Properties

Label 69.6.c.b.68.2
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 68.2
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.32

$q$-expansion

\(f(q)\) \(=\) \(q-9.90483i q^{2} +(13.3502 - 8.04819i) q^{3} -66.1056 q^{4} +91.0951 q^{5} +(-79.7159 - 132.231i) q^{6} -106.321i q^{7} +337.810i q^{8} +(113.453 - 214.889i) q^{9} +O(q^{10})\) \(q-9.90483i q^{2} +(13.3502 - 8.04819i) q^{3} -66.1056 q^{4} +91.0951 q^{5} +(-79.7159 - 132.231i) q^{6} -106.321i q^{7} +337.810i q^{8} +(113.453 - 214.889i) q^{9} -902.281i q^{10} -429.596 q^{11} +(-882.520 + 532.031i) q^{12} -363.595 q^{13} -1053.10 q^{14} +(1216.13 - 733.150i) q^{15} +1230.57 q^{16} +1775.89 q^{17} +(-2128.44 - 1123.74i) q^{18} +1106.92i q^{19} -6021.90 q^{20} +(-855.695 - 1419.41i) q^{21} +4255.07i q^{22} +(2031.78 + 1519.28i) q^{23} +(2718.76 + 4509.82i) q^{24} +5173.31 q^{25} +3601.35i q^{26} +(-214.848 - 3781.90i) q^{27} +7028.45i q^{28} +3057.54i q^{29} +(-7261.73 - 12045.6i) q^{30} -6824.43 q^{31} -1378.69i q^{32} +(-5735.17 + 3457.47i) q^{33} -17589.9i q^{34} -9685.36i q^{35} +(-7499.90 + 14205.4i) q^{36} -3538.10i q^{37} +10963.9 q^{38} +(-4854.06 + 2926.28i) q^{39} +30772.9i q^{40} -15552.1i q^{41} +(-14059.0 + 8475.52i) q^{42} +15844.9i q^{43} +28398.7 q^{44} +(10335.0 - 19575.3i) q^{45} +(15048.2 - 20124.4i) q^{46} +1848.69i q^{47} +(16428.4 - 9903.89i) q^{48} +5502.74 q^{49} -51240.8i q^{50} +(23708.4 - 14292.7i) q^{51} +24035.7 q^{52} +29357.1 q^{53} +(-37459.0 + 2128.04i) q^{54} -39134.0 q^{55} +35916.5 q^{56} +(8908.74 + 14777.6i) q^{57} +30284.4 q^{58} +17358.4i q^{59} +(-80393.3 + 48465.4i) q^{60} -25278.1i q^{61} +67594.8i q^{62} +(-22847.3 - 12062.5i) q^{63} +25722.7 q^{64} -33121.8 q^{65} +(34245.6 + 56805.9i) q^{66} +12342.5i q^{67} -117396. q^{68} +(39352.0 + 3930.44i) q^{69} -95931.9 q^{70} -84587.6i q^{71} +(72591.8 + 38325.7i) q^{72} -8013.84 q^{73} -35044.3 q^{74} +(69064.5 - 41635.8i) q^{75} -73174.0i q^{76} +45675.2i q^{77} +(28984.3 + 48078.6i) q^{78} +66223.2i q^{79} +112099. q^{80} +(-33305.7 - 48759.8i) q^{81} -154041. q^{82} +45004.7 q^{83} +(56566.3 + 93830.9i) q^{84} +161775. q^{85} +156941. q^{86} +(24607.6 + 40818.6i) q^{87} -145122. i q^{88} -23975.3 q^{89} +(-193890. - 102367. i) q^{90} +38658.0i q^{91} +(-134312. - 100433. i) q^{92} +(-91107.1 + 54924.3i) q^{93} +18311.0 q^{94} +100835. i q^{95} +(-11096.0 - 18405.8i) q^{96} -96721.1i q^{97} -54503.7i q^{98} +(-48739.1 + 92315.4i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.90483i 1.75094i −0.483270 0.875471i \(-0.660551\pi\)
0.483270 0.875471i \(-0.339449\pi\)
\(3\) 13.3502 8.04819i 0.856413 0.516292i
\(4\) −66.1056 −2.06580
\(5\) 91.0951 1.62956 0.814779 0.579772i \(-0.196858\pi\)
0.814779 + 0.579772i \(0.196858\pi\)
\(6\) −79.7159 132.231i −0.903997 1.49953i
\(7\) 106.321i 0.820117i −0.912059 0.410059i \(-0.865508\pi\)
0.912059 0.410059i \(-0.134492\pi\)
\(8\) 337.810i 1.86616i
\(9\) 113.453 214.889i 0.466886 0.884317i
\(10\) 902.281i 2.85326i
\(11\) −429.596 −1.07048 −0.535240 0.844700i \(-0.679779\pi\)
−0.535240 + 0.844700i \(0.679779\pi\)
\(12\) −882.520 + 532.031i −1.76918 + 1.06656i
\(13\) −363.595 −0.596705 −0.298353 0.954456i \(-0.596437\pi\)
−0.298353 + 0.954456i \(0.596437\pi\)
\(14\) −1053.10 −1.43598
\(15\) 1216.13 733.150i 1.39557 0.841327i
\(16\) 1230.57 1.20173
\(17\) 1775.89 1.49037 0.745184 0.666859i \(-0.232362\pi\)
0.745184 + 0.666859i \(0.232362\pi\)
\(18\) −2128.44 1123.74i −1.54839 0.817491i
\(19\) 1106.92i 0.703452i 0.936103 + 0.351726i \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(20\) −6021.90 −3.36634
\(21\) −855.695 1419.41i −0.423420 0.702359i
\(22\) 4255.07i 1.87435i
\(23\) 2031.78 + 1519.28i 0.800861 + 0.598850i
\(24\) 2718.76 + 4509.82i 0.963481 + 1.59820i
\(25\) 5173.31 1.65546
\(26\) 3601.35i 1.04480i
\(27\) −214.848 3781.90i −0.0567182 0.998390i
\(28\) 7028.45i 1.69420i
\(29\) 3057.54i 0.675113i 0.941305 + 0.337557i \(0.109600\pi\)
−0.941305 + 0.337557i \(0.890400\pi\)
\(30\) −7261.73 12045.6i −1.47312 2.44357i
\(31\) −6824.43 −1.27545 −0.637723 0.770266i \(-0.720123\pi\)
−0.637723 + 0.770266i \(0.720123\pi\)
\(32\) 1378.69i 0.238009i
\(33\) −5735.17 + 3457.47i −0.916772 + 0.552679i
\(34\) 17589.9i 2.60955i
\(35\) 9685.36i 1.33643i
\(36\) −7499.90 + 14205.4i −0.964494 + 1.82682i
\(37\) 3538.10i 0.424879i −0.977174 0.212440i \(-0.931859\pi\)
0.977174 0.212440i \(-0.0681409\pi\)
\(38\) 10963.9 1.23170
\(39\) −4854.06 + 2926.28i −0.511026 + 0.308074i
\(40\) 30772.9i 3.04101i
\(41\) 15552.1i 1.44488i −0.691436 0.722438i \(-0.743022\pi\)
0.691436 0.722438i \(-0.256978\pi\)
\(42\) −14059.0 + 8475.52i −1.22979 + 0.741383i
\(43\) 15844.9i 1.30683i 0.757000 + 0.653415i \(0.226664\pi\)
−0.757000 + 0.653415i \(0.773336\pi\)
\(44\) 28398.7 2.21140
\(45\) 10335.0 19575.3i 0.760818 1.44105i
\(46\) 15048.2 20124.4i 1.04855 1.40226i
\(47\) 1848.69i 0.122073i 0.998136 + 0.0610365i \(0.0194406\pi\)
−0.998136 + 0.0610365i \(0.980559\pi\)
\(48\) 16428.4 9903.89i 1.02918 0.620444i
