Properties

Label 177.9.c.a.58.16
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 58.16
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.65

$q$-expansion

\(f(q)\) \(=\) \(q-20.7097i q^{2} +46.7654 q^{3} -172.891 q^{4} -840.056 q^{5} -968.496i q^{6} -4543.72 q^{7} -1721.16i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-20.7097i q^{2} +46.7654 q^{3} -172.891 q^{4} -840.056 q^{5} -968.496i q^{6} -4543.72 q^{7} -1721.16i q^{8} +2187.00 q^{9} +17397.3i q^{10} -24898.4i q^{11} -8085.30 q^{12} -50820.4i q^{13} +94099.0i q^{14} -39285.5 q^{15} -79904.8 q^{16} -124308. q^{17} -45292.1i q^{18} +132560. q^{19} +145238. q^{20} -212489. q^{21} -515637. q^{22} -269266. i q^{23} -80490.9i q^{24} +315069. q^{25} -1.05247e6 q^{26} +102276. q^{27} +785567. q^{28} -711317. q^{29} +813591. i q^{30} +85871.3i q^{31} +1.21418e6i q^{32} -1.16438e6i q^{33} +2.57438e6i q^{34} +3.81698e6 q^{35} -378112. q^{36} +391679. i q^{37} -2.74527e6i q^{38} -2.37663e6i q^{39} +1.44587e6i q^{40} +4.31923e6 q^{41} +4.40057e6i q^{42} +1.63923e6i q^{43} +4.30470e6i q^{44} -1.83720e6 q^{45} -5.57642e6 q^{46} -4.88539e6i q^{47} -3.73678e6 q^{48} +1.48806e7 q^{49} -6.52498e6i q^{50} -5.81332e6 q^{51} +8.78637e6i q^{52} -4.36472e6 q^{53} -2.11810e6i q^{54} +2.09160e7i q^{55} +7.82049e6i q^{56} +6.19920e6 q^{57} +1.47311e7i q^{58} +(-1.09079e7 + 5.27712e6i) q^{59} +6.79211e6 q^{60} +9.09407e6i q^{61} +1.77837e6 q^{62} -9.93712e6 q^{63} +4.68975e6 q^{64} +4.26919e7i q^{65} -2.41140e7 q^{66} -2.19803e6i q^{67} +2.14917e7 q^{68} -1.25923e7i q^{69} -7.90484e7i q^{70} -1.67746e7 q^{71} -3.76419e6i q^{72} +838268. i q^{73} +8.11154e6 q^{74} +1.47343e7 q^{75} -2.29184e7 q^{76} +1.13131e8i q^{77} -4.92193e7 q^{78} +3.35946e7 q^{79} +6.71245e7 q^{80} +4.78297e6 q^{81} -8.94499e7i q^{82} -7.13611e7i q^{83} +3.67374e7 q^{84} +1.04426e8 q^{85} +3.39480e7 q^{86} -3.32650e7 q^{87} -4.28542e7 q^{88} +2.85634e7i q^{89} +3.80479e7i q^{90} +2.30913e8i q^{91} +4.65537e7i q^{92} +4.01580e6i q^{93} -1.01175e8 q^{94} -1.11358e8 q^{95} +5.67818e7i q^{96} +1.66487e7i q^{97} -3.08172e8i q^{98} -5.44527e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.7097i 1.29435i −0.762339 0.647177i \(-0.775949\pi\)
0.762339 0.647177i \(-0.224051\pi\)
\(3\) 46.7654 0.577350
\(4\) −172.891 −0.675355
\(5\) −840.056 −1.34409 −0.672045 0.740510i \(-0.734584\pi\)
−0.672045 + 0.740510i \(0.734584\pi\)
\(6\) 968.496i 0.747296i
\(7\) −4543.72 −1.89243 −0.946214 0.323541i \(-0.895127\pi\)
−0.946214 + 0.323541i \(0.895127\pi\)
\(8\) 1721.16i 0.420206i
\(9\) 2187.00 0.333333
\(10\) 17397.3i 1.73973i
\(11\) 24898.4i 1.70059i −0.526305 0.850296i \(-0.676423\pi\)
0.526305 0.850296i \(-0.323577\pi\)
\(12\) −8085.30 −0.389916
\(13\) 50820.4i 1.77936i −0.456583 0.889681i \(-0.650927\pi\)
0.456583 0.889681i \(-0.349073\pi\)
\(14\) 94099.0i 2.44947i
\(15\) −39285.5 −0.776011
\(16\) −79904.8 −1.21925
\(17\) −124308. −1.48835 −0.744173 0.667987i \(-0.767156\pi\)
−0.744173 + 0.667987i \(0.767156\pi\)
\(18\) 45292.1i 0.431452i
\(19\) 132560. 1.01718 0.508589 0.861009i \(-0.330167\pi\)
0.508589 + 0.861009i \(0.330167\pi\)
\(20\) 145238. 0.907737
\(21\) −212489. −1.09259
\(22\) −515637. −2.20117
\(23\) 269266.i 0.962212i −0.876662 0.481106i \(-0.840235\pi\)
0.876662 0.481106i \(-0.159765\pi\)
\(24\) 80490.9i 0.242606i
\(25\) 315069. 0.806577
\(26\) −1.05247e6 −2.30313
\(27\) 102276. 0.192450
\(28\) 785567. 1.27806
\(29\) −711317. −1.00571 −0.502853 0.864372i \(-0.667716\pi\)
−0.502853 + 0.864372i \(0.667716\pi\)
\(30\) 813591.i 1.00443i
\(31\) 85871.3i 0.0929825i 0.998919 + 0.0464913i \(0.0148040\pi\)
−0.998919 + 0.0464913i \(0.985196\pi\)
\(32\) 1.21418e6i 1.15794i
\(33\) 1.16438e6i 0.981837i
\(34\) 2.57438e6i 1.92645i
\(35\) 3.81698e6 2.54359
\(36\) −378112. −0.225118
\(37\) 391679.i 0.208989i 0.994525 + 0.104494i \(0.0333225\pi\)
−0.994525 + 0.104494i \(0.966678\pi\)
\(38\) 2.74527e6i 1.31659i
\(39\) 2.37663e6i 1.02732i
\(40\) 1.44587e6i 0.564795i
\(41\) 4.31923e6 1.52852 0.764260 0.644908i \(-0.223104\pi\)
0.764260 + 0.644908i \(0.223104\pi\)
\(42\) 4.40057e6i 1.41420i
\(43\) 1.63923e6i 0.479476i 0.970838 + 0.239738i \(0.0770616\pi\)
−0.970838 + 0.239738i \(0.922938\pi\)
\(44\) 4.30470e6i 1.14850i
\(45\) −1.83720e6 −0.448030
\(46\) −5.57642e6 −1.24544
\(47\) 4.88539e6i 1.00117i −0.865687 0.500585i \(-0.833118\pi\)
0.865687 0.500585i \(-0.166882\pi\)
