Properties

Label 69.6.c.b.68.8
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 68.8
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.26

$q$-expansion

\(f(q)\) \(=\) \(q-7.06404i q^{2} +(-15.4896 + 1.75248i) q^{3} -17.9007 q^{4} +82.3579 q^{5} +(12.3796 + 109.419i) q^{6} -96.3127i q^{7} -99.5980i q^{8} +(236.858 - 54.2905i) q^{9} +O(q^{10})\) \(q-7.06404i q^{2} +(-15.4896 + 1.75248i) q^{3} -17.9007 q^{4} +82.3579 q^{5} +(12.3796 + 109.419i) q^{6} -96.3127i q^{7} -99.5980i q^{8} +(236.858 - 54.2905i) q^{9} -581.779i q^{10} -87.8590 q^{11} +(277.275 - 31.3706i) q^{12} +303.810 q^{13} -680.357 q^{14} +(-1275.69 + 144.330i) q^{15} -1276.39 q^{16} -460.998 q^{17} +(-383.510 - 1673.17i) q^{18} -1560.29i q^{19} -1474.26 q^{20} +(168.786 + 1491.85i) q^{21} +620.640i q^{22} +(-2440.41 + 693.361i) q^{23} +(174.543 + 1542.74i) q^{24} +3657.82 q^{25} -2146.13i q^{26} +(-3573.70 + 1256.03i) q^{27} +1724.07i q^{28} -4091.99i q^{29} +(1019.56 + 9011.55i) q^{30} +1861.74 q^{31} +5829.32i q^{32} +(1360.90 - 153.971i) q^{33} +3256.51i q^{34} -7932.11i q^{35} +(-4239.92 + 971.838i) q^{36} -11817.5i q^{37} -11021.9 q^{38} +(-4705.91 + 532.421i) q^{39} -8202.68i q^{40} +12179.1i q^{41} +(10538.5 - 1192.31i) q^{42} -22461.2i q^{43} +1572.74 q^{44} +(19507.1 - 4471.25i) q^{45} +(4897.93 + 17239.2i) q^{46} +2743.55i q^{47} +(19770.8 - 2236.84i) q^{48} +7530.86 q^{49} -25839.0i q^{50} +(7140.70 - 807.889i) q^{51} -5438.42 q^{52} +11551.9 q^{53} +(8872.63 + 25244.7i) q^{54} -7235.88 q^{55} -9592.56 q^{56} +(2734.37 + 24168.3i) q^{57} -28906.0 q^{58} +39947.0i q^{59} +(22835.8 - 2583.61i) q^{60} +24443.4i q^{61} -13151.4i q^{62} +(-5228.87 - 22812.4i) q^{63} +334.155 q^{64} +25021.2 q^{65} +(-1087.66 - 9613.48i) q^{66} +41740.7i q^{67} +8252.20 q^{68} +(36585.9 - 15016.7i) q^{69} -56032.8 q^{70} -33816.0i q^{71} +(-5407.23 - 23590.6i) q^{72} +63699.0 q^{73} -83479.5 q^{74} +(-56658.2 + 6410.24i) q^{75} +27930.2i q^{76} +8461.94i q^{77} +(3761.04 + 33242.8i) q^{78} +41670.6i q^{79} -105121. q^{80} +(53154.1 - 25718.2i) q^{81} +86034.0 q^{82} +72364.0 q^{83} +(-3021.39 - 26705.2i) q^{84} -37966.8 q^{85} -158667. q^{86} +(7171.13 + 63383.5i) q^{87} +8750.58i q^{88} -9268.15 q^{89} +(-31585.1 - 137799. i) q^{90} -29260.8i q^{91} +(43685.0 - 12411.6i) q^{92} +(-28837.6 + 3262.65i) q^{93} +19380.5 q^{94} -128502. i q^{95} +(-10215.8 - 90294.0i) q^{96} -28465.2i q^{97} -53198.3i q^{98} +(-20810.1 + 4769.91i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.06404i 1.24876i −0.781121 0.624379i \(-0.785352\pi\)
0.781121 0.624379i \(-0.214648\pi\)
\(3\) −15.4896 + 1.75248i −0.993661 + 0.112422i
\(4\) −17.9007 −0.559397
\(5\) 82.3579 1.47326 0.736631 0.676295i \(-0.236415\pi\)
0.736631 + 0.676295i \(0.236415\pi\)
\(6\) 12.3796 + 109.419i 0.140387 + 1.24084i
\(7\) 96.3127i 0.742914i −0.928450 0.371457i \(-0.878858\pi\)
0.928450 0.371457i \(-0.121142\pi\)
\(8\) 99.5980i 0.550207i
\(9\) 236.858 54.2905i 0.974723 0.223418i
\(10\) 581.779i 1.83975i
\(11\) −87.8590 −0.218930 −0.109465 0.993991i \(-0.534914\pi\)
−0.109465 + 0.993991i \(0.534914\pi\)
\(12\) 277.275 31.3706i 0.555851 0.0628883i
\(13\) 303.810 0.498591 0.249295 0.968428i \(-0.419801\pi\)
0.249295 + 0.968428i \(0.419801\pi\)
\(14\) −680.357 −0.927720
\(15\) −1275.69 + 144.330i −1.46392 + 0.165626i
\(16\) −1276.39 −1.24647
\(17\) −460.998 −0.386881 −0.193440 0.981112i \(-0.561965\pi\)
−0.193440 + 0.981112i \(0.561965\pi\)
\(18\) −383.510 1673.17i −0.278995 1.21719i
\(19\) 1560.29i 0.991563i −0.868447 0.495781i \(-0.834882\pi\)
0.868447 0.495781i \(-0.165118\pi\)
\(20\) −1474.26 −0.824138
\(21\) 168.786 + 1491.85i 0.0835195 + 0.738205i
\(22\) 620.640i 0.273390i
\(23\) −2440.41 + 693.361i −0.961929 + 0.273300i
\(24\) 174.543 + 1542.74i 0.0618551 + 0.546719i
\(25\) 3657.82 1.17050
\(26\) 2146.13i 0.622619i
\(27\) −3573.70 + 1256.03i −0.943427 + 0.331581i
\(28\) 1724.07i 0.415584i
\(29\) 4091.99i 0.903525i −0.892138 0.451762i \(-0.850796\pi\)
0.892138 0.451762i \(-0.149204\pi\)
\(30\) 1019.56 + 9011.55i 0.206827 + 1.82809i
\(31\) 1861.74 0.347947 0.173974 0.984750i \(-0.444339\pi\)
0.173974 + 0.984750i \(0.444339\pi\)
\(32\) 5829.32i 1.00634i
\(33\) 1360.90 153.971i 0.217542 0.0246124i
\(34\) 3256.51i 0.483120i
\(35\) 7932.11i 1.09451i
\(36\) −4239.92 + 971.838i −0.545257 + 0.124979i
\(37\) 11817.5i 1.41913i −0.704640 0.709565i \(-0.748891\pi\)
0.704640 0.709565i \(-0.251109\pi\)
\(38\) −11021.9 −1.23822
\(39\) −4705.91 + 532.421i −0.495430 + 0.0560523i
\(40\) 8202.68i 0.810599i
\(41\) 12179.1i 1.13151i 0.824574 + 0.565754i \(0.191415\pi\)
−0.824574 + 0.565754i \(0.808585\pi\)
\(42\) 10538.5 1192.31i 0.921839 0.104296i
\(43\) 22461.2i 1.85252i −0.376888 0.926259i \(-0.623006\pi\)
0.376888 0.926259i \(-0.376994\pi\)
\(44\) 1572.74 0.122469
\(45\) 19507.1 4471.25i 1.43602 0.329153i
\(46\) 4897.93 + 17239.2i 0.341286 + 1.20122i
\(47\) 2743.55i 0.181162i 0.995889 + 0.0905811i \(0.0288724\pi\)
−0.995889 + 0.0905811i \(0.971128\pi\)
