Properties

Label 69.6.c.b.68.7
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 68.7
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.25

$q$-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} +(-39016.1 - 6463.15i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9} - 2484 q^{12} + 520 q^{13} + 4936 q^{16} + 7188 q^{18} + 18660 q^{24} + 36032 q^{25} - 22032 q^{27} + 6544 q^{31} - 33912 q^{36} - 63912 q^{39} + 54328 q^{46} + 88284 q^{48} - 207664 q^{49} + 46296 q^{52} - 38628 q^{54} - 139296 q^{55} - 184144 q^{58} + 486584 q^{64} - 113580 q^{69} + 37176 q^{70} - 15504 q^{72} - 93896 q^{73} + 249840 q^{75} + 368028 q^{78} - 339372 q^{81} - 23512 q^{82} + 259584 q^{85} + 509928 q^{87} + 82740 q^{93} - 562000 q^{94} + 1404 q^{96}+O(q^{100}) \) Copy content Toggle raw display

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 \(-0.763585\pi\)
−0.736631 + 0.676295i \(0.763585\pi\)
\(6\) 12.3796 + 109.419i 0.140387 + 1.24084i
\(7\) 96.3127i 0.742914i 0.928450 + 0.371457i \(0.121142\pi\)
−0.928450 + 0.371457i \(0.878858\pi\)
\(8\) 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 \(-0.465086\pi\)
0.109465 + 0.993991i \(0.465086\pi\)
\(12\) 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 \(-0.438035\pi\)
0.193440 + 0.981112i \(0.438035\pi\)
\(18\) −383.510 1673.17i −0.278995 1.21719i
\(19\) 1560.29i 0.991563i 0.868447 + 0.495781i \(0.165118\pi\)
−0.868447 + 0.495781i \(0.834882\pi\)
\(20\) 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 \(0.251109\pi\)
−0.704640 + 0.709565i \(0.748891\pi\)
\(38\) 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 \(0.376994\pi\)
−0.376888 + 0.926259i \(0.623006\pi\)
\(44\) −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 \(-0.591146\pi\)
−0.282445 + 0.959283i \(0.591146\pi\)
\(54\) 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 \(-0.861841\pi\)
0.907274 0.420540i \(-0.138159\pi\)
\(62\) 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 \(-0.807720\pi\)
0.823034 0.567992i \(-0.192280\pi\)
\(68\) −8252.20 −0.216420
\(69\) −39016.1 6463.15i −0.986556 0.163426i
\(70\) −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 \(-0.877435\pi\)
0.926780 0.375605i \(-0.122565\pi\)
\(80\) 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 \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(84\) 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 \(-0.480248\pi\)
0.0620137 + 0.998075i \(0.480248\pi\)
\(90\) 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 \(0.0490825\pi\)
−0.988135 + 0.153587i \(0.950918\pi\)
\(98\) 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 \(0.417374\pi\)
−0.256673 + 0.966498i \(0.582626\pi\)
\(104\) 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 \(-0.217642\pi\)
0.775215 + 0.631698i \(0.217642\pi\)
\(108\) 63971.7 22483.8i 0.527750 0.185485i
\(109\) 114970.i 0.926868i −0.886131 0.463434i \(-0.846617\pi\)
0.886131 0.463434i \(-0.153383\pi\)
\(110\) 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 \(-0.740581\pi\)
−0.685876 + 0.727719i \(0.740581\pi\)
\(114\) −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 \(-0.620544\pi\)
−0.369714 + 0.929146i \(0.620544\pi\)
\(138\) −45655.9 + 275612.i −0.204080 + 1.23197i
\(139\) 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 \(-0.710788\pi\)
−0.614862 + 0.788635i \(0.710788\pi\)
\(150\) 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 \(0.182970\pi\)
−0.839292 + 0.543680i \(0.817030\pi\)
\(158\) −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 \(0.150600\pi\)
−0.890149 + 0.455669i \(0.849400\pi\)
\(182\) 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 \(-0.297856\pi\)