\(48\) −3.73678e6 −0.703935
\(49\) 1.48806e7 2.58128
\(50\) 6.52498e6i 1.04400i
\(51\) −5.81332e6 −0.859297
\(52\) 8.78637e6i 1.20170i
\(53\) −4.36472e6 −0.553163 −0.276581 0.960990i \(-0.589202\pi\)
−0.276581 + 0.960990i \(0.589202\pi\)
\(54\) 2.11810e6i 0.249099i
\(55\) 2.09160e7i 2.28575i
\(56\) 7.82049e6i 0.795210i
\(57\) 6.19920e6 0.587268
\(58\) 1.47311e7i 1.30174i
\(59\) −1.09079e7 + 5.27712e6i −0.900188 + 0.435501i
\(60\) 6.79211e6 0.524082
\(61\) 9.09407e6i 0.656809i 0.944537 + 0.328405i \(0.106511\pi\)
−0.944537 + 0.328405i \(0.893489\pi\)
\(62\) 1.77837e6 0.120352
\(63\) −9.93712e6 −0.630809
\(64\) 4.68975e6 0.279531
\(65\) 4.26919e7i 2.39162i
\(66\) −2.41140e7 −1.27085
\(67\) 2.19803e6i 0.109077i −0.998512 0.0545386i \(-0.982631\pi\)
0.998512 0.0545386i \(-0.0173688\pi\)
\(68\) 2.14917e7 1.00516
\(69\) 1.25923e7i 0.555534i
\(70\) 7.90484e7i 3.29231i
\(71\) −1.67746e7 −0.660113 −0.330057 0.943961i \(-0.607068\pi\)
−0.330057 + 0.943961i \(0.607068\pi\)
\(72\) 3.76419e6i 0.140069i
\(73\) 838268.i 0.0295183i 0.999891 + 0.0147591i \(0.00469815\pi\)
−0.999891 + 0.0147591i \(0.995302\pi\)
\(74\) 8.11154e6 0.270506
\(75\) 1.47343e7 0.465677
\(76\) −2.29184e7 −0.686956
\(77\) 1.13131e8i 3.21825i
\(78\) −4.92193e7 −1.32971
\(79\) 3.35946e7 0.862505 0.431253 0.902231i \(-0.358072\pi\)
0.431253 + 0.902231i \(0.358072\pi\)
\(80\) 6.71245e7 1.63878
\(81\) 4.78297e6 0.111111
\(82\) 8.94499e7i 1.97845i
\(83\) 7.13611e7i 1.50366i −0.659358 0.751829i \(-0.729172\pi\)
0.659358 0.751829i \(-0.270828\pi\)
\(84\) 3.67374e7 0.737888
\(85\) 1.04426e8 2.00047
\(86\) 3.39480e7 0.620613
\(87\) −3.32650e7 −0.580645
\(88\) −4.28542e7 −0.714599
\(89\) 2.85634e7i 0.455249i 0.973749 + 0.227625i \(0.0730959\pi\)
−0.973749 + 0.227625i \(0.926904\pi\)
\(90\) 3.80479e7i 0.579910i
\(91\) 2.30913e8i 3.36731i
\(92\) 4.65537e7i 0.649835i
\(93\) 4.01580e6i 0.0536835i
\(94\) −1.01175e8 −1.29587
\(95\) −1.11358e8 −1.36718
\(96\) 5.67818e7i 0.668535i
\(97\) 1.66487e7i 0.188058i 0.995569 + 0.0940292i \(0.0299747\pi\)
−0.995569 + 0.0940292i \(0.970025\pi\)
\(98\) 3.08172e8i 3.34110i
\(99\) 5.44527e7i 0.566864i
\(100\) −5.44726e7 −0.544726
\(101\) 2.97927e7i 0.286302i −0.989701 0.143151i \(-0.954277\pi\)
0.989701 0.143151i \(-0.0457235\pi\)
\(102\) 1.20392e8i 1.11224i
\(103\) 1.76307e8i 1.56646i −0.621730 0.783232i \(-0.713570\pi\)
0.621730 0.783232i \(-0.286430\pi\)
\(104\) −8.74702e7 −0.747699
\(105\) 1.78502e8 1.46854
\(106\) 9.03920e7i 0.715989i
\(107\) 1.33388e8 1.01761 0.508804 0.860883i \(-0.330088\pi\)
0.508804 + 0.860883i \(0.330088\pi\)
\(108\) −1.76826e7 −0.129972
\(109\) 6.03788e7i 0.427738i −0.976862 0.213869i \(-0.931393\pi\)
0.976862 0.213869i \(-0.0686066\pi\)
\(110\) 4.33164e8 2.95857
\(111\) 1.83170e7i 0.120660i
\(112\) 3.63065e8 2.30734
\(113\) 3.07112e8i 1.88358i −0.336206 0.941788i \(-0.609144\pi\)
0.336206 0.941788i \(-0.390856\pi\)
\(114\) 1.28384e8i 0.760133i
\(115\) 2.26199e8i 1.29330i
\(116\) 1.22980e8 0.679208
\(117\) 1.11144e8i 0.593121i
\(118\) 1.09288e8 + 2.25899e8i 0.563693 + 1.16516i
\(119\) 5.64821e8 2.81659
\(120\) 6.76169e7i 0.326084i
\(121\) −4.05570e8 −1.89201
\(122\) 1.88335e8 0.850144
\(123\) 2.01991e8 0.882492
\(124\) 1.48464e7i 0.0627962i
\(125\) 6.34711e7 0.259978
\(126\) 2.05794e8i 0.816491i
\(127\) −1.43879e8 −0.553075 −0.276537 0.961003i \(-0.589187\pi\)
−0.276537 + 0.961003i \(0.589187\pi\)
\(128\) 2.13708e8i 0.796125i
\(129\) 7.66594e7i 0.276826i
\(130\) 8.84137e8 3.09561
\(131\) 3.51695e8i 1.19421i −0.802163 0.597105i \(-0.796318\pi\)
0.802163 0.597105i \(-0.203682\pi\)
\(132\) 2.01311e8i 0.663088i
\(133\) −6.02314e8 −1.92494
\(134\) −4.55205e7 −0.141185
\(135\) −8.59175e7 −0.258670
\(136\) 2.13955e8i 0.625412i
\(137\) 5.18425e8 1.47165 0.735823 0.677174i \(-0.236795\pi\)
0.735823 + 0.677174i \(0.236795\pi\)
\(138\) −2.60783e8 −0.719058
\(139\) 1.33649e8 0.358021 0.179010 0.983847i \(-0.442710\pi\)
0.179010 + 0.983847i \(0.442710\pi\)
\(140\) −6.59921e8 −1.71783
\(141\) 2.28467e8i 0.578026i
\(142\) 3.47396e8i 0.854421i
\(143\) −1.26534e9 −3.02597
\(144\) −1.74752e8 −0.406417
\(145\) 5.97546e8 1.35176
\(146\) 1.73603e7 0.0382072
\(147\) 6.95896e8 1.49031
\(148\) 6.77177e7i 0.141142i
\(149\) 1.12096e8i 0.227428i 0.993514 + 0.113714i \(0.0362748\pi\)
−0.993514 + 0.113714i \(0.963725\pi\)
\(150\) 3.05143e8i 0.602752i
\(151\) 2.71112e8i 0.521484i −0.965409 0.260742i \(-0.916033\pi\)
