Properties

Label 177.9.c.a.58.4
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 58.4
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.77

$q$-expansion

\(f(q)\) \(=\) \(q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-29.4383i q^{2} -46.7654 q^{3} -610.615 q^{4} -616.312 q^{5} +1376.69i q^{6} -3233.41 q^{7} +10439.3i q^{8} +2187.00 q^{9} +18143.2i q^{10} -16327.4i q^{11} +28555.6 q^{12} +22558.2i q^{13} +95186.3i q^{14} +28822.1 q^{15} +150997. q^{16} -11817.3 q^{17} -64381.6i q^{18} +184894. q^{19} +376330. q^{20} +151212. q^{21} -480653. q^{22} +365066. i q^{23} -488197. i q^{24} -10784.2 q^{25} +664076. q^{26} -102276. q^{27} +1.97437e6 q^{28} +333403. q^{29} -848474. i q^{30} -730489. i q^{31} -1.77266e6i q^{32} +763559. i q^{33} +347881. i q^{34} +1.99279e6 q^{35} -1.33542e6 q^{36} +2.68652e6i q^{37} -5.44297e6i q^{38} -1.05494e6i q^{39} -6.43385e6i q^{40} -5.13105e6 q^{41} -4.45142e6i q^{42} +1.15417e6i q^{43} +9.96978e6i q^{44} -1.34787e6 q^{45} +1.07469e7 q^{46} +6.97887e6i q^{47} -7.06145e6 q^{48} +4.69017e6 q^{49} +317469. i q^{50} +552639. q^{51} -1.37744e7i q^{52} -1.05640e7 q^{53} +3.01083e6i q^{54} +1.00628e7i q^{55} -3.37545e7i q^{56} -8.64663e6 q^{57} -9.81481e6i q^{58} +(-1.21170e7 - 90073.3i) q^{59} -1.75992e7 q^{60} -1.31445e7i q^{61} -2.15044e7 q^{62} -7.07148e6 q^{63} -1.35287e7 q^{64} -1.39029e7i q^{65} +2.24779e7 q^{66} -9.27099e6i q^{67} +7.21581e6 q^{68} -1.70725e7i q^{69} -5.86645e7i q^{70} -6.40244e6 q^{71} +2.28307e7i q^{72} -1.74523e7i q^{73} +7.90865e7 q^{74} +504327. q^{75} -1.12899e8 q^{76} +5.27934e7i q^{77} -3.10558e7 q^{78} +5.50300e7 q^{79} -9.30615e7 q^{80} +4.78297e6 q^{81} +1.51050e8i q^{82} +6.16543e6i q^{83} -9.23322e7 q^{84} +7.28313e6 q^{85} +3.39770e7 q^{86} -1.55917e7 q^{87} +1.70447e8 q^{88} -7.65784e7i q^{89} +3.96792e7i q^{90} -7.29401e7i q^{91} -2.22915e8i q^{92} +3.41616e7i q^{93} +2.05446e8 q^{94} -1.13952e8 q^{95} +8.28989e7i q^{96} +6.58511e7i q^{97} -1.38071e8i q^{98} -3.57081e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 29.4383i 1.83990i −0.392041 0.919948i \(-0.628231\pi\)
0.392041 0.919948i \(-0.371769\pi\)
\(3\) −46.7654 −0.577350
\(4\) −610.615 −2.38522
\(5\) −616.312 −0.986100 −0.493050 0.870001i \(-0.664118\pi\)
−0.493050 + 0.870001i \(0.664118\pi\)
\(6\) 1376.69i 1.06226i
\(7\) −3233.41 −1.34670 −0.673348 0.739326i \(-0.735144\pi\)
−0.673348 + 0.739326i \(0.735144\pi\)
\(8\) 10439.3i 2.54865i
\(9\) 2187.00 0.333333
\(10\) 18143.2i 1.81432i
\(11\) 16327.4i 1.11519i −0.830114 0.557593i \(-0.811725\pi\)
0.830114 0.557593i \(-0.188275\pi\)
\(12\) 28555.6 1.37710
\(13\) 22558.2i 0.789826i 0.918719 + 0.394913i \(0.129225\pi\)
−0.918719 + 0.394913i \(0.870775\pi\)
\(14\) 95186.3i 2.47778i
\(15\) 28822.1 0.569325
\(16\) 150997. 2.30404
\(17\) −11817.3 −0.141489 −0.0707444 0.997494i \(-0.522537\pi\)
−0.0707444 + 0.997494i \(0.522537\pi\)
\(18\) 64381.6i 0.613299i
\(19\) 184894. 1.41876 0.709379 0.704828i \(-0.248976\pi\)
0.709379 + 0.704828i \(0.248976\pi\)
\(20\) 376330. 2.35206
\(21\) 151212. 0.777515
\(22\) −480653. −2.05183
\(23\) 365066.i 1.30455i 0.757983 + 0.652274i \(0.226185\pi\)
−0.757983 + 0.652274i \(0.773815\pi\)
\(24\) 488197.i 1.47146i
\(25\) −10784.2 −0.0276075
\(26\) 664076. 1.45320
\(27\) −102276. −0.192450
\(28\) 1.97437e6 3.21216
\(29\) 333403. 0.471386 0.235693 0.971828i \(-0.424264\pi\)
0.235693 + 0.971828i \(0.424264\pi\)
\(30\) 848474.i 1.04750i
\(31\) 730489.i 0.790982i −0.918470 0.395491i \(-0.870574\pi\)
0.918470 0.395491i \(-0.129426\pi\)
\(32\) 1.77266e6i 1.69054i
\(33\) 763559.i 0.643853i
\(34\) 347881.i 0.260324i
\(35\) 1.99279e6 1.32798
\(36\) −1.33542e6 −0.795072
\(37\) 2.68652e6i 1.43345i 0.697356 + 0.716725i \(0.254360\pi\)
−0.697356 + 0.716725i \(0.745640\pi\)
\(38\) 5.44297e6i 2.61037i
\(39\) 1.05494e6i 0.456006i
\(40\) 6.43385e6i 2.51322i
\(41\) −5.13105e6 −1.81581 −0.907906 0.419173i \(-0.862320\pi\)
−0.907906 + 0.419173i \(0.862320\pi\)
\(42\) 4.45142e6i 1.43055i
\(43\) 1.15417e6i 0.337596i 0.985651 + 0.168798i \(0.0539886\pi\)
−0.985651 + 0.168798i \(0.946011\pi\)
\(44\) 9.96978e6i 2.65996i
\(45\) −1.34787e6 −0.328700
\(46\) 1.07469e7 2.40023
\(47\) 6.97887e6i 1.43019i 0.699027 + 0.715095i \(0.253617\pi\)
−0.699027 + 0.715095i \(0.746383\pi\)
\(48\) −7.06145e6 −1.33024
\(49\) 4.69017e6 0.813588
\(50\) 317469.i 0.0507950i