0.593222 + 0.805039i \(0.297856\pi\)
\(192\) −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 \(-0.791861\pi\)
0.793724 0.608278i \(-0.208139\pi\)
\(200\) 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
\(207\) 615672. + 31736.9i 0.998674 + 0.0514800i
\(208\) −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 \(-0.708836\pi\)
−0.610013 + 0.792392i \(0.708836\pi\)
\(228\) 48947.1 + 432629.i 0.0623577 + 0.551161i
\(229\) 47648.3i 0.0600425i −0.999549 0.0300213i \(-0.990443\pi\)
0.999549 0.0300213i \(-0.00955750\pi\)
\(230\) −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 \(-0.934092\pi\)
0.978641 0.205579i \(-0.0659078\pi\)
\(242\) 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 \(-0.533391\pi\)
−0.104709 + 0.994503i \(0.533391\pi\)
\(252\) −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 \(-0.250462\pi\)
0.706080 + 0.708132i \(0.250462\pi\)
\(264\) 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
\(276\) 698416. + 115695.i 0.551876 + 0.0914200i
\(277\) 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 \(-0.354277\pi\)
0.441977 + 0.897026i \(0.354277\pi\)
\(282\) −300197. + 33963.9i −0.224794 + 0.0254329i
\(283\) 1.19800e6i 0.889179i 0.895734 + 0.444589i \(0.146650\pi\)
−0.895734 + 0.444589i \(0.853350\pi\)
\(284\) 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 \(-0.775570\pi\)
−0.761568 + 0.648085i \(0.775570\pi\)
\(294\) 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 \(-0.915147\pi\)
0.964679 0.263429i \(-0.0848535\pi\)
\(314\) 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 \(-0.977522\pi\)
0.997508 0.0705583i \(-0.0224781\pi\)
\(338\) 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
\(345\) 3.21329e6 + 532291.i 1.45345 + 0.240769i
\(346\) 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 \(-0.691511\pi\)
−0.566002 + 0.824404i \(0.691511\pi\)
\(360\) 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 \(-0.894870\pi\)
0.945953 0.324305i \(-0.105130\pi\)
\(368\) −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 \(0.0294536\pi\)
−0.995722 + 0.0923993i \(0.970546\pi\)
\(374\) 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 \(-0.795879\pi\)
0.801340 0.598209i \(-0.204121\pi\)
\(380\) 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 \(-0.518788\pi\)
−0.0589904 + 0.998259i \(0.518788\pi\)
\(384\) −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 \(-0.675454\pi\)
−0.523714 + 0.851894i \(0.675454\pi\)
\(390\) −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 \(-0.540730\pi\)
−0.127608 + 0.991825i \(0.540730\pi\)
\(402\) 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
\(414\) 224191. 4.34914e6i 0.0642860 1.24710i
\(415\) 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 \(-0.480078\pi\)
0.0625448 + 0.998042i \(0.480078\pi\)
\(420\) −248835. 2.19938e6i −0.0688316 0.608383i
\(421\) 4.57385e6i 1.25770i −0.777527 0.628850i \(-0.783526\pi\)
0.777527 0.628850i \(-0.216474\pi\)
\(422\) 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 \(-0.297190\pi\)
0.594904 + 0.803797i \(0.297190\pi\)
\(432\) 4.56142e6 1.60318e6i 1.17595 0.413307i
\(433\) 2.65527e6i 0.680596i 0.940318 + 0.340298i \(0.110528\pi\)
−0.940318 + 0.340298i \(0.889472\pi\)
\(434\) 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 \(0.171836\pi\)
−0.857792 + 0.513996i \(0.828164\pi\)
\(458\) −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 \(-0.322381\pi\)
0.529496 + 0.848312i \(0.322381\pi\)
\(468\) −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 \(-0.427565\pi\)
0.225601 + 0.974220i \(0.427565\pi\)
\(480\) 841347. + 7.43642e6i 0.166676 + 1.47320i
\(481\) 3.59029e6i 0.707565i
