Properties

Label 69.7.d.a.22.7
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.7
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.8

$q$-expansion

\(f(q)\) \(=\) \(q-8.53823 q^{2} -15.5885 q^{3} +8.90142 q^{4} -233.104i q^{5} +133.098 q^{6} -155.980i q^{7} +470.445 q^{8} +243.000 q^{9} +O(q^{10})\) \(q-8.53823 q^{2} -15.5885 q^{3} +8.90142 q^{4} -233.104i q^{5} +133.098 q^{6} -155.980i q^{7} +470.445 q^{8} +243.000 q^{9} +1990.29i q^{10} -880.164i q^{11} -138.759 q^{12} +3100.64 q^{13} +1331.79i q^{14} +3633.73i q^{15} -4586.46 q^{16} -5586.40i q^{17} -2074.79 q^{18} -9608.40i q^{19} -2074.95i q^{20} +2431.49i q^{21} +7515.05i q^{22} +(12069.8 - 1534.74i) q^{23} -7333.50 q^{24} -38712.4 q^{25} -26474.0 q^{26} -3788.00 q^{27} -1388.44i q^{28} +14991.2 q^{29} -31025.6i q^{30} -49729.0 q^{31} +9051.77 q^{32} +13720.4i q^{33} +47698.0i q^{34} -36359.5 q^{35} +2163.04 q^{36} +7101.92i q^{37} +82038.7i q^{38} -48334.2 q^{39} -109662. i q^{40} +39666.9 q^{41} -20760.6i q^{42} -97163.8i q^{43} -7834.71i q^{44} -56644.2i q^{45} +(-103055. + 13104.0i) q^{46} -14422.3 q^{47} +71495.8 q^{48} +93319.3 q^{49} +330536. q^{50} +87083.4i q^{51} +27600.1 q^{52} +196331. i q^{53} +32342.8 q^{54} -205170. q^{55} -73379.9i q^{56} +149780. i q^{57} -127998. q^{58} +177846. q^{59} +32345.3i q^{60} +343123. i q^{61} +424597. q^{62} -37903.1i q^{63} +216247. q^{64} -722772. i q^{65} -117148. i q^{66} +300398. i q^{67} -49726.9i q^{68} +(-188150. + 23924.2i) q^{69} +310446. q^{70} -104094. q^{71} +114318. q^{72} -466983. q^{73} -60637.8i q^{74} +603467. q^{75} -85528.3i q^{76} -137288. q^{77} +412689. q^{78} -780636. i q^{79} +1.06912e6i q^{80} +59049.0 q^{81} -338685. q^{82} -608861. i q^{83} +21643.7i q^{84} -1.30221e6 q^{85} +829607. i q^{86} -233689. q^{87} -414068. i q^{88} +346420. i q^{89} +483642. i q^{90} -483638. i q^{91} +(107438. - 13661.4i) q^{92} +775198. q^{93} +123141. q^{94} -2.23975e6 q^{95} -141103. q^{96} +691811. i q^{97} -796782. q^{98} -213880. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + O(q^{10}) \) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + 384q^{13} + 29544q^{16} - 4860q^{18} + 29336q^{23} - 39204q^{24} - 61272q^{25} + 10088q^{26} + 64672q^{29} + 9696q^{31} - 319620q^{32} - 225744q^{35} + 198288q^{36} - 11664q^{39} + 135280q^{41} + 233232q^{46} - 74336q^{47} + 552096q^{48} - 722136q^{49} + 619324q^{50} + 1059720q^{52} - 78732q^{54} - 1019328q^{55} - 694344q^{58} + 1057648q^{59} - 488776q^{62} - 273888q^{64} - 23328q^{69} + 2785512q^{70} - 255392q^{71} - 228420q^{72} - 322560q^{73} - 365472q^{75} - 1002960q^{77} - 171072q^{78} + 1417176q^{81} - 5732712q^{82} - 2704704q^{85} + 611712q^{87} - 1611444q^{92} + 2484432q^{93} - 147720q^{94} - 1672656q^{95} - 1818612q^{96} + 9104212q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.53823 −1.06728 −0.533640 0.845712i \(-0.679176\pi\)
−0.533640 + 0.845712i \(0.679176\pi\)
\(3\) −15.5885 −0.577350
\(4\) 8.90142 0.139085
\(5\) 233.104i 1.86483i −0.361388 0.932415i \(-0.617697\pi\)
0.361388 0.932415i \(-0.382303\pi\)
\(6\) 133.098 0.616194
\(7\) 155.980i 0.454752i −0.973807 0.227376i \(-0.926985\pi\)
0.973807 0.227376i \(-0.0730146\pi\)
\(8\) 470.445 0.918837
\(9\) 243.000 0.333333
\(10\) 1990.29i 1.99029i
\(11\) 880.164i 0.661280i −0.943757 0.330640i \(-0.892735\pi\)
0.943757 0.330640i \(-0.107265\pi\)
\(12\) −138.759 −0.0803005
\(13\) 3100.64 1.41131 0.705654 0.708557i \(-0.250653\pi\)
0.705654 + 0.708557i \(0.250653\pi\)
\(14\) 1331.79i 0.485347i
\(15\) 3633.73i 1.07666i
\(16\) −4586.46 −1.11974
\(17\) 5586.40i 1.13707i −0.822661 0.568533i \(-0.807511\pi\)
0.822661 0.568533i \(-0.192489\pi\)
\(18\) −2074.79 −0.355760
\(19\) 9608.40i 1.40084i −0.713729 0.700422i \(-0.752995\pi\)
0.713729 0.700422i \(-0.247005\pi\)
\(20\) 2074.95i 0.259369i
\(21\) 2431.49i 0.262551i
\(22\) 7515.05i 0.705771i
\(23\) 12069.8 1534.74i 0.992013 0.126140i
\(24\) −7333.50 −0.530491
\(25\) −38712.4 −2.47759
\(26\) −26474.0 −1.50626
\(27\) −3788.00 −0.192450
\(28\) 1388.44i 0.0632490i
\(29\) 14991.2 0.614669 0.307334 0.951602i \(-0.400563\pi\)
0.307334 + 0.951602i \(0.400563\pi\)
\(30\) 31025.6i 1.14910i
\(31\) −49729.0 −1.66926 −0.834630 0.550810i \(-0.814319\pi\)
−0.834630 + 0.550810i \(0.814319\pi\)
\(32\) 9051.77 0.276238
\(33\) 13720.4i 0.381790i
\(34\) 47698.0i 1.21357i
\(35\) −36359.5 −0.848035
\(36\) 2163.04 0.0463615
\(37\) 7101.92i 0.140207i 0.997540 + 0.0701036i \(0.0223330\pi\)