\(49\) 5502.74 0.327408
\(50\) 51240.8i 2.89862i
\(51\) 23708.4 14292.7i 1.27637 0.769465i
\(52\) 24035.7 1.23267
\(53\) 29357.1 1.43557 0.717784 0.696266i \(-0.245157\pi\)
0.717784 + 0.696266i \(0.245157\pi\)
\(54\) −37459.0 + 2128.04i −1.74812 + 0.0993104i
\(55\) −39134.0 −1.74441
\(56\) 35916.5 1.53047
\(57\) 8908.74 + 14777.6i 0.363186 + 0.602445i
\(58\) 30284.4 1.18208
\(59\) 17358.4i 0.649200i 0.945851 + 0.324600i \(0.105230\pi\)
−0.945851 + 0.324600i \(0.894770\pi\)
\(60\) −80393.3 + 48465.4i −2.88298 + 1.73801i
\(61\) 25278.1i 0.869802i −0.900478 0.434901i \(-0.856783\pi\)
0.900478 0.434901i \(-0.143217\pi\)
\(62\) 67594.8i 2.23323i
\(63\) −22847.3 12062.5i −0.725244 0.382901i
\(64\) 25722.7 0.784993
\(65\) −33121.8 −0.972366
\(66\) 34245.6 + 56805.9i 0.967710 + 1.60522i
\(67\) 12342.5i 0.335904i 0.985795 + 0.167952i \(0.0537153\pi\)
−0.985795 + 0.167952i \(0.946285\pi\)
\(68\) −117396. −3.07880
\(69\) 39352.0 + 3930.44i 0.995049 + 0.0993846i
\(70\) −95931.9 −2.34001
\(71\) 84587.6i 1.99141i −0.0925811 0.995705i \(-0.529512\pi\)
0.0925811 0.995705i \(-0.470488\pi\)
\(72\) 72591.8 + 38325.7i 1.65027 + 0.871283i
\(73\) −8013.84 −0.176008 −0.0880042 0.996120i \(-0.528049\pi\)
−0.0880042 + 0.996120i \(0.528049\pi\)
\(74\) −35044.3 −0.743940
\(75\) 69064.5 41635.8i 1.41776 0.854700i
\(76\) 73174.0i 1.45319i
\(77\) 45675.2i 0.877918i
\(78\) 28984.3 + 48078.6i 0.539420 + 0.894778i
\(79\) 66223.2i 1.19383i 0.802305 + 0.596915i \(0.203607\pi\)
−0.802305 + 0.596915i \(0.796393\pi\)
\(80\) 112099. 1.95829
\(81\) −33305.7 48759.8i −0.564035 0.825751i
\(82\) −154041. −2.52989
\(83\) 45004.7 0.717072 0.358536 0.933516i \(-0.383276\pi\)
0.358536 + 0.933516i \(0.383276\pi\)
\(84\) 56566.3 + 93830.9i 0.874701 + 1.45093i
\(85\) 161775. 2.42864
\(86\) 156941. 2.28818
\(87\) 24607.6 + 40818.6i 0.348555 + 0.578175i
\(88\) 145122.i 1.99768i
\(89\) −23975.3 −0.320841 −0.160420 0.987049i \(-0.551285\pi\)
−0.160420 + 0.987049i \(0.551285\pi\)
\(90\) −193890. 102367.i −2.52319 1.33215i
\(91\) 38658.0i 0.489368i
\(92\) −134312. 100433.i −1.65442 1.23710i
\(93\) −91107.1 + 54924.3i −1.09231 + 0.658502i
\(94\) 18311.0 0.213743
\(95\) 100835.i 1.14632i
\(96\) −11096.0 18405.8i −0.122882 0.203834i
\(97\) 96721.1i 1.04374i −0.853025 0.521869i \(-0.825235\pi\)
0.853025 0.521869i \(-0.174765\pi\)
\(98\) 54503.7i 0.573272i
\(99\) −48739.1 + 92315.4i −0.499792 + 0.946643i
\(100\) −341985. −3.41985
\(101\) 12371.5i 0.120676i 0.998178 + 0.0603378i \(0.0192178\pi\)
−0.998178 + 0.0603378i \(0.980782\pi\)
\(102\) −141567. 234828.i −1.34729 2.23485i
\(103\) 177600.i 1.64950i 0.565501 + 0.824748i \(0.308683\pi\)
−0.565501 + 0.824748i \(0.691317\pi\)
\(104\) 122826.i 1.11355i
\(105\) −77949.6 129301.i −0.689987 1.14453i
\(106\) 290777.i 2.51360i
\(107\) 77063.6 0.650713 0.325357 0.945591i \(-0.394516\pi\)
0.325357 + 0.945591i \(0.394516\pi\)
\(108\) 14202.7 + 250005.i 0.117169 + 2.06248i
\(109\) 104977.i 0.846304i 0.906059 + 0.423152i \(0.139076\pi\)
−0.906059 + 0.423152i \(0.860924\pi\)
\(110\) 387616.i 3.05436i
\(111\) −28475.3 47234.2i −0.219362 0.363872i
\(112\) 130836.i 0.985562i
\(113\) −11275.6 −0.0830702 −0.0415351 0.999137i \(-0.513225\pi\)
−0.0415351 + 0.999137i \(0.513225\pi\)
\(114\) 146370. 88239.5i 1.05485 0.635918i
\(115\) 185085. + 138399.i 1.30505 + 0.975860i
\(116\) 202120.i 1.39465i
\(117\) −41251.1 + 78132.7i −0.278594 + 0.527677i
\(118\) 171931. 1.13671
\(119\) 188815.i 1.22228i
\(120\) 247666. + 410823.i 1.57005 + 2.60436i
\(121\) 23501.4 0.145925
\(122\) −250376. −1.52297
\(123\) −125167. 207623.i −0.745977 1.23741i
\(124\) 451133. 2.63482
\(125\) 186591. 1.06811
\(126\) −119477. + 226299.i −0.670438 + 1.26986i
\(127\) 125559. 0.690780 0.345390 0.938459i \(-0.387747\pi\)
0.345390 + 0.938459i \(0.387747\pi\)
\(128\) 298897.i 1.61249i
\(129\) 127523. + 211532.i 0.674705 + 1.11919i
\(130\) 328065.i 1.70256i
\(131\) 193572.i 0.985518i 0.870166 + 0.492759i \(0.164012\pi\)
−0.870166 + 0.492759i \(0.835988\pi\)
\(132\) 379127. 228558.i 1.89387 1.14173i
\(133\) 117690. 0.576913
\(134\) 122250. 0.588148
\(135\) −19571.6 344512.i −0.0924257 1.62693i
\(136\) 599914.i 2.78126i
\(137\) −408836. −1.86100 −0.930502 0.366287i \(-0.880629\pi\)
−0.930502 + 0.366287i \(0.880629\pi\)
\(138\) 38930.4 389775.i 0.174017 1.74227i
\(139\) 56526.6 0.248151 0.124076 0.992273i \(-0.460403\pi\)
0.124076 + 0.992273i \(0.460403\pi\)
\(140\) 640257.i 2.76080i
\(141\) 14878.6 + 24680.3i 0.0630253 + 0.104545i
\(142\) −837826. −3.48685
\(143\) 156199. 0.638761
\(144\) 139613. 264437.i 0.561072 1.06271i
\(145\) 278526.i 1.10014i
\(146\) 79375.7i 0.308181i
\(147\) 73462.5 44287.1i 0.280396 0.169038i
\(148\) 233888.i 0.877716i
\(149\) 22027.5 0.0812831 0.0406416 0.999174i \(-0.487060\pi\)
0.0406416 + 0.999174i \(0.487060\pi\)
\(150\) −412395. 684072.i −1.49653 2.48241i
\(151\) 188664. 0.673359 0.336679 0.941619i \(-0.390696\pi\)
0.336679 + 0.941619i \(0.390696\pi\)
\(152\) −373931. −1.31275