\(48\) 19770.8 2236.84i 1.23857 0.140130i
\(49\) 7530.86 0.448079
\(50\) 25839.0i 1.46167i
\(51\) 7140.70 807.889i 0.384428 0.0434937i
\(52\) −5438.42 −0.278910
\(53\) 11551.9 0.564891 0.282445 0.959283i \(-0.408854\pi\)
0.282445 + 0.959283i \(0.408854\pi\)
\(54\) 8872.63 + 25244.7i 0.414065 + 1.17811i
\(55\) −7235.88 −0.322541
\(56\) −9592.56 −0.408756
\(57\) 2734.37 + 24168.3i 0.111473 + 0.985277i
\(58\) −28906.0 −1.12828
\(59\) 39947.0i 1.49401i 0.664817 + 0.747006i \(0.268509\pi\)
−0.664817 + 0.747006i \(0.731491\pi\)
\(60\) 22835.8 2583.61i 0.818914 0.0926509i
\(61\) 24443.4i 0.841079i 0.907274 + 0.420540i \(0.138159\pi\)
−0.907274 + 0.420540i \(0.861841\pi\)
\(62\) 13151.4i 0.434502i
\(63\) −5228.87 22812.4i −0.165980 0.724135i
\(64\) 334.155 0.0101976
\(65\) 25021.2 0.734555
\(66\) −1087.66 9613.48i −0.0307349 0.271657i
\(67\) 41740.7i 1.13598i 0.823034 + 0.567992i \(0.192280\pi\)
−0.823034 + 0.567992i \(0.807720\pi\)
\(68\) 8252.20 0.216420
\(69\) 36585.9 15016.7i 0.925106 0.379709i
\(70\) −56032.8 −1.36677
\(71\) 33816.0i 0.796115i −0.917360 0.398058i \(-0.869684\pi\)
0.917360 0.398058i \(-0.130316\pi\)
\(72\) −5407.23 23590.6i −0.122926 0.536299i
\(73\) 63699.0 1.39902 0.699512 0.714621i \(-0.253401\pi\)
0.699512 + 0.714621i \(0.253401\pi\)
\(74\) −83479.5 −1.77215
\(75\) −56658.2 + 6410.24i −1.16308 + 0.131589i
\(76\) 27930.2i 0.554677i
\(77\) 8461.94i 0.162646i
\(78\) 3761.04 + 33242.8i 0.0699958 + 0.618672i
\(79\) 41670.6i 0.751210i 0.926780 + 0.375605i \(0.122565\pi\)
−0.926780 + 0.375605i \(0.877435\pi\)
\(80\) −105121. −1.83638
\(81\) 53154.1 25718.2i 0.900169 0.435541i
\(82\) 86034.0 1.41298
\(83\) 72364.0 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(84\) −3021.39 26705.2i −0.0467206 0.412949i
\(85\) −37966.8 −0.569977
\(86\) −158667. −2.31335
\(87\) 7171.13 + 63383.5i 0.101576 + 0.897797i
\(88\) 8750.58i 0.120457i
\(89\) −9268.15 −0.124027 −0.0620137 0.998075i \(-0.519752\pi\)
−0.0620137 + 0.998075i \(0.519752\pi\)
\(90\) −31585.1 137799.i −0.411032 1.79324i
\(91\) 29260.8i 0.370410i
\(92\) 43685.0 12411.6i 0.538100 0.152883i
\(93\) −28837.6 + 3262.65i −0.345742 + 0.0391168i
\(94\) 19380.5 0.226228
\(95\) 128502.i 1.46083i
\(96\) −10215.8 90294.0i −0.113134 0.999956i
\(97\) 28465.2i 0.307174i −0.988135 0.153587i \(-0.950918\pi\)
0.988135 0.153587i \(-0.0490825\pi\)
\(98\) 53198.3i 0.559542i
\(99\) −20810.1 + 4769.91i −0.213396 + 0.0489127i
\(100\) −65477.5 −0.654775
\(101\) 105391.i 1.02802i 0.857785 + 0.514008i \(0.171840\pi\)
−0.857785 + 0.514008i \(0.828160\pi\)
\(102\) −5706.97 50442.2i −0.0543131 0.480058i
\(103\) 208125.i 1.93300i −0.256673 0.966498i \(-0.582626\pi\)
0.256673 0.966498i \(-0.417374\pi\)
\(104\) 30258.9i 0.274328i
\(105\) 13900.8 + 122866.i 0.123046 + 1.08757i
\(106\) 81603.3i 0.705412i
\(107\) −183616. −1.55043 −0.775215 0.631698i \(-0.782358\pi\)
−0.775215 + 0.631698i \(0.782358\pi\)
\(108\) 63971.7 22483.8i 0.527750 0.185485i
\(109\) 114970.i 0.926868i 0.886131 + 0.463434i \(0.153383\pi\)
−0.886131 + 0.463434i \(0.846617\pi\)
\(110\) 51114.6i 0.402775i
\(111\) 20710.0 + 183049.i 0.159541 + 1.41013i
\(112\) 122932.i 0.926022i
\(113\) 186197. 1.37175 0.685876 0.727719i \(-0.259419\pi\)
0.685876 + 0.727719i \(0.259419\pi\)
\(114\) 170726. 19315.7i 1.23037 0.139203i
\(115\) −200987. + 57103.7i −1.41717 + 0.402643i
\(116\) 73249.6i 0.505429i
\(117\) 71959.8 16494.0i 0.485988 0.111394i
\(118\) 282187. 1.86566
\(119\) 44400.0i 0.287419i
\(120\) 14375.0 + 127057.i 0.0911287 + 0.805460i
\(121\) −153332. −0.952070
\(122\) 172669. 1.05030
\(123\) −21343.7 188651.i −0.127206 1.12433i
\(124\) −33326.4 −0.194641
\(125\) 43881.6 0.251193
\(126\) −161148. + 36936.9i −0.904270 + 0.207269i
\(127\) 130830. 0.719777 0.359888 0.932995i \(-0.382815\pi\)
0.359888 + 0.932995i \(0.382815\pi\)
\(128\) 184178.i 0.993601i
\(129\) 39362.8 + 347916.i 0.208263 + 1.84077i
\(130\) 176751.i 0.917281i
\(131\) 54027.3i 0.275065i −0.990497 0.137532i \(-0.956083\pi\)
0.990497 0.137532i \(-0.0439171\pi\)
\(132\) −24361.1 + 2756.19i −0.121692 + 0.0137681i
\(133\) −150275. −0.736646
\(134\) 294858. 1.41857
\(135\) −294322. + 103444.i −1.38991 + 0.488506i
\(136\) 45914.5i 0.212864i
\(137\) 162442. 0.739428 0.369714 0.929146i \(-0.379456\pi\)
0.369714 + 0.929146i \(0.379456\pi\)
\(138\) −106078. 258445.i −0.474165 1.15523i
\(139\) 142959. 0.627587 0.313794 0.949491i \(-0.398400\pi\)
0.313794 + 0.949491i \(0.398400\pi\)
\(140\) 141990.i 0.612264i
\(141\) −4808.00 42496.5i −0.0203665 0.180014i
\(142\) −238877. −0.994156
\(143\) −26692.5 −0.109156
\(144\) −302322. + 69295.7i −1.21496 + 0.278484i
\(145\) 337008.i 1.33113i
\(146\) 449972.i 1.74704i
\(147\) −116650. + 13197.7i −0.445238 + 0.0503737i
\(148\) 211542.i 0.793857i
\(149\) 333252. 1.22972 0.614862 0.788635i \(-0.289212\pi\)
0.614862 + 0.788635i \(0.289212\pi\)
\(150\) 45282.2 + 400236.i 0.164323 + 1.45241i
\(151\) 510659. 1.82259 0.911295 0.411755i \(-0.135084\pi\)
0.911295 + 0.411755i \(0.135084\pi\)
