Properties

Label 177.9.c.a.58.20
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 58.20
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.61

$q$-expansion

\(f(q)\) \(=\) \(q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} -10127.7i q^{10} +14544.7i q^{11} +5413.53 q^{12} +49404.0i q^{13} -12698.4i q^{14} -24564.3 q^{15} -81770.2 q^{16} -70791.4 q^{17} -42167.7i q^{18} +94835.6 q^{19} -60804.6 q^{20} -30799.4 q^{21} +280436. q^{22} -232818. i q^{23} +126453. i q^{24} -114720. q^{25} +952561. q^{26} -102276. q^{27} -76238.4 q^{28} -742936. q^{29} +473626. i q^{30} -644602. i q^{31} +884395. i q^{32} -680186. i q^{33} +1.36493e6i q^{34} +345937. q^{35} -253166. q^{36} -2.71240e6i q^{37} -1.82853e6i q^{38} -2.31040e6i q^{39} -1.42032e6i q^{40} -5.07256e6 q^{41} +593845. i q^{42} -4.10695e6i q^{43} -1.68368e6i q^{44} +1.14876e6 q^{45} -4.48899e6 q^{46} -1.20234e6i q^{47} +3.82401e6 q^{48} -5.33106e6 q^{49} +2.21191e6i q^{50} +3.31059e6 q^{51} -5.71898e6i q^{52} -1.48565e6 q^{53} +1.97199e6i q^{54} +7.63983e6i q^{55} -1.78083e6i q^{56} -4.43502e6 q^{57} +1.43246e7i q^{58} +(-7.46187e6 - 9.54730e6i) q^{59} +2.84355e6 q^{60} +3.27863e6i q^{61} -1.24286e7 q^{62} +1.44034e6 q^{63} -3.88108e6 q^{64} +2.59503e7i q^{65} -1.31147e7 q^{66} -1.38873e7i q^{67} +8.19477e6 q^{68} +1.08878e7i q^{69} -6.67004e6i q^{70} -1.94846e7 q^{71} -5.91362e6i q^{72} -3.54200e7i q^{73} -5.22980e7 q^{74} +5.36490e6 q^{75} -1.09781e7 q^{76} +9.57902e6i q^{77} -4.45469e7 q^{78} +4.27188e7 q^{79} -4.29512e7 q^{80} +4.78297e6 q^{81} +9.78044e7i q^{82} +4.18077e7i q^{83} +3.56532e6 q^{84} -3.71844e7 q^{85} -7.91865e7 q^{86} +3.47437e7 q^{87} +3.93286e7 q^{88} +1.03706e7i q^{89} -2.21493e7i q^{90} +3.25371e7i q^{91} +2.69509e7i q^{92} +3.01451e7i q^{93} -2.31823e7 q^{94} +4.98140e7 q^{95} -4.13591e7i q^{96} -9.94679e7i q^{97} +1.02788e8i q^{98} +3.18092e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.2811i 1.20507i −0.798094 0.602533i \(-0.794158\pi\)
0.798094 0.602533i \(-0.205842\pi\)
\(3\) −46.7654 −0.577350
\(4\) −115.759 −0.452185
\(5\) 525.267 0.840427 0.420214 0.907425i \(-0.361955\pi\)
0.420214 + 0.907425i \(0.361955\pi\)
\(6\) 901.686i 0.695745i
\(7\) 658.593 0.274300 0.137150 0.990550i \(-0.456206\pi\)
0.137150 + 0.990550i \(0.456206\pi\)
\(8\) 2703.99i 0.660153i
\(9\) 2187.00 0.333333
\(10\) 10127.7i 1.01277i
\(11\) 14544.7i 0.993420i 0.867917 + 0.496710i \(0.165459\pi\)
−0.867917 + 0.496710i \(0.834541\pi\)
\(12\) 5413.53 0.261069
\(13\) 49404.0i 1.72977i 0.501969 + 0.864885i \(0.332609\pi\)
−0.501969 + 0.864885i \(0.667391\pi\)
\(14\) 12698.4i 0.330549i
\(15\) −24564.3 −0.485221
\(16\) −81770.2 −1.24771
\(17\) −70791.4 −0.847588 −0.423794 0.905759i \(-0.639302\pi\)
−0.423794 + 0.905759i \(0.639302\pi\)
\(18\) 42167.7i 0.401689i
\(19\) 94835.6 0.727708 0.363854 0.931456i \(-0.381461\pi\)
0.363854 + 0.931456i \(0.381461\pi\)
\(20\) −60804.6 −0.380029
\(21\) −30799.4 −0.158367
\(22\) 280436. 1.19714
\(23\) 232818.i 0.831967i −0.909372 0.415983i \(-0.863437\pi\)
0.909372 0.415983i \(-0.136563\pi\)
\(24\) 126453.i 0.381140i
\(25\) −114720. −0.293682
\(26\) 952561. 2.08449
\(27\) −102276. −0.192450
\(28\) −76238.4 −0.124034
\(29\) −742936. −1.05041 −0.525206 0.850975i \(-0.676012\pi\)
−0.525206 + 0.850975i \(0.676012\pi\)
\(30\) 473626.i 0.584723i
\(31\) 644602.i 0.697983i −0.937126 0.348992i \(-0.886524\pi\)
0.937126 0.348992i \(-0.113476\pi\)
\(32\) 884395.i 0.843425i
\(33\) 680186.i 0.573551i
\(34\) 1.36493e6i 1.02140i
\(35\) 345937. 0.230529
\(36\) −253166. −0.150728
\(37\) 2.71240e6i 1.44726i −0.690187 0.723631i \(-0.742472\pi\)
0.690187 0.723631i \(-0.257528\pi\)
\(38\) 1.82853e6i 0.876936i
\(39\) 2.31040e6i 0.998684i
\(40\) 1.42032e6i 0.554811i
\(41\) −5.07256e6 −1.79511 −0.897557 0.440899i \(-0.854660\pi\)
−0.897557 + 0.440899i \(0.854660\pi\)
\(42\) 593845.i 0.190843i
\(43\) 4.10695e6i 1.20129i −0.799518 0.600643i \(-0.794912\pi\)
0.799518 0.600643i \(-0.205088\pi\)
\(44\) 1.68368e6i 0.449210i
\(45\) 1.14876e6 0.280142
\(46\) −4.48899e6 −1.00258
\(47\) 1.20234e6i 0.246397i −0.992382 0.123198i \(-0.960685\pi\)
0.992382 0.123198i \(-0.0393151\pi\)
\(48\) 3.82401e6 0.720368
\(49\) −5.33106e6 −0.924760
\(50\) 2.21191e6i 0.353906i
\(51\) 3.31059e6 0.489355
\(52\) 5.71898e6i 0.782177i
\(53\) −1.48565e6 −0.188283 −0.0941416 0.995559i \(-0.530011\pi\)