\(153\) 201481. 381619.i 0.695832 1.31796i
\(154\) 452405. 1.53718
\(155\) −621672. −2.07841
\(156\) 320880. 193444.i 1.05568 0.636420i
\(157\) 347055.i 1.12370i −0.827240 0.561848i \(-0.810091\pi\)
0.827240 0.561848i \(-0.189909\pi\)
\(158\) 655929. 2.09033
\(159\) 391922. 236272.i 1.22944 0.741171i
\(160\) 125592.i 0.387849i
\(161\) 161532. 216022.i 0.491127 0.656800i
\(162\) −482957. + 329887.i −1.44584 + 0.987592i
\(163\) −313519. −0.924262 −0.462131 0.886812i \(-0.652915\pi\)
−0.462131 + 0.886812i \(0.652915\pi\)
\(164\) 1.02808e6i 2.98483i
\(165\) −522446. + 314958.i −1.49393 + 0.900623i
\(166\) 445764.i 1.25555i
\(167\) 521073.i 1.44580i 0.690954 + 0.722899i \(0.257191\pi\)
−0.690954 + 0.722899i \(0.742809\pi\)
\(168\) 479491. 289063.i 1.31071 0.790167i
\(169\) −239091. −0.643943
\(170\) 1.60235e6i 4.25241i
\(171\) 237866. + 125584.i 0.622074 + 0.328432i
\(172\) 1.04744e6i 2.69965i
\(173\) 246126.i 0.625234i −0.949879 0.312617i \(-0.898794\pi\)
0.949879 0.312617i \(-0.101206\pi\)
\(174\) 404301. 243734.i 1.01235 0.610300i
\(175\) 550034.i 1.35767i
\(176\) −528649. −1.28643
\(177\) 139703. + 231737.i 0.335176 + 0.555983i
\(178\) 237472.i 0.561774i
\(179\) 109168.i 0.254661i 0.991860 + 0.127330i \(0.0406409\pi\)
−0.991860 + 0.127330i \(0.959359\pi\)
\(180\) −683204. + 1.29404e6i −1.57170 + 2.97692i
\(181\) 578258.i 1.31197i 0.754773 + 0.655986i \(0.227747\pi\)
−0.754773 + 0.655986i \(0.772253\pi\)
\(182\) 382901. 0.856856
\(183\) −203443. 337467.i −0.449072 0.744910i
\(184\) −513228. + 686357.i −1.11755 + 1.49453i
\(185\) 322303.i 0.692366i
\(186\) 544015. + 902401.i 1.15300 + 1.91257i
\(187\) −762914. −1.59541
\(188\) 122209.i 0.252179i
\(189\) −402097. + 22843.0i −0.818797 + 0.0465156i
\(190\) 998757. 2.00713
\(191\) −432293. −0.857422 −0.428711 0.903442i \(-0.641032\pi\)
−0.428711 + 0.903442i \(0.641032\pi\)
\(192\) 343401. 207021.i 0.672278 0.405285i
\(193\) 59028.8 0.114070 0.0570349 0.998372i \(-0.481835\pi\)
0.0570349 + 0.998372i \(0.481835\pi\)
\(194\) −958006. −1.82753
\(195\) −442181. + 266570.i −0.832747 + 0.502024i
\(196\) −363762. −0.676359
\(197\) 102969.i 0.189035i −0.995523 0.0945173i \(-0.969869\pi\)
0.995523 0.0945173i \(-0.0301308\pi\)
\(198\) 914369. + 482752.i 1.65752 + 0.875107i
\(199\) 441031.i 0.789471i −0.918795 0.394735i \(-0.870836\pi\)
0.918795 0.394735i \(-0.129164\pi\)
\(200\) 1.74760e6i 3.08935i
\(201\) 99334.5 + 164774.i 0.173424 + 0.287672i
\(202\) 122538. 0.211296
\(203\) 325082. 0.553672
\(204\) −1.56726e6 + 944827.i −2.63673 + 1.58956i
\(205\) 1.41672e6i 2.35451i
\(206\) 1.75910e6 2.88817
\(207\) 556989. 264241.i 0.903484 0.428621i
\(208\) −447431. −0.717080
\(209\) 475530.i 0.753030i
\(210\) −1.28071e6 + 772078.i −2.00402 + 1.20813i
\(211\) −108642. −0.167993 −0.0839967 0.996466i \(-0.526769\pi\)
−0.0839967 + 0.996466i \(0.526769\pi\)
\(212\) −1.94067e6 −2.96560
\(213\) −680777. 1.12926e6i −1.02815 1.70547i
\(214\) 763301.i 1.13936i
\(215\) 1.44339e6i 2.12956i
\(216\) 1.27756e6 72578.0i 1.86315 0.105845i
\(217\) 725583.i 1.04601i
\(218\) 1.03978e6 1.48183
\(219\) −106986. + 64496.9i −0.150736 + 0.0908716i
\(220\) 2.58698e6 3.60360
\(221\) −645705. −0.889311
\(222\) −467846. + 282043.i −0.637119 + 0.384090i
\(223\) −210918. −0.284021 −0.142011 0.989865i \(-0.545357\pi\)
−0.142011 + 0.989865i \(0.545357\pi\)
\(224\) −146585. −0.195195
\(225\) 586930. 1.11169e6i 0.772911 1.46395i
\(226\) 111683.i 0.145451i
\(227\) −146307. −0.188452 −0.0942260 0.995551i \(-0.530038\pi\)
−0.0942260 + 0.995551i \(0.530038\pi\)
\(228\) −588918. 976884.i −0.750270 1.24453i
\(229\) 1.11197e6i 1.40122i 0.713547 + 0.700608i \(0.247088\pi\)
−0.713547 + 0.700608i \(0.752912\pi\)
\(230\) 1.37082e6 1.83324e6i 1.70868 2.28507i
\(231\) 367603. + 609772.i 0.453262 + 0.751861i
\(232\) −1.03287e6 −1.25987
\(233\) 1.34569e6i 1.62389i 0.583734 + 0.811945i \(0.301591\pi\)
−0.583734 + 0.811945i \(0.698409\pi\)
\(234\) 773891. + 408585.i 0.923932 + 0.487801i
\(235\) 168407.i 0.198925i
\(236\) 1.14748e6i 1.34112i
\(237\) 532976. + 884089.i 0.616364 + 1.02241i
\(238\) −1.87018e6 −2.14014
\(239\) 95336.4i 0.107960i 0.998542 + 0.0539802i \(0.0171908\pi\)
−0.998542 + 0.0539802i \(0.982809\pi\)
\(240\) 1.49654e6 902196.i 1.67711 1.01105i
\(241\) 171943.i 0.190696i −0.995444 0.0953481i \(-0.969604\pi\)
0.995444 0.0953481i \(-0.0303964\pi\)
\(242\) 232778.i 0.255507i
\(243\) −837064. 382900.i −0.909375 0.415978i
\(244\) 1.67103e6i 1.79684i
\(245\) 501273. 0.533530
\(246\) −2.05647e6 + 1.23975e6i −2.16663 + 1.30616i
\(247\) 402473.i 0.419753i
\(248\) 2.30536e6i 2.38018i
\(249\) 600820. 362206.i 0.614110 0.370218i
\(250\) 1.84815e6i 1.87020i
\(251\) −510614. −0.511574 −0.255787 0.966733i \(-0.582335\pi\)
−0.255787 + 0.966733i \(0.582335\pi\)
\(252\) 1.51034e6 + 797401.i 1.49821 + 0.790998i
\(253\) −872844. 652675.i −0.857305 0.641056i
\(254\) 1.24364e6i 1.20952i
\(255\) 2.15972e6 1.30199e6i 2.07992 1.25389i
\(256\) −2.13740e6 −2.03838
\(257\) 1.06311e6i 1.00403i 0.864860 + 0.502013i \(0.167407\pi\)