\(152\) −155401. −0.545564
\(153\) −109191. + 25027.8i −0.377101 + 0.0864360i
\(154\) 59775.5 0.203105
\(155\) 153329. 0.512618
\(156\) 84239.1 9530.71i 0.277142 0.0313555i
\(157\) 335833.i 1.08736i −0.839292 0.543680i \(-0.817030\pi\)
0.839292 0.543680i \(-0.182970\pi\)
\(158\) 294363. 0.938080
\(159\) −178935. + 20244.5i −0.561310 + 0.0635059i
\(160\) 480090.i 1.48260i
\(161\) 66779.5 + 235042.i 0.203039 + 0.714631i
\(162\) −181675. 375483.i −0.543885 1.12409i
\(163\) 371286. 1.09456 0.547279 0.836950i \(-0.315664\pi\)
0.547279 + 0.836950i \(0.315664\pi\)
\(164\) 218015.i 0.632962i
\(165\) 112081. 12680.7i 0.320496 0.0362605i
\(166\) 511182.i 1.43981i
\(167\) 352931.i 0.979262i 0.871930 + 0.489631i \(0.162869\pi\)
−0.871930 + 0.489631i \(0.837131\pi\)
\(168\) 148585. 16810.7i 0.406165 0.0459530i
\(169\) −278992. −0.751407
\(170\) 268199.i 0.711763i
\(171\) −84708.7 369566.i −0.221533 0.966499i
\(172\) 402072.i 1.03629i
\(173\) 522540.i 1.32741i 0.747995 + 0.663704i \(0.231017\pi\)
−0.747995 + 0.663704i \(0.768983\pi\)
\(174\) 447744. 50657.2i 1.12113 0.126843i
\(175\) 352294.i 0.869582i
\(176\) 112142. 0.272890
\(177\) −70006.2 618765.i −0.167959 1.48454i
\(178\) 65470.6i 0.154880i
\(179\) 45906.4i 0.107088i −0.998565 0.0535440i \(-0.982948\pi\)
0.998565 0.0535440i \(-0.0170517\pi\)
\(180\) −349191. + 80038.5i −0.803306 + 0.184127i
\(181\) 401676.i 0.911337i −0.890149 0.455669i \(-0.849400\pi\)
0.890149 0.455669i \(-0.150600\pi\)
\(182\) −206700. −0.462553
\(183\) −42836.5 378619.i −0.0945554 0.835747i
\(184\) 69057.4 + 243060.i 0.150372 + 0.529260i
\(185\) 973266.i 2.09075i
\(186\) 23047.5 + 203710.i 0.0488474 + 0.431748i
\(187\) 40502.9 0.0846997
\(188\) 49111.4i 0.101342i
\(189\) 120971. + 344192.i 0.246336 + 0.700885i
\(190\) −907742. −1.82423
\(191\) −598178. −1.18644 −0.593222 0.805039i \(-0.702144\pi\)
−0.593222 + 0.805039i \(0.702144\pi\)
\(192\) −5175.95 + 585.600i −0.0101330 + 0.00114643i
\(193\) −535462. −1.03475 −0.517375 0.855759i \(-0.673091\pi\)
−0.517375 + 0.855759i \(0.673091\pi\)
\(194\) −201079. −0.383586
\(195\) −387569. + 43849.0i −0.729898 + 0.0825797i
\(196\) −134808. −0.250654
\(197\) 620923.i 1.13991i 0.821675 + 0.569957i \(0.193040\pi\)
−0.821675 + 0.569957i \(0.806960\pi\)
\(198\) 33694.8 + 147003.i 0.0610802 + 0.266480i
\(199\) 679618.i 1.21656i 0.793724 + 0.608278i \(0.208139\pi\)
−0.793724 + 0.608278i \(0.791861\pi\)
\(200\) 364311.i 0.644017i
\(201\) −73149.6 646548.i −0.127709 1.12878i
\(202\) 744486. 1.28374
\(203\) −394111. −0.671241
\(204\) −127823. + 14461.8i −0.215048 + 0.0243303i
\(205\) 1.00305e6i 1.66701i
\(206\) −1.47020e6 −2.41385
\(207\) −540386. + 296719.i −0.876554 + 0.481304i
\(208\) −387780. −0.621479
\(209\) 137085.i 0.217083i
\(210\) 867927. 98196.2i 1.35811 0.153655i
\(211\) −99148.1 −0.153313 −0.0766564 0.997058i \(-0.524424\pi\)
−0.0766564 + 0.997058i \(0.524424\pi\)
\(212\) −206788. −0.315998
\(213\) 59261.7 + 523797.i 0.0895005 + 0.791069i
\(214\) 1.29707e6i 1.93611i
\(215\) 1.84986e6i 2.72924i
\(216\) 125098. + 355933.i 0.182438 + 0.519080i
\(217\) 179309.i 0.258495i
\(218\) 812152. 1.15743
\(219\) −986674. + 111631.i −1.39016 + 0.157280i
\(220\) 129527. 0.180428
\(221\) −140056. −0.192895
\(222\) 1.29307e6 146296.i 1.76092 0.199228i
\(223\) 434908. 0.585646 0.292823 0.956167i \(-0.405405\pi\)
0.292823 + 0.956167i \(0.405405\pi\)
\(224\) 561438. 0.747621
\(225\) 866382. 198585.i 1.14091 0.261511i
\(226\) 1.31530e6i 1.71299i
\(227\) 947182. 1.22003 0.610013 0.792392i \(-0.291164\pi\)
0.610013 + 0.792392i \(0.291164\pi\)
\(228\) −48947.1 432629.i −0.0623577 0.551161i
\(229\) 47648.3i 0.0600425i 0.999549 + 0.0300213i \(0.00955750\pi\)
−0.999549 + 0.0300213i \(0.990443\pi\)
\(230\) 403383. + 1.41978e6i 0.502803 + 1.76971i
\(231\) −14829.4 131072.i −0.0182849 0.161615i
\(232\) −407555. −0.497125
\(233\) 292242.i 0.352657i −0.984331 0.176328i \(-0.943578\pi\)
0.984331 0.176328i \(-0.0564221\pi\)
\(234\) −116514. 508327.i −0.139104 0.606881i
\(235\) 225953.i 0.266899i
\(236\) 715079.i 0.835746i
\(237\) −73026.7 645462.i −0.0844522 0.746448i
\(238\) 313644. 0.358917
\(239\) 1.53813e6i 1.74180i 0.491459 + 0.870901i \(0.336464\pi\)
−0.491459 + 0.870901i \(0.663536\pi\)
\(240\) 1.62828e6 184221.i 1.82474 0.206449i
\(241\) 370725.i 0.411158i 0.978641 + 0.205579i \(0.0659078\pi\)
−0.978641 + 0.205579i \(0.934092\pi\)
\(242\) 1.08314e6i 1.18890i
\(243\) −778267. + 491517.i −0.845498 + 0.533978i
\(244\) 437554.i 0.470497i
\(245\) 620225. 0.660137
\(246\) −1.33264e6 + 150773.i −1.40402 + 0.158849i
\(247\) 474031.i 0.494384i
\(248\) 185425.i 0.191443i
\(249\) −1.12089e6 + 126816.i −1.14569 + 0.129621i
\(250\) 309981.i 0.313679i
\(251\) 209024. 0.209417 0.104709 0.994503i \(-0.466609\pi\)
0.104709 + 0.994503i \(0.466609\pi\)
\(252\) 93600.4 + 408358.i 0.0928488 + 0.405079i
\(253\) 214412. 60918.0i 0.210595 0.0598335i
\(254\) 924189.i 0.898827i
\(255\) 588092. 66536.0i 0.566363 0.0640776i
\(256\) 1.31173e6 1.25097
