Properties

Label 69.6.c.b.68.16
Level $69$
Weight $6$
Character 69.68
Analytic conductor $11.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 68.16
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.18

$q$-expansion

\(f(q)\) \(=\) \(q-1.27619i q^{2} +(11.5059 + 10.5173i) q^{3} +30.3713 q^{4} +80.0597 q^{5} +(13.4221 - 14.6838i) q^{6} -196.848i q^{7} -79.5978i q^{8} +(21.7727 + 242.023i) q^{9} +O(q^{10})\) \(q-1.27619i q^{2} +(11.5059 + 10.5173i) q^{3} +30.3713 q^{4} +80.0597 q^{5} +(13.4221 - 14.6838i) q^{6} -196.848i q^{7} -79.5978i q^{8} +(21.7727 + 242.023i) q^{9} -102.171i q^{10} -20.8886 q^{11} +(349.450 + 319.425i) q^{12} -791.678 q^{13} -251.216 q^{14} +(921.160 + 842.012i) q^{15} +870.301 q^{16} -174.605 q^{17} +(308.867 - 27.7861i) q^{18} -892.972i q^{19} +2431.52 q^{20} +(2070.32 - 2264.92i) q^{21} +26.6578i q^{22} +(-2039.46 + 1508.96i) q^{23} +(837.154 - 915.846i) q^{24} +3284.55 q^{25} +1010.33i q^{26} +(-2294.91 + 3013.68i) q^{27} -5978.55i q^{28} +5427.01i q^{29} +(1074.57 - 1175.58i) q^{30} +3748.89 q^{31} -3657.80i q^{32} +(-240.343 - 219.692i) q^{33} +222.829i q^{34} -15759.6i q^{35} +(661.265 + 7350.55i) q^{36} +10793.1i q^{37} -1139.60 q^{38} +(-9108.99 - 8326.32i) q^{39} -6372.57i q^{40} +5102.57i q^{41} +(-2890.48 - 2642.12i) q^{42} +10175.5i q^{43} -634.414 q^{44} +(1743.11 + 19376.2i) q^{45} +(1925.72 + 2602.74i) q^{46} +2207.39i q^{47} +(10013.6 + 9153.22i) q^{48} -21942.3 q^{49} -4191.71i q^{50} +(-2008.99 - 1836.37i) q^{51} -24044.3 q^{52} -38439.7 q^{53} +(3846.04 + 2928.75i) q^{54} -1672.33 q^{55} -15668.7 q^{56} +(9391.65 - 10274.5i) q^{57} +6925.91 q^{58} -49618.2i q^{59} +(27976.9 + 25573.0i) q^{60} -28860.1i q^{61} -4784.31i q^{62} +(47641.8 - 4285.92i) q^{63} +23181.6 q^{64} -63381.5 q^{65} +(-280.369 + 306.723i) q^{66} +61124.2i q^{67} -5302.99 q^{68} +(-39336.0 - 4087.65i) q^{69} -20112.3 q^{70} -11772.5i q^{71} +(19264.5 - 1733.06i) q^{72} +48746.9 q^{73} +13774.0 q^{74} +(37791.8 + 34544.6i) q^{75} -27120.7i q^{76} +4111.89i q^{77} +(-10626.0 + 11624.8i) q^{78} -65855.0i q^{79} +69676.0 q^{80} +(-58100.9 + 10539.0i) q^{81} +6511.86 q^{82} -53578.7 q^{83} +(62878.2 - 68788.8i) q^{84} -13978.8 q^{85} +12985.9 q^{86} +(-57077.5 + 62442.8i) q^{87} +1662.69i q^{88} +106893. q^{89} +(24727.8 - 2224.55i) q^{90} +155841. i q^{91} +(-61941.1 + 45829.1i) q^{92} +(43134.5 + 39428.3i) q^{93} +2817.05 q^{94} -71491.0i q^{95} +(38470.2 - 42086.4i) q^{96} -59613.7i q^{97} +28002.6i q^{98} +(-454.800 - 5055.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 408q^{4} - 528q^{6} - 444q^{9} + O(q^{10}) \) \( 32q - 408q^{4} - 528q^{6} - 444q^{9} - 2484q^{12} + 520q^{13} + 4936q^{16} + 7188q^{18} + 18660q^{24} + 36032q^{25} - 22032q^{27} + 6544q^{31} - 33912q^{36} - 63912q^{39} + 54328q^{46} + 88284q^{48} - 207664q^{49} + 46296q^{52} - 38628q^{54} - 139296q^{55} - 184144q^{58} + 486584q^{64} - 113580q^{69} + 37176q^{70} - 15504q^{72} - 93896q^{73} + 249840q^{75} + 368028q^{78} - 339372q^{81} - 23512q^{82} + 259584q^{85} + 509928q^{87} + 82740q^{93} - 562000q^{94} + 1404q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27619i 0.225601i −0.993618 0.112800i \(-0.964018\pi\)
0.993618 0.112800i \(-0.0359821\pi\)
\(3\) 11.5059 + 10.5173i 0.738106 + 0.674685i
\(4\) 30.3713 0.949104
\(5\) 80.0597 1.43215 0.716075 0.698023i \(-0.245937\pi\)
0.716075 + 0.698023i \(0.245937\pi\)
\(6\) 13.4221 14.6838i 0.152210 0.166517i
\(7\) 196.848i 1.51840i −0.650856 0.759201i \(-0.725590\pi\)
0.650856 0.759201i \(-0.274410\pi\)
\(8\) 79.5978i 0.439720i
\(9\) 21.7727 + 242.023i 0.0895995 + 0.995978i
\(10\) 102.171i 0.323095i
\(11\) −20.8886 −0.0520508 −0.0260254 0.999661i \(-0.508285\pi\)
−0.0260254 + 0.999661i \(0.508285\pi\)
\(12\) 349.450 + 319.425i 0.700539 + 0.640347i
\(13\) −791.678 −1.29924 −0.649621 0.760258i \(-0.725073\pi\)
−0.649621 + 0.760258i \(0.725073\pi\)
\(14\) −251.216 −0.342553
\(15\) 921.160 + 842.012i 1.05708 + 0.966251i
\(16\) 870.301 0.849903
\(17\) −174.605 −0.146533 −0.0732663 0.997312i \(-0.523342\pi\)
−0.0732663 + 0.997312i \(0.523342\pi\)
\(18\) 308.867 27.7861i 0.224694 0.0202137i
\(19\) 892.972i 0.567484i −0.958901 0.283742i \(-0.908424\pi\)
0.958901 0.283742i \(-0.0915759\pi\)
\(20\) 2431.52 1.35926
\(21\) 2070.32 2264.92i 1.02444 1.12074i
\(22\) 26.6578i 0.0117427i
\(23\) −2039.46 + 1508.96i −0.803887 + 0.594781i
\(24\) 837.154 915.846i 0.296672 0.324560i
\(25\) 3284.55 1.05106
\(26\) 1010.33i 0.293110i
\(27\) −2294.91 + 3013.68i −0.605838 + 0.795588i
\(28\) 5978.55i 1.44112i
\(29\) 5427.01i 1.19830i 0.800637 + 0.599150i \(0.204495\pi\)
−0.800637 + 0.599150i \(0.795505\pi\)
\(30\) 1074.57 1175.58i 0.217987 0.238478i
\(31\) 3748.89 0.700647 0.350323 0.936629i \(-0.386072\pi\)
0.350323 + 0.936629i \(0.386072\pi\)
\(32\) 3657.80i 0.631459i
\(33\) −240.343 219.692i −0.0384190 0.0351179i
\(34\) 222.829i 0.0330579i
\(35\) 15759.6i 2.17458i
\(36\) 661.265 + 7350.55i 0.0850393 + 0.945287i
\(37\) 10793.1i 1.29611i 0.761596 + 0.648053i \(0.224416\pi\)
−0.761596 + 0.648053i \(0.775584\pi\)
\(38\) −1139.60 −0.128025