−0.0941416 + 0.995559i \(0.530011\pi\)
\(54\) 1.97199e6i 0.231915i
\(55\) 7.63983e6i 0.834897i
\(56\) 1.78083e6i 0.181080i
\(57\) −4.43502e6 −0.420142
\(58\) 1.43246e7i 1.26582i
\(59\) −7.46187e6 9.54730e6i −0.615800 0.787902i
\(60\) 2.84355e6 0.219410
\(61\) 3.27863e6i 0.236796i 0.992966 + 0.118398i \(0.0377758\pi\)
−0.992966 + 0.118398i \(0.962224\pi\)
\(62\) −1.24286e7 −0.841116
\(63\) 1.44034e6 0.0914332
\(64\) −3.88108e6 −0.231331
\(65\) 2.59503e7i 1.45375i
\(66\) −1.31147e7 −0.691167
\(67\) 1.38873e7i 0.689160i −0.938757 0.344580i \(-0.888021\pi\)
0.938757 0.344580i \(-0.111979\pi\)
\(68\) 8.19477e6 0.383267
\(69\) 1.08878e7i 0.480336i
\(70\) 6.67004e6i 0.277803i
\(71\) −1.94846e7 −0.766757 −0.383379 0.923591i \(-0.625240\pi\)
−0.383379 + 0.923591i \(0.625240\pi\)
\(72\) 5.91362e6i 0.220051i
\(73\) 3.54200e7i 1.24726i −0.781719 0.623631i \(-0.785657\pi\)
0.781719 0.623631i \(-0.214343\pi\)
\(74\) −5.22980e7 −1.74405
\(75\) 5.36490e6 0.169557
\(76\) −1.09781e7 −0.329059
\(77\) 9.57902e6i 0.272495i
\(78\) −4.45469e7 −1.20348
\(79\) 4.27188e7 1.09676 0.548379 0.836230i \(-0.315245\pi\)
0.548379 + 0.836230i \(0.315245\pi\)
\(80\) −4.29512e7 −1.04861
\(81\) 4.78297e6 0.111111
\(82\) 9.78044e7i 2.16323i
\(83\) 4.18077e7i 0.880935i 0.897769 + 0.440468i \(0.145187\pi\)
−0.897769 + 0.440468i \(0.854813\pi\)
\(84\) 3.56532e6 0.0716112
\(85\) −3.71844e7 −0.712336
\(86\) −7.91865e7 −1.44763
\(87\) 3.47437e7 0.606456
\(88\) 3.93286e7 0.655809
\(89\) 1.03706e7i 0.165290i 0.996579 + 0.0826448i \(0.0263367\pi\)
−0.996579 + 0.0826448i \(0.973663\pi\)
\(90\) 2.21493e7i 0.337590i
\(91\) 3.25371e7i 0.474476i
\(92\) 2.69509e7i 0.376203i
\(93\) 3.01451e7i 0.402981i
\(94\) −2.31823e7 −0.296924
\(95\) 4.98140e7 0.611586
\(96\) 4.13591e7i 0.486952i
\(97\) 9.94679e7i 1.12356i −0.827287 0.561780i \(-0.810117\pi\)
0.827287 0.561780i \(-0.189883\pi\)
\(98\) 1.02788e8i 1.11440i
\(99\) 3.18092e7i 0.331140i
\(100\) 1.32799e7 0.132799
\(101\) 7.18300e7i 0.690272i −0.938553 0.345136i \(-0.887833\pi\)
0.938553 0.345136i \(-0.112167\pi\)
\(102\) 6.38316e7i 0.589706i
\(103\) 6.61524e7i 0.587755i 0.955843 + 0.293878i \(0.0949458\pi\)
−0.955843 + 0.293878i \(0.905054\pi\)
\(104\) 1.33588e8 1.14191
\(105\) −1.61779e7 −0.133096
\(106\) 2.86448e7i 0.226894i
\(107\) −7.05875e7 −0.538509 −0.269254 0.963069i \(-0.586777\pi\)
−0.269254 + 0.963069i \(0.586777\pi\)
\(108\) 1.18394e7 0.0870231
\(109\) 1.69697e8i 1.20218i 0.799182 + 0.601089i \(0.205266\pi\)
−0.799182 + 0.601089i \(0.794734\pi\)
\(110\) 1.47304e8 1.00611
\(111\) 1.26847e8i 0.835577i
\(112\) −5.38533e7 −0.342247
\(113\) 5.74155e7i 0.352140i 0.984378 + 0.176070i \(0.0563385\pi\)
−0.984378 + 0.176070i \(0.943661\pi\)
\(114\) 8.55120e7i 0.506299i
\(115\) 1.22292e8i 0.699208i
\(116\) 8.60019e7 0.474981
\(117\) 1.08047e8i 0.576590i
\(118\) −1.84082e8 + 1.43873e8i −0.949475 + 0.742080i
\(119\) −4.66228e7 −0.232493
\(120\) 6.64216e7i 0.320320i
\(121\) 2.81185e6 0.0131175
\(122\) 6.32156e7 0.285354
\(123\) 2.37220e8 1.03641
\(124\) 7.46188e7i 0.315618i
\(125\) −2.65441e8 −1.08725
\(126\) 2.77714e7i 0.110183i
\(127\) −1.66958e8 −0.641790 −0.320895 0.947115i \(-0.603984\pi\)
−0.320895 + 0.947115i \(0.603984\pi\)
\(128\) 3.01237e8i 1.12219i
\(129\) 1.92063e8i 0.693562i
\(130\) 5.00349e8 1.75186
\(131\) 1.16246e7i 0.0394724i −0.999805 0.0197362i \(-0.993717\pi\)
0.999805 0.0197362i \(-0.00628264\pi\)
\(132\) 7.87380e7i 0.259351i
\(133\) 6.24581e7 0.199610
\(134\) −2.67763e8 −0.830483
\(135\) −5.37221e7 −0.161740
\(136\) 1.91419e8i 0.559538i
\(137\) 5.56986e7 0.158111 0.0790555 0.996870i \(-0.474810\pi\)
0.0790555 + 0.996870i \(0.474810\pi\)
\(138\) 2.09929e8 0.578837
\(139\) 3.54284e8 0.949057 0.474528 0.880240i \(-0.342619\pi\)
0.474528 + 0.880240i \(0.342619\pi\)
\(140\) −4.00455e7 −0.104242
\(141\) 5.62278e7i 0.142257i
\(142\) 3.75684e8i 0.923993i
\(143\) −7.18564e8 −1.71839
\(144\) −1.78831e8 −0.415905
\(145\) −3.90240e8 −0.882795
\(146\) −6.82936e8 −1.50303
\(147\) 2.49309e8 0.533910
\(148\) 3.13986e8i 0.654431i
\(149\) 8.93096e8i 1.81198i −0.423301 0.905989i \(-0.639129\pi\)
0.423301 0.905989i \(-0.360871\pi\)
\(150\) 1.03441e8i 0.204328i
\(151\) 5.44878e8i 1.04807i 0.851696 + 0.524037i \(0.175575\pi\)
−0.851696 + 0.524037i \(0.824425\pi\)
\(152\) 2.56434e8i 0.480399i
\(153\) −1.54821e8 −0.282529
\(154\) 1.84694e8 0.328374