\(257\) 580419.i 0.548162i 0.961707 + 0.274081i \(0.0883736\pi\)
−0.961707 + 0.274081i \(0.911626\pi\)
\(258\) 2.45770e6 278061.i 2.29868 0.260070i
\(259\) −1.13818e6 −1.05429
\(260\) −447896. −0.410908
\(261\) −222156. 969220.i −0.201863 0.880686i
\(262\) −381651. −0.343490
\(263\) −1.58407e6 −1.41216 −0.706080 0.708132i \(-0.749538\pi\)
−0.706080 + 0.708132i \(0.749538\pi\)
\(264\) −15335.2 135543.i −0.0135419 0.119693i
\(265\) 951391. 0.832232
\(266\) 1.06155e6i 0.919893i
\(267\) 143560. 16242.2i 0.123241 0.0139434i
\(268\) 747188.i 0.635466i
\(269\) 1.99855e6i 1.68397i −0.539500 0.841986i \(-0.681387\pi\)
0.539500 0.841986i \(-0.318613\pi\)
\(270\) 730731. + 2.07910e6i 0.610026 + 1.73567i
\(271\) 1.37973e6 1.14122 0.570612 0.821220i \(-0.306706\pi\)
0.570612 + 0.821220i \(0.306706\pi\)
\(272\) 588412. 0.482236
\(273\) 51278.9 + 453239.i 0.0416421 + 0.368062i
\(274\) 1.14749e6i 0.923367i
\(275\) −321372. −0.256257
\(276\) −654914. + 268809.i −0.517501 + 0.212408i
\(277\) 1.43497e6 1.12369 0.561843 0.827244i \(-0.310093\pi\)
0.561843 + 0.827244i \(0.310093\pi\)
\(278\) 1.00987e6i 0.783705i
\(279\) 440966. 101075.i 0.339152 0.0777376i
\(280\) −790023. −0.602205
\(281\) −1.17003e6 −0.883954 −0.441977 0.897026i \(-0.645723\pi\)
−0.441977 + 0.897026i \(0.645723\pi\)
\(282\) −300197. + 33963.9i −0.224794 + 0.0254329i
\(283\) 1.19800e6i 0.889179i −0.895734 0.444589i \(-0.853350\pi\)
0.895734 0.444589i \(-0.146650\pi\)
\(284\) 605330.i 0.445345i
\(285\) 225197. + 1.99045e6i 0.164229 + 1.45157i
\(286\) 188557.i 0.136310i
\(287\) 1.17301e6 0.840613
\(288\) 316477. + 1.38072e6i 0.224833 + 0.980898i
\(289\) −1.20734e6 −0.850323
\(290\) −2.38064e6 −1.66226
\(291\) 49884.5 + 440915.i 0.0345329 + 0.305226i
\(292\) −1.14026e6 −0.782610
\(293\) 2.23825e6 1.52314 0.761568 0.648085i \(-0.224430\pi\)
0.761568 + 0.648085i \(0.224430\pi\)
\(294\) 93228.8 + 824022.i 0.0629045 + 0.555995i
\(295\) 3.28995e6i 2.20107i
\(296\) −1.17700e6 −0.780815
\(297\) 313981. 110353.i 0.206544 0.0725929i
\(298\) 2.35411e6i 1.53563i
\(299\) −741421. + 210650.i −0.479609 + 0.136265i
\(300\) 1.01422e6 114748.i 0.650624 0.0736108i
\(301\) −2.16330e6 −1.37626
\(302\) 3.60732e6i 2.27597i
\(303\) −184695. 1.63247e6i −0.115571 1.02150i
\(304\) 1.99153e6i 1.23596i
\(305\) 2.01310e6i 1.23913i
\(306\) 176798. + 771330.i 0.107938 + 0.470909i
\(307\) −2.25941e6 −1.36820 −0.684100 0.729388i \(-0.739805\pi\)
−0.684100 + 0.729388i \(0.739805\pi\)
\(308\) 151475.i 0.0909836i
\(309\) 364734. + 3.22378e6i 0.217310 + 1.92074i
\(310\) 1.08312e6i 0.640136i
\(311\) 1.35140e6i 0.792285i −0.918189 0.396142i \(-0.870349\pi\)
0.918189 0.396142i \(-0.129651\pi\)
\(312\) 53028.1 + 468700.i 0.0308404 + 0.272589i
\(313\) 913176.i 0.526858i 0.964679 + 0.263429i \(0.0848535\pi\)
−0.964679 + 0.263429i \(0.915147\pi\)
\(314\) −2.37234e6 −1.35785
\(315\) −430638. 1.87878e6i −0.244532 1.06684i
\(316\) 745932.i 0.420225i
\(317\) 2.07585e6i 1.16024i 0.814532 + 0.580119i \(0.196994\pi\)
−0.814532 + 0.580119i \(0.803006\pi\)
\(318\) 143008. + 1.26400e6i 0.0793035 + 0.700940i
\(319\) 359518.i 0.197808i
\(320\) 27520.3 0.0150238
\(321\) 2.84415e6 321784.i 1.54060 0.174302i
\(322\) 1.66035e6 471733.i 0.892401 0.253546i
\(323\) 719289.i 0.383617i
\(324\) −951495. + 460374.i −0.503552 + 0.243640i
\(325\) 1.11128e6 0.583601
\(326\) 2.62278e6i 1.36684i
\(327\) −201482. 1.78084e6i −0.104200 0.920992i
\(328\) 1.21302e6 0.622563
\(329\) 264238. 0.134588
\(330\) −89577.1 791746.i −0.0452806 0.400222i
\(331\) −1.93557e6 −0.971043 −0.485522 0.874225i \(-0.661370\pi\)
−0.485522 + 0.874225i \(0.661370\pi\)
\(332\) −1.29537e6 −0.644982
\(333\) −641579. 2.79907e6i −0.317059 1.38326i
\(334\) 2.49312e6 1.22286
\(335\) 3.43767e6i 1.67360i
\(336\) −215436. 1.90418e6i −0.104105 0.920151i
\(337\) 294207.i 0.141117i 0.997508 + 0.0705583i \(0.0224781\pi\)
−0.997508 + 0.0705583i \(0.977522\pi\)
\(338\) 1.97081e6i 0.938326i
\(339\) −2.88412e6 + 326305.i −1.36306 + 0.154214i
\(340\) 679633. 0.318843
\(341\) −163570. −0.0761760
\(342\) −2.61063e6 + 598386.i −1.20692 + 0.276641i
\(343\) 2.34405e6i 1.07580i
\(344\) −2.23709e6 −1.01927
\(345\) 3.01314e6 1.23674e6i 1.36292 0.559411i
\(346\) 3.69125e6 1.65761
\(347\) 3.21410e6i 1.43296i −0.697606 0.716482i \(-0.745751\pi\)
0.697606 0.716482i \(-0.254249\pi\)
\(348\) −128368. 1.13461e6i −0.0568211 0.502225i
\(349\) 464451. 0.204116 0.102058 0.994778i \(-0.467457\pi\)
0.102058 + 0.994778i \(0.467457\pi\)
\(350\) −2.48862e6 −1.08590
\(351\) −1.08573e6 + 381594.i −0.470384 + 0.165323i
\(352\) 512158.i 0.220317i
\(353\) 923698.i 0.394542i −0.980349 0.197271i \(-0.936792\pi\)
0.980349 0.197271i \(-0.0632079\pi\)
\(354\) −4.37098e6 + 494527.i −1.85383 + 0.209740i
\(355\) 2.78501e6i 1.17289i
\(356\) 165906. 0.0693806
\(357\) −77810.0 687740.i −0.0323121 0.285597i
\(358\) −324285. −0.133727
\(359\) 2.76429e6 1.13200 0.566002 0.824404i \(-0.308489\pi\)
0.566002 + 0.824404i \(0.308489\pi\)
\(360\) −445328. 1.94287e6i −0.181102 0.790109i
\(361\) 41606.1 0.0168031