−0.864860 + 0.502013i \(0.832593\pi\)
\(258\) 2.09519e6 1.26309e6i 1.95963 1.18137i
\(259\) −376176. −0.348451
\(260\) 2.18953e6 2.00872
\(261\) 657031. + 346888.i 0.597014 + 0.315201i
\(262\) 1.91730e6 1.72559
\(263\) −868216. −0.773995 −0.386998 0.922081i \(-0.626488\pi\)
−0.386998 + 0.922081i \(0.626488\pi\)
\(264\) −1.16797e6 1.93740e6i −1.03139 1.71084i
\(265\) 2.67429e6 2.33934
\(266\) 1.16570e6i 1.01014i
\(267\) −320074. + 192958.i −0.274772 + 0.165647i
\(268\) 815907.i 0.693911i
\(269\) 169298.i 0.142650i 0.997453 + 0.0713251i \(0.0227228\pi\)
−0.997453 + 0.0713251i \(0.977277\pi\)
\(270\) −3.41233e6 + 193854.i −2.84867 + 0.161832i
\(271\) −2.33325e6 −1.92992 −0.964959 0.262400i \(-0.915486\pi\)
−0.964959 + 0.262400i \(0.915486\pi\)
\(272\) 2.18536e6 1.79102
\(273\) 311127. + 516090.i 0.252657 + 0.419101i
\(274\) 4.04945e6i 3.25851i
\(275\) −2.22243e6 −1.77214
\(276\) −2.60139e6 259825.i −2.05557 0.205309i
\(277\) 942252. 0.737849 0.368925 0.929459i \(-0.379726\pi\)
0.368925 + 0.929459i \(0.379726\pi\)
\(278\) 559887.i 0.434498i
\(279\) −774254. + 1.46649e6i −0.595488 + 1.12790i
\(280\) 3.27182e6 2.49399
\(281\) 1.20393e6 0.909567 0.454783 0.890602i \(-0.349717\pi\)
0.454783 + 0.890602i \(0.349717\pi\)
\(282\) 244454. 147370.i 0.183052 0.110354i
\(283\) 1.82107e6i 1.35164i 0.737067 + 0.675820i \(0.236210\pi\)
−0.737067 + 0.675820i \(0.763790\pi\)
\(284\) 5.59172e6i 4.11386i
\(285\) 811542. + 1.34617e6i 0.591833 + 0.981719i
\(286\) 1.54712e6i 1.11843i
\(287\) −1.65353e6 −1.18497
\(288\) −296266. 156417.i −0.210475 0.111123i
\(289\) 1.73393e6 1.22120
\(290\) 2.75876e6 1.92628
\(291\) −778429. 1.29124e6i −0.538873 0.893871i
\(292\) 529760. 0.363598
\(293\) 1.56595e6 1.06563 0.532816 0.846231i \(-0.321134\pi\)
0.532816 + 0.846231i \(0.321134\pi\)
\(294\) −438656. 727633.i −0.295976 0.490958i
\(295\) 1.58126e6i 1.05791i
\(296\) 1.19521e6 0.792891
\(297\) 92297.9 + 1.62469e6i 0.0607157 + 1.06876i
\(298\) 218179.i 0.142322i
\(299\) −738746. 552403.i −0.477878 0.357337i
\(300\) −4.56555e6 + 2.75236e6i −2.92880 + 1.76564i
\(301\) 1.68466e6 1.07175
\(302\) 1.86868e6i 1.17901i
\(303\) 99568.3 + 165162.i 0.0623038 + 0.103348i
\(304\) 1.36215e6i 0.845361i
\(305\) 2.30271e6i 1.41739i
\(306\) −3.77987e6 1.99563e6i −2.30767 1.21836i
\(307\) 118971. 0.0720435 0.0360218 0.999351i \(-0.488531\pi\)
0.0360218 + 0.999351i \(0.488531\pi\)
\(308\) 3.01939e6i 1.81360i
\(309\) 1.42936e6 + 2.37099e6i 0.851620 + 1.41265i
\(310\) 6.15755e6i 3.63918i
\(311\) 1.39044e6i 0.815175i −0.913166 0.407587i \(-0.866370\pi\)
0.913166 0.407587i \(-0.133630\pi\)
\(312\) −988529. 1.63975e6i −0.574914 0.953655i
\(313\) 2.09007e6i 1.20587i −0.797792 0.602933i \(-0.793999\pi\)
0.797792 0.602933i \(-0.206001\pi\)
\(314\) −3.43752e6 −1.96753
\(315\) −2.08128e6 1.09884e6i −1.18183 0.623960i
\(316\) 4.37772e6i 2.46621i
\(317\) 204837.i 0.114488i −0.998360 0.0572440i \(-0.981769\pi\)
0.998360 0.0572440i \(-0.0182313\pi\)
\(318\) −2.34023e6 3.88192e6i −1.29775 2.15268i
\(319\) 1.31350e6i 0.722694i
\(320\) 2.34321e6 1.27919
\(321\) 1.02881e6 620222.i 0.557279 0.335958i
\(322\) −2.13966e6 1.59995e6i −1.15002 0.859935i
\(323\) 1.96578e6i 1.04840i
\(324\) 2.20169e6 + 3.22330e6i 1.16518 + 1.70584i
\(325\) −1.88099e6 −0.987822
\(326\) 3.10535e6i 1.61833i
\(327\) 844871. + 1.40145e6i 0.436939 + 0.724786i
\(328\) 5.25367e6 2.69636
\(329\) 196556. 0.100114
\(330\) 3.11961e6 + 5.17473e6i 1.57694 + 2.61579i
\(331\) −3.31167e6 −1.66141 −0.830706 0.556711i \(-0.812063\pi\)
−0.830706 + 0.556711i \(0.812063\pi\)
\(332\) −2.97507e6 −1.48133
\(333\) −760299. 401409.i −0.375728 0.198370i
\(334\) 5.16114e6 2.53151
\(335\) 1.12434e6i 0.547375i
\(336\) −1.05300e6 1.74669e6i −0.508837 0.844048i
\(337\) 2.72902e6i 1.30898i 0.756072 + 0.654489i \(0.227116\pi\)
−0.756072 + 0.654489i \(0.772884\pi\)
\(338\) 2.36816e6i 1.12751i
\(339\) −150532. + 90748.5i −0.0711424 + 0.0428885i
\(340\) −1.06942e7 −5.01709
\(341\) 2.93174e6 1.36534
\(342\) 1.24389e6 2.35602e6i 0.575065 1.08922i
\(343\) 2.37200e6i 1.08863i
\(344\) −5.35258e6 −2.43875
\(345\) 3.58478e6 + 358044.i 1.62149 + 0.161953i
\(346\) −2.43784e6 −1.09475
\(347\) 366434.i 0.163370i 0.996658 + 0.0816849i \(0.0260301\pi\)
−0.996658 + 0.0816849i \(0.973970\pi\)
\(348\) −1.62670e6 2.69834e6i −0.720045 1.19440i
\(349\) −1.55226e6 −0.682184 −0.341092 0.940030i \(-0.610797\pi\)
−0.341092 + 0.940030i \(0.610797\pi\)
\(350\) −5.44799e6 −2.37720
\(351\) 78117.9 + 1.37508e6i 0.0338441 + 0.595745i
\(352\) 592281.i 0.254783i
\(353\) 1.97096e6i 0.841860i −0.907093 0.420930i \(-0.861704\pi\)
0.907093 0.420930i \(-0.138296\pi\)
\(354\) 2.29531e6 1.38374e6i 0.973495 0.586875i
\(355\) 7.70551e6i 3.24512i
\(356\) 1.58490e6 0.662793
\(357\) −1.51962e6 2.52071e6i −0.631051 1.04677i
\(358\) 1.08129e6 0.445897
\(359\) −988239. −0.404693 −0.202347 0.979314i \(-0.564857\pi\)
−0.202347 + 0.979314i \(0.564857\pi\)
\(360\) 6.61275e6 + 3.49128e6i 2.68922 + 1.41981i
\(361\) 1.25082e6 0.505156
