Properties

Label 69.6.c.b.68.4
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 68.4
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.30

$q$-expansion

\(f(q)\) \(=\) \(q-9.59549i q^{2} +(-8.65480 - 12.9651i) q^{3} -60.0734 q^{4} +42.3345 q^{5} +(-124.407 + 83.0470i) q^{6} +238.780i q^{7} +269.378i q^{8} +(-93.1890 + 224.421i) q^{9} +O(q^{10})\) \(q-9.59549i q^{2} +(-8.65480 - 12.9651i) q^{3} -60.0734 q^{4} +42.3345 q^{5} +(-124.407 + 83.0470i) q^{6} +238.780i q^{7} +269.378i q^{8} +(-93.1890 + 224.421i) q^{9} -406.221i q^{10} -261.465 q^{11} +(519.923 + 778.859i) q^{12} -36.2446 q^{13} +2291.21 q^{14} +(-366.397 - 548.873i) q^{15} +662.466 q^{16} -1880.68 q^{17} +(2153.43 + 894.194i) q^{18} +1308.83i q^{19} -2543.18 q^{20} +(3095.82 - 2066.60i) q^{21} +2508.89i q^{22} +(666.102 - 2447.99i) q^{23} +(3492.52 - 2331.41i) q^{24} -1332.79 q^{25} +347.784i q^{26} +(3716.18 - 734.110i) q^{27} -14344.4i q^{28} +2237.25i q^{29} +(-5266.70 + 3515.76i) q^{30} -3176.90 q^{31} +2263.42i q^{32} +(2262.93 + 3389.93i) q^{33} +18046.0i q^{34} +10108.7i q^{35} +(5598.18 - 13481.7i) q^{36} -11958.2i q^{37} +12558.9 q^{38} +(313.689 + 469.915i) q^{39} +11404.0i q^{40} +13987.9i q^{41} +(-19830.0 - 29705.9i) q^{42} +11520.1i q^{43} +15707.1 q^{44} +(-3945.12 + 9500.76i) q^{45} +(-23489.7 - 6391.57i) q^{46} -104.625i q^{47} +(-5733.51 - 8588.96i) q^{48} -40209.1 q^{49} +12788.7i q^{50} +(16276.9 + 24383.2i) q^{51} +2177.34 q^{52} -3042.21 q^{53} +(-7044.15 - 35658.6i) q^{54} -11069.0 q^{55} -64322.2 q^{56} +(16969.1 - 11327.7i) q^{57} +21467.5 q^{58} -42246.8i q^{59} +(22010.7 + 32972.7i) q^{60} -19631.7i q^{61} +30483.9i q^{62} +(-53587.3 - 22251.7i) q^{63} +42917.5 q^{64} -1534.40 q^{65} +(32528.0 - 21713.9i) q^{66} +53147.1i q^{67} +112979. q^{68} +(-37503.5 + 12550.8i) q^{69} +96997.5 q^{70} +7483.69i q^{71} +(-60454.1 - 25103.1i) q^{72} -3498.30 q^{73} -114744. q^{74} +(11535.0 + 17279.7i) q^{75} -78625.9i q^{76} -62432.7i q^{77} +(4509.07 - 3010.00i) q^{78} -21637.3i q^{79} +28045.2 q^{80} +(-41680.6 - 41827.2i) q^{81} +134221. q^{82} +40321.6 q^{83} +(-185976. + 124147. i) q^{84} -79617.7 q^{85} +110541. q^{86} +(29006.2 - 19362.9i) q^{87} -70433.0i q^{88} -25017.5 q^{89} +(91164.5 + 37855.3i) q^{90} -8654.49i q^{91} +(-40015.0 + 147059. i) q^{92} +(27495.4 + 41188.9i) q^{93} -1003.93 q^{94} +55408.7i q^{95} +(29345.5 - 19589.4i) q^{96} +86126.2i q^{97} +385826. i q^{98} +(24365.7 - 58678.3i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.59549i 1.69626i −0.529789 0.848129i \(-0.677729\pi\)
0.529789 0.848129i \(-0.322271\pi\)
\(3\) −8.65480 12.9651i −0.555205 0.831713i
\(4\) −60.0734 −1.87729
\(5\) 42.3345 0.757303 0.378652 0.925539i \(-0.376388\pi\)
0.378652 + 0.925539i \(0.376388\pi\)
\(6\) −124.407 + 83.0470i −1.41080 + 0.941772i
\(7\) 238.780i 1.84185i 0.389744 + 0.920923i \(0.372564\pi\)
−0.389744 + 0.920923i \(0.627436\pi\)
\(8\) 269.378i 1.48812i
\(9\) −93.1890 + 224.421i −0.383494 + 0.923543i
\(10\) 406.221i 1.28458i
\(11\) −261.465 −0.651526 −0.325763 0.945451i \(-0.605621\pi\)
−0.325763 + 0.945451i \(0.605621\pi\)
\(12\) 519.923 + 778.859i 1.04228 + 1.56137i
\(13\) −36.2446 −0.0594819 −0.0297409 0.999558i \(-0.509468\pi\)
−0.0297409 + 0.999558i \(0.509468\pi\)
\(14\) 2291.21 3.12425
\(15\) −366.397 548.873i −0.420459 0.629859i
\(16\) 662.466 0.646939
\(17\) −1880.68 −1.57831 −0.789155 0.614194i \(-0.789481\pi\)
−0.789155 + 0.614194i \(0.789481\pi\)
\(18\) 2153.43 + 894.194i 1.56657 + 0.650505i
\(19\) 1308.83i 0.831762i 0.909419 + 0.415881i \(0.136527\pi\)
−0.909419 + 0.415881i \(0.863473\pi\)
\(20\) −2543.18 −1.42168
\(21\) 3095.82 2066.60i 1.53189 1.02260i
\(22\) 2508.89i 1.10516i
\(23\) 666.102 2447.99i 0.262555 0.964917i
\(24\) 3492.52 2331.41i 1.23769 0.826211i
\(25\) −1332.79 −0.426492
\(26\) 347.784i 0.100897i
\(27\) 3716.18 734.110i 0.981041 0.193799i
\(28\) 14344.4i 3.45769i
\(29\) 2237.25i 0.493992i 0.969017 + 0.246996i \(0.0794434\pi\)
−0.969017 + 0.246996i \(0.920557\pi\)
\(30\) −5266.70 + 3515.76i −1.06840 + 0.713207i
\(31\) −3176.90 −0.593744 −0.296872 0.954917i \(-0.595943\pi\)
−0.296872 + 0.954917i \(0.595943\pi\)
\(32\) 2263.42i 0.390741i
\(33\) 2262.93 + 3389.93i 0.361731 + 0.541883i
\(34\) 18046.0i 2.67722i
\(35\) 10108.7i 1.39484i
\(36\) 5598.18 13481.7i 0.719931 1.73376i
\(37\) 11958.2i 1.43602i −0.696033 0.718010i \(-0.745053\pi\)
0.696033 0.718010i \(-0.254947\pi\)
\(38\) 12558.9 1.41088
\(39\) 313.689 + 469.915i 0.0330247 + 0.0494719i
\(40\) 11404.0i 1.12696i
\(41\) 13987.9i 1.29955i 0.760125 + 0.649777i \(0.225138\pi\)
−0.760125 + 0.649777i \(0.774862\pi\)
\(42\) −19830.0 29705.9i −1.73460 2.59848i
\(43\) 11520.1i 0.950133i 0.879950 + 0.475067i \(0.157576\pi\)
−0.879950 + 0.475067i \(0.842424\pi\)
\(44\) 15707.1 1.22311
\(45\) −3945.12 + 9500.76i −0.290421 + 0.699403i
\(46\) −23489.7 6391.57i −1.63675 0.445362i
\(47\) 104.625i 0.00690864i −0.999994 0.00345432i \(-0.998900\pi\)
0.999994 0.00345432i \(-0.00109955\pi\)