−0.997540 + 0.0701036i \(0.977667\pi\)
\(38\) 82038.7i 1.49509i
\(39\) −48334.2 −0.814819
\(40\) 109662.i 1.71348i
\(41\) 39666.9 0.575541 0.287770 0.957699i \(-0.407086\pi\)
0.287770 + 0.957699i \(0.407086\pi\)
\(42\) 20760.6i 0.280215i
\(43\) 97163.8i 1.22208i −0.791600 0.611039i \(-0.790752\pi\)
0.791600 0.611039i \(-0.209248\pi\)
\(44\) 7834.71i 0.0919739i
\(45\) 56644.2i 0.621610i
\(46\) −103055. + 13104.0i −1.05875 + 0.134626i
\(47\) −14422.3 −0.138913 −0.0694564 0.997585i \(-0.522126\pi\)
−0.0694564 + 0.997585i \(0.522126\pi\)
\(48\) 71495.8 0.646482
\(49\) 93319.3 0.793201
\(50\) 330536. 2.64428
\(51\) 87083.4i 0.656485i
\(52\) 27600.1 0.196291
\(53\) 196331.i 1.31874i 0.751816 + 0.659372i \(0.229178\pi\)
−0.751816 + 0.659372i \(0.770822\pi\)
\(54\) 32342.8 0.205398
\(55\) −205170. −1.23318
\(56\) 73379.9i 0.417843i
\(57\) 149780.i 0.808778i
\(58\) −127998. −0.656023
\(59\) 177846. 0.865942 0.432971 0.901408i \(-0.357465\pi\)
0.432971 + 0.901408i \(0.357465\pi\)
\(60\) 32345.3i 0.149747i
\(61\) 343123.i 1.51168i 0.654756 + 0.755840i \(0.272771\pi\)
−0.654756 + 0.755840i \(0.727229\pi\)
\(62\) 424597. 1.78157
\(63\) 37903.1i 0.151584i
\(64\) 216247. 0.824917
\(65\) 722772.i 2.63185i
\(66\) 117148.i 0.407477i
\(67\) 300398.i 0.998785i 0.866376 + 0.499393i \(0.166444\pi\)
−0.866376 + 0.499393i \(0.833556\pi\)
\(68\) 49726.9i 0.158148i
\(69\) −188150. + 23924.2i −0.572739 + 0.0728267i
\(70\) 310446. 0.905090
\(71\) −104094. −0.290838 −0.145419 0.989370i \(-0.546453\pi\)
−0.145419 + 0.989370i \(0.546453\pi\)
\(72\) 114318. 0.306279
\(73\) −466983. −1.20042 −0.600208 0.799844i \(-0.704916\pi\)
−0.600208 + 0.799844i \(0.704916\pi\)
\(74\) 60637.8i 0.149640i
\(75\) 603467. 1.43044
\(76\) 85528.3i 0.194836i
\(77\) −137288. −0.300718
\(78\) 412689. 0.869639
\(79\) 780636.i 1.58332i −0.610965 0.791658i \(-0.709218\pi\)
0.610965 0.791658i \(-0.290782\pi\)
\(80\) 1.06912e6i 2.08813i
\(81\) 59049.0 0.111111
\(82\) −338685. −0.614263
\(83\) 608861.i 1.06484i −0.846481 0.532420i \(-0.821283\pi\)
0.846481 0.532420i \(-0.178717\pi\)
\(84\) 21643.7i 0.0365168i
\(85\) −1.30221e6 −2.12043
\(86\) 829607.i 1.30430i
\(87\) −233689. −0.354879
\(88\) 414068.i 0.607609i
\(89\) 346420.i 0.491398i 0.969346 + 0.245699i \(0.0790174\pi\)
−0.969346 + 0.245699i \(0.920983\pi\)
\(90\) 483642.i 0.663432i
\(91\) 483638.i 0.641795i
\(92\) 107438. 13661.4i 0.137974 0.0175441i
\(93\) 775198. 0.963748
\(94\) 123141. 0.148259
\(95\) −2.23975e6 −2.61234
\(96\) −141103. −0.159486
\(97\) 691811.i 0.758005i 0.925396 + 0.379002i \(0.123733\pi\)
−0.925396 + 0.379002i \(0.876267\pi\)
\(98\) −796782. −0.846567
\(99\) 213880.i 0.220427i
\(100\) −344595. −0.344595
\(101\) −193600. −0.187906 −0.0939530 0.995577i \(-0.529950\pi\)
−0.0939530 + 0.995577i \(0.529950\pi\)
\(102\) 743538.i 0.700653i
\(103\) 925480.i 0.846945i 0.905909 + 0.423472i \(0.139189\pi\)
−0.905909 + 0.423472i \(0.860811\pi\)
\(104\) 1.45868e6 1.29676
\(105\) 566789. 0.489613
\(106\) 1.67632e6i 1.40747i
\(107\) 835236.i 0.681801i −0.940099 0.340901i \(-0.889268\pi\)
0.940099 0.340901i \(-0.110732\pi\)
\(108\) −33718.5 −0.0267668
\(109\) 1.68824e6i 1.30363i 0.758377 + 0.651817i \(0.225993\pi\)
−0.758377 + 0.651817i \(0.774007\pi\)
\(110\) 1.75179e6 1.31614
\(111\) 110708.i 0.0809487i
\(112\) 715395.i 0.509204i
\(113\) 562684.i 0.389968i −0.980806 0.194984i \(-0.937534\pi\)
0.980806 0.194984i \(-0.0624655\pi\)
\(114\) 1.27886e6i 0.863192i
\(115\) −357754. 2.81352e6i −0.235229 1.84994i
\(116\) 133443. 0.0854910
\(117\) 753456. 0.470436
\(118\) −1.51849e6 −0.924202
\(119\) −871366. −0.517083
\(120\) 1.70947e6i 0.989276i
\(121\) 996872. 0.562708
\(122\) 2.92966e6i 1.61339i
\(123\) −618345. −0.332289
\(124\) −442658. −0.232169
\(125\) 5.38176e6i 2.75546i
\(126\) 323626.i 0.161782i
\(127\) −232896. −0.113698 −0.0568489 0.998383i \(-0.518105\pi\)
−0.0568489 + 0.998383i \(0.518105\pi\)
\(128\) −2.42568e6 −1.15665
\(129\) 1.51463e6i 0.705567i
\(130\) 6.17119e6i 2.80892i
\(131\) 1.02283e6 0.454976 0.227488 0.973781i \(-0.426949\pi\)
0.227488 + 0.973781i \(0.426949\pi\)
\(132\) 122131.i 0.0531012i
\(133\) −1.49872e6 −0.637037
\(134\) 2.56487e6i 1.06598i
\(135\) 882996.i 0.358887i
\(136\) 2.62809e6i 1.04478i
\(137\) 1.41970e6i 0.552121i −0.961140 0.276060i \(-0.910971\pi\)
0.961140 0.276060i \(-0.0890290\pi\)
\(138\) 1.60647e6 204271.i 0.611272 0.0777264i
\(139\) −487470. −0.181511 −0.0907556 0.995873i \(-0.528928\pi\)
−0.0907556 + 0.995873i \(0.528928\pi\)
