Properties

Label 177.9.c.a.58.13
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.13
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.68

$q$-expansion

\(f(q)\) \(=\) \(q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} -22054.7i q^{10} +8879.23i q^{11} -14559.6 q^{12} +30696.0i q^{13} +75662.2i q^{14} +43301.9 q^{15} -48309.2 q^{16} -7149.59 q^{17} -52091.6i q^{18} -83033.0 q^{19} -288275. q^{20} -148554. q^{21} +211492. q^{22} +117469. i q^{23} +61634.5i q^{24} +466740. q^{25} +731139. q^{26} +102276. q^{27} +988973. q^{28} -1.19671e6 q^{29} -1.03140e6i q^{30} +138856. i q^{31} +1.48806e6i q^{32} +415240. i q^{33} +170294. i q^{34} -2.94133e6 q^{35} -680884. q^{36} -1.23654e6i q^{37} +1.97774e6i q^{38} +1.43551e6i q^{39} +1.22034e6i q^{40} -1.16558e6 q^{41} +3.53837e6i q^{42} +3.96763e6i q^{43} -2.76439e6i q^{44} +2.02503e6 q^{45} +2.79798e6 q^{46} +3.87623e6i q^{47} -2.25920e6 q^{48} +4.32588e6 q^{49} -1.11172e7i q^{50} -334353. q^{51} -9.55665e6i q^{52} -9.23542e6 q^{53} -2.43608e6i q^{54} +8.22163e6i q^{55} -4.18658e6i q^{56} -3.88307e6 q^{57} +2.85042e7i q^{58} +(-1.00090e7 + 6.83014e6i) q^{59} -1.34813e7 q^{60} +1.02656e7i q^{61} +3.30737e6 q^{62} -6.94719e6 q^{63} +2.30766e7 q^{64} +2.84226e7i q^{65} +9.89050e6 q^{66} +1.75285e7i q^{67} +2.22590e6 q^{68} +5.49350e6i q^{69} +7.00587e7i q^{70} +8.47639e6 q^{71} +2.88236e6i q^{72} +2.09288e7i q^{73} -2.94529e7 q^{74} +2.18273e7 q^{75} +2.58509e7 q^{76} -2.82056e7i q^{77} +3.41920e7 q^{78} +2.15211e7 q^{79} -4.47314e7 q^{80} +4.78297e6 q^{81} +2.77625e7i q^{82} -6.11488e7i q^{83} +4.62497e7 q^{84} -6.62010e6 q^{85} +9.45039e7 q^{86} -5.59647e7 q^{87} -1.17024e7 q^{88} -2.64859e7i q^{89} -4.82337e7i q^{90} -9.75082e7i q^{91} -3.65721e7i q^{92} +6.49365e6i q^{93} +9.23270e7 q^{94} -7.68836e7 q^{95} +6.95897e7i q^{96} -6.83477e7i q^{97} -1.03037e8i q^{98} +1.94189e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.8187i 1.48867i −0.667806 0.744336i \(-0.732766\pi\)
0.667806 0.744336i \(-0.267234\pi\)
\(3\) 46.7654 0.577350
\(4\) −311.333 −1.21614
\(5\) 925.940 1.48150 0.740752 0.671779i \(-0.234469\pi\)
0.740752 + 0.671779i \(0.234469\pi\)
\(6\) 1113.89i 0.859485i
\(7\) −3176.58 −1.32302 −0.661512 0.749934i \(-0.730085\pi\)
−0.661512 + 0.749934i \(0.730085\pi\)
\(8\) 1317.95i 0.321765i
\(9\) 2187.00 0.333333
\(10\) 22054.7i 2.20547i
\(11\) 8879.23i 0.606463i 0.952917 + 0.303232i \(0.0980656\pi\)
−0.952917 + 0.303232i \(0.901934\pi\)
\(12\) −14559.6 −0.702140
\(13\) 30696.0i 1.07475i 0.843343 + 0.537375i \(0.180584\pi\)
−0.843343 + 0.537375i \(0.819416\pi\)
\(14\) 75662.2i 1.96955i
\(15\) 43301.9 0.855347
\(16\) −48309.2 −0.737140
\(17\) −7149.59 −0.0856024 −0.0428012 0.999084i \(-0.513628\pi\)
−0.0428012 + 0.999084i \(0.513628\pi\)
\(18\) 52091.6i 0.496224i
\(19\) −83033.0 −0.637142 −0.318571 0.947899i \(-0.603203\pi\)
−0.318571 + 0.947899i \(0.603203\pi\)
\(20\) −288275. −1.80172
\(21\) −148554. −0.763849
\(22\) 211492. 0.902824
\(23\) 117469.i 0.419772i 0.977726 + 0.209886i \(0.0673093\pi\)
−0.977726 + 0.209886i \(0.932691\pi\)
\(24\) 61634.5i 0.185771i
\(25\) 466740. 1.19485
\(26\) 731139. 1.59995
\(27\) 102276. 0.192450
\(28\) 988973. 1.60899
\(29\) −1.19671e6 −1.69199 −0.845996 0.533190i \(-0.820993\pi\)
−0.845996 + 0.533190i \(0.820993\pi\)
\(30\) 1.03140e6i 1.27333i
\(31\) 138856.i 0.150355i 0.997170 + 0.0751774i \(0.0239523\pi\)
−0.997170 + 0.0751774i \(0.976048\pi\)
\(32\) 1.48806e6i 1.41912i
\(33\) 415240.i 0.350142i
\(34\) 170294.i 0.127434i
\(35\) −2.94133e6 −1.96007
\(36\) −680884. −0.405381
\(37\) 1.23654e6i 0.659784i −0.944019 0.329892i \(-0.892988\pi\)
0.944019 0.329892i \(-0.107012\pi\)
\(38\) 1.97774e6i 0.948496i
\(39\) 1.43551e6i 0.620508i
\(40\) 1.22034e6i 0.476697i
\(41\) −1.16558e6 −0.412482 −0.206241 0.978501i \(-0.566123\pi\)
−0.206241 + 0.978501i \(0.566123\pi\)
\(42\) 3.53837e6i 1.13712i
\(43\) 3.96763e6i 1.16053i 0.814427 + 0.580266i \(0.197051\pi\)
−0.814427 + 0.580266i \(0.802949\pi\)
\(44\) 2.76439e6i 0.737546i
\(45\) 2.02503e6 0.493835
\(46\) 2.79798e6 0.624903
\(47\) 3.87623e6i 0.794362i 0.917740 + 0.397181i \(0.130012\pi\)
−0.917740 + 0.397181i \(0.869988\pi\)
\(48\) −2.25920e6 −0.425588
\(49\) 4.32588e6 0.750395
\(50\) 1.11172e7i 1.77875i
\(51\) −334353. −0.0494225
\(52\) 9.55665e6i 1.30705i
\(53\) −9.23542e6 −1.17045 −0.585225 0.810871i \(-0.698994\pi\)