0.965409 0.260742i \(-0.0839672\pi\)
\(152\) 2.28157e8i 0.427425i
\(153\) −2.71862e8 −0.496115
\(154\) 2.34291e9 4.16556
\(155\) 7.21367e7i 0.124977i
\(156\) 4.10898e8i 0.693802i
\(157\) 8.46853e7i 0.139383i −0.997569 0.0696914i \(-0.977799\pi\)
0.997569 0.0696914i \(-0.0222015\pi\)
\(158\) 6.95734e8i 1.11639i
\(159\) −2.04118e8 −0.319369
\(160\) 1.01998e9i 1.55637i
\(161\) 1.22347e9i 1.82092i
\(162\) 9.90538e7i 0.143817i
\(163\) 3.76158e8 0.532868 0.266434 0.963853i \(-0.414154\pi\)
0.266434 + 0.963853i \(0.414154\pi\)
\(164\) −7.46756e8 −1.03229
\(165\) 9.78146e8i 1.31968i
\(166\) −1.47787e9 −1.94627
\(167\) −7.52892e8 −0.967982 −0.483991 0.875073i \(-0.660813\pi\)
−0.483991 + 0.875073i \(0.660813\pi\)
\(168\) 3.65728e8i 0.459115i
\(169\) −1.76698e9 −2.16613
\(170\) 2.16262e9i 2.58932i
\(171\) 2.89908e8 0.339059
\(172\) 2.83409e8i 0.323817i
\(173\) 1.48929e9i 1.66263i −0.555803 0.831314i \(-0.687589\pi\)
0.555803 0.831314i \(-0.312411\pi\)
\(174\) 6.88907e8i 0.751560i
\(175\) −1.43159e9 −1.52639
\(176\) 1.98950e9i 2.07345i
\(177\) −5.10112e8 + 2.46787e8i −0.519724 + 0.251437i
\(178\) 5.91538e8 0.589254
\(179\) 8.56853e8i 0.834631i 0.908762 + 0.417315i \(0.137029\pi\)
−0.908762 + 0.417315i \(0.862971\pi\)
\(180\) 3.17635e8 0.302579
\(181\) −1.69536e9 −1.57960 −0.789801 0.613363i \(-0.789816\pi\)
−0.789801 + 0.613363i \(0.789816\pi\)
\(182\) 4.78214e9 4.35850
\(183\) 4.25288e8i 0.379209i
\(184\) −4.63452e8 −0.404328
\(185\) 3.29032e8i 0.280900i
\(186\) 8.31660e7 0.0694855
\(187\) 3.09507e9i 2.53107i
\(188\) 8.44640e8i 0.676146i
\(189\) −4.64713e8 −0.364198
\(190\) 2.30618e9i 1.76961i
\(191\) 9.34661e8i 0.702297i −0.936320 0.351149i \(-0.885791\pi\)
0.936320 0.351149i \(-0.114209\pi\)
\(192\) 2.19318e8 0.161387
\(193\) 1.11844e9 0.806092 0.403046 0.915180i \(-0.367951\pi\)
0.403046 + 0.915180i \(0.367951\pi\)
\(194\) 3.44789e8 0.243414
\(195\) 1.99650e9i 1.38080i
\(196\) −2.57272e9 −1.74328
\(197\) 1.06355e9 0.706145 0.353073 0.935596i \(-0.385137\pi\)
0.353073 + 0.935596i \(0.385137\pi\)
\(198\) −1.12770e9 −0.733723
\(199\) −4.25436e8 −0.271283 −0.135641 0.990758i \(-0.543310\pi\)
−0.135641 + 0.990758i \(0.543310\pi\)
\(200\) 5.42286e8i 0.338929i
\(201\) 1.02792e8i 0.0629758i
\(202\) −6.16997e8 −0.370576
\(203\) 3.23203e9 1.90323
\(204\) 1.00507e9 0.580330
\(205\) −3.62840e9 −2.05447
\(206\) −3.65126e9 −2.02756
\(207\) 5.88886e8i 0.320737i
\(208\) 4.06079e9i 2.16949i
\(209\) 3.30052e9i 1.72981i
\(210\) 3.69673e9i 1.90082i
\(211\) 2.35827e8i 0.118977i 0.998229 + 0.0594887i \(0.0189470\pi\)
−0.998229 + 0.0594887i \(0.981053\pi\)
\(212\) 7.54620e8 0.373581
\(213\) −7.84470e8 −0.381117
\(214\) 2.76241e9i 1.31714i
\(215\) 1.37705e9i 0.644459i
\(216\) 1.76034e8i 0.0808687i
\(217\) 3.90175e8i 0.175963i
\(218\) −1.25043e9 −0.553645
\(219\) 3.92019e7i 0.0170424i
\(220\) 3.61619e9i 1.54369i
\(221\) 6.31738e9i 2.64831i
\(222\) 3.79339e8 0.156177
\(223\) −8.10341e6 −0.00327679 −0.00163839 0.999999i \(-0.500522\pi\)
−0.00163839 + 0.999999i \(0.500522\pi\)
\(224\) 5.51692e9i 2.19131i
\(225\) 6.89056e8 0.268859
\(226\) −6.36020e9 −2.43802
\(227\) 4.59683e9i 1.73123i −0.500710 0.865615i \(-0.666928\pi\)
0.500710 0.865615i \(-0.333072\pi\)
\(228\) −1.07179e9 −0.396614
\(229\) 8.36769e8i 0.304273i −0.988359 0.152137i \(-0.951385\pi\)
0.988359 0.152137i \(-0.0486154\pi\)
\(230\) 4.68451e9 1.67399
\(231\) 5.29062e9i 1.85806i
\(232\) 1.22429e9i 0.422604i
\(233\) 1.78391e9i 0.605269i 0.953107 + 0.302634i \(0.0978661\pi\)
−0.953107 + 0.302634i \(0.902134\pi\)
\(234\) −2.30176e9 −0.767709
\(235\) 4.10401e9i 1.34566i
\(236\) 1.88588e9 9.12366e8i 0.607946 0.294118i
\(237\) 1.57107e9 0.497968
\(238\) 1.16973e10i 3.64566i
\(239\) 4.17187e8 0.127861 0.0639307 0.997954i \(-0.479636\pi\)
0.0639307 + 0.997954i \(0.479636\pi\)
\(240\) 3.13910e9 0.946151
\(241\) −2.94836e8 −0.0874003 −0.0437001 0.999045i \(-0.513915\pi\)
−0.0437001 + 0.999045i \(0.513915\pi\)
\(242\) 8.39922e9i 2.44894i
\(243\) 2.23677e8 0.0641500
\(244\) 1.57228e9i 0.443579i
\(245\) −1.25005e10 −3.46948
\(246\) 4.18316e9i 1.14226i
\(247\) 6.73673e9i 1.80993i
\(248\) 1.47799e8 0.0390718
\(249\) 3.33723e9i 0.868138i
\(250\) 1.31447e9i 0.336503i
\(251\) 7.08685e8 0.178549 0.0892746 0.996007i \(-0.471545\pi\)
0.0892746 + 0.996007i \(0.471545\pi\)
\(252\) 1.71804e9 0.426020
\(253\) −6.70429e9 −1.63633