\(48\) −5733.51 8588.96i −0.359184 0.538068i
\(49\) −40209.1 −2.39240
\(50\) 12788.7i 0.723440i
\(51\) 16276.9 + 24383.2i 0.876286 + 1.31270i
\(52\) 2177.34 0.111665
\(53\) −3042.21 −0.148765 −0.0743823 0.997230i \(-0.523699\pi\)
−0.0743823 + 0.997230i \(0.523699\pi\)
\(54\) −7044.15 35658.6i −0.328734 1.66410i
\(55\) −11069.0 −0.493403
\(56\) −64322.2 −2.74089
\(57\) 16969.1 11327.7i 0.691788 0.461799i
\(58\) 21467.5 0.837938
\(59\) 42246.8i 1.58003i −0.613090 0.790013i \(-0.710074\pi\)
0.613090 0.790013i \(-0.289926\pi\)
\(60\) 22010.7 + 32972.7i 0.789325 + 1.18243i
\(61\) 19631.7i 0.675511i −0.941234 0.337755i \(-0.890332\pi\)
0.941234 0.337755i \(-0.109668\pi\)
\(62\) 30483.9i 1.00714i
\(63\) −53587.3 22251.7i −1.70103 0.706337i
\(64\) 42917.5 1.30974
\(65\) −1534.40 −0.0450458
\(66\) 32528.0 21713.9i 0.919174 0.613589i
\(67\) 53147.1i 1.44641i 0.690631 + 0.723207i \(0.257333\pi\)
−0.690631 + 0.723207i \(0.742667\pi\)
\(68\) 112979. 2.96295
\(69\) −37503.5 + 12550.8i −0.948306 + 0.317356i
\(70\) 96997.5 2.36600
\(71\) 7483.69i 0.176185i 0.996112 + 0.0880926i \(0.0280772\pi\)
−0.996112 + 0.0880926i \(0.971923\pi\)
\(72\) −60454.1 25103.1i −1.37434 0.570684i
\(73\) −3498.30 −0.0768333 −0.0384167 0.999262i \(-0.512231\pi\)
−0.0384167 + 0.999262i \(0.512231\pi\)
\(74\) −114744. −2.43586
\(75\) 11535.0 + 17279.7i 0.236790 + 0.354719i
\(76\) 78625.9i 1.56146i
\(77\) 62432.7i 1.20001i
\(78\) 4509.07 3010.00i 0.0839171 0.0560184i
\(79\) 21637.3i 0.390063i −0.980797 0.195031i \(-0.937519\pi\)
0.980797 0.195031i \(-0.0624808\pi\)
\(80\) 28045.2 0.489929
\(81\) −41680.6 41827.2i −0.705865 0.708347i
\(82\) 134221. 2.20438
\(83\) 40321.6 0.642455 0.321228 0.947002i \(-0.395905\pi\)
0.321228 + 0.947002i \(0.395905\pi\)
\(84\) −185976. + 124147.i −2.87581 + 1.91973i
\(85\) −79617.7 −1.19526
\(86\) 110541. 1.61167
\(87\) 29006.2 19362.9i 0.410860 0.274267i
\(88\) 70433.0i 0.969548i
\(89\) −25017.5 −0.334788 −0.167394 0.985890i \(-0.553535\pi\)
−0.167394 + 0.985890i \(0.553535\pi\)
\(90\) 91164.5 + 37855.3i 1.18637 + 0.492630i
\(91\) 8654.49i 0.109556i
\(92\) −40015.0 + 147059.i −0.492894 + 1.81143i
\(93\) 27495.4 + 41188.9i 0.329650 + 0.493825i
\(94\) −1003.93 −0.0117188
\(95\) 55408.7i 0.629896i
\(96\) 29345.5 19589.4i 0.324985 0.216942i
\(97\) 86126.2i 0.929407i 0.885466 + 0.464703i \(0.153839\pi\)
−0.885466 + 0.464703i \(0.846161\pi\)
\(98\) 385826.i 4.05813i
\(99\) 24365.7 58678.3i 0.249856 0.601713i
\(100\) 80065.0 0.800650
\(101\) 33574.1i 0.327493i −0.986502 0.163746i \(-0.947642\pi\)
0.986502 0.163746i \(-0.0523578\pi\)
\(102\) 233969. 156185.i 2.22668 1.48641i
\(103\) 146840.i 1.36380i −0.731446 0.681900i \(-0.761154\pi\)
0.731446 0.681900i \(-0.238846\pi\)
\(104\) 9763.50i 0.0885161i
\(105\) 131060. 87488.4i 1.16010 0.774421i
\(106\) 29191.5i 0.252343i
\(107\) 154244. 1.30242 0.651209 0.758899i \(-0.274262\pi\)
0.651209 + 0.758899i \(0.274262\pi\)
\(108\) −223244. + 44100.5i −1.84170 + 0.363818i
\(109\) 236967.i 1.91039i 0.295982 + 0.955194i \(0.404353\pi\)
−0.295982 + 0.955194i \(0.595647\pi\)
\(110\) 106213.i 0.836939i
\(111\) −155039. + 103495.i −1.19436 + 0.797286i
\(112\) 158184.i 1.19156i
\(113\) −186109. −1.37110 −0.685552 0.728024i \(-0.740439\pi\)
−0.685552 + 0.728024i \(0.740439\pi\)
\(114\) −108694. 162827.i −0.783330 1.17345i
\(115\) 28199.1 103635.i 0.198834 0.730735i
\(116\) 134399.i 0.927368i
\(117\) 3377.60 8134.04i 0.0228109 0.0549341i
\(118\) −405379. −2.68013
\(119\) 449069.i 2.90701i
\(120\) 147854. 98699.3i 0.937305 0.625693i
\(121\) −92687.0 −0.575513
\(122\) −188375. −1.14584
\(123\) 181355. 121063.i 1.08086 0.721519i
\(124\) 190847. 1.11463
\(125\) −188718. −1.08029
\(126\) −213516. + 514197.i −1.19813 + 2.88538i
\(127\) 111909. 0.615679 0.307839 0.951438i \(-0.400394\pi\)
0.307839 + 0.951438i \(0.400394\pi\)
\(128\) 339385.i 1.83091i
\(129\) 149359. 99704.0i 0.790238 0.527519i
\(130\) 14723.3i 0.0764094i
\(131\) 45103.0i 0.229629i −0.993387 0.114815i \(-0.963373\pi\)
0.993387 0.114815i \(-0.0366274\pi\)
\(132\) −135942. 203645.i −0.679075 1.01727i
\(133\) −312523. −1.53198
\(134\) 509973. 2.45349
\(135\) 157323. 31078.2i 0.742946 0.146765i
\(136\) 506614.i 2.34871i
\(137\) 38559.8 0.175523 0.0877614 0.996142i \(-0.472029\pi\)
0.0877614 + 0.996142i \(0.472029\pi\)
\(138\) 120431. + 359864.i 0.538318 + 1.60857i
\(139\) −248892. −1.09263 −0.546317 0.837579i \(-0.683971\pi\)
−0.546317 + 0.837579i \(0.683971\pi\)
\(140\) 607262.i 2.61852i
\(141\) −1356.48 + 905.512i −0.00574601 + 0.00383572i
\(142\) 71809.6 0.298856
\(143\) 9476.69 0.0387540
\(144\) −61734.6 + 148671.i −0.248097 + 0.597477i
\(145\) 94713.0i 0.374102i
\(146\) 33567.9i 0.130329i
\(147\) 348001. + 521316.i 1.32827 + 1.98979i
\(148\) 718368.i 2.69583i
\(149\) −271774. −1.00286 −0.501432 0.865197i \(-0.667193\pi\)
−0.501432 + 0.865197i \(0.667193\pi\)
\(150\) 165808. 110684.i 0.601695 0.401658i
\(151\) 372890. 1.33088 0.665439 0.746452i \(-0.268244\pi\)
0.665439 + 0.746452i \(0.268244\pi\)
\(152\) −352570. −1.23776