\(140\) −323651. −0.117949
\(141\) 224822. 0.0802014
\(142\) 888781. 0.310406
\(143\) 2.72908e6i 0.933270i
\(144\) −1.11451e6 −0.373247
\(145\) 3.49450e6i 1.14625i
\(146\) 3.98721e6 1.28118
\(147\) −1.45470e6 −0.457955
\(148\) 63217.1i 0.0195007i
\(149\) 3.65532e6i 1.10501i −0.833509 0.552506i \(-0.813672\pi\)
0.833509 0.552506i \(-0.186328\pi\)
\(150\) −5.15254e6 −1.52668
\(151\) 5.75177e6 1.67059 0.835296 0.549801i \(-0.185296\pi\)
0.835296 + 0.549801i \(0.185296\pi\)
\(152\) 4.52022e6i 1.28715i
\(153\) 1.35750e6i 0.379022i
\(154\) 1.17220e6 0.320950
\(155\) 1.15920e7i 3.11289i
\(156\) −430243. −0.113329
\(157\) 20743.8i 0.00536031i −0.999996 0.00268016i \(-0.999147\pi\)
0.999996 0.00268016i \(-0.000853121\pi\)
\(158\) 6.66526e6i 1.68984i
\(159\) 3.06049e6i 0.761378i
\(160\) 2.11000e6i 0.515138i
\(161\) −239389. 1.88265e6i −0.0573622 0.451119i
\(162\) −504174. −0.118587
\(163\) −4.04646e6 −0.934356 −0.467178 0.884163i \(-0.654729\pi\)
−0.467178 + 0.884163i \(0.654729\pi\)
\(164\) 353091. 0.0800489
\(165\) 3.19828e6 0.711975
\(166\) 5.19860e6i 1.13648i
\(167\) −1.52335e6 −0.327077 −0.163539 0.986537i \(-0.552291\pi\)
−0.163539 + 0.986537i \(0.552291\pi\)
\(168\) 1.14388e6i 0.241242i
\(169\) 4.78718e6 0.991790
\(170\) 1.11186e7 2.26310
\(171\) 2.33484e6i 0.466948i
\(172\) 864895.i 0.169972i
\(173\) 6.58097e6 1.27102 0.635509 0.772094i \(-0.280790\pi\)
0.635509 + 0.772094i \(0.280790\pi\)
\(174\) 1.99529e6 0.378755
\(175\) 6.03836e6i 1.12669i
\(176\) 4.03683e6i 0.740462i
\(177\) −2.77235e6 −0.499952
\(178\) 2.95781e6i 0.524458i
\(179\) −3.00610e6 −0.524136 −0.262068 0.965049i \(-0.584405\pi\)
−0.262068 + 0.965049i \(0.584405\pi\)
\(180\) 504214.i 0.0864564i
\(181\) 2.95903e6i 0.499014i −0.968373 0.249507i \(-0.919731\pi\)
0.968373 0.249507i \(-0.0802686\pi\)
\(182\) 4.12941e6i 0.684974i
\(183\) 5.34876e6i 0.872769i
\(184\) 5.67818e6 722010.i 0.911498 0.115902i
\(185\) 1.65548e6 0.261463
\(186\) −6.61882e6 −1.02859
\(187\) −4.91695e6 −0.751919
\(188\) −128379. −0.0193206
\(189\) 590851.i 0.0875170i
\(190\) 1.91235e7 2.78809
\(191\) 907350.i 0.130219i 0.997878 + 0.0651095i \(0.0207397\pi\)
−0.997878 + 0.0651095i \(0.979260\pi\)
\(192\) −3.37096e6 −0.476266
\(193\) 7.22908e6 1.00557 0.502783 0.864412i \(-0.332309\pi\)
0.502783 + 0.864412i \(0.332309\pi\)
\(194\) 5.90684e6i 0.809003i
\(195\) 1.12669e7i 1.51950i
\(196\) 830674. 0.110322
\(197\) −4.23662e6 −0.554141 −0.277071 0.960850i \(-0.589364\pi\)
−0.277071 + 0.960850i \(0.589364\pi\)
\(198\) 1.82616e6i 0.235257i
\(199\) 1.50761e6i 0.191307i −0.995415 0.0956535i \(-0.969506\pi\)
0.995415 0.0956535i \(-0.0304941\pi\)
\(200\) −1.82120e7 −2.27650
\(201\) 4.68274e6i 0.576649i
\(202\) 1.65300e6 0.200548
\(203\) 2.33832e6i 0.279522i
\(204\) 775166.i 0.0913070i
\(205\) 9.24650e6i 1.07329i
\(206\) 7.90196e6i 0.903927i
\(207\) 2.93297e6 372942.i 0.330671 0.0420465i
\(208\) −1.42210e7 −1.58030
\(209\) −8.45697e6 −0.926351
\(210\) −4.83937e6 −0.522554
\(211\) −3.83645e6 −0.408396 −0.204198 0.978930i \(-0.565459\pi\)
−0.204198 + 0.978930i \(0.565459\pi\)
\(212\) 1.74762e6i 0.183417i
\(213\) 1.62267e6 0.167916
\(214\) 7.13144e6i 0.727672i
\(215\) −2.26493e7 −2.27897
\(216\) −1.78204e6 −0.176830
\(217\) 7.75671e6i 0.759099i
\(218\) 1.44146e7i 1.39134i
\(219\) 7.27954e6 0.693061
\(220\) −1.82630e6 −0.171516
\(221\) 1.73214e7i 1.60475i
\(222\) 945250.i 0.0863949i
\(223\) −1.17209e7 −1.05693 −0.528466 0.848954i \(-0.677233\pi\)
−0.528466 + 0.848954i \(0.677233\pi\)
\(224\) 1.41189e6i 0.125620i
\(225\) −9.40711e6 −0.825865
\(226\) 4.80433e6i 0.416205i
\(227\) 319941.i 0.0273522i 0.999906 + 0.0136761i \(0.00435337\pi\)
−0.999906 + 0.0136761i \(0.995647\pi\)
\(228\) 1.33325e6i 0.112489i
\(229\) 1.58296e7i 1.31814i 0.752079 + 0.659072i \(0.229051\pi\)
−0.752079 + 0.659072i \(0.770949\pi\)
\(230\) 3.05459e6 + 2.40225e7i 0.251055 + 1.97440i
\(231\) 2.14011e6 0.173620
\(232\) 7.05251e6 0.564781
\(233\) −1.39552e7 −1.10323 −0.551616 0.834098i \(-0.685989\pi\)
−0.551616 + 0.834098i \(0.685989\pi\)
\(234\) −6.43319e6 −0.502086
\(235\) 3.36190e6i 0.259049i
\(236\) 1.58308e6 0.120439
\(237\) 1.21689e7i 0.914128i
\(238\) 7.43993e6 0.551871
\(239\) 1.19906e7 0.878309 0.439154 0.898412i \(-0.355278\pi\)
0.439154 + 0.898412i \(0.355278\pi\)
\(240\) 1.66659e7i 1.20558i
\(241\) 2.51859e7i 1.79931i 0.436598 + 0.899657i \(0.356183\pi\)
−0.436598 + 0.899657i \(0.643817\pi\)
\(242\) −8.51152e6 −0.600567
\(243\) −920483. −0.0641500