\(51\) 552639. 0.0816886
\(52\) 1.37744e7i 1.88390i
\(53\) −1.05640e7 −1.33883 −0.669413 0.742890i \(-0.733454\pi\)
−0.669413 + 0.742890i \(0.733454\pi\)
\(54\) 3.01083e6i 0.354088i
\(55\) 1.00628e7i 1.09968i
\(56\) 3.37545e7i 3.43226i
\(57\) −8.64663e6 −0.819120
\(58\) 9.81481e6i 0.867301i
\(59\) −1.21170e7 90073.3i −0.999972 0.00743341i
\(60\) −1.75992e7 −1.35796
\(61\) 1.31445e7i 0.949345i −0.880162 0.474673i \(-0.842567\pi\)
0.880162 0.474673i \(-0.157433\pi\)
\(62\) −2.15044e7 −1.45533
\(63\) −7.07148e6 −0.448898
\(64\) −1.35287e7 −0.806373
\(65\) 1.39029e7i 0.778847i
\(66\) 2.24779e7 1.18462
\(67\) 9.27099e6i 0.460073i −0.973182 0.230037i \(-0.926115\pi\)
0.973182 0.230037i \(-0.0738846\pi\)
\(68\) 7.21581e6 0.337481
\(69\) 1.70725e7i 0.753181i
\(70\) 5.86645e7i 2.44334i
\(71\) −6.40244e6 −0.251949 −0.125974 0.992034i \(-0.540206\pi\)
−0.125974 + 0.992034i \(0.540206\pi\)
\(72\) 2.28307e7i 0.849551i
\(73\) 1.74523e7i 0.614554i −0.951620 0.307277i \(-0.900582\pi\)
0.951620 0.307277i \(-0.0994178\pi\)
\(74\) 7.90865e7 2.63740
\(75\) 504327. 0.0159392
\(76\) −1.12899e8 −3.38404
\(77\) 5.27934e7i 1.50182i
\(78\) −3.10558e7 −0.839004
\(79\) 5.50300e7 1.41284 0.706418 0.707795i \(-0.250310\pi\)
0.706418 + 0.707795i \(0.250310\pi\)
\(80\) −9.30615e7 −2.27201
\(81\) 4.78297e6 0.111111
\(82\) 1.51050e8i 3.34091i
\(83\) 6.16543e6i 0.129912i 0.997888 + 0.0649562i \(0.0206908\pi\)
−0.997888 + 0.0649562i \(0.979309\pi\)
\(84\) −9.23322e7 −1.85454
\(85\) 7.28313e6 0.139522
\(86\) 3.39770e7 0.621142
\(87\) −1.55917e7 −0.272155
\(88\) 1.70447e8 2.84222
\(89\) 7.65784e7i 1.22052i −0.792200 0.610262i \(-0.791064\pi\)
0.792200 0.610262i \(-0.208936\pi\)
\(90\) 3.96792e7i 0.604773i
\(91\) 7.29401e7i 1.06365i
\(92\) 2.22915e8i 3.11163i
\(93\) 3.41616e7i 0.456674i
\(94\) 2.05446e8 2.63140
\(95\) −1.13952e8 −1.39904
\(96\) 8.28989e7i 0.976032i
\(97\) 6.58511e7i 0.743834i 0.928266 + 0.371917i \(0.121299\pi\)
−0.928266 + 0.371917i \(0.878701\pi\)
\(98\) 1.38071e8i 1.49692i
\(99\) 3.57081e7i 0.371729i
\(100\) 6.58499e6 0.0658499
\(101\) 1.13495e8i 1.09067i 0.838219 + 0.545334i \(0.183597\pi\)
−0.838219 + 0.545334i \(0.816403\pi\)
\(102\) 1.62688e7i 0.150298i
\(103\) 1.77831e8i 1.58000i 0.613105 + 0.790002i \(0.289920\pi\)
−0.613105 + 0.790002i \(0.710080\pi\)
\(104\) −2.35491e8 −2.01299
\(105\) −9.31937e7 −0.766707
\(106\) 3.10986e8i 2.46330i
\(107\) −6.98484e7 −0.532870 −0.266435 0.963853i \(-0.585846\pi\)
−0.266435 + 0.963853i \(0.585846\pi\)
\(108\) 6.24512e7 0.459035
\(109\) 8.41201e6i 0.0595928i −0.999556 0.0297964i \(-0.990514\pi\)
0.999556 0.0297964i \(-0.00948589\pi\)
\(110\) 2.96232e8 2.02330
\(111\) 1.25636e8i 0.827603i
\(112\) −4.88237e8 −3.10284
\(113\) 1.36911e8i 0.839699i −0.907594 0.419850i \(-0.862083\pi\)
0.907594 0.419850i \(-0.137917\pi\)
\(114\) 2.54542e8i 1.50710i
\(115\) 2.24995e8i 1.28641i
\(116\) −2.03581e8 −1.12436
\(117\) 4.93348e7i 0.263275i
\(118\) −2.65161e6 + 3.56705e8i −0.0136767 + 1.83984i
\(119\) 3.82102e7 0.190542
\(120\) 3.00882e8i 1.45101i
\(121\) −5.22265e7 −0.243640
\(122\) −3.86952e8 −1.74670
\(123\) 2.39956e8 1.04836
\(124\) 4.46048e8i 1.88666i
\(125\) 2.47393e8 1.01332
\(126\) 2.08172e8i 0.825926i
\(127\) −9.99127e7 −0.384066 −0.192033 0.981388i \(-0.561508\pi\)
−0.192033 + 0.981388i \(0.561508\pi\)
\(128\) 5.55379e7i 0.206895i
\(129\) 5.39754e7i 0.194911i
\(130\) −4.09278e8 −1.43300
\(131\) 5.59034e8i 1.89825i 0.314902 + 0.949124i \(0.398028\pi\)
−0.314902 + 0.949124i \(0.601972\pi\)
\(132\) 4.66241e8i 1.53573i
\(133\) −5.97839e8 −1.91063
\(134\) −2.72923e8 −0.846487
\(135\) 6.30339e7 0.189775
\(136\) 1.23364e8i 0.360605i
\(137\) 2.76211e8 0.784078 0.392039 0.919949i \(-0.371770\pi\)
0.392039 + 0.919949i \(0.371770\pi\)
\(138\) −5.02584e8 −1.38577
\(139\) 2.88032e8 0.771582 0.385791 0.922586i \(-0.373929\pi\)
0.385791 + 0.922586i \(0.373929\pi\)
\(140\) −1.21683e9 −3.16751
\(141\) 3.26370e8i 0.825721i
\(142\) 1.88477e8i 0.463559i
\(143\) 3.68318e8 0.880803
\(144\) 3.30231e8 0.768012
\(145\) −2.05480e8 −0.464834
\(146\) −5.13765e8 −1.13072
\(147\) −2.19338e8 −0.469725
\(148\) 1.64043e9i 3.41909i
\(149\) 3.52277e8i 0.714725i −0.933966 0.357363i \(-0.883676\pi\)
0.933966 0.357363i \(-0.116324\pi\)
\(150\) 1.48465e7i 0.0293265i
\(151\) 8.12741e7i 0.156331i 0.996940 + 0.0781653i \(0.0249062\pi\)
−0.996940 + 0.0781653i \(0.975094\pi\)
