Properties

Label 69.6.c.b.68.19
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 68.19
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.13

$q$-expansion

\(f(q)\) \(=\) \(q+1.57119i q^{2} +(-12.8969 + 8.75610i) q^{3} +29.5314 q^{4} -37.1969 q^{5} +(-13.7575 - 20.2635i) q^{6} +122.242i q^{7} +96.6776i q^{8} +(89.6613 - 225.854i) q^{9} +O(q^{10})\) \(q+1.57119i q^{2} +(-12.8969 + 8.75610i) q^{3} +29.5314 q^{4} -37.1969 q^{5} +(-13.7575 - 20.2635i) q^{6} +122.242i q^{7} +96.6776i q^{8} +(89.6613 - 225.854i) q^{9} -58.4435i q^{10} -321.586 q^{11} +(-380.864 + 258.580i) q^{12} -207.773 q^{13} -192.066 q^{14} +(479.726 - 325.700i) q^{15} +793.104 q^{16} -1644.37 q^{17} +(354.859 + 140.875i) q^{18} -2885.27i q^{19} -1098.48 q^{20} +(-1070.37 - 1576.55i) q^{21} -505.273i q^{22} +(-2534.43 - 114.122i) q^{23} +(-846.519 - 1246.84i) q^{24} -1741.39 q^{25} -326.451i q^{26} +(821.243 + 3697.90i) q^{27} +3609.98i q^{28} -2444.83i q^{29} +(511.737 + 753.742i) q^{30} -244.199 q^{31} +4339.80i q^{32} +(4147.47 - 2815.84i) q^{33} -2583.63i q^{34} -4547.03i q^{35} +(2647.82 - 6669.76i) q^{36} +9937.02i q^{37} +4533.31 q^{38} +(2679.63 - 1819.28i) q^{39} -3596.11i q^{40} +17465.4i q^{41} +(2477.06 - 1681.75i) q^{42} +3358.44i q^{43} -9496.87 q^{44} +(-3335.12 + 8401.06i) q^{45} +(179.307 - 3982.07i) q^{46} -15047.0i q^{47} +(-10228.6 + 6944.50i) q^{48} +1863.84 q^{49} -2736.06i q^{50} +(21207.4 - 14398.3i) q^{51} -6135.81 q^{52} +7910.60 q^{53} +(-5810.11 + 1290.33i) q^{54} +11962.0 q^{55} -11818.1 q^{56} +(25263.7 + 37211.1i) q^{57} +3841.31 q^{58} -11354.1i q^{59} +(14167.0 - 9618.37i) q^{60} +25900.1i q^{61} -383.684i q^{62} +(27608.8 + 10960.4i) q^{63} +18560.7 q^{64} +7728.51 q^{65} +(4424.22 + 6516.47i) q^{66} +36948.4i q^{67} -48560.6 q^{68} +(33685.6 - 20719.9i) q^{69} +7144.27 q^{70} +52830.9i q^{71} +(21835.0 + 8668.24i) q^{72} -71803.2 q^{73} -15613.0 q^{74} +(22458.6 - 15247.8i) q^{75} -85205.9i q^{76} -39311.4i q^{77} +(2858.44 + 4210.21i) q^{78} -43369.5i q^{79} -29501.0 q^{80} +(-42970.7 - 40500.7i) q^{81} -27441.5 q^{82} -107131. q^{83} +(-31609.3 - 46557.6i) q^{84} +61165.6 q^{85} -5276.76 q^{86} +(21407.2 + 31530.8i) q^{87} -31090.1i q^{88} +1120.11 q^{89} +(-13199.7 - 5240.12i) q^{90} -25398.6i q^{91} +(-74845.1 - 3370.17i) q^{92} +(3149.42 - 2138.23i) q^{93} +23641.7 q^{94} +107323. i q^{95} +(-37999.8 - 55970.1i) q^{96} +26716.2i q^{97} +2928.45i q^{98} +(-28833.8 + 72631.3i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57119i 0.277750i 0.990310 + 0.138875i \(0.0443487\pi\)
−0.990310 + 0.138875i \(0.955651\pi\)
\(3\) −12.8969 + 8.75610i −0.827338 + 0.561704i
\(4\) 29.5314 0.922855
\(5\) −37.1969 −0.665399 −0.332699 0.943033i \(-0.607959\pi\)
−0.332699 + 0.943033i \(0.607959\pi\)
\(6\) −13.7575 20.2635i −0.156013 0.229793i
\(7\) 122.242i 0.942923i 0.881887 + 0.471461i \(0.156273\pi\)
−0.881887 + 0.471461i \(0.843727\pi\)
\(8\) 96.6776i 0.534073i
\(9\) 89.6613 225.854i 0.368976 0.929439i
\(10\) 58.4435i 0.184815i
\(11\) −321.586 −0.801337 −0.400669 0.916223i \(-0.631222\pi\)
−0.400669 + 0.916223i \(0.631222\pi\)
\(12\) −380.864 + 258.580i −0.763513 + 0.518372i
\(13\) −207.773 −0.340981 −0.170491 0.985359i \(-0.554535\pi\)
−0.170491 + 0.985359i \(0.554535\pi\)
\(14\) −192.066 −0.261897
\(15\) 479.726 325.700i 0.550510 0.373757i
\(16\) 793.104 0.774516
\(17\) −1644.37 −1.38000 −0.689999 0.723811i \(-0.742389\pi\)
−0.689999 + 0.723811i \(0.742389\pi\)
\(18\) 354.859 + 140.875i 0.258152 + 0.102483i
\(19\) 2885.27i 1.83359i −0.399357 0.916795i \(-0.630767\pi\)
0.399357 0.916795i \(-0.369233\pi\)
\(20\) −1098.48 −0.614066
\(21\) −1070.37 1576.55i −0.529644 0.780116i
\(22\) 505.273i 0.222572i
\(23\) −2534.43 114.122i −0.998988 0.0449831i
\(24\) −846.519 1246.84i −0.299991 0.441859i
\(25\) −1741.39 −0.557245
\(26\) 326.451i 0.0947076i
\(27\) 821.243 + 3697.90i 0.216801 + 0.976216i
\(28\) 3609.98i 0.870181i
\(29\) 2444.83i 0.539827i −0.962885 0.269913i \(-0.913005\pi\)
0.962885 0.269913i \(-0.0869951\pi\)
\(30\) 511.737 + 753.742i 0.103811 + 0.152904i
\(31\) −244.199 −0.0456394 −0.0228197 0.999740i \(-0.507264\pi\)
−0.0228197 + 0.999740i \(0.507264\pi\)
\(32\) 4339.80i 0.749195i
\(33\) 4147.47 2815.84i 0.662977 0.450114i
\(34\) 2583.63i 0.383294i
\(35\) 4547.03i 0.627420i
\(36\) 2647.82 6669.76i 0.340512 0.857737i
\(37\) 9937.02i 1.19331i 0.802499 + 0.596653i \(0.203503\pi\)
−0.802499 + 0.596653i \(0.796497\pi\)
\(38\) 4533.31 0.509280
\(39\) 2679.63 1819.28i 0.282107 0.191531i
\(40\) 3596.11i 0.355372i
\(41\) 17465.4i 1.62263i 0.584611 + 0.811313i \(0.301247\pi\)
−0.584611 + 0.811313i \(0.698753\pi\)
\(42\) 2477.06 1681.75i 0.216677 0.147109i
\(43\) 3358.44i 0.276992i 0.990363 + 0.138496i \(0.0442268\pi\)
−0.990363 + 0.138496i \(0.955773\pi\)
\(44\) −9496.87 −0.739518
\(45\) −3335.12 + 8401.06i −0.245516 + 0.618447i
\(46\) 179.307 3982.07i 0.0124941 0.277469i
\(47\) 15047.0i 0.993583i −0.867870 0.496791i \(-0.834511\pi\)
0.867870 0.496791i \(-0.165489\pi\)