\(254\) 2.97970e9i 0.715875i
\(255\) 4.88351e9 1.15497
\(256\) 5.62640e9 1.31000
\(257\) −2.28871e9 −0.524637 −0.262318 0.964981i \(-0.584487\pi\)
−0.262318 + 0.964981i \(0.584487\pi\)
\(258\) 1.58759e9 0.358311
\(259\) 1.77968e9i 0.395497i
\(260\) 7.38105e9i 1.61519i
\(261\) −1.55565e9 −0.335235
\(262\) −7.28349e9 −1.54573
\(263\) 8.89682e9 1.85957 0.929783 0.368108i \(-0.119994\pi\)
0.929783 + 0.368108i \(0.119994\pi\)
\(264\) −2.00409e9 −0.412574
\(265\) 3.66661e9 0.743500
\(266\) 1.24737e10i 2.49155i
\(267\) 1.33578e9i 0.262838i
\(268\) 3.80019e8i 0.0736658i
\(269\) 4.26909e9i 0.815317i 0.913135 + 0.407658i \(0.133655\pi\)
−0.913135 + 0.407658i \(0.866345\pi\)
\(270\) 1.77932e9i 0.334811i
\(271\) −1.99409e9 −0.369715 −0.184858 0.982765i \(-0.559182\pi\)
−0.184858 + 0.982765i \(0.559182\pi\)
\(272\) 9.93282e9 1.81467
\(273\) 1.07988e10i 1.94412i
\(274\) 1.07364e10i 1.90483i
\(275\) 7.84471e9i 1.37166i
\(276\) 2.17710e9i 0.375182i
\(277\) 3.08122e9 0.523363 0.261681 0.965154i \(-0.415723\pi\)
0.261681 + 0.965154i \(0.415723\pi\)
\(278\) 2.76784e9i 0.463406i
\(279\) 1.87801e8i 0.0309942i
\(280\) 6.56965e9i 1.06883i
\(281\) 7.73056e9 1.23990 0.619948 0.784643i \(-0.287153\pi\)
0.619948 + 0.784643i \(0.287153\pi\)
\(282\) −4.73148e9 −0.748171
\(283\) 1.40153e8i 0.0218503i −0.999940 0.0109252i \(-0.996522\pi\)
0.999940 0.0109252i \(-0.00347765\pi\)
\(284\) 2.90017e9 0.445811
\(285\) −5.20768e9 −0.789341
\(286\) 2.62049e10i 3.91668i
\(287\) −1.96254e10 −2.89262
\(288\) 2.65542e9i 0.385979i
\(289\) 8.47676e9 1.21517
\(290\) 1.23750e10i 1.74966i
\(291\) 7.78581e8i 0.108576i
\(292\) 1.44929e8i 0.0199353i
\(293\) 1.15041e9 0.156092 0.0780462 0.996950i \(-0.475132\pi\)
0.0780462 + 0.996950i \(0.475132\pi\)
\(294\) 1.44118e10i 1.92898i
\(295\) 9.16325e9 4.43308e9i 1.20993 0.585352i
\(296\) 6.74144e8 0.0878185
\(297\) 2.54650e9i 0.327279i
\(298\) 2.32147e9 0.294373
\(299\) −1.36842e10 −1.71212
\(300\) −2.54743e9 −0.314497
\(301\) 7.44822e9i 0.907375i
\(302\) −5.61464e9 −0.674985
\(303\) 1.39327e9i 0.165297i
\(304\) −1.05922e10 −1.24020
\(305\) 7.63953e9i 0.882810i
\(306\) 5.63017e9i 0.642149i
\(307\) −6.59310e9 −0.742226 −0.371113 0.928588i \(-0.621024\pi\)
−0.371113 + 0.928588i \(0.621024\pi\)
\(308\) 1.95593e10i 2.17346i
\(309\) 8.24506e9i 0.904398i
\(310\) −1.49393e9 −0.161764
\(311\) 4.88204e9 0.521867 0.260933 0.965357i \(-0.415970\pi\)
0.260933 + 0.965357i \(0.415970\pi\)
\(312\) −4.09058e9 −0.431684
\(313\) 1.44353e10i 1.50401i 0.659160 + 0.752003i \(0.270912\pi\)
−0.659160 + 0.752003i \(0.729088\pi\)
\(314\) −1.75381e9 −0.180411
\(315\) 8.34773e9 0.847864
\(316\) −5.80821e9 −0.582497
\(317\) 2.88442e9 0.285642 0.142821 0.989749i \(-0.454383\pi\)
0.142821 + 0.989749i \(0.454383\pi\)
\(318\) 4.22721e9i 0.413376i
\(319\) 1.77106e10i 1.71030i
\(320\) −3.93965e9 −0.375714
\(321\) 6.23792e9 0.587516
\(322\) 2.53377e10 2.35691
\(323\) −1.64782e10 −1.51391
\(324\) −8.26931e8 −0.0750394
\(325\) 1.60119e10i 1.43519i
\(326\) 7.79011e9i 0.689721i
\(327\) 2.82364e9i 0.246955i
\(328\) 7.43411e9i 0.642294i
\(329\) 2.21979e10i 1.89464i
\(330\) 2.02571e10 1.70813
\(331\) −6.73106e9 −0.560753 −0.280377 0.959890i \(-0.590459\pi\)
−0.280377 + 0.959890i \(0.590459\pi\)
\(332\) 1.23377e10i 1.01550i
\(333\) 8.56602e8i 0.0696630i
\(334\) 1.55922e10i 1.25291i
\(335\) 1.84647e9i 0.146610i
\(336\) 1.69789e10 1.33215
\(337\) 6.26340e9i 0.485614i −0.970075 0.242807i \(-0.921932\pi\)
0.970075 0.242807i \(-0.0780681\pi\)
\(338\) 3.65935e10i 2.80374i
\(339\) 1.43622e10i 1.08748i
\(340\) −1.80543e10 −1.35103
\(341\) 2.13806e9 0.158125
\(342\) 6.00390e9i 0.438863i
\(343\) −4.14196e10 −2.99247
\(344\) 2.82139e9 0.201479
\(345\) 1.05783e10i 0.746687i
\(346\) −3.08427e10 −2.15203
\(347\) 1.66110e10i 1.14572i 0.819655 + 0.572858i \(0.194165\pi\)
−0.819655 + 0.572858i \(0.805835\pi\)
\(348\) 5.75121e9 0.392141
\(349\) 4.18146e9i 0.281855i 0.990020 + 0.140928i \(0.0450085\pi\)
−0.990020 + 0.140928i \(0.954992\pi\)
\(350\) 2.96477e10i 1.97569i
\(351\) 5.19770e9i 0.342438i
\(352\) 3.02312e10 1.96918
\(353\) 1.36943e10i 0.881945i 0.897521 + 0.440973i \(0.145366\pi\)
−0.897521 + 0.440973i \(0.854634\pi\)
\(354\) 5.11087e9 + 1.05643e10i 0.325448 + 0.672707i
\(355\) 1.40916e10 0.887251
\(356\) 4.93834e9i 0.307455i
\(357\) 2.64141e10 1.62616
\(358\) 1.77452e10 1.08031
\(359\) 1.48079e10 0.891486 0.445743 0.895161i \(-0.352940\pi\)