\(152\) 1.93016e9i 3.61592i
\(153\) −2.58444e7 −0.0471629
\(154\) 1.55415e9 2.76318
\(155\) 4.50209e8i 0.779987i
\(156\) 6.44164e8i 1.08767i
\(157\) 2.90473e8i 0.478088i −0.971009 0.239044i \(-0.923166\pi\)
0.971009 0.239044i \(-0.0768340\pi\)
\(158\) 1.61999e9i 2.59947i
\(159\) 4.94029e8 0.772972
\(160\) 1.09251e9i 1.66704i
\(161\) 1.18041e9i 1.75683i
\(162\) 1.40803e8i 0.204433i
\(163\) −5.34854e8 −0.757679 −0.378839 0.925462i \(-0.623677\pi\)
−0.378839 + 0.925462i \(0.623677\pi\)
\(164\) 3.13310e9 4.33110
\(165\) 4.70591e8i 0.634903i
\(166\) 1.81500e8 0.239025
\(167\) −7.99654e8 −1.02810 −0.514051 0.857760i \(-0.671856\pi\)
−0.514051 + 0.857760i \(0.671856\pi\)
\(168\) 1.57854e9i 1.98161i
\(169\) 3.06858e8 0.376175
\(170\) 2.14403e8i 0.256706i
\(171\) 4.04363e8 0.472919
\(172\) 7.04756e8i 0.805240i
\(173\) 1.00169e9i 1.11828i −0.829074 0.559138i \(-0.811132\pi\)
0.829074 0.559138i \(-0.188868\pi\)
\(174\) 4.58993e8i 0.500737i
\(175\) 3.48698e7 0.0371789
\(176\) 2.46540e9i 2.56943i
\(177\) 5.66657e8 + 4.21231e6i 0.577334 + 0.00429168i
\(178\) −2.25434e9 −2.24564
\(179\) 5.88886e8i 0.573613i −0.957989 0.286806i \(-0.907406\pi\)
0.957989 0.286806i \(-0.0925937\pi\)
\(180\) 8.23033e8 0.784020
\(181\) 1.08898e9 1.01462 0.507310 0.861763i \(-0.330640\pi\)
0.507310 + 0.861763i \(0.330640\pi\)
\(182\) −2.14723e9 −1.95701
\(183\) 6.14707e8i 0.548105i
\(184\) −3.81103e9 −3.32484
\(185\) 1.65573e9i 1.41352i
\(186\) 1.00566e9 0.840232
\(187\) 1.92946e8i 0.157786i
\(188\) 4.26141e9i 3.41131i
\(189\) 3.30700e8 0.259172
\(190\) 3.35457e9i 2.57408i
\(191\) 1.49793e9i 1.12554i −0.826615 0.562768i \(-0.809737\pi\)
0.826615 0.562768i \(-0.190263\pi\)
\(192\) 6.32674e8 0.465560
\(193\) −2.05695e9 −1.48250 −0.741251 0.671228i \(-0.765767\pi\)
−0.741251 + 0.671228i \(0.765767\pi\)
\(194\) 1.93855e9 1.36858
\(195\) 6.50175e8i 0.449668i
\(196\) −2.86389e9 −1.94058
\(197\) 1.32713e9 0.881146 0.440573 0.897717i \(-0.354775\pi\)
0.440573 + 0.897717i \(0.354775\pi\)
\(198\) −1.05119e9 −0.683942
\(199\) −1.43410e9 −0.914464 −0.457232 0.889347i \(-0.651159\pi\)
−0.457232 + 0.889347i \(0.651159\pi\)
\(200\) 1.12579e8i 0.0703620i
\(201\) 4.33561e8i 0.265623i
\(202\) 3.34111e9 2.00672
\(203\) −1.07803e9 −0.634814
\(204\) −3.37450e8 −0.194845
\(205\) 3.16233e9 1.79057
\(206\) 5.23504e9 2.90704
\(207\) 7.98400e8i 0.434849i
\(208\) 3.40623e9i 1.81979i
\(209\) 3.01884e9i 1.58218i
\(210\) 2.74347e9i 1.41066i
\(211\) 9.39980e8i 0.474230i −0.971482 0.237115i \(-0.923798\pi\)
0.971482 0.237115i \(-0.0762018\pi\)
\(212\) 6.45053e9 3.19339
\(213\) 2.99412e8 0.145463
\(214\) 2.05622e9i 0.980426i
\(215\) 7.11332e8i 0.332903i
\(216\) 1.06769e9i 0.490488i
\(217\) 2.36197e9i 1.06521i
\(218\) −2.47636e8 −0.109645
\(219\) 8.16161e8i 0.354813i
\(220\) 6.14450e9i 2.62298i
\(221\) 2.66577e8i 0.111751i
\(222\) −3.69851e9 −1.52270
\(223\) −3.59919e9 −1.45541 −0.727705 0.685891i \(-0.759413\pi\)
−0.727705 + 0.685891i \(0.759413\pi\)
\(224\) 5.73173e9i 2.27664i
\(225\) −2.35850e7 −0.00920251
\(226\) −4.03042e9 −1.54496
\(227\) 2.67506e9i 1.00747i −0.863859 0.503733i \(-0.831960\pi\)
0.863859 0.503733i \(-0.168040\pi\)
\(228\) 5.27976e9 1.95378
\(229\) 8.27102e8i 0.300758i −0.988628 0.150379i \(-0.951951\pi\)
0.988628 0.150379i \(-0.0480494\pi\)
\(230\) −6.62347e9 −2.36687
\(231\) 2.46890e9i 0.867074i
\(232\) 3.48048e9i 1.20140i
\(233\) 4.11175e7i 0.0139509i −0.999976 0.00697546i \(-0.997780\pi\)
0.999976 0.00697546i \(-0.00222038\pi\)
\(234\) 1.45233e9 0.484399
\(235\) 4.30116e9i 1.41031i
\(236\) 7.39884e9 + 5.50001e7i 2.38515 + 0.0177303i
\(237\) −2.57350e9 −0.815701
\(238\) 1.12484e9i 0.350578i
\(239\) −5.22238e9 −1.60058 −0.800289 0.599614i \(-0.795321\pi\)
−0.800289 + 0.599614i \(0.795321\pi\)
\(240\) 4.35206e9 1.31175
\(241\) 2.85572e9 0.846539 0.423270 0.906004i \(-0.360882\pi\)
0.423270 + 0.906004i \(0.360882\pi\)
\(242\) 1.53746e9i 0.448273i
\(243\) −2.23677e8 −0.0641500
\(244\) 8.02622e9i 2.26439i
\(245\) −2.89061e9 −0.802278
\(246\) 7.06389e9i 1.92887i
\(247\) 4.17088e9i 1.12057i
\(248\) 7.62578e9 2.01594
\(249\) 2.88328e8i 0.0750050i
\(250\) 7.28285e9i 1.86441i
\(251\) 6.65166e9 1.67585 0.837926 0.545784i \(-0.183768\pi\)
0.837926 + 0.545784i \(0.183768\pi\)
\(252\) 4.31795e9 1.07072
\(253\) 5.96059e9 1.45481
\(254\) 2.94126e9i 0.706641i
\(255\) −3.40598e8 −0.0805531