\(48\) −10228.6 + 6944.50i −0.640786 + 0.435049i
\(49\) 1863.84 0.110896
\(50\) 2736.06i 0.154775i
\(51\) 21207.4 14398.3i 1.14172 0.775150i
\(52\) −6135.81 −0.314676
\(53\) 7910.60 0.386830 0.193415 0.981117i \(-0.438044\pi\)
0.193415 + 0.981117i \(0.438044\pi\)
\(54\) −5810.11 + 1290.33i −0.271144 + 0.0602166i
\(55\) 11962.0 0.533209
\(56\) −11818.1 −0.503590
\(57\) 25263.7 + 37211.1i 1.02994 + 1.51700i
\(58\) 3841.31 0.149937
\(59\) 11354.1i 0.424640i −0.977200 0.212320i \(-0.931898\pi\)
0.977200 0.212320i \(-0.0681019\pi\)
\(60\) 14167.0 9618.37i 0.508041 0.344924i
\(61\) 25900.1i 0.891204i 0.895231 + 0.445602i \(0.147010\pi\)
−0.895231 + 0.445602i \(0.852990\pi\)
\(62\) 383.684i 0.0126764i
\(63\) 27608.8 + 10960.4i 0.876389 + 0.347916i
\(64\) 18560.7 0.566427
\(65\) 7728.51 0.226888
\(66\) 4424.22 + 6516.47i 0.125019 + 0.184142i
\(67\) 36948.4i 1.00556i 0.864414 + 0.502781i \(0.167690\pi\)
−0.864414 + 0.502781i \(0.832310\pi\)
\(68\) −48560.6 −1.27354
\(69\) 33685.6 20719.9i 0.851768 0.523920i
\(70\) 7144.27 0.174266
\(71\) 52830.9i 1.24378i 0.783106 + 0.621888i \(0.213634\pi\)
−0.783106 + 0.621888i \(0.786366\pi\)
\(72\) 21835.0 + 8668.24i 0.496388 + 0.197060i
\(73\) −71803.2 −1.57702 −0.788510 0.615023i \(-0.789147\pi\)
−0.788510 + 0.615023i \(0.789147\pi\)
\(74\) −15613.0 −0.331441
\(75\) 22458.6 15247.8i 0.461030 0.313007i
\(76\) 85205.9i 1.69214i
\(77\) 39311.4i 0.755599i
\(78\) 2858.44 + 4210.21i 0.0531976 + 0.0783552i
\(79\) 43369.5i 0.781839i −0.920425 0.390919i \(-0.872157\pi\)
0.920425 0.390919i \(-0.127843\pi\)
\(80\) −29501.0 −0.515362
\(81\) −42970.7 40500.7i −0.727713 0.685882i
\(82\) −27441.5 −0.450685
\(83\) −107131. −1.70694 −0.853471 0.521140i \(-0.825507\pi\)
−0.853471 + 0.521140i \(0.825507\pi\)
\(84\) −31609.3 46557.6i −0.488784 0.719934i
\(85\) 61165.6 0.918248
\(86\) −5276.76 −0.0769345
\(87\) 21407.2 + 31530.8i 0.303223 + 0.446619i
\(88\) 31090.1i 0.427973i
\(89\) 1120.11 0.0149895 0.00749474 0.999972i \(-0.497614\pi\)
0.00749474 + 0.999972i \(0.497614\pi\)
\(90\) −13199.7 5240.12i −0.171774 0.0681923i
\(91\) 25398.6i 0.321519i
\(92\) −74845.1 3370.17i −0.921921 0.0415129i
\(93\) 3149.42 2138.23i 0.0377592 0.0256359i
\(94\) 23641.7 0.275968
\(95\) 107323.i 1.22007i
\(96\) −37999.8 55970.1i −0.420826 0.619838i
\(97\) 26716.2i 0.288301i 0.989556 + 0.144150i \(0.0460449\pi\)
−0.989556 + 0.144150i \(0.953955\pi\)
\(98\) 2928.45i 0.0308015i
\(99\) −28833.8 + 72631.3i −0.295675 + 0.744794i
\(100\) −51425.6 −0.514256
\(101\) 79301.9i 0.773536i −0.922177 0.386768i \(-0.873591\pi\)
0.922177 0.386768i \(-0.126409\pi\)
\(102\) 22622.5 + 33320.8i 0.215298 + 0.317114i
\(103\) 79210.1i 0.735678i −0.929890 0.367839i \(-0.880098\pi\)
0.929890 0.367839i \(-0.119902\pi\)
\(104\) 20087.0i 0.182109i
\(105\) 39814.3 + 58642.8i 0.352424 + 0.519088i
\(106\) 12429.1i 0.107442i
\(107\) 191353. 1.61576 0.807878 0.589350i \(-0.200616\pi\)
0.807878 + 0.589350i \(0.200616\pi\)
\(108\) 24252.4 + 109204.i 0.200076 + 0.900905i
\(109\) 123427.i 0.995047i 0.867451 + 0.497523i \(0.165757\pi\)
−0.867451 + 0.497523i \(0.834243\pi\)
\(110\) 18794.6i 0.148099i
\(111\) −87009.5 128157.i −0.670285 0.987267i
\(112\) 96950.8i 0.730309i
\(113\) 52135.8 0.384096 0.192048 0.981386i \(-0.438487\pi\)
0.192048 + 0.981386i \(0.438487\pi\)
\(114\) −58465.8 + 39694.2i −0.421347 + 0.286065i
\(115\) 94272.9 + 4244.98i 0.664725 + 0.0299317i
\(116\) 72199.3i 0.498182i
\(117\) −18629.2 + 46926.2i −0.125814 + 0.316921i
\(118\) 17839.4 0.117944
\(119\) 201012.i 1.30123i
\(120\) 31487.9 + 46378.7i 0.199614 + 0.294013i
\(121\) −57633.5 −0.357859
\(122\) −40694.1 −0.247532
\(123\) −152929. 225250.i −0.911437 1.34246i
\(124\) −7211.53 −0.0421185
\(125\) 181015. 1.03619
\(126\) −17220.9 + 43378.8i −0.0966338 + 0.243417i
\(127\) −104033. −0.572349 −0.286174 0.958178i \(-0.592384\pi\)
−0.286174 + 0.958178i \(0.592384\pi\)
\(128\) 168036.i 0.906520i
\(129\) −29406.9 43313.6i −0.155588 0.229166i
\(130\) 12143.0i 0.0630183i
\(131\) 319871.i 1.62853i 0.580491 + 0.814267i \(0.302861\pi\)
−0.580491 + 0.814267i \(0.697139\pi\)
\(132\) 122480. 83155.5i 0.611831 0.415390i
\(133\) 352702. 1.72893
\(134\) −58053.1 −0.279295
\(135\) −30547.7 137551.i −0.144259 0.649573i
\(136\) 158974.i 0.737020i
\(137\) 202011. 0.919546 0.459773 0.888037i \(-0.347931\pi\)
0.459773 + 0.888037i \(0.347931\pi\)
\(138\) 32554.9 + 52926.5i 0.145519 + 0.236579i
\(139\) −197570. −0.867330 −0.433665 0.901074i \(-0.642780\pi\)
−0.433665 + 0.901074i \(0.642780\pi\)
\(140\) 134280.i 0.579017i
\(141\) 131753. + 194059.i 0.558100 + 0.822029i
\(142\) −83007.5 −0.345459
\(143\) 66816.8 0.273241
\(144\) 71110.8 179125.i 0.285778 0.719865i
\(145\) 90940.3i 0.359200i
\(146\) 112817.i 0.438017i
\(147\) −24037.8 + 16320.0i −0.0917489 + 0.0622910i
\(148\) 293454.i 1.10125i
\(149\) 206334. 0.761385 0.380692 0.924702i \(-0.375686\pi\)
0.380692 + 0.924702i \(0.375686\pi\)
\(150\) 23957.2 + 35286.7i 0.0869377 + 0.128051i
\(151\) −72590.0 −0.259080 −0.129540 0.991574i \(-0.541350\pi\)