0.445743 + 0.895161i \(0.352940\pi\)
\(360\) 3.16213e9i 0.188265i
\(361\) 5.88508e8 0.0346516
\(362\) 3.51104e10i 2.04457i
\(363\) −1.89666e10 −1.09235
\(364\) 3.99228e10i 2.27413i
\(365\) 7.04192e8i 0.0396752i
\(366\) 8.80757e9 0.490831
\(367\) 1.10191e10i 0.607408i 0.952766 + 0.303704i \(0.0982235\pi\)
−0.952766 + 0.303704i \(0.901777\pi\)
\(368\) 2.15157e10i 1.17318i
\(369\) 9.44616e9 0.509507
\(370\) −6.81415e9 −0.363584
\(371\) 1.98321e10 1.04682
\(372\) 6.94296e8i 0.0362554i
\(373\) 2.84790e10 1.47126 0.735629 0.677385i \(-0.236887\pi\)
0.735629 + 0.677385i \(0.236887\pi\)
\(374\) 6.40979e10 3.27610
\(375\) 2.96825e9 0.150098
\(376\) −8.40857e9 −0.420698
\(377\) 3.61494e10i 1.78952i
\(378\) 9.62406e9i 0.471401i
\(379\) −5.75537e9 −0.278944 −0.139472 0.990226i \(-0.544540\pi\)
−0.139472 + 0.990226i \(0.544540\pi\)
\(380\) 1.92527e10 0.923331
\(381\) −6.72857e9 −0.319318
\(382\) −1.93565e10 −0.909022
\(383\) −8.57438e8 −0.0398481 −0.0199240 0.999801i \(-0.506342\pi\)
−0.0199240 + 0.999801i \(0.506342\pi\)
\(384\) 9.99414e9i 0.459643i
\(385\) 9.50366e10i 4.32561i
\(386\) 2.31626e10i 1.04337i
\(387\) 3.58501e9i 0.159825i
\(388\) 2.87840e9i 0.127006i
\(389\) −1.61501e10 −0.705306 −0.352653 0.935754i \(-0.614720\pi\)
−0.352653 + 0.935754i \(0.614720\pi\)
\(390\) 4.13470e10 1.78725
\(391\) 3.34720e10i 1.43210i
\(392\) 2.56120e10i 1.08467i
\(393\) 1.64471e10i 0.689477i
\(394\) 2.20258e10i 0.914003i
\(395\) −2.82214e10 −1.15928
\(396\) 9.41438e9i 0.382834i
\(397\) 3.60875e10i 1.45276i 0.687292 + 0.726381i \(0.258799\pi\)
−0.687292 + 0.726381i \(0.741201\pi\)
\(398\) 8.81065e9i 0.351136i
\(399\) −2.81674e10 −1.11136
\(400\) −2.51755e10 −0.983420
\(401\) 9.33954e8i 0.0361200i 0.999837 + 0.0180600i \(0.00574899\pi\)
−0.999837 + 0.0180600i \(0.994251\pi\)
\(402\) −2.12878e9 −0.0815130
\(403\) 4.36401e9 0.165450
\(404\) 5.15088e9i 0.193355i
\(405\) −4.01796e9 −0.149343
\(406\) 6.69342e10i 2.46345i
\(407\) 9.75216e9 0.355405
\(408\) 1.00057e10i 0.361082i
\(409\) 3.19361e10i 1.14127i 0.821204 + 0.570635i \(0.193303\pi\)
−0.821204 + 0.570635i \(0.806697\pi\)
\(410\) 7.51430e10i 2.65921i
\(411\) 2.42443e10 0.849655
\(412\) 3.04818e10i 1.05792i
\(413\) 4.95625e10 2.39778e10i 1.70354 0.824154i
\(414\) −1.21956e10 −0.415148
\(415\) 5.99473e10i 2.02105i
\(416\) 6.17053e10 2.06039
\(417\) 6.25017e9 0.206703
\(418\) −6.83527e10 −2.23898
\(419\) 4.81100e10i 1.56091i −0.625210 0.780457i \(-0.714987\pi\)
0.625210 0.780457i \(-0.285013\pi\)
\(420\) −3.08614e10 −0.991788
\(421\) 5.57972e10i 1.77617i −0.459682 0.888084i \(-0.652036\pi\)
0.459682 0.888084i \(-0.347964\pi\)
\(422\) 4.88391e9 0.153999
\(423\) 1.06844e10i 0.333724i
\(424\) 7.51240e9i 0.232442i
\(425\) −3.91657e10 −1.20047
\(426\) 1.62461e10i 0.493300i
\(427\) 4.13209e10i 1.24296i
\(428\) −2.30615e10 −0.687246
\(429\) −5.91743e10 −1.74704
\(430\) −2.85182e10 −0.834159
\(431\) 2.56565e10i 0.743514i 0.928330 + 0.371757i \(0.121244\pi\)
−0.928330 + 0.371757i \(0.878756\pi\)
\(432\) −8.17233e9 −0.234645
\(433\) −3.15184e10 −0.896628 −0.448314 0.893876i \(-0.647975\pi\)
−0.448314 + 0.893876i \(0.647975\pi\)
\(434\) −8.08040e9 −0.227758
\(435\) 2.79445e10 0.780439
\(436\) 1.04389e10i 0.288875i
\(437\) 3.56939e10i 0.978741i
\(438\) 8.11859e8 0.0220589
\(439\) −4.77667e10 −1.28608 −0.643039 0.765834i \(-0.722327\pi\)
−0.643039 + 0.765834i \(0.722327\pi\)
\(440\) 3.59999e10 0.960486
\(441\) 3.25439e10 0.860428
\(442\) 1.30831e11 3.42785
\(443\) 6.06381e10i 1.57446i −0.616662 0.787228i \(-0.711516\pi\)
0.616662 0.787228i \(-0.288484\pi\)
\(444\) 3.16684e9i 0.0814882i
\(445\) 2.39948e10i 0.611896i
\(446\) 1.67819e8i 0.00424133i
\(447\) 5.24220e9i 0.131306i
\(448\) −2.13089e10 −0.528992
\(449\) −3.18003e10 −0.782431 −0.391216 0.920299i \(-0.627945\pi\)
−0.391216 + 0.920299i \(0.627945\pi\)
\(450\) 1.42701e10i 0.347999i
\(451\) 1.07542e11i 2.59939i
\(452\) 5.30969e10i 1.27208i
\(453\) 1.26787e10i 0.301079i
\(454\) −9.51988e10 −2.24083
\(455\) 1.93980e11i 4.52597i
\(456\) 1.06698e10i 0.246774i
\(457\) 2.02468e8i 0.00464186i −0.999997 0.00232093i \(-0.999261\pi\)
0.999997 0.00232093i \(-0.000738776\pi\)
\(458\) −1.73292e10 −0.393838
\(459\) −1.27137e10 −0.286432
\(460\) 3.91077e10i 0.873436i
\(461\) 1.84288e10 0.408031 0.204015 0.978968i \(-0.434601\pi\)
0.204015 + 0.978968i \(0.434601\pi\)
\(462\) 1.09567e11 2.40498