\(155\) 3.38588e8i 0.586604i
\(156\) 2.67450e8i 0.451590i
\(157\) 7.55451e8i 1.24339i 0.783259 + 0.621695i \(0.213556\pi\)
−0.783259 + 0.621695i \(0.786444\pi\)
\(158\) 8.23664e8i 1.32167i
\(159\) 6.94768e7 0.108705
\(160\) 4.64544e8i 0.708837i
\(161\) 1.53333e8i 0.228208i
\(162\) 9.22207e7i 0.133896i
\(163\) −1.03534e9 −1.46667 −0.733333 0.679870i \(-0.762036\pi\)
−0.733333 + 0.679870i \(0.762036\pi\)
\(164\) 5.87197e8 0.811724
\(165\) 3.57279e8i 0.482028i
\(166\) 8.06097e8 1.06159
\(167\) −9.88619e8 −1.27105 −0.635526 0.772080i \(-0.719217\pi\)
−0.635526 + 0.772080i \(0.719217\pi\)
\(168\) 8.32811e7i 0.104546i
\(169\) −1.62502e9 −1.99211
\(170\) 7.16955e8i 0.858413i
\(171\) 2.07405e8 0.242569
\(172\) 4.75419e8i 0.543203i
\(173\) 9.39023e8i 1.04831i −0.851621 0.524157i \(-0.824380\pi\)
0.851621 0.524157i \(-0.175620\pi\)
\(174\) 6.69895e8i 0.730819i
\(175\) −7.55535e7 −0.0805569
\(176\) 1.18932e9i 1.23950i
\(177\) 3.48957e8 + 4.46483e8i 0.355532 + 0.454896i
\(178\) 1.99957e8 0.199185
\(179\) 1.29444e9i 1.26087i 0.776241 + 0.630436i \(0.217124\pi\)
−0.776241 + 0.630436i \(0.782876\pi\)
\(180\) −1.32980e8 −0.126676
\(181\) 2.02213e9 1.88406 0.942029 0.335531i \(-0.108916\pi\)
0.942029 + 0.335531i \(0.108916\pi\)
\(182\) 6.27351e8 0.571775
\(183\) 1.53327e8i 0.136714i
\(184\) −6.29538e8 −0.549226
\(185\) 1.42474e9i 1.21632i
\(186\) 5.81229e8 0.485619
\(187\) 1.02964e9i 0.842011i
\(188\) 1.39182e8i 0.111417i
\(189\) −6.73582e7 −0.0527890
\(190\) 9.60467e8i 0.737001i
\(191\) 2.35687e8i 0.177093i 0.996072 + 0.0885467i \(0.0282223\pi\)
−0.996072 + 0.0885467i \(0.971778\pi\)
\(192\) 1.81500e8 0.133559
\(193\) 1.43890e9 1.03705 0.518526 0.855062i \(-0.326481\pi\)
0.518526 + 0.855062i \(0.326481\pi\)
\(194\) −1.91785e9 −1.35396
\(195\) 1.21357e9i 0.839321i
\(196\) 6.17120e8 0.418163
\(197\) −4.37660e8 −0.290584 −0.145292 0.989389i \(-0.546412\pi\)
−0.145292 + 0.989389i \(0.546412\pi\)
\(198\) 6.13315e8 0.399046
\(199\) −1.99159e9 −1.26996 −0.634978 0.772530i \(-0.718991\pi\)
−0.634978 + 0.772530i \(0.718991\pi\)
\(200\) 3.10200e8i 0.193875i
\(201\) 6.49447e8i 0.397887i
\(202\) −1.38496e9 −0.831823
\(203\) −4.89293e8 −0.288128
\(204\) −3.83232e8 −0.221279
\(205\) −2.66445e9 −1.50866
\(206\) 1.27549e9 0.708284
\(207\) 5.09174e8i 0.277322i
\(208\) 4.03977e9i 2.15826i
\(209\) 1.37935e9i 0.722919i
\(210\) 3.11927e8i 0.160389i
\(211\) 1.62074e9i 0.817680i 0.912606 + 0.408840i \(0.134067\pi\)
−0.912606 + 0.408840i \(0.865933\pi\)
\(212\) 1.71978e8 0.0851389
\(213\) 9.11204e8 0.442687
\(214\) 1.36100e9i 0.648939i
\(215\) 2.15725e9i 1.00959i
\(216\) 2.76553e8i 0.127047i
\(217\) 4.24531e8i 0.191457i
\(218\) 3.27194e9 1.44870
\(219\) 1.65643e9i 0.720107i
\(220\) 8.84382e8i 0.377528i
\(221\) 3.49738e9i 1.46613i
\(222\) 2.44574e9 1.00693
\(223\) 9.20977e8 0.372417 0.186208 0.982510i \(-0.440380\pi\)
0.186208 + 0.982510i \(0.440380\pi\)
\(224\) 5.82457e8i 0.231351i
\(225\) −2.50892e8 −0.0978940
\(226\) 1.10703e9 0.424352
\(227\) 3.74299e9i 1.40966i −0.709376 0.704831i \(-0.751023\pi\)
0.709376 0.704831i \(-0.248977\pi\)
\(228\) 5.13396e8 0.189982
\(229\) 1.40653e9i 0.511453i −0.966749 0.255727i \(-0.917685\pi\)
0.966749 0.255727i \(-0.0823147\pi\)
\(230\) −2.35792e9 −0.842592
\(231\) 4.47966e8i 0.157325i
\(232\) 2.00889e9i 0.693433i
\(233\) 4.23543e8i 0.143706i 0.997415 + 0.0718528i \(0.0228912\pi\)
−0.997415 + 0.0718528i \(0.977109\pi\)
\(234\) 2.08325e9 0.694830
\(235\) 6.31548e8i 0.207079i
\(236\) 8.63782e8 + 1.10519e9i 0.278456 + 0.356278i
\(237\) −1.99776e9 −0.633214
\(238\) 8.98937e8i 0.280170i
\(239\) −2.73773e9 −0.839070 −0.419535 0.907739i \(-0.637807\pi\)
−0.419535 + 0.907739i \(0.637807\pi\)
\(240\) 2.00863e9 0.605417
\(241\) 4.73208e9 1.40276 0.701381 0.712786i \(-0.252567\pi\)
0.701381 + 0.712786i \(0.252567\pi\)
\(242\) 5.42155e7i 0.0158075i
\(243\) −2.23677e8 −0.0641500
\(244\) 3.79533e8i 0.107076i
\(245\) −2.80023e9 −0.777193
\(246\) 4.57386e9i 1.24894i
\(247\) 4.68526e9i 1.25877i
\(248\) −1.74300e9 −0.460776
\(249\) 1.95515e9i 0.508608i
\(250\) 5.11798e9i 1.31020i
\(251\) −2.00699e9 −0.505651 −0.252826 0.967512i \(-0.581360\pi\)
−0.252826 + 0.967512i \(0.581360\pi\)
\(252\) −1.66733e8 −0.0413448
\(253\) 3.38626e9 0.826492
\(254\) 3.21913e9i 0.773399i
\(255\) 1.73894e9 0.411268
\(256\) 4.81460e9 1.12099
\(257\) 6.66006e9 1.52667 0.763336 0.646002i \(-0.223560\pi\)