\(39\) −9108.99 8326.32i −0.958978 0.876580i
\(40\) 6372.57i 0.629745i
\(41\) 5102.57i 0.474056i 0.971503 + 0.237028i \(0.0761733\pi\)
−0.971503 + 0.237028i \(0.923827\pi\)
\(42\) −2890.48 2642.12i −0.252840 0.231116i
\(43\) 10175.5i 0.839240i 0.907700 + 0.419620i \(0.137837\pi\)
−0.907700 + 0.419620i \(0.862163\pi\)
\(44\) −634.414 −0.0494016
\(45\) 1743.11 + 19376.2i 0.128320 + 1.42639i
\(46\) 1925.72 + 2602.74i 0.134183 + 0.181358i
\(47\) 2207.39i 0.145759i 0.997341 + 0.0728794i \(0.0232188\pi\)
−0.997341 + 0.0728794i \(0.976781\pi\)
\(48\) 10013.6 + 9153.22i 0.627318 + 0.573417i
\(49\) −21942.3 −1.30555
\(50\) 4191.71i 0.237119i
\(51\) −2008.99 1836.37i −0.108157 0.0988634i
\(52\) −24044.3 −1.23312
\(53\) −38439.7 −1.87971 −0.939854 0.341576i \(-0.889039\pi\)
−0.939854 + 0.341576i \(0.889039\pi\)
\(54\) 3846.04 + 2928.75i 0.179485 + 0.136678i
\(55\) −1672.33 −0.0745446
\(56\) −15668.7 −0.667672
\(57\) 9391.65 10274.5i 0.382873 0.418863i
\(58\) 6925.91 0.270338
\(59\) 49618.2i 1.85571i −0.372937 0.927856i \(-0.621649\pi\)
0.372937 0.927856i \(-0.378351\pi\)
\(60\) 27976.9 + 25573.0i 1.00328 + 0.917073i
\(61\) 28860.1i 0.993053i −0.868021 0.496527i \(-0.834608\pi\)
0.868021 0.496527i \(-0.165392\pi\)
\(62\) 4784.31i 0.158067i
\(63\) 47641.8 4285.92i 1.51230 0.136048i
\(64\) 23181.6 0.707445
\(65\) −63381.5 −1.86071
\(66\) −280.369 + 306.723i −0.00792263 + 0.00866736i
\(67\) 61124.2i 1.66351i 0.555140 + 0.831757i \(0.312665\pi\)
−0.555140 + 0.831757i \(0.687335\pi\)
\(68\) −5302.99 −0.139075
\(69\) −39336.0 4087.65i −0.994644 0.103360i
\(70\) −20112.3 −0.490588
\(71\) 11772.5i 0.277154i −0.990352 0.138577i \(-0.955747\pi\)
0.990352 0.138577i \(-0.0442529\pi\)
\(72\) 19264.5 1733.06i 0.437951 0.0393987i
\(73\) 48746.9 1.07063 0.535316 0.844652i \(-0.320193\pi\)
0.535316 + 0.844652i \(0.320193\pi\)
\(74\) 13774.0 0.292403
\(75\) 37791.8 + 34544.6i 0.775790 + 0.709132i
\(76\) 27120.7i 0.538602i
\(77\) 4111.89i 0.0790341i
\(78\) −10626.0 + 11624.8i −0.197757 + 0.216346i
\(79\) 65855.0i 1.18719i −0.804763 0.593596i \(-0.797708\pi\)
0.804763 0.593596i \(-0.202292\pi\)
\(80\) 69676.0 1.21719
\(81\) −58100.9 + 10539.0i −0.983944 + 0.178478i
\(82\) 6511.86 0.106947
\(83\) −53578.7 −0.853683 −0.426842 0.904326i \(-0.640374\pi\)
−0.426842 + 0.904326i \(0.640374\pi\)
\(84\) 62878.2 68788.8i 0.972304 1.06370i
\(85\) −13978.8 −0.209857
\(86\) 12985.9 0.189333
\(87\) −57077.5 + 62442.8i −0.808476 + 0.884472i
\(88\) 1662.69i 0.0228878i
\(89\) 106893. 1.43045 0.715227 0.698892i \(-0.246323\pi\)
0.715227 + 0.698892i \(0.246323\pi\)
\(90\) 24727.8 2224.55i 0.321795 0.0289491i
\(91\) 155841.i 1.97277i
\(92\) −61941.1 + 45829.1i −0.762973 + 0.564510i
\(93\) 43134.5 + 39428.3i 0.517151 + 0.472716i
\(94\) 2817.05 0.0328833
\(95\) 71491.0i 0.812723i
\(96\) 38470.2 42086.4i 0.426036 0.466083i
\(97\) 59613.7i 0.643304i −0.946858 0.321652i \(-0.895762\pi\)
0.946858 0.321652i \(-0.104238\pi\)
\(98\) 28002.6i 0.294533i
\(99\) −454.800 5055.51i −0.00466372 0.0518414i
\(100\) 99756.1 0.997561
\(101\) 8155.58i 0.0795521i 0.999209 + 0.0397760i \(0.0126644\pi\)
−0.999209 + 0.0397760i \(0.987336\pi\)
\(102\) −2343.57 + 2563.86i −0.0223037 + 0.0244002i
\(103\) 54139.3i 0.502828i −0.967880 0.251414i \(-0.919104\pi\)
0.967880 0.251414i \(-0.0808956\pi\)
\(104\) 63015.8i 0.571303i
\(105\) 165749. 181329.i 1.46716 1.60507i
\(106\) 49056.4i 0.424064i
\(107\) 60053.1 0.507079 0.253540 0.967325i \(-0.418405\pi\)
0.253540 + 0.967325i \(0.418405\pi\)
\(108\) −69699.5 + 91529.6i −0.575003 + 0.755096i
\(109\) 152525.i 1.22963i −0.788670 0.614816i \(-0.789230\pi\)
0.788670 0.614816i \(-0.210770\pi\)
\(110\) 2134.22i 0.0168173i
\(111\) −113514. + 124184.i −0.874463 + 0.956662i
\(112\) 171317.i 1.29049i
\(113\) 25828.9 0.190287 0.0951436 0.995464i \(-0.469669\pi\)
0.0951436 + 0.995464i \(0.469669\pi\)
\(114\) −13112.2 11985.6i −0.0944959 0.0863766i
\(115\) −163278. + 120807.i −1.15129 + 0.851817i
\(116\) 164826.i 1.13731i
\(117\) −17237.0 191604.i −0.116412 1.29402i
\(118\) −63322.3 −0.418651
\(119\) 34370.7i 0.222496i
\(120\) 67022.3 73322.3i 0.424880 0.464818i
\(121\) −160615. −0.997291
\(122\) −36831.0 −0.224034
\(123\) −53665.3 + 58709.8i −0.319838 + 0.349903i
\(124\) 113859. 0.664987
\(125\) 12773.4 0.0731192
\(126\) −5469.65 60800.1i −0.0306926 0.341175i
\(127\) 234394. 1.28955 0.644775 0.764373i \(-0.276951\pi\)
0.644775 + 0.764373i \(0.276951\pi\)
\(128\) 146634.i 0.791059i
\(129\) −107019. + 117079.i −0.566223 + 0.619447i
\(130\) 80886.9i 0.419778i
\(131\) 50125.1i 0.255198i 0.991826 + 0.127599i \(0.0407270\pi\)
−0.991826 + 0.127599i \(0.959273\pi\)
\(132\) −7299.52 6672.33i −0.0364636 0.0333305i
\(133\) −175780. −0.861669
\(134\) 78006.3 0.375290
\(135\) −183730. + 241275.i −0.867651 + 1.13940i
\(136\) 13898.2i 0.0644333i
\(137\) −346120. −1.57553 −0.787763 0.615979i \(-0.788761\pi\)
−0.787763 + 0.615979i \(0.788761\pi\)
\(138\) −5216.62 + 50200.3i −0.0233180 + 0.224393i
\(139\) 5881.35 0.0258191 0.0129095 0.999917i \(-0.495891\pi\)
0.0129095 + 0.999917i \(0.495891\pi\)
\(140\) 478641.i 2.06390i