−0.585225 + 0.810871i \(0.698994\pi\)
\(54\) 2.43608e6i 0.286495i
\(55\) 8.22163e6i 0.898478i
\(56\) 4.18658e6i 0.425704i
\(57\) −3.88307e6 −0.367854
\(58\) 2.85042e7i 2.51882i
\(59\) −1.00090e7 + 6.83014e6i −0.826003 + 0.563666i
\(60\) −1.34813e7 −1.04022
\(61\) 1.02656e7i 0.741419i 0.928749 + 0.370710i \(0.120886\pi\)
−0.928749 + 0.370710i \(0.879114\pi\)
\(62\) 3.30737e6 0.223829
\(63\) −6.94719e6 −0.441008
\(64\) 2.30766e7 1.37547
\(65\) 2.84226e7i 1.59225i
\(66\) 9.89050e6 0.521246
\(67\) 1.75285e7i 0.869851i 0.900466 + 0.434926i \(0.143225\pi\)
−0.900466 + 0.434926i \(0.856775\pi\)
\(68\) 2.22590e6 0.104105
\(69\) 5.49350e6i 0.242356i
\(70\) 7.00587e7i 2.91790i
\(71\) 8.47639e6 0.333563 0.166781 0.985994i \(-0.446663\pi\)
0.166781 + 0.985994i \(0.446663\pi\)
\(72\) 2.88236e6i 0.107255i
\(73\) 2.09288e7i 0.736976i 0.929633 + 0.368488i \(0.120124\pi\)
−0.929633 + 0.368488i \(0.879876\pi\)
\(74\) −2.94529e7 −0.982201
\(75\) 2.18273e7 0.689849
\(76\) 2.58509e7 0.774856
\(77\) 2.82056e7i 0.802366i
\(78\) 3.41920e7 0.923732
\(79\) 2.15211e7 0.552531 0.276265 0.961081i \(-0.410903\pi\)
0.276265 + 0.961081i \(0.410903\pi\)
\(80\) −4.47314e7 −1.09208
\(81\) 4.78297e6 0.111111
\(82\) 2.77625e7i 0.614050i
\(83\) 6.11488e7i 1.28847i −0.764826 0.644237i \(-0.777175\pi\)
0.764826 0.644237i \(-0.222825\pi\)
\(84\) 4.62497e7 0.928949
\(85\) −6.62010e6 −0.126820
\(86\) 9.45039e7 1.72765
\(87\) −5.59647e7 −0.976872
\(88\) −1.17024e7 −0.195139
\(89\) 2.64859e7i 0.422138i −0.977471 0.211069i \(-0.932306\pi\)
0.977471 0.211069i \(-0.0676944\pi\)
\(90\) 4.82337e7i 0.735158i
\(91\) 9.75082e7i 1.42192i
\(92\) 3.65721e7i 0.510503i
\(93\) 6.49365e6i 0.0868074i
\(94\) 9.23270e7 1.18254
\(95\) −7.68836e7 −0.943929
\(96\) 6.95897e7i 0.819332i
\(97\) 6.83477e7i 0.772035i −0.922491 0.386017i \(-0.873850\pi\)
0.922491 0.386017i \(-0.126150\pi\)
\(98\) 1.03037e8i 1.11709i
\(99\) 1.94189e7i 0.202154i
\(100\) −1.45311e8 −1.45311
\(101\) 1.43956e8i 1.38339i 0.722189 + 0.691696i \(0.243136\pi\)
−0.722189 + 0.691696i \(0.756864\pi\)
\(102\) 7.96388e6i 0.0735739i
\(103\) 9.23448e7i 0.820471i −0.911980 0.410236i \(-0.865446\pi\)
0.911980 0.410236i \(-0.134554\pi\)
\(104\) −4.04558e7 −0.345818
\(105\) −1.37552e8 −1.13165
\(106\) 2.19976e8i 1.74242i
\(107\) 8.88588e7 0.677899 0.338950 0.940805i \(-0.389928\pi\)
0.338950 + 0.940805i \(0.389928\pi\)
\(108\) −3.18418e7 −0.234047
\(109\) 2.61781e8i 1.85452i −0.374414 0.927262i \(-0.622156\pi\)
0.374414 0.927262i \(-0.377844\pi\)
\(110\) 1.95829e8 1.33754
\(111\) 5.78273e7i 0.380926i
\(112\) 1.53458e8 0.975254
\(113\) 6.11567e7i 0.375086i −0.982256 0.187543i \(-0.939948\pi\)
0.982256 0.187543i \(-0.0600523\pi\)
\(114\) 9.24899e7i 0.547614i
\(115\) 1.08770e8i 0.621894i
\(116\) 3.72576e8 2.05770
\(117\) 6.71321e7i 0.358250i
\(118\) 1.62685e8 + 2.38401e8i 0.839113 + 1.22965i
\(119\) 2.27113e7 0.113254
\(120\) 5.70698e7i 0.275221i
\(121\) 1.35518e8 0.632203
\(122\) 2.44513e8 1.10373
\(123\) −5.45086e7 −0.238147
\(124\) 4.32304e7i 0.182853i
\(125\) 7.04779e7 0.288677
\(126\) 1.65473e8i 0.656516i
\(127\) −1.68592e8 −0.648070 −0.324035 0.946045i \(-0.605040\pi\)
−0.324035 + 0.946045i \(0.605040\pi\)
\(128\) 1.68711e8i 0.628499i
\(129\) 1.85548e8i 0.670034i
\(130\) 6.76991e8 2.37033
\(131\) 1.64969e8i 0.560165i 0.959976 + 0.280083i \(0.0903619\pi\)
−0.959976 + 0.280083i \(0.909638\pi\)
\(132\) 1.29278e8i 0.425822i
\(133\) 2.63761e8 0.842955
\(134\) 4.17506e8 1.29492
\(135\) 9.47013e7 0.285116
\(136\) 9.42282e6i 0.0275439i
\(137\) 6.18803e6 0.0175659 0.00878295 0.999961i \(-0.497204\pi\)
0.00878295 + 0.999961i \(0.497204\pi\)
\(138\) 1.30848e8 0.360788
\(139\) 5.51090e8 1.47626 0.738131 0.674658i \(-0.235709\pi\)
0.738131 + 0.674658i \(0.235709\pi\)
\(140\) 9.15730e8 2.38372
\(141\) 1.81274e8i 0.458625i
\(142\) 2.01897e8i 0.496565i
\(143\) −2.72556e8 −0.651797
\(144\) −1.05652e8 −0.245713
\(145\) −1.10808e9 −2.50669
\(146\) 4.98498e8 1.09711
\(147\) 2.02301e8 0.433241
\(148\) 3.84975e8i 0.802391i
\(149\) 2.41337e7i 0.0489642i −0.999700 0.0244821i \(-0.992206\pi\)
0.999700 0.0244821i \(-0.00779367\pi\)
\(150\) 5.19898e8i 1.02696i
\(151\) 7.10939e8i 1.36749i 0.729721 + 0.683745i \(0.239650\pi\)
−0.729721 + 0.683745i \(0.760350\pi\)
\(152\) 1.09433e8i 0.205010i
\(153\) −1.56362e7 −0.0285341
\(154\) −6.71822e8 −1.19446
