.00549e7i −0.745121 1.29059i −0.950138 0.311829i \(-0.899059\pi\)
0.205018 0.978758i \(-0.434275\pi\)
\(572\) −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 −0.978808 0.204779i \(-0.934352\pi\)
0.312060 0.950062i \(-0.398981\pi\)
\(578\) 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 \(-0.814762\pi\)
−0.835396 + 0.549648i \(0.814762\pi\)
\(588\) 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 0.283691 + 0.958916i \(0.408441\pi\)
−0.972291 + 0.233774i \(0.924892\pi\)
\(594\) 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 0.963365 0.268192i \(-0.0864262\pi\)
−0.713944 + 0.700203i \(0.753093\pi\)
\(600\) −521899. + 903956.i −0.0591846 + 0.102511i
\(601\) 688570. 0.0777610 0.0388805 0.999244i \(-0.487621\pi\)
0.0388805 + 0.999244i \(0.487621\pi\)
\(602\) 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 −0.483541 0.875322i \(-0.660650\pi\)
0.999821 0.0189023i \(-0.00601715\pi\)
\(608\) −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 0.918359 0.395748i \(-0.129515\pi\)
−0.801907 + 0.597449i \(0.796181\pi\)
\(614\) 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 \(-0.130017\pi\)
−0.802850 + 0.596181i \(0.796684\pi\)
\(620\) −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 0.882689 + 0.469958i \(0.155731\pi\)
−0.0343490 + 0.999410i \(0.510936\pi\)
\(642\) 1.00421e6 1.73935e6i 0.0961586 0.166552i
\(643\) 898309. 0.0856837 0.0428419 0.999082i \(-0.486359\pi\)
0.0428419 + 0.999082i \(0.486359\pi\)
\(644\) 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 \(-0.145929\pi\)
−0.831636 + 0.555321i \(0.812596\pi\)
\(648\) 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 −0.111345 0.993782i \(-0.535516\pi\)
0.916313 0.400464i \(-0.131151\pi\)
\(654\) −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 \(-0.0497468\pi\)
−0.628702 + 0.777646i \(0.716414\pi\)
\(662\) 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 \(-0.903345\pi\)
0.736073 + 0.676903i \(0.236678\pi\)
\(678\) −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 0.714608 0.699525i \(-0.246605\pi\)
−0.963110 + 0.269107i \(0.913272\pi\)
\(684\) 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 \(-0.928117\pi\)
0.681219 + 0.732080i \(0.261450\pi\)
\(692\) −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 0.325454 + 0.945558i \(0.394483\pi\)
−0.981604 + 0.190927i \(0.938851\pi\)
\(710\) −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 \(-0.739050\pi\)
0.974256 + 0.225445i \(0.0723836\pi\)
\(720\) 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 \(-0.320967\pi\)
0.533258 + 0.845952i \(0.320967\pi\)
\(728\) 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 \(-0.897600\pi\)
0.748170 + 0.663507i \(0.230933\pi\)
\(734\) −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 0.736096 0.676877i \(-0.236667\pi\)
−0.954241 + 0.299039i \(0.903334\pi\)
\(740\) 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 −0.829334 0.558753i \(-0.811280\pi\)
0.898561 + 0.438848i \(0.144613\pi\)
\(752\) −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 \(-0.932559\pi\)
0.670937 + 0.741514i \(0.265892\pi\)
\(762\) −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 \(-0.947294\pi\)
−0.986323 + 0.164825i \(0.947294\pi\)
\(770\) 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 \(-0.255942\pi\)
−0.970589 + 0.240743i \(0.922609\pi\)
\(774\) −27258.7 47213.4i −0.00163551