\(362\) −2.83746e6 −1.13804
\(363\) 2.37505e6 268711.i 0.946034 0.107033i
\(364\) 523789.i 0.207206i
\(365\) 5.24611e6 2.06113
\(366\) −2.67458e6 + 302599.i −1.04365 + 0.118077i
\(367\) 1.67359e6i 0.648610i 0.945953 + 0.324305i \(0.105130\pi\)
−0.945953 + 0.324305i \(0.894870\pi\)
\(368\) 3.11491e6 884997.i 1.19902 0.340661i
\(369\) 661212. + 2.88472e6i 0.252799 + 1.10291i
\(370\) −6.87520e6 −2.61084
\(371\) 1.11260e6i 0.419665i
\(372\) 516213. 58403.7i 0.193407 0.0218818i
\(373\) 496559.i 0.184799i −0.995722 0.0923993i \(-0.970546\pi\)
0.995722 0.0923993i \(-0.0294536\pi\)
\(374\) 286114.i 0.105769i
\(375\) −679709. + 76901.5i −0.249600 + 0.0282395i
\(376\) 273252. 0.0996766
\(377\) 1.24319e6i 0.450489i
\(378\) 2.43139e6 854548.i 0.875236 0.307614i
\(379\) 3.34566e6i 1.19642i 0.801340 + 0.598209i \(0.204121\pi\)
−0.801340 + 0.598209i \(0.795879\pi\)
\(380\) 2.30027e6i 0.817185i
\(381\) −2.02651e6 + 229277.i −0.715214 + 0.0809184i
\(382\) 4.22556e6i 1.48158i
\(383\) 338695. 0.117981 0.0589904 0.998259i \(-0.481212\pi\)
0.0589904 + 0.998259i \(0.481212\pi\)
\(384\) −322767. 2.85285e6i −0.111702 0.987302i
\(385\) 696907.i 0.239620i
\(386\) 3.78252e6i 1.29215i
\(387\) −1.21943e6 5.32011e6i −0.413885 1.80569i
\(388\) 509546.i 0.171832i
\(389\) 3.12606e6 1.04743 0.523714 0.851894i \(-0.324546\pi\)
0.523714 + 0.851894i \(0.324546\pi\)
\(390\) 309751. + 2.73780e6i 0.103122 + 0.911466i
\(391\) 1.12502e6 319638.i 0.372152 0.105735i
\(392\) 750059.i 0.246536i
\(393\) 94681.7 + 836864.i 0.0309232 + 0.273321i
\(394\) 4.38622e6 1.42348
\(395\) 3.43190e6i 1.10673i
\(396\) 372515. 85384.7i 0.119373 0.0273616i
\(397\) −1.16181e6 −0.369964 −0.184982 0.982742i \(-0.559223\pi\)
−0.184982 + 0.982742i \(0.559223\pi\)
\(398\) 4.80085e6 1.51918
\(399\) 2.32771e6 263354.i 0.731976 0.0828149i
\(400\) −4.66879e6 −1.45900
\(401\) 821803. 0.255215 0.127608 0.991825i \(-0.459270\pi\)
0.127608 + 0.991825i \(0.459270\pi\)
\(402\) −4.56724e6 + 516732.i −1.40958 + 0.159478i
\(403\) 565614. 0.173483
\(404\) 1.88657e6i 0.575069i
\(405\) 4.37766e6 2.11810e6i 1.32618 0.641665i
\(406\) 2.78402e6i 0.838218i
\(407\) 1.03828e6i 0.310690i
\(408\) −80464.2 711199.i −0.0239305 0.211515i
\(409\) −2.29307e6 −0.677810 −0.338905 0.940821i \(-0.610057\pi\)
−0.338905 + 0.940821i \(0.610057\pi\)
\(410\) 7.08558e6 2.08169
\(411\) −2.51616e6 + 284675.i −0.734741 + 0.0831276i
\(412\) 3.72558e6i 1.08131i
\(413\) 3.84741e6 1.10992
\(414\) 2.09603e6 + 3.81731e6i 0.601032 + 1.09460i
\(415\) 5.95974e6 1.69866
\(416\) 1.77101e6i 0.501749i
\(417\) −2.21438e6 + 250532.i −0.623609 + 0.0705543i
\(418\) 968376. 0.271084
\(419\) −449527. −0.125090 −0.0625448 0.998042i \(-0.519922\pi\)
−0.0625448 + 0.998042i \(0.519922\pi\)
\(420\) −248835. 2.19938e6i −0.0688316 0.608383i
\(421\) 4.57385e6i 1.25770i 0.777527 + 0.628850i \(0.216474\pi\)
−0.777527 + 0.628850i \(0.783526\pi\)
\(422\) 700387.i 0.191451i
\(423\) 148948. + 649830.i 0.0404748 + 0.176583i
\(424\) 1.15055e6i 0.310807i
\(425\) −1.68625e6 −0.452844
\(426\) 3.70013e6 418628.i 0.987853 0.111764i
\(427\) 2.35421e6 0.624849
\(428\) 3.28686e6 0.867306
\(429\) 413457. 46778.0i 0.108464 0.0122715i
\(430\) −1.30675e7 −3.40817
\(431\) −4.58849e6 −1.18981 −0.594904 0.803797i \(-0.702810\pi\)
−0.594904 + 0.803797i \(0.702810\pi\)
\(432\) 4.56142e6 1.60318e6i 1.17595 0.413307i
\(433\) 2.65527e6i 0.680596i −0.940318 0.340298i \(-0.889472\pi\)
0.940318 0.340298i \(-0.110528\pi\)
\(434\) −1.26665e6 −0.322798
\(435\) 590599. + 5.22013e6i 0.149647 + 1.32269i
\(436\) 2.05804e6i 0.518487i
\(437\) 1.08184e6 + 3.80774e6i 0.270994 + 0.953813i
\(438\) 788566. + 6.96991e6i 0.196405 + 1.73597i
\(439\) −3.66951e6 −0.908754 −0.454377 0.890810i \(-0.650138\pi\)
−0.454377 + 0.890810i \(0.650138\pi\)
\(440\) 720679.i 0.177464i
\(441\) 1.78374e6 408854.i 0.436752 0.100109i
\(442\) 989362.i 0.240879i
\(443\) 670900.i 0.162423i 0.996697 + 0.0812117i \(0.0258790\pi\)
−0.996697 + 0.0812117i \(0.974121\pi\)
\(444\) −370723. 3.27671e6i −0.0892466 0.788825i
\(445\) −763305. −0.182725
\(446\) 3.07221e6i 0.731330i
\(447\) −5.16196e6 + 584017.i −1.22193 + 0.138247i
\(448\) 32183.4i 0.00757595i
\(449\) 5.53849e6i 1.29651i −0.761423 0.648255i \(-0.775499\pi\)
0.761423 0.648255i \(-0.224501\pi\)
\(450\) −1.40281e6 6.12016e6i −0.326563 1.42473i
\(451\) 1.07005e6i 0.247720i
\(452\) −3.33305e6 −0.767354
\(453\) −7.90993e6 + 894919.i −1.81104 + 0.204898i
\(454\) 6.69094e6i 1.52352i
\(455\) 2.40986e6i 0.545711i
\(456\) 2.40711e6 272338.i 0.542106 0.0613332i
\(457\) 4.58966e6i 1.02799i −0.857792 0.513996i \(-0.828164\pi\)
0.857792 0.513996i \(-0.171836\pi\)
\(458\) 336590. 0.0749786
\(459\) 1.64747e6 579027.i 0.364994 0.128282i
\(460\) 3.59781e6 1.02220e6i 0.792762 0.225237i
\(461\) 4.47210e6i 0.980074i −0.871702 0.490037i \(-0.836983\pi\)
0.871702 0.490037i \(-0.163017\pi\)
\(462\) −925901. + 104755.i −0.201818 + 0.0228334i
\(463\) 1.82230e6 0.395065 0.197532 0.980296i \(-0.436707\pi\)
0.197532 + 0.980296i \(0.436707\pi\)