\(155\) 1.28572e8i 0.222751i
\(156\) 4.46920e8i 0.754626i
\(157\) 3.99591e8i 0.657684i −0.944385 0.328842i \(-0.893342\pi\)
0.944385 0.328842i \(-0.106658\pi\)
\(158\) 5.12606e8i 0.822537i
\(159\) −4.31898e8 −0.675760
\(160\) 1.37785e9i 2.10244i
\(161\) 3.73152e8i 0.555369i
\(162\) 1.13924e8i 0.165408i
\(163\) −3.44412e8 −0.487896 −0.243948 0.969788i \(-0.578443\pi\)
−0.243948 + 0.969788i \(0.578443\pi\)
\(164\) 3.62882e8 0.501637
\(165\) 3.84488e8i 0.518736i
\(166\) −1.45649e9 −1.91811
\(167\) 7.07060e8 0.909055 0.454528 0.890733i \(-0.349808\pi\)
0.454528 + 0.890733i \(0.349808\pi\)
\(168\) 1.95787e8i 0.245780i
\(169\) −1.26511e8 −0.155089
\(170\) 1.57682e8i 0.188794i
\(171\) −1.81593e8 −0.212381
\(172\) 1.23525e9i 1.41137i
\(173\) 1.20190e9i 1.34179i 0.741552 + 0.670896i \(0.234090\pi\)
−0.741552 + 0.670896i \(0.765910\pi\)
\(174\) 1.33301e9i 1.45424i
\(175\) −1.48264e9 −1.58082
\(176\) 4.28948e8i 0.447048i
\(177\) −4.68074e8 + 3.19414e8i −0.476893 + 0.325432i
\(178\) −6.30860e8 −0.628424
\(179\) 2.78198e8i 0.270983i −0.990778 0.135492i \(-0.956739\pi\)
0.990778 0.135492i \(-0.0432614\pi\)
\(180\) −6.30458e8 −0.600573
\(181\) −1.66642e9 −1.55264 −0.776318 0.630341i \(-0.782915\pi\)
−0.776318 + 0.630341i \(0.782915\pi\)
\(182\) −2.32252e9 −2.11677
\(183\) 4.80073e8i 0.428059i
\(184\) −1.54819e8 −0.135068
\(185\) 1.14496e9i 0.977472i
\(186\) 1.54671e8 0.129228
\(187\) 6.34829e7i 0.0519147i
\(188\) 1.20680e9i 0.966058i
\(189\) −3.24888e8 −0.254616
\(190\) 1.83127e9i 1.40520i
\(191\) 1.72448e9i 1.29576i −0.761741 0.647882i \(-0.775655\pi\)
0.761741 0.647882i \(-0.224345\pi\)
\(192\) 1.07918e9 0.794128
\(193\) −1.65533e9 −1.19304 −0.596522 0.802597i \(-0.703451\pi\)
−0.596522 + 0.802597i \(0.703451\pi\)
\(194\) −1.62796e9 −1.14931
\(195\) 1.32919e9i 0.919285i
\(196\) −1.34679e9 −0.912587
\(197\) 1.44601e9 0.960077 0.480039 0.877247i \(-0.340623\pi\)
0.480039 + 0.877247i \(0.340623\pi\)
\(198\) 4.62533e8 0.300941
\(199\) 2.48184e9 1.58256 0.791281 0.611453i \(-0.209415\pi\)
0.791281 + 0.611453i \(0.209415\pi\)
\(200\) 6.15140e8i 0.384463i
\(201\) 8.19726e8i 0.502209i
\(202\) 3.42886e9 2.05942
\(203\) 3.80146e9 2.23855
\(204\) 1.04095e8 0.0601049
\(205\) −1.07925e9 −0.611094
\(206\) −2.19954e9 −1.22141
\(207\) 2.56906e8i 0.139924i
\(208\) 1.48290e9i 0.792241i
\(209\) 7.37269e8i 0.386403i
\(210\) 3.27632e9i 1.68465i
\(211\) 1.23047e8i 0.0620786i 0.999518 + 0.0310393i \(0.00988171\pi\)
−0.999518 + 0.0310393i \(0.990118\pi\)
\(212\) 2.87529e9 1.42343
\(213\) 3.96401e8 0.192583
\(214\) 2.11650e9i 1.00917i
\(215\) 3.67379e9i 1.71933i
\(216\) 1.34795e8i 0.0619238i
\(217\) 4.41087e8i 0.198923i
\(218\) −6.23530e9 −2.76078
\(219\) 9.78744e8i 0.425493i
\(220\) 2.55966e9i 1.09268i
\(221\) 2.19464e8i 0.0920012i
\(222\) −1.37737e9 −0.567074
\(223\) −2.92225e9 −1.18167 −0.590837 0.806791i \(-0.701202\pi\)
−0.590837 + 0.806791i \(0.701202\pi\)
\(224\) 4.72694e9i 1.87754i
\(225\) 1.02076e9 0.398285
\(226\) −1.45668e9 −0.558379
\(227\) 3.19057e9i 1.20161i 0.799395 + 0.600806i \(0.205154\pi\)
−0.799395 + 0.600806i \(0.794846\pi\)
\(228\) 1.20893e9 0.447363
\(229\) 1.08652e9i 0.395089i 0.980294 + 0.197544i \(0.0632966\pi\)
−0.980294 + 0.197544i \(0.936703\pi\)
\(230\) 2.59076e9 0.925796
\(231\) 1.31905e9i 0.463246i
\(232\) 1.57721e9i 0.544424i
\(233\) 1.44416e9i 0.489995i 0.969524 + 0.244998i \(0.0787872\pi\)
−0.969524 + 0.244998i \(0.921213\pi\)
\(234\) 1.59900e9 0.533317
\(235\) 3.58916e9i 1.17685i
\(236\) 3.11612e9 2.12644e9i 1.00454 0.685498i
\(237\) 1.00644e9 0.319004
\(238\) 5.40954e8i 0.168598i
\(239\) −1.66479e9 −0.510232 −0.255116 0.966910i \(-0.582114\pi\)
−0.255116 + 0.966910i \(0.582114\pi\)
\(240\) −2.09188e9 −0.630510
\(241\) −3.43370e9 −1.01787 −0.508937 0.860804i \(-0.669961\pi\)
−0.508937 + 0.860804i \(0.669961\pi\)
\(242\) 3.22787e9i 0.941142i
\(243\) 2.23677e8 0.0641500
\(244\) 3.19601e9i 0.901672i
\(245\) 4.00550e9 1.11171
\(246\) 1.29833e9i 0.354522i
\(247\) 2.54878e9i 0.684769i
\(248\) −1.83005e8 −0.0483790
\(249\) 2.85965e9i 0.743901i
\(250\) 1.67869e9i 0.429746i
\(251\) 2.77076e9 0.698077 0.349039 0.937108i \(-0.386508\pi\)
0.349039 + 0.937108i \(0.386508\pi\)
\(252\) 2.16289e9 0.536329
\(253\) −1.04304e9 −0.254576
\(254\) 4.01565e9i 0.964764i
\(255\) −3.09591e8 −0.0732197
\(256\) 1.88911e9 0.439842
\(257\) −2.75354e9 −0.631188 −0.315594 0.948894i \(-0.602204\pi\)