\(141\) −23215.8 + 25398.1i −0.0983413 + 0.107585i
\(142\) −15023.9 −0.0625262
\(143\) 16537.0 0.0676266
\(144\) 18948.8 + 210632.i 0.0761509 + 0.846485i
\(145\) 434485.i 1.71615i
\(146\) 62210.5i 0.241536i
\(147\) −252467. 230774.i −0.963631 0.880833i
\(148\) 327800.i 1.23014i
\(149\) 153793. 0.567505 0.283753 0.958898i \(-0.408421\pi\)
0.283753 + 0.958898i \(0.408421\pi\)
\(150\) 44085.5 48229.6i 0.159981 0.175019i
\(151\) −90252.7 −0.322120 −0.161060 0.986945i \(-0.551491\pi\)
−0.161060 + 0.986945i \(0.551491\pi\)
\(152\) −71078.6 −0.249534
\(153\) −3801.62 42258.4i −0.0131293 0.145943i
\(154\) 5247.56 0.0178302
\(155\) 300135. 1.00343
\(156\) −276652. 252881.i −0.910170 0.831966i
\(157\) 259521.i 0.840280i −0.907459 0.420140i \(-0.861981\pi\)
0.907459 0.420140i \(-0.138019\pi\)
\(158\) −84043.6 −0.267832
\(159\) −442285. 404282.i −1.38742 1.26821i
\(160\) 292842.i 0.904344i
\(161\) 297036. + 401464.i 0.903118 + 1.22062i
\(162\) 13449.7 + 74147.9i 0.0402649 + 0.221979i
\(163\) 223631. 0.659271 0.329635 0.944108i \(-0.393074\pi\)
0.329635 + 0.944108i \(0.393074\pi\)
\(164\) 154972.i 0.449928i
\(165\) −19241.7 17588.4i −0.0550218 0.0502941i
\(166\) 68376.7i 0.192592i
\(167\) 635080.i 1.76213i 0.472998 + 0.881064i \(0.343172\pi\)
−0.472998 + 0.881064i \(0.656828\pi\)
\(168\) −180283. 164793.i −0.492812 0.450468i
\(169\) 255461. 0.688032
\(170\) 17839.7i 0.0473439i
\(171\) 216119. 19442.4i 0.565202 0.0508463i
\(172\) 309044.i 0.796526i
\(173\) 273947.i 0.695907i −0.937512 0.347953i \(-0.886877\pi\)
0.937512 0.347953i \(-0.113123\pi\)
\(174\) 79689.0 + 72841.9i 0.199538 + 0.182393i
\(175\) 646558.i 1.59593i
\(176\) −18179.3 −0.0442381
\(177\) 521849. 570903.i 1.25202 1.36971i
\(178\) 136416.i 0.322712i
\(179\) 100929.i 0.235442i 0.993047 + 0.117721i \(0.0375589\pi\)
−0.993047 + 0.117721i \(0.962441\pi\)
\(180\) 52940.7 + 588483.i 0.121789 + 1.35379i
\(181\) 347500.i 0.788421i −0.919020 0.394211i \(-0.871018\pi\)
0.919020 0.394211i \(-0.128982\pi\)
\(182\) 198883. 0.445060
\(183\) 303530. 332062.i 0.669999 0.732978i
\(184\) 120110. + 162336.i 0.261537 + 0.353485i
\(185\) 864089.i 1.85622i
\(186\) 50318.0 55047.9i 0.106645 0.116670i
\(187\) 3647.25 0.00762714
\(188\) 67041.4i 0.138340i
\(189\) 593239. + 451750.i 1.20802 + 0.919906i
\(190\) −91236.2 −0.183351
\(191\) 869385. 1.72436 0.862182 0.506599i \(-0.169097\pi\)
0.862182 + 0.506599i \(0.169097\pi\)
\(192\) 266725. + 243808.i 0.522169 + 0.477303i
\(193\) 202279. 0.390893 0.195447 0.980714i \(-0.437384\pi\)
0.195447 + 0.980714i \(0.437384\pi\)
\(194\) −76078.5 −0.145130
\(195\) −729263. 666602.i −1.37340 1.25539i
\(196\) −666418. −1.23910
\(197\) 812892.i 1.49234i −0.665757 0.746169i \(-0.731891\pi\)
0.665757 0.746169i \(-0.268109\pi\)
\(198\) −6451.80 + 580.413i −0.0116955 + 0.00105214i
\(199\) 40521.5i 0.0725358i 0.999342 + 0.0362679i \(0.0115470\pi\)
−0.999342 + 0.0362679i \(0.988453\pi\)
\(200\) 261443.i 0.462170i
\(201\) −642862. + 703291.i −1.12235 + 1.22785i
\(202\) 10408.1 0.0179470
\(203\) 1.06830e6 1.81950
\(204\) −61015.8 55773.1i −0.102652 0.0938317i
\(205\) 408510.i 0.678919i
\(206\) −69092.1 −0.113438
\(207\) −409606. 460741.i −0.664417 0.747362i
\(208\) −688998. −1.10423
\(209\) 18652.9i 0.0295380i
\(210\) −231411. 211527.i −0.362105 0.330992i
\(211\) 716481. 1.10789 0.553947 0.832552i \(-0.313121\pi\)
0.553947 + 0.832552i \(0.313121\pi\)
\(212\) −1.16747e6 −1.78404
\(213\) 123815. 135453.i 0.186992 0.204569i
\(214\) 76639.2i 0.114398i
\(215\) 814650.i 1.20192i
\(216\) 239883. + 182670.i 0.349836 + 0.266399i
\(217\) 737964.i 1.06386i
\(218\) −194651. −0.277406
\(219\) 560879. + 512686.i 0.790239 + 0.722340i
\(220\) −50791.0 −0.0707506
\(221\) 138231. 0.190381
\(222\) 158483. + 144865.i 0.215824 + 0.197280i
\(223\) −145527. −0.195966 −0.0979831 0.995188i \(-0.531239\pi\)
−0.0979831 + 0.995188i \(0.531239\pi\)
\(224\) −720032. −0.958809
\(225\) 71513.4 + 794935.i 0.0941740 + 1.04683i
\(226\) 32962.6i 0.0429290i
\(227\) 544805. 0.701740 0.350870 0.936424i \(-0.385886\pi\)
0.350870 + 0.936424i \(0.385886\pi\)
\(228\) 285237. 312049.i 0.363387 0.397545i
\(229\) 1734.50i 0.00218567i 0.999999 + 0.00109284i \(0.000347861\pi\)
−0.999999 + 0.00109284i \(0.999652\pi\)
\(230\) 154172. + 208374.i 0.192171 + 0.259732i
\(231\) −43246.0 + 47311.1i −0.0533231 + 0.0583355i
\(232\) 431978. 0.526917
\(233\) 309502.i 0.373485i −0.982409 0.186742i \(-0.940207\pi\)
0.982409 0.186742i \(-0.0597930\pi\)
\(234\) −244524. + 21997.7i −0.291932 + 0.0262625i
\(235\) 176723.i 0.208749i
\(236\) 1.50697e6i 1.76126i
\(237\) 692617. 757723.i 0.800981 0.876273i
\(238\) 43863.6 0.0501952
\(239\) 1.15098e6i 1.30339i −0.758483 0.651693i \(-0.774059\pi\)
0.758483 0.651693i \(-0.225941\pi\)
\(240\) 801687. + 732803.i 0.898414 + 0.821220i
\(241\) 1.55779e6i 1.72769i 0.503756 + 0.863846i \(0.331951\pi\)
−0.503756 + 0.863846i \(0.668049\pi\)
\(242\) 204975.i 0.224990i
\(243\) −779346. 489804.i −0.846671 0.532117i
\(244\) 876518.i 0.942511i
\(245\) −1.75670e6 −1.86974
\(246\) 74925.0 + 68487.2i 0.0789385 + 0.0721559i
\(247\) 706946.i 0.737300i
