Properties

Label 177.9.c.a.58.9
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 58.9
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.72

$q$-expansion

\(f(q)\) \(=\) \(q-25.6810i q^{2} +46.7654 q^{3} -403.515 q^{4} +951.178 q^{5} -1200.98i q^{6} +4182.78 q^{7} +3788.34i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-25.6810i q^{2} +46.7654 q^{3} -403.515 q^{4} +951.178 q^{5} -1200.98i q^{6} +4182.78 q^{7} +3788.34i q^{8} +2187.00 q^{9} -24427.2i q^{10} +17992.5i q^{11} -18870.5 q^{12} +12240.6i q^{13} -107418. i q^{14} +44482.2 q^{15} -6011.37 q^{16} +21398.1 q^{17} -56164.4i q^{18} -176067. q^{19} -383815. q^{20} +195609. q^{21} +462066. q^{22} -346513. i q^{23} +177163. i q^{24} +514114. q^{25} +314351. q^{26} +102276. q^{27} -1.68781e6 q^{28} +1.08118e6 q^{29} -1.14235e6i q^{30} +659909. i q^{31} +1.12419e6i q^{32} +841425. i q^{33} -549526. i q^{34} +3.97856e6 q^{35} -882488. q^{36} +809547. i q^{37} +4.52157e6i q^{38} +572435. i q^{39} +3.60339e6i q^{40} +2.01892e6 q^{41} -5.02344e6i q^{42} -2.82734e6i q^{43} -7.26024e6i q^{44} +2.08023e6 q^{45} -8.89881e6 q^{46} -3.68905e6i q^{47} -281124. q^{48} +1.17308e7 q^{49} -1.32030e7i q^{50} +1.00069e6 q^{51} -4.93926e6i q^{52} +1.08310e7 q^{53} -2.62655e6i q^{54} +1.71140e7i q^{55} +1.58458e7i q^{56} -8.23382e6 q^{57} -2.77658e7i q^{58} +(3.87060e6 - 1.14825e7i) q^{59} -1.79492e7 q^{60} +1.10547e7i q^{61} +1.69471e7 q^{62} +9.14773e6 q^{63} +2.73315e7 q^{64} +1.16430e7i q^{65} +2.16087e7 q^{66} -3.56627e7i q^{67} -8.63447e6 q^{68} -1.62048e7i q^{69} -1.02174e8i q^{70} -4.05386e7 q^{71} +8.28510e6i q^{72} -1.60542e7i q^{73} +2.07900e7 q^{74} +2.40427e7 q^{75} +7.10456e7 q^{76} +7.52586e7i q^{77} +1.47007e7 q^{78} +1.42083e7 q^{79} -5.71788e6 q^{80} +4.78297e6 q^{81} -5.18479e7i q^{82} +9.26581e7i q^{83} -7.89313e7 q^{84} +2.03534e7 q^{85} -7.26089e7 q^{86} +5.05618e7 q^{87} -6.81617e7 q^{88} -2.50440e7i q^{89} -5.34223e7i q^{90} +5.11996e7i q^{91} +1.39823e8i q^{92} +3.08609e7i q^{93} -9.47386e7 q^{94} -1.67471e8 q^{95} +5.25733e7i q^{96} +8.23795e7i q^{97} -3.01260e8i q^{98} +3.93496e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.6810i 1.60506i −0.596609 0.802532i \(-0.703486\pi\)
0.596609 0.802532i \(-0.296514\pi\)
\(3\) 46.7654 0.577350
\(4\) −403.515 −1.57623
\(5\) 951.178 1.52188 0.760942 0.648820i \(-0.224737\pi\)