\(153\) 175259. 422064.i 0.605272 1.45764i
\(154\) −599073. −2.03553
\(155\) −134493. −0.449644
\(156\) −18844.4 28229.4i −0.0619970 0.0928732i
\(157\) 213649.i 0.691754i 0.938280 + 0.345877i \(0.112418\pi\)
−0.938280 + 0.345877i \(0.887582\pi\)
\(158\) −207620. −0.661647
\(159\) 26329.7 + 39442.7i 0.0825949 + 0.123730i
\(160\) 95820.7i 0.295910i
\(161\) 584532. + 159052.i 1.77723 + 0.483587i
\(162\) −401352. + 399946.i −1.20154 + 1.19733i
\(163\) −558201. −1.64559 −0.822795 0.568338i \(-0.807587\pi\)
−0.822795 + 0.568338i \(0.807587\pi\)
\(164\) 840303.i 2.43964i
\(165\) 95800.0 + 143511.i 0.273940 + 0.410370i
\(166\) 386906.i 1.08977i
\(167\) 367432.i 1.01950i 0.860324 + 0.509748i \(0.170261\pi\)
−0.860324 + 0.509748i \(0.829739\pi\)
\(168\) 556696. + 833946.i 1.52175 + 2.27963i
\(169\) −369979. −0.996462
\(170\) 763971.i 2.02747i
\(171\) −293729. 121969.i −0.768168 0.318976i
\(172\) 692051.i 1.78368i
\(173\) 308503.i 0.783689i 0.920031 + 0.391844i \(0.128163\pi\)
−0.920031 + 0.391844i \(0.871837\pi\)
\(174\) −185797. 278329.i −0.465228 0.696924i
\(175\) 318243.i 0.785532i
\(176\) −173212. −0.421498
\(177\) −547736. + 365638.i −1.31413 + 0.877239i
\(178\) 240056.i 0.567887i
\(179\) 377659.i 0.880982i 0.897757 + 0.440491i \(0.145196\pi\)
−0.897757 + 0.440491i \(0.854804\pi\)
\(180\) 236997. 570743.i 0.545206 1.31298i
\(181\) 71598.6i 0.162446i 0.996696 + 0.0812228i \(0.0258825\pi\)
−0.996696 + 0.0812228i \(0.974117\pi\)
\(182\) −83044.1 −0.185836
\(183\) −254527. + 169908.i −0.561831 + 0.375047i
\(184\) 659435. + 179433.i 1.43591 + 0.390714i
\(185\) 506244.i 1.08750i
\(186\) 395228. 263832.i 0.837654 0.559171i
\(187\) 491732. 1.02831
\(188\) 6285.21i 0.0129696i
\(189\) 175291. + 887351.i 0.356948 + 1.80693i
\(190\) 531674. 1.06847
\(191\) 240272. 0.476562 0.238281 0.971196i \(-0.423416\pi\)
0.238281 + 0.971196i \(0.423416\pi\)
\(192\) −371442. 556431.i −0.727174 1.08933i
\(193\) 464503. 0.897626 0.448813 0.893626i \(-0.351847\pi\)
0.448813 + 0.893626i \(0.351847\pi\)
\(194\) 826423. 1.57651
\(195\) 13279.9 + 19893.7i 0.0250097 + 0.0374652i
\(196\) 2.41550e6 4.49124
\(197\) 284782.i 0.522814i 0.965229 + 0.261407i \(0.0841864\pi\)
−0.965229 + 0.261407i \(0.915814\pi\)
\(198\) −563047. 233801.i −1.02066 0.423821i
\(199\) 201795.i 0.361225i 0.983554 + 0.180612i \(0.0578080\pi\)
−0.983554 + 0.180612i \(0.942192\pi\)
\(200\) 359023.i 0.634670i
\(201\) 689059. 459977.i 1.20300 0.803057i
\(202\) −322160. −0.555512
\(203\) −534212. −0.909857
\(204\) −977808. 1.46478e6i −1.64505 2.46433i
\(205\) 592173.i 0.984156i
\(206\) −1.40900e6 −2.31336
\(207\) 487307. + 377613.i 0.790454 + 0.612521i
\(208\) −24010.8 −0.0384812
\(209\) 342213.i 0.541915i
\(210\) −839494. 1.25759e6i −1.31362 1.96784i
\(211\) 201305. 0.311278 0.155639 0.987814i \(-0.450256\pi\)
0.155639 + 0.987814i \(0.450256\pi\)
\(212\) 182756. 0.279275
\(213\) 97026.9 64769.8i 0.146536 0.0978190i
\(214\) 1.48005e6i 2.20924i
\(215\) 487697.i 0.719539i
\(216\) 197753. + 1.00106e6i 0.288396 + 1.45991i
\(217\) 758581.i 1.09358i
\(218\) 2.27381e6 3.24051
\(219\) 30277.1 + 45355.9i 0.0426583 + 0.0639033i
\(220\) 664953. 0.926263
\(221\) 68164.4 0.0938808
\(222\) 993090. + 1.48768e6i 1.35240 + 2.02594i
\(223\) −95000.1 −0.127927 −0.0639635 0.997952i \(-0.520374\pi\)
−0.0639635 + 0.997952i \(0.520374\pi\)
\(224\) −540459. −0.719686
\(225\) 124201. 299105.i 0.163557 0.393883i
\(226\) 1.78580e6i 2.32575i
\(227\) 608206. 0.783405 0.391702 0.920092i \(-0.371886\pi\)
0.391702 + 0.920092i \(0.371886\pi\)
\(228\) −1.01939e6 + 680491.i −1.29869 + 0.866932i
\(229\) 1.17155e6i 1.47629i −0.674643 0.738144i \(-0.735703\pi\)
0.674643 0.738144i \(-0.264297\pi\)
\(230\) −994424. 270584.i −1.23952 0.337274i
\(231\) −809448. + 540342.i −0.998066 + 0.666253i
\(232\) −602667. −0.735118
\(233\) 1.20936e6i 1.45937i −0.683785 0.729683i \(-0.739668\pi\)
0.683785 0.729683i \(-0.260332\pi\)
\(234\) −78050.1 32409.7i −0.0931824 0.0386933i
\(235\) 4429.27i 0.00523194i
\(236\) 2.53791e6i 2.96617i
\(237\) −280530. + 187266.i −0.324420 + 0.216565i
\(238\) −4.30904e6 −4.93103
\(239\) 1.09845e6i 1.24390i −0.783056 0.621951i \(-0.786340\pi\)
0.783056 0.621951i \(-0.213660\pi\)
\(240\) −242725. 363610.i −0.272011 0.407481i
\(241\) 716834.i 0.795016i −0.917599 0.397508i \(-0.869875\pi\)
0.917599 0.397508i \(-0.130125\pi\)
\(242\) 889377.i 0.976220i
\(243\) −181557. + 902400.i −0.197241 + 0.980355i
\(244\) 1.17934e6i 1.26813i
\(245\) −1.70223e6 −1.81177
\(246\) −1.16166e6 1.74019e6i −1.22388 1.83341i
\(247\) 47438.0i 0.0494748i
\(248\) 855787.i 0.883561i
\(249\) −348976. 522775.i −0.356695 0.534339i
\(250\) 1.81084e6i 1.83245i
\(251\) 1.70891e6 1.71213 0.856063 0.516871i \(-0.172903\pi\)
0.856063 + 0.516871i \(0.172903\pi\)
\(252\) 3.21917e6 + 1.33674e6i 3.19333 + 1.32600i
\(253\) −174162. + 640064.i −0.171062 + 0.628669i
\(254\) 1.07382e6i 1.04435i
\(255\) 689075. + 1.03225e6i 0.663615 + 0.994113i
\(256\) −1.88321e6 −1.79597
\(257\) 136300.i 0.128725i 0.997927 + 0.0643623i \(0.0205013\pi\)