\(244\) 3.05428e6i 0.210252i
\(245\) 2.17531e7i 1.47919i
\(246\) 5.27957e6 0.354645
\(247\) 2.97922e7i 1.97702i
\(248\) −2.33947e7 −1.53378
\(249\) 9.49121e6i 0.614785i
\(250\) 4.59507e7i 2.94085i
\(251\) 3.11906e7i 1.97243i 0.165457 + 0.986217i \(0.447090\pi\)
−0.165457 + 0.986217i \(0.552910\pi\)
\(252\) 337391.i 0.0210830i
\(253\) −1.35082e6 1.06234e7i −0.0834136 0.655998i
\(254\) 1.98852e6 0.121347
\(255\) 2.02995e7 1.22423
\(256\) 6.87122e6 0.409556
\(257\) 1.48329e7 0.873829 0.436914 0.899503i \(-0.356071\pi\)
0.436914 + 0.899503i \(0.356071\pi\)
\(258\) 1.29323e7i 0.753037i
\(259\) 1.10776e6 0.0637595
\(260\) 6.43369e6i 0.366050i
\(261\) 3.64285e6 0.204890
\(262\) −8.73313e6 −0.485586
\(263\) 5.01534e6i 0.275698i 0.990453 + 0.137849i \(0.0440188\pi\)
−0.990453 + 0.137849i \(0.955981\pi\)
\(264\) 6.45469e6i 0.350803i
\(265\) 4.57655e7 2.45924
\(266\) 1.27964e7 0.679896
\(267\) 5.40015e6i 0.283708i
\(268\) 2.67396e6i 0.138916i
\(269\) 3.20238e7 1.64519 0.822596 0.568627i \(-0.192525\pi\)
0.822596 + 0.568627i \(0.192525\pi\)
\(270\) 7.53923e6i 0.383032i
\(271\) 4.61616e6 0.231939 0.115969 0.993253i \(-0.463003\pi\)
0.115969 + 0.993253i \(0.463003\pi\)
\(272\) 2.56218e7i 1.27322i
\(273\) 7.53917e6i 0.370540i
\(274\) 1.21217e7i 0.589267i
\(275\) 3.40733e7i 1.63838i
\(276\) −1.67480e6 + 212960.i −0.0796591 + 0.0101291i
\(277\) −1.97766e6 −0.0930490 −0.0465245 0.998917i \(-0.514815\pi\)
−0.0465245 + 0.998917i \(0.514815\pi\)
\(278\) 4.16213e6 0.193723
\(279\) −1.20841e7 −0.556420
\(280\) −1.71051e7 −0.779206
\(281\) 4.00608e7i 1.80551i −0.430154 0.902756i \(-0.641541\pi\)
0.430154 0.902756i \(-0.358459\pi\)
\(282\) −1.91958e6 −0.0855972
\(283\) 1.57392e7i 0.694422i 0.937787 + 0.347211i \(0.112871\pi\)
−0.937787 + 0.347211i \(0.887129\pi\)
\(284\) −926586. −0.0404511
\(285\) 3.49143e7 1.50823
\(286\) 2.33015e7i 0.996060i
\(287\) 6.18723e6i 0.261728i
\(288\) 2.19958e6 0.0920794
\(289\) −7.07033e6 −0.292918
\(290\) 2.98368e7i 1.22337i
\(291\) 1.07843e7i 0.437634i
\(292\) −4.15681e6 −0.166960
\(293\) 1.98649e7i 0.789740i −0.918737 0.394870i \(-0.870790\pi\)
0.918737 0.394870i \(-0.129210\pi\)
\(294\) 1.24206e7 0.488766
\(295\) 4.14567e7i 1.61484i
\(296\) 3.34106e6i 0.128828i
\(297\) 3.33406e6i 0.127263i
\(298\) 3.12100e7i 1.17936i
\(299\) 3.74242e7 4.75868e6i 1.40004 0.178022i
\(300\) 5.37171e6 0.198952
\(301\) −1.51556e7 −0.555742
\(302\) −4.91099e7 −1.78299
\(303\) 3.01792e6 0.108488
\(304\) 4.40685e7i 1.56858i
\(305\) 7.99832e7 2.81903
\(306\) 1.15906e7i 0.404522i
\(307\) −4.37453e7 −1.51188 −0.755938 0.654643i \(-0.772819\pi\)
−0.755938 + 0.654643i \(0.772819\pi\)
\(308\) −1.22206e6 −0.0418253
\(309\) 1.44268e7i 0.488984i
\(310\) 9.89753e7i 3.32232i
\(311\) 559668. 0.0186058 0.00930292 0.999957i \(-0.497039\pi\)
0.00930292 + 0.999957i \(0.497039\pi\)
\(312\) −2.27386e7 −0.748686
\(313\) 4.87636e7i 1.59024i 0.606451 + 0.795121i \(0.292592\pi\)
−0.606451 + 0.795121i \(0.707408\pi\)
\(314\) 177116.i 0.00572095i
\(315\) −8.83536e6 −0.282678
\(316\) 6.94877e6i 0.220215i
\(317\) 3.15059e7 0.989042 0.494521 0.869166i \(-0.335344\pi\)
0.494521 + 0.869166i \(0.335344\pi\)
\(318\) 2.61312e7i 0.812603i
\(319\) 1.31947e7i 0.406469i
\(320\) 5.04080e7i 1.53833i
\(321\) 1.30200e7i 0.393638i
\(322\) 2.04396e6 + 1.60745e7i 0.0612215 + 0.481470i
\(323\) −5.36764e7 −1.59285
\(324\) 525620. 0.0154538
\(325\) −1.20033e8 −3.49665
\(326\) 3.45496e7 0.997219
\(327\) 2.63171e7i 0.752653i
\(328\) 1.86611e7 0.528828
\(329\) 2.24960e6i 0.0631708i
\(330\) −2.73076e7 −0.759876
\(331\) 1.24947e7 0.344541 0.172270 0.985050i \(-0.444890\pi\)
0.172270 + 0.985050i \(0.444890\pi\)
\(332\) 5.41973e6i 0.148103i
\(333\) 1.72577e6i 0.0467358i
\(334\) 1.30067e7 0.349083
\(335\) 7.00239e7 1.86257
\(336\) 1.11519e7i 0.293989i
\(337\) 1.79945e7i 0.470166i −0.971975 0.235083i \(-0.924464\pi\)
0.971975 0.235083i \(-0.0755361\pi\)
\(338\) −4.08741e7 −1.05852
\(339\) 8.77138e6i 0.225148i
\(340\) −1.15915e7 −0.294920
\(341\) 4.37696e7i 1.10385i
\(342\) 1.99354e7i 0.498364i
\(343\) 3.29068e7i 0.815461i
\(344\) 4.57102e7i 1.12289i
\(345\) 5.57683e6 + 4.38584e7i 0.135810 + 1.06806i
\(346\) −5.61899e7 −1.35653
\(347\) 3.46526e7 0.829369 0.414685 0.909965i \(-0.363892\pi\)
0.414685 + 0.909965i \(0.363892\pi\)
\(348\) −2.08016e6 −0.0493583
\(349\) −9.71946e6 −0.228647 −0.114324 0.993444i \(-0.536470\pi\)
−0.114324 + 0.993444i \(0.536470\pi\)
\(350\) 5.15569e7i 1.20249i
\(351\) −1.17452e7 −0.271606