0.760942 + 0.648820i \(0.224737\pi\)
\(6\) 1200.98i 0.926684i
\(7\) 4182.78 1.74210 0.871049 0.491196i \(-0.163440\pi\)
0.871049 + 0.491196i \(0.163440\pi\)
\(8\) 3788.34i 0.924888i
\(9\) 2187.00 0.333333
\(10\) 24427.2i 2.44272i
\(11\) 17992.5i 1.22891i 0.788951 + 0.614456i \(0.210624\pi\)
−0.788951 + 0.614456i \(0.789376\pi\)
\(12\) −18870.5 −0.910038
\(13\) 12240.6i 0.428577i 0.976770 + 0.214288i \(0.0687432\pi\)
−0.976770 + 0.214288i \(0.931257\pi\)
\(14\) 107418.i 2.79618i
\(15\) 44482.2 0.878660
\(16\) −6011.37 −0.0917262
\(17\) 21398.1 0.256201 0.128100 0.991761i \(-0.459112\pi\)
0.128100 + 0.991761i \(0.459112\pi\)
\(18\) 56164.4i 0.535021i
\(19\) −176067. −1.35102 −0.675511 0.737350i \(-0.736077\pi\)
−0.675511 + 0.737350i \(0.736077\pi\)
\(20\) −383815. −2.39884
\(21\) 195609. 1.00580
\(22\) 462066. 1.97248
\(23\) 346513.i 1.23825i −0.785293 0.619125i \(-0.787488\pi\)
0.785293 0.619125i \(-0.212512\pi\)
\(24\) 177163.i 0.533984i
\(25\) 514114. 1.31613
\(26\) 314351. 0.687893
\(27\) 102276. 0.192450
\(28\) −1.68781e6 −2.74595
\(29\) 1.08118e6 1.52864 0.764322 0.644835i \(-0.223074\pi\)
0.764322 + 0.644835i \(0.223074\pi\)
\(30\) 1.14235e6i 1.41031i
\(31\) 659909.i 0.714557i 0.933998 + 0.357279i \(0.116295\pi\)
−0.933998 + 0.357279i \(0.883705\pi\)
\(32\) 1.12419e6i 1.07211i
\(33\) 841425.i 0.709512i
\(34\) 549526.i 0.411218i
\(35\) 3.97856e6 2.65127
\(36\) −882488. −0.525410
\(37\) 809547.i 0.431951i 0.976399 + 0.215976i \(0.0692932\pi\)
−0.976399 + 0.215976i \(0.930707\pi\)
\(38\) 4.52157e6i 2.16848i
\(39\) 572435.i 0.247439i
\(40\) 3.60339e6i 1.40757i
\(41\) 2.01892e6 0.714468 0.357234 0.934015i \(-0.383720\pi\)
0.357234 + 0.934015i \(0.383720\pi\)
\(42\) 5.02344e6i 1.61437i
\(43\) 2.82734e6i 0.826997i −0.910505 0.413498i \(-0.864307\pi\)
0.910505 0.413498i \(-0.135693\pi\)
\(44\) 7.26024e6i 1.93705i
\(45\) 2.08023e6 0.507295
\(46\) −8.89881e6 −1.98747
\(47\) 3.68905e6i 0.756002i −0.925805 0.378001i \(-0.876612\pi\)
0.925805 0.378001i \(-0.123388\pi\)
\(48\) −281124. −0.0529582
\(49\) 1.17308e7 2.03490
\(50\) 1.32030e7i 2.11248i
\(51\) 1.00069e6 0.147917
\(52\) 4.93926e6i 0.675536i
\(53\) 1.08310e7 1.37266 0.686332 0.727289i \(-0.259220\pi\)
0.686332 + 0.727289i \(0.259220\pi\)
\(54\) 2.62655e6i 0.308895i
\(55\) 1.71140e7i 1.87026i
\(56\) 1.58458e7i 1.61125i
\(57\) −8.23382e6 −0.780013
\(58\) 2.77658e7i 2.45357i