−0.997927 + 0.0643623i \(0.979499\pi\)
\(258\) −956708. 1.43318e6i −0.894809 1.34045i
\(259\) 2.85538e6 2.64493
\(260\) 92176.5 0.0845643
\(261\) −502086. 208487.i −0.456223 0.189443i
\(262\) −432785. −0.389510
\(263\) 115648. 0.103098 0.0515488 0.998670i \(-0.483584\pi\)
0.0515488 + 0.998670i \(0.483584\pi\)
\(264\) −913173. + 609583.i −0.806386 + 0.538298i
\(265\) −128791. −0.112660
\(266\) 2.99881e6i 2.59863i
\(267\) 216522. + 324356.i 0.185876 + 0.278447i
\(268\) 3.19273e6i 2.71535i
\(269\) 1.33952e6i 1.12867i −0.825545 0.564336i \(-0.809132\pi\)
0.825545 0.564336i \(-0.190868\pi\)
\(270\) −298211. 1.50959e6i −0.248951 1.26023i
\(271\) 598555. 0.495086 0.247543 0.968877i \(-0.420377\pi\)
0.247543 + 0.968877i \(0.420377\pi\)
\(272\) −1.24589e6 −1.02107
\(273\) −112207. + 74902.9i −0.0911196 + 0.0608263i
\(274\) 370000.i 0.297732i
\(275\) 348477. 0.277871
\(276\) 2.25296e6 753966.i 1.78025 0.595771i
\(277\) 804088. 0.629657 0.314828 0.949149i \(-0.398053\pi\)
0.314828 + 0.949149i \(0.398053\pi\)
\(278\) 2.38824e6i 1.85339i
\(279\) 296052. 712963.i 0.227697 0.548348i
\(280\) −2.72305e6 −2.07568
\(281\) −193375. −0.146095 −0.0730475 0.997328i \(-0.523272\pi\)
−0.0730475 + 0.997328i \(0.523272\pi\)
\(282\) 8688.83 + 13016.1i 0.00650637 + 0.00974672i
\(283\) 1.88789e6i 1.40123i 0.713539 + 0.700615i \(0.247091\pi\)
−0.713539 + 0.700615i \(0.752909\pi\)
\(284\) 449571.i 0.330752i
\(285\) 718381. 479551.i 0.523893 0.349722i
\(286\) 90933.5i 0.0657368i
\(287\) −3.34004e6 −2.39358
\(288\) −507958. 210926.i −0.360867 0.149847i
\(289\) 2.11710e6 1.49106
\(290\) 908818. 0.634573
\(291\) 1.11664e6 745404.i 0.773000 0.516011i
\(292\) 210155. 0.144239
\(293\) 974967. 0.663469 0.331735 0.943373i \(-0.392366\pi\)
0.331735 + 0.943373i \(0.392366\pi\)
\(294\) 5.00228e6 3.33924e6i 3.37520 2.25309i
\(295\) 1.78850e6i 1.19656i
\(296\) 3.22127e6 2.13697
\(297\) −971651. + 191944.i −0.639174 + 0.126265i
\(298\) 2.60780e6i 1.70112i
\(299\) −24142.6 + 88726.3i −0.0156173 + 0.0573951i
\(300\) −692946. 1.03805e6i −0.444525 0.665911i
\(301\) −2.75077e6 −1.75000
\(302\) 3.57806e6i 2.25751i
\(303\) −435293. + 290577.i −0.272380 + 0.181826i
\(304\) 867055.i 0.538100i
\(305\) 831097.i 0.511567i
\(306\) −4.04991e6 1.68169e6i −2.47253 1.02670i
\(307\) −2.41673e6 −1.46346 −0.731731 0.681593i \(-0.761287\pi\)
−0.731731 + 0.681593i \(0.761287\pi\)
\(308\) 3.75055e6i 2.25278i
\(309\) −1.90380e6 + 1.27087e6i −1.13429 + 0.757189i
\(310\) 1.29052e6i 0.762713i
\(311\) 1.22914e6i 0.720610i 0.932835 + 0.360305i \(0.117327\pi\)
−0.932835 + 0.360305i \(0.882673\pi\)
\(312\) −126585. + 84501.1i −0.0736200 + 0.0491446i
\(313\) 2.09149e6i 1.20669i 0.797480 + 0.603345i \(0.206166\pi\)
−0.797480 + 0.603345i \(0.793834\pi\)
\(314\) 2.05007e6 1.17339
\(315\) −2.26860e6 942016.i −1.28819 0.534912i
\(316\) 1.29982e6i 0.732262i
\(317\) 1.80590e6i 1.00936i −0.863308 0.504678i \(-0.831611\pi\)
0.863308 0.504678i \(-0.168389\pi\)
\(318\) 378472. 252647.i 0.209877 0.140102i
\(319\) 584963.i 0.321849i
\(320\) 1.81689e6 0.991869
\(321\) −1.33495e6 1.99980e6i −0.723109 1.08324i
\(322\) 1.52618e6 5.60887e6i 0.820289 3.01464i
\(323\) 2.46149e6i 1.31278i
\(324\) 2.50390e6 + 2.51270e6i 1.32512 + 1.32978i
\(325\) 48306.3 0.0253685
\(326\) 5.35621e6i 2.79135i
\(327\) 3.07231e6 2.05090e6i 1.58889 1.06066i
\(328\) −3.76805e6 −1.93389
\(329\) 24982.5 0.0127247
\(330\) 1.37706e6 919248.i 0.696094 0.464673i
\(331\) 2.12287e6 1.06501 0.532505 0.846427i \(-0.321251\pi\)
0.532505 + 0.846427i \(0.321251\pi\)
\(332\) −2.42226e6 −1.20608
\(333\) 2.68366e6 + 1.11437e6i 1.32623 + 0.550705i
\(334\) 3.52569e6 1.72933
\(335\) 2.24996e6i 1.09537i
\(336\) 2.05087e6 1.36905e6i 0.991039 0.661562i
\(337\) 2.65650e6i 1.27419i 0.770783 + 0.637097i \(0.219865\pi\)
−0.770783 + 0.637097i \(0.780135\pi\)
\(338\) 3.55013e6i 1.69026i
\(339\) 1.61073e6 + 2.41292e6i 0.761244 + 1.14037i
\(340\) 4.78291e6 2.24385
\(341\) 830648. 0.386840
\(342\) −1.17035e6 + 2.81847e6i −0.541065 + 1.30301i
\(343\) 5.58795e6i 2.56459i
\(344\) −3.10326e6 −1.41391
\(345\) −1.58769e6 + 531330.i −0.718156 + 0.240335i
\(346\) 2.96023e6 1.32934
\(347\) 76257.0i 0.0339982i 0.999856 + 0.0169991i \(0.00541124\pi\)
−0.999856 + 0.0169991i \(0.994589\pi\)
\(348\) −1.74250e6 + 1.16320e6i −0.771304 + 0.514880i
\(349\) −3.01230e6 −1.32384 −0.661918 0.749576i \(-0.730257\pi\)
−0.661918 + 0.749576i \(0.730257\pi\)
\(350\) −3.05370e6 −1.33247
\(351\) −134691. + 26607.5i −0.0583542 + 0.0115275i
\(352\) 591804.i 0.254578i
\(353\) 307452.i 0.131323i 0.997842 + 0.0656614i \(0.0209157\pi\)
−0.997842 + 0.0656614i \(0.979084\pi\)
\(354\) 3.50847e6 + 5.25579e6i 1.48802 + 2.22910i
\(355\) 316818.i 0.133426i
\(356\) 1.50289e6 0.628495
\(357\) −5.82224e6 + 3.88660e6i −2.41779 + 1.61398i
\(358\) 3.62382e6 1.49437
\(359\) 1.84486e6 0.755488 0.377744 0.925910i \(-0.376700\pi\)
0.377744 + 0.925910i \(0.376700\pi\)
\(360\) −2.55930e6 1.06273e6i −1.04079 0.432181i
\(361\) 763064. 0.308172