0.763336 + 0.646002i \(0.223560\pi\)
\(258\) 3.70318e9 0.835789
\(259\) 1.78637e9i 0.396984i
\(260\) 3.00399e9i 0.657363i
\(261\) −1.62480e9 −0.350137
\(262\) −2.24135e8 −0.0475669
\(263\) 8.23322e9 1.72087 0.860433 0.509564i \(-0.170193\pi\)
0.860433 + 0.509564i \(0.170193\pi\)
\(264\) −1.83922e9 −0.378632
\(265\) −7.80361e8 −0.158238
\(266\) 1.20426e9i 0.240543i
\(267\) 4.84987e8i 0.0954300i
\(268\) 1.60759e9i 0.311628i
\(269\) 4.98586e9i 0.952206i −0.879390 0.476103i \(-0.842049\pi\)
0.879390 0.476103i \(-0.157951\pi\)
\(270\) 1.03582e9i 0.194908i
\(271\) 5.48294e9 1.01657 0.508284 0.861189i \(-0.330280\pi\)
0.508284 + 0.861189i \(0.330280\pi\)
\(272\) 5.78863e9 1.05755
\(273\) 1.52161e9i 0.273939i
\(274\) 1.07393e9i 0.190534i
\(275\) 1.66856e9i 0.291749i
\(276\) 1.26037e9i 0.217201i
\(277\) 3.95689e9 0.672101 0.336050 0.941844i \(-0.390909\pi\)
0.336050 + 0.941844i \(0.390909\pi\)
\(278\) 6.83097e9i 1.14368i
\(279\) 1.40974e9i 0.232661i
\(280\) 9.35411e8i 0.152184i
\(281\) 7.39388e9 1.18590 0.592949 0.805240i \(-0.297964\pi\)
0.592949 + 0.805240i \(0.297964\pi\)
\(282\) 1.08413e9 0.171429
\(283\) 2.48452e9i 0.387343i −0.981066 0.193672i \(-0.937960\pi\)
0.981066 0.193672i \(-0.0620397\pi\)
\(284\) 2.25553e9 0.346716
\(285\) −2.32957e9 −0.353099
\(286\) 1.38547e10i 2.07077i
\(287\) −3.34076e9 −0.492399
\(288\) 1.93417e9i 0.281142i
\(289\) −1.96433e9 −0.281594
\(290\) 7.52424e9i 1.06383i
\(291\) 4.65165e9i 0.648687i
\(292\) 4.10020e9i 0.563993i
\(293\) −8.92655e9 −1.21119 −0.605596 0.795772i \(-0.707065\pi\)
−0.605596 + 0.795772i \(0.707065\pi\)
\(294\) 4.80694e9i 0.643397i
\(295\) −3.91948e9 5.01488e9i −0.517535 0.662175i
\(296\) −7.33430e9 −0.955415
\(297\) 1.48757e9i 0.191184i
\(298\) −1.72198e10 −2.18355
\(299\) 1.15022e10 1.43911
\(300\) −6.21038e8 −0.0766713
\(301\) 2.70481e9i 0.329512i
\(302\) 1.05058e10 1.26300
\(303\) 3.35915e9i 0.398529i
\(304\) −7.75472e9 −0.907971
\(305\) 1.72216e9i 0.199010i
\(306\) 2.98511e9i 0.340467i
\(307\) −1.02239e10 −1.15097 −0.575486 0.817812i \(-0.695187\pi\)
−0.575486 + 0.817812i \(0.695187\pi\)
\(308\) 1.10886e9i 0.123218i
\(309\) 3.09364e9i 0.339341i
\(310\) −6.52834e9 −0.706897
\(311\) −2.42846e9 −0.259591 −0.129796 0.991541i \(-0.541432\pi\)
−0.129796 + 0.991541i \(0.541432\pi\)
\(312\) −6.24728e9 −0.659284
\(313\) 5.66977e9i 0.590729i 0.955385 + 0.295364i \(0.0954410\pi\)
−0.955385 + 0.295364i \(0.904559\pi\)
\(314\) 1.45659e10 1.49837
\(315\) 7.56565e8 0.0768430
\(316\) −4.94511e9 −0.495938
\(317\) 5.22965e9 0.517888 0.258944 0.965892i \(-0.416626\pi\)
0.258944 + 0.965892i \(0.416626\pi\)
\(318\) 1.33959e9i 0.130997i
\(319\) 1.08058e10i 1.04350i
\(320\) −2.03861e9 −0.194417
\(321\) 3.30105e9 0.310908
\(322\) −2.95642e9 −0.275006
\(323\) −6.71355e9 −0.616797
\(324\) −5.53674e8 −0.0502428
\(325\) 5.66760e9i 0.508002i
\(326\) 1.99624e10i 1.76743i
\(327\) 7.93595e9i 0.694078i
\(328\) 1.37161e10i 1.18505i
\(329\) 7.91852e8i 0.0675865i
\(330\) −6.88873e9 −0.580876
\(331\) −2.09706e10 −1.74702 −0.873512 0.486803i \(-0.838163\pi\)
−0.873512 + 0.486803i \(0.838163\pi\)
\(332\) 4.83964e9i 0.398346i
\(333\) 5.93202e9i 0.482421i
\(334\) 1.90616e10i 1.53170i
\(335\) 7.29456e9i 0.579189i
\(336\) 2.51847e9 0.197597
\(337\) 1.22375e10i 0.948797i 0.880310 + 0.474398i \(0.157334\pi\)
−0.880310 + 0.474398i \(0.842666\pi\)
\(338\) 3.13322e10i 2.40062i
\(339\) 2.68506e9i 0.203308i
\(340\) 4.30444e9 0.322108
\(341\) 9.37552e9 0.693390
\(342\) 3.99900e9i 0.292312i
\(343\) −7.30766e9 −0.527961
\(344\) −1.11052e10 −0.793032
\(345\) 5.71902e9i 0.403688i
\(346\) −1.81054e10 −1.26329
\(347\) 1.91444e9i 0.132046i −0.997818 0.0660229i \(-0.978969\pi\)
0.997818 0.0660229i \(-0.0210310\pi\)
\(348\) −4.02191e9 −0.274230
\(349\) 1.67521e10i 1.12919i −0.825367 0.564597i \(-0.809032\pi\)
0.825367 0.564597i \(-0.190968\pi\)
\(350\) 1.45675e9i 0.0970764i
\(351\) 5.05284e9i 0.332895i
\(352\) −1.28632e10 −0.837875
\(353\) 1.32816e10i 0.855364i 0.903929 + 0.427682i \(0.140670\pi\)
−0.903929 + 0.427682i \(0.859330\pi\)
\(354\) 8.60867e9 6.72827e9i 0.548180 0.428440i
\(355\) −1.02346e10 −0.644404
\(356\) 1.20050e9i 0.0747415i
\(357\) 2.18033e9 0.134230
\(358\) 2.49583e10 1.51944
\(359\) 1.98321e10 1.19396 0.596982 0.802255i \(-0.296366\pi\)
0.596982 + 0.802255i \(0.296366\pi\)
\(360\) 3.10623e9i 0.184937i
\(361\) −7.98977e9 −0.470441