\(248\) 298404.i 0.308088i
\(249\) −616472. 563503.i −0.630108 0.575968i
\(250\) 16301.3i 0.0164958i
\(251\) −22290.6 −0.0223325 −0.0111663 0.999938i \(-0.503554\pi\)
−0.0111663 + 0.999938i \(0.503554\pi\)
\(252\) 1.44694e6 130169.i 1.43533 0.129124i
\(253\) 42601.4 31520.0i 0.0418430 0.0309588i
\(254\) 299132.i 0.290924i
\(255\) −160839. 147019.i −0.154896 0.141587i
\(256\) 554677. 0.528982
\(257\) 1.38634e6i 1.30929i 0.755935 + 0.654647i \(0.227183\pi\)
−0.755935 + 0.654647i \(0.772817\pi\)
\(258\) 149415. + 136577.i 0.139748 + 0.127740i
\(259\) 2.12460e6 1.96801
\(260\) −1.92498e6 −1.76601
\(261\) −1.31346e6 + 118161.i −1.19348 + 0.107367i
\(262\) 63969.2 0.0575729
\(263\) −1.66301e6 −1.48254 −0.741269 0.671208i \(-0.765776\pi\)
−0.741269 + 0.671208i \(0.765776\pi\)
\(264\) −17487.0 + 19130.7i −0.0154420 + 0.0168936i
\(265\) −3.07747e6 −2.69203
\(266\) 224329.i 0.194393i
\(267\) 1.22990e6 + 1.12422e6i 1.05583 + 0.965106i
\(268\) 1.85642e6i 1.57885i
\(269\) 1.60222e6i 1.35002i −0.737809 0.675010i \(-0.764139\pi\)
0.737809 0.675010i \(-0.235861\pi\)
\(270\) 307913. + 234474.i 0.257050 + 0.195743i
\(271\) −255594. −0.211411 −0.105705 0.994397i \(-0.533710\pi\)
−0.105705 + 0.994397i \(0.533710\pi\)
\(272\) −151959. −0.124539
\(273\) −1.63902e6 + 1.79309e6i −1.33100 + 1.45612i
\(274\) 441716.i 0.355440i
\(275\) −68609.6 −0.0547083
\(276\) −1.19469e6 124147.i −0.944021 0.0980990i
\(277\) −922483. −0.722369 −0.361184 0.932494i \(-0.617627\pi\)
−0.361184 + 0.932494i \(0.617627\pi\)
\(278\) 7505.74i 0.00582480i
\(279\) 81623.5 + 907317.i 0.0627776 + 0.697828i
\(280\) −1.25443e6 −0.956207
\(281\) −992232. −0.749631 −0.374815 0.927100i \(-0.622294\pi\)
−0.374815 + 0.927100i \(0.622294\pi\)
\(282\) 32412.8 + 29627.8i 0.0242714 + 0.0221859i
\(283\) 292415.i 0.217037i −0.994094 0.108518i \(-0.965389\pi\)
0.994094 0.108518i \(-0.0346106\pi\)
\(284\) 357545.i 0.263048i
\(285\) 751893. 822570.i 0.548332 0.599875i
\(286\) 21104.4i 0.0152566i
\(287\) 1.00443e6 0.719807
\(288\) 885270. 79640.1i 0.628919 0.0565784i
\(289\) −1.38937e6 −0.978528
\(290\) 554486. 0.387164
\(291\) 626975. 685910.i 0.434028 0.474827i
\(292\) 1.48051e6 1.01614
\(293\) 150873. 0.102670 0.0513349 0.998681i \(-0.483652\pi\)
0.0513349 + 0.998681i \(0.483652\pi\)
\(294\) −294512. + 322196.i −0.198717 + 0.217396i
\(295\) 3.97241e6i 2.65766i
\(296\) 859104. 0.569923
\(297\) 47937.4 62951.6i 0.0315343 0.0414110i
\(298\) 196269.i 0.128030i
\(299\) 1.61459e6 1.19461e6i 1.04444 0.772766i
\(300\) 1.14779e6 + 1.04917e6i 0.736305 + 0.673040i
\(301\) 2.00304e6 1.27430
\(302\) 115180.i 0.0726706i
\(303\) −85774.7 + 93837.5i −0.0536726 + 0.0587178i
\(304\) 777154.i 0.482306i
\(305\) 2.31053e6i 1.42220i
\(306\) −53929.8 + 4851.59i −0.0329249 + 0.00296197i
\(307\) 1.91204e6 1.15785 0.578924 0.815382i \(-0.303473\pi\)
0.578924 + 0.815382i \(0.303473\pi\)
\(308\) 124883.i 0.0750116i
\(309\) 569399. 622923.i 0.339251 0.371140i
\(310\) 383030.i 0.226375i
\(311\) 1.82521e6i 1.07007i 0.844829 + 0.535036i \(0.179702\pi\)
−0.844829 + 0.535036i \(0.820298\pi\)
\(312\) −662757. + 725056.i −0.385450 + 0.421682i
\(313\) 2.85121e6i 1.64501i 0.568759 + 0.822504i \(0.307424\pi\)
−0.568759 + 0.822504i \(0.692576\pi\)
\(314\) −331199. −0.189568
\(315\) 3.81419e6 343129.i 2.16584 0.194841i
\(316\) 2.00010e6i 1.12677i
\(317\) 2.10359e6i 1.17575i 0.808953 + 0.587873i \(0.200035\pi\)
−0.808953 + 0.587873i \(0.799965\pi\)
\(318\) −515942. + 564440.i −0.286110 + 0.313004i
\(319\) 113363.i 0.0623725i
\(320\) 1.85591e6 1.01317
\(321\) 690966. + 631596.i 0.374278 + 0.342119i
\(322\) 512345. 379075.i 0.275374 0.203744i
\(323\) 155917.i 0.0831550i
\(324\) −1.76460e6 + 320082.i −0.933865 + 0.169394i
\(325\) −2.60031e6 −1.36558
\(326\) 285397.i 0.148732i
\(327\) 1.60415e6 1.75494e6i 0.829615 0.907598i
\(328\) 406153. 0.208452
\(329\) 434522. 0.221320
\(330\) −22446.2 + 24556.2i −0.0113464 + 0.0124130i
\(331\) 1.56186e6 0.783559 0.391779 0.920059i \(-0.371860\pi\)
0.391779 + 0.920059i \(0.371860\pi\)
\(332\) −1.62726e6 −0.810234
\(333\) −2.61216e6 + 234994.i −1.29089 + 0.116130i
\(334\) 810484. 0.397538
\(335\) 4.89359e6i 2.38240i
\(336\) 1.80180e6 1.97116e6i 0.870678 0.952521i
\(337\) 1.97846e6i 0.948970i −0.880264 0.474485i \(-0.842634\pi\)
0.880264 0.474485i \(-0.157366\pi\)
\(338\) 326018.i 0.155221i
\(339\) 297185. + 271650.i 0.140452 + 0.128384i
\(340\) −424555. −0.199176
\(341\) −78309.1 −0.0364692
\(342\) −24812.2 275810.i −0.0114710 0.127510i
\(343\) 1.01088e6i 0.463943i
\(344\) 809950. 0.369030
\(345\) −3.14923e6 327256.i −1.42448 0.148026i
\(346\) −349609. −0.156997
\(347\) 1.37659e6i 0.613734i −0.951752 0.306867i \(-0.900719\pi\)
0.951752 0.306867i \(-0.0992806\pi\)
\(348\) −1.73352e6 + 1.89647e6i −0.767328 + 0.839456i
\(349\) −1.69269e6 −0.743897 −0.371948 0.928253i \(-0.621310\pi\)
−0.371948 + 0.928253i \(0.621310\pi\)
\(350\) −825133. −0.360042
\(351\) 1.81683e6 2.38587e6i 0.787130 1.03366i
\(352\) 76406.3i 0.0328679i
\(353\) 2.61540e6i 1.11712i −0.829463 0.558561i \(-0.811353\pi\)
0.829463 0.558561i \(-0.188647\pi\)