\(59\) 3.87060e6 1.14825e7i 0.319426 0.947611i
\(60\) −1.79492e7 −1.38497
\(61\) 1.10547e7i 0.798414i 0.916861 + 0.399207i \(0.130715\pi\)
−0.916861 + 0.399207i \(0.869285\pi\)
\(62\) 1.69471e7 1.14691
\(63\) 9.14773e6 0.580699
\(64\) 2.73315e7 1.62909
\(65\) 1.16430e7i 0.652244i
\(66\) 2.16087e7 1.13881
\(67\) 3.56627e7i 1.76976i −0.465817 0.884881i \(-0.654240\pi\)
0.465817 0.884881i \(-0.345760\pi\)
\(68\) −8.63447e6 −0.403831
\(69\) 1.62048e7i 0.714904i
\(70\) 1.02174e8i 4.25546i
\(71\) −4.05386e7 −1.59527 −0.797637 0.603138i \(-0.793917\pi\)
−0.797637 + 0.603138i \(0.793917\pi\)
\(72\) 8.28510e6i 0.308296i
\(73\) 1.60542e7i 0.565322i −0.959220 0.282661i \(-0.908783\pi\)
0.959220 0.282661i \(-0.0912172\pi\)
\(74\) 2.07900e7 0.693310
\(75\) 2.40427e7 0.759869
\(76\) 7.10456e7 2.12952
\(77\) 7.52586e7i 2.14088i
\(78\) 1.47007e7 0.397155
\(79\) 1.42083e7 0.364781 0.182391 0.983226i \(-0.441616\pi\)
0.182391 + 0.983226i \(0.441616\pi\)
\(80\) −5.71788e6 −0.139597
\(81\) 4.78297e6 0.111111
\(82\) 5.18479e7i 1.14677i
\(83\) 9.26581e7i 1.95241i 0.216852 + 0.976205i \(0.430421\pi\)
−0.216852 + 0.976205i \(0.569579\pi\)
\(84\) −7.89313e7 −1.58537
\(85\) 2.03534e7 0.389908
\(86\) −7.26089e7 −1.32738
\(87\) 5.05618e7 0.882563
\(88\) −6.81617e7 −1.13661
\(89\) 2.50440e7i 0.399157i −0.979882 0.199579i \(-0.936043\pi\)
0.979882 0.199579i \(-0.0639573\pi\)
\(90\) 5.34223e7i 0.814241i
\(91\) 5.11996e7i 0.746623i
\(92\) 1.39823e8i 1.95177i
\(93\) 3.08609e7i 0.412550i
\(94\) −9.47386e7 −1.21343
\(95\) −1.67471e8 −2.05610
\(96\) 5.25733e7i 0.618986i
\(97\) 8.23795e7i 0.930534i 0.885170 + 0.465267i \(0.154042\pi\)
−0.885170 + 0.465267i \(0.845958\pi\)
\(98\) 3.01260e8i 3.26615i
\(99\) 3.93496e7i 0.409637i
\(100\) −2.07453e8 −2.07453
\(101\) 1.45553e8i 1.39873i 0.714763 + 0.699367i \(0.246535\pi\)
−0.714763 + 0.699367i \(0.753465\pi\)
\(102\) 2.56988e7i 0.237417i
\(103\) 1.57948e8i 1.40335i −0.712497 0.701675i \(-0.752436\pi\)
0.712497 0.701675i \(-0.247564\pi\)
\(104\) −4.63715e7 −0.396386
\(105\) 1.86059e8 1.53071
\(106\) 2.78150e8i 2.20321i
\(107\) 3.86465e7 0.294833 0.147416 0.989075i \(-0.452904\pi\)
0.147416 + 0.989075i \(0.452904\pi\)
\(108\) −4.12699e7 −0.303346
\(109\) 1.37706e8i 0.975543i 0.872971 + 0.487771i \(0.162190\pi\)
−0.872971 + 0.487771i \(0.837810\pi\)
\(110\) 4.39506e8 3.00189
\(111\) 3.78587e7i 0.249387i