−0.129540 + 0.991574i \(0.541350\pi\)
\(152\) 278941. 0.979272
\(153\) −147437. + 371388.i −0.509186 + 1.28262i
\(154\) 61765.7 0.209868
\(155\) 9083.46 0.0303684
\(156\) 79133.1 53725.8i 0.260343 0.176755i
\(157\) 344412.i 1.11514i 0.830131 + 0.557569i \(0.188266\pi\)
−0.830131 + 0.557569i \(0.811734\pi\)
\(158\) 68141.9 0.217156
\(159\) −102022. + 69266.0i −0.320039 + 0.217284i
\(160\) 161427.i 0.498514i
\(161\) 13950.5 309814.i 0.0424156 0.941968i
\(162\) 63634.3 67515.2i 0.190504 0.202122i
\(163\) 52358.0 0.154353 0.0771764 0.997017i \(-0.475410\pi\)
0.0771764 + 0.997017i \(0.475410\pi\)
\(164\) 515777.i 1.49745i
\(165\) −154273. + 104741.i −0.441144 + 0.299506i
\(166\) 168323.i 0.474103i
\(167\) 464676.i 1.28931i −0.764472 0.644657i \(-0.777000\pi\)
0.764472 0.644657i \(-0.223000\pi\)
\(168\) 152417. 103480.i 0.416639 0.282869i
\(169\) −328123. −0.883732
\(170\) 96103.0i 0.255044i
\(171\) −651649. 258697.i −1.70421 0.676552i
\(172\) 99179.4i 0.255623i
\(173\) 7055.13i 0.0179221i −0.999960 0.00896107i \(-0.997148\pi\)
0.999960 0.00896107i \(-0.00285243\pi\)
\(174\) −49541.0 + 33634.9i −0.124049 + 0.0842203i
\(175\) 212871.i 0.525439i
\(176\) −255051. −0.620648
\(177\) 99417.3 + 146432.i 0.238522 + 0.351321i
\(178\) 1759.91i 0.00416333i
\(179\) 610113.i 1.42324i 0.702565 + 0.711619i \(0.252038\pi\)
−0.702565 + 0.711619i \(0.747962\pi\)
\(180\) −98490.7 + 248095.i −0.226576 + 0.570737i
\(181\) 58467.9i 0.132654i 0.997798 + 0.0663271i \(0.0211281\pi\)
−0.997798 + 0.0663271i \(0.978872\pi\)
\(182\) 39906.1 0.0893019
\(183\) −226784. 334032.i −0.500593 0.737327i
\(184\) 11033.0 245022.i 0.0240243 0.533533i
\(185\) 369626.i 0.794024i
\(186\) 3359.58 + 4948.34i 0.00712036 + 0.0104876i
\(187\) 528807. 1.10584
\(188\) 444357.i 0.916932i
\(189\) −452040. + 100391.i −0.920496 + 0.204427i
\(190\) −168625. −0.338874
\(191\) −326167. −0.646929 −0.323464 0.946240i \(-0.604848\pi\)
−0.323464 + 0.946240i \(0.604848\pi\)
\(192\) −239376. + 162519.i −0.468626 + 0.318164i
\(193\) 196437. 0.379603 0.189802 0.981822i \(-0.439216\pi\)
0.189802 + 0.981822i \(0.439216\pi\)
\(194\) −41976.4 −0.0800757
\(195\) −99674.0 + 67671.6i −0.187713 + 0.127444i
\(196\) 55041.6 0.102341
\(197\) 66505.9i 0.122094i 0.998135 + 0.0610471i \(0.0194440\pi\)
−0.998135 + 0.0610471i \(0.980556\pi\)
\(198\) −114118. 45303.4i −0.206867 0.0821237i
\(199\) 826467.i 1.47942i −0.672923 0.739712i \(-0.734962\pi\)
0.672923 0.739712i \(-0.265038\pi\)
\(200\) 168353.i 0.297609i
\(201\) −323524. 476521.i −0.564829 0.831940i
\(202\) 124599. 0.214850
\(203\) 298862. 0.509015
\(204\) 626282. 425201.i 1.05365 0.715351i
\(205\) 649659.i 1.07969i
\(206\) 124454. 0.204335
\(207\) −253015. + 562177.i −0.410412 + 0.911900i
\(208\) −164785. −0.264095
\(209\) 927862.i 1.46932i
\(210\) −92139.0 + 62555.9i −0.144177 + 0.0978859i
\(211\) 69431.8 0.107362 0.0536812 0.998558i \(-0.482905\pi\)
0.0536812 + 0.998558i \(0.482905\pi\)
\(212\) 233611. 0.356988
\(213\) −462593. 681356.i −0.698635 1.02902i
\(214\) 300652.i 0.448776i
\(215\) 124924.i 0.184310i
\(216\) −357504. + 79395.8i −0.521371 + 0.115788i
\(217\) 29851.5i 0.0430344i
\(218\) −193927. −0.276374
\(219\) 926041. 628717.i 1.30473 0.885818i
\(220\) 353254. 0.492074
\(221\) 341656. 0.470553
\(222\) 201359. 136709.i 0.274214 0.186172i
\(223\) −1.36980e6 −1.84456 −0.922282 0.386517i \(-0.873678\pi\)
−0.922282 + 0.386517i \(0.873678\pi\)
\(224\) −530507. −0.706433
\(225\) −156135. + 393299.i −0.205610 + 0.517925i
\(226\) 81915.3i 0.106683i
\(227\) −999585. −1.28752 −0.643762 0.765226i \(-0.722627\pi\)
−0.643762 + 0.765226i \(0.722627\pi\)
\(228\) 746072. + 1.09889e6i 0.950481 + 1.39997i
\(229\) 675351.i 0.851022i 0.904953 + 0.425511i \(0.139906\pi\)
−0.904953 + 0.425511i \(0.860094\pi\)
\(230\) −6669.69 + 148121.i −0.00831354 + 0.184628i
\(231\) 344214. + 506996.i 0.424423 + 0.625136i
\(232\) 236361. 0.288307
\(233\) 537073.i 0.648102i 0.946040 + 0.324051i \(0.105045\pi\)
−0.946040 + 0.324051i \(0.894955\pi\)
\(234\) −73730.1 29270.0i −0.0880249 0.0349449i
\(235\) 559700.i 0.661129i
\(236\) 335301.i 0.391881i
\(237\) 379748. + 559334.i 0.439162 + 0.646845i
\(238\) 315828. 0.361417
\(239\) 1.04144e6i 1.17934i −0.807644 0.589670i \(-0.799258\pi\)
0.807644 0.589670i \(-0.200742\pi\)
\(240\) 380473. 258314.i 0.426379 0.289481i
\(241\) 993176.i 1.10150i −0.834671 0.550749i \(-0.814342\pi\)
0.834671 0.550749i \(-0.185658\pi\)
\(242\) 90553.4i 0.0993954i
\(243\) 908818. + 146078.i 0.987327 + 0.158697i
\(244\) 764866.i 0.822452i
\(245\) −69329.0 −0.0737904
\(246\) 353911. 240281.i 0.372869 0.253152i
\(247\) 599481.i 0.625220i
\(248\) 23608.6i 0.0243748i
\(249\) 1.38166e6 938048.i 1.41222 0.958797i
\(250\) 284409.i 0.287802i
\(251\) −648746. −0.649966 −0.324983 0.945720i \(-0.605359\pi\)
−0.324983 + 0.945720i \(0.605359\pi\)
\(252\) 815327. + 323675.i 0.808780 + 0.321076i
\(253\) 815036. + 36700.0i 0.800526 + 0.0360466i
\(254\) 163455.i 0.158970i
\(255\) −788848. + 535573.i −0.759702 + 0.515784i
\(256\) 329925. 0.314641