\(464\) 5.22297e6i 1.12622i
\(465\) −2.37500e6 + 268705.i −0.509368 + 0.0576293i
\(466\) −2.06441e6 −0.440383
\(467\) −4.99097e6 −1.05899 −0.529496 0.848312i \(-0.677619\pi\)
−0.529496 + 0.848312i \(0.677619\pi\)
\(468\) −1.28813e6 + 295254.i −0.271860 + 0.0623134i
\(469\) 4.02016e6 0.843939
\(470\) 1.59614e6 0.333293
\(471\) 588539. + 5.20192e6i 0.122243 + 1.08047i
\(472\) 3.97864e6 0.822015
\(473\) 1.97342e6i 0.405571i
\(474\) −4.55957e6 + 515864.i −0.932133 + 0.105460i
\(475\) 5.70724e6i 1.16063i
\(476\) 794792.i 0.160781i
\(477\) 2.73616e6 627159.i 0.550612 0.126207i
\(478\) 1.08654e7 2.17509
\(479\) −2.26574e6 −0.451202 −0.225601 0.974220i \(-0.572435\pi\)
−0.225601 + 0.974220i \(0.572435\pi\)
\(480\) −841347. 7.43642e6i −0.166676 1.47320i
\(481\) 3.59029e6i 0.707565i
\(482\) 2.61881e6 0.513437
\(483\) −1.44630e6 3.52369e6i −0.282091 0.687274i
\(484\) 2.74475e6 0.532585
\(485\) 2.34433e6i 0.452547i
\(486\) 3.47210e6 + 5.49771e6i 0.666809 + 1.05582i
\(487\) 919704. 0.175722 0.0878609 0.996133i \(-0.471997\pi\)
0.0878609 + 0.996133i \(0.471997\pi\)
\(488\) 2.43451e6 0.462767
\(489\) −5.75108e6 + 650670.i −1.08762 + 0.123052i
\(490\) 4.38130e6i 0.824352i
\(491\) 6.77346e6i 1.26796i 0.773348 + 0.633982i \(0.218580\pi\)
−0.773348 + 0.633982i \(0.781420\pi\)
\(492\) 382067. + 3.37698e6i 0.0711585 + 0.628949i
\(493\) 1.88640e6i 0.349556i
\(494\) −3.34858e6 −0.617366
\(495\) −1.71387e6 + 392839.i −0.314388 + 0.0720613i
\(496\) −2.37630e6 −0.433707
\(497\) −3.25691e6 −0.591445
\(498\) 895836. + 7.91803e6i 0.161866 + 1.43068i
\(499\) −2.57927e6 −0.463709 −0.231855 0.972750i \(-0.574479\pi\)
−0.231855 + 0.972750i \(0.574479\pi\)
\(500\) −785511. −0.140516
\(501\) −618504. 5.46678e6i −0.110090 0.973054i
\(502\) 1.47656e6i 0.261512i
\(503\) −2.59926e6 −0.458068 −0.229034 0.973418i \(-0.573557\pi\)
−0.229034 + 0.973418i \(0.573557\pi\)
\(504\) −2.27207e6 + 520785.i −0.398424 + 0.0913234i
\(505\) 8.67977e6i 1.51454i
\(506\) −430327. 1.51461e6i −0.0747176 0.262982i
\(507\) 4.32149e6 488928.i 0.746644 0.0844744i
\(508\) −2.34195e6 −0.402641
\(509\) 7.89088e6i 1.34999i 0.737822 + 0.674996i \(0.235854\pi\)
−0.737822 + 0.674996i \(0.764146\pi\)
\(510\) −470013. 4.15431e6i −0.0800175 0.707251i
\(511\) 6.13502e6i 1.03935i
\(512\) 3.37245e6i 0.568552i
\(513\) 1.95976e6 + 5.57599e6i 0.328784 + 0.935467i
\(514\) 4.10011e6 0.684522
\(515\) 1.71407e7i 2.84781i
\(516\) −704622. 6.22795e6i −0.116502 1.02972i
\(517\) 241045.i 0.0396618i
\(518\) 8.04014e6i 1.31656i
\(519\) −915740. 8.09396e6i −0.149229 1.31899i
\(520\) 2.49206e6i 0.404157i
\(521\) −9.26811e6 −1.49588 −0.747940 0.663766i \(-0.768957\pi\)
−0.747940 + 0.663766i \(0.768957\pi\)
\(522\) −6.84661e6 + 1.56932e6i −1.09976 + 0.252078i
\(523\) 7.44892e6i 1.19080i 0.803429 + 0.595401i \(0.203007\pi\)
−0.803429 + 0.595401i \(0.796993\pi\)
\(524\) 967127.i 0.153871i
\(525\) 617388. + 5.45691e6i 0.0977597 + 0.864069i
\(526\) 1.11899e7i 1.76345i
\(527\) −858257. −0.134614
\(528\) −1.73704e6 + 196527.i −0.271160 + 0.0306787i
\(529\) 5.47484e6 3.38417e6i 0.850614 0.525790i
\(530\) 6.72067e6i 1.03926i
\(531\) 2.16874e6 + 9.46175e6i 0.333789 + 1.45625i
\(532\) 2.69004e6 0.412078
\(533\) 3.70015e6i 0.564159i
\(534\) −114736. 1.01412e6i −0.0174119 0.153898i
\(535\) −1.51223e7 −2.28419
\(536\) 4.15729e6 0.625026
\(537\) 80450.0 + 711074.i 0.0120390 + 0.106409i
\(538\) −1.41179e7 −2.10287
\(539\) −661654. −0.0980977
\(540\) 5.26857e6 1.85172e6i 0.777514 0.273269i
\(541\) 1.12804e6 0.165703 0.0828517 0.996562i \(-0.473597\pi\)
0.0828517 + 0.996562i \(0.473597\pi\)
\(542\) 9.74648e6i 1.42511i
\(543\) 703928. + 6.22181e6i 0.102454 + 0.905560i
\(544\) 2.68731e6i 0.389332i
\(545\) 9.46867e6i 1.36552i
\(546\) 3.20170e6 362236.i 0.459620 0.0520009i
\(547\) −816790. −0.116719 −0.0583596 0.998296i \(-0.518587\pi\)
−0.0583596 + 0.998296i \(0.518587\pi\)
\(548\) −2.90782e6 −0.413634
\(549\) 1.32704e6 + 5.78960e6i 0.187912 + 0.819819i
\(550\) 2.27019e6i 0.320003i
\(551\) −6.38468e6 −0.895901
\(552\) −1.49563e6 3.64389e6i −0.208918 0.508999i
\(553\) 4.01341e6 0.558085
\(554\) 1.01367e7i 1.40321i
\(555\) 1.70563e6 + 1.50755e7i 0.235045 + 2.07750i
\(556\) −2.55906e6 −0.351070
\(557\) −62846.8 −0.00858311 −0.00429156 0.999991i \(-0.501366\pi\)
−0.00429156 + 0.999991i \(0.501366\pi\)
\(558\) −713995. 3.11500e6i −0.0970755 0.423519i
\(559\) 6.82395e6i 0.923648i
\(560\) 1.01244e7i 1.36427i
\(561\) −627375. + 70980.4i −0.0841627 + 0.00952206i
\(562\) 8.26512e6i 1.10385i
\(563\) 6.57966e6 0.874848 0.437424 0.899255i \(-0.355891\pi\)
0.437424 + 0.899255i \(0.355891\pi\)
\(564\) 86066.6 + 760718.i 0.0113930 + 0.100699i
\(565\) 1.53347e7 2.02095
\(566\) −8.46269e6 −1.11037
\(567\) −2.47699e6 5.11942e6i −0.323569 0.668748i
\(568\) −3.36800e6 −0.438028
\(569\) 8.19458e6 1.06108 0.530538 0.847661i \(-0.321990\pi\)
0.530538 + 0.847661i \(0.321990\pi\)
\(570\) 1.40606e7 1.59080e6i 1.81266 0.205082i
\(571\) 3.95838e6i 0.508074i 0.967195 + 0.254037i \(0.0817585\pi\)