\(362\) 3.89888e10i 2.27042i
\(363\) −1.31497e8 −0.00757339
\(364\) 3.76648e9i 0.214551i
\(365\) 1.86050e10i 1.04823i
\(366\) −2.95630e9 −0.164749
\(367\) 2.73377e10i 1.50694i 0.657480 + 0.753472i \(0.271622\pi\)
−0.657480 + 0.753472i \(0.728378\pi\)
\(368\) 1.90376e10i 1.03806i
\(369\) −1.10937e10 −0.598371
\(370\) −2.74704e10 −1.46575
\(371\) −9.78437e8 −0.0516460
\(372\) 3.48958e9i 0.182222i
\(373\) 2.49022e9 0.128648 0.0643240 0.997929i \(-0.479511\pi\)
0.0643240 + 0.997929i \(0.479511\pi\)
\(374\) −1.98525e10 −1.01468
\(375\) 1.24134e10 0.627722
\(376\) −3.25111e9 −0.162660
\(377\) 3.67040e10i 1.81697i
\(378\) 1.29874e9i 0.0636142i
\(379\) −2.25638e10 −1.09359 −0.546796 0.837266i \(-0.684153\pi\)
−0.546796 + 0.837266i \(0.684153\pi\)
\(380\) −5.76644e9 −0.276550
\(381\) 7.80786e9 0.370538
\(382\) 4.54430e9 0.213409
\(383\) 1.56501e9 0.0727316 0.0363658 0.999339i \(-0.488422\pi\)
0.0363658 + 0.999339i \(0.488422\pi\)
\(384\) 1.40874e10i 0.647899i
\(385\) 5.03154e9i 0.229012i
\(386\) 2.77435e10i 1.24972i
\(387\) 8.98191e9i 0.400428i
\(388\) 1.15143e10i 0.508057i
\(389\) −7.34970e9 −0.320975 −0.160487 0.987038i \(-0.551307\pi\)
−0.160487 + 0.987038i \(0.551307\pi\)
\(390\) −2.33990e10 −1.01144
\(391\) 1.64815e10i 0.705165i
\(392\) 1.44151e10i 0.610483i
\(393\) 5.43630e8i 0.0227894i
\(394\) 8.43856e9i 0.350173i
\(395\) 2.24388e10 0.921746
\(396\) 3.68221e9i 0.149737i
\(397\) 3.21142e10i 1.29281i 0.762994 + 0.646405i \(0.223728\pi\)
−0.762994 + 0.646405i \(0.776272\pi\)
\(398\) 3.84001e10i 1.53038i
\(399\) −2.92088e9 −0.115245
\(400\) 9.38063e9 0.366431
\(401\) 3.08504e10i 1.19312i −0.802569 0.596559i \(-0.796534\pi\)
0.802569 0.596559i \(-0.203466\pi\)
\(402\) 1.25220e10 0.479480
\(403\) 3.18459e10 1.20735
\(404\) 8.31500e9i 0.312131i
\(405\) 2.51234e9 0.0933808
\(406\) 9.43409e9i 0.347213i
\(407\) 3.94510e10 1.43774
\(408\) 8.95178e9i 0.323049i
\(409\) 2.38353e10i 0.851781i −0.904775 0.425890i \(-0.859961\pi\)
0.904775 0.425890i \(-0.140039\pi\)
\(410\) 5.13734e10i 1.81804i
\(411\) −2.60476e9 −0.0912854
\(412\) 7.65776e9i 0.265774i
\(413\) −4.91434e9 6.28779e9i −0.168914 0.216121i
\(414\) −9.81741e9 −0.334192
\(415\) 2.19602e10i 0.740362i
\(416\) −4.36926e10 −1.45893
\(417\) −1.65682e10 −0.547938
\(418\) 2.65954e10 0.871166
\(419\) 4.71036e10i 1.52826i 0.645061 + 0.764131i \(0.276832\pi\)
−0.645061 + 0.764131i \(0.723168\pi\)
\(420\) 1.87274e9 0.0601840
\(421\) 7.15646e9i 0.227808i 0.993492 + 0.113904i \(0.0363357\pi\)
−0.993492 + 0.113904i \(0.963664\pi\)
\(422\) 3.12496e10 0.985359
\(423\) 2.62951e9i 0.0821322i
\(424\) 4.01717e9i 0.124296i
\(425\) 8.12116e9 0.248921
\(426\) 1.75690e10i 0.533468i
\(427\) 2.15929e9i 0.0649530i
\(428\) 8.17117e9 0.243506
\(429\) 3.36039e10 0.992112
\(430\) −4.15940e10 −1.21663
\(431\) 6.27989e10i 1.81988i 0.414738 + 0.909941i \(0.363873\pi\)
−0.414738 + 0.909941i \(0.636127\pi\)
\(432\) 8.36311e9 0.240123
\(433\) 4.22007e10 1.20052 0.600258 0.799806i \(-0.295065\pi\)
0.600258 + 0.799806i \(0.295065\pi\)
\(434\) −8.18541e9 −0.230718
\(435\) 1.82497e10 0.509682
\(436\) 1.96441e10i 0.543607i
\(437\) 2.20795e10i 0.605429i
\(438\) 3.19377e10 0.867776
\(439\) −2.45400e10 −0.660718 −0.330359 0.943855i \(-0.607170\pi\)
−0.330359 + 0.943855i \(0.607170\pi\)
\(440\) 2.06580e10 0.551160
\(441\) −1.16590e10 −0.308253
\(442\) −6.74332e10 −1.76679
\(443\) 1.75287e10i 0.455129i 0.973763 + 0.227564i \(0.0730762\pi\)
−0.973763 + 0.227564i \(0.926924\pi\)
\(444\) 1.46837e10i 0.377836i
\(445\) 5.44735e9i 0.138914i
\(446\) 1.77574e10i 0.448787i
\(447\) 4.17660e10i 1.04615i
\(448\) −2.55606e9 −0.0634539
\(449\) −6.68959e10 −1.64594 −0.822971 0.568084i \(-0.807685\pi\)
−0.822971 + 0.568084i \(0.807685\pi\)
\(450\) 4.83746e9i 0.117969i
\(451\) 7.37787e10i 1.78330i
\(452\) 6.64639e9i 0.159233i
\(453\) 2.54814e10i 0.605105i
\(454\) −7.21688e10 −1.69874
\(455\) 1.70907e10i 0.398762i
\(456\) 1.19922e10i 0.277358i
\(457\) 3.38572e10i 0.776223i 0.921612 + 0.388112i \(0.126873\pi\)
−0.921612 + 0.388112i \(0.873127\pi\)
\(458\) −2.71193e10 −0.616335
\(459\) 7.24025e9 0.163118
\(460\) 1.41564e10i 0.316171i
\(461\) 2.71005e10 0.600030 0.300015 0.953934i \(-0.403008\pi\)
0.300015 + 0.953934i \(0.403008\pi\)
\(462\) −8.63727e9 −0.189587
\(463\) 4.49647e10i 0.978471i 0.872152 + 0.489235i \(0.162724\pi\)
−0.872152 + 0.489235i \(0.837276\pi\)
\(464\) 6.07500e10 1.31061