\(257\) 950768.i 0.897929i 0.893550 + 0.448964i \(0.148207\pi\)
−0.893550 + 0.448964i \(0.851793\pi\)
\(258\) 68054.0 46203.9i 0.0636509 0.0432145i
\(259\) −1.21472e6 −1.12520
\(260\) 228233. 0.209385
\(261\) −552175. 219207.i −0.501736 0.199183i
\(262\) −502579. −0.452326
\(263\) 1.18331e6 1.05490 0.527450 0.849586i \(-0.323148\pi\)
0.527450 + 0.849586i \(0.323148\pi\)
\(264\) 272229. + 400967.i 0.240394 + 0.354078i
\(265\) −294250. −0.257396
\(266\) 554162.i 0.480212i
\(267\) −14446.0 + 9807.82i −0.0124014 + 0.00841966i
\(268\) 1.09114e6i 0.927988i
\(269\) 1.60834e6i 1.35518i −0.735441 0.677588i \(-0.763025\pi\)
0.735441 0.677588i \(-0.236975\pi\)
\(270\) 216118. 47996.3i 0.180419 0.0400681i
\(271\) 453181. 0.374842 0.187421 0.982280i \(-0.439987\pi\)
0.187421 + 0.982280i \(0.439987\pi\)
\(272\) −1.30416e6 −1.06883
\(273\) 222393. + 327564.i 0.180599 + 0.266005i
\(274\) 317398.i 0.255404i
\(275\) 560006. 0.446541
\(276\) 994781. 611886.i 0.786058 0.483502i
\(277\) 530675. 0.415555 0.207778 0.978176i \(-0.433377\pi\)
0.207778 + 0.978176i \(0.433377\pi\)
\(278\) 310421.i 0.240901i
\(279\) −21895.2 + 55153.3i −0.0168399 + 0.0424190i
\(280\) 439596. 0.335088
\(281\) 141938. 0.107234 0.0536171 0.998562i \(-0.482925\pi\)
0.0536171 + 0.998562i \(0.482925\pi\)
\(282\) −304905. + 207009.i −0.228319 + 0.155012i
\(283\) 1.59400e6i 1.18310i −0.806268 0.591550i \(-0.798516\pi\)
0.806268 0.591550i \(-0.201484\pi\)
\(284\) 1.56017e6i 1.14783i
\(285\) −939733. 1.38414e6i −0.685318 1.00941i
\(286\) 104982.i 0.0758927i
\(287\) −2.13501e6 −1.53001
\(288\) 980160. + 389112.i 0.696331 + 0.276435i
\(289\) 1.28411e6 0.904392
\(290\) −142885. −0.0997679
\(291\) −233930. 344557.i −0.161940 0.238522i
\(292\) −2.12045e6 −1.45536
\(293\) 831087. 0.565558 0.282779 0.959185i \(-0.408744\pi\)
0.282779 + 0.959185i \(0.408744\pi\)
\(294\) −25641.8 37767.9i −0.0173013 0.0254833i
\(295\) 422336.i 0.282555i
\(296\) −960687. −0.637313
\(297\) −264100. 1.18919e6i −0.173731 0.782278i
\(298\) 324190.i 0.211475i
\(299\) 526585. + 23711.4i 0.340636 + 0.0153384i
\(300\) 663232. 450288.i 0.425463 0.288860i
\(301\) −410544. −0.261182
\(302\) 114053.i 0.0719596i
\(303\) 694376. + 1.02275e6i 0.434498 + 0.639975i
\(304\) 2.28832e6i 1.42015i
\(305\) 963405.i 0.593006i
\(306\) −583521. 231651.i −0.356249 0.141427i
\(307\) 1.41110e6 0.854499 0.427250 0.904134i \(-0.359483\pi\)
0.427250 + 0.904134i \(0.359483\pi\)
\(308\) 1.16092e6i 0.697308i
\(309\) 693572. + 1.02157e6i 0.413233 + 0.608654i
\(310\) 14271.9i 0.00843483i
\(311\) 885448.i 0.519113i 0.965728 + 0.259557i \(0.0835764\pi\)
−0.965728 + 0.259557i \(0.916424\pi\)
\(312\) 175884. + 259060.i 0.102291 + 0.150666i
\(313\) 1.01876e6i 0.587776i 0.955840 + 0.293888i \(0.0949492\pi\)
−0.955840 + 0.293888i \(0.905051\pi\)
\(314\) −541137. −0.309730
\(315\) −1.02696e6 407693.i −0.583148 0.231503i
\(316\) 1.28076e6i 0.721524i
\(317\) 75162.2i 0.0420099i −0.999779 0.0210049i \(-0.993313\pi\)
0.999779 0.0210049i \(-0.00668657\pi\)
\(318\) −108830. 160297.i −0.0603506 0.0888909i
\(319\) 786224.i 0.432583i
\(320\) −690400. −0.376900
\(321\) −2.46786e6 + 1.67551e6i −1.33678 + 0.907577i
\(322\) 486777. + 21918.9i 0.261632 + 0.0117809i
\(323\) 4.74446e6i 2.53035i
\(324\) −1.26898e6 1.19604e6i −0.671573 0.632970i
\(325\) 361813. 0.190010
\(326\) 82264.6i 0.0428715i
\(327\) −1.08074e6 1.59183e6i −0.558922 0.823240i
\(328\) −1.68851e6 −0.866602
\(329\) 1.83937e6 0.936872
\(330\) −164568. 242393.i −0.0831877 0.122528i
\(331\) −574036. −0.287985 −0.143992 0.989579i \(-0.545994\pi\)
−0.143992 + 0.989579i \(0.545994\pi\)
\(332\) −3.16371e6 −1.57526
\(333\) 2.24431e6 + 890966.i 1.10910 + 0.440302i
\(334\) 730095. 0.358107
\(335\) 1.37437e6i 0.669100i
\(336\) −848912. 1.25037e6i −0.410218 0.604212i
\(337\) 751869.i 0.360635i −0.983608 0.180317i \(-0.942288\pi\)
0.983608 0.180317i \(-0.0577125\pi\)
\(338\) 515545.i 0.245457i
\(339\) −672391. + 456506.i −0.317777 + 0.215748i
\(340\) 1.80630e6 0.847410
\(341\) 78531.0 0.0365725
\(342\) 406463. 1.02387e6i 0.187912 0.473345i
\(343\) 2.28236e6i 1.04749i
\(344\) −324686. −0.147934
\(345\) −1.25300e6 + 770716.i −0.566765 + 0.348615i
\(346\) 11085.0 0.00497788
\(347\) 4.25948e6i 1.89903i −0.313715 0.949517i \(-0.601574\pi\)
0.313715 0.949517i \(-0.398426\pi\)
\(348\) 632184. + 931149.i 0.279831 + 0.412165i
\(349\) 918884. 0.403829 0.201914 0.979403i \(-0.435284\pi\)
0.201914 + 0.979403i \(0.435284\pi\)
\(350\) 334462. 0.145941
\(351\) −170632. 768323.i −0.0739252 0.332871i
\(352\) 1.39562e6i 0.600358i
\(353\) 1.12183e6i 0.479170i −0.970875 0.239585i \(-0.922989\pi\)
0.970875 0.239585i \(-0.0770114\pi\)
\(354\) −230073. + 156204.i −0.0975795 + 0.0662496i
\(355\) 1.96515e6i 0.827607i
\(356\) 33078.4 0.0138331
\(357\) 1.76008e6 + 2.59243e6i 0.730907 + 1.07656i
\(358\) −958605. −0.395305
\(359\) −2.22040e6 −0.909273 −0.454636 0.890677i \(-0.650231\pi\)
−0.454636 + 0.890677i \(0.650231\pi\)
\(360\) −812194. 322432.i −0.330296 0.131124i
\(361\) −5.84868e6 −2.36206