\(362\) 687024. 0.275550
\(363\) 802187. + 1.20170e6i 0.319528 + 0.478662i
\(364\) 519905.i 0.205670i
\(365\) −148099. −0.0581862
\(366\) 1.63035e6 + 2.44231e6i 0.636177 + 0.953011i
\(367\) 2.45837e6i 0.952755i 0.879241 + 0.476378i \(0.158050\pi\)
−0.879241 + 0.476378i \(0.841950\pi\)
\(368\) 441270. 1.62171e6i 0.169857 0.624243i
\(369\) −3.13919e6 1.30352e6i −1.20019 0.498371i
\(370\) −4.85765e6 −1.84469
\(371\) 726420.i 0.274002i
\(372\) −1.65174e6 2.47436e6i −0.618849 0.927054i
\(373\) 1.32615e6i 0.493539i 0.969074 + 0.246769i \(0.0793690\pi\)
−0.969074 + 0.246769i \(0.920631\pi\)
\(374\) 4.71841e6i 1.74428i
\(375\) 1.63332e6 + 2.44676e6i 0.599781 + 0.898489i
\(376\) 28183.8 0.0102809
\(377\) 81088.2i 0.0293836i
\(378\) 8.51456e6 1.68200e6i 3.06502 0.605477i
\(379\) 997226.i 0.356612i −0.983975 0.178306i \(-0.942938\pi\)
0.983975 0.178306i \(-0.0570616\pi\)
\(380\) 3.32859e6i 1.18250i
\(381\) −968546. 1.45091e6i −0.341828 0.512068i
\(382\) 2.30553e6i 0.808373i
\(383\) −5.12880e6 −1.78656 −0.893282 0.449496i \(-0.851603\pi\)
−0.893282 + 0.449496i \(0.851603\pi\)
\(384\) −4.40017e6 + 2.93731e6i −1.52279 + 1.01653i
\(385\) 2.64306e6i 0.908773i
\(386\) 4.45713e6i 1.52261i
\(387\) −2.58535e6 1.07355e6i −0.877489 0.364370i
\(388\) 5.17389e6i 1.74477i
\(389\) −2.66611e6 −0.893314 −0.446657 0.894705i \(-0.647386\pi\)
−0.446657 + 0.894705i \(0.647386\pi\)
\(390\) 190889. 127427.i 0.0635507 0.0424229i
\(391\) −1.25272e6 + 4.60388e6i −0.414394 + 1.52294i
\(392\) 1.08314e7i 3.56017i
\(393\) −584766. + 390357.i −0.190985 + 0.127491i
\(394\) 2.73262e6 0.886827
\(395\) 916003.i 0.295396i
\(396\) −1.46373e6 + 3.52500e6i −0.469054 + 1.12959i
\(397\) 656587. 0.209082 0.104541 0.994521i \(-0.466663\pi\)
0.104541 + 0.994521i \(0.466663\pi\)
\(398\) 1.93632e6 0.612731
\(399\) 2.70482e6 + 4.05190e6i 0.850563 + 1.27417i
\(400\) −882926. −0.275914
\(401\) −4.02814e6 −1.25096 −0.625480 0.780240i \(-0.715097\pi\)
−0.625480 + 0.780240i \(0.715097\pi\)
\(402\) −4.41371e6 6.61186e6i −1.36219 2.04060i
\(403\) 115145. 0.0353170
\(404\) 2.01691e6i 0.614800i
\(405\) −1.76453e6 1.77073e6i −0.534554 0.536433i
\(406\) 5.12602e6i 1.54335i
\(407\) 3.12664e6i 0.935605i
\(408\) −6.56831e6 + 4.38464e6i −1.95345 + 1.30402i
\(409\) −2.84042e6 −0.839603 −0.419802 0.907616i \(-0.637900\pi\)
−0.419802 + 0.907616i \(0.637900\pi\)
\(410\) 5.68219e6 1.66938
\(411\) −333727. 499933.i −0.0974512 0.145985i
\(412\) 8.82117e6i 2.56025i
\(413\) 1.00877e7 2.91017
\(414\) 3.62338e6 4.67595e6i 1.03899 1.34081i
\(415\) 1.70700e6 0.486534
\(416\) 82036.5i 0.0232420i
\(417\) 2.15411e6 + 3.22692e6i 0.606636 + 0.908758i
\(418\) −3.28370e6 −0.919228
\(419\) 730556. 0.203291 0.101646 0.994821i \(-0.467589\pi\)
0.101646 + 0.994821i \(0.467589\pi\)
\(420\) −7.87322e6 + 5.25572e6i −2.17786 + 1.45382i
\(421\) 4.57249e6i 1.25733i −0.777678 0.628663i \(-0.783603\pi\)
0.777678 0.628663i \(-0.216397\pi\)
\(422\) 1.93162e6i 0.528009i
\(423\) 23480.2 + 9749.95i 0.00638043 + 0.00264942i
\(424\) 819505.i 0.221379i
\(425\) 2.50654e6 0.673136
\(426\) −621498. 931021.i −0.165926 0.248562i
\(427\) 4.68765e6 1.24419
\(428\) −9.26599e6 −2.44502
\(429\) −82018.8 122867.i −0.0215164 0.0322322i
\(430\) 4.67970e6 1.22052
\(431\) −3.59508e6 −0.932214 −0.466107 0.884728i \(-0.654344\pi\)
−0.466107 + 0.884728i \(0.654344\pi\)
\(432\) 2.46184e6 486323.i 0.634674 0.125376i
\(433\) 2.87279e6i 0.736351i 0.929756 + 0.368175i \(0.120017\pi\)
−0.929756 + 0.368175i \(0.879983\pi\)
\(434\) −7.27895e6 −1.85500
\(435\) 1.22797e6 819722.i 0.311145 0.207703i
\(436\) 1.42354e7i 3.58636i
\(437\) 3.20400e6 + 871814.i 0.802581 + 0.218384i
\(438\) 435212. 290523.i 0.108397 0.0723595i
\(439\) −2.20954e6 −0.547193 −0.273597 0.961845i \(-0.588213\pi\)
−0.273597 + 0.961845i \(0.588213\pi\)
\(440\) 2.98175e6i 0.734242i
\(441\) 3.74704e6 9.02376e6i 0.917471 2.20948i
\(442\) 654071.i 0.159246i
\(443\) 3.21150e6i 0.777497i 0.921344 + 0.388748i \(0.127092\pi\)
−0.921344 + 0.388748i \(0.872908\pi\)
\(444\) 9.31373e6 6.21733e6i 2.24216 1.49674i
\(445\) −1.05911e6 −0.253536
\(446\) 911572.i 0.216997i
\(447\) 2.35215e6 + 3.52358e6i 0.556796 + 0.834096i
\(448\) 1.02479e7i 2.41234i
\(449\) 5.52846e6i 1.29416i −0.762421 0.647081i \(-0.775990\pi\)
0.762421 0.647081i \(-0.224010\pi\)
\(450\) −2.87006e6 1.19177e6i −0.668128 0.277435i
\(451\) 3.65736e6i 0.846693i
\(452\) 1.11802e7 2.57397
\(453\) −3.22729e6 4.83456e6i −0.738910 1.10691i
\(454\) 5.83604e6i 1.32886i
\(455\) 366384.i 0.0829675i
\(456\) 3.05142e6 + 4.57112e6i 0.687211 + 1.02946i
\(457\) 4.18096e6i 0.936453i 0.883609 + 0.468226i \(0.155107\pi\)
−0.883609 + 0.468226i \(0.844893\pi\)
\(458\) −1.12416e7 −2.50417
\(459\) −6.98894e6 + 1.38063e6i −1.54839 + 0.305875i
\(460\) −1.69402e6 + 6.22568e6i −0.373270 + 1.37180i
\(461\) 2.12110e6i 0.464847i 0.972615 + 0.232423i \(0.0746655\pi\)
−0.972615 + 0.232423i \(0.925335\pi\)
\(462\) 5.18485e6 + 7.76705e6i 1.13014 + 1.69298i
\(463\) 5.07644e6 1.10054 0.550271 0.834986i \(-0.314524\pi\)