\(465\) 1.58342e10i 0.338676i
\(466\) 8.16636e9 0.173175
\(467\) 3.77697e10i 0.794101i −0.917797 0.397051i \(-0.870034\pi\)
0.917797 0.397051i \(-0.129966\pi\)
\(468\) 1.25074e10i 0.260726i
\(469\) 9.14611e9i 0.189036i
\(470\) −1.21769e10 −0.249543
\(471\) 3.53289e10i 0.717872i
\(472\) −2.58158e10 + 2.01768e10i −0.520136 + 0.406522i
\(473\) 5.97342e10 1.19338
\(474\) 3.85190e10i 0.763065i
\(475\) −1.08795e10 −0.213715
\(476\) 5.39703e9 0.105130
\(477\) −3.24911e9 −0.0627611
\(478\) 5.27863e10i 1.01114i
\(479\) −1.97679e10 −0.375507 −0.187753 0.982216i \(-0.560121\pi\)
−0.187753 + 0.982216i \(0.560121\pi\)
\(480\) 2.17246e10i 0.409247i
\(481\) 1.34003e11 2.50343
\(482\) 9.12396e10i 1.69042i
\(483\) 7.17066e9i 0.131756i
\(484\) −3.25499e8 −0.00593154
\(485\) 5.22472e10i 0.944270i
\(486\) 4.31274e9i 0.0773051i
\(487\) 7.20058e10 1.28012 0.640061 0.768324i \(-0.278909\pi\)
0.640061 + 0.768324i \(0.278909\pi\)
\(488\) 8.86539e9 0.156321
\(489\) 4.84179e10 0.846780
\(490\) 5.39914e10i 0.936570i
\(491\) −3.57453e10 −0.615026 −0.307513 0.951544i \(-0.599497\pi\)
−0.307513 + 0.951544i \(0.599497\pi\)
\(492\) −2.74605e10 −0.468649
\(493\) 5.25935e10 0.890317
\(494\) 9.03367e10 1.51690
\(495\) 1.67083e10i 0.278299i
\(496\) 5.27092e10i 0.870883i
\(497\) −1.28324e10 −0.210321
\(498\) −3.76974e10 −0.612907
\(499\) −6.71121e10 −1.08243 −0.541213 0.840885i \(-0.682035\pi\)
−0.541213 + 0.840885i \(0.682035\pi\)
\(500\) 3.07273e10 0.491636
\(501\) 4.62331e10 0.733842
\(502\) 3.86970e10i 0.609343i
\(503\) 2.60027e10i 0.406206i −0.979157 0.203103i \(-0.934897\pi\)
0.979157 0.203103i \(-0.0651026\pi\)
\(504\) 3.89467e9i 0.0603599i
\(505\) 3.77299e10i 0.580123i
\(506\) 6.52908e10i 0.995978i
\(507\) 7.59948e10 1.15014
\(508\) 1.93270e10 0.290208
\(509\) 8.39364e10i 1.25049i 0.780430 + 0.625243i \(0.215000\pi\)
−0.780430 + 0.625243i \(0.785000\pi\)
\(510\) 3.35287e10i 0.495605i
\(511\) 2.33274e10i 0.342123i
\(512\) 1.57141e10i 0.228671i
\(513\) −9.69939e9 −0.140047
\(514\) 1.28413e11i 1.83974i
\(515\) 3.47477e10i 0.493966i
\(516\) 2.22331e10i 0.313619i
\(517\) 1.74876e10 0.244775
\(518\) −3.44431e10 −0.478392
\(519\) 4.39137e10i 0.605245i
\(520\) 7.01692e10 0.959695
\(521\) −8.32616e10 −1.13004 −0.565020 0.825077i \(-0.691132\pi\)
−0.565020 + 0.825077i \(0.691132\pi\)
\(522\) 3.13279e10i 0.421939i
\(523\) 1.25002e11 1.67075 0.835374 0.549682i \(-0.185251\pi\)
0.835374 + 0.549682i \(0.185251\pi\)
\(524\) 1.34566e9i 0.0178489i
\(525\) 3.53329e9 0.0465095
\(526\) 1.58745e11i 2.07376i
\(527\) 4.56323e10i 0.591602i
\(528\) 5.56189e10i 0.715628i
\(529\) 2.41066e10 0.307831
\(530\) 1.50462e10i 0.190688i
\(531\) −1.63191e10 2.08799e10i −0.205267 0.262634i
\(532\) −7.23012e9 −0.0902607
\(533\) 2.50605e11i 3.10514i
\(534\) −9.35106e9 −0.114999
\(535\) −3.70773e10 −0.452577
\(536\) −3.75512e10 −0.454951
\(537\) 6.05352e10i 0.727965i
\(538\) −9.61327e10 −1.14747
\(539\) 7.75384e10i 0.918674i
\(540\) 6.21885e9 0.0731366
\(541\) 9.03667e10i 1.05492i −0.849580 0.527460i \(-0.823145\pi\)
0.849580 0.527460i \(-0.176855\pi\)
\(542\) 1.05717e11i 1.22503i
\(543\) −9.45656e10 −1.08776
\(544\) 6.26076e10i 0.714877i
\(545\) 8.91363e10i 1.01034i
\(546\) −2.93383e10 −0.330114
\(547\) −1.07991e11 −1.20625 −0.603126 0.797646i \(-0.706078\pi\)
−0.603126 + 0.797646i \(0.706078\pi\)
\(548\) −6.44764e9 −0.0714954
\(549\) 7.17037e9i 0.0789319i
\(550\) −3.21715e10 −0.351577
\(551\) −7.04568e10 −0.764393
\(552\) 2.94406e10 0.317096
\(553\) 2.81343e10 0.300840
\(554\) 7.62930e10i 0.809926i
\(555\) 6.66283e10i 0.702242i
\(556\) −4.10117e10 −0.429150
\(557\) −8.96481e10 −0.931366 −0.465683 0.884952i \(-0.654191\pi\)
−0.465683 + 0.884952i \(0.654191\pi\)
\(558\) −2.71814e10 −0.280372
\(559\) 2.02900e11 2.07795
\(560\) −2.82874e10 −0.287634
\(561\) 4.81513e10i 0.486135i
\(562\) 1.42562e11i 1.42908i
\(563\) 1.59253e11i 1.58509i −0.609813 0.792545i \(-0.708756\pi\)
0.609813 0.792545i \(-0.291244\pi\)
\(564\) 6.50889e9i 0.0643266i
\(565\) 3.01585e10i 0.295948i
\(566\) −4.79041e10 −0.466775
\(567\) 3.15003e9 0.0304777
\(568\) 5.26861e10i 0.506177i
\(569\) 1.92778e11i 1.83912i −0.392955 0.919558i \(-0.628547\pi\)
0.392955 0.919558i \(-0.371453\pi\)
\(570\) 4.49166e10i 0.425508i
\(571\) 1.41928e11i 1.33513i −0.744551 0.667566i \(-0.767336\pi\)
0.744551 0.667566i \(-0.232664\pi\)
\(572\) 8.31806e10 0.777030