\(362\) −91864.4 −0.0368447
\(363\) 743295. 504645.i 0.296070 0.201011i
\(364\) 750055.i 0.296715i
\(365\) 2.67086e6 1.04935
\(366\) 524828. 356322.i 0.204793 0.139040i
\(367\) 4.35641e6i 1.68835i −0.536064 0.844177i \(-0.680090\pi\)
0.536064 0.844177i \(-0.319910\pi\)
\(368\) −2.01006e6 90510.6i −0.773732 0.0348401i
\(369\) 3.94462e6 + 1.56597e6i 1.50813 + 0.598711i
\(370\) 580754. 0.220540
\(371\) 967010.i 0.364751i
\(372\) 93006.6 63144.9i 0.0348463 0.0236582i
\(373\) 4.60335e6i 1.71318i 0.516001 + 0.856588i \(0.327420\pi\)
−0.516001 + 0.856588i \(0.672580\pi\)
\(374\) 830858.i 0.307148i
\(375\) −2.33453e6 + 1.58498e6i −0.857278 + 0.582032i
\(376\) 1.45470e6 0.530646
\(377\) 507970.i 0.184071i
\(378\) −157733. 710241.i −0.0567797 0.255668i
\(379\) 496941.i 0.177708i 0.996045 + 0.0888541i \(0.0283205\pi\)
−0.996045 + 0.0888541i \(0.971680\pi\)
\(380\) 3.16940e6i 1.12595i
\(381\) 1.34170e6 910922.i 0.473526 0.321491i
\(382\) 512471.i 0.179685i
\(383\) 3.80492e6 1.32540 0.662702 0.748883i \(-0.269410\pi\)
0.662702 + 0.748883i \(0.269410\pi\)
\(384\) −1.47134e6 2.16715e6i −0.509196 0.749999i
\(385\) 1.46226e6i 0.502775i
\(386\) 308640.i 0.105435i
\(387\) 758517. + 301122.i 0.257447 + 0.102204i
\(388\) 788967.i 0.266060i
\(389\) 1.45736e6 0.488306 0.244153 0.969737i \(-0.421490\pi\)
0.244153 + 0.969737i \(0.421490\pi\)
\(390\) −106325. 156607.i −0.0353976 0.0521374i
\(391\) 4.16754e6 + 187659.i 1.37860 + 0.0620766i
\(392\) 180191.i 0.0592268i
\(393\) −2.80082e6 4.12535e6i −0.914755 1.34735i
\(394\) −104494. −0.0339117
\(395\) 1.61321e6i 0.520234i
\(396\) −851501. + 2.14490e6i −0.272865 + 0.687336i
\(397\) −4.37853e6 −1.39429 −0.697144 0.716931i \(-0.745546\pi\)
−0.697144 + 0.716931i \(0.745546\pi\)
\(398\) 1.29854e6 0.410911
\(399\) −4.54877e6 + 3.08829e6i −1.43041 + 0.971150i
\(400\) −1.38110e6 −0.431595
\(401\) 3.59017e6 1.11495 0.557473 0.830195i \(-0.311771\pi\)
0.557473 + 0.830195i \(0.311771\pi\)
\(402\) 748706. 508319.i 0.231071 0.156881i
\(403\) 50737.9 0.0155622
\(404\) 2.34189e6i 0.713861i
\(405\) 1.59838e6 + 1.50650e6i 0.484219 + 0.456385i
\(406\) 469570.i 0.141379i
\(407\) 3.19560e6i 0.956240i
\(408\) 1.39199e6 + 2.05028e6i 0.413987 + 0.609764i
\(409\) 6.32230e6 1.86882 0.934409 0.356202i \(-0.115929\pi\)
0.934409 + 0.356202i \(0.115929\pi\)
\(410\) 1.02074e6 0.299885
\(411\) −2.60532e6 + 1.76883e6i −0.760775 + 0.516513i
\(412\) 2.33918e6i 0.678924i
\(413\) 1.38795e6 0.400403
\(414\) −883288. 397535.i −0.253280 0.113992i
\(415\) 3.98493e6 1.13580
\(416\) 901693.i 0.255461i
\(417\) 2.54805e6 1.72995e6i 0.717575 0.487183i
\(418\) −1.45785e6 −0.408105
\(419\) 5.31646e6 1.47941 0.739704 0.672933i \(-0.234966\pi\)
0.739704 + 0.672933i \(0.234966\pi\)
\(420\) 1.17577e6 + 1.73180e6i 0.325237 + 0.479043i
\(421\) 5.94869e6i 1.63575i 0.575399 + 0.817873i \(0.304847\pi\)
−0.575399 + 0.817873i \(0.695153\pi\)
\(422\) 109091.i 0.0298199i
\(423\) −3.39841e6 1.34913e6i −0.923474 0.366609i
\(424\) 764778.i 0.206595i
\(425\) 2.86349e6 0.768996
\(426\) 1.07054e6 726823.i 0.285811 0.194046i
\(427\) −3.16609e6 −0.840337
\(428\) 5.65091e6 1.49111
\(429\) −861731. + 585055.i −0.226063 + 0.153481i
\(430\) 196279. 0.0511922
\(431\) −738404. −0.191470 −0.0957351 0.995407i \(-0.530520\pi\)
−0.0957351 + 0.995407i \(0.530520\pi\)
\(432\) 651331. + 2.93282e6i 0.167916 + 0.756095i
\(433\) 546533.i 0.140087i −0.997544 0.0700433i \(-0.977686\pi\)
0.997544 0.0700433i \(-0.0223137\pi\)
\(434\) 46902.4 0.0119528
\(435\) −796283. 1.17285e6i −0.201764 0.297180i
\(436\) 3.64496e6i 0.918284i
\(437\) −329273. + 7.31251e6i −0.0824806 + 1.83173i
\(438\) 987835. + 1.45499e6i 0.246036 + 0.362388i
\(439\) −4.25006e6 −1.05253 −0.526264 0.850321i \(-0.676408\pi\)
−0.526264 + 0.850321i \(0.676408\pi\)
\(440\) 1.15646e6i 0.284773i
\(441\) 167114. 420954.i 0.0409182 0.103071i
\(442\) 536807.i 0.130696i
\(443\) 4.67645e6i 1.13216i −0.824351 0.566079i \(-0.808460\pi\)
0.824351 0.566079i \(-0.191540\pi\)
\(444\) −2.56951e6 3.78465e6i −0.618576 0.911104i
\(445\) −41664.7 −0.00997398
\(446\) 2.15221e6i 0.512328i
\(447\) −2.66107e6 + 1.80668e6i −0.629923 + 0.427673i
\(448\) 2.26890e6i 0.534097i
\(449\) 2.01589e6i 0.471900i −0.971765 0.235950i \(-0.924180\pi\)
0.971765 0.235950i \(-0.0758202\pi\)
\(450\) −617948. 245318.i −0.143854 0.0571083i
\(451\) 5.61662e6i 1.30027i
\(452\) 1.53964e6 0.354465
\(453\) 936188. 635606.i 0.214347 0.145527i
\(454\) 1.57054e6i 0.357610i
\(455\) 944750.i 0.213938i
\(456\) −3.59748e6 + 2.44244e6i −0.810189 + 0.550061i
\(457\) 8.34776e6i 1.86973i −0.355001 0.934866i \(-0.615519\pi\)
0.355001 0.934866i \(-0.384481\pi\)
\(458\) −1.06111e6 −0.236371
\(459\) −1.35043e6 6.08073e6i −0.299185 1.34717i
\(460\) 2.78401e6 + 125360.i 0.613445 + 0.0276226i
\(461\) 6.19226e6i 1.35705i 0.734576 + 0.678526i \(0.237381\pi\)
−0.734576 + 0.678526i \(0.762619\pi\)
\(462\) −796588. + 540827.i −0.173632 + 0.117884i
\(463\) 6.00846e6 1.30260 0.651300 0.758821i \(-0.274224\pi\)
0.651300 + 0.758821i \(0.274224\pi\)