0.550271 + 0.834986i \(0.314524\pi\)
\(464\) 1.48210e6i 0.319583i
\(465\) 1.16401e6 + 1.74371e6i 0.249645 + 0.373975i
\(466\) −1.16044e7 −2.47546
\(467\) 1.39124e6 0.295196 0.147598 0.989047i \(-0.452846\pi\)
0.147598 + 0.989047i \(0.452846\pi\)
\(468\) −202904. + 488640.i −0.0428228 + 0.103127i
\(469\) −1.26905e7 −2.66407
\(470\) −42501.0 −0.00887472
\(471\) 2.76998e6 1.84909e6i 0.575341 0.384065i
\(472\) 1.13804e7 2.35127
\(473\) 3.01210e6i 0.619037i
\(474\) 1.79691e6 + 2.69182e6i 0.367350 + 0.550301i
\(475\) 1.74439e6i 0.354740i
\(476\) 2.69771e7i 5.45730i
\(477\) 283501. 682736.i 0.0570504 0.137391i
\(478\) −1.05402e7 −2.10998
\(479\) −1.02165e6 −0.203453 −0.101727 0.994812i \(-0.532437\pi\)
−0.101727 + 0.994812i \(0.532437\pi\)
\(480\) 1.24233e6 829308.i 0.246112 0.164291i
\(481\) 433419.i 0.0854171i
\(482\) −6.87837e6 −1.34855
\(483\) −2.99687e6 8.95509e6i −0.584521 1.74664i
\(484\) 5.56802e6 1.08041
\(485\) 3.64611e6i 0.703843i
\(486\) 8.65897e6 + 1.74213e6i 1.66294 + 0.334573i
\(487\) 7.39100e6 1.41215 0.706075 0.708138i \(-0.250464\pi\)
0.706075 + 0.708138i \(0.250464\pi\)
\(488\) 5.28834e6 1.00524
\(489\) 4.83112e6 + 7.23715e6i 0.913641 + 1.36866i
\(490\) 1.63338e7i 3.07323i
\(491\) 3.70147e6i 0.692900i −0.938068 0.346450i \(-0.887387\pi\)
0.938068 0.346450i \(-0.112613\pi\)
\(492\) −1.08946e7 + 7.27265e6i −2.02908 + 1.35450i
\(493\) 4.20755e6i 0.779672i
\(494\) −455191. −0.0839220
\(495\) 1.03151e6 2.48412e6i 0.189217 0.455679i
\(496\) −2.10459e6 −0.384116
\(497\) −1.78696e6 −0.324506
\(498\) −5.01628e6 + 3.34859e6i −0.906377 + 0.605047i
\(499\) −3.46388e6 −0.622748 −0.311374 0.950288i \(-0.600789\pi\)
−0.311374 + 0.950288i \(0.600789\pi\)
\(500\) 1.13370e7 2.02802
\(501\) 4.76380e6 3.18004e6i 0.847928 0.566029i
\(502\) 1.63979e7i 2.90421i
\(503\) −79065.9 −0.0139338 −0.00696689 0.999976i \(-0.502218\pi\)
−0.00696689 + 0.999976i \(0.502218\pi\)
\(504\) 5.99413e6 1.44353e7i 1.05111 2.53133i
\(505\) 1.42135e6i 0.248011i
\(506\) 6.14173e6 + 1.67117e6i 1.06639 + 0.290165i
\(507\) 3.20210e6 + 4.79683e6i 0.553241 + 0.828771i
\(508\) −6.72273e6 −1.15581
\(509\) 1.50028e6i 0.256672i 0.991731 + 0.128336i \(0.0409636\pi\)
−0.991731 + 0.128336i \(0.959036\pi\)
\(510\) 9.90498e6 6.61201e6i 1.68627 1.12566i
\(511\) 835325.i 0.141515i
\(512\) 7.20996e6i 1.21551i
\(513\) 960825. + 4.86385e6i 0.161195 + 0.815993i
\(514\) 1.30786e6 0.218350
\(515\) 6.21639e6i 1.03281i
\(516\) −8.97253e6 + 5.98956e6i −1.48351 + 0.990308i
\(517\) 27355.9i 0.00450116i
\(518\) 2.73987e7i 4.48648i
\(519\) 3.99978e6 2.67003e6i 0.651804 0.435108i
\(520\) 413333.i 0.0670335i
\(521\) −1.32448e6 −0.213771 −0.106886 0.994271i \(-0.534088\pi\)
−0.106886 + 0.994271i \(0.534088\pi\)
\(522\) −2.00054e6 + 4.81776e6i −0.321344 + 0.773872i
\(523\) 7.72536e6i 1.23499i 0.786573 + 0.617497i \(0.211853\pi\)
−0.786573 + 0.617497i \(0.788147\pi\)
\(524\) 2.70949e6i 0.431081i
\(525\) −4.12606e6 + 2.75433e6i −0.653338 + 0.436132i
\(526\) 1.10970e6i 0.174880i
\(527\) 5.97472e6 0.937112
\(528\) 1.49911e6 + 2.24571e6i 0.234018 + 0.350566i
\(529\) −5.54896e6 3.26122e6i −0.862129 0.506688i
\(530\) 1.23581e6i 0.191100i
\(531\) 9.48108e6 + 3.93694e6i 1.45922 + 0.605930i
\(532\) 1.87743e7 2.87597
\(533\) 506987.i 0.0772999i
\(534\) 3.11235e6 2.07763e6i 0.472319 0.315294i
\(535\) 6.52987e6 0.986325
\(536\) −1.43167e7 −2.15244
\(537\) 4.89639e6 3.26856e6i 0.732724 0.489126i
\(538\) −1.28533e7 −1.91452
\(539\) 1.05133e7 1.55871
\(540\) −9.45092e6 + 1.86698e6i −1.39473 + 0.275521i
\(541\) 1.20047e6 0.176343 0.0881716 0.996105i \(-0.471898\pi\)
0.0881716 + 0.996105i \(0.471898\pi\)
\(542\) 5.74342e6i 0.839794i
\(543\) 928285. 619671.i 0.135108 0.0901907i
\(544\) 4.25676e6i 0.616711i
\(545\) 1.00319e7i 1.44674i
\(546\) 718730. + 1.07668e6i 0.103177 + 0.154562i
\(547\) −7.08747e6 −1.01280 −0.506399 0.862299i \(-0.669024\pi\)
−0.506399 + 0.862299i \(0.669024\pi\)
\(548\) −2.31642e6 −0.329508
\(549\) 4.40576e6 + 1.82945e6i 0.623863 + 0.259054i
\(550\) 3.34381e6i 0.471340i
\(551\) −2.92818e6 −0.410884
\(552\) −3.38090e6 1.01026e7i −0.472264 1.41119i
\(553\) 5.16655e6 0.718436
\(554\) 7.71561e6i 1.06806i
\(555\) −6.56351e6 + 4.38143e6i −0.904490 + 0.603787i
\(556\) 1.49518e7 2.05119
\(557\) −1.19085e7 −1.62637 −0.813183 0.582008i \(-0.802267\pi\)
−0.813183 + 0.582008i \(0.802267\pi\)
\(558\) −6.84123e6 2.84076e6i −0.930140 0.386233i
\(559\) 417540.i 0.0565157i
\(560\) 6.69664e6i 0.902375i
\(561\) −4.25584e6 6.37537e6i −0.570924 0.855260i
\(562\) 1.85553e6i 0.247815i
\(563\) −3.48037e6 −0.462759 −0.231379 0.972864i \(-0.574324\pi\)
−0.231379 + 0.972864i \(0.574324\pi\)
\(564\) 81488.5 54397.2i 0.0107870 0.00720077i
\(565\) −7.87883e6 −1.03834
\(566\) 1.81152e7 2.37685
\(567\) 9.98750e6 9.95251e6i 1.30467 1.30009i
\(568\) −2.01594e6 −0.262185
\(569\) −8.76497e6 −1.13493 −0.567466 0.823397i \(-0.692076\pi\)
−0.567466 + 0.823397i \(0.692076\pi\)
\(570\) −4.60153e6 6.89322e6i −0.593219 0.888658i
\(571\) 1.28771e7i 1.65283i 0.563058 + 0.826417i \(0.309625\pi\)