−0.967195 + 0.254037i \(0.918242\pi\)
\(572\) 477814. 0.0610617
\(573\) 9.26556e6 1.04829e6i 1.17892 0.133382i
\(574\) 8.28617e6i 1.04972i
\(575\) −8.92656e6 + 2.53619e6i −1.12594 + 0.319898i
\(576\) 79147.3 18141.5i 0.00993985 0.00227833i
\(577\) −5.93437e6 −0.742053 −0.371027 0.928622i \(-0.620994\pi\)
−0.371027 + 0.928622i \(0.620994\pi\)
\(578\) 8.52868e6i 1.06185i
\(579\) 8.29411e6 938385.i 1.02819 0.116328i
\(580\) 6.03268e6i 0.744629i
\(581\) 6.96958e6i 0.856576i
\(582\) 3.11464e6 352387.i 0.381154 0.0431233i
\(583\) −1.01494e6 −0.123671
\(584\) 6.34429e6i 0.769752i
\(585\) 5.92645e6 1.35841e6i 0.715987 0.164112i
\(586\) 1.58111e7i 1.90203i
\(587\) 1.32192e7i 1.58347i −0.610866 0.791734i \(-0.709179\pi\)
0.610866 0.791734i \(-0.290821\pi\)
\(588\) 2.08812e6 236247.i 0.249065 0.0281789i
\(589\) 2.90484e6i 0.345012i
\(590\) 2.32403e7 2.74861
\(591\) −1.08815e6 9.61787e6i −0.128151 1.13269i
\(592\) 1.50837e7i 1.76891i
\(593\) 7.51285e6i 0.877340i −0.898648 0.438670i \(-0.855450\pi\)
0.898648 0.438670i \(-0.144550\pi\)
\(594\) −779541. 2.21798e6i −0.0906510 0.257924i
\(595\) 3.65669e6i 0.423444i
\(596\) −5.96545e6 −0.687904
\(597\) −1.19101e6 1.05270e7i −0.136767 1.20884i
\(598\) 1.48804e6 + 5.23743e6i 0.170162 + 0.598915i
\(599\) 7.65322e6i 0.871519i 0.900063 + 0.435760i \(0.143520\pi\)
−0.900063 + 0.435760i \(0.856480\pi\)
\(600\) 638447. + 5.64305e6i 0.0724014 + 0.639935i
\(601\) −462278. −0.0522056 −0.0261028 0.999659i \(-0.508310\pi\)
−0.0261028 + 0.999659i \(0.508310\pi\)
\(602\) 1.52817e7i 1.71862i
\(603\) 2.26612e6 + 9.88660e6i 0.253799 + 1.10727i
\(604\) −9.14116e6 −1.01955
\(605\) −1.26281e7 −1.40265
\(606\) −1.15318e7 + 1.30470e6i −1.27561 + 0.144320i
\(607\) −4.48728e6 −0.494323 −0.247162 0.968974i \(-0.579498\pi\)
−0.247162 + 0.968974i \(0.579498\pi\)
\(608\) 9.09540e6 0.997845
\(609\) 6.10464e6 690671.i 0.666986 0.0754619i
\(610\) 1.42207e7 1.54737
\(611\) 833517.i 0.0903258i
\(612\) 1.95460e6 448016.i 0.210949 0.0483520i
\(613\) 3.41404e6i 0.366959i 0.983024 + 0.183479i \(0.0587361\pi\)
−0.983024 + 0.183479i \(0.941264\pi\)
\(614\) 1.59606e7i 1.70855i
\(615\) −1.75782e6 1.55369e7i −0.187407 1.65644i
\(616\) 842793. 0.0894889
\(617\) −1.60232e7 −1.69448 −0.847238 0.531214i \(-0.821736\pi\)
−0.847238 + 0.531214i \(0.821736\pi\)
\(618\) 2.27729e7 2.57650e6i 2.39854 0.271368i
\(619\) 1.72859e7i 1.81328i −0.421901 0.906642i \(-0.638637\pi\)
0.421901 0.906642i \(-0.361363\pi\)
\(620\) −2.74469e6 −0.286757
\(621\) 7.85040e6 5.54308e6i 0.816888 0.576796i
\(622\) −9.54631e6 −0.989372
\(623\) 892640.i 0.0921418i
\(624\) 6.00657e6 679575.i 0.617539 0.0698676i
\(625\) −7.81668e6 −0.800428
\(626\) 6.45071e6 0.657918
\(627\) −240239. 2.12340e6i −0.0244047 0.215706i
\(628\) 6.01164e6i 0.608266i
\(629\) 5.44786e6i 0.549034i
\(630\) −1.32718e7 + 3.04205e6i −1.33223 + 0.305362i
\(631\) 4.13451e6i 0.413382i 0.978406 + 0.206691i \(0.0662694\pi\)
−0.978406 + 0.206691i \(0.933731\pi\)
\(632\) 4.15031e6 0.413321
\(633\) 1.53577e6 173755.i 0.152341 0.0172357i
\(634\) 1.46639e7 1.44886
\(635\) 1.07749e7 1.06042
\(636\) 3.20306e6 362391.i 0.313995 0.0355250i
\(637\) 2.28795e6 0.223408
\(638\) 2.53965e6 0.247015
\(639\) −1.83589e6 8.00957e6i −0.177866 0.775992i
\(640\) 1.51685e7i 1.46383i
\(641\) −8.64292e6 −0.830836 −0.415418 0.909631i \(-0.636365\pi\)
−0.415418 + 0.909631i \(0.636365\pi\)
\(642\) −2.27309e6 2.00912e7i −0.217661 1.92384i
\(643\) 1.25671e6i 0.119870i −0.998202 0.0599348i \(-0.980911\pi\)
0.998202 0.0599348i \(-0.0190893\pi\)
\(644\) −1.19540e6 4.20742e6i −0.113579 0.399762i
\(645\) 3.24184e6 + 2.86536e7i 0.306826 + 2.71194i
\(646\) 5.08109e6 0.479044
\(647\) 3.40198e6i 0.319500i −0.987157 0.159750i \(-0.948931\pi\)
0.987157 0.159750i \(-0.0510689\pi\)
\(648\) −2.56149e6 5.29404e6i −0.239637 0.495279i
\(649\) 3.50970e6i 0.327084i
\(650\) 7.85014e6i 0.728776i
\(651\) 314235. + 2.77743e6i 0.0290604 + 0.256856i
\(652\) −6.64627e6 −0.612293
\(653\) 2.05797e7i 1.88867i −0.328990 0.944333i \(-0.606708\pi\)
0.328990 0.944333i \(-0.393292\pi\)
\(654\) −1.25799e7 + 1.42328e6i −1.15010 + 0.130120i
\(655\) 4.44958e6i 0.405243i
\(656\) 1.55453e7i 1.41039i
\(657\) 1.50876e7 3.45825e6i 1.36366 0.312567i
\(658\) 1.86659e6i 0.168068i
\(659\) 1.51070e7 1.35508 0.677539 0.735486i \(-0.263046\pi\)
0.677539 + 0.735486i \(0.263046\pi\)
\(660\) −2.00633e6 + 226994.i −0.179284 + 0.0202840i
\(661\) 1.12641e7i 1.00275i 0.865229 + 0.501376i \(0.167173\pi\)
−0.865229 + 0.501376i \(0.832827\pi\)
\(662\) 1.36729e7i 1.21260i
\(663\) 2.16942e6 245445.i 0.191672 0.0216856i
\(664\) 7.20731e6i 0.634385i
\(665\) −1.23764e7 −1.08527
\(666\) −1.97728e7 + 4.53214e6i −1.72736 + 0.395930i
\(667\) 2.83723e6 + 9.98614e6i 0.246933 + 0.869126i
\(668\) 6.31772e6i 0.547796i
\(669\) −6.73656e6 + 762166.i −0.581933 + 0.0658392i
\(670\) 2.42839e7 2.08993
\(671\) 2.14757e6i 0.184137i
\(672\) −8.69646e6 + 983907.i −0.742881 + 0.0840487i
\(673\) −1.33396e7 −1.13528 −0.567642 0.823276i \(-0.692144\pi\)