\(354\) −728582. 665980.i −0.309008 0.282457i
\(355\) 942499.i 0.396927i
\(356\) 3.24648e6 1.35765
\(357\) −361487. + 395467.i −0.150114 + 0.164225i
\(358\) 128805. 0.0531159
\(359\) −3.58025e6 −1.46615 −0.733073 0.680150i \(-0.761915\pi\)
−0.733073 + 0.680150i \(0.761915\pi\)
\(360\) 1.54231e6 138748.i 0.627212 0.0564248i
\(361\) 1.67870e6 0.677962
\(362\) −443476. −0.177869
\(363\) −1.84802e6 1.68923e6i −0.736106 0.672857i
\(364\) 4.73309e6i 1.87237i
\(365\) 3.90266e6 1.53331
\(366\) −423774. 387362.i −0.165361 0.151152i
\(367\) 3.14970e6i 1.22068i 0.792138 + 0.610342i \(0.208968\pi\)
−0.792138 + 0.610342i \(0.791032\pi\)
\(368\) −1.77494e6 + 1.31325e6i −0.683226 + 0.505507i
\(369\) −1.23494e6 + 111097.i −0.472149 + 0.0424752i
\(370\) 1.10274e6 0.418765
\(371\) 7.56680e6i 2.85415i
\(372\) 1.31005e6 + 1.19749e6i 0.490830 + 0.448657i
\(373\) 2.01867e6i 0.751266i 0.926769 + 0.375633i \(0.122575\pi\)
−0.926769 + 0.375633i \(0.877425\pi\)
\(374\) 4654.59i 0.00172069i
\(375\) 146970. + 134342.i 0.0539697 + 0.0493325i
\(376\) 175703. 0.0640930
\(377\) 4.29645e6i 1.55688i
\(378\) 576519. 757087.i 0.207532 0.272531i
\(379\) 1.69715e6i 0.606908i −0.952846 0.303454i \(-0.901860\pi\)
0.952846 0.303454i \(-0.0981399\pi\)
\(380\) 2.17128e6i 0.771359i
\(381\) 2.69693e6 + 2.46520e6i 0.951824 + 0.870040i
\(382\) 1.10950e6i 0.389018i
\(383\) 1.88013e6 0.654924 0.327462 0.944864i \(-0.393807\pi\)
0.327462 + 0.944864i \(0.393807\pi\)
\(384\) 1.54219e6 1.68716e6i 0.533716 0.583885i
\(385\) 329196.i 0.113189i
\(386\) 258147.i 0.0881859i
\(387\) −2.46271e6 + 221549.i −0.835864 + 0.0751954i
\(388\) 1.81055e6i 0.610563i
\(389\) −1.23969e6 −0.415373 −0.207687 0.978195i \(-0.566593\pi\)
−0.207687 + 0.978195i \(0.566593\pi\)
\(390\) −850712. + 930679.i −0.283218 + 0.309841i
\(391\) 356100. 263472.i 0.117796 0.0871549i
\(392\) 1.74656e6i 0.574075i
\(393\) −527181. + 576736.i −0.172178 + 0.188363i
\(394\) −1.03741e6 −0.336673
\(395\) 5.27233e6i 1.70024i
\(396\) −13812.9 153543.i −0.00442636 0.0492029i
\(397\) 556498. 0.177210 0.0886049 0.996067i \(-0.471759\pi\)
0.0886049 + 0.996067i \(0.471759\pi\)
\(398\) 51713.2 0.0163641
\(399\) −2.02251e6 1.84873e6i −0.636003 0.581356i
\(400\) 2.85854e6 0.893295
\(401\) 2.64380e6 0.821047 0.410523 0.911850i \(-0.365346\pi\)
0.410523 + 0.911850i \(0.365346\pi\)
\(402\) 897534. + 820415.i 0.277004 + 0.253203i
\(403\) −2.96792e6 −0.910310
\(404\) 247696.i 0.0755032i
\(405\) −4.65154e6 + 843746.i −1.40916 + 0.255608i
\(406\) 1.36335e6i 0.410482i
\(407\) 225452.i 0.0674633i
\(408\) −146171. + 159911.i −0.0434722 + 0.0475586i
\(409\) −3.94099e6 −1.16492 −0.582461 0.812859i \(-0.697910\pi\)
−0.582461 + 0.812859i \(0.697910\pi\)
\(410\) 521337. 0.153165
\(411\) −3.98243e6 3.64025e6i −1.16290 1.06298i
\(412\) 1.64428e6i 0.477236i
\(413\) −9.76726e6 −2.81772
\(414\) −587994. + 522736.i −0.168606 + 0.149893i
\(415\) −4.28949e6 −1.22260
\(416\) 2.89580e6i 0.820418i
\(417\) 67670.4 + 61856.0i 0.0190572 + 0.0174197i
\(418\) 23804.7 0.00666380
\(419\) 2.63743e6 0.733917 0.366958 0.930237i \(-0.380399\pi\)
0.366958 + 0.930237i \(0.380399\pi\)
\(420\) 5.03401e6 5.50721e6i 1.39249 1.52338i
\(421\) 599700.i 0.164903i 0.996595 + 0.0824515i \(0.0262750\pi\)
−0.996595 + 0.0824515i \(0.973725\pi\)
\(422\) 914367.i 0.249942i
\(423\) −534239. + 48060.8i −0.145172 + 0.0130599i
\(424\) 3.05972e6i 0.826545i
\(425\) −573499. −0.154014
\(426\) −172864. 158011.i −0.0461510 0.0421855i
\(427\) −5.68106e6 −1.50786
\(428\) 1.82389e6 0.481271
\(429\) 190274. + 173925.i 0.0499156 + 0.0456267i
\(430\) 1.03965e6 0.271154
\(431\) 6.87699e6 1.78322 0.891610 0.452804i \(-0.149576\pi\)
0.891610 + 0.452804i \(0.149576\pi\)
\(432\) −1.99726e6 + 2.62281e6i −0.514903 + 0.676173i
\(433\) 6.73591e6i 1.72654i 0.504743 + 0.863270i \(0.331587\pi\)
−0.504743 + 0.863270i \(0.668413\pi\)
\(434\) −941784. −0.240009
\(435\) −4.56961e6 + 4.99915e6i −1.15786 + 1.26670i
\(436\) 4.63239e6i 1.16705i
\(437\) 1.34746e6 + 1.82118e6i 0.337529 + 0.456193i
\(438\) 654286. 715789.i 0.162961 0.178279i
\(439\) 1.75564e6 0.434784 0.217392 0.976084i \(-0.430245\pi\)
0.217392 + 0.976084i \(0.430245\pi\)
\(440\) 133114.i 0.0327787i
\(441\) −477743. 5.31054e6i −0.116976 1.30030i
\(442\) 176409.i 0.0429503i
\(443\) 7.53505e6i 1.82422i −0.409946 0.912110i \(-0.634453\pi\)
0.409946 0.912110i \(-0.365547\pi\)
\(444\) −3.44757e6 + 3.77164e6i −0.829957 + 0.907972i
\(445\) 8.55781e6 2.04863
\(446\) 185720.i 0.0442102i
\(447\) 1.76953e6 + 1.61748e6i 0.418879 + 0.382887i
\(448\) 4.56326e6i 1.07419i
\(449\) 5.86864e6i 1.37379i 0.726755 + 0.686897i \(0.241028\pi\)
−0.726755 + 0.686897i \(0.758972\pi\)
\(450\) 1.01449e6 91264.8i 0.236165 0.0212458i
\(451\) 106585.i 0.0246750i
\(452\) 784458. 0.180602
\(453\) −1.03844e6 949215.i −0.237759 0.217330i
\(454\) 695275.i 0.158313i
\(455\) 1.24765e7i 2.82531i
\(456\) −817825. 747555.i −0.184182 0.168357i
\(457\) 5.34684e6i 1.19759i 0.800904 + 0.598793i \(0.204353\pi\)
−0.800904 + 0.598793i \(0.795647\pi\)
\(458\) 2213.55 0.000493090
\(459\) 400703. 526204.i 0.0887750 0.116580i
\(460\) −4.95898e6 + 3.66906e6i −1.09269 + 0.808463i