\(362\) 5.72754e6 2.29719
\(363\) 313748. 189144.i 0.124972 0.0753400i
\(364\) 2.55551e6i 1.01094i
\(365\) −730021. −0.286816
\(366\) −3.34255e6 + 2.01507e6i −1.30429 + 0.786299i
\(367\) 1.66563e6i 0.645526i −0.946480 0.322763i \(-0.895388\pi\)
0.946480 0.322763i \(-0.104612\pi\)
\(368\) 2.50026e6 + 1.86958e6i 0.962421 + 0.719657i
\(369\) −3.34199e6 1.76444e6i −1.27773 0.674592i
\(370\) −3.19236e6 −1.21229
\(371\) 3.12129e6i 1.17733i
\(372\) 6.02270e6 3.63080e6i 2.25649 1.36033i
\(373\) 749868.i 0.279070i −0.990217 0.139535i \(-0.955439\pi\)
0.990217 0.139535i \(-0.0445607\pi\)
\(374\) 7.55654e6i 2.79347i
\(375\) 2.49102e6 1.50172e6i 0.914743 0.551456i
\(376\) −624507. −0.227807
\(377\) 1.11171e6i 0.402844i
\(378\) 226256. + 3.98270e6i 0.0814462 + 1.43367i
\(379\) 1.95458e6i 0.698966i −0.936943 0.349483i \(-0.886357\pi\)
0.936943 0.349483i \(-0.113643\pi\)
\(380\) 6.66579e6i 2.36806i
\(381\) 1.67624e6 1.01053e6i 0.591593 0.356644i
\(382\) 4.28179e6i 1.50130i
\(383\) 1.10006e6 0.383195 0.191597 0.981474i \(-0.438633\pi\)
0.191597 + 0.981474i \(0.438633\pi\)
\(384\) −2.40558e6 3.99032e6i −0.832513 1.38095i
\(385\) 4.16079e6i 1.43062i
\(386\) 584670.i 0.199730i
\(387\) 3.40490e6 + 1.79766e6i 1.15565 + 0.610141i
\(388\) 6.39381e6i 2.15616i
\(389\) −4.15611e6 −1.39256 −0.696278 0.717772i \(-0.745162\pi\)
−0.696278 + 0.717772i \(0.745162\pi\)
\(390\) 2.64033e6 + 4.37972e6i 0.879016 + 1.45809i
\(391\) 3.60822e6 + 2.69807e6i 1.19358 + 0.892507i
\(392\) 1.85888e6i 0.610994i
\(393\) 1.55790e6 + 2.58422e6i 0.508814 + 0.844010i
\(394\) −1.01989e6 −0.330989
\(395\) 6.03260e6i 1.94541i
\(396\) 3.22193e6 6.10257e6i 1.03247 1.95558i
\(397\) −2.25716e6 −0.718763 −0.359382 0.933191i \(-0.617012\pi\)
−0.359382 + 0.933191i \(0.617012\pi\)
\(398\) −4.36833e6 −1.38232
\(399\) 1.57118e6 947190.i 0.494076 0.297855i
\(400\) 6.36614e6 1.98942
\(401\) 3.44745e6 1.07063 0.535313 0.844654i \(-0.320194\pi\)
0.535313 + 0.844654i \(0.320194\pi\)
\(402\) 1.63206e6 983891.i 0.503698 0.303656i
\(403\) 2.48133e6 0.761065
\(404\) 817827.i 0.249292i
\(405\) −3.03398e6 4.44178e6i −0.919127 1.34561i
\(406\) 3.21988e6i 0.969448i
\(407\) 1.51995e6i 0.454824i
\(408\) 4.82822e6 + 8.00895e6i 1.43594 + 2.38191i
\(409\) −3.68766e6 −1.09004 −0.545021 0.838422i \(-0.683478\pi\)
−0.545021 + 0.838422i \(0.683478\pi\)
\(410\) −1.40324e7 −4.12261
\(411\) −5.45802e6 + 3.29039e6i −1.59379 + 0.960821i
\(412\) 1.17404e7i 3.40753i
\(413\) 1.84557e6 0.532420
\(414\) −2.61726e6 5.51688e6i −0.750491 1.58195i
\(415\) 4.09971e6 1.16851
\(416\) 501287.i 0.142021i
\(417\) 754639. 454937.i 0.212520 0.128118i
\(418\) −4.71004e6 −1.31851
\(419\) 4.00739e6 1.11513 0.557566 0.830132i \(-0.311735\pi\)
0.557566 + 0.830132i \(0.311735\pi\)
\(420\) 5.15291e6 + 8.54753e6i 1.42538 + 2.36438i
\(421\) 735310.i 0.202192i −0.994877 0.101096i \(-0.967765\pi\)
0.994877 0.101096i \(-0.0322350\pi\)
\(422\) 1.07608e6i 0.294147i
\(423\) 397264. + 209740.i 0.107951 + 0.0569942i
\(424\) 9.91714e6i 2.67899i
\(425\) 9.18723e6 2.46725
\(426\) −1.11851e7 + 6.74298e6i −2.98618 + 1.80023i
\(427\) −2.68761e6 −0.713340
\(428\) −5.09434e6 −1.34424
\(429\) 2.08528e6 1.25712e6i 0.547043 0.329787i
\(430\) 1.42966e7 3.72873
\(431\) −5.54306e6 −1.43733 −0.718664 0.695357i \(-0.755246\pi\)
−0.718664 + 0.695357i \(0.755246\pi\)
\(432\) −264387. 4.65391e6i −0.0681602 1.19980i
\(433\) 2.50040e6i 0.640898i 0.947266 + 0.320449i \(0.103834\pi\)
−0.947266 + 0.320449i \(0.896166\pi\)
\(434\) 7.18678e6 1.83151
\(435\) 2.24163e6 + 3.71837e6i 0.567991 + 0.942171i
\(436\) 6.93954e6i 1.74830i
\(437\) −1.68173e6 + 2.24903e6i −0.421262 + 0.563367i
\(438\) 638830. + 1.05968e6i 0.159111 + 0.263930i
\(439\) −2.72593e6 −0.675076 −0.337538 0.941312i \(-0.609594\pi\)
−0.337538 + 0.941312i \(0.609594\pi\)
\(440\) 1.32199e7i 3.25534i
\(441\) 624304. 1.18248e6i 0.152862 0.289532i
\(442\) 6.39560e6i 1.55713i
\(443\) 3.79610e6i 0.919027i −0.888171 0.459513i \(-0.848024\pi\)
0.888171 0.459513i \(-0.151976\pi\)
\(444\) 1.88238e6 + 3.12244e6i 0.453157 + 0.751688i
\(445\) −2.18403e6 −0.522829
\(446\) 2.08910e6i 0.497305i
\(447\) 294071. 177282.i 0.0696119 0.0419658i
\(448\) 2.73487e6i 0.643786i
\(449\) 926346.i 0.216849i 0.994105 + 0.108424i \(0.0345806\pi\)
−0.994105 + 0.108424i \(0.965419\pi\)
\(450\) −1.10111e7 5.81344e6i −2.56330 1.35332i
\(451\) 6.68113e6i 1.54671i
\(452\) 745384. 0.171607
\(453\) 2.51869e6 1.51840e6i 0.576673 0.347649i
\(454\) 1.44915e6i 0.329969i
\(455\) 3.52155e6i 0.797454i
\(456\) −4.99203e6 + 3.00947e6i −1.12426 + 0.677762i
\(457\) 4.48757e6i 1.00513i −0.864541 0.502563i \(-0.832391\pi\)
0.864541 0.502563i \(-0.167609\pi\)
\(458\) 1.10139e7 2.45345
\(459\) −381547. 6.71623e6i −0.0845311 1.48797i
\(460\) −1.22352e7 9.14894e6i −2.69597 2.01593i
\(461\) 1.17047e6i 0.256512i −0.991741 0.128256i \(-0.959062\pi\)
0.991741 0.128256i \(-0.0409380\pi\)
\(462\) 6.03968e6 3.64104e6i 1.31646 0.793635i
\(463\) −710023. −0.153929 −0.0769644 0.997034i \(-0.524523\pi\)