−0.315594 + 0.948894i \(0.602204\pi\)
\(258\) 4.41951e9 0.997460
\(259\) 3.92797e9i 0.872910i
\(260\) 8.84888e9i 1.93640i
\(261\) −2.61721e9 −0.563997
\(262\) 3.92935e9 0.833902
\(263\) −5.38741e9 −1.12605 −0.563024 0.826441i \(-0.690362\pi\)
−0.563024 + 0.826441i \(0.690362\pi\)
\(264\) −5.47266e8 −0.112663
\(265\) −8.55144e9 −1.73403
\(266\) 6.28246e9i 1.25488i
\(267\) 1.23862e9i 0.243721i
\(268\) 5.45718e9i 1.05786i
\(269\) 9.59021e9i 1.83155i −0.401690 0.915776i \(-0.631577\pi\)
0.401690 0.915776i \(-0.368423\pi\)
\(270\) 2.25567e9i 0.424443i
\(271\) 6.67311e9 1.23723 0.618616 0.785694i \(-0.287694\pi\)
0.618616 + 0.785694i \(0.287694\pi\)
\(272\) 3.45391e8 0.0631009
\(273\) 4.56001e9i 0.820947i
\(274\) 1.47391e8i 0.0261499i
\(275\) 4.14429e9i 0.724635i
\(276\) 1.71031e9i 0.294739i
\(277\) −8.90902e9 −1.51325 −0.756625 0.653849i \(-0.773153\pi\)
−0.756625 + 0.653849i \(0.773153\pi\)
\(278\) 1.31263e10i 2.19767i
\(279\) 3.03678e8i 0.0501183i
\(280\) 3.87652e9i 0.630682i
\(281\) −7.50541e9 −1.20379 −0.601893 0.798577i \(-0.705586\pi\)
−0.601893 + 0.798577i \(0.705586\pi\)
\(282\) 4.31771e9 0.682742
\(283\) 5.74822e9i 0.896164i 0.893993 + 0.448082i \(0.147893\pi\)
−0.893993 + 0.448082i \(0.852107\pi\)
\(284\) −2.63898e9 −0.405660
\(285\) −3.59549e9 −0.544978
\(286\) 6.49195e9i 0.970311i
\(287\) 3.70255e9 0.545724
\(288\) 3.25439e9i 0.473041i
\(289\) −6.92464e9 −0.992672
\(290\) 2.63932e10i 3.73164i
\(291\) 3.19631e9i 0.445735i
\(292\) 6.51582e9i 0.896268i
\(293\) −9.53755e9 −1.29410 −0.647048 0.762449i \(-0.723997\pi\)
−0.647048 + 0.762449i \(0.723997\pi\)
\(294\) 4.81856e9i 0.644953i
\(295\) −9.26771e9 + 6.32430e9i −1.22373 + 0.835073i
\(296\) 1.62970e9 0.212296
\(297\) 9.08131e8i 0.116714i
\(298\) −5.74834e8 −0.0728916
\(299\) −3.60584e9 −0.451151
\(300\) −6.79554e9 −0.838955
\(301\) 1.26035e10i 1.53541i
\(302\) 1.69337e10 2.03574
\(303\) 6.73217e9i 0.798702i
\(304\) 4.01126e9 0.469663
\(305\) 9.50531e9i 1.09842i
\(306\) 3.72434e8i 0.0424779i
\(307\) 1.74059e10 1.95949 0.979744 0.200255i \(-0.0641770\pi\)
0.979744 + 0.200255i \(0.0641770\pi\)
\(308\) 8.78132e9i 0.975791i
\(309\) 4.31854e9i 0.473699i
\(310\) 3.06243e9 0.331604
\(311\) −1.67200e9 −0.178729 −0.0893643 0.995999i \(-0.528484\pi\)
−0.0893643 + 0.995999i \(0.528484\pi\)
\(312\) −1.89193e9 −0.199658
\(313\) 1.74970e10i 1.82300i −0.411304 0.911498i \(-0.634926\pi\)
0.411304 0.911498i \(-0.365074\pi\)
\(314\) −9.51777e9 −0.979076
\(315\) −6.43268e9 −0.653356
\(316\) −6.70022e9 −0.671956
\(317\) 1.12301e10 1.11211 0.556053 0.831147i \(-0.312315\pi\)
0.556053 + 0.831147i \(0.312315\pi\)
\(318\) 1.02873e10i 1.00598i
\(319\) 1.06259e10i 1.02613i
\(320\) 2.13675e10 2.03776
\(321\) 4.15551e9 0.391385
\(322\) −8.88800e9 −0.826762
\(323\) 5.93653e8 0.0545409
\(324\) −1.48909e9 −0.135127
\(325\) 1.43270e10i 1.28417i
\(326\) 8.20346e9i 0.726317i
\(327\) 1.22423e10i 1.07071i
\(328\) 1.53617e9i 0.132722i
\(329\) 1.23132e10i 1.05096i
\(330\) 9.15801e9 0.772228
\(331\) 1.13799e10 0.948043 0.474022 0.880513i \(-0.342802\pi\)
0.474022 + 0.880513i \(0.342802\pi\)
\(332\) 1.90376e10i 1.56697i
\(333\) 2.70432e9i 0.219928i
\(334\) 1.68413e10i 1.35328i
\(335\) 1.62303e10i 1.28869i
\(336\) 7.17653e9 0.563063
\(337\) 2.74377e9i 0.212730i 0.994327 + 0.106365i \(0.0339212\pi\)
−0.994327 + 0.106365i \(0.966079\pi\)
\(338\) 3.01333e9i 0.230877i
\(339\) 2.86002e9i 0.216556i
\(340\) 2.06105e9 0.154232
\(341\) −1.23293e9 −0.0911847
\(342\) 4.32532e9i 0.316165i
\(343\) 4.57086e9 0.330234
\(344\) −5.22914e9 −0.373419
\(345\) 5.08666e9i 0.359051i
\(346\) 2.86278e10 1.99749
\(347\) 7.58960e9i 0.523481i 0.965138 + 0.261741i \(0.0842965\pi\)
−0.965138 + 0.261741i \(0.915704\pi\)
\(348\) 1.74236e10 1.18802
\(349\) 1.19166e8i 0.00803249i 0.999992 + 0.00401624i \(0.00127841\pi\)
−0.999992 + 0.00401624i \(0.998722\pi\)
\(350\) 3.53146e10i 2.35332i
\(351\) 3.13946e9i 0.206836i
\(352\) −1.32128e10 −0.860646
\(353\) 2.67034e10i 1.71976i 0.510497 + 0.859880i \(0.329462\pi\)
−0.510497 + 0.859880i \(0.670538\pi\)
\(354\) 7.60804e9 + 1.11489e10i 0.484462 + 0.709937i
\(355\) 7.84863e9 0.494174
\(356\) 8.24591e9i 0.513380i
\(357\) 1.06210e9 0.0653873
\(358\) −6.62634e9 −0.403405
\(359\) −1.92840e10 −1.16096 −0.580482 0.814273i \(-0.697136\pi\)
−0.580482 + 0.814273i \(0.697136\pi\)
\(360\) 2.66889e9i 0.158899i