\(461\) 5.80691e6i 1.27260i −0.771441 0.636301i \(-0.780464\pi\)
0.771441 0.636301i \(-0.219536\pi\)
\(462\) 60378.0 + 55190.1i 0.0131605 + 0.0120297i
\(463\) −4.53602e6 −0.983383 −0.491691 0.870769i \(-0.663621\pi\)
−0.491691 + 0.870769i \(0.663621\pi\)
\(464\) 4.72313e6i 1.01844i
\(465\) 3.45333e6 + 3.15661e6i 0.740638 + 0.677000i
\(466\) −394983. −0.0842586
\(467\) 2.16503e6 0.459379 0.229689 0.973264i \(-0.426229\pi\)
0.229689 + 0.973264i \(0.426229\pi\)
\(468\) −523509. 5.81927e6i −0.110487 1.22816i
\(469\) 1.20322e7 2.52588
\(470\) 225532. 0.0470939
\(471\) 2.72947e6 2.98603e6i 0.566925 0.620215i
\(472\) −3.94950e6 −0.815994
\(473\) 212552.i 0.0436831i
\(474\) −967000. 883912.i −0.197688 0.180702i
\(475\) 2.93301e6i 0.596457i
\(476\) 1.04389e6i 0.211171i
\(477\) −836935. 9.30328e6i −0.168421 1.87215i
\(478\) −1.46887e6 −0.294045
\(479\) 4.63191e6 0.922403 0.461202 0.887295i \(-0.347418\pi\)
0.461202 + 0.887295i \(0.347418\pi\)
\(480\) 3.07991e6 3.36942e6i 0.610148 0.667501i
\(481\) 8.54463e6i 1.68396i
\(482\) 1.98804e6 0.389769
\(483\) −804647. + 7.74324e6i −0.156941 + 1.51027i
\(484\) −4.87808e6 −0.946533
\(485\) 4.77265e6i 0.921309i
\(486\) −625084. + 994595.i −0.120046 + 0.191010i
\(487\) 9.50630e6 1.81631 0.908153 0.418638i \(-0.137492\pi\)
0.908153 + 0.418638i \(0.137492\pi\)
\(488\) −2.29720e6 −0.436665
\(489\) 2.57309e6 + 2.35200e6i 0.486611 + 0.444800i
\(490\) 2.24188e6i 0.421815i
\(491\) 4.09756e6i 0.767047i 0.923531 + 0.383523i \(0.125289\pi\)
−0.923531 + 0.383523i \(0.874711\pi\)
\(492\) −1.62989e6 + 1.78309e6i −0.303560 + 0.332095i
\(493\) 947583.i 0.175590i
\(494\) 902199. 0.166336
\(495\) −36411.2 404742.i −0.00667916 0.0742447i
\(496\) 3.26267e6 0.595482
\(497\) −2.31739e6 −0.420832
\(498\) −719138. + 786737.i −0.129939 + 0.142153i
\(499\) −1443.25 −0.000259472 −0.000129736 1.00000i \(-0.500041\pi\)
−0.000129736 1.00000i \(0.500041\pi\)
\(500\) 387945. 0.0693978
\(501\) −6.67933e6 + 7.30718e6i −1.18888 + 1.30064i
\(502\) 28447.1i 0.00503824i
\(503\) −5.18638e6 −0.913996 −0.456998 0.889468i \(-0.651075\pi\)
−0.456998 + 0.889468i \(0.651075\pi\)
\(504\) −341150. 3.79218e6i −0.0598231 0.664986i
\(505\) 652933.i 0.113931i
\(506\) −40225.5 54367.6i −0.00698435 0.00943982i
\(507\) 2.93932e6 + 2.68677e6i 0.507840 + 0.464205i
\(508\) 7.11887e6 1.22392
\(509\) 4.48149e6i 0.766705i 0.923602 + 0.383353i \(0.125231\pi\)
−0.923602 + 0.383353i \(0.874769\pi\)
\(510\) −187625. + 205262.i −0.0319422 + 0.0349448i
\(511\) 9.59576e6i 1.62565i
\(512\) 5.40015e6i 0.910398i
\(513\) 2.69113e6 + 2.04929e6i 0.451484 + 0.343803i
\(514\) 1.76924e6 0.295378
\(515\) 4.33437e6i 0.720125i
\(516\) −3.25031e6 + 3.55584e6i −0.537404 + 0.587920i
\(517\) 46109.3i 0.00758686i
\(518\) 2.71139e6i 0.443985i
\(519\) 2.88118e6 3.15201e6i 0.469518 0.513653i
\(520\) 5.04503e6i 0.818192i
\(521\) 1.55720e6 0.251333 0.125667 0.992073i \(-0.459893\pi\)
0.125667 + 0.992073i \(0.459893\pi\)
\(522\) 150796. + 1.67623e6i 0.0242221 + 0.269250i
\(523\) 5.42090e6i 0.866597i 0.901251 + 0.433298i \(0.142650\pi\)
−0.901251 + 0.433298i \(0.857350\pi\)
\(524\) 1.52237e6i 0.242209i
\(525\) 6.80005e6 7.43925e6i 1.07675 1.17796i
\(526\) 2.12232e6i 0.334462i
\(527\) −654576. −0.102668
\(528\) −209170. 191198.i −0.0326524 0.0298468i
\(529\) 1.88244e6 6.15491e6i 0.292470 0.956275i
\(530\) 3.92744e6i 0.607324i
\(531\) 1.20087e7 1.08032e6i 1.84825 0.166271i
\(532\) −5.33868e6 −0.817814
\(533\) 4.03959e6i 0.615913i
\(534\) 1.43473e6 1.56959e6i 0.217729 0.238195i
\(535\) 4.80783e6 0.726214
\(536\) 4.86535e6 0.731480
\(537\) −1.06150e6 + 1.16128e6i −0.158849 + 0.173781i
\(538\) −2.04473e6 −0.304566
\(539\) 458344. 0.0679547
\(540\) −5.58012e6 + 7.32783e6i −0.823491 + 1.08141i
\(541\) 5.88262e6 0.864127 0.432064 0.901843i \(-0.357786\pi\)
0.432064 + 0.901843i \(0.357786\pi\)
\(542\) 326187.i 0.0476945i
\(543\) 3.65476e6 3.99831e6i 0.531936 0.581938i
\(544\) 638670.i 0.0925293i
\(545\) 1.22111e7i 1.76102i
\(546\) 2.28833e6 + 2.09171e6i 0.328501 + 0.300275i
\(547\) −8.94337e6 −1.27801 −0.639003 0.769204i \(-0.720653\pi\)
−0.639003 + 0.769204i \(0.720653\pi\)
\(548\) −1.05121e7 −1.49534
\(549\) 6.98479e6 628361.i 0.989059 0.0889771i
\(550\) 87559.0i 0.0123422i
\(551\) 4.84617e6 0.680017
\(552\) −325368. + 3.13106e6i −0.0454493 + 0.437365i
\(553\) −1.29635e7 −1.80264
\(554\) 1.17726e6i 0.162967i
\(555\) −9.08788e6 + 9.94214e6i −1.25236 + 1.37008i
\(556\) 178625. 0.0245050
\(557\) 76523.7 0.0104510 0.00522550 0.999986i \(-0.498337\pi\)
0.00522550 + 0.999986i \(0.498337\pi\)
\(558\) 1.15791e6 104167.i 0.157431 0.0141627i
\(559\) 8.05575e6i 1.09038i
\(560\) 1.37156e7i 1.84818i
\(561\) 41965.0 + 38359.3i 0.00562963 + 0.00514592i
\(562\) 1.26628e6i 0.169117i
\(563\) −7.73965e6 −1.02908 −0.514542 0.857465i \(-0.672038\pi\)
−0.514542 + 0.857465i \(0.672038\pi\)
\(564\) −705095. + 771374.i −0.0933361 + 0.102110i
\(565\) 2.06785e6 0.272520
\(566\) −373177. −0.0489637
\(567\) 2.07458e6 + 1.14371e7i 0.271002 + 1.49402i
\(568\) −937062. −0.121870
\(569\) −1.52774e7 −1.97819 −0.989096 0.147271i \(-0.952951\pi\)