\(482\) −2.61881e6 −0.513437
\(483\) 622483. 3.75775e6i 0.121412 0.732926i
\(484\) 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 \(-0.426443\pi\)
0.229034 + 0.973418i \(0.426443\pi\)
\(504\) 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 \(-0.231043\pi\)
0.747940 + 0.663766i \(0.231043\pi\)
\(522\) −6.84661e6 + 1.56932e6i −1.09976 + 0.252078i
\(523\) 7.44892e6i 1.19080i −0.803429 0.595401i \(-0.796993\pi\)
0.803429 0.595401i \(-0.203007\pi\)
\(524\) 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
\(552\) −643717. + 3.88593e6i −0.0899181 + 0.542809i
\(553\) 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 \(-0.498634\pi\)
0.00429156 + 0.999991i \(0.498634\pi\)
\(558\) −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 \(-0.644109\pi\)
−0.437424 + 0.899255i \(0.644109\pi\)
\(564\) 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 \(-0.678010\pi\)
−0.530538 + 0.847661i \(0.678010\pi\)
\(570\) 1.40606e7 1.59080e6i 1.81266 0.205082i
\(571\) 3.95838e6i 0.508074i −0.967195 0.254037i \(-0.918242\pi\)
0.967195 0.254037i \(-0.0817585\pi\)
\(572\) −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 \(-0.941264\pi\)
0.983024 0.183479i \(-0.0587361\pi\)
\(614\) 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 \(-0.178264\pi\)
0.847238 + 0.531214i \(0.178264\pi\)
\(618\) −2.27729e7 + 2.57650e6i −2.39854 + 0.271368i
\(619\) 1.72859e7i 1.81328i 0.421901 + 0.906642i \(0.361363\pi\)
−0.421901 + 0.906642i \(0.638637\pi\)
\(620\) 2.74469e6 0.286757
\(621\) −9.59216e6 + 587360.i −0.998130 + 0.0611188i
\(622\) −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 \(-0.933731\pi\)
0.978406 0.206691i \(-0.0662694\pi\)
\(632\) −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 \(-0.363635\pi\)
0.415418 + 0.909631i \(0.363635\pi\)
\(642\) 2.27309e6 + 2.00912e7i 0.217661 + 1.92384i
\(643\) 1.25671e6i 0.119870i 0.998202 + 0.0599348i \(0.0190893\pi\)
−0.998202 + 0.0599348i \(0.980911\pi\)
\(644\) 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 \(-0.736954\pi\)
−0.677539 + 0.735486i \(0.736954\pi\)
\(660\) −2.00633e6 + 226994.i −0.179284 + 0.0202840i
\(661\) 1.12641e7i 1.00275i −0.865229 0.501376i \(-0.832827\pi\)
0.865229 0.501376i \(-0.167173\pi\)
\(662\) 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 \(-0.424452\pi\)
0.235118 + 0.971967i \(0.424452\pi\)
\(678\) −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
\(690\) 3.76013e6 2.26988e7i 0.300663 1.81501i
\(691\) 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 \(-0.168764\pi\)
0.862713 + 0.505695i \(0.168764\pi\)
\(702\) 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 \(0.310956\pi\)
−0.559596 + 0.828766i \(0.689044\pi\)
\(710\) 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 \(0.127142\pi\)
−0.921283 + 0.388892i \(0.872858\pi\)
\(728\) 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 \(0.0835413\pi\)
−0.965757 + 0.259450i \(0.916459\pi\)
\(734\) −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 \(-0.553961\pi\)
−0.168713 + 0.985665i \(0.553961\pi\)
\(744\) 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 \(-0.807432\pi\)
0.822519 0.568737i \(-0.192568\pi\)
\(752\) 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 \(-0.807384\pi\)
0.822433 0.568862i \(-0.192616\pi\)
\(758\) −2.36339e7 −1.49404
\(759\) −3.42792e6 567846.i −0.215986 0.0357788i
\(760\) −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 \(0.240655\pi\)
−0.727559 + 0.686045i \(0.759345\pi\)
\(770\) −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 \(-0.415927\pi\)
0.261061 + 0.965322i \(0.415927\pi\)
\(774\) 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