−0.563058 + 0.826417i \(0.690375\pi\)
\(572\) −569297. −0.0727527
\(573\) −2.07951e6 3.11516e6i −0.264590 0.396363i
\(574\) 3.20494e7i 4.06013i
\(575\) −887771. + 3.26265e6i −0.111978 + 0.411529i
\(576\) −3.99944e6 + 9.63159e6i −0.502277 + 1.20960i
\(577\) 1.41805e7 1.77318 0.886589 0.462559i \(-0.153069\pi\)
0.886589 + 0.462559i \(0.153069\pi\)
\(578\) 2.03146e7i 2.52923i
\(579\) −4.02018e6 6.02234e6i −0.498367 0.746567i
\(580\) 5.68973e6i 0.702299i
\(581\) 9.62802e6i 1.18330i
\(582\) −7.15252e6 1.07147e7i −0.875289 1.31121i
\(583\) 795432. 0.0969241
\(584\) 942365.i 0.114337i
\(585\) 142989. 344351.i 0.0172748 0.0416018i
\(586\) 9.35529e6i 1.12542i
\(587\) 4.31162e6i 0.516470i 0.966082 + 0.258235i \(0.0831409\pi\)
−0.966082 + 0.258235i \(0.916859\pi\)
\(588\) −2.09056e7 3.13172e7i −2.49356 3.73542i
\(589\) 4.15802e6i 0.493853i
\(590\) −1.71615e7 −2.02967
\(591\) 3.69224e6 2.46473e6i 0.434831 0.290269i
\(592\) 7.92188e6i 0.929018i
\(593\) 1.53560e7i 1.79325i 0.442787 + 0.896627i \(0.353990\pi\)
−0.442787 + 0.896627i \(0.646010\pi\)
\(594\) 1.84180e6 + 9.32347e6i 0.214179 + 1.08421i
\(595\) 1.90111e7i 2.20148i
\(596\) 1.63264e7 1.88267
\(597\) 2.61630e6 1.74649e6i 0.300436 0.200554i
\(598\) 851373. + 231660.i 0.0973569 + 0.0264910i
\(599\) 8.95775e6i 1.02007i −0.860152 0.510037i \(-0.829632\pi\)
0.860152 0.510037i \(-0.170368\pi\)
\(600\) −4.65479e6 + 3.10727e6i −0.527863 + 0.352372i
\(601\) 2.98822e6 0.337463 0.168732 0.985662i \(-0.446033\pi\)
0.168732 + 0.985662i \(0.446033\pi\)
\(602\) 2.63950e7i 2.96845i
\(603\) −1.19273e7 4.95273e6i −1.33583 0.554691i
\(604\) −2.24008e7 −2.49845
\(605\) −3.92386e6 −0.435838
\(606\) 2.78823e6 + 4.17685e6i 0.308423 + 0.462027i
\(607\) −1.01901e7 −1.12255 −0.561277 0.827628i \(-0.689690\pi\)
−0.561277 + 0.827628i \(0.689690\pi\)
\(608\) −2.96243e6 −0.325004
\(609\) 4.62349e6 + 6.92612e6i 0.505158 + 0.756740i
\(610\) −7.97478e6 −0.867749
\(611\) 3792.11i 0.000410939i
\(612\) −1.05284e7 + 2.53548e7i −1.13627 + 2.73642i
\(613\) 6.67644e6i 0.717619i 0.933411 + 0.358809i \(0.116817\pi\)
−0.933411 + 0.358809i \(0.883183\pi\)
\(614\) 2.31897e7i 2.48241i
\(615\) 7.67760e6 5.12514e6i 0.818536 0.546409i
\(616\) 1.68180e7 1.78576
\(617\) 1.07353e7 1.13528 0.567638 0.823278i \(-0.307857\pi\)
0.567638 + 0.823278i \(0.307857\pi\)
\(618\) 1.21946e7 + 1.82679e7i 1.28439 + 1.92405i
\(619\) 1.50784e7i 1.58172i 0.612000 + 0.790858i \(0.290365\pi\)
−0.612000 + 0.790858i \(0.709635\pi\)
\(620\) 8.07943e6 0.844114
\(621\) 678260. 9.58616e6i 0.0705776 0.997506i
\(622\) 1.17942e7 1.22234
\(623\) 5.97370e6i 0.616628i
\(624\) 207809. + 311303.i 0.0213650 + 0.0320053i
\(625\) −3.82435e6 −0.391613
\(626\) 2.00689e7 2.04686
\(627\) −4.43684e6 + 2.96179e6i −0.450718 + 0.300874i
\(628\) 1.28346e7i 1.29862i
\(629\) 2.24895e7i 2.26648i
\(630\) −9.03911e6 + 2.17683e7i −0.907348 + 2.18511i
\(631\) 234707.i 0.0234667i 0.999931 + 0.0117334i \(0.00373493\pi\)
−0.999931 + 0.0117334i \(0.996265\pi\)
\(632\) 5.82860e6 0.580459
\(633\) −1.74226e6 2.60995e6i −0.172823 0.258894i
\(634\) −1.73285e7 −1.71213
\(635\) 4.73760e6 0.466256
\(636\) −1.58172e6 2.36946e6i −0.155055 0.232277i
\(637\) 1.45736e6 0.142304
\(638\) −5.61301e6 −0.545939
\(639\) −1.67950e6 697397.i −0.162715 0.0675660i
\(640\) 1.43677e7i 1.38656i
\(641\) 1.01915e7 0.979701 0.489850 0.871807i \(-0.337051\pi\)
0.489850 + 0.871807i \(0.337051\pi\)
\(642\) −1.91891e7 + 1.28095e7i −1.83745 + 1.22658i
\(643\) 4.79332e6i 0.457203i −0.973520 0.228601i \(-0.926585\pi\)
0.973520 0.228601i \(-0.0734152\pi\)
\(644\) −3.51148e7 9.55480e6i −3.33638 0.907835i
\(645\) 6.32306e6 4.22092e6i 0.598450 0.399492i
\(646\) −2.36192e7 −2.22681
\(647\) 9.51131e6i 0.893264i 0.894718 + 0.446632i \(0.147377\pi\)
−0.894718 + 0.446632i \(0.852623\pi\)
\(648\) 1.12673e7 1.12278e7i 1.05410 1.05041i
\(649\) 1.10461e7i 1.02943i
\(650\) 463522.i 0.0430316i
\(651\) −9.83510e6 + 6.56536e6i −0.909549 + 0.607164i
\(652\) 3.35330e7 3.08926
\(653\) 2.01707e7i 1.85113i −0.378585 0.925566i \(-0.623589\pi\)
0.378585 0.925566i \(-0.376411\pi\)
\(654\) −1.96794e7 2.94803e7i −1.79915 2.69518i
\(655\) 1.90941e6i 0.173899i
\(656\) 9.26653e6i 0.840732i
\(657\) 326003. 785092.i 0.0294651 0.0709589i
\(658\) 239719.i 0.0215843i
\(659\) 1.48161e7 1.32898 0.664491 0.747296i \(-0.268648\pi\)
0.664491 + 0.747296i \(0.268648\pi\)
\(660\) −5.75503e6 8.62120e6i −0.514266 0.770385i
\(661\) 1.86036e6i 0.165613i 0.996566 + 0.0828064i \(0.0263883\pi\)
−0.996566 + 0.0828064i \(0.973612\pi\)
\(662\) 2.03700e7i 1.80653i
\(663\) −589949. 883760.i −0.0521231 0.0780819i
\(664\) 1.08618e7i 0.956050i
\(665\) −1.32305e7 −1.16017
\(666\) 1.06929e7 2.57511e7i 0.934138 2.24962i
\(667\) 5.47677e6 + 1.49024e6i 0.476661 + 0.129700i
\(668\) 2.20729e7i 1.91389i
\(669\) 822206. + 1.23169e6i 0.0710257 + 0.106399i
\(670\) 2.15895e7 1.85804
\(671\) 5.13299e6i 0.440113i
\(672\) 4.67756e6 + 7.00712e6i 0.399573 + 0.598572i
\(673\) −1.03407e6 −0.0880061 −0.0440031 0.999031i \(-0.514011\pi\)