\(464\) 1.93901e6i 0.418105i
\(465\) −117149. + 79535.7i −0.0251249 + 0.0170581i
\(466\) −843845. −0.180010
\(467\) −5.16831e6 −1.09662 −0.548311 0.836275i \(-0.684729\pi\)
−0.548311 + 0.836275i \(0.684729\pi\)
\(468\) −550145. + 1.38580e6i −0.116108 + 0.292472i
\(469\) −4.51666e6 −0.948168
\(470\) −879397. −0.183629
\(471\) −3.01570e6 4.44185e6i −0.626378 0.922596i
\(472\) 1.09768e6 0.226789
\(473\) 1.08003e6i 0.221964i
\(474\) −878821. + 596657.i −0.179661 + 0.121977i
\(475\) 5.02438e6i 1.02176i
\(476\) 5.93615e6i 1.20085i
\(477\) 709275. 1.78664e6i 0.142731 0.359535i
\(478\) 1.63630e6 0.327562
\(479\) −7.21936e6 −1.43767 −0.718836 0.695180i \(-0.755325\pi\)
−0.718836 + 0.695180i \(0.755325\pi\)
\(480\) 1.41347e6 + 2.08192e6i 0.280017 + 0.412439i
\(481\) 2.06464e6i 0.406895i
\(482\) 1.56047e6 0.305941
\(483\) 2.53284e6 + 4.11780e6i 0.494016 + 0.803151i
\(484\) −1.70200e6 −0.330252
\(485\) 993762.i 0.191835i
\(486\) −229516. + 1.42793e6i −0.0440781 + 0.274230i
\(487\) −1.69573e6 −0.323991 −0.161996 0.986791i \(-0.551793\pi\)
−0.161996 + 0.986791i \(0.551793\pi\)
\(488\) −2.50396e6 −0.475968
\(489\) −675258. + 458452.i −0.127702 + 0.0867006i
\(490\) 108929.i 0.0204953i
\(491\) 1.97941e6i 0.370537i −0.982688 0.185269i \(-0.940684\pi\)
0.982688 0.185269i \(-0.0593155\pi\)
\(492\) −4.51619e6 6.65193e6i −0.841124 1.23890i
\(493\) 4.02022e6i 0.744960i
\(494\) −941899. −0.173655
\(495\) 1.07253e6 2.70166e6i 0.196741 0.495585i
\(496\) −193675. −0.0353484
\(497\) −6.45817e6 −1.17279
\(498\) 1.47385e6 + 2.17085e6i 0.266306 + 0.392244i
\(499\) −5.04988e6 −0.907882 −0.453941 0.891032i \(-0.649982\pi\)
−0.453941 + 0.891032i \(0.649982\pi\)
\(500\) 5.34561e6 0.956252
\(501\) 4.06875e6 + 5.99289e6i 0.724213 + 1.06670i
\(502\) 1.01930e6i 0.180528i
\(503\) −1.44925e6 −0.255402 −0.127701 0.991813i \(-0.540760\pi\)
−0.127701 + 0.991813i \(0.540760\pi\)
\(504\) −1.05962e6 + 2.66916e6i −0.185813 + 0.468056i
\(505\) 2.94979e6i 0.514710i
\(506\) −57662.7 + 1.28058e6i −0.0100120 + 0.222346i
\(507\) 4.23178e6 2.87308e6i 0.731145 0.496396i
\(508\) −3.07223e6 −0.528195
\(509\) 1.18111e6i 0.202068i 0.994883 + 0.101034i \(0.0322150\pi\)
−0.994883 + 0.101034i \(0.967785\pi\)
\(510\) −841488. 1.23943e6i −0.143259 0.211007i
\(511\) 8.77739e6i 1.48701i
\(512\) 5.89553e6i 0.993912i
\(513\) 1.06694e7 2.36951e6i 1.78998 0.397525i
\(514\) −1.49384e6 −0.249400
\(515\) 2.94637e6i 0.489519i
\(516\) −868425. 1.27911e6i −0.143585 0.211487i
\(517\) 4.83889e6i 0.796195i
\(518\) 1.90856e6i 0.312523i
\(519\) 61775.4 + 90989.5i 0.0100669 + 0.0148277i
\(520\) 747174.i 0.121175i
\(521\) −8.05639e6 −1.30031 −0.650154 0.759802i \(-0.725296\pi\)
−0.650154 + 0.759802i \(0.725296\pi\)
\(522\) 344416. 867573.i 0.0553232 0.139357i
\(523\) 2.65776e6i 0.424875i −0.977175 0.212437i \(-0.931860\pi\)
0.977175 0.212437i \(-0.0681401\pi\)
\(524\) 9.44623e6i 1.50290i
\(525\) 1.86392e6 + 2.74538e6i 0.295141 + 0.434715i
\(526\) 1.85922e6i 0.292998i
\(527\) 401555. 0.0629822
\(528\) 3.28937e6 2.23325e6i 0.513486 0.348621i
\(529\) 6.41030e6 + 578467.i 0.995953 + 0.0898752i
\(530\) 462323.i 0.0714918i
\(531\) −2.56435e6 1.01802e6i −0.394677 0.156682i
\(532\) 1.04158e7 1.59556
\(533\) 3.62883e6i 0.553285i
\(534\) −15410.0 22697.5i −0.00233856 0.00344448i
\(535\) −7.11774e6 −1.07512
\(536\) −3.57209e6 −0.537044
\(537\) −5.34221e6 7.86858e6i −0.799439 1.17750i
\(538\) 2.52700e6 0.376401
\(539\) −599384. −0.0888655
\(540\) −902115. 4.06205e6i −0.133130 0.599461i
\(541\) −2.23163e6 −0.327816 −0.163908 0.986476i \(-0.552410\pi\)
−0.163908 + 0.986476i \(0.552410\pi\)
\(542\) 712035.i 0.104113i
\(543\) −511951. 754056.i −0.0745125 0.109750i
\(544\) 7.13626e6i 1.03389i
\(545\) 4.59110e6i 0.662103i
\(546\) −514666. + 349422.i −0.0738829 + 0.0501613i
\(547\) 7.42757e6 1.06140 0.530699 0.847560i \(-0.321929\pi\)
0.530699 + 0.847560i \(0.321929\pi\)
\(548\) 5.96565e6 0.848607
\(549\) 5.84964e6 + 2.32224e6i 0.828320 + 0.328833i
\(550\) 879877.i 0.124027i
\(551\) −7.05401e6 −0.989822
\(552\) 2.00315e6 + 3.25664e6i 0.279811 + 0.454906i
\(553\) 5.30159e6 0.737213
\(554\) 833792.i 0.115421i
\(555\) 3.23649e6 + 4.76704e6i 0.446007 + 0.656926i
\(556\) −5.83452e6 −0.800420
\(557\) −1.07965e7 −1.47450 −0.737252 0.675618i \(-0.763877\pi\)
−0.737252 + 0.675618i \(0.763877\pi\)
\(558\) −86656.4 34401.6i −0.0117819 0.00467728i
\(559\) 697793.i 0.0944490i
\(560\) 3.60627e6i 0.485947i
\(561\) −6.81999e6 + 4.63029e6i −0.914906 + 0.621157i
\(562\) 223012.i 0.0297843i
\(563\) 995065. 0.132306 0.0661531 0.997809i \(-0.478927\pi\)
0.0661531 + 0.997809i \(0.478927\pi\)
\(564\) 3.89084e6 + 5.73084e6i 0.515045 + 0.758613i
\(565\) −1.93929e6 −0.255577
\(566\) 2.50448e6 0.328606
\(567\) 4.95089e6 5.25284e6i 0.646734 0.686177i
\(568\) −5.10757e6 −0.664268
\(569\) −1.08672e7 −1.40714 −0.703568 0.710628i \(-0.748411\pi\)
−0.703568 + 0.710628i \(0.748411\pi\)
\(570\) 2.17475e6 1.47650e6i 0.280364 0.190347i
\(571\) 3.65300e6i 0.468878i −0.972131 0.234439i \(-0.924675\pi\)