−0.0769644 + 0.997034i \(0.524523\pi\)
\(464\) 3.76252e6i 0.811305i
\(465\) −8.29941e6 + 5.00333e6i −1.77998 + 1.07307i
\(466\) 1.33289e7 2.84334
\(467\) 1.07076e6 0.227195 0.113597 0.993527i \(-0.463763\pi\)
0.113597 + 0.993527i \(0.463763\pi\)
\(468\) 2.72693e6 5.16501e6i 0.575519 1.09008i
\(469\) 1.31227e6 0.275481
\(470\) 1.66804e6 0.348307
\(471\) −2.79316e6 4.63324e6i −0.580155 0.962348i
\(472\) −5.86383e6 −1.21151
\(473\) 6.80691e6i 1.39893i
\(474\) 8.75675e6 5.27904e6i 1.79018 1.07922i
\(475\) 5.72647e6i 1.16454i
\(476\) 1.24817e7i 2.52498i
\(477\) 3.33066e6 6.30852e6i 0.670247 1.26950i
\(478\) 944291. 0.189032
\(479\) −318202. −0.0633671 −0.0316835 0.999498i \(-0.510087\pi\)
−0.0316835 + 0.999498i \(0.510087\pi\)
\(480\) −1.01079e6 1.67668e6i −0.200243 0.332159i
\(481\) 1.28644e6i 0.253528i
\(482\) −1.70307e6 −0.333898
\(483\) 417891. 4.18397e6i 0.0815070 0.816057i
\(484\) −1.55358e6 −0.301453
\(485\) 8.81081e6i 1.70083i
\(486\) −3.79256e6 + 8.29097e6i −0.728353 + 1.59226i
\(487\) −1.94918e6 −0.372417 −0.186209 0.982510i \(-0.559620\pi\)
−0.186209 + 0.982510i \(0.559620\pi\)
\(488\) 8.53922e6 1.62319
\(489\) −4.18553e6 + 2.52326e6i −0.791550 + 0.477189i
\(490\) 4.96502e6i 0.934180i
\(491\) 9.83002e6i 1.84014i −0.391754 0.920070i \(-0.628132\pi\)
0.391754 0.920070i \(-0.371868\pi\)
\(492\) 8.27421e6 + 1.37251e7i 1.54104 + 2.55624i
\(493\) 5.42984e6i 1.00617i
\(494\) −3.98642e6 −0.734964
\(495\) −4.43989e6 + 8.40948e6i −0.814440 + 1.54261i
\(496\) −8.39796e6 −1.53274
\(497\) −8.99348e6 −1.63319
\(498\) −3.58759e6 5.95102e6i −0.648231 1.07527i
\(499\) 9.33546e6 1.67836 0.839178 0.543856i \(-0.183036\pi\)
0.839178 + 0.543856i \(0.183036\pi\)
\(500\) −1.23347e7 −2.20650
\(501\) 4.19369e6 + 6.95641e6i 0.746453 + 1.23820i
\(502\) 5.05755e6i 0.895737i
\(503\) 1.08142e6 0.190579 0.0952894 0.995450i \(-0.469622\pi\)
0.0952894 + 0.995450i \(0.469622\pi\)
\(504\) 4.07485e6 7.71807e6i 0.714554 1.35342i
\(505\) 1.12698e6i 0.196648i
\(506\) −6.46464e6 + 8.64538e6i −1.12245 + 1.50109i
\(507\) −3.19191e6 + 1.92425e6i −0.551481 + 0.332462i
\(508\) −8.30018e6 −1.42701
\(509\) 2.59686e6i 0.444277i 0.975015 + 0.222139i \(0.0713038\pi\)
−0.975015 + 0.222139i \(0.928696\pi\)
\(510\) −1.28960e7 2.13916e7i −2.19548 3.64182i
\(511\) 852043.i 0.144348i
\(512\) 1.16058e7i 1.95660i
\(513\) 4.18628e6 237821.i 0.702319 0.0398985i
\(514\) 1.05299e7 1.75799
\(515\) 1.61785e7i 2.68795i
\(516\) −8.42998e6 1.39835e7i −1.39381 2.31202i
\(517\) 794190.i 0.130677i
\(518\) 3.72596e6i 0.610118i
\(519\) −1.98087e6 3.28582e6i −0.322803 0.535458i
\(520\) 1.11889e7i 1.81459i
\(521\) −2.67623e6 −0.431946 −0.215973 0.976399i \(-0.569292\pi\)
−0.215973 + 0.976399i \(0.569292\pi\)
\(522\) 3.43586e6 6.50778e6i 0.551899 1.04534i
\(523\) 1.30259e6i 0.208235i 0.994565 + 0.104118i \(0.0332019\pi\)
−0.994565 + 0.104118i \(0.966798\pi\)
\(524\) 1.27962e7i 2.03588i
\(525\) −4.42678e6 7.34304e6i −0.700954 1.16273i
\(526\) 8.59953e6i 1.35522i
\(527\) −1.21194e7 −1.90088
\(528\) −7.05755e6 + 4.25467e6i −1.10171 + 0.664173i
\(529\) 1.81993e6 + 6.17368e6i 0.282758 + 0.959191i
\(530\) 2.64884e7i 4.09605i
\(531\) 3.73012e6 + 1.96936e6i 0.574099 + 0.303102i
\(532\) −7.77997e6 −1.19179
\(533\) 5.65469e6i 0.862165i
\(534\) 1.91122e6 + 3.17028e6i 0.290039 + 0.481111i
\(535\) 7.02011e6 1.06038
\(536\) −4.16941e6 −0.626849
\(537\) 878604. + 1.45741e6i 0.131479 + 0.218095i
\(538\) 1.67687e6 0.249772
\(539\) −2.36395e6 −0.350483
\(540\) 1.29380e6 + 2.27742e7i 0.190933 + 3.36092i
\(541\) −9.58678e6 −1.40825 −0.704125 0.710076i \(-0.748661\pi\)
−0.704125 + 0.710076i \(0.748661\pi\)
\(542\) 2.31105e7i 3.37918i
\(543\) 4.65393e6 + 7.71983e6i 0.677361 + 1.12359i
\(544\) 2.44841e6i 0.354721i
\(545\) 9.56285e6i 1.37910i
\(546\) 5.11179e6 3.08166e6i 0.733823 0.442388i
\(547\) 1.15831e7 1.65522 0.827609 0.561306i \(-0.189701\pi\)
0.827609 + 0.561306i \(0.189701\pi\)
\(548\) 2.70263e7 3.84446
\(549\) −5.43200e6 2.86789e6i −0.769181 0.406099i
\(550\) 2.20128e7i 3.10291i
\(551\) −3.38446e6 −0.474909
\(552\) −1.32775e6 + 1.32935e7i −0.185467 + 1.85692i
\(553\) 7.04094e6 0.979080
\(554\) 9.33284e6i 1.29193i
\(555\) −2.59396e6 4.30280e6i −0.357463 0.592951i
\(556\) −3.73673e6 −0.512631
\(557\) −1.87141e6 −0.255583 −0.127791 0.991801i \(-0.540789\pi\)
−0.127791 + 0.991801i \(0.540789\pi\)
\(558\) 1.45254e7 + 7.66885e6i 1.97489 + 1.04267i
\(559\) 5.76114e6i 0.779793i
\(560\) 1.19186e7i 1.60603i
\(561\) −1.01850e7 + 6.14008e6i −1.36633 + 0.823696i
\(562\) 1.19247e7i 1.59260i
\(563\) −3.40573e6 −0.452834 −0.226417 0.974030i \(-0.572701\pi\)
−0.226417 + 0.974030i \(0.572701\pi\)
\(564\) −983560. 1.63151e6i −0.130198 0.215969i
\(565\) −1.02716e6 −0.135368
\(566\) 1.80374e7 2.36664
\(567\) −5.18421e6 + 3.54111e6i −0.677213 + 0.462575i
\(568\) 2.85746e7 3.71628
\(569\) 1.46985e7 1.90324 0.951618 0.307283i \(-0.0994199\pi\)
0.951618 + 0.307283i \(0.0994199\pi\)
\(570\) 1.33336e7 8.03819e6i 1.71893 1.03627i
\(571\) 3.73074e6i 0.478856i 0.970914 + 0.239428i \(0.0769598\pi\)