\(256\) −5.09829e9 −1.18704
\(257\) −4.78161e9 −1.09608 −0.548039 0.836453i \(-0.684626\pi\)
−0.548039 + 0.836453i \(0.684626\pi\)
\(258\) −1.58894e9 −0.358616
\(259\) 8.68662e9i 1.93042i
\(260\) 8.48932e9i 1.85772i
\(261\) 7.29151e8 0.157129
\(262\) 1.64570e10 3.49258
\(263\) −3.74519e9 −0.782800 −0.391400 0.920221i \(-0.628009\pi\)
−0.391400 + 0.920221i \(0.628009\pi\)
\(264\) −7.97100e9 −1.64096
\(265\) 6.51071e9 1.32022
\(266\) 1.75994e10i 3.51537i
\(267\) 3.58122e9i 0.704670i
\(268\) 5.66101e9i 1.09737i
\(269\) 9.90529e9i 1.89173i 0.324567 + 0.945863i \(0.394781\pi\)
−0.324567 + 0.945863i \(0.605219\pi\)
\(270\) 1.85561e9i 0.349166i
\(271\) −7.68454e9 −1.42476 −0.712379 0.701795i \(-0.752382\pi\)
−0.712379 + 0.701795i \(0.752382\pi\)
\(272\) −1.78438e9 −0.325995
\(273\) 3.41107e9i 0.614101i
\(274\) 8.13120e9i 1.44262i
\(275\) 1.76078e8i 0.0307875i
\(276\) 1.04247e10i 1.79650i
\(277\) 1.39902e9 0.237633 0.118816 0.992916i \(-0.462090\pi\)
0.118816 + 0.992916i \(0.462090\pi\)
\(278\) 8.47919e9i 1.41963i
\(279\) 1.59758e9i 0.263661i
\(280\) 2.08033e10i 3.38455i
\(281\) −2.81269e8 −0.0451124 −0.0225562 0.999746i \(-0.507180\pi\)
−0.0225562 + 0.999746i \(0.507180\pi\)
\(282\) −9.60777e9 −1.51924
\(283\) 3.94330e9i 0.614772i 0.951585 + 0.307386i \(0.0994542\pi\)
−0.951585 + 0.307386i \(0.900546\pi\)
\(284\) 3.90943e9 0.600952
\(285\) 5.32903e9 0.807734
\(286\) 1.08427e10i 1.62059i
\(287\) 1.65908e10 2.44535
\(288\) 3.87680e9i 0.563512i
\(289\) −6.83611e9 −0.979981
\(290\) 6.04899e9i 0.855246i
\(291\) 3.07955e9i 0.429453i
\(292\) 1.06566e10i 1.46584i
\(293\) 1.41198e10 1.91584 0.957918 0.287042i \(-0.0926718\pi\)
0.957918 + 0.287042i \(0.0926718\pi\)
\(294\) 6.45693e9i 0.864245i
\(295\) 7.46787e9 + 5.55133e7i 0.986072 + 0.00733008i
\(296\) −2.80453e10 −3.65336
\(297\) 1.66990e9i 0.214618i
\(298\) −1.03704e10 −1.31502
\(299\) −8.23524e9 −1.03037
\(300\) −3.07950e8 −0.0380185
\(301\) 3.73192e9i 0.454639i
\(302\) 2.39257e9 0.287632
\(303\) 5.30765e9i 0.629697i
\(304\) 2.79185e10 3.26887
\(305\) 8.10110e9i 0.936149i
\(306\) 7.60816e8i 0.0867748i
\(307\) 8.30008e9 0.934391 0.467195 0.884154i \(-0.345264\pi\)
0.467195 + 0.884154i \(0.345264\pi\)
\(308\) 3.22364e10i 3.58215i
\(309\) 8.31632e9i 0.912215i
\(310\) 1.32534e10 1.43510
\(311\) 6.15653e9 0.658103 0.329052 0.944312i \(-0.393271\pi\)
0.329052 + 0.944312i \(0.393271\pi\)
\(312\) 1.10128e10 1.16220
\(313\) 1.44649e10i 1.50708i −0.657399 0.753542i \(-0.728343\pi\)
0.657399 0.753542i \(-0.271657\pi\)
\(314\) −8.55105e9 −0.879631
\(315\) 4.35824e9 0.442658
\(316\) −3.36022e10 −3.36992
\(317\) −1.63270e10 −1.61685 −0.808424 0.588601i \(-0.799679\pi\)
−0.808424 + 0.588601i \(0.799679\pi\)
\(318\) 1.45434e10i 1.42219i
\(319\) 5.44361e9i 0.525683i
\(320\) 8.33790e9 0.795164
\(321\) 3.26649e9 0.307653
\(322\) −3.47493e10 −3.23238
\(323\) −2.18494e9 −0.200738
\(324\) −2.92055e9 −0.265024
\(325\) 2.43272e8i 0.0218051i
\(326\) 1.57452e10i 1.39405i
\(327\) 3.93391e8i 0.0344059i
\(328\) 5.35645e10i 4.62787i
\(329\) 2.25656e10i 1.92603i
\(330\) −1.38534e10 −1.16816
\(331\) 8.97447e9 0.747648 0.373824 0.927500i \(-0.378046\pi\)
0.373824 + 0.927500i \(0.378046\pi\)
\(332\) 3.76470e9i 0.309869i
\(333\) 5.87541e9i 0.477817i
\(334\) 2.35405e10i 1.89160i
\(335\) 5.71383e9i 0.453678i
\(336\) 2.28326e10 1.79142
\(337\) 1.97815e10i 1.53369i 0.641830 + 0.766847i \(0.278176\pi\)
−0.641830 + 0.766847i \(0.721824\pi\)
\(338\) 9.03338e9i 0.692123i
\(339\) 6.40268e9i 0.484800i
\(340\) −4.44719e9 −0.332790
\(341\) −1.19270e10 −0.882093
\(342\) 1.19038e10i 0.870122i
\(343\) 3.47473e9 0.251041
\(344\) −1.20487e10 −0.860415
\(345\) 1.05220e10i 0.742712i
\(346\) −2.94881e10 −2.05751
\(347\) 1.90497e10i 1.31392i −0.753925 0.656961i \(-0.771842\pi\)
0.753925 0.656961i \(-0.228158\pi\)
\(348\) 9.52052e9 0.649148
\(349\) 2.41925e10i 1.63072i −0.578953 0.815361i \(-0.696539\pi\)
0.578953 0.815361i \(-0.303461\pi\)
\(350\) 1.02651e9i 0.0684053i
\(351\) 2.30716e9i 0.152002i
\(352\) −2.89429e10 −1.88526
\(353\) 1.42526e9i 0.0917900i −0.998946 0.0458950i \(-0.985386\pi\)
0.998946 0.0458950i \(-0.0146140\pi\)
\(354\) 1.24003e8 1.66814e10i 0.00789625 1.06223i
\(355\) 3.94590e9 0.248446
\(356\) 4.67599e10i 2.91121i
\(357\) −1.78691e9 −0.110010
\(358\) −1.73358e10 −1.05539
\(359\) −2.34055e10 −1.40910 −0.704548 0.709656i \(-0.748850\pi\)