\(361\) −1.00891e10 −0.594050
\(362\) 3.96920e10i 2.31137i
\(363\) 6.33756e9 0.365002
\(364\) 3.03575e10i 1.72926i
\(365\) 1.93788e10i 1.09183i
\(366\) 1.14347e10 0.637239
\(367\) 1.69746e10i 0.935697i −0.883809 0.467848i \(-0.845029\pi\)
0.883809 0.467848i \(-0.154971\pi\)
\(368\) 5.67486e9i 0.309431i
\(369\) −2.54911e9 −0.137494
\(370\) −2.72716e10 −1.45514
\(371\) 2.93371e10 1.54853
\(372\) 2.02168e9i 0.105570i
\(373\) −1.24757e10 −0.644511 −0.322256 0.946653i \(-0.604441\pi\)
−0.322256 + 0.946653i \(0.604441\pi\)
\(374\) −1.51208e9 −0.0772839
\(375\) 3.29592e9 0.166668
\(376\) −5.10869e9 −0.255598
\(377\) 3.67343e10i 1.81847i
\(378\) 7.73842e9i 0.379040i
\(379\) −2.77496e10 −1.34493 −0.672466 0.740128i \(-0.734765\pi\)
−0.672466 + 0.740128i \(0.734765\pi\)
\(380\) 2.39364e10 1.14795
\(381\) −7.88427e9 −0.374164
\(382\) −4.10751e10 −1.92897
\(383\) −9.19768e9 −0.427448 −0.213724 0.976894i \(-0.568559\pi\)
−0.213724 + 0.976894i \(0.568559\pi\)
\(384\) 7.88985e9i 0.362864i
\(385\) 2.61167e10i 1.18871i
\(386\) 3.94280e10i 1.77605i
\(387\) 8.67720e9i 0.386844i
\(388\) 2.12789e10i 0.938905i
\(389\) −5.01240e9 −0.218901 −0.109450 0.993992i \(-0.534909\pi\)
−0.109450 + 0.993992i \(0.534909\pi\)
\(390\) 3.16597e10 1.36851
\(391\) 8.39859e8i 0.0359335i
\(392\) 5.70129e9i 0.241451i
\(393\) 7.71482e9i 0.323412i
\(394\) 3.44421e10i 1.42924i
\(395\) 1.99273e10 0.818577
\(396\) 6.04572e9i 0.245849i
\(397\) 4.62675e10i 1.86258i 0.364282 + 0.931289i \(0.381315\pi\)
−0.364282 + 0.931289i \(0.618685\pi\)
\(398\) 5.91142e10i 2.35591i
\(399\) 1.23349e10 0.486680
\(400\) −2.25478e10 −0.880774
\(401\) 1.80362e10i 0.697539i −0.937209 0.348770i \(-0.886600\pi\)
0.937209 0.348770i \(-0.113400\pi\)
\(402\) 1.95248e10 0.747624
\(403\) −4.26231e9 −0.161594
\(404\) 4.48183e10i 1.68240i
\(405\) 4.42874e9 0.164612
\(406\) 9.05460e10i 3.33246i
\(407\) 1.09795e10 0.400135
\(408\) 4.40661e8i 0.0159025i
\(409\) 2.93023e10i 1.04715i 0.851979 + 0.523575i \(0.175402\pi\)
−0.851979 + 0.523575i \(0.824598\pi\)
\(410\) 2.57064e10i 0.909718i
\(411\) 2.89386e8 0.0101417
\(412\) 2.87499e10i 0.997810i
\(413\) 3.17943e10 2.16965e10i 1.09282 0.745744i
\(414\) 6.11917e9 0.208301
\(415\) 5.66201e10i 1.90888i
\(416\) −4.56774e10 −1.52520
\(417\) 2.57719e10 0.852320
\(418\) −1.75608e10 −0.575228
\(419\) 3.66218e10i 1.18818i 0.804398 + 0.594091i \(0.202488\pi\)
−0.804398 + 0.594091i \(0.797512\pi\)
\(420\) 4.28245e10 1.37624
\(421\) 5.62614e9i 0.179094i −0.995983 0.0895472i \(-0.971458\pi\)
0.995983 0.0895472i \(-0.0285420\pi\)
\(422\) 2.93083e9 0.0924147
\(423\) 8.47732e9i 0.264787i
\(424\) 1.21718e10i 0.376610i
\(425\) −3.33700e9 −0.102282
\(426\) 9.44179e9i 0.286692i
\(427\) 3.26095e10i 0.980916i
\(428\) −2.76646e10 −0.824422
\(429\) −1.27462e10 −0.376315
\(430\) 8.75050e10 2.55952
\(431\) 4.51983e10i 1.30983i −0.755704 0.654913i \(-0.772705\pi\)
0.755704 0.654913i \(-0.227295\pi\)
\(432\) −4.94086e9 −0.141863
\(433\) −6.64155e8 −0.0188937 −0.00944687 0.999955i \(-0.503007\pi\)
−0.00944687 + 0.999955i \(0.503007\pi\)
\(434\) −1.05061e10 −0.296131
\(435\) −5.18200e10 −1.44724
\(436\) 8.15010e10i 2.25536i
\(437\) 9.75385e9i 0.267455i
\(438\) 2.33124e10 0.633419
\(439\) 3.66246e10 0.986087 0.493044 0.870005i \(-0.335884\pi\)
0.493044 + 0.870005i \(0.335884\pi\)
\(440\) −1.08357e10 −0.289099
\(441\) 9.46069e9 0.250132
\(442\) −5.22735e9 −0.136960
\(443\) 1.40820e10i 0.365636i 0.983147 + 0.182818i \(0.0585219\pi\)
−0.983147 + 0.182818i \(0.941478\pi\)
\(444\) 1.80035e10i 0.463261i
\(445\) 2.45243e10i 0.625399i
\(446\) 6.96043e10i 1.75913i
\(447\) 1.12862e9i 0.0282695i
\(448\) −7.33046e10 −1.81978
\(449\) 5.89422e9 0.145024 0.0725122 0.997368i \(-0.476898\pi\)
0.0725122 + 0.997368i \(0.476898\pi\)
\(450\) 2.43132e10i 0.592915i
\(451\) 1.03494e10i 0.250155i
\(452\) 1.90401e10i 0.456158i
\(453\) 3.32473e10i 0.789521i
\(454\) 7.59953e10 1.78881
\(455\) 9.02868e10i 2.10658i
\(456\) 5.11770e9i 0.118363i
\(457\) 5.48090e10i 1.25657i −0.777983 0.628286i \(-0.783757\pi\)
0.777983 0.628286i \(-0.216243\pi\)
\(458\) 2.58795e10 0.588157
\(459\) −7.31231e8 −0.0164742
\(460\) 3.38635e10i 0.756312i
\(461\) −8.10683e8 −0.0179493 −0.00897465 0.999960i \(-0.502857\pi\)
−0.00897465 + 0.999960i \(0.502857\pi\)
\(462\) −3.14180e10 −0.689621
\(463\) 8.44778e10i 1.83831i 0.393897 + 0.919155i \(0.371127\pi\)
−0.393897 + 0.919155i \(0.628873\pi\)