−0.970914 + 0.239428i \(0.923040\pi\)
\(572\) −1.03256e7 −1.31955
\(573\) −5.77118e6 + 3.47918e6i −0.734308 + 0.442680i
\(574\) 1.63779e7i 2.07481i
\(575\) 1.05110e7 + 7.85970e6i 1.32579 + 0.991372i
\(576\) 2.91832e6 5.52752e6i 0.366502 0.694183i
\(577\) −2.38914e6 −0.298746 −0.149373 0.988781i \(-0.547725\pi\)
−0.149373 + 0.988781i \(0.547725\pi\)
\(578\) 1.71742e7i 2.13825i
\(579\) 788044. 475075.i 0.0976908 0.0588933i
\(580\) 1.84122e7i 2.27266i
\(581\) 4.78497e6i 0.588083i
\(582\) −1.27895e7 + 7.71021e6i −1.56512 + 0.943537i
\(583\) −1.26117e7 −1.53674
\(584\) 2.70716e6i 0.328459i
\(585\) −3.75777e6 + 7.11750e6i −0.453984 + 0.859880i
\(586\) 1.55104e7i 1.86586i
\(587\) 88203.1i 0.0105655i 0.999986 + 0.00528273i \(0.00168155\pi\)
−0.999986 + 0.00528273i \(0.998318\pi\)
\(588\) −4.85628e6 + 2.92763e6i −0.579243 + 0.349199i
\(589\) 7.55413e6i 0.897214i
\(590\) 1.56621e7 1.85234
\(591\) −828714. 1.37465e6i −0.0975969 0.161892i
\(592\) 4.35389e6i 0.510591i
\(593\) 1.88014e6i 0.219560i −0.993956 0.109780i \(-0.964985\pi\)
0.993956 0.109780i \(-0.0350147\pi\)
\(594\) 1.60922e7 914195.i 1.87133 0.106310i
\(595\) 1.72001e7i 1.99177i
\(596\) −1.45614e6 −0.167915
\(597\) −3.54950e6 5.88783e6i −0.407597 0.676113i
\(598\) −5.47145e6 + 7.31716e6i −0.625676 + 0.836738i
\(599\) 1.26695e7i 1.44276i −0.692541 0.721378i \(-0.743509\pi\)
0.692541 0.721378i \(-0.256491\pi\)
\(600\) 1.40650e7 + 2.33307e7i 1.59500 + 2.64576i
\(601\) 1.09195e7 1.23315 0.616574 0.787297i \(-0.288520\pi\)
0.616574 + 0.787297i \(0.288520\pi\)
\(602\) 1.66862e7i 1.87658i
\(603\) 2.65226e6 + 1.40029e6i 0.297046 + 0.156829i
\(604\) −1.24718e7 −1.39103
\(605\) 2.14086e6 0.237794
\(606\) 1.63590e6 986207.i 0.180957 0.109090i
\(607\) −5.76812e6 −0.635423 −0.317711 0.948187i \(-0.602914\pi\)
−0.317711 + 0.948187i \(0.602914\pi\)
\(608\) 1.52611e6 0.167428
\(609\) 4.33989e6 2.61632e6i 0.474172 0.285856i
\(610\) −2.28080e7 −2.48178
\(611\) 672176.i 0.0728417i
\(612\) −1.33190e7 + 2.52272e7i −1.43745 + 2.72264i
\(613\) 224080.i 0.0240853i −0.999927 0.0120427i \(-0.996167\pi\)
0.999927 0.0120427i \(-0.00383339\pi\)
\(614\) 1.17839e6i 0.126144i
\(615\) −1.14021e7 1.89135e7i −1.21561 2.01643i
\(616\) −1.54296e7 −1.63833
\(617\) −3.12193e6 −0.330149 −0.165075 0.986281i \(-0.552786\pi\)
−0.165075 + 0.986281i \(0.552786\pi\)
\(618\) 2.34843e7 1.41576e7i 2.47347 1.49114i
\(619\) 8.70665e6i 0.913324i −0.889640 0.456662i \(-0.849045\pi\)
0.889640 0.456662i \(-0.150955\pi\)
\(620\) 4.10960e7 4.29359
\(621\) 5.30923e6 8.01040e6i 0.552462 0.833538i
\(622\) −1.37721e7 −1.42732
\(623\) 2.54909e6i 0.263127i
\(624\) −5.97328e6 + 3.60101e6i −0.614117 + 0.370223i
\(625\) 830934. 0.0850876
\(626\) −2.07017e7 −2.11140
\(627\) −3.82716e6 6.34840e6i −0.388783 0.644905i
\(628\) 2.29423e7i 2.32133i
\(629\) 6.28327e6i 0.633227i
\(630\) −1.08838e7 + 2.06147e7i −1.09252 + 2.06931i
\(631\) 285663.i 0.0285614i −0.999898 0.0142807i \(-0.995454\pi\)
0.999898 0.0142807i \(-0.00454585\pi\)
\(632\) −2.23709e7 −2.22787
\(633\) −1.45039e6 + 874373.i −0.143872 + 0.0867336i
\(634\) −2.02888e6 −0.200462
\(635\) 1.14378e7 1.12567
\(636\) −2.59082e7 + 1.56189e7i −2.53978 + 1.53111i
\(637\) −2.00077e6 −0.195366
\(638\) −1.30100e7 −1.26540
\(639\) −1.81770e7 9.59674e6i −1.76104 0.929762i
\(640\) 2.72280e7i 2.62764i
\(641\) 1.12266e7 1.07920 0.539601 0.841921i \(-0.318575\pi\)
0.539601 + 0.841921i \(0.318575\pi\)
\(642\) −6.14319e6 1.01902e7i −0.588243 0.975764i
\(643\) 3.68982e6i 0.351948i 0.984395 + 0.175974i \(0.0563074\pi\)
−0.984395 + 0.175974i \(0.943693\pi\)
\(644\) −1.06782e7 + 1.42803e7i −1.01457 + 1.35682i
\(645\) 1.16167e7 + 1.92695e7i 1.09947 + 1.82378i
\(646\) 1.94707e7 1.83569
\(647\) 1.53881e7i 1.44519i −0.691273 0.722594i \(-0.742950\pi\)
0.691273 0.722594i \(-0.257050\pi\)
\(648\) 1.64716e7 1.12510e7i 1.54098 1.05258i
\(649\) 7.45707e6i 0.694955i
\(650\) 1.86309e7i 1.72962i
\(651\) 5.83963e6 + 9.68665e6i 0.540049 + 0.895821i
\(652\) 2.07254e7 1.90934
\(653\) 7.65531e6i 0.702554i −0.936272 0.351277i \(-0.885747\pi\)
0.936272 0.351277i \(-0.114253\pi\)
\(654\) 1.38812e7 8.36831e6i 1.26906 0.765056i
\(655\) 1.76335e7i 1.60596i
\(656\) 1.91381e7i 1.73635i
\(657\) −909197. + 1.72209e6i −0.0821759 + 0.155647i
\(658\) 1.94685e6i 0.175294i
\(659\) −3.28275e6 −0.294458 −0.147229 0.989102i \(-0.547035\pi\)
−0.147229 + 0.989102i \(0.547035\pi\)
\(660\) 3.45366e7 2.08205e7i 3.08617 1.86051i
\(661\) 1.61641e7i 1.43896i 0.694512 + 0.719481i \(0.255620\pi\)
−0.694512 + 0.719481i \(0.744380\pi\)
\(662\) 3.28016e7i 2.90904i
\(663\) −8.62027e6 + 5.19676e6i −0.761617 + 0.459144i
\(664\) 1.52031e7i 1.33817i
\(665\) 1.07210e7 0.940113
\(666\) −3.97589e6 + 7.53063e6i −0.347335 + 0.657879i
\(667\) −4.64525e6 + 6.21224e6i −0.404291 + 0.540672i
\(668\) 3.44459e7i 2.98673i
\(669\) −2.81578e6 + 1.69751e6i −0.243240 + 0.146638i
\(670\) 1.11364e7 0.958422
\(671\) 1.08594e7i 0.931105i
\(672\) −1.95693e6 + 1.17974e6i −0.167168 + 0.100778i