\(573\) 1.10220e10i 0.102245i
\(574\) 6.44133e10i 0.593374i
\(575\) 2.67088e10i 0.244334i
\(576\) −8.48793e9 −0.0771102
\(577\) 1.17501e11 1.06008 0.530040 0.847972i \(-0.322177\pi\)
0.530040 + 0.847972i \(0.322177\pi\)
\(578\) 3.78744e10i 0.339340i
\(579\) −6.72905e10 −0.598742
\(580\) 4.51740e10 0.399187
\(581\) 2.75343e10i 0.241640i
\(582\) 8.96888e10 0.781711
\(583\) 2.16082e10i 0.187044i
\(584\) −9.57753e10 −0.823383
\(585\) 5.67533e10i 0.484582i
\(586\) 1.72113e11i 1.45957i
\(587\) 6.44382e9i 0.0542739i −0.999632 0.0271369i \(-0.991361\pi\)
0.999632 0.0271369i \(-0.00863901\pi\)
\(588\) −2.88598e10 −0.241426
\(589\) 6.11312e10i 0.507928i
\(590\) −9.66922e10 + 7.55717e10i −0.797965 + 0.623664i
\(591\) 2.04673e10 0.167769
\(592\) 2.21794e11i 1.80577i
\(593\) 1.22849e11 0.993466 0.496733 0.867903i \(-0.334533\pi\)
0.496733 + 0.867903i \(0.334533\pi\)
\(594\) −2.86819e10 −0.230389
\(595\) −2.44894e10 −0.195394
\(596\) 1.03384e11i 0.819350i
\(597\) 9.31376e10 0.733209
\(598\) 2.21774e11i 1.73423i
\(599\) 4.42262e10 0.343536 0.171768 0.985137i \(-0.445052\pi\)
0.171768 + 0.985137i \(0.445052\pi\)
\(600\) 1.45066e10i 0.111934i
\(601\) 2.24116e11i 1.71781i 0.512137 + 0.858904i \(0.328854\pi\)
−0.512137 + 0.858904i \(0.671146\pi\)
\(602\) −5.21517e10 −0.397084
\(603\) 3.03716e10i 0.229720i
\(604\) 6.30748e10i 0.473923i
\(605\) 1.47697e9 0.0110243
\(606\) 6.47681e10 0.480253
\(607\) 2.43376e10 0.179276 0.0896380 0.995974i \(-0.471429\pi\)
0.0896380 + 0.995974i \(0.471429\pi\)
\(608\) 8.38722e10i 0.613767i
\(609\) 2.28820e10 0.166351
\(610\) 3.32051e10 0.239820
\(611\) 5.94003e10 0.426210
\(612\) 1.79220e10 0.127756
\(613\) 3.23496e10i 0.229101i 0.993417 + 0.114550i \(0.0365428\pi\)
−0.993417 + 0.114550i \(0.963457\pi\)
\(614\) 1.97128e11i 1.38700i
\(615\) 1.24604e11 0.871027
\(616\) 2.59015e10 0.179888
\(617\) −1.44980e11 −1.00038 −0.500192 0.865915i \(-0.666737\pi\)
−0.500192 + 0.865915i \(0.666737\pi\)
\(618\) −5.96487e10 −0.408928
\(619\) −7.94802e10 −0.541373 −0.270686 0.962668i \(-0.587251\pi\)
−0.270686 + 0.962668i \(0.587251\pi\)
\(620\) 3.91948e10i 0.265254i
\(621\) 2.38117e10i 0.160112i
\(622\) 4.68233e10i 0.312824i
\(623\) 6.83003e9i 0.0453389i
\(624\) 1.88921e11i 1.24607i
\(625\) −9.46150e10 −0.620069
\(626\) 1.09319e11 0.711867
\(627\) 6.45059e10i 0.417378i
\(628\) 8.74506e10i 0.562243i
\(629\) 1.92015e11i 1.22668i
\(630\) 1.45874e10i 0.0926009i
\(631\) −2.09094e11 −1.31894 −0.659470 0.751731i \(-0.729219\pi\)
−0.659470 + 0.751731i \(0.729219\pi\)
\(632\) 1.15511e11i 0.724029i
\(633\) 7.57945e10i 0.472088i
\(634\) 1.00833e11i 0.624089i
\(635\) −8.76976e10 −0.539378
\(636\) −8.04259e9 −0.0491550
\(637\) 2.63375e11i 1.59962i
\(638\) −2.08346e11 −1.25749
\(639\) −4.26128e10 −0.255586
\(640\) 1.58230e11i 0.943122i
\(641\) −1.17100e11 −0.693622 −0.346811 0.937935i \(-0.612736\pi\)
−0.346811 + 0.937935i \(0.612736\pi\)
\(642\) 6.36478e10i 0.374665i
\(643\) 5.14729e10 0.301116 0.150558 0.988601i \(-0.451893\pi\)
0.150558 + 0.988601i \(0.451893\pi\)
\(644\) 1.77497e10i 0.103192i
\(645\) 1.00885e11i 0.582889i
\(646\) 1.29444e11i 0.743281i
\(647\) −2.12044e11 −1.21006 −0.605032 0.796201i \(-0.706840\pi\)
−0.605032 + 0.796201i \(0.706840\pi\)
\(648\) 1.29331e10i 0.0733503i
\(649\) 1.38862e11 1.08530e11i 0.782718 0.611748i
\(650\) −1.09277e11 −0.612177
\(651\) 1.98533e10i 0.110538i
\(652\) 1.19850e11 0.663205
\(653\) −1.00559e11 −0.553056 −0.276528 0.961006i \(-0.589184\pi\)
−0.276528 + 0.961006i \(0.589184\pi\)
\(654\) −1.53014e11 −0.836410
\(655\) 6.10604e9i 0.0331737i
\(656\) 4.14784e11 2.23979
\(657\) 7.74636e10i 0.415754i
\(658\) −1.52677e10 −0.0814463
\(659\) 2.49578e11i 1.32332i −0.749804 0.661660i \(-0.769852\pi\)
0.749804 0.661660i \(-0.230148\pi\)
\(660\) 4.13585e10i 0.217966i
\(661\) 1.91052e11 1.00080 0.500399 0.865795i \(-0.333187\pi\)
0.500399 + 0.865795i \(0.333187\pi\)
\(662\) 4.04335e11i 2.10528i
\(663\) 1.63556e11i 0.846472i
\(664\) 1.13048e11 0.581552
\(665\) 3.28072e10 0.167758
\(666\) −1.14376e11 −0.581349
\(667\) 1.72969e11i 0.873908i
\(668\) 1.14442e11 0.574751
\(669\) −4.30698e10 −0.215015
\(670\) −1.40647e11 −0.697961
\(671\) −4.76866e10 −0.235237
\(672\) 2.72388e10i 0.133571i
\(673\) 1.66582e11i 0.812021i 0.913868 + 0.406011i \(0.133080\pi\)
−0.913868 + 0.406011i \(0.866920\pi\)
\(674\) 2.35952e11 1.14336
\(675\) 1.17330e10 0.0565191