−0.989096 + 0.147271i \(0.952951\pi\)
\(570\) −1.04976e6 959559.i −0.135332 0.123704i
\(571\) 1.36736e6i 0.175506i −0.996142 0.0877532i \(-0.972031\pi\)
0.996142 0.0877532i \(-0.0279687\pi\)
\(572\) 502252. 0.0641847
\(573\) 1.00031e7 + 9.14359e6i 1.27276 + 1.16340i
\(574\) 1.28185e6i 0.162389i
\(575\) −6.69870e6 + 4.95624e6i −0.844930 + 0.625148i
\(576\) 504725. + 5.61046e6i 0.0633867 + 0.704600i
\(577\) −7.52623e6 −0.941105 −0.470552 0.882372i \(-0.655945\pi\)
−0.470552 + 0.882372i \(0.655945\pi\)
\(578\) 1.77310e6i 0.220757i
\(579\) 2.32741e6 + 2.12743e6i 0.288520 + 0.263730i
\(580\) 1.31959e7i 1.62880i
\(581\) 1.05469e7i 1.29624i
\(582\) −875353. 800140.i −0.107121 0.0979171i
\(583\) 802951. 0.0978403
\(584\) 3.88015e6i 0.470778i
\(585\) −1.37998e6 1.53398e7i −0.166719 1.85323i
\(586\) 192543.i 0.0231624i
\(587\) 620332.i 0.0743069i −0.999310 0.0371534i \(-0.988171\pi\)
0.999310 0.0371534i \(-0.0118290\pi\)
\(588\) −7.66775e6 7.00892e6i −0.914587 0.836003i
\(589\) 3.34766e6i 0.397606i
\(590\) −5.06956e6 −0.599571
\(591\) 8.54943e6 9.35307e6i 1.00686 1.10150i
\(592\) 9.39321e6i 1.10156i
\(593\) 4.96024e6i 0.579250i 0.957140 + 0.289625i \(0.0935307\pi\)
−0.957140 + 0.289625i \(0.906469\pi\)
\(594\) −80338.3 61177.4i −0.00934236 0.00711418i
\(595\) 2.75171e6i 0.318647i
\(596\) 4.67089e6 0.538622
\(597\) −426177. + 466237.i −0.0489388 + 0.0535391i
\(598\) −1.52455e6 2.06053e6i −0.174337 0.235628i
\(599\) 2.30566e6i 0.262560i 0.991345 + 0.131280i \(0.0419087\pi\)
−0.991345 + 0.131280i \(0.958091\pi\)
\(600\) 2.74967e6 3.00814e6i 0.311819 0.341130i
\(601\) −3.65731e6 −0.413025 −0.206512 0.978444i \(-0.566211\pi\)
−0.206512 + 0.978444i \(0.566211\pi\)
\(602\) 2.55626e6i 0.287484i
\(603\) −1.47934e7 + 1.33084e6i −1.65682 + 0.149050i
\(604\) −2.74110e6 −0.305726
\(605\) −1.28588e7 −1.42827
\(606\) 119755. + 109465.i 0.0132468 + 0.0121086i
\(607\) 5.25634e6 0.579044 0.289522 0.957171i \(-0.406504\pi\)
0.289522 + 0.957171i \(0.406504\pi\)
\(608\) −3.26631e6 −0.358343
\(609\) 1.22918e7 + 1.12356e7i 1.34299 + 1.22759i
\(610\) −2.94867e6 −0.320850
\(611\) 1.74754e6i 0.189376i
\(612\) −115460. 1.28344e6i −0.0124610 0.138515i
\(613\) 3.67092e6i 0.394570i 0.980346 + 0.197285i \(0.0632124\pi\)
−0.980346 + 0.197285i \(0.936788\pi\)
\(614\) 2.44013e6i 0.261212i
\(615\) −4.29642e6 + 4.70029e6i −0.458057 + 0.501114i
\(616\) 327297. 0.0347528
\(617\) 1.73511e6 0.183490 0.0917451 0.995783i \(-0.470755\pi\)
0.0917451 + 0.995783i \(0.470755\pi\)
\(618\) −794969. 726663.i −0.0837296 0.0765353i
\(619\) 7.42838e6i 0.779233i 0.920977 + 0.389617i \(0.127393\pi\)
−0.920977 + 0.389617i \(0.872607\pi\)
\(620\) 9.11551e6 0.952361
\(621\) 132853. 9.60921e6i 0.0138242 0.999904i
\(622\) 2.32932e6 0.241409
\(623\) 2.10417e7i 2.17200i
\(624\) −7.92756e6 7.24640e6i −0.815038 0.745008i
\(625\) −9.24158e6 −0.946338
\(626\) 3.63869e6 0.371115
\(627\) −196178. + 214619.i −0.0199289 + 0.0218022i
\(628\) 7.88201e6i 0.797513i
\(629\) 1.88452e6i 0.189922i
\(630\) −437899. 4.86763e6i −0.0439564 0.488615i
\(631\) 9.24226e6i 0.924070i 0.886862 + 0.462035i \(0.152880\pi\)
−0.886862 + 0.462035i \(0.847120\pi\)
\(632\) −5.24191e6 −0.522032
\(633\) 8.24378e6 + 7.53545e6i 0.817743 + 0.747480i
\(634\) 2.68459e6 0.265249
\(635\) 1.87655e7 1.84683
\(636\) −1.34328e7 1.22786e7i −1.31681 1.20366i
\(637\) 1.73713e7 1.69622
\(638\) −144672. −0.0140713
\(639\) 2.84920e6 256318.i 0.276039 0.0248329i
\(640\) 1.17394e7i 1.13292i
\(641\) −8.97691e6 −0.862942 −0.431471 0.902127i \(-0.642005\pi\)
−0.431471 + 0.902127i \(0.642005\pi\)
\(642\) 806038. 881805.i 0.0771823 0.0844374i
\(643\) 5.63467e6i 0.537453i 0.963216 + 0.268727i \(0.0866029\pi\)
−0.963216 + 0.268727i \(0.913397\pi\)
\(644\) 9.02138e6 + 1.21930e7i 0.857153 + 1.15850i
\(645\) −8.56792e6 + 9.37330e6i −0.810916 + 0.887142i
\(646\) 198980. 0.0187598
\(647\) 1.01191e7i 0.950349i −0.879892 0.475174i \(-0.842385\pi\)
0.879892 0.475174i \(-0.157615\pi\)
\(648\) 838878. + 4.62470e6i 0.0784804 + 0.432660i
\(649\) 1.03645e6i 0.0965913i
\(650\) 3.31849e6i 0.308075i
\(651\) 7.76139e6 8.49096e6i 0.717773 0.785244i
\(652\) 6.79198e6 0.625717
\(653\) 4.41505e6i 0.405184i −0.979263 0.202592i \(-0.935063\pi\)
0.979263 0.202592i \(-0.0649365\pi\)
\(654\) −2.23964e6 2.04721e6i −0.204755 0.187162i
\(655\) 4.01300e6i 0.365482i
\(656\) 4.44077e6i 0.402901i
\(657\) 1.06135e6 + 1.17979e7i 0.0959281 + 1.06633i
\(658\) 554533.i 0.0499301i
\(659\) −7.07020e6 −0.634188 −0.317094 0.948394i \(-0.602707\pi\)
−0.317094 + 0.948394i \(0.602707\pi\)
\(660\) −584397. 534184.i −0.0522214 0.0477344i
\(661\) 1.36132e6i 0.121187i −0.998163 0.0605937i \(-0.980701\pi\)
0.998163 0.0605937i \(-0.0192994\pi\)
\(662\) 1.99323e6i 0.176772i
\(663\) 1.59048e6 + 1.45382e6i 0.140522 + 0.128448i
\(664\) 4.26474e6i 0.375381i
\(665\) −1.40729e7 −1.23404
\(666\) 299897. + 3.33362e6i 0.0261991 + 0.291226i
\(667\) −8.18913e6 1.10682e7i −0.712727 0.963299i
\(668\) 1.92882e7i 1.67244i
\(669\) −1.67442e6 1.53055e6i −0.144644 0.132216i
\(670\) 6.24515e6 0.537472
\(671\) 602846.i 0.0516892i
\(672\) −8.28464e6 7.57280e6i −0.707702 0.646894i