\(463\) 5.51189e10i 1.19943i 0.800212 + 0.599717i \(0.204720\pi\)
−0.800212 + 0.599717i \(0.795280\pi\)
\(464\) 5.68376e10 1.22621
\(465\) 3.37350e9i 0.0721554i
\(466\) 3.69441e10 0.783433
\(467\) 2.34956e10i 0.493991i 0.969017 + 0.246996i \(0.0794433\pi\)
−0.969017 + 0.246996i \(0.920557\pi\)
\(468\) 1.92158e10i 0.400567i
\(469\) 9.98723e9i 0.206421i
\(470\) 8.49926e10 1.74177
\(471\) 3.96034e9i 0.0804727i
\(472\) 9.08280e9 + 1.87743e10i 0.183000 + 0.378265i
\(473\) 4.08143e10 0.815394
\(474\) 3.25363e10i 0.644547i
\(475\) 4.17655e10 0.820433
\(476\) −9.76524e10 −1.90220
\(477\) −9.54564e9 −0.184388
\(478\) 8.63981e9i 0.165498i
\(479\) −3.87685e10 −0.736438 −0.368219 0.929739i \(-0.620032\pi\)
−0.368219 + 0.929739i \(0.620032\pi\)
\(480\) 4.76999e10i 0.898571i
\(481\) 1.99053e10 0.371867
\(482\) 6.10597e9i 0.113127i
\(483\) 5.72161e10i 1.05131i
\(484\) 7.01193e10 1.27778
\(485\) 1.39858e10i 0.252767i
\(486\) 4.63229e9i 0.0830329i
\(487\) −1.06085e11 −1.88598 −0.942990 0.332820i \(-0.892000\pi\)
−0.942990 + 0.332820i \(0.892000\pi\)
\(488\) 1.56524e10 0.275995
\(489\) 1.75912e10 0.307652
\(490\) 2.58882e11i 4.49074i
\(491\) −1.01600e11 −1.74810 −0.874049 0.485838i \(-0.838514\pi\)
−0.874049 + 0.485838i \(0.838514\pi\)
\(492\) −3.49223e10 −0.595995
\(493\) 8.84225e10 1.49684
\(494\) −1.39516e11 −2.34269
\(495\) 4.57433e10i 0.761916i
\(496\) 6.86153e9i 0.113369i
\(497\) 7.62190e10 1.24922
\(498\) −6.91129e10 −1.12368
\(499\) −4.47378e10 −0.721560 −0.360780 0.932651i \(-0.617490\pi\)
−0.360780 + 0.932651i \(0.617490\pi\)
\(500\) −1.09736e10 −0.175577
\(501\) −3.52093e10 −0.558864
\(502\) 1.46766e10i 0.231106i
\(503\) 7.34878e9i 0.114800i 0.998351 + 0.0574002i \(0.0182811\pi\)
−0.998351 + 0.0574002i \(0.981719\pi\)
\(504\) 1.71034e10i 0.265070i
\(505\) 2.50275e10i 0.384816i
\(506\) 1.38844e11i 2.11799i
\(507\) −8.26334e10 −1.25062
\(508\) 2.48754e10 0.373522
\(509\) 5.25488e10i 0.782874i 0.920205 + 0.391437i \(0.128022\pi\)
−0.920205 + 0.391437i \(0.871978\pi\)
\(510\) 1.01136e11i 1.49494i
\(511\) 3.80885e9i 0.0558613i
\(512\) 6.18117e10i 0.899479i
\(513\) 1.35577e10 0.195756
\(514\) 4.73985e10i 0.679066i
\(515\) 1.48108e11i 2.10547i
\(516\) 1.32537e10i 0.186956i
\(517\) −1.21638e11 −1.70258
\(518\) −3.68566e10 −0.511913
\(519\) 6.96472e10i 0.959919i
\(520\) 7.34799e10 1.00497
\(521\) 3.02402e10 0.410426 0.205213 0.978717i \(-0.434211\pi\)
0.205213 + 0.978717i \(0.434211\pi\)
\(522\) 3.22170e10i 0.433914i
\(523\) 9.02188e10 1.20584 0.602921 0.797801i \(-0.294003\pi\)
0.602921 + 0.797801i \(0.294003\pi\)
\(524\) 6.08048e10i 0.806515i
\(525\) −6.69487e10 −0.881261
\(526\) 1.84250e11i 2.40694i
\(527\) 1.06745e10i 0.138390i
\(528\) 9.30397e10i 1.19711i
\(529\) 5.80656e9 0.0741475
\(530\) 7.59343e10i 0.962353i
\(531\) −2.38556e10 + 1.15411e10i −0.300063 + 0.145167i
\(532\) 1.04135e11 1.30002
\(533\) 2.19505e11i 2.71979i
\(534\) 2.76635e10 0.340206
\(535\) −1.12053e11 −1.36776
\(536\) −3.78317e9 −0.0458349
\(537\) 4.00711e10i 0.481874i
\(538\) 8.84115e10 1.05531
\(539\) 3.70502e11i 4.38971i
\(540\) 1.48543e10 0.174694
\(541\) 2.53245e9i 0.0295632i −0.999891 0.0147816i \(-0.995295\pi\)
0.999891 0.0147816i \(-0.00470530\pi\)
\(542\) 4.12969e10i 0.478543i
\(543\) −7.92842e10 −0.911984
\(544\) 1.50933e11i 1.72341i
\(545\) 5.07216e10i 0.574919i
\(546\) 2.23639e11 2.51638
\(547\) −2.40448e10 −0.268579 −0.134289 0.990942i \(-0.542875\pi\)
−0.134289 + 0.990942i \(0.542875\pi\)
\(548\) −8.96309e10 −0.993883
\(549\) 1.98887e10i 0.218936i
\(550\) −1.62461e11 −1.77541
\(551\) −9.42920e10 −1.02298
\(552\) −2.16735e10 −0.233439
\(553\) −1.52645e11 −1.63223
\(554\) 6.38110e10i 0.677417i
\(555\) 1.53873e10i 0.162178i
\(556\) −2.31068e10 −0.241791
\(557\) 6.66433e10 0.692366 0.346183 0.938167i \(-0.387478\pi\)
0.346183 + 0.938167i \(0.387478\pi\)
\(558\) 3.88929e9 0.0401175
\(559\) 8.33065e10 0.853162
\(560\) −3.04995e11 −3.10128
\(561\) 1.44742e11i 1.46131i
\(562\) 1.60097e11i 1.60487i
\(563\) 1.64430e11i 1.63661i −0.574781 0.818307i \(-0.694913\pi\)
0.574781 0.818307i \(-0.305087\pi\)
\(564\) 3.94999e10i 0.390373i
\(565\) 2.57991e11i 2.53170i
\(566\) −2.90253e9 −0.0282820
\(567\) −2.17325e10 −0.210270
\(568\) 2.88718e10i 0.277384i
\(569\) 1.01693e11i 0.970162i 0.874469 + 0.485081i \(0.161210\pi\)
−0.874469 + 0.485081i \(0.838790\pi\)
\(570\) 1.07849e11i 1.02169i
\(571\) 1.81949e10i 0.171161i −0.996331 0.0855806i \(-0.972725\pi\)