\(112\) −2.51442e7 −0.159796
\(113\) 1.35512e8i 0.831120i −0.909566 0.415560i \(-0.863586\pi\)
0.909566 0.415560i \(-0.136414\pi\)
\(114\) 2.11453e8i 1.25197i
\(115\) 3.29595e8i 1.88447i
\(116\) −4.36273e8 −2.40950
\(117\) 2.67701e7i 0.142859i
\(118\) −2.94884e8 9.94011e7i −1.52098 0.512700i
\(119\) 8.95036e7 0.446326
\(120\) 1.68514e8i 0.812663i
\(121\) −1.09371e8 −0.510222
\(122\) 2.83897e8 1.28151
\(123\) 9.44154e7 0.412499
\(124\) 2.66283e8i 1.12631i
\(125\) 1.17460e8 0.481115
\(126\) 2.34923e8i 0.932060i
\(127\) 9.80202e6 0.0376791 0.0188396 0.999823i \(-0.494003\pi\)
0.0188396 + 0.999823i \(0.494003\pi\)
\(128\) 4.14108e8i 1.54267i
\(129\) 1.32222e8i 0.477467i
\(130\) 2.99003e8 1.04689
\(131\) 7.85281e7i 0.266649i −0.991072 0.133324i \(-0.957435\pi\)
0.991072 0.133324i \(-0.0425652\pi\)
\(132\) 3.39528e8i 1.11836i
\(133\) −7.36447e8 −2.35361
\(134\) −9.15855e8 −2.84058
\(135\) 9.72825e7 0.292887
\(136\) 8.10634e7i 0.236957i
\(137\) −6.23729e8 −1.77057 −0.885287 0.465045i \(-0.846038\pi\)
−0.885287 + 0.465045i \(0.846038\pi\)
\(138\) −4.16156e8 −1.14747
\(139\) −1.27501e8 −0.341551 −0.170776 0.985310i \(-0.554627\pi\)
−0.170776 + 0.985310i \(0.554627\pi\)
\(140\) −1.60541e9 −4.17902
\(141\) 1.72520e8i 0.436478i
\(142\) 1.04107e9i 2.56052i
\(143\) −2.20238e8 −0.526683
\(144\) −1.31469e7 −0.0305754
\(145\) 1.02839e9 2.32642
\(146\) −4.12287e8 −0.907378
\(147\) 5.48596e8 1.17485
\(148\) 3.26664e8i 0.680855i
\(149\) 7.13072e8i 1.44673i −0.690465 0.723366i \(-0.742594\pi\)
0.690465 0.723366i \(-0.257406\pi\)
\(150\) 6.17442e8i 1.21964i
\(151\) 3.74058e8i 0.719501i 0.933049 + 0.359751i \(0.117138\pi\)
−0.933049 + 0.359751i \(0.882862\pi\)
\(152\) 6.67001e8i 1.24954i
\(153\) 4.67977e7 0.0854002
\(154\) 1.93272e9 3.43625
\(155\) 6.27690e8i 1.08747i
\(156\) 2.30986e8i 0.390021i
\(157\) 7.36816e8i 1.21272i −0.795190 0.606360i \(-0.792629\pi\)
0.795190 0.606360i \(-0.207371\pi\)
\(158\) 3.64883e8i 0.585498i
\(159\) 5.06514e8 0.792507
\(160\) 1.06931e9i 1.63163i
\(161\) 1.44939e9i 2.15715i
\(162\) 1.22832e8i 0.178340i
\(163\) −4.00064e8 −0.566733 −0.283367 0.959012i \(-0.591451\pi\)
−0.283367 + 0.959012i \(0.591451\pi\)
\(164\) −8.14664e8 −1.12617
\(165\) 8.00345e8i 1.07980i
\(166\) 2.37955e9 3.13374
\(167\) 6.04579e8 0.777297 0.388648 0.921386i \(-0.372942\pi\)
0.388648 + 0.921386i \(0.372942\pi\)