\(676\) 1.88112e11 0.900801
\(677\) −1.88891e11 −0.899201 −0.449600 0.893230i \(-0.648434\pi\)
−0.449600 + 0.893230i \(0.648434\pi\)
\(678\) −5.17708e10 −0.245000
\(679\) 6.55089e10i 0.308192i
\(680\) 1.00546e11i 0.470251i
\(681\) 1.75042e11i 0.813868i
\(682\) 1.80770e11i 0.835581i
\(683\) 9.51587e10i 0.437286i 0.975805 + 0.218643i \(0.0701631\pi\)
−0.975805 + 0.218643i \(0.929837\pi\)
\(684\) −2.40091e10 −0.109686
\(685\) 2.92566e10 0.132881
\(686\) 1.40899e11i 0.636228i
\(687\) 6.57768e10i 0.295288i
\(688\) 3.35826e11i 1.49886i
\(689\) 7.33968e10i 0.325687i
\(690\) 1.10269e11 0.486471
\(691\) 4.93618e9i 0.0216511i −0.999941 0.0108255i \(-0.996554\pi\)
0.999941 0.0108255i \(-0.00344594\pi\)
\(692\) 1.08701e11i 0.474032i
\(693\) 2.09493e10i 0.0908316i
\(694\) −3.69125e10 −0.159124
\(695\) 1.86094e11 0.797613
\(696\) 9.39465e10i 0.400354i
\(697\) 3.59094e11 1.52152
\(698\) −3.22999e11 −1.36075
\(699\) 1.98071e10i 0.0829685i
\(700\) 8.74603e9 0.0364266
\(701\) 4.07228e11i 1.68642i 0.537585 + 0.843210i \(0.319337\pi\)
−0.537585 + 0.843210i \(0.680663\pi\)
\(702\) −9.74240e10 −0.401160
\(703\) 2.57232e11i 1.05318i
\(704\) 5.64490e10i 0.229808i
\(705\) 2.95346e10i 0.119557i
\(706\) 2.56083e11 1.03077
\(707\) 4.73067e10i 0.189341i
\(708\) −4.03951e10 5.16846e10i −0.160767 0.205697i
\(709\) −1.16346e11 −0.460432 −0.230216 0.973140i \(-0.573943\pi\)
−0.230216 + 0.973140i \(0.573943\pi\)
\(710\) 1.97334e11i 0.776549i
\(711\) 9.34261e10 0.365586
\(712\) 2.80421e10 0.109116
\(713\) −1.50075e11 −0.580699
\(714\) 4.20391e10i 0.161756i
\(715\) −3.77438e11 −1.44418
\(716\) 1.49844e11i 0.570148i
\(717\) 1.28031e11 0.484438
\(718\) 3.82384e11i 1.43881i
\(719\) 1.41372e10i 0.0528992i −0.999650 0.0264496i \(-0.991580\pi\)
0.999650 0.0264496i \(-0.00842015\pi\)
\(720\) −9.39342e10 −0.349538
\(721\) 4.35675e10i 0.161221i
\(722\) 1.54051e11i 0.566913i
\(723\) −2.21298e11 −0.809885
\(724\) −2.34080e11 −0.851943
\(725\) 8.52293e10 0.308487
\(726\) 2.53541e9i 0.00912644i
\(727\) 3.23346e11 1.15752 0.578761 0.815497i \(-0.303536\pi\)
0.578761 + 0.815497i \(0.303536\pi\)
\(728\) 8.79800e10 0.313227
\(729\) 1.04604e10 0.0370370
\(730\) −3.58724e11 −1.26319
\(731\) 2.90737e11i 1.01820i
\(732\) 1.77490e10i 0.0618201i
\(733\) −4.27347e11 −1.48035 −0.740175 0.672414i \(-0.765258\pi\)
−0.740175 + 0.672414i \(0.765258\pi\)
\(734\) 5.27099e11 1.81597
\(735\) 1.30954e11 0.448713
\(736\) 2.05903e11 0.701702
\(737\) 2.01987e11 0.684625
\(738\) 2.13898e11i 0.721077i
\(739\) 7.27228e9i 0.0243833i 0.999926 + 0.0121917i \(0.00388082\pi\)
−0.999926 + 0.0121917i \(0.996119\pi\)
\(740\) 1.64927e11i 0.550001i
\(741\) 2.19108e11i 0.726750i
\(742\) 1.88653e10i 0.0622369i
\(743\) −3.32988e11 −1.09263 −0.546316 0.837579i \(-0.683970\pi\)
−0.546316 + 0.837579i \(0.683970\pi\)
\(744\) 8.15119e10 0.266029
\(745\) 4.69114e11i 1.52284i
\(746\) 4.80141e10i 0.155029i
\(747\) 9.14335e10i 0.293645i
\(748\) 1.19190e11i 0.380745i
\(749\) −4.64885e10 −0.147713
\(750\) 2.39344e11i 0.756446i
\(751\) 3.90325e11i 1.22706i 0.789670 + 0.613531i \(0.210252\pi\)
−0.789670 + 0.613531i \(0.789748\pi\)
\(752\) 9.83153e10i 0.307433i
\(753\) 9.38578e10 0.291938
\(754\) −7.07692e11 −2.18957
\(755\) 2.86207e11i 0.880829i
\(756\) 7.79735e9 0.0238704
\(757\) 5.46555e11 1.66437 0.832186 0.554497i \(-0.187089\pi\)
0.832186 + 0.554497i \(0.187089\pi\)
\(758\) 4.35054e11i 1.31785i
\(759\) −1.58360e11 −0.477175
\(760\) 1.34696e11i 0.403740i
\(761\) −3.47259e11 −1.03542 −0.517708 0.855557i \(-0.673215\pi\)
−0.517708 + 0.855557i \(0.673215\pi\)
\(762\) 1.50544e11i 0.446522i
\(763\) 1.11761e11i 0.329757i
\(764\) 2.72830e10i 0.0800791i
\(765\) −8.13223e10 −0.237445
\(766\) 3.01751e10i 0.0876464i
\(767\) 4.71675e11 3.68646e11i 1.36289 1.06519i
\(768\) −2.25157e11 −0.647202
\(769\) 3.50765e11i 1.00302i −0.865151 0.501512i \(-0.832777\pi\)
0.865151 0.501512i \(-0.167223\pi\)
\(770\) 9.70135e10 0.275975
\(771\) −3.11460e11 −0.881425
\(772\) −1.66566e11 −0.468939
\(773\) 2.03514e11i 0.570001i −0.958527 0.285001i \(-0.908006\pi\)
0.958527 0.285001i \(-0.0919938\pi\)
\(774\) −1.73181e11 −0.482543
\(775\) 7.39485e10i 0.204985i
\(776\) −2.68960e11 −0.741721
\(777\) 8.35403e10i 0.229199i
\(778\) 1.41710e11i 0.386796i
\(779\) −4.81060e11 −1.30632
\(780\) 1.40483e11i 0.379529i
\(781\) 2.83397e11i 0.761712i
\(782\) 3.17782e11 0.849771