0.996331 0.0855806i \(-0.0272745\pi\)
\(572\) 2.18766e11 2.04360
\(573\) 4.37098e10i 0.405471i
\(574\) 4.06435e11i 3.74407i
\(575\) 8.48376e10i 0.776098i
\(576\) 1.02565e10 0.0931769
\(577\) 1.56217e11 1.40937 0.704684 0.709521i \(-0.251089\pi\)
0.704684 + 0.709521i \(0.251089\pi\)
\(578\) 1.75551e11i 1.57287i
\(579\) 5.23044e10 0.465397
\(580\) −1.03310e11 −0.912917
\(581\) 3.24245e11i 2.84557i
\(582\) 1.61242e10 0.140535
\(583\) 1.08674e11i 0.940704i
\(584\) 1.44280e9 0.0124038
\(585\) 9.33673e10i 0.797207i
\(586\) 2.38246e10i 0.202039i
\(587\) 1.71108e11i 1.44118i 0.693361 + 0.720591i \(0.256129\pi\)
−0.693361 + 0.720591i \(0.743871\pi\)
\(588\) −1.20314e11 −1.00648
\(589\) 1.13831e10i 0.0945798i
\(590\) −9.18076e10 1.89768e11i −0.757654 1.56608i
\(591\) 4.97374e10 0.407693
\(592\) 3.12970e10i 0.254810i
\(593\) −7.33238e10 −0.592961 −0.296481 0.955039i \(-0.595813\pi\)
−0.296481 + 0.955039i \(0.595813\pi\)
\(594\) −5.27372e10 −0.423615
\(595\) −4.74482e11 −3.78575
\(596\) 1.93803e10i 0.153595i
\(597\) −1.98957e10 −0.156625
\(598\) 2.83396e11i 2.21610i
\(599\) 1.65450e11 1.28516 0.642582 0.766217i \(-0.277863\pi\)
0.642582 + 0.766217i \(0.277863\pi\)
\(600\) 2.53602e10i 0.195681i
\(601\) 6.47113e10i 0.496001i −0.968760 0.248000i \(-0.920227\pi\)
0.968760 0.248000i \(-0.0797734\pi\)
\(602\) −1.54250e11 −1.17446
\(603\) 4.80709e9i 0.0363591i
\(604\) 4.68728e10i 0.352187i
\(605\) 3.40701e11 2.54304
\(606\) −2.88541e10 −0.213952
\(607\) 1.06456e11 0.784178 0.392089 0.919927i \(-0.371752\pi\)
0.392089 + 0.919927i \(0.371752\pi\)
\(608\) 1.60952e11i 1.17783i
\(609\) 1.51147e11 1.09883
\(610\) −1.58212e11 −1.14267
\(611\) −2.48278e11 −1.78145
\(612\) 4.70024e10 0.335054
\(613\) 1.71688e11i 1.21590i −0.793976 0.607950i \(-0.791992\pi\)
0.793976 0.607950i \(-0.208008\pi\)
\(614\) 1.36541e11i 0.960704i
\(615\) −1.69683e11 −1.18615
\(616\) 1.94717e11 1.35233
\(617\) 6.22771e8 0.00429722 0.00214861 0.999998i \(-0.499316\pi\)
0.00214861 + 0.999998i \(0.499316\pi\)
\(618\) −1.70752e11 −1.17061
\(619\) 1.40781e11 0.958921 0.479460 0.877564i \(-0.340832\pi\)
0.479460 + 0.877564i \(0.340832\pi\)
\(620\) 1.24718e10i 0.0844037i
\(621\) 2.75395e10i 0.185178i
\(622\) 1.01105e11i 0.675481i
\(623\) 1.29784e11i 0.861526i
\(624\) 1.89904e11i 1.25255i
\(625\) −1.76393e11 −1.15601
\(626\) 2.98951e11 1.94672
\(627\) 1.54350e11i 0.998703i
\(628\) 1.46413e10i 0.0941329i
\(629\) 4.86889e10i 0.311048i
\(630\) 1.72879e11i 1.09744i
\(631\) 3.02486e11 1.90804 0.954022 0.299736i \(-0.0968987\pi\)
0.954022 + 0.299736i \(0.0968987\pi\)
\(632\) 5.78219e10i 0.362430i
\(633\) 1.10286e10i 0.0686916i
\(634\) 5.97355e10i 0.369722i
\(635\) 1.20867e11 0.743382
\(636\) 3.52901e10 0.215687
\(637\) 7.56237e11i 4.59304i
\(638\) 3.66781e11 2.21373
\(639\) −3.66860e10 −0.220038
\(640\) 1.79527e11i 1.07006i
\(641\) 2.62634e11 1.55567 0.777837 0.628466i \(-0.216317\pi\)
0.777837 + 0.628466i \(0.216317\pi\)
\(642\) 1.29185e11i 0.760454i
\(643\) 1.74145e11 1.01875 0.509374 0.860545i \(-0.329877\pi\)
0.509374 + 0.860545i \(0.329877\pi\)
\(644\) 2.11527e11i 1.22977i
\(645\) 6.43982e10i 0.372079i
\(646\) 3.41259e11i 1.95954i
\(647\) 6.34406e9 0.0362035 0.0181017 0.999836i \(-0.494238\pi\)
0.0181017 + 0.999836i \(0.494238\pi\)
\(648\) 8.23228e9i 0.0466896i
\(649\) 1.31392e11 + 2.71589e11i 0.740609 + 1.53085i
\(650\) −3.31602e11 −1.85765
\(651\) 1.82467e10i 0.101592i
\(652\) −6.50343e10 −0.359875
\(653\) −3.28080e11 −1.80437 −0.902187 0.431346i \(-0.858039\pi\)
−0.902187 + 0.431346i \(0.858039\pi\)
\(654\) −5.84766e10 −0.319647
\(655\) 2.95443e11i 1.60513i
\(656\) −3.45128e11 −1.86365
\(657\) 1.83329e9i 0.00983943i
\(658\) 4.59711e11 2.45234
\(659\) 3.44431e11i 1.82625i −0.407678 0.913126i \(-0.633661\pi\)
0.407678 0.913126i \(-0.366339\pi\)
\(660\) 1.69112e11i 0.891250i
\(661\) 1.08781e11 0.569833 0.284916 0.958552i \(-0.408034\pi\)
0.284916 + 0.958552i \(0.408034\pi\)
\(662\) 1.39398e11i 0.725813i
\(663\) 2.95435e11i 1.52900i
\(664\) −1.22824e11 −0.631847
\(665\) 5.05978e11 2.58729
\(666\) 1.77399e10 0.0901686
\(667\) 1.91534e11i 0.967703i
\(668\) 1.30168e11 0.653731
\(669\) −3.78959e8 −0.00189185
\(670\) 3.82397e10 0.189765
\(671\) 2.26428e11 1.11696
\(672\) 2.58001e11i 1.26515i
\(673\) 3.75875e9i 0.0183224i −0.999958 0.00916122i \(-0.997084\pi\)
0.999958 0.00916122i \(-0.00291615\pi\)