0.972131 0.234439i \(-0.0753253\pi\)
\(572\) 1.97319e6 0.252162
\(573\) 4.20655e6 2.85595e6i 0.535229 0.363383i
\(574\) 3.35451e6i 0.424961i
\(575\) 4.41342e6 + 198731.i 0.556680 + 0.0250666i
\(576\) 1.66417e6 4.19199e6i 0.208998 0.526459i
\(577\) −6.62252e6 −0.828102 −0.414051 0.910254i \(-0.635886\pi\)
−0.414051 + 0.910254i \(0.635886\pi\)
\(578\) 2.01758e6i 0.251195i
\(579\) −2.53343e6 + 1.72002e6i −0.314060 + 0.213225i
\(580\) 2.68559e6i 0.331490i
\(581\) 1.30959e7i 1.60951i
\(582\) 541366. 367549.i 0.0662496 0.0449788i
\(583\) −2.54394e6 −0.309981
\(584\) 6.94176e6i 0.842244i
\(585\) 692948. 1.74551e6i 0.0837165 0.210879i
\(586\) 1.30580e6i 0.157084i
\(587\) 2.94644e6i 0.352941i 0.984306 + 0.176471i \(0.0564681\pi\)
−0.984306 + 0.176471i \(0.943532\pi\)
\(588\) −709868. + 481950.i −0.0846709 + 0.0574856i
\(589\) 704581.i 0.0836840i
\(590\) −663571. −0.0784797
\(591\) −582333. 857722.i −0.0685808 0.101013i
\(592\) 7.88109e6i 0.924234i
\(593\) 6.52249e6i 0.761687i 0.924639 + 0.380844i \(0.124366\pi\)
−0.924639 + 0.380844i \(0.875634\pi\)
\(594\) 1.86845e6 414952.i 0.217278 0.0482538i
\(595\) 7.47702e6i 0.865837i
\(596\) 6.09331e6 0.702648
\(597\) 7.23663e6 + 1.06589e7i 0.830999 + 1.22398i
\(598\) −37255.2 + 827366.i −0.00426024 + 0.0946117i
\(599\) 1.00980e7i 1.14993i 0.818179 + 0.574964i \(0.194984\pi\)
−0.818179 + 0.574964i \(0.805016\pi\)
\(600\) 1.47412e6 + 2.17124e6i 0.167168 + 0.246224i
\(601\) 1.44237e7 1.62889 0.814445 0.580240i \(-0.197041\pi\)
0.814445 + 0.580240i \(0.197041\pi\)
\(602\) 645043.i 0.0725433i
\(603\) 8.34494e6 + 3.31284e6i 0.934609 + 0.371029i
\(604\) −2.14368e6 −0.239094
\(605\) 2.14379e6 0.238119
\(606\) −1.60694e6 + 1.09100e6i −0.177753 + 0.120682i
\(607\) 1.46050e6 0.160890 0.0804451 0.996759i \(-0.474366\pi\)
0.0804451 + 0.996759i \(0.474366\pi\)
\(608\) 1.25215e7 1.37372
\(609\) −3.85440e6 + 2.61687e6i −0.421128 + 0.285916i
\(610\) 1.51369e6 0.164708
\(611\) 3.12635e6i 0.338793i
\(612\) −4.35400e6 + 1.09676e7i −0.469905 + 1.18367i
\(613\) 1.39592e6i 0.150040i −0.997182 0.0750202i \(-0.976098\pi\)
0.997182 0.0750202i \(-0.0239021\pi\)
\(614\) 2.21711e6i 0.237337i
\(615\) 5.68848e6 + 8.37860e6i 0.606469 + 0.893272i
\(616\) 3.80053e6 0.403545
\(617\) 1.33277e7 1.40943 0.704714 0.709492i \(-0.251075\pi\)
0.704714 + 0.709492i \(0.251075\pi\)
\(618\) −1.60508e6 + 1.08974e6i −0.169054 + 0.114776i
\(619\) 1.40755e7i 1.47651i 0.674519 + 0.738257i \(0.264351\pi\)
−0.674519 + 0.738257i \(0.735649\pi\)
\(620\) 268247. 0.0280256
\(621\) −1.65937e6 9.46578e6i −0.172669 0.984980i
\(622\) −1.39121e6 −0.144184
\(623\) 136925.i 0.0141339i
\(624\) 2.12523e6 1.44288e6i 0.218496 0.148343i
\(625\) −1.29135e6 −0.132234
\(626\) −1.60067e6 −0.163255
\(627\) −8.12446e6 1.19666e7i −0.825326 1.21563i
\(628\) 1.01709e7i 1.02911i
\(629\) 1.63402e7i 1.64676i
\(630\) 640564. 1.61356e6i 0.0643000 0.161970i
\(631\) 9.75276e6i 0.975112i −0.873092 0.487556i \(-0.837889\pi\)
0.873092 0.487556i \(-0.162111\pi\)
\(632\) 4.19286e6 0.417559
\(633\) −895457. + 607952.i −0.0888250 + 0.0603060i
\(634\) 118094. 0.0116682
\(635\) 3.86970e6 0.380840
\(636\) −3.01286e6 + 2.04552e6i −0.295349 + 0.200522i
\(637\) −387255. −0.0378136
\(638\) −1.23531e6 −0.120150
\(639\) 1.19321e7 + 4.73689e6i 1.15601 + 0.458924i
\(640\) 6.25042e6i 0.603197i
\(641\) −1.64249e7 −1.57891 −0.789454 0.613810i \(-0.789636\pi\)
−0.789454 + 0.613810i \(0.789636\pi\)
\(642\) −2.63254e6 3.87749e6i −0.252080 0.371290i
\(643\) 6.63786e6i 0.633141i 0.948569 + 0.316571i \(0.102531\pi\)
−0.948569 + 0.316571i \(0.897469\pi\)
\(644\) 411978. 9.14923e6i 0.0391434 0.869300i
\(645\) 1.09385e6 + 1.61113e6i 0.103528 + 0.152487i
\(646\) −7.45446e6 −0.702805
\(647\) 1.25537e7i 1.17899i 0.807772 + 0.589495i \(0.200673\pi\)
−0.807772 + 0.589495i \(0.799327\pi\)
\(648\) 3.91551e6 4.15430e6i 0.366311 0.388652i
\(649\) 3.65130e6i 0.340280i
\(650\) 568478.i 0.0527753i
\(651\) 261382. + 384992.i 0.0241726 + 0.0356040i
\(652\) 1.54620e6 0.142445
\(653\) 9.03858e6i 0.829502i 0.909935 + 0.414751i \(0.136131\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(654\) 2.50107e6 1.69805e6i 0.228655 0.155241i
\(655\) 1.18982e7i 1.08362i
\(656\) 1.38519e7i 1.25675i
\(657\) −6.43797e6 + 1.62170e7i −0.581883 + 1.46574i
\(658\) 2.89001e6i 0.260216i
\(659\) −658736. −0.0590878 −0.0295439 0.999563i \(-0.509405\pi\)
−0.0295439 + 0.999563i \(0.509405\pi\)
\(660\) −4.55589e6 + 3.09313e6i −0.407112 + 0.276400i
\(661\) 2.00503e7i 1.78491i −0.451132 0.892457i \(-0.648980\pi\)
0.451132 0.892457i \(-0.351020\pi\)
\(662\) 901921.i 0.0799878i
\(663\) −4.40631e6 + 2.99158e6i −0.389306 + 0.264312i
\(664\) 1.03571e7i 0.911632i
\(665\) −1.31194e7 −1.15043
\(666\) −1.39988e6 + 3.52624e6i −0.122294 + 0.308054i
\(667\) −279009. + 6.19625e6i −0.0242831 + 0.539280i
\(668\) 1.37225e7i 1.18985i
\(669\) 1.76662e7 1.19941e7i 1.52608 1.03610i
\(670\) 2.15940e6 0.185843
\(671\) 8.32911e6i 0.714155i
\(672\) 6.84191e6 4.64518e6i 0.584459 0.396807i
\(673\) −1.79212e7 −1.52521 −0.762604 0.646866i \(-0.776079\pi\)