\(352\) 7.96705e6i 0.182671i
\(353\) −5.53376e7 −1.25805 −0.629023 0.777387i \(-0.716545\pi\)
−0.629023 + 0.777387i \(0.716545\pi\)
\(354\) 2.36710e7 0.533588
\(355\) 2.42648e7i 0.542364i
\(356\) 3.08363e6i 0.0683458i
\(357\) 1.35833e7 0.298538
\(358\) 2.56668e7 0.559400
\(359\) 2.79634e7i 0.604374i 0.953249 + 0.302187i \(0.0977167\pi\)
−0.953249 + 0.302187i \(0.902283\pi\)
\(360\) 2.66480e7i 0.571158i
\(361\) −4.52754e7 −0.962366
\(362\) 2.52648e7i 0.532588i
\(363\) −1.55397e7 −0.324880
\(364\) 4.30506e6i 0.0892638i
\(365\) 1.08855e8i 2.23857i
\(366\) 4.56689e7i 0.931488i
\(367\) 8.28559e7i 1.67620i 0.545518 + 0.838099i \(0.316333\pi\)
−0.545518 + 0.838099i \(0.683667\pi\)
\(368\) −5.53577e7 + 7.03902e6i −1.11080 + 0.141244i
\(369\) 9.63905e6 0.191847
\(370\) −1.41349e7 −0.279054
\(371\) 3.06236e7 0.599702
\(372\) 6.90036e6 0.134043
\(373\) 1.22033e7i 0.235153i 0.993064 + 0.117576i \(0.0375125\pi\)
−0.993064 + 0.117576i \(0.962488\pi\)
\(374\) 4.19821e7 0.802508
\(375\) 8.38934e7i 1.59087i
\(376\) −6.78491e6 −0.127638
\(377\) 4.64822e7 0.867487
\(378\) 5.04482e6i 0.0934051i
\(379\) 9.11449e7i 1.67423i −0.547028 0.837114i \(-0.684241\pi\)
0.547028 0.837114i \(-0.315759\pi\)
\(380\) −1.99370e7 −0.363336
\(381\) 3.63050e6 0.0656434
\(382\) 7.74716e6i 0.138980i
\(383\) 5.39033e7i 0.959442i −0.877421 0.479721i \(-0.840738\pi\)
0.877421 0.479721i \(-0.159262\pi\)
\(384\) 3.78126e7 0.667795
\(385\) 3.20023e7i 0.560789i
\(386\) −6.17235e7 −1.07322
\(387\) 2.36108e7i 0.407359i
\(388\) 6.15809e6i 0.105427i
\(389\) 3.68792e6i 0.0626517i 0.999509 + 0.0313258i \(0.00997295\pi\)
−0.999509 + 0.0313258i \(0.990027\pi\)
\(390\) 9.61994e7i 1.62173i
\(391\) −8.57368e6 6.74269e7i −0.143429 1.12798i
\(392\) 4.39015e7 0.728822
\(393\) −1.59443e7 −0.262680
\(394\) 3.61732e7 0.591423
\(395\) −1.81969e8 −2.95262
\(396\) 1.90383e6i 0.0306580i
\(397\) 4.27706e7 0.683556 0.341778 0.939781i \(-0.388971\pi\)
0.341778 + 0.939781i \(0.388971\pi\)
\(398\) 1.28724e7i 0.204178i
\(399\) 2.33627e7 0.367793
\(400\) 1.77553e8 2.77426
\(401\) 1.03595e8i 1.60659i −0.595581 0.803295i \(-0.703078\pi\)
0.595581 0.803295i \(-0.296922\pi\)
\(402\) 3.99823e7i 0.615445i
\(403\) −1.54192e8 −2.35584
\(404\) −1.72331e6 −0.0261348
\(405\) 1.37645e7i 0.207203i
\(406\) 1.99651e7i 0.298328i
\(407\) 6.25086e6 0.0927163
\(408\) 4.09679e7i 0.603203i
\(409\) 3.94971e7 0.577292 0.288646 0.957436i \(-0.406795\pi\)
0.288646 + 0.957436i \(0.406795\pi\)
\(410\) 7.89487e7i 1.14550i
\(411\) 2.21309e7i 0.318767i
\(412\) 8.23808e6i 0.117797i
\(413\) 2.77404e7i 0.393789i
\(414\) −2.50423e7 + 3.18426e6i −0.352918 + 0.0448754i
\(415\) −1.41928e8 −1.98574
\(416\) 2.80663e7 0.389857
\(417\) 7.59890e6 0.104796
\(418\) 7.22075e7 0.988675
\(419\) 4.99743e7i 0.679368i 0.940540 + 0.339684i \(0.110320\pi\)
−0.940540 + 0.339684i \(0.889680\pi\)
\(420\) 5.04522e6 0.0680977
\(421\) 2.83213e7i 0.379549i −0.981828 0.189774i \(-0.939224\pi\)
0.981828 0.189774i \(-0.0607756\pi\)
\(422\) 3.27565e7 0.435873
\(423\) −3.50463e6 −0.0463043
\(424\) 9.23628e7i 1.21171i
\(425\) 2.16263e8i 2.81719i
\(426\) −1.38547e7 −0.179213
\(427\) 5.35202e7 0.687439
\(428\) 7.43478e6i 0.0948281i
\(429\) 4.25421e7i 0.538824i
\(430\) 1.93385e8 2.43230
\(431\) 4.75872e7i 0.594372i −0.954820 0.297186i \(-0.903952\pi\)
0.954820 0.297186i \(-0.0960481\pi\)
\(432\) 1.73735e7 0.215494
\(433\) 9.11510e7i 1.12279i −0.827549 0.561394i \(-0.810265\pi\)
0.827549 0.561394i \(-0.189735\pi\)
\(434\) 6.62286e7i 0.810171i
\(435\) 5.44738e7i 0.661790i
\(436\) 1.50278e7i 0.181315i
\(437\) −1.47464e7 1.15972e8i −0.176702 1.38966i
\(438\) −6.21544e7 −0.739689
\(439\) 6.55753e7 0.775080 0.387540 0.921853i \(-0.373325\pi\)
0.387540 + 0.921853i \(0.373325\pi\)
\(440\) −9.65209e7 −1.13309
\(441\) 2.26766e7 0.264400
\(442\) 1.47895e8i 1.71272i
\(443\) −8.27131e7 −0.951400 −0.475700 0.879608i \(-0.657805\pi\)
−0.475700 + 0.879608i \(0.657805\pi\)
\(444\) 985458.i 0.0112587i
\(445\) 8.07518e7 0.916373
\(446\) 1.00076e8 1.12804
\(447\) 5.69808e7i 0.637979i
\(448\) 3.37302e7i 0.375132i
\(449\) 6.56635e7 0.725412 0.362706 0.931904i \(-0.381853\pi\)
0.362706 + 0.931904i \(0.381853\pi\)
\(450\) 8.03201e7 0.881428
\(451\) 3.49133e7i 0.380594i
\(452\) 5.00868e6i 0.0542386i
\(453\) −8.96612e7 −0.964517
\(454\) 2.73173e6i 0.0291924i
\(455\) −1.12738e8 −1.19684
\(456\) 7.04632e7i 0.743135i
\(457\) 1.41479e8i 1.48233i −0.671325 0.741163i \(-0.734274\pi\)
0.671325 0.741163i \(-0.265726\pi\)