−0.0440031 + 0.999031i \(0.514011\pi\)
\(674\) 2.54905e7 2.16136
\(675\) −4.95287e6 + 978412.i −0.418406 + 0.0826537i
\(676\) 2.22259e7 1.87065
\(677\) 1.20130e7 1.00735 0.503676 0.863893i \(-0.331981\pi\)
0.503676 + 0.863893i \(0.331981\pi\)
\(678\) 2.31532e7 1.54558e7i 1.93436 1.29127i
\(679\) −2.05652e7 −1.71182
\(680\) 2.14473e7i 1.77869i
\(681\) −5.26390e6 7.88547e6i −0.434951 0.651568i
\(682\) 7.97047e6i 0.656180i
\(683\) 6.04943e6i 0.496207i −0.968734 0.248104i \(-0.920193\pi\)
0.968734 0.248104i \(-0.0798073\pi\)
\(684\) 1.76453e7 + 7.32707e6i 1.44208 + 0.598811i
\(685\) 1.63241e6 0.132924
\(686\) −5.36191e7 −4.35020
\(687\) −1.51893e7 + 1.01395e7i −1.22785 + 0.819643i
\(688\) 7.63166e6i 0.614679i
\(689\) 110264. 0.00884880
\(690\) 5.09837e6 + 1.52347e7i 0.407670 + 1.21818i
\(691\) −1.22344e6 −0.0974736 −0.0487368 0.998812i \(-0.515520\pi\)
−0.0487368 + 0.998812i \(0.515520\pi\)
\(692\) 1.85328e7i 1.47121i
\(693\) 1.40112e7 + 5.81805e6i 1.10826 + 0.460197i
\(694\) 731723. 0.0576698
\(695\) −1.05367e7 −0.827455
\(696\) 5.21596e6 + 7.81365e6i 0.408142 + 0.611408i
\(697\) 2.63068e7i 2.05110i
\(698\) 2.89045e7i 2.24557i
\(699\) −1.56795e7 + 1.04667e7i −1.21377 + 0.810248i
\(700\) 1.91180e7i 1.47467i
\(701\) −494965. −0.0380434 −0.0190217 0.999819i \(-0.506055\pi\)
−0.0190217 + 0.999819i \(0.506055\pi\)
\(702\) 255312. + 1.29243e6i 0.0195537 + 0.0989838i
\(703\) 1.56512e7 1.19443
\(704\) −1.12214e7 −0.853329
\(705\) −57426.1 + 38334.4i −0.00435147 + 0.00290480i
\(706\) 2.95015e6 0.222757
\(707\) 8.01684e6 0.603191
\(708\) 3.29044e7 2.19651e7i 2.46701 1.64684i
\(709\) 1.61820e6i 0.120897i −0.998171 0.0604486i \(-0.980747\pi\)
0.998171 0.0604486i \(-0.0192531\pi\)
\(710\) 3.04003e6 0.226325
\(711\) 4.85585e6 + 2.01635e6i 0.360240 + 0.149587i
\(712\) 6.73918e6i 0.498204i
\(713\) −2.11614e6 + 7.77701e6i −0.155891 + 0.572913i
\(714\) 3.72938e7 + 5.58672e7i 2.73774 + 4.10121i
\(715\) 401191. 0.0293485
\(716\) 2.26872e7i 1.65386i
\(717\) −1.42416e7 + 9.50687e6i −1.03457 + 0.690621i
\(718\) 1.77023e7i 1.28150i
\(719\) 1.10050e7i 0.793902i 0.917840 + 0.396951i \(0.129932\pi\)
−0.917840 + 0.396951i \(0.870068\pi\)
\(720\) −2.61351e6 + 6.29393e6i −0.187885 + 0.452471i
\(721\) 3.50624e7 2.51191
\(722\) 7.32197e6i 0.522739i
\(723\) −9.29384e6 + 6.20405e6i −0.661225 + 0.441397i
\(724\) 4.30117e6i 0.304958i
\(725\) 2.98178e6i 0.210683i
\(726\) 1.15309e7 7.69738e6i 0.811935 0.542002i
\(727\) 1.01959e7i 0.715469i 0.933823 + 0.357734i \(0.116451\pi\)
−0.933823 + 0.357734i \(0.883549\pi\)
\(728\) 2.33133e6 0.163033
\(729\) 1.32711e7 5.45617e6i 0.924884 0.380250i
\(730\) 1.42108e6i 0.0986988i
\(731\) 2.16656e7i 1.49960i
\(732\) 1.52903e7 1.02069e7i 1.05472 0.704074i
\(733\) 3.14789e6i 0.216401i −0.994129 0.108201i \(-0.965491\pi\)
0.994129 0.108201i \(-0.0345089\pi\)
\(734\) 2.35892e7 1.61612
\(735\) 1.47325e7 + 2.20697e7i 1.00591 + 1.50687i
\(736\) 5.54082e6 + 1.50767e6i 0.377033 + 0.102591i
\(737\) 1.38961e7i 0.942377i
\(738\) −1.25079e7 + 3.01220e7i −0.845366 + 2.03584i
\(739\) −2.23241e7 −1.50371 −0.751853 0.659330i \(-0.770840\pi\)
−0.751853 + 0.659330i \(0.770840\pi\)
\(740\) 3.04118e7i 2.04156i
\(741\) −615039. + 410566.i −0.0411488 + 0.0274687i
\(742\) −6.97036e6 −0.464778
\(743\) −5.25688e6 −0.349346 −0.174673 0.984626i \(-0.555887\pi\)
−0.174673 + 0.984626i \(0.555887\pi\)
\(744\) −1.10954e7 + 7.40666e6i −0.734869 + 0.490558i
\(745\) −1.15054e7 −0.759473
\(746\) 1.27251e7 0.837169
\(747\) −3.75754e6 + 9.04902e6i −0.246378 + 0.593335i
\(748\) −2.95400e7 −1.93044
\(749\) 3.68305e7i 2.39885i
\(750\) 2.34778e7 1.56725e7i 1.52407 1.01738i
\(751\) 1.06147e7i 0.686766i 0.939196 + 0.343383i \(0.111573\pi\)
−0.939196 + 0.343383i \(0.888427\pi\)
\(752\) 69310.8i 0.00446947i
\(753\) −1.47903e7 2.21563e7i −0.950582 1.42400i
\(754\) −778081. −0.0498421
\(755\) 1.57861e7 1.00788
\(756\) −1.05303e7 5.33062e7i −0.670097 3.39213i
\(757\) 1.03081e7i 0.653791i 0.945061 + 0.326895i \(0.106002\pi\)
−0.945061 + 0.326895i \(0.893998\pi\)
\(758\) −9.56887e6 −0.604906
\(759\) 9.80585e6 3.28158e6i 0.617847 0.206766i
\(760\) −1.49259e7 −0.937360
\(761\) 6.30344e6i 0.394563i −0.980347 0.197281i \(-0.936789\pi\)
0.980347 0.197281i \(-0.0632112\pi\)
\(762\) −1.39222e7 + 9.29367e6i −0.868600 + 0.579829i
\(763\) −5.65830e7 −3.51864
\(764\) −1.44340e7 −0.894648
\(765\) 7.41950e6 1.78679e7i 0.458375 1.10387i
\(766\) 4.92133e7i 3.03048i
\(767\) 1.53122e6i 0.0939829i
\(768\) 1.62988e7 + 2.44160e7i 0.997129 + 1.49373i
\(769\) 9.63731e6i 0.587679i −0.955855 0.293839i \(-0.905067\pi\)
0.955855 0.293839i \(-0.0949331\pi\)
\(770\) −2.53615e7 −1.54151
\(771\) 1.76714e6 1.17964e6i 0.107062 0.0714686i
\(772\) −2.79043e7 −1.68511
\(773\) 5.63328e6 0.339088 0.169544 0.985523i \(-0.445771\pi\)
0.169544 + 0.985523i \(0.445771\pi\)
\(774\) −1.03012e7 + 2.48077e7i −0.618066 + 1.48845i
\(775\) 4.23413e6 0.253227
\(776\) −2.32005e7 −1.38307
\(777\) −2.47127e7 3.70203e7i −1.46848 2.19982i
\(778\) 2.55826e7i 1.51529i
\(779\) −1.830