\(673\) 1.60775e7 1.36830 0.684148 0.729344i \(-0.260174\pi\)
0.684148 + 0.729344i \(0.260174\pi\)
\(674\) −2.52489e6 −0.214089
\(675\) −7.53774e6 + 9.89859e6i −0.636769 + 0.836207i
\(676\) 7.75870e6 0.653014
\(677\) 9.18709e6 0.770382 0.385191 0.922837i \(-0.374135\pi\)
0.385191 + 0.922837i \(0.374135\pi\)
\(678\) 346678. 379265.i 0.0289636 0.0316861i
\(679\) −1.17349e7 −0.976795
\(680\) 1.11268e6i 0.0922782i
\(681\) 6.26848e6 + 5.72988e6i 0.517958 + 0.473454i
\(682\) 99937.4i 0.00822749i
\(683\) 3.89239e6i 0.319275i −0.987176 0.159637i \(-0.948967\pi\)
0.987176 0.159637i \(-0.0510325\pi\)
\(684\) 6.56383e6 590491.i 0.536435 0.0482584i
\(685\) −2.77103e7 −2.25639
\(686\) 1.29008e6 0.104666
\(687\) −18242.3 + 19957.0i −0.00147464 + 0.00161326i
\(688\) 8.85577e6i 0.713272i
\(689\) 3.04319e7 2.44220
\(690\) −417641. + 4.01902e6i −0.0333949 + 0.321364i
\(691\) 1.11648e7 0.889518 0.444759 0.895650i \(-0.353289\pi\)
0.444759 + 0.895650i \(0.353289\pi\)
\(692\) 8.32013e6i 0.660488i
\(693\) −995169. + 89526.8i −0.0787162 + 0.00708141i
\(694\) −1.75679e6 −0.138459
\(695\) 470859. 0.0369768
\(696\) 4.97031e6 + 4.54324e6i 0.388920 + 0.355503i
\(697\) 890934.i 0.0694646i
\(698\) 2.16019e6i 0.167824i
\(699\) 3.25512e6 3.56110e6i 0.251985 0.275671i
\(700\) 1.96368e7i 1.51470i
\(701\) −4.27810e6 −0.328818 −0.164409 0.986392i \(-0.552572\pi\)
−0.164409 + 0.986392i \(0.552572\pi\)
\(702\) −3.04483e6 2.31862e6i −0.233195 0.177577i
\(703\) 9.63790e6 0.735519
\(704\) −484230. −0.0368231
\(705\) −1.85865e6 + 2.03336e6i −0.140840 + 0.154078i
\(706\) −3.33775e6 −0.252024
\(707\) 1.60541e6 0.120792
\(708\) 1.58493e7 1.73391e7i 1.18830 1.30000i
\(709\) 4.55553e6i 0.340348i −0.985414 0.170174i \(-0.945567\pi\)
0.985414 0.170174i \(-0.0544330\pi\)
\(710\) −1.20281e6 −0.0895470
\(711\) 1.59384e7 1.43384e6i 1.18242 0.106372i
\(712\) 8.50844e6i 0.628999i
\(713\) −7.64571e6 + 5.65692e6i −0.563241 + 0.416732i
\(714\) 504692. + 461327.i 0.0370494 + 0.0338660i
\(715\) 1.32395e6 0.0968515
\(716\) 3.06535e6i 0.223459i
\(717\) 1.21052e7 1.32431e7i 0.879375 0.962036i
\(718\) 4.56909e6i 0.330764i
\(719\) 1.76274e6i 0.127164i −0.997977 0.0635821i \(-0.979748\pi\)
0.997977 0.0635821i \(-0.0202525\pi\)
\(720\) 1.51703e6 + 1.68632e7i 0.109060 + 1.21229i
\(721\) −1.06572e7 −0.763495
\(722\) 2.14234e6i 0.152949i
\(723\) −1.63838e7 + 1.79238e7i −1.16565 + 1.27522i
\(724\) 1.05540e7i 0.748294i
\(725\) 1.78253e7i 1.25948i
\(726\) −2.15579e6 + 2.35843e6i −0.151797 + 0.166066i
\(727\) 222075.i 0.0155834i 0.999970 + 0.00779172i \(0.00248021\pi\)
−0.999970 + 0.00779172i \(0.997520\pi\)
\(728\) 1.24046e7 0.867468
\(729\) −3.81568e6 1.38323e7i −0.265921 0.963995i
\(730\) 4.98055e6i 0.345915i
\(731\) 1.77670e6i 0.122976i
\(732\) 9.21861e6 1.00852e7i 0.635898 0.695673i
\(733\) 3.03919e6i 0.208929i −0.994529 0.104464i \(-0.966687\pi\)
0.994529 0.104464i \(-0.0333128\pi\)
\(734\) 4.01962e6 0.275388
\(735\) −2.02124e7 1.84757e7i −1.38007 1.26149i
\(736\) 5.51946e6 + 7.45993e6i 0.375580 + 0.507622i
\(737\) 1.27680e6i 0.0865872i
\(738\) 141781. + 1.57602e6i 0.00958244 + 0.106517i
\(739\) 1.00967e7 0.680096 0.340048 0.940408i \(-0.389557\pi\)
0.340048 + 0.940408i \(0.389557\pi\)
\(740\) 2.62435e7i 1.76174i
\(741\) −7.43517e6 + 8.13407e6i −0.497445 + 0.544205i
\(742\) 9.65669e6 0.643900
\(743\) 5.27625e6 0.350633 0.175317 0.984512i \(-0.443905\pi\)
0.175317 + 0.984512i \(0.443905\pi\)
\(744\) 3.13840e6 3.43341e6i 0.207863 0.227402i
\(745\) 1.23126e7 0.812753
\(746\) 2.57621e6 0.169486
\(747\) −1.16655e6 1.29673e7i −0.0764896 0.850250i
\(748\) 110772. 0.00723895
\(749\) 1.18214e7i 0.769950i
\(750\) 171446. 187562.i 0.0111295 0.0121756i
\(751\) 8.55220e6i 0.553322i 0.960968 + 0.276661i \(0.0892279\pi\)
−0.960968 + 0.276661i \(0.910772\pi\)
\(752\) 1.92109e6i 0.123881i
\(753\) −256474. 234437.i −0.0164838 0.0150674i
\(754\) −5.48309e6 −0.351234
\(755\) −7.22560e6 −0.461325
\(756\) 1.80175e7 + 1.37202e7i 1.14654 + 0.873086i
\(757\) 2.04752e7i 1.29864i −0.760516 0.649320i \(-0.775054\pi\)
0.760516 0.649320i \(-0.224946\pi\)
\(758\) −2.16589e6 −0.136919
\(759\) 821674. + 85385.2i 0.0517720 + 0.00537995i
\(760\) −5.69053e6 −0.357370
\(761\) 1.69707e6i 0.106228i 0.998588 + 0.0531140i \(0.0169147\pi\)
−0.998588 + 0.0531140i \(0.983085\pi\)
\(762\) 3.14607e6 3.44179e6i 0.196282 0.214732i
\(763\) −3.00243e7 −1.86708
\(764\) 2.64044e7 1.63660
\(765\) −304356. 3.38319e6i −0.0188031 0.209013i
\(766\) 2.39941e6i 0.147751i
\(767\) 3.92816e7i 2.41102i
\(768\) 6.38208e6 + 5.83371e6i 0.390444 + 0.356896i
\(769\) 8.50809e6i 0.518819i 0.965767 + 0.259410i \(0.0835280\pi\)
−0.965767 + 0.259410i \(0.916472\pi\)
\(770\) 420117. 0.0255355
\(771\) −1.45806e7 + 1.59511e7i −0.883361 + 0.966397i
\(772\) 6.14349e6 0.370998
\(773\) −1.74244e7 −1.04884 −0.524420 0.851460i \(-0.675718\pi\)
−0.524420 + 0.851460i \(0.675718\pi\)
\(774\) 282738. + 3.14289e6i 0.0169642 + 0.188572i
\(775\) 1.23134e7 0.736418
\(776\) −4.74512e6 −0.282874
\(777\) 2.44455e7 + 2.23450e7i 1.45260 + 1.32779i
\(778\) 1.58208e6i 0.0937087i
\(779\) 4.55645e6