\(458\) 1.35157e8i 1.40683i
\(459\) 2.11613e7i 0.218828i
\(460\) −3.18452e6 2.50443e7i −0.0327167 0.257298i
\(461\) 6.07075e7 0.619641 0.309820 0.950795i \(-0.399731\pi\)
0.309820 + 0.950795i \(0.399731\pi\)
\(462\) −1.82727e7 −0.185301
\(463\) −1.44944e8 −1.46035 −0.730176 0.683259i \(-0.760562\pi\)
−0.730176 + 0.683259i \(0.760562\pi\)
\(464\) −6.87563e7 −0.688270
\(465\) 1.80702e8i 1.79723i
\(466\) 1.19152e8 1.17746
\(467\) 4.86379e7i 0.477556i −0.971074 0.238778i \(-0.923253\pi\)
0.971074 0.238778i \(-0.0767468\pi\)
\(468\) 6.70683e6 0.0654304
\(469\) 4.68560e7 0.454199
\(470\) 2.87047e7i 0.276477i
\(471\) 323364.i 0.00309478i
\(472\) 8.36668e7 0.795660
\(473\) −8.55201e7 −0.808136
\(474\) 1.03901e8i 0.975629i
\(475\) 3.71964e8i 3.47072i
\(476\) −7.75639e6 −0.0719182
\(477\) 4.77084e7i 0.439582i
\(478\) −1.02379e8 −0.937401
\(479\) 1.16190e8i 1.05721i −0.848867 0.528607i \(-0.822715\pi\)
0.848867 0.528607i \(-0.177285\pi\)
\(480\) 3.28917e7i 0.297415i
\(481\) 2.20205e7i 0.197876i
\(482\) 2.15043e8i 1.92037i
\(483\) 3.73170e6 + 2.93476e7i 0.0331181 + 0.260454i
\(484\) 8.87357e6 0.0782641
\(485\) 1.61264e8 1.41355
\(486\) 7.85930e6 0.0684660
\(487\) 3.04632e7 0.263748 0.131874 0.991266i \(-0.457901\pi\)
0.131874 + 0.991266i \(0.457901\pi\)
\(488\) 1.61420e8i 1.38899i
\(489\) 6.30781e7 0.539451
\(490\) 1.85733e8i 1.57870i
\(491\) −8.17805e7 −0.690885 −0.345442 0.938440i \(-0.612271\pi\)
−0.345442 + 0.938440i \(0.612271\pi\)
\(492\) −5.50415e6 −0.0462163
\(493\) 8.37467e7i 0.698919i
\(494\) 2.54373e8i 2.11004i
\(495\) −4.98562e7 −0.411059
\(496\) 2.28080e8 1.86914
\(497\) 1.62366e7i 0.132259i
\(498\) 8.10381e7i 0.656147i
\(499\) 2.46779e8 1.98613 0.993063 0.117585i \(-0.0375154\pi\)
0.993063 + 0.117585i \(0.0375154\pi\)
\(500\) 4.79053e7i 0.383242i
\(501\) 2.37467e7 0.188838
\(502\) 2.66313e8i 2.10514i
\(503\) 4.84475e7i 0.380686i −0.981718 0.190343i \(-0.939040\pi\)
0.981718 0.190343i \(-0.0609600\pi\)
\(504\) 1.78313e7i 0.139281i
\(505\) 4.51288e7i 0.350413i
\(506\) 1.15336e7 + 9.07052e7i 0.0890256 + 0.700133i
\(507\) −7.46248e7 −0.572610
\(508\) −2.07311e6 −0.0158136
\(509\) −1.85245e8 −1.40473 −0.702365 0.711817i \(-0.747873\pi\)
−0.702365 + 0.711817i \(0.747873\pi\)
\(510\) −1.73322e8 −1.30660
\(511\) 7.28399e7i 0.545892i
\(512\) 9.65755e7 0.719544
\(513\) 3.63966e7i 0.269593i
\(514\) −1.26647e8 −0.932619
\(515\) 2.15733e8 1.57941
\(516\) 1.34824e7i 0.0981336i
\(517\) 1.26940e7i 0.0918603i
\(518\) −9.45828e6 −0.0680492
\(519\) −1.02587e8 −0.733822
\(520\) 3.40024e8i 2.41824i
\(521\) 6.41523e7i 0.453627i 0.973938 + 0.226814i \(0.0728309\pi\)
−0.973938 + 0.226814i \(0.927169\pi\)
\(522\) −3.11035e7 −0.218674
\(523\) 1.79460e8i 1.25448i 0.778826 + 0.627240i \(0.215815\pi\)
−0.778826 + 0.627240i \(0.784185\pi\)
\(524\) 9.10461e6 0.0632801
\(525\) 9.41286e7i 0.650495i
\(526\) 4.28222e7i 0.294246i
\(527\) 2.77806e8i 1.89806i
\(528\) 6.29280e7i 0.427506i
\(529\) 1.43325e8 3.70481e7i 0.968178 0.250264i
\(530\) −3.90756e8 −2.62469
\(531\) 4.32167e7 0.288647
\(532\) −1.33407e7 −0.0886020
\(533\) 1.22993e8 0.812265
\(534\) 4.61078e7i 0.302796i
\(535\) −1.94697e8 −1.27144
\(536\) 1.41320e8i 0.917721i
\(537\) 4.68605e7 0.302610
\(538\) −2.73427e8 −1.75588
\(539\) 8.21363e7i 0.524528i
\(540\) 7.85992e6i 0.0499156i
\(541\) −6.40754e7 −0.404669 −0.202334 0.979316i \(-0.564853\pi\)
−0.202334 + 0.979316i \(0.564853\pi\)
\(542\) −3.94139e7 −0.247543
\(543\) 4.61266e7i 0.288106i
\(544\) 5.05669e7i 0.314101i
\(545\) 3.93536e8 2.43106
\(546\) 6.43712e7i 0.395470i
\(547\) −2.23997e8 −1.36861 −0.684307 0.729194i \(-0.739895\pi\)
−0.684307 + 0.729194i \(0.739895\pi\)
\(548\) 1.26373e7i 0.0767915i
\(549\) 8.33788e7i 0.503894i
\(550\) 2.90926e8i 1.74861i
\(551\) 1.44041e8i 0.861056i
\(552\) −8.85140e7 + 1.12550e7i −0.526253 + 0.0669159i
\(553\) −1.21764e8 −0.720016
\(554\) 1.68857e7 0.0993092
\(555\) −2.58065e7 −0.150956
\(556\) −4.33917e6 −0.0252454
\(557\) 7.97533e6i 0.0461512i 0.999734 + 0.0230756i \(0.00734584\pi\)
−0.999734 + 0.0230756i \(0.992654\pi\)
\(558\) 1.03177e8 0.593856
\(559\) 3.01270e8i 1.72473i
\(560\) 1.66761e8 0.949579
\(561\) 7.66477e7 0.434121
\(562\) 3.42048e8i 1.92698i
\(563\) 1.94553e8i 1.09022i −0.838366 0.545108i \(-0.816489\pi\)
0.838366 0.545108i \(-0.183511\pi\)
\(564\) 2.00124e6 0.0111548
\(565\) −1.31164e8 −0.727225
\(566\) 1.34385e8i 0.741142i
\(567\) 9.21045e6i 0.0505280i
\(568\) −4.89706e7 −0.267233
\(569\) 1.28517e8i 0.697626i −0.937192 0.348813i \(-0.886585\pi\)