\(464\) 5.78122e10 1.24723
\(465\) 6.01273e9i 0.128606i
\(466\) 3.43981e10 0.729442
\(467\) 3.28861e10i 0.691424i 0.938341 + 0.345712i \(0.112363\pi\)
−0.938341 + 0.345712i \(0.887637\pi\)
\(468\) 2.09004e10i 0.435683i
\(469\) 5.56807e10i 1.15083i
\(470\) 8.54893e10 1.75194
\(471\) 1.86870e10i 0.379714i
\(472\) −9.00179e9 1.31913e10i −0.181368 0.265779i
\(473\) −3.52295e10 −0.703820
\(474\) 2.39722e10i 0.474892i
\(475\) −3.87548e10 −0.761292
\(476\) −7.07076e9 −0.137733
\(477\) −2.01979e10 −0.390150
\(478\) 3.96532e10i 0.759567i
\(479\) −2.74359e10 −0.521168 −0.260584 0.965451i \(-0.583915\pi\)
−0.260584 + 0.965451i \(0.583915\pi\)
\(480\) 6.44359e10i 1.21384i
\(481\) 3.79568e10 0.709103
\(482\) 8.17864e10i 1.51528i
\(483\) 1.74506e10i 0.320643i
\(484\) −4.21912e10 −0.768848
\(485\) 6.32859e10i 1.14377i
\(486\) 5.32771e9i 0.0954983i
\(487\) 4.77225e10 0.848413 0.424206 0.905566i \(-0.360553\pi\)
0.424206 + 0.905566i \(0.360553\pi\)
\(488\) −1.35295e10 −0.238563
\(489\) −1.61065e10 −0.281687
\(490\) 9.54060e10i 1.65498i
\(491\) −2.30522e10 −0.396631 −0.198316 0.980138i \(-0.563547\pi\)
−0.198316 + 0.980138i \(0.563547\pi\)
\(492\) 1.69703e10 0.289620
\(493\) 8.55601e9 0.144838
\(494\) −6.07087e10 −1.01940
\(495\) 1.79807e10i 0.299493i
\(496\) 6.70802e9i 0.110833i
\(497\) −2.69260e10 −0.441312
\(498\) −6.81132e10 −1.10742
\(499\) −2.51107e10 −0.405002 −0.202501 0.979282i \(-0.564907\pi\)
−0.202501 + 0.979282i \(0.564907\pi\)
\(500\) −2.19420e10 −0.351073
\(501\) 3.30659e10 0.524843
\(502\) 6.59959e10i 1.03921i
\(503\) 7.61944e10i 1.19029i −0.803620 0.595143i \(-0.797096\pi\)
0.803620 0.595143i \(-0.202904\pi\)
\(504\) 9.15605e9i 0.141901i
\(505\) 1.33295e11i 2.04950i
\(506\) 2.48439e10i 0.378981i
\(507\) −5.91633e9 −0.0895407
\(508\) 5.24882e10 0.788146
\(509\) 1.02580e11i 1.52824i −0.645073 0.764121i \(-0.723173\pi\)
0.645073 0.764121i \(-0.276827\pi\)
\(510\) 7.37407e9i 0.109000i
\(511\) 6.64821e10i 0.975037i
\(512\) 8.81863e10i 1.28328i
\(513\) −8.49228e9 −0.122618
\(514\) 6.55858e10i 0.939631i
\(515\) 8.55057e10i 1.21553i
\(516\) 5.77670e10i 0.814856i
\(517\) −3.44180e10 −0.481751
\(518\) 9.35594e10 1.29948
\(519\) 5.62075e10i 0.774684i
\(520\) −3.74596e10 −0.512330
\(521\) −9.90363e10 −1.34414 −0.672068 0.740489i \(-0.734594\pi\)
−0.672068 + 0.740489i \(0.734594\pi\)
\(522\) 6.23387e10i 0.839606i
\(523\) −7.70542e10 −1.02989 −0.514944 0.857224i \(-0.672187\pi\)
−0.514944 + 0.857224i \(0.672187\pi\)
\(524\) 5.13601e10i 0.681241i
\(525\) −6.93361e10 −0.912688
\(526\) 1.28321e11i 1.67631i
\(527\) 9.92763e8i 0.0128707i
\(528\) 2.00599e10i 0.258103i
\(529\) 6.45119e10 0.823791
\(530\) 2.03685e11i 2.58140i
\(531\) −2.18896e10 + 1.49375e10i −0.275334 + 0.187889i
\(532\) −8.21175e10 −1.02515
\(533\) 3.57785e10i 0.443315i
\(534\) −2.95024e10 −0.362821
\(535\) 8.22779e10 1.00431
\(536\) −2.31017e10 −0.279888
\(537\) 1.30101e10i 0.156452i
\(538\) −2.28427e11 −2.72658
\(539\) 3.84104e10i 0.455087i
\(540\) −2.94836e10 −0.346741
\(541\) 1.47107e11i 1.71729i 0.512567 + 0.858647i \(0.328695\pi\)
−0.512567 + 0.858647i \(0.671305\pi\)
\(542\) 1.58945e11i 1.84183i
\(543\) −7.79307e10 −0.896415
\(544\) 1.06390e10i 0.121480i
\(545\) 2.42394e11i 2.74748i
\(546\) −1.08614e11 −1.22212
\(547\) −1.13267e11 −1.26518 −0.632592 0.774485i \(-0.718009\pi\)
−0.632592 + 0.774485i \(0.718009\pi\)
\(548\) −1.92654e9 −0.0213626
\(549\) 2.24508e10i 0.247140i
\(550\) 9.87118e10 1.07874
\(551\) 9.93667e10 1.07804
\(552\) −7.24017e9 −0.0779817
\(553\) −6.83636e10 −0.731012
\(554\) 2.12202e11i 2.25273i
\(555\) 5.35446e10i 0.564344i
\(556\) −1.71572e11 −1.79534
\(557\) −6.78423e10 −0.704823 −0.352411 0.935845i \(-0.614638\pi\)
−0.352411 + 0.935845i \(0.614638\pi\)
\(558\) 7.23322e9 0.0746097
\(559\) −1.21790e11 −1.24728
\(560\) 1.42093e11 1.44484
\(561\) 2.96880e9i 0.0299730i
\(562\) 1.78769e11i 1.79204i
\(563\) 1.92579e11i 1.91679i −0.285445 0.958395i \(-0.592141\pi\)
0.285445 0.958395i \(-0.407859\pi\)
\(564\) 5.64363e10i 0.557754i
\(565\) 5.66275e10i 0.555691i
\(566\) 1.36915e11 1.33409
\(567\) −1.51935e10 −0.147003
\(568\) 1.11715e10i 0.107329i
\(569\) 4.04335e10i 0.385738i −0.981225 0.192869i \(-0.938221\pi\)
0.981225 0.192869i \(-0.0617792\pi\)
\(570\) 8.56401e10i 0.811293i
\(571\) 5.37255e10i 0.505401i 0.967545 + 0.252701i \(0.0813187\pi\)
−0.967545 + 0.252701i \(0.918681\pi\)
