Properties

Label 49.6.c.h.18.1
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 18.1
Root \(-4.10797 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.6.c.h.30.1

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

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

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 −0.951723 0.306958i \(-0.900689\pi\)
0.741695 + 0.670737i \(0.234022\pi\)
\(4\) 12.0377 20.8499i 0.376178 0.651559i
\(5\) 22.9955 + 39.8294i 0.411356 + 0.712490i 0.995038 0.0994921i \(-0.0317218\pi\)
−0.583682 + 0.811982i \(0.698388\pi\)
\(6\) 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 \(-0.145182\pi\)
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 −0.504545 0.863386i \(-0.668340\pi\)
0.999986 + 0.00525555i \(0.00167290\pi\)
\(18\) 281.681 487.886i 0.204916 0.354925i
\(19\) 583.063 + 1009.89i 0.370537 + 0.641789i 0.989648 0.143514i \(-0.0458404\pi\)
−0.619111 + 0.785303i \(0.712507\pi\)
\(20\) 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 \(0.473161\pi\)
−0.905057 + 0.425290i \(0.860172\pi\)
\(32\) −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 \(-0.701975\pi\)
−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 0.710961 0.703231i \(-0.248260\pi\)
−0.964497 + 0.264095i \(0.914927\pi\)
\(48\) 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 −0.943350 0.331798i \(-0.892345\pi\)
0.759021 + 0.651066i \(0.225678\pi\)
\(60\) −3625.15 + 6278.94i −0.130001 + 0.225169i
\(61\) 19258.9 + 33357.5i 0.662686 + 1.14781i 0.979907 + 0.199454i \(0.0639169\pi\)
−0.317221 + 0.948352i \(0.602750\pi\)
\(62\) 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 −0.876007 0.482299i \(-0.839802\pi\)
0.855686 + 0.517495i \(0.173135\pi\)
\(74\) 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 \(-0.773405\pi\)
−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 0.629062 0.777355i \(-0.283439\pi\)
−0.987740 + 0.156106i \(0.950106\pi\)
\(90\) 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 −0.914349 0.404927i \(-0.867297\pi\)
0.807852 + 0.589386i \(0.200630\pi\)
\(102\) 10882.1 18848.4i 0.103565 0.179380i
\(103\) −32670.7 56587.3i −0.303435 0.525565i 0.673477 0.739208i \(-0.264800\pi\)
−0.976912 + 0.213644i \(0.931467\pi\)
\(104\) −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 \(-0.943467\pi\)
0.339134 0.940738i \(-0.389866\pi\)
\(132\) 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 \(-0.347267\pi\)
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 0.706934 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 −0.934159 0.356857i \(-0.883848\pi\)
0.776127 + 0.630577i \(0.217182\pi\)
\(158\) 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 \(-0.715562\pi\)
−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 0.527441 0.849592i \(-0.323152\pi\)
−0.999488 + 0.0319815i \(0.989818\pi\)
\(174\) 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 \(-0.641644\pi\)
−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 0.807552 + 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 −0.757783 0.652507i \(-0.773717\pi\)
0.943979 + 0.330006i \(0.107051\pi\)
\(200\) −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 −0.944463 0.328618i \(-0.893417\pi\)
0.756823 + 0.653620i \(0.226750\pi\)
\(228\) −91917.5 + 159206.i −0.117101 + 0.202825i
\(229\) 615202. + 1.06556e6i 0.775227 + 1.34273i 0.934667 + 0.355526i \(0.115698\pi\)
−0.159439 + 0.987208i \(0.550969\pi\)
\(230\) −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 −0.998428 0.0560501i \(-0.982149\pi\)
0.547755 + 0.836639i \(0.315483\pi\)
\(242\) −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 0.918693 + 0.394973i \(0.129246\pi\)
−0.117290 + 0.993098i \(0.537421\pi\)
\(258\) −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 \(0.427442\pi\)
−0.956612 + 0.291364i \(0.905891\pi\)
\(270\) −187831. + 325333.i −0.156804 + 0.271593i
\(271\) −184521. 319600.i −0.152624 0.264352i 0.779567 0.626318i \(-0.215439\pi\)
−0.932191 + 0.361966i \(0.882106\pi\)
\(272\) −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 \(-0.602729\pi\)
0.979894 0.199517i \(-0.0639374\pi\)