0.937192 0.348813i \(-0.113415\pi\)
\(570\) −2.98106e8 −1.60971
\(571\) 4.75561e7i 0.255445i −0.991810 0.127723i \(-0.959233\pi\)
0.991810 0.127723i \(-0.0407667\pi\)
\(572\) 2.42926e7i 0.129804i
\(573\) 1.41442e7i 0.0751820i
\(574\) 5.28280e7i 0.279337i
\(575\) −4.67252e8 + 5.94135e7i −2.45780 + 0.312523i
\(576\) 5.25480e7 0.274972
\(577\) 2.94461e7 0.153285 0.0766425 0.997059i \(-0.475580\pi\)
0.0766425 + 0.997059i \(0.475580\pi\)
\(578\) 6.03681e7 0.312625
\(579\) −1.12690e8 −0.580564
\(580\) 3.11060e7i 0.159426i
\(581\) −9.49701e7 −0.484237
\(582\) 9.20785e7i 0.467078i
\(583\) 1.72803e8 0.872060
\(584\) −2.19689e8 −1.10299
\(585\) 1.75634e8i 0.877283i
\(586\) 1.69611e8i 0.842873i
\(587\) 1.53077e8 0.756824 0.378412 0.925637i \(-0.376470\pi\)
0.378412 + 0.925637i \(0.376470\pi\)
\(588\) −1.29489e7 −0.0636945
\(589\) 4.77815e8i 2.33838i
\(590\) 3.53967e8i 1.72348i
\(591\) 6.60423e7 0.319934
\(592\) 3.25726e7i 0.156996i
\(593\) −2.42998e7 −0.116530 −0.0582651 0.998301i \(-0.518557\pi\)
−0.0582651 + 0.998301i \(0.518557\pi\)
\(594\) 2.84670e7i 0.135826i
\(595\) 2.03119e8i 0.964271i
\(596\) 3.25375e7i 0.153690i
\(597\) 2.35014e7i 0.110451i
\(598\) −3.19536e8 + 4.06307e7i −1.49423 + 0.189999i
\(599\) −3.22739e7 −0.150166 −0.0750828 0.997177i \(-0.523922\pi\)
−0.0750828 + 0.997177i \(0.523922\pi\)
\(600\) 2.83898e8 1.31434
\(601\) 9.65355e7 0.444697 0.222348 0.974967i \(-0.428628\pi\)
0.222348 + 0.974967i \(0.428628\pi\)
\(602\) 1.29402e8 0.593132
\(603\) 7.29966e7i 0.332928i
\(604\) 5.11989e7 0.232354
\(605\) 2.32375e8i 1.04936i
\(606\) −2.57677e7 −0.115786
\(607\) 1.84789e8 0.826248 0.413124 0.910675i \(-0.364438\pi\)
0.413124 + 0.910675i \(0.364438\pi\)
\(608\) 8.69730e7i 0.386967i
\(609\) 3.64508e7i 0.161382i
\(610\) −6.82916e8 −3.00869
\(611\) −4.47186e7 −0.196049
\(612\) 1.20836e7i 0.0527161i
\(613\) 3.35927e8i 1.45836i −0.684324 0.729178i \(-0.739903\pi\)
0.684324 0.729178i \(-0.260097\pi\)
\(614\) 3.73507e8 1.61359
\(615\) 1.44139e8i 0.619662i
\(616\) −6.45863e7 −0.276311
\(617\) 5.50327e7i 0.234296i 0.993114 + 0.117148i \(0.0373752\pi\)
−0.993114 + 0.117148i \(0.962625\pi\)
\(618\) 1.23179e8i 0.521882i
\(619\) 2.90917e7i 0.122658i −0.998118 0.0613291i \(-0.980466\pi\)
0.998118 0.0613291i \(-0.0195339\pi\)
\(620\) 1.03185e8i 0.432955i
\(621\) −4.57204e7 + 5.81359e6i −0.190913 + 0.0242756i
\(622\) −4.77857e6 −0.0198576
\(623\) 5.40345e7 0.223464
\(624\) 2.21683e8 0.912386
\(625\) 6.49628e8 2.66088
\(626\) 4.16355e8i 1.69723i
\(627\) 1.31831e8 0.534829
\(628\) 184650.i 0.000745537i
\(629\) 3.96742e7 0.159425
\(630\) 7.54384e7 0.301697
\(631\) 1.47047e8i 0.585285i −0.956222 0.292642i \(-0.905465\pi\)
0.956222 0.292642i \(-0.0945345\pi\)
\(632\) 3.67246e8i 1.45481i
\(633\) 5.98043e7 0.235788
\(634\) −2.69005e8 −1.05558
\(635\) 5.42891e7i 0.212027i
\(636\) 2.72427e7i 0.105896i
\(637\) 2.89350e8 1.11945
\(638\) 1.12659e8i 0.433815i
\(639\) −2.52949e7 −0.0969461
\(640\) 5.65436e8i 2.15697i
\(641\) 3.77045e8i 1.43159i 0.698309 + 0.715796i \(0.253936\pi\)
−0.698309 + 0.715796i \(0.746064\pi\)
\(642\) 1.11168e8i 0.420122i
\(643\) 2.19355e8i 0.825116i −0.910931 0.412558i \(-0.864635\pi\)
0.910931 0.412558i \(-0.135365\pi\)
\(644\) −2.13090e6 1.67582e7i −0.00797820 0.0627438i
\(645\) 3.53067e8 1.31576
\(646\) 4.58301e8 1.70002
\(647\) 1.87104e8 0.690829 0.345415 0.938450i \(-0.387738\pi\)
0.345415 + 0.938450i \(0.387738\pi\)
\(648\) 2.77793e7 0.102093
\(649\) 1.56534e8i 0.572630i
\(650\) 1.02487e9 3.73190
\(651\) 1.20915e8i 0.438266i
\(652\) −3.60192e7 −0.129955
\(653\) 4.22342e7 0.151679 0.0758394 0.997120i \(-0.475836\pi\)
0.0758394 + 0.997120i \(0.475836\pi\)
\(654\) 2.24702e8i 0.803291i
\(655\) 2.38425e8i 0.848453i
\(656\) −1.81930e8 −0.644456
\(657\) −1.13477e8 −0.400139
\(658\) 1.92076e7i 0.0674209i
\(659\) 3.47285e8i 1.21347i −0.794904 0.606736i \(-0.792479\pi\)
0.794904 0.606736i \(-0.207521\pi\)
\(660\) 2.84692e7 0.0990247
\(661\) 4.59695e7i 0.159172i 0.996828 + 0.0795858i \(0.0253598\pi\)
−0.996828 + 0.0795858i \(0.974640\pi\)
\(662\) −1.06682e8 −0.367721
\(663\) 2.70015e8i 0.926503i
\(664\) 2.86435e8i 0.978414i
\(665\) 3.49356e8i 1.18797i
\(666\) 1.47350e7i 0.0498801i
\(667\) 1.80941e8 2.30075e7i 0.609759 0.0775341i
\(668\) −1.35600e7 −0.0454914
\(669\) 1.82711e8 0.610221
\(670\) −5.97880e8 −1.98788
\(671\) 3.02004e8 0.999645
\(672\) 2.20093e7i 0.0725266i
\(673\) 3.08900e8 1.01338 0.506690 0.862128i \(-0.330869\pi\)