\(673\) 1.47135e7 1.25221 0.626106 0.779738i \(-0.284648\pi\)
0.626106 + 0.779738i \(0.284648\pi\)
\(674\) 2.70305e7 2.29194
\(675\) −1.11148e6 1.95649e7i −0.0938948 1.65279i
\(676\) 1.58053e7 1.33026
\(677\) 2.08650e7 1.74963 0.874816 0.484455i \(-0.160982\pi\)
0.874816 + 0.484455i \(0.160982\pi\)
\(678\) 898849. + 1.49099e6i 0.0750952 + 0.124566i
\(679\) −1.02835e7 −0.855988
\(680\) 5.46492e7i 4.53223i
\(681\) −1.95322e6 + 1.17751e6i −0.161393 + 0.0972962i
\(682\) 2.90384e7i 2.39063i
\(683\) 5.62315e6i 0.461241i −0.973044 0.230620i \(-0.925924\pi\)
0.973044 0.230620i \(-0.0740756\pi\)
\(684\) −1.57243e7 8.30183e6i −1.28508 0.678475i
\(685\) −3.72429e7 −3.03261
\(686\) −2.34943e7 −1.90613
\(687\) 8.94935e6 + 1.48450e7i 0.723436 + 1.20002i
\(688\) 1.94984e7i 1.57046i
\(689\) −1.06741e7 −0.856611
\(690\) 3.54637e6 3.55066e7i 0.283570 2.83914i
\(691\) −913111. −0.0727492 −0.0363746 0.999338i \(-0.511581\pi\)
−0.0363746 + 0.999338i \(0.511581\pi\)
\(692\) 1.62703e7i 1.29161i
\(693\) 9.81511e6 + 5.18201e6i 0.776358 + 0.409888i
\(694\) 3.62946e6 0.286051
\(695\) 5.14930e6 0.404377
\(696\) −1.37889e7 + 8.31271e6i −1.07897 + 0.650458i
\(697\) 2.76189e7i 2.15340i
\(698\) 1.53749e7i 1.19447i
\(699\) 1.08304e7 + 1.79652e7i 0.838401 + 1.39072i
\(700\) 3.63604e7i 2.80468i
\(701\) −1.66750e7 −1.28165 −0.640826 0.767686i \(-0.721408\pi\)
−0.640826 + 0.767686i \(0.721408\pi\)
\(702\) 1.36199e7 773744.i 1.04312 0.0592591i
\(703\) 3.91641e6 0.298882
\(704\) −1.10503e7 −0.840319
\(705\) 1.35537e6 + 2.24826e6i 0.102703 + 0.170362i
\(706\) −1.95220e7 −1.47405
\(707\) 1.31536e6 0.0989682
\(708\) −9.23517e6 1.53191e7i −0.692408 1.14855i
\(709\) 681530.i 0.0509178i 0.999676 + 0.0254589i \(0.00810469\pi\)
−0.999676 + 0.0254589i \(0.991895\pi\)
\(710\) −7.63218e7 −5.68202
\(711\) 1.42306e7 + 7.51324e6i 1.05572 + 0.557382i
\(712\) 8.09912e6i 0.598739i
\(713\) −1.38657e7 1.03682e7i −1.02146 0.763800i
\(714\) −2.49672e7 + 1.50516e7i −1.83284 + 1.10493i
\(715\) 1.42290e7 1.04090
\(716\) 7.21661e6i 0.526079i
\(717\) 767286. + 1.27276e6i 0.0557390 + 0.0924586i
\(718\) 9.78834e6i 0.708594i
\(719\) 1.36916e7i 0.987713i −0.869543 0.493857i \(-0.835587\pi\)
0.869543 0.493857i \(-0.164413\pi\)
\(720\) 1.27180e7 2.40889e7i 0.914300 1.73175i
\(721\) 1.88827e7 1.35278
\(722\) 1.23891e7i 0.884499i
\(723\) −1.38383e6 2.29547e6i −0.0984549 0.163315i
\(724\) 3.82261e7i 2.71028i
\(725\) 1.58176e7i 1.11762i
\(726\) −1.87344e6 3.10762e6i −0.131916 0.218819i
\(727\) 1.83897e6i 0.129044i −0.997916 0.0645221i \(-0.979448\pi\)
0.997916 0.0645221i \(-0.0205523\pi\)
\(728\) −1.30591e7 −0.913238
\(729\) −1.42566e7 + 1.62507e6i −0.993566 + 0.113254i
\(730\) 7.23073e6i 0.502198i
\(731\) 2.81388e7i 1.94766i
\(732\) 1.34487e7 + 2.23085e7i 0.927693 + 1.53884i
\(733\) 2.18827e7i 1.50432i 0.658979 + 0.752162i \(0.270989\pi\)
−0.658979 + 0.752162i \(0.729011\pi\)
\(734\) −1.64978e7 −1.13028
\(735\) 6.69207e6 4.03434e6i 0.456922 0.275457i
\(736\) 2.09462e6 2.80120e6i 0.142531 0.190612i
\(737\) 5.30227e6i 0.359578i
\(738\) −1.74765e7 + 3.31018e7i −1.18117 + 2.23723i
\(739\) 2.21664e7 1.49308 0.746541 0.665340i \(-0.231713\pi\)
0.746541 + 0.665340i \(0.231713\pi\)
\(740\) 2.13061e7i 1.43029i
\(741\) −3.23918e6 5.37308e6i −0.216715 0.359482i
\(742\) −3.09159e7 −2.06144
\(743\) −1.24012e7 −0.824126 −0.412063 0.911155i \(-0.635192\pi\)
−0.412063 + 0.911155i \(0.635192\pi\)
\(744\) −1.85540e7 3.07769e7i −1.22887 2.03842i
\(745\) 2.00660e6 0.132456
\(746\) −7.42731e6 −0.488635
\(747\) 5.10594e6 9.67103e6i 0.334791 0.634119i
\(748\) 5.04329e7 3.29580
\(749\) 8.19351e6i 0.533661i
\(750\) −1.48743e7 2.46731e7i −0.965568 1.60166i
\(751\) 1.39231e7i 0.900818i −0.892822 0.450409i \(-0.851278\pi\)
0.892822 0.450409i \(-0.148722\pi\)
\(752\) 2.27495e6i 0.146699i
\(753\) −6.81678e6 + 4.10952e6i −0.438119 + 0.264121i
\(754\) −1.10113e7 −0.705356
\(755\) 1.71864e7 1.09728
\(756\) 2.65809e7 1.51005e6i 1.69147 0.0960920i
\(757\) 2.60434e7i 1.65180i −0.563817 0.825900i \(-0.690668\pi\)
0.563817 0.825900i \(-0.309332\pi\)
\(758\) −1.93598e7 −1.22385
\(759\) −1.69055e7 1.68850e6i −1.06518 0.106389i
\(760\) −3.40633e7 −2.13920
\(761\) 9.67510e6i 0.605611i −0.953052 0.302805i \(-0.902077\pi\)
0.953052 0.302805i \(-0.0979232\pi\)
\(762\) −1.00091e7 1.66028e7i −0.624463 1.03585i
\(763\) 1.11613e7 0.694068
\(764\) 2.85770e7 1.77126
\(765\) 1.83539e7 3.47636e7i 1.13390 2.14769i
\(766\) 1.08959e7i 0.670952i
\(767\) 6.31142e6i 0.387381i
\(768\) −2.85346e7 + 1.72022e7i −1.74569 + 1.05240i
\(769\) 205320.i 0.0125203i −0.999980 0.00626017i \(-0.998007\pi\)
0.999980 0.00626017i \(-0.00199269\pi\)
\(770\) 4.12119e7 2.50493
\(771\) 8.55609e6 + 1.41927e7i 0.518370 + 0.859860i
\(772\) −3.90214e6 −0.235645
\(773\) 8.35486e6 0.502910 0.251455 0.967869i \(-0.419091\pi\)
0.251455 + 0.967869i \(0.419091\pi\)
\(774\) 1.78055e7 3.37250e7i 1.06832 2.02348i
\(775\) −3.53049e7 −2.11145
\(776\) 3.26734e7 1.94778
\(777\) −5.02201e6 + 3.02753e6i −0.298418 + 0.179902i
\(778\) 4.11655e7i