\(284\) −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 −0.964392 0.264476i \(-0.914801\pi\)
0.711239 + 0.702950i \(0.248134\pi\)
\(312\) 565454. 979396.i 0.328860 0.569602i
\(313\) −550235. 953035.i −0.317459 0.549855i 0.662498 0.749063i \(-0.269496\pi\)
−0.979957 + 0.199209i \(0.936163\pi\)
\(314\) 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 \(-0.514710\pi\)
−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 −0.111798 0.993731i \(-0.535661\pi\)
0.916495 0.400045i \(-0.131006\pi\)
\(354\) −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 −0.679369 0.733796i \(-0.737747\pi\)
0.975171 + 0.221453i \(0.0710799\pi\)
\(368\) −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 0.812553 0.582887i \(-0.198077\pi\)
−0.911072 + 0.412248i \(0.864744\pi\)
\(384\) −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 0.739067 0.673632i \(-0.235267\pi\)
−0.952916 + 0.303235i \(0.901933\pi\)
\(398\) −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 −0.953345 0.301882i \(-0.902385\pi\)
0.738110 + 0.674680i \(0.235718\pi\)
\(410\) −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 −0.261633 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 \(-0.660667\pi\)
−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 0.682913 0.730500i \(-0.260713\pi\)
−0.974088 + 0.226170i \(0.927379\pi\)
\(440\) −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 \(-0.465381\pi\)
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 0.956699 + 0.291080i \(0.0940147\pi\)
−0.226266 + 0.974066i \(0.572652\pi\)
\(468\) 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 \(-0.652149\pi\)
0.998960 0.0455914i \(-0.0145172\pi\)
\(480\) 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 \(-0.116445\pi\)
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 −0.946964 0.321340i \(-0.895867\pi\)
0.195194 0.980765i \(-0.437466\pi\)
\(510\) 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 −0.872493 0.488626i \(-0.837498\pi\)
0.859409 + 0.511288i \(0.170832\pi\)
\(522\) 937721. 1.62418e6i 0.150625 0.260890i
\(523\) 3.57422e6 + 6.19073e6i 0.571383 + 0.989664i 0.996424 + 0.0844904i \(0.0269262\pi\)
−0.425041 + 0.905174i \(0.639740\pi\)
\(524\) −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 −0.839829 0.542851i \(-0.817345\pi\)
0.890037 + 0.455888i \(0.150678\pi\)
\(564\) 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 \(0.398981\pi\)
−0.978808 + 0.204779i \(0.934352\pi\)
\(578\) 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 −0.972291 0.233774i \(-0.924892\pi\)
0.283691 0.958916i \(-0.408441\pi\)
\(594\) 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 \(-0.487621\pi\)
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 0.999821 + 0.0189023i \(0.00601715\pi\)
−0.483541 + 0.875322i \(0.660650\pi\)
\(608\) −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 −0.802850 0.596181i \(-0.796684\pi\)
0.917733 + 0.397198i \(0.130017\pi\)
\(620\) −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 \(-0.486359\pi\)
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 −0.831636 0.555321i \(-0.812596\pi\)
0.896740 + 0.442558i \(0.145929\pi\)
\(648\) 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 −0.628702 0.777646i \(-0.716414\pi\)
0.987812 + 0.155649i \(0.0497468\pi\)
\(662\) 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 0.736073 0.676903i \(-0.236678\pi\)
−0.954251 + 0.299006i \(0.903345\pi\)
\(678\) −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 0.681219 0.732080i \(-0.261450\pi\)
−0.974609 + 0.223912i \(0.928117\pi\)
\(692\) −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 0.974256 0.225445i \(-0.0723836\pi\)
−0.682369 + 0.731008i \(0.739050\pi\)
\(720\) 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 0.748170 0.663507i \(-0.230933\pi\)
−0.948699 + 0.316180i \(0.897600\pi\)
\(734\) −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 0.670937 0.741514i \(-0.265892\pi\)
−0.977639 + 0.210292i \(0.932559\pi\)
\(762\) −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 −0.970589 0.240743i \(-0.922609\pi\)
0.693784 + 0.720183i \(0.255942\pi\)
\(774\) −27258.7 + 47213.4i −0.00163551 +