\(674\) −1.29713e11 −0.628556
\(675\) 3.22240e10 0.155226
\(676\) 3.05494e11 1.46291
\(677\) −8.68097e10 −0.413251 −0.206625 0.978420i \(-0.566248\pi\)
−0.206625 + 0.978420i \(0.566248\pi\)
\(678\) −2.97437e11 −1.40759
\(679\) 7.56469e10i 0.355887i
\(680\) 1.79734e11i 0.840610i
\(681\) 2.14972e11i 0.999526i
\(682\) 4.42784e10i 0.204670i
\(683\) 1.53291e11i 0.704425i −0.935920 0.352213i \(-0.885429\pi\)
0.935920 0.352213i \(-0.114571\pi\)
\(684\) −5.01224e10 −0.228985
\(685\) −4.35506e11 −1.97802
\(686\) 8.57787e11i 3.87332i
\(687\) 3.91318e10i 0.175672i
\(688\) 1.30983e11i 0.584602i
\(689\) 2.21817e11i 0.984277i
\(690\) 2.19073e11 0.966478
\(691\) 4.99163e10i 0.218942i 0.993990 + 0.109471i \(0.0349157\pi\)
−0.993990 + 0.109471i \(0.965084\pi\)
\(692\) 2.57485e11i 1.12286i
\(693\) 2.47418e11i 1.07275i
\(694\) 3.44008e11 1.48296
\(695\) −1.12273e11 −0.481212
\(696\) 5.72545e10i 0.243991i
\(697\) −5.36916e11 −2.27497
\(698\) 8.65966e10 0.364821
\(699\) 8.34250e10i 0.349452i
\(700\) 2.47508e11 1.03085
\(701\) 7.98312e10i 0.330598i −0.986243 0.165299i \(-0.947141\pi\)
0.986243 0.165299i \(-0.0528590\pi\)
\(702\) −1.07643e11 −0.443237
\(703\) 5.19208e10i 0.212579i
\(704\) 1.16767e11i 0.475368i
\(705\) 1.91925e11i 0.776919i
\(706\) 2.83605e11 1.14155
\(707\) 1.35370e11i 0.541806i
\(708\) 8.81937e10 4.26671e10i 0.350998 0.169809i
\(709\) −1.26648e11 −0.501202 −0.250601 0.968090i \(-0.580628\pi\)
−0.250601 + 0.968090i \(0.580628\pi\)
\(710\) 2.91832e11i 1.14842i
\(711\) 7.34715e10 0.287502
\(712\) 4.91622e10 0.191299
\(713\) 2.31223e10 0.0894689
\(714\) 5.47027e11i 2.10483i
\(715\) 1.06296e12 4.06717
\(716\) 1.48142e11i 0.563672i
\(717\) 1.95099e10 0.0738208
\(718\) 3.06666e11i 1.15390i
\(719\) 5.88819e10i 0.220326i 0.993914 + 0.110163i \(0.0351373\pi\)
−0.993914 + 0.110163i \(0.964863\pi\)
\(720\) 1.46801e11 0.546261
\(721\) 8.01089e11i 2.96442i
\(722\) 1.21878e10i 0.0448515i
\(723\) −1.37881e10 −0.0504606
\(724\) 2.93112e11 1.06679
\(725\) −2.24114e11 −0.811180
\(726\) 3.92793e11i 1.41389i
\(727\) 2.41969e10 0.0866209 0.0433104 0.999062i \(-0.486210\pi\)
0.0433104 + 0.999062i \(0.486210\pi\)
\(728\) 3.97440e11 1.41497
\(729\) 1.04604e10 0.0370370
\(730\) −1.45836e10 −0.0513538
\(731\) 2.03770e11i 0.713627i
\(732\) 7.35283e10i 0.256100i
\(733\) −3.00481e11 −1.04088 −0.520441 0.853897i \(-0.674233\pi\)
−0.520441 + 0.853897i \(0.674233\pi\)
\(734\) 2.28201e11 0.786202
\(735\) −5.84592e11 −2.00310
\(736\) 3.26939e11 1.11418
\(737\) −5.47273e10 −0.185496
\(738\) 1.95627e11i 0.659483i
\(739\) 2.67704e11i 0.897587i 0.893636 + 0.448793i \(0.148146\pi\)
−0.893636 + 0.448793i \(0.851854\pi\)
\(740\) 5.68866e10i 0.189707i
\(741\) 3.15046e11i 1.04496i
\(742\) 4.10716e11i 1.35496i
\(743\) −1.01469e11 −0.332948 −0.166474 0.986046i \(-0.553238\pi\)
−0.166474 + 0.986046i \(0.553238\pi\)
\(744\) 6.91186e9 0.0225581
\(745\) 9.41668e10i 0.305684i
\(746\) 5.89790e11i 1.90433i
\(747\) 1.56067e11i 0.501219i
\(748\) 5.35109e11i 1.70937i
\(749\) −6.06076e11 −1.92575
\(750\) 6.14715e10i 0.194280i
\(751\) 3.88339e11i 1.22082i −0.792086 0.610409i \(-0.791005\pi\)
0.792086 0.610409i \(-0.208995\pi\)
\(752\) 3.90367e11i 1.22068i
\(753\) 3.31419e10 0.103085
\(754\) 7.48642e11 2.31627
\(755\) 2.27749e11i 0.700921i
\(756\) 8.03446e10 0.245963
\(757\) −4.92875e10 −0.150091 −0.0750453 0.997180i \(-0.523910\pi\)
−0.0750453 + 0.997180i \(0.523910\pi\)
\(758\) 1.19192e11i 0.361052i
\(759\) −3.13529e11 −0.944736
\(760\) 1.91665e11i 0.574497i
\(761\) −4.76705e11 −1.42138 −0.710692 0.703504i \(-0.751618\pi\)
−0.710692 + 0.703504i \(0.751618\pi\)
\(762\) 1.39347e11i 0.413311i
\(763\) 2.74344e11i 0.809464i
\(764\) 1.61594e11i 0.474300i
\(765\) 2.28379e11 0.666823
\(766\) 1.77573e10i 0.0515776i
\(767\) 2.68185e11 + 5.54344e11i 0.774914 + 1.60176i
\(768\) 2.63121e11 0.756328
\(769\) 3.24575e11i 0.928132i −0.885801 0.464066i \(-0.846390\pi\)
0.885801 0.464066i \(-0.153610\pi\)
\(770\) −1.96818e12 −5.59888
\(771\) −1.07033e11 −0.302899
\(772\) −1.93368e11 −0.544398
\(773\) 5.12558e10i 0.143557i −0.997421 0.0717786i \(-0.977132\pi\)
0.997421 0.0717786i \(-0.0228675\pi\)
\(774\) 7.42443e10 0.206871
\(775\) 2.70554e10i 0.0749976i
\(776\) 2.86551e10 0.0790233
\(777\) 8.32274e10i 0.228340i
\(778\) 3.34464e11i 0.912916i
\(779\) 5.72556e11 1.55478
\(780\) 3.45177e11i 0.932532i
\(781\) 4.17660e11i 1.12258i
\(782\) 6.93195e11 1.85365