−0.704548 + 0.709656i \(0.748850\pi\)
\(360\) 1.40708e10i 0.837742i
\(361\) 1.72022e10 1.01287
\(362\) 3.20576e10i 1.86680i
\(363\) 2.44239e9 0.140666
\(364\) 4.45383e10i 2.53705i
\(365\) 1.07560e10i 0.606011i
\(366\) 1.80959e10 1.00846
\(367\) 1.28919e10i 0.710646i −0.934744 0.355323i \(-0.884371\pi\)
0.934744 0.355323i \(-0.115629\pi\)
\(368\) 5.51240e10i 3.00573i
\(369\) −1.12216e10 −0.605271
\(370\) −4.87420e10 −2.60074
\(371\) 3.41577e10 1.80299
\(372\) 2.08596e10i 1.08927i
\(373\) 5.00658e9 0.258646 0.129323 0.991603i \(-0.458720\pi\)
0.129323 + 0.991603i \(0.458720\pi\)
\(374\) 5.68001e9 0.290310
\(375\) −1.15694e10 −0.585043
\(376\) −7.28544e10 −3.64506
\(377\) 7.52097e9i 0.372313i
\(378\) 9.73526e9i 0.476849i
\(379\) 2.65952e9 0.128898 0.0644490 0.997921i \(-0.479471\pi\)
0.0644490 + 0.997921i \(0.479471\pi\)
\(380\) 6.95810e10 3.33700
\(381\) 4.67245e9 0.221741
\(382\) −4.40967e10 −2.07087
\(383\) −9.02518e9 −0.419431 −0.209716 0.977762i \(-0.567254\pi\)
−0.209716 + 0.977762i \(0.567254\pi\)
\(384\) 2.59725e9i 0.119451i
\(385\) 3.25372e10i 1.48094i
\(386\) 6.05533e10i 2.72765i
\(387\) 2.52418e9i 0.112532i
\(388\) 4.02097e10i 1.77420i
\(389\) 3.33795e10 1.45775 0.728873 0.684649i \(-0.240045\pi\)
0.728873 + 0.684649i \(0.240045\pi\)
\(390\) 1.91401e10 0.827341
\(391\) 4.31409e9i 0.184579i
\(392\) 4.89620e10i 2.07355i
\(393\) 2.61434e10i 1.09595i
\(394\) 3.90684e10i 1.62122i
\(395\) −3.39157e10 −1.39320
\(396\) 2.18039e10i 0.886653i
\(397\) 4.12240e10i 1.65954i 0.558103 + 0.829771i \(0.311529\pi\)
−0.558103 + 0.829771i \(0.688471\pi\)
\(398\) 4.22175e10i 1.68252i
\(399\) 2.79581e10 1.10310
\(400\) −1.62839e9 −0.0636088
\(401\) 9.37756e9i 0.362671i −0.983421 0.181335i \(-0.941958\pi\)
0.983421 0.181335i \(-0.0580419\pi\)
\(402\) 1.27633e10 0.488719
\(403\) 1.64785e10 0.624738
\(404\) 6.93020e10i 2.60148i
\(405\) −2.94780e9 −0.109567
\(406\) 3.17354e10i 1.16799i
\(407\) 4.38639e10 1.59856
\(408\) 5.76916e9i 0.208196i
\(409\) 1.15949e10i 0.414355i 0.978303 + 0.207178i \(0.0664278\pi\)
−0.978303 + 0.207178i \(0.933572\pi\)
\(410\) 9.30937e10i 3.29447i
\(411\) −1.29171e10 −0.452688
\(412\) 1.08586e11i 3.76865i
\(413\) 3.91794e10 + 2.91244e8i 1.34666 + 0.0100105i
\(414\) 2.35035e10 0.800077
\(415\) 3.79983e9i 0.128107i
\(416\) 3.99880e10 1.33523
\(417\) −1.34699e10 −0.445473
\(418\) −8.88697e10 −2.91104
\(419\) 1.45775e10i 0.472963i −0.971636 0.236482i \(-0.924006\pi\)
0.971636 0.236482i \(-0.0759943\pi\)
\(420\) 5.69055e10 1.82876
\(421\) 5.70750e10i 1.81684i 0.418054 + 0.908422i \(0.362712\pi\)
−0.418054 + 0.908422i \(0.637288\pi\)
\(422\) −2.76714e10 −0.872533
\(423\) 1.52628e10i 0.476730i
\(424\) 1.10280e11i 3.41220i
\(425\) 1.27440e8 0.00390616
\(426\) 8.81420e9i 0.267636i
\(427\) 4.25016e10i 1.27848i
\(428\) 4.26505e10 1.27101
\(429\) −1.72245e10 −0.508532
\(430\) −2.09404e10 −0.612508
\(431\) 1.05104e10i 0.304588i 0.988335 + 0.152294i \(0.0486660\pi\)
−0.988335 + 0.152294i \(0.951334\pi\)
\(432\) −1.54434e10 −0.443412
\(433\) −5.48474e9 −0.156029 −0.0780144 0.996952i \(-0.524858\pi\)
−0.0780144 + 0.996952i \(0.524858\pi\)
\(434\) 6.95326e10 1.95988
\(435\) 9.60935e9 0.268372
\(436\) 5.13650e9i 0.142142i
\(437\) 6.74985e10i 1.85084i
\(438\) 2.40264e10 0.652819
\(439\) 5.74417e10 1.54657 0.773285 0.634059i \(-0.218612\pi\)
0.773285 + 0.634059i \(0.218612\pi\)
\(440\) −1.05048e11 −2.80271
\(441\) 1.02574e10 0.271196
\(442\) −7.84757e9 −0.205611
\(443\) 8.28816e8i 0.0215200i 0.999942 + 0.0107600i \(0.00342509\pi\)
−0.999942 + 0.0107600i \(0.996575\pi\)
\(444\) 7.67152e10i 1.97401i
\(445\) 4.71962e10i 1.20356i
\(446\) 1.05954e11i 2.67780i
\(447\) 1.64744e10i 0.412647i
\(448\) 4.37439e10 1.08594
\(449\) 7.91407e9 0.194722 0.0973609 0.995249i \(-0.468960\pi\)
0.0973609 + 0.995249i \(0.468960\pi\)
\(450\) 6.94304e8i 0.0169317i
\(451\) 8.37770e10i 2.02497i
\(452\) 8.35998e10i 2.00286i
\(453\) 3.80081e9i 0.0902576i
\(454\) −7.87493e10 −1.85363
\(455\) 4.49539e10i 1.04887i
\(456\) 9.02646e10i 2.08765i
\(457\) 1.24447e9i 0.0285312i 0.999898 + 0.0142656i \(0.00454103\pi\)
−0.999898 + 0.0142656i \(0.995459\pi\)
\(458\) −2.43485e10 −0.553363
\(459\) 1.20862e9 0.0272295
\(460\) 1.37385e11i 3.06838i
\(461\) −6.86301e10 −1.51954 −0.759768 0.650195i \(-0.774687\pi\)
−0.759768 + 0.650195i \(0.774687\pi\)
\(462\) −7.26804e10 −1.59533