\(572\) 8.48556e10 0.792678
\(573\) 8.06462e10i 0.748110i
\(574\) 8.81900e10i 0.812404i
\(575\) 5.48277e10i 0.501567i
\(576\) 5.04684e10 0.458490
\(577\) −4.05383e10 −0.365731 −0.182865 0.983138i \(-0.558537\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(578\) 1.64936e11i 1.47776i
\(579\) −7.74123e10 −0.688804
\(580\) 3.44983e11 3.04849
\(581\) 1.94244e11i 1.70468i
\(582\) −7.61320e10 −0.663552
\(583\) 8.20033e10i 0.709835i
\(584\) −2.75831e10 −0.237133
\(585\) 6.21603e10i 0.530749i
\(586\) 2.27173e11i 1.92648i
\(587\) 9.05099e10i 0.762331i −0.924507 0.381166i \(-0.875523\pi\)
0.924507 0.381166i \(-0.124477\pi\)
\(588\) −6.29830e10 −0.526882
\(589\) 1.15296e10i 0.0957975i
\(590\) 1.50637e11 + 2.20745e11i 1.24315 + 1.82173i
\(591\) 6.76232e10 0.554301
\(592\) 5.97363e10i 0.486353i
\(593\) 1.25627e11 1.01593 0.507966 0.861377i \(-0.330397\pi\)
0.507966 + 0.861377i \(0.330397\pi\)
\(594\) 2.16305e10 0.173749
\(595\) 2.10293e10 0.167786
\(596\) 7.51360e9i 0.0595475i
\(597\) 1.16064e11 0.913693
\(598\) 8.58865e10i 0.671615i
\(599\) −1.49470e11 −1.16104 −0.580519 0.814247i \(-0.697150\pi\)
−0.580519 + 0.814247i \(0.697150\pi\)
\(600\) 2.87673e10i 0.221970i
\(601\) 2.03842e10i 0.156241i −0.996944 0.0781205i \(-0.975108\pi\)
0.996944 0.0781205i \(-0.0248919\pi\)
\(602\) −3.00200e11 −2.28573
\(603\) 3.83348e10i 0.289950i
\(604\) 2.21338e11i 1.66306i
\(605\) 1.25482e11 0.936611
\(606\) 1.60352e11 1.18900
\(607\) 3.36149e10 0.247615 0.123808 0.992306i \(-0.460489\pi\)
0.123808 + 0.992306i \(0.460489\pi\)
\(608\) 1.23558e11i 0.904184i
\(609\) 1.77777e11 1.29243
\(610\) 2.26404e11 1.63518
\(611\) −1.18985e11 −0.853741
\(612\) 4.86805e9 0.0347016
\(613\) 9.02842e10i 0.639396i 0.947520 + 0.319698i \(0.103581\pi\)
−0.947520 + 0.319698i \(0.896419\pi\)
\(614\) 4.14586e11i 2.91703i
\(615\) −5.04717e10 −0.352815
\(616\) 3.71736e10 0.258174
\(617\) 6.24555e10 0.430953 0.215477 0.976509i \(-0.430870\pi\)
0.215477 + 0.976509i \(0.430870\pi\)
\(618\) −1.02862e11 −0.705183
\(619\) −1.95074e11 −1.32873 −0.664366 0.747408i \(-0.731298\pi\)
−0.664366 + 0.747408i \(0.731298\pi\)
\(620\) 4.00287e10i 0.270897i
\(621\) 1.20143e10i 0.0807852i
\(622\) 3.98249e10i 0.266068i
\(623\) 8.41345e10i 0.558499i
\(624\) 6.93482e10i 0.457401i
\(625\) −1.17062e11 −0.767178
\(626\) −4.16756e11 −2.71384
\(627\) 3.44787e10i 0.223090i
\(628\) 1.24406e11i 0.799838i
\(629\) 8.84077e9i 0.0564791i
\(630\) 1.53218e11i 0.972632i
\(631\) 1.44763e11 0.913146 0.456573 0.889686i \(-0.349077\pi\)
0.456573 + 0.889686i \(0.349077\pi\)
\(632\) 2.83638e10i 0.177785i
\(633\) 5.75435e9i 0.0358411i
\(634\) 2.67487e11i 1.65556i
\(635\) −1.56106e11 −0.960119
\(636\) 1.34464e11 0.821820
\(637\) 1.32787e11i 0.806487i
\(638\) −2.53095e11 −1.52757
\(639\) 1.85379e10 0.111188
\(640\) 1.56217e11i 0.931123i
\(641\) 2.45615e11 1.45486 0.727432 0.686180i \(-0.240714\pi\)
0.727432 + 0.686180i \(0.240714\pi\)
\(642\) 9.89791e10i 0.582644i
\(643\) 1.83446e11 1.07316 0.536580 0.843849i \(-0.319716\pi\)
0.536580 + 0.843849i \(0.319716\pi\)
\(644\) 1.16174e11i 0.675408i
\(645\) 1.71806e11i 0.992657i
\(646\) 1.41401e10i 0.0811935i
\(647\) −2.70631e11 −1.54440 −0.772201 0.635378i \(-0.780844\pi\)
−0.772201 + 0.635378i \(0.780844\pi\)
\(648\) 6.30372e9i 0.0357517i
\(649\) −6.06464e10 8.88720e10i −0.341842 0.500940i
\(650\) 3.41252e11 1.91171
\(651\) 2.06276e10i 0.114848i
\(652\) 1.07227e11 0.593352
\(653\) 1.17779e11 0.647760 0.323880 0.946098i \(-0.395013\pi\)
0.323880 + 0.946098i \(0.395013\pi\)
\(654\) −2.91596e11 −1.59393
\(655\) 1.52751e11i 0.829887i
\(656\) 5.63080e10 0.304057
\(657\) 4.57713e10i 0.245659i
\(658\) −2.93284e11 −1.56454
\(659\) 2.67635e11i 1.41906i 0.704675 + 0.709530i \(0.251093\pi\)
−0.704675 + 0.709530i \(0.748907\pi\)
\(660\) 1.19703e11i 0.630857i
\(661\) 1.10057e11 0.576516 0.288258 0.957553i \(-0.406924\pi\)
0.288258 + 0.957553i \(0.406924\pi\)
\(662\) 2.71056e11i 1.41133i
\(663\) 1.02633e10i 0.0531169i
\(664\) 8.05912e10 0.414586
\(665\) 2.44227e11 1.24884
\(666\) −6.44134e10 −0.327400
\(667\) 1.40577e11i 0.710251i
\(668\) −2.20131e11 −1.10554
\(669\) −1.36660e11 −0.682240
\(670\) 3.86586e11 1.91843
\(671\) −9.11504e10 −0.449644
\(672\) 2.21057e11i 1.08400i
\(673\) 1.24589e11i 0.607323i −0.952780 0.303662i \(-0.901791\pi\)
0.952780 0.303662i \(-0.0982092\pi\)
\(674\) 6.53532e10 0.316685