−0.762604 + 0.646866i \(0.776079\pi\)
\(674\) 1.18133e6 0.100166
\(675\) −1.43010e6 6.43948e6i −0.120811 0.543991i
\(676\) −9.68993e6 −0.815556
\(677\) −1.91825e7 −1.60854 −0.804271 0.594262i \(-0.797444\pi\)
−0.804271 + 0.594262i \(0.797444\pi\)
\(678\) −717259. 1.05646e6i −0.0599241 0.0882626i
\(679\) −3.26585e6 −0.271846
\(680\) 5.91335e6i 0.490412i
\(681\) 1.28916e7 8.75247e6i 1.06522 0.723207i
\(682\) 123387.i 0.0101580i
\(683\) 5.30024e6i 0.434754i 0.976088 + 0.217377i \(0.0697502\pi\)
−0.976088 + 0.217377i \(0.930250\pi\)
\(684\) −1.92441e7 7.63967e6i −1.57274 0.624359i
\(685\) −7.51418e6 −0.611865
\(686\) −3.58603e6 −0.290940
\(687\) −5.91344e6 8.70995e6i −0.478023 0.704083i
\(688\) 2.66360e6i 0.214535i
\(689\) −1.64361e6 −0.131902
\(690\) −1.21094e6 1.96870e6i −0.0968280 0.157419i
\(691\) 7.36822e6 0.587040 0.293520 0.955953i \(-0.405173\pi\)
0.293520 + 0.955953i \(0.405173\pi\)
\(692\) 208348.i 0.0165395i
\(693\) −8.87862e6 3.52471e6i −0.702283 0.278798i
\(694\) 6.69246e6 0.527457
\(695\) 7.34900e6 0.577120
\(696\) −3.04833e6 + 2.06960e6i −0.238527 + 0.161943i
\(697\) 2.87196e7i 2.23922i
\(698\) 1.44374e6i 0.112163i
\(699\) −4.70267e6 6.92659e6i −0.364042 0.536199i
\(700\) 6.28638e6i 0.484904i
\(701\) −6.12013e6 −0.470398 −0.235199 0.971947i \(-0.575574\pi\)
−0.235199 + 0.971947i \(0.575574\pi\)
\(702\) 1.20718e6 268096.i 0.0924550 0.0205327i
\(703\) 2.86710e7 2.18803
\(704\) −5.96885e6 −0.453899
\(705\) −4.90079e6 7.21841e6i −0.371359 0.546977i
\(706\) 1.76261e6 0.133090
\(707\) 9.69404e6 0.729384
\(708\) 2.93593e6 + 4.32435e6i 0.220121 + 0.324218i
\(709\) 1.54351e7i 1.15317i 0.817036 + 0.576587i \(0.195616\pi\)
−0.817036 + 0.576587i \(0.804384\pi\)
\(710\) 3.08762e6 0.229868
\(711\) −9.79517e6 3.88857e6i −0.726671 0.288480i
\(712\) 108290.i 0.00800548i
\(713\) 618905. + 27868.5i 0.0455932 + 0.00205300i
\(714\) −4.07321e6 + 2.76543e6i −0.299014 + 0.203010i
\(715\) −2.48538e6 −0.181814
\(716\) 1.80175e7i 1.31344i
\(717\) 9.11894e6 + 1.34314e7i 0.662440 + 0.975713i
\(718\) 3.48867e6i 0.252551i
\(719\) 1.94171e7i 1.40076i −0.713772 0.700378i \(-0.753015\pi\)
0.713772 0.700378i \(-0.246985\pi\)
\(720\) −2.64510e6 + 6.66292e6i −0.190156 + 0.478997i
\(721\) 9.68282e6 0.693688
\(722\) 9.18941e6i 0.656061i
\(723\) 8.69635e6 + 1.28089e7i 0.618716 + 0.911311i
\(724\) 1.72664e6i 0.122421i
\(725\) 4.25741e6i 0.300816i
\(726\) 792895. + 1.16786e6i 0.0558308 + 0.0822336i
\(727\) 1.77689e7i 1.24688i 0.781872 + 0.623439i \(0.214265\pi\)
−0.781872 + 0.623439i \(0.785735\pi\)
\(728\) 2.45548e6 0.171715
\(729\) −1.30000e7 + 6.07375e6i −0.905994 + 0.423290i
\(730\) 4.19643e6i 0.291456i
\(731\) 5.52254e6i 0.382248i
\(732\) −6.69724e6 9.86441e6i −0.461975 0.680446i
\(733\) 5.47786e6i 0.376575i 0.982114 + 0.188287i \(0.0602936\pi\)
−0.982114 + 0.188287i \(0.939706\pi\)
\(734\) 6.84476e6 0.468941
\(735\) 894131. 607052.i 0.0610496 0.0414484i
\(736\) 495267. 1.09989e7i 0.0337011 0.748437i
\(737\) 1.18821e7i 0.805794i
\(738\) −2.46044e6 + 6.19776e6i −0.166292 + 0.418884i
\(739\) −5.18027e6 −0.348933 −0.174466 0.984663i \(-0.555820\pi\)
−0.174466 + 0.984663i \(0.555820\pi\)
\(740\) 1.09156e7i 0.732769i
\(741\) −5.24911e6 7.73146e6i −0.351189 0.517268i
\(742\) −1.51936e6 −0.101310
\(743\) 1.14016e7 0.757697 0.378848 0.925459i \(-0.376320\pi\)
0.378848 + 0.925459i \(0.376320\pi\)
\(744\) 206719. + 304478.i 0.0136914 + 0.0201662i
\(745\) −7.67497e6 −0.506625
\(746\) −7.23275e6 −0.475835
\(747\) −9.60548e6 + 2.41959e7i −0.629821 + 1.58650i
\(748\) 1.56164e7 1.02053
\(749\) 2.33914e7i 1.52353i
\(750\) −2.49031e6 3.66800e6i −0.161659 0.238109i
\(751\) 2.39349e7i 1.54857i 0.632836 + 0.774286i \(0.281891\pi\)
−0.632836 + 0.774286i \(0.718109\pi\)
\(752\) 1.19338e7i 0.769545i
\(753\) 8.36683e6 5.68049e6i 0.537741 0.365089i
\(754\) −798119. −0.0511257
\(755\) 2.70013e6 0.172392
\(756\) −1.33493e7 + 2.96467e6i −0.849484 + 0.188656i
\(757\) 1.62210e7i 1.02882i −0.857546 0.514408i \(-0.828012\pi\)
0.857546 0.514408i \(-0.171988\pi\)
\(758\) −780791. −0.0493585
\(759\) −1.08328e7 + 6.66322e6i −0.682553 + 0.419836i
\(760\) −1.03757e7 −0.651606
\(761\) 1.90740e7i 1.19393i 0.802265 + 0.596967i \(0.203628\pi\)
−0.802265 + 0.596967i \(0.796372\pi\)
\(762\) 1.43123e6 + 2.10807e6i 0.0892941 + 0.131522i
\(763\) −1.50880e7 −0.938252
\(764\) −9.63215e6 −0.597021
\(765\) 5.48419e6 1.38145e7i 0.338812 0.853456i
\(766\) 5.97825e6i 0.368131i
\(767\) 2.35906e6i 0.144794i
\(768\) −4.25501e6 + 2.88885e6i −0.260314 + 0.176735i
\(769\) 1.31501e7i 0.801885i 0.916103 + 0.400943i \(0.131317\pi\)
−0.916103 + 0.400943i \(0.868683\pi\)
\(770\) −2.29749e6 −0.139646
\(771\) −8.32502e6 1.22620e7i −0.504370 0.742891i
\(772\) 5.80105e6 0.350318
\(773\) 4.24089e6 0.255275 0.127638 0.991821i \(-0.459261\pi\)
0.127638 + 0.991821i \(0.459261\pi\)
\(774\) −473121. + 1.19178e6i −0.0283870 + 0.0715060i
\(775\) 425246. 0.0254323
\(776\) −2.58286e6 −0.153974
\(777\) 1.56662e7 1.06362e7i 0.930917 0.632027i
\(778\) 2.28979e6i 0.135627i
\(779\)