\(463\) 1.84478e10i 0.401441i 0.979649 + 0.200720i \(0.0643283\pi\)
−0.979649 + 0.200720i \(0.935672\pi\)
\(464\) 5.03429e10 1.08609
\(465\) 2.10542e10i 0.450326i
\(466\) −1.21043e9 −0.0256682
\(467\) 1.62022e10i 0.340647i −0.985388 0.170324i \(-0.945519\pi\)
0.985388 0.170324i \(-0.0544813\pi\)
\(468\) 3.01246e10i 0.627968i
\(469\) 2.99770e10i 0.619578i
\(470\) −1.26619e11 −2.59482
\(471\) 1.35841e10i 0.276024i
\(472\) 9.40300e8 1.26493e11i 0.0189452 2.54858i
\(473\) 1.88447e10 0.376483
\(474\) 7.57596e10i 1.50080i
\(475\) −1.99393e9 −0.0391684
\(476\) −2.33317e10 −0.454484
\(477\) −2.31034e10 −0.446276
\(478\) 1.53738e11i 2.94490i
\(479\) −5.69459e10 −1.08173 −0.540867 0.841108i \(-0.681904\pi\)
−0.540867 + 0.841108i \(0.681904\pi\)
\(480\) 5.10916e10i 0.962464i
\(481\) −6.06030e10 −1.13218
\(482\) 8.40675e10i 1.55754i
\(483\) 5.52023e10i 1.01431i
\(484\) 3.18903e10 0.581134
\(485\) 4.05848e10i 0.733494i
\(486\) 6.58469e9i 0.118029i
\(487\) 7.90104e10 1.40465 0.702325 0.711856i \(-0.252145\pi\)
0.702325 + 0.711856i \(0.252145\pi\)
\(488\) 1.37219e11 2.41955
\(489\) 2.50127e10 0.437446
\(490\) 8.50947e10i 1.47611i
\(491\) 6.68721e9 0.115059 0.0575293 0.998344i \(-0.481678\pi\)
0.0575293 + 0.998344i \(0.481678\pi\)
\(492\) −1.46521e11 −2.50056
\(493\) −3.93991e9 −0.0666958
\(494\) 1.22784e11 2.06173
\(495\) 2.20073e10i 0.366562i
\(496\) 1.10302e11i 1.82245i
\(497\) 2.07017e10 0.339298
\(498\) −8.48791e9 −0.138001
\(499\) 4.76231e10 0.768095 0.384048 0.923313i \(-0.374530\pi\)
0.384048 + 0.923313i \(0.374530\pi\)
\(500\) −1.51062e11 −2.41699
\(501\) 3.73961e10 0.593575
\(502\) 1.95814e11i 3.08339i
\(503\) 7.43371e10i 1.16127i −0.814164 0.580636i \(-0.802804\pi\)
0.814164 0.580636i \(-0.197196\pi\)
\(504\) 7.38211e10i 1.14409i
\(505\) 6.99486e10i 1.07551i
\(506\) 1.75470e11i 2.67671i
\(507\) −1.43503e10 −0.217185
\(508\) 6.10082e10 0.916080
\(509\) 3.07711e10i 0.458428i −0.973376 0.229214i \(-0.926384\pi\)
0.973376 0.229214i \(-0.0736156\pi\)
\(510\) 1.00267e10i 0.148209i
\(511\) 5.64304e10i 0.827617i
\(512\) 1.35867e11i 1.97713i
\(513\) −1.89102e10 −0.273040
\(514\) 1.40763e11i 2.01667i
\(515\) 1.09599e11i 1.55804i
\(516\) 3.29582e10i 0.464905i
\(517\) 1.13947e11 1.59493
\(518\) −2.55720e11 −3.55177
\(519\) 4.68444e10i 0.645637i
\(520\) 1.45136e11 1.98501
\(521\) 1.13520e11 1.54071 0.770354 0.637617i \(-0.220080\pi\)
0.770354 + 0.637617i \(0.220080\pi\)
\(522\) 2.14650e10i 0.289100i
\(523\) 4.57237e10 0.611131 0.305566 0.952171i \(-0.401154\pi\)
0.305566 + 0.952171i \(0.401154\pi\)
\(524\) 3.41355e11i 4.52773i
\(525\) −1.63070e9 −0.0214653
\(526\) 1.10252e11i 1.44027i
\(527\) 8.63239e9i 0.111915i
\(528\) 1.15295e11i 1.48346i
\(529\) −5.49623e10 −0.701846
\(530\) 1.91665e11i 2.42906i
\(531\) −2.64999e10 1.96990e8i −0.333324 0.00247780i
\(532\) 3.65049e11 4.55727
\(533\) 1.15747e11i 1.43418i
\(534\) 1.05425e11 1.29652
\(535\) 4.30485e10 0.525463
\(536\) 9.67825e10 1.17257
\(537\) 2.75395e10i 0.331176i
\(538\) 2.91595e11 3.48058
\(539\) 7.65785e10i 0.907302i
\(540\) −3.84894e10 −0.452654
\(541\) 9.23499e10i 1.07807i 0.842283 + 0.539036i \(0.181211\pi\)
−0.842283 + 0.539036i \(0.818789\pi\)
\(542\) 2.26220e11i 2.62141i
\(543\) −5.09263e10 −0.585792
\(544\) 2.09480e10i 0.239192i
\(545\) 5.18443e9i 0.0587644i
\(546\) 1.00416e11 1.12988
\(547\) −1.17140e11 −1.30845 −0.654225 0.756300i \(-0.727005\pi\)
−0.654225 + 0.756300i \(0.727005\pi\)
\(548\) −1.68659e11 −1.87019
\(549\) 2.87470e10i 0.316448i
\(550\) 5.18345e9 0.0566459
\(551\) 6.16441e10 0.668783
\(552\) 1.78224e11 1.91960
\(553\) −1.77935e11 −1.90266
\(554\) 4.11850e10i 0.437220i
\(555\) 7.74309e10i 0.816099i
\(556\) −1.75877e11 −1.84039
\(557\) 2.93443e10 0.304861 0.152431 0.988314i \(-0.451290\pi\)
0.152431 + 0.988314i \(0.451290\pi\)
\(558\) −4.70301e10 −0.485108
\(559\) −2.60361e10 −0.266642
\(560\) 3.00907e11 3.05971
\(561\) 9.02319e9i 0.0910979i
\(562\) 8.28008e9i 0.0830021i
\(563\) 5.32789e10i 0.530300i −0.964207 0.265150i \(-0.914579\pi\)
0.964207 0.265150i \(-0.0854215\pi\)
\(564\) 1.99286e11i 1.96952i
\(565\) 8.43797e10i 0.828027i
\(566\) 1.16084e11 1.13112
\(567\) −1.54653e10 −0.149633
\(568\) 6.68368e10i 0.642129i
\(569\) 8.35642e10i 0.797207i 0.917123 + 0.398604i \(0.130505\pi\)
−0.917123 + 0.398604i \(0.869495\pi\)
\(570\) 1.56878e11i 1.48615i
\(571\) 1.30068e11i 1.22357i −0.791025 0.611783i \(-0.790452\pi\)