\(675\) 4.77362e10 0.229950
\(676\) 3.93870e10 0.188610
\(677\) 2.46766e11 1.17471 0.587356 0.809329i \(-0.300169\pi\)
0.587356 + 0.809329i \(0.300169\pi\)
\(678\) −6.81220e10 −0.322380
\(679\) 2.17112e11i 1.02142i
\(680\) 8.72496e9i 0.0408064i
\(681\) 1.49208e11i 0.693751i
\(682\) 2.93669e10i 0.135744i
\(683\) 2.14225e11i 0.984437i −0.870472 0.492218i \(-0.836186\pi\)
0.870472 0.492218i \(-0.163814\pi\)
\(684\) 5.65359e10 0.258285
\(685\) 5.72975e9 0.0260240
\(686\) 1.08872e11i 0.491610i
\(687\) 5.08114e10i 0.228105i
\(688\) 1.91673e11i 0.855474i
\(689\) 2.83490e11i 1.25794i
\(690\) 1.21158e11 0.534509
\(691\) 3.64118e10i 0.159709i −0.996807 0.0798545i \(-0.974554\pi\)
0.996807 0.0798545i \(-0.0254456\pi\)
\(692\) 3.74192e11i 1.63181i
\(693\) 6.16856e10i 0.267455i
\(694\) 1.80775e11 0.779291
\(695\) 5.10276e11 2.18709
\(696\) 7.37588e10i 0.314323i
\(697\) 8.33339e9 0.0353094
\(698\) 2.83838e9 0.0119577
\(699\) 6.75367e10i 0.282899i
\(700\) 4.61593e11 1.92250
\(701\) 4.29534e11i 1.77879i 0.457138 + 0.889396i \(0.348875\pi\)
−0.457138 + 0.889396i \(0.651125\pi\)
\(702\) 7.47779e10 0.307911
\(703\) 1.02674e11i 0.420376i
\(704\) 2.04902e11i 0.834172i
\(705\) 1.67848e11i 0.679455i
\(706\) 6.36041e11 2.56016
\(707\) 4.57289e11i 1.83026i
\(708\) 1.45727e11 9.94440e10i 0.579970 0.395772i
\(709\) 5.68750e10 0.225080 0.112540 0.993647i \(-0.464101\pi\)
0.112540 + 0.993647i \(0.464101\pi\)
\(710\) 1.86944e11i 0.735663i
\(711\) 4.70667e10 0.184177
\(712\) 3.49071e10 0.135829
\(713\) −1.63113e10 −0.0631148
\(714\) 2.52979e10i 0.0973401i
\(715\) −2.52371e11 −0.965639
\(716\) 8.66122e10i 0.329554i
\(717\) −7.78544e10 −0.294582
\(718\) 4.59320e11i 1.72829i
\(719\) 1.39660e11i 0.522586i −0.965259 0.261293i \(-0.915851\pi\)
0.965259 0.261293i \(-0.0841489\pi\)
\(720\) −9.78276e10 −0.364025
\(721\) 2.93341e11i 1.08550i
\(722\) 2.40309e11i 0.884345i
\(723\) −1.60578e11 −0.587670
\(724\) 5.18810e11 1.88823
\(725\) −5.58554e11 −2.02168
\(726\) 1.50953e11i 0.543368i
\(727\) 2.91728e11 1.04434 0.522168 0.852842i \(-0.325123\pi\)
0.522168 + 0.852842i \(0.325123\pi\)
\(728\) 1.28511e11 0.457525
\(729\) 1.04604e10 0.0370370
\(730\) 4.61579e11 1.62538
\(731\) 2.83669e10i 0.0993443i
\(732\) 1.49462e11i 0.520580i
\(733\) −1.99431e11 −0.690838 −0.345419 0.938448i \(-0.612263\pi\)
−0.345419 + 0.938448i \(0.612263\pi\)
\(734\) −4.04313e11 −1.39295
\(735\) 1.87319e11 0.641848
\(736\) −1.74802e11 −0.595709
\(737\) −1.55639e11 −0.527533
\(738\) 6.07167e10i 0.204683i
\(739\) 3.66763e11i 1.22972i 0.788635 + 0.614862i \(0.210788\pi\)
−0.788635 + 0.614862i \(0.789212\pi\)
\(740\) 3.56464e11i 1.18875i
\(741\) 1.19195e11i 0.395352i
\(742\) 6.98772e11i 2.30526i
\(743\) 1.14130e11 0.374493 0.187246 0.982313i \(-0.440044\pi\)
0.187246 + 0.982313i \(0.440044\pi\)
\(744\) −8.55831e9 −0.0279316
\(745\) 2.23464e10i 0.0725407i
\(746\) 2.97156e11i 0.959465i
\(747\) 1.33732e11i 0.429491i
\(748\) 1.97643e10i 0.0631356i
\(749\) −2.82267e11 −0.896878
\(750\) 7.85047e10i 0.248114i
\(751\) 2.45993e9i 0.00773326i 0.999993 + 0.00386663i \(0.00123079\pi\)
−0.999993 + 0.00386663i \(0.998769\pi\)
\(752\) 1.87258e11i 0.585556i
\(753\) 1.29575e11 0.403035
\(754\) −8.74964e11 −2.70710
\(755\) 6.58287e11i 2.02594i
\(756\) 1.01148e11 0.309650
\(757\) 3.77625e10 0.114995 0.0574973 0.998346i \(-0.481688\pi\)
0.0574973 + 0.998346i \(0.481688\pi\)
\(758\) 6.60962e11i 2.00216i
\(759\) −4.87781e10 −0.146980
\(760\) 1.01329e11i 0.303724i
\(761\) 4.66930e11 1.39224 0.696118 0.717928i \(-0.254909\pi\)
0.696118 + 0.717928i \(0.254909\pi\)
\(762\) 1.87793e11i 0.557007i
\(763\) 8.31569e11i 2.45358i
\(764\) 5.36888e11i 1.57583i
\(765\) −1.44781e10 −0.0422734
\(766\) 2.19077e11i 0.636330i
\(767\) −2.09658e11 3.07235e11i −0.605800 0.887747i
\(768\) 8.83448e10 0.253943
\(769\) 4.41563e11i 1.26266i 0.775513 + 0.631331i \(0.217491\pi\)
−0.775513 + 0.631331i \(0.782509\pi\)
\(770\) −6.22067e11 −1.76960
\(771\) −1.28770e11 −0.364416
\(772\) 5.15359e11 1.45091
\(773\) 1.37042e11i 0.383826i −0.981412 0.191913i \(-0.938531\pi\)
0.981412 0.191913i \(-0.0614692\pi\)
\(774\) 2.06680e11 0.575884
\(775\) 6.48096e10i 0.179652i
\(776\) 9.00789e10 0.248414
\(777\) 1.83693e11i 0.503975i
\(778\) 1.19389e11i 0.325872i
\(779\) 9.67813e10 0.262810
\(780\) 4.13821e11i 1.11798i
\(781\) 7.52638e10i 0.202293i
\(782\) −2.00044e10 −0.0534932