0.506690 + 0.862128i \(0.330869\pi\)
\(674\) 1.53642e8i 0.501798i
\(675\) 1.46642e8 0.476813
\(676\) 4.26127e7 0.137943
\(677\) 4.53814e8i 1.46255i 0.682080 + 0.731277i \(0.261075\pi\)
−0.682080 + 0.731277i \(0.738925\pi\)
\(678\) 7.48921e7i 0.240296i
\(679\) 1.07909e8 0.344704
\(680\) −6.12619e8 −1.94833
\(681\) 4.98738e6i 0.0157918i
\(682\) 3.73715e8i 1.17812i
\(683\) −5.29830e8 −1.66293 −0.831466 0.555576i \(-0.812498\pi\)
−0.831466 + 0.555576i \(0.812498\pi\)
\(684\) 2.07834e7i 0.0649453i
\(685\) −3.30937e8 −1.02961
\(686\) 2.80966e8i 0.870325i
\(687\) 2.46759e8i 0.761031i
\(688\) 4.45637e8i 1.36841i
\(689\) 6.08752e8i 1.86116i
\(690\) −4.76163e7 3.74474e8i −0.144947 1.13992i
\(691\) −1.82674e8 −0.553659 −0.276830 0.960919i \(-0.589284\pi\)
−0.276830 + 0.960919i \(0.589284\pi\)
\(692\) 5.85799e7 0.176779
\(693\) −3.33610e7 −0.100239
\(694\) −2.95872e8 −0.885168
\(695\) 1.13631e8i 0.338488i
\(696\) −1.09938e8 −0.326076
\(697\) 2.21595e8i 0.654428i
\(698\) 8.29870e7 0.244030
\(699\) 2.17539e8 0.636951
\(700\) 5.37499e7i 0.156705i
\(701\) 3.20737e8i 0.931098i −0.885022 0.465549i \(-0.845857\pi\)
0.885022 0.465549i \(-0.154143\pi\)
\(702\) 1.00283e8 0.289880
\(703\) 6.82381e7 0.196409
\(704\) 1.90333e8i 0.545501i
\(705\) 5.24069e7i 0.149562i
\(706\) 4.72485e8 1.34269
\(707\) 3.01977e7i 0.0854506i
\(708\) −2.46778e7 −0.0695356
\(709\) 6.61878e8i 1.85712i 0.371186 + 0.928559i \(0.378951\pi\)
−0.371186 + 0.928559i \(0.621049\pi\)
\(710\) 2.07178e8i 0.578854i
\(711\) 1.89695e8i 0.527772i
\(712\) 1.62971e8i 0.451514i
\(713\) −6.00219e8 + 7.63210e7i −1.65593 + 0.210560i
\(714\) −1.15977e8 −0.318623
\(715\) −6.36158e8 −1.74039
\(716\) −2.67585e7 −0.0728993
\(717\) −1.86915e8 −0.507092
\(718\) 2.38758e8i 0.645036i
\(719\) −3.51124e8 −0.944656 −0.472328 0.881423i \(-0.656586\pi\)
−0.472328 + 0.881423i \(0.656586\pi\)
\(720\) 2.59796e8i 0.696042i
\(721\) 1.44356e8 0.385150
\(722\) 3.86572e8 1.02711
\(723\) 3.92610e8i 1.03883i
\(724\) 2.63395e7i 0.0694052i
\(725\) −5.80344e8 −1.52290
\(726\) 1.32682e8 0.346737
\(727\) 6.22025e8i 1.61884i 0.587229 + 0.809421i \(0.300219\pi\)
−0.587229 + 0.809421i \(0.699781\pi\)
\(728\) 2.27525e8i 0.589705i
\(729\) 1.43489e7 0.0370370
\(730\) 9.29433e8i 2.38918i
\(731\) −5.42796e8 −1.38958
\(732\) 4.76115e7i 0.121389i
\(733\) 4.80767e7i 0.122074i −0.998136 0.0610369i \(-0.980559\pi\)
0.998136 0.0610369i \(-0.0194407\pi\)
\(734\) 7.07443e8i 1.78897i
\(735\) 3.39097e8i 0.854008i
\(736\) 1.09253e8 1.38921e7i 0.274032 0.0348446i
\(737\) 2.64399e8 0.660477
\(738\) −8.23004e7 −0.204754
\(739\) −2.92154e8 −0.723901 −0.361951 0.932197i \(-0.617889\pi\)
−0.361951 + 0.932197i \(0.617889\pi\)
\(740\) 1.47362e7 0.0363655
\(741\) 4.64415e8i 1.14144i
\(742\) −2.61472e8 −0.640049
\(743\) 1.89488e8i 0.461971i 0.972957 + 0.230985i \(0.0741949\pi\)
−0.972957 + 0.230985i \(0.925805\pi\)
\(744\) 3.64687e8 0.885528
\(745\) −8.52070e8 −2.06066
\(746\) 1.04194e8i 0.250973i
\(747\) 1.47953e8i 0.354946i
\(748\) −4.37678e7 −0.104580
\(749\) −1.30280e8 −0.310050
\(750\) 7.16301e8i 1.69790i
\(751\) 1.03335e7i 0.0243965i 0.999926 + 0.0121982i \(0.00388291\pi\)
−0.999926 + 0.0121982i \(0.996117\pi\)
\(752\) 6.61474e7 0.155546
\(753\) 4.86213e8i 1.13879i
\(754\) −3.96876e8 −0.925851
\(755\) 1.34076e9i 3.11537i
\(756\) 5.25941e6i 0.0121723i
\(757\) 7.76020e7i 0.178890i −0.995992 0.0894448i \(-0.971491\pi\)
0.995992 0.0894448i \(-0.0285093\pi\)
\(758\) 7.78216e8i 1.78687i
\(759\) 2.10573e7 + 1.65603e8i 0.0481589 + 0.378741i
\(760\) −1.05368e9 −2.40031
\(761\) 6.53691e8 1.48326 0.741632 0.670807i \(-0.234052\pi\)
0.741632 + 0.670807i \(0.234052\pi\)
\(762\) −3.09980e7 −0.0700598
\(763\) 2.63332e8 0.592830
\(764\) 8.07670e6i 0.0181115i
\(765\) −3.16438e8 −0.706812
\(766\) 4.60239e8i 1.02399i
\(767\) 5.51438e8 1.22211
\(768\) −1.07112e8 −0.236458
\(769\) 9.05773e8i 1.99177i −0.0906001 0.995887i \(-0.528879\pi\)
0.0906001 0.995887i \(-0.471121\pi\)
\(770\) 2.73243e8i 0.598518i
\(771\) −2.31222e8 −0.504505
\(772\) 6.43490e7 0.139859
\(773\) 4.32370e7i 0.0936088i 0.998904 + 0.0468044i \(0.0149037\pi\)
−0.998904 + 0.0468044i \(0.985096\pi\)
\(774\) 2.01594e8i 0.434766i
\(775\) 1.92513e9 4.13575
\(776\) 3.25459e8i 0.696483i
\(777\) −1.72682e7 −0.0368116
\(778\) 3.14883e7i 0.0668668i
\(779\) 3.81135e8i 0.806244i
\(780\) 1.00291e8i 0.211339i
\(781\) 9.16200e7i 0.192326i
\(782\) 7.32041e7 + 5.75706e8i 0.153079 + 1.20387i
\(783\) −5.67864e7 −0.118293
\(784\) −4.28005e8 −0.888179