0.791025 0.611783i \(-0.209548\pi\)
\(572\) −2.24901e11 −2.10090
\(573\) 7.00514e10i 0.649828i
\(574\) 4.88406e11i 4.49918i
\(575\) 3.93694e9i 0.0360154i
\(576\) −2.95872e10 −0.268791
\(577\) 9.70636e10 0.875695 0.437848 0.899049i \(-0.355741\pi\)
0.437848 + 0.899049i \(0.355741\pi\)
\(578\) 2.01244e11i 1.80306i
\(579\) 9.61942e10 0.855923
\(580\) 1.25469e11 1.10873
\(581\) 1.99354e10i 0.174952i
\(582\) −9.06568e10 −0.790148
\(583\) 1.72483e11i 1.49304i
\(584\) 1.82189e11 1.56628
\(585\) 3.04057e10i 0.259616i
\(586\) 4.15664e11i 3.52494i
\(587\) 3.18566e10i 0.268317i −0.990960 0.134158i \(-0.957167\pi\)
0.990960 0.134158i \(-0.0428331\pi\)
\(588\) 1.33931e11 1.12040
\(589\) 1.35063e11i 1.12221i
\(590\) 1.63422e9 2.19842e11i 0.0134866 1.81427i
\(591\) −6.20636e10 −0.508730
\(592\) 4.05657e11i 3.30272i
\(593\) 3.25607e10 0.263314 0.131657 0.991295i \(-0.457970\pi\)
0.131657 + 0.991295i \(0.457970\pi\)
\(594\) 4.91592e10 0.394874
\(595\) −2.35494e10 −0.187894
\(596\) 2.15106e11i 1.70477i
\(597\) 6.70661e10 0.527966
\(598\) 2.42432e11i 1.89577i
\(599\) 1.11453e11 0.865733 0.432867 0.901458i \(-0.357502\pi\)
0.432867 + 0.901458i \(0.357502\pi\)
\(600\) 5.26481e9i 0.0406235i
\(601\) 1.13029e11i 0.866350i −0.901310 0.433175i \(-0.857393\pi\)
0.901310 0.433175i \(-0.142607\pi\)
\(602\) −1.09862e11 −0.836488
\(603\) 2.02757e10i 0.153358i
\(604\) 4.96272e10i 0.372882i
\(605\) 3.21878e10 0.240254
\(606\) −1.56248e11 −1.15858
\(607\) 8.24145e10 0.607084 0.303542 0.952818i \(-0.401831\pi\)
0.303542 + 0.952818i \(0.401831\pi\)
\(608\) 3.27753e11i 2.39846i
\(609\) 5.04144e10 0.366510
\(610\) 2.38483e11 1.72242
\(611\) −1.57431e11 −1.12960
\(612\) 1.57810e10 0.112494
\(613\) 1.46159e11i 1.03510i −0.855652 0.517551i \(-0.826844\pi\)
0.855652 0.517551i \(-0.173156\pi\)
\(614\) 2.44340e11i 1.71918i
\(615\) −1.47888e11 −1.03379
\(616\) −5.51125e11 −3.82761
\(617\) 3.77837e10 0.260714 0.130357 0.991467i \(-0.458388\pi\)
0.130357 + 0.991467i \(0.458388\pi\)
\(618\) −2.44819e11 −1.67838
\(619\) −8.71499e10 −0.593614 −0.296807 0.954937i \(-0.595922\pi\)
−0.296807 + 0.954937i \(0.595922\pi\)
\(620\) 2.74905e11i 1.86044i
\(621\) 3.73375e10i 0.251060i
\(622\) 1.81238e11i 1.21084i
\(623\) 2.47610e11i 1.64367i
\(624\) 1.59294e11i 1.05066i
\(625\) −1.48259e11 −0.971630
\(626\) −4.25822e11 −2.77288
\(627\) 1.41177e11i 0.913471i
\(628\) 1.77367e11i 1.14034i
\(629\) 3.17473e10i 0.202817i
\(630\) 1.28299e11i 0.814445i
\(631\) 1.73868e10 0.109673 0.0548367 0.998495i \(-0.482536\pi\)
0.0548367 + 0.998495i \(0.482536\pi\)
\(632\) 5.74474e11i 3.60082i
\(633\) 4.39585e10i 0.273797i
\(634\) 4.80639e11i 2.97483i
\(635\) 6.15774e10 0.378727
\(636\) −3.01661e11 −1.84370
\(637\) 1.05802e11i 0.642592i
\(638\) −1.60251e11 −0.967203
\(639\) −1.40021e10 −0.0839829
\(640\) 3.42287e10i 0.204019i
\(641\) −1.81064e11 −1.07251 −0.536254 0.844057i \(-0.680161\pi\)
−0.536254 + 0.844057i \(0.680161\pi\)
\(642\) 9.61600e10i 0.566049i
\(643\) 2.43062e11 1.42191 0.710957 0.703236i \(-0.248262\pi\)
0.710957 + 0.703236i \(0.248262\pi\)
\(644\) 7.20776e11i 4.19041i
\(645\) 3.32657e10i 0.192202i
\(646\) 6.43211e10i 0.369337i
\(647\) −5.58877e9 −0.0318933 −0.0159467 0.999873i \(-0.505076\pi\)
−0.0159467 + 0.999873i \(0.505076\pi\)
\(648\) 4.99307e10i 0.283184i
\(649\) −1.47067e9 + 1.97840e11i −0.00828964 + 1.11516i
\(650\) −7.16153e9 −0.0401192
\(651\) 1.10459e11i 0.615001i
\(652\) 3.26590e11 1.80723
\(653\) −1.06895e11 −0.587903 −0.293951 0.955820i \(-0.594970\pi\)
−0.293951 + 0.955820i \(0.594970\pi\)
\(654\) 1.15808e10 0.0633033
\(655\) 3.44539e11i 1.87186i
\(656\) −7.74776e11 −4.18370
\(657\) 3.81681e10i 0.204851i
\(658\) −6.64293e11 −3.54369
\(659\) 4.28516e10i 0.227209i −0.993526 0.113604i \(-0.963760\pi\)
0.993526 0.113604i \(-0.0362397\pi\)
\(660\) 2.87350e11i 1.51438i
\(661\) −1.87993e11 −0.984772 −0.492386 0.870377i \(-0.663875\pi\)
−0.492386 + 0.870377i \(0.663875\pi\)
\(662\) 2.64193e11i 1.37559i
\(663\) 1.24666e10i 0.0645197i
\(664\) −6.43626e10 −0.331102
\(665\) 3.68455e11 1.88408
\(666\) 1.72962e11 0.879132
\(667\) 1.21714e11i 0.614946i
\(668\) 4.88281e11 2.45225
\(669\) 1.68317e11 0.840281
\(670\) 1.68206e11 0.834720
\(671\) −2.14616e11 −1.05870
\(672\) 2.68047e11i 1.31442i
\(673\) 4.47608e10i 0.218191i 0.994031 + 0.109096i \(0.0347955\pi\)
−0.994031 + 0.109096i \(0.965204\pi\)