−0.567642 + 0.823276i \(0.692144\pi\)
\(674\) 2.07829e6 0.176221
\(675\) −1.30719e7 + 4.59432e6i −1.10428 + 0.388116i
\(676\) 4.99416e6 0.420335
\(677\) −5.60773e6 −0.470236 −0.235118 0.971967i \(-0.575548\pi\)
−0.235118 + 0.971967i \(0.575548\pi\)
\(678\) 2.30503e6 + 2.03735e7i 0.192576 + 1.70213i
\(679\) −2.74156e6 −0.228204
\(680\) 3.78142e6i 0.313605i
\(681\) −1.46715e7 + 1.65992e6i −1.21229 + 0.137157i
\(682\) 1.15547e6i 0.0951254i
\(683\) 2.32238e7i 1.90494i 0.304637 + 0.952469i \(0.401465\pi\)
−0.304637 + 0.952469i \(0.598535\pi\)
\(684\) 1.51635e6 + 6.61549e6i 0.123925 + 0.540657i
\(685\) 1.33783e7 1.08937
\(686\) −1.65584e7 −1.34341
\(687\) −83502.6 738055.i −0.00675007 0.0596619i
\(688\) 2.86692e7i 2.30911i
\(689\) 3.50959e6 0.281649
\(690\) −8.73639e6 2.12849e7i −0.698569 1.70196i
\(691\) 1.09068e7 0.868964 0.434482 0.900681i \(-0.356932\pi\)
0.434482 + 0.900681i \(0.356932\pi\)
\(692\) 9.35384e6i 0.742548i
\(693\) 459403. + 2.00428e6i 0.0363380 + 0.158535i
\(694\) −2.27045e7 −1.78943
\(695\) 1.17738e7 0.924601
\(696\) 6.31287e6 714230.i 0.493974 0.0558876i
\(697\) 5.61457e6i 0.437758i
\(698\) 3.28090e6i 0.254891i
\(699\) 512147. + 4.52672e6i 0.0396462 + 0.350421i
\(700\) 6.30631e6i 0.486441i
\(701\) −2.24487e7 −1.72543 −0.862713 0.505695i \(-0.831236\pi\)
−0.862713 + 0.505695i \(0.831236\pi\)
\(702\) 2.69560e6 + 7.66961e6i 0.206449 + 0.587396i
\(703\) −1.84387e7 −1.40716
\(704\) −29358.6 −0.00223256
\(705\) −395977. 3.49992e6i −0.0300052 0.265207i
\(706\) −6.52504e6 −0.492687
\(707\) 1.01505e7 0.763728
\(708\) 1.25316e6 + 1.10763e7i 0.0939558 + 0.830448i
\(709\) 2.21859e7i 1.65753i −0.559596 0.828766i \(-0.689044\pi\)
0.559596 0.828766i \(-0.310956\pi\)
\(710\) −1.96734e7 −1.46465
\(711\) 2.26231e6 + 9.86999e6i 0.167834 + 0.732222i
\(712\) 923089.i 0.0682407i
\(713\) −4.54339e6 + 1.29085e6i −0.334701 + 0.0950941i
\(714\) −4.85823e6 + 549654.i −0.356642 + 0.0403500i
\(715\) −2.19833e6 −0.160816
\(716\) 821757.i 0.0599047i
\(717\) −2.69554e6 2.38251e7i −0.195816 1.73076i
\(718\) 1.95271e7i 1.41360i
\(719\) 471342.i 0.0340028i 0.999855 + 0.0170014i \(0.00541197\pi\)
−0.999855 + 0.0170014i \(0.994588\pi\)
\(720\) −2.48986e7 + 5.70704e6i −1.78996 + 0.410280i
\(721\) −2.00451e7 −1.43605
\(722\) 293907.i 0.0209830i
\(723\) −649687. 5.74239e6i −0.0462230 0.408552i
\(724\) 7.19028e6i 0.509799i
\(725\) 1.49678e7i 1.05758i
\(726\) −1.89818e6 1.67775e7i −0.133658 1.18137i
\(727\) 1.10840e7i 0.777784i −0.921283 0.388892i \(-0.872858\pi\)
0.921283 0.388892i \(-0.127142\pi\)
\(728\) −2.91432e6 −0.203802
\(729\) 1.11937e7 8.97732e6i 0.780108 0.625645i
\(730\) 3.70587e7i 2.57385i
\(731\) 1.03546e7i 0.716703i
\(732\) 766803. + 6.77755e6i 0.0528940 + 0.467514i
\(733\) 7.54820e6i 0.518900i −0.965757 0.259450i \(-0.916459\pi\)
0.965757 0.259450i \(-0.0835413\pi\)
\(734\) 1.18223e7 0.809957
\(735\) −9.60706e6 + 1.08693e6i −0.655952 + 0.0742136i
\(736\) −4.04182e6 1.42259e7i −0.275032 0.968023i
\(737\) 3.66729e6i 0.248701i
\(738\) 2.03778e7 4.67083e6i 1.37726 0.315684i
\(739\) 2.33132e7 1.57033 0.785164 0.619287i \(-0.212578\pi\)
0.785164 + 0.619287i \(0.212578\pi\)
\(740\) 1.74222e7i 1.16956i
\(741\) 830729. + 7.34257e6i 0.0555794 + 0.491250i
\(742\) −7.85943e6 −0.524061
\(743\) 5.07752e6 0.337427 0.168713 0.985665i \(-0.446039\pi\)
0.168713 + 0.985665i \(0.446039\pi\)
\(744\) 324954. + 2.87217e6i 0.0215223 + 0.190229i
\(745\) 2.74459e7 1.81171
\(746\) −3.50771e6 −0.230769
\(747\) 1.71400e7 3.92868e6i 1.12385 0.257599i
\(748\) −725030. −0.0473807
\(749\) 1.76846e7i 1.15184i
\(750\) 543235. + 4.80150e6i 0.0352643 + 0.311690i
\(751\) 1.75809e7i 1.13747i 0.822519 + 0.568737i \(0.192568\pi\)
−0.822519 + 0.568737i \(0.807432\pi\)
\(752\) 3.50183e6i 0.225814i
\(753\) −3.23771e6 + 366311.i −0.208090 + 0.0235430i
\(754\) −8.78195e6 −0.562552
\(755\) 4.20568e7 2.68515
\(756\) −2.16547e6 6.16129e6i −0.137800 0.392073i
\(757\) 1.79381e7i 1.13772i 0.822433 + 0.568862i \(0.192616\pi\)
−0.822433 + 0.568862i \(0.807384\pi\)
\(758\) 2.36339e7 1.49404
\(759\) −3.21440e6 + 1.31935e6i −0.202533 + 0.0831296i
\(760\) −1.27985e7 −0.803759
\(761\) 1.50206e7i 0.940214i 0.882609 + 0.470107i \(0.155785\pi\)
−0.882609 + 0.470107i \(0.844215\pi\)
\(762\) 1.61962e6 + 1.43153e7i 0.101048 + 0.893129i
\(763\) 1.10731e7 0.688583
\(764\) 1.07078e7 0.663693
\(765\) −8.99274e6 + 2.06124e6i −0.555569 + 0.127343i
\(766\) 2.39255e6i 0.147329i
\(767\) 1.21363e7i 0.744901i
\(768\) −2.03183e7 + 2.29878e6i −1.24303 + 0.140635i
\(769\) 2.25008e7i 1.37209i −0.727559 0.686045i \(-0.759345\pi\)
0.727559 0.686045i \(-0.240655\pi\)
\(770\) 4.92298e6 0.299228
\(771\) −1.01717e6 8.99048e6i −0.0616252 0.544687i
\(772\) 9.58514e6 0.578836
\(773\) −8.67404e6 −0.522123 −0.261061 0.965322i \(-0.584073\pi\)
−0.261061 + 0.965322i \(0.584073\pi\)
\(774\) −3.75815e7 + 8.61411e6i −2.25487 + 0.516842i
\(775\) 6.80988e6 0.407273
\(776\) −2.83507e6 −0.169009
\(777\) 1.76300e7 1.99463e6i 1.04761 0.118525i
\(778\) 2.20827e7i 1.30798i
\(779\)