\(674\) 5.82333e11 2.82184
\(675\) 1.10296e9 0.00531307
\(676\) −1.87372e11 −0.897259
\(677\) 3.80002e11 1.80897 0.904484 0.426508i \(-0.140256\pi\)
0.904484 + 0.426508i \(0.140256\pi\)
\(678\) 1.88484e11 0.891982
\(679\) 2.12924e11i 1.00172i
\(680\) 7.60307e10i 0.355593i
\(681\) 1.25100e11i 0.581661i
\(682\) 3.51111e11i 1.62296i
\(683\) 2.97625e11i 1.36769i −0.729629 0.683843i \(-0.760307\pi\)
0.729629 0.683843i \(-0.239693\pi\)
\(684\) −2.46910e11 −1.12801
\(685\) −1.70232e11 −0.773179
\(686\) 1.02290e11i 0.461889i
\(687\) 3.86797e10i 0.173643i
\(688\) 1.74277e11i 0.777834i
\(689\) 2.38305e11i 1.05744i
\(690\) 3.09749e11 1.36651
\(691\) 1.55039e11i 0.680033i 0.940420 + 0.340016i \(0.110433\pi\)
−0.940420 + 0.340016i \(0.889567\pi\)
\(692\) 6.11648e11i 2.66733i
\(693\) 1.15459e11i 0.500605i
\(694\) −5.60790e11 −2.41748
\(695\) −1.77518e11 −0.760857
\(696\) 1.62766e11i 0.693628i
\(697\) 6.06351e10 0.256917
\(698\) −7.12188e11 −3.00036
\(699\) 1.92288e9i 0.00805457i
\(700\) −2.12920e10 −0.0886798
\(701\) 1.01201e11i 0.419096i −0.977798 0.209548i \(-0.932801\pi\)
0.977798 0.209548i \(-0.0671993\pi\)
\(702\) −6.79190e10 −0.279668
\(703\) 4.96720e11i 2.03372i
\(704\) 2.20889e11i 0.899256i
\(705\) 2.01146e11i 0.814243i
\(706\) −4.19573e10 −0.168884
\(707\) 3.66978e11i 1.46880i
\(708\) −3.46010e11 2.57210e9i −1.37707 0.0102366i
\(709\) −3.76546e10 −0.149016 −0.0745081 0.997220i \(-0.523739\pi\)
−0.0745081 + 0.997220i \(0.523739\pi\)
\(710\) 1.16161e11i 0.457115i
\(711\) 1.20351e11 0.470945
\(712\) 7.99423e11 3.11069
\(713\) 2.66677e11 1.03187
\(714\) 5.26037e10i 0.202406i
\(715\) −2.26999e11 −0.868559
\(716\) 3.59583e11i 1.36819i
\(717\) 2.44227e11 0.924094
\(718\) 6.89020e11i 2.59259i
\(719\) 4.00517e11i 1.49867i −0.662191 0.749335i \(-0.730373\pi\)
0.662191 0.749335i \(-0.269627\pi\)
\(720\) −2.03526e11 −0.757337
\(721\) 5.75001e11i 2.12778i
\(722\) 5.06404e11i 1.86358i
\(723\) −1.33549e11 −0.488750
\(724\) −6.64945e11 −2.42009
\(725\) −3.59548e9 −0.0130138
\(726\) 7.18999e10i 0.258810i
\(727\) 1.06855e11 0.382524 0.191262 0.981539i \(-0.438742\pi\)
0.191262 + 0.981539i \(0.438742\pi\)
\(728\) 7.61442e11 2.71089
\(729\) 1.04604e10 0.0370370
\(730\) 3.16640e11 1.11500
\(731\) 1.36392e10i 0.0477661i
\(732\) 3.75349e11i 1.30735i
\(733\) 4.55913e11 1.57931 0.789653 0.613554i \(-0.210261\pi\)
0.789653 + 0.613554i \(0.210261\pi\)
\(734\) −3.79517e11 −1.30751
\(735\) 1.35180e11 0.463196
\(736\) 6.47137e11 2.20539
\(737\) −1.51372e11 −0.513067
\(738\) 3.30346e11i 1.11364i
\(739\) 2.16091e10i 0.0724534i 0.999344 + 0.0362267i \(0.0115338\pi\)
−0.999344 + 0.0362267i \(0.988466\pi\)
\(740\) 1.01102e12i 3.37156i
\(741\) 1.95053e11i 0.646962i
\(742\) 1.00555e12i 3.31732i
\(743\) 1.25286e11 0.411100 0.205550 0.978647i \(-0.434102\pi\)
0.205550 + 0.978647i \(0.434102\pi\)
\(744\) −3.56622e11 −1.16390
\(745\) 2.17113e11i 0.704790i
\(746\) 1.47385e11i 0.475882i
\(747\) 1.34838e10i 0.0433042i
\(748\) 1.17816e11i 0.376354i
\(749\) 2.25849e11 0.717614
\(750\) 3.40585e11i 1.07642i
\(751\) 4.84579e11i 1.52337i −0.647949 0.761683i \(-0.724373\pi\)
0.647949 0.761683i \(-0.275627\pi\)
\(752\) 1.05379e12i 3.29521i
\(753\) −3.11068e11 −0.967553
\(754\) 2.21405e11 0.685017
\(755\) 5.00902e10i 0.154158i
\(756\) −2.01931e11 −0.618180
\(757\) 3.11094e11 0.947346 0.473673 0.880701i \(-0.342928\pi\)
0.473673 + 0.880701i \(0.342928\pi\)
\(758\) 7.82918e10i 0.237159i
\(759\) −2.78749e11 −0.839937
\(760\) 1.18958e12i 3.56566i
\(761\) 5.50313e11 1.64086 0.820429 0.571749i \(-0.193735\pi\)
0.820429 + 0.571749i \(0.193735\pi\)
\(762\) 1.37549e11i 0.407979i
\(763\) 2.71995e10i 0.0802533i
\(764\) 9.14661e11i 2.68464i
\(765\) 1.59282e10 0.0465073
\(766\) 2.65686e11i 0.771709i
\(767\) 2.03189e9 2.73338e11i 0.00587110 0.789804i
\(768\) 2.38423e11 0.685336
\(769\) 3.14849e11i 0.900321i −0.892948 0.450161i \(-0.851367\pi\)
0.892948 0.450161i \(-0.148633\pi\)
\(770\) −9.57841e11 −2.72477
\(771\) 2.23614e11 0.632821
\(772\) 1.25601e12 3.53609
\(773\) 3.75244e11i 1.05098i −0.850799 0.525492i \(-0.823881\pi\)
0.850799 0.525492i \(-0.176119\pi\)
\(774\) 7.43076e10 0.207047
\(775\) 7.87773e9i 0.0218371i
\(776\) −6.87438e11 −1.89577
\(777\) 4.06233e11i 1.11453i
\(778\) 9.82637e11i 2.68210i
\(779\) −9.48700e11 −2.57620
\(780\) 3.97006e11i 1.07255i
\(781\) 1.04535e11i 0.280970i
\(782\) −1.27000e11 −0.339606