\(168\) 7.41034e8i 0.930253i
\(169\) 6.65899e8 0.816322
\(170\) 5.22697e8i 0.625827i
\(171\) −3.85058e8 −0.450341
\(172\) 1.14087e9i 1.30354i
\(173\) 1.13601e9i 1.26822i 0.773241 + 0.634112i \(0.218634\pi\)
−0.773241 + 0.634112i \(0.781366\pi\)
\(174\) 1.29848e9i 1.41657i
\(175\) 2.15042e9 2.29283
\(176\) 1.08160e8i 0.112723i
\(177\) 1.81010e8 5.36986e8i 0.184421 0.547104i
\(178\) −6.43156e8 −0.640673
\(179\) 1.64528e9i 1.60261i 0.598257 + 0.801304i \(0.295860\pi\)
−0.598257 + 0.801304i \(0.704140\pi\)
\(180\) −8.39403e8 −0.799614
\(181\) −1.27022e9 −1.18349 −0.591747 0.806124i \(-0.701562\pi\)
−0.591747 + 0.806124i \(0.701562\pi\)
\(182\) 1.31486e9 1.19838
\(183\) 5.16978e8i 0.460965i
\(184\) 1.31271e9 1.14524
\(185\) 7.70023e8i 0.657380i
\(186\) 7.92539e8 0.662169
\(187\) 3.85005e8i 0.314848i
\(188\) 1.48859e9i 1.19163i
\(189\) 4.27797e8 0.335267
\(190\) 4.30082e9i 3.30017i
\(191\) 5.84587e8i 0.439254i 0.975584 + 0.219627i \(0.0704840\pi\)
−0.975584 + 0.219627i \(0.929516\pi\)
\(192\) 1.27817e9 0.940554
\(193\) −5.03544e8 −0.362918 −0.181459 0.983399i \(-0.558082\pi\)
−0.181459 + 0.983399i \(0.558082\pi\)
\(194\) 2.11559e9 1.49357
\(195\) 5.44488e8i 0.376573i
\(196\) −4.73356e9 −3.20748
\(197\) −9.45241e8 −0.627593 −0.313796 0.949490i \(-0.601601\pi\)
−0.313796 + 0.949490i \(0.601601\pi\)
\(198\) 1.01054e9 0.657494
\(199\) −3.11939e8 −0.198910 −0.0994550 0.995042i \(-0.531710\pi\)
−0.0994550 + 0.995042i \(0.531710\pi\)
\(200\) 1.94764e9i 1.21727i
\(201\) 1.66778e9i 1.02177i
\(202\) 3.73794e9 2.24506
\(203\) 4.52234e9 2.66305
\(204\) −4.03794e8 −0.233152
\(205\) 1.92035e9 1.08734
\(206\) −4.05627e9 −2.25247
\(207\) 7.57824e8i 0.412750i
\(208\) 7.35827e7i 0.0393117i
\(209\) 3.16788e9i 1.66029i
\(210\) 4.77819e9i 2.45689i
\(211\) 4.38644e8i 0.221300i −0.993859 0.110650i \(-0.964707\pi\)
0.993859 0.110650i \(-0.0352933\pi\)
\(212\) −4.37046e9 −2.16363
\(213\) −1.89580e9 −0.921031
\(214\) 9.92483e8i 0.473225i
\(215\) 2.68930e9i 1.25859i
\(216\) 3.87456e8i 0.177995i
\(217\) 2.76025e9i 1.24483i
\(218\) 3.53643e9 1.56581
\(219\) 7.50779e8i 0.326389i
\(220\) 6.90578e9i 2.94796i
\(221\) 2.61925e8i 0.109802i
\(222\) 9.72251e8 0.400283
\(223\) 2.71647e9 1.09846 0.549232 0.835670i \(-0.314920\pi\)
0.549232 + 0.835670i \(0.314920\pi\)
\(224\) 4.70225e9i 1.86773i
\(225\) 1.12437e9 0.438710
\(226\) −3.48009e9 −1.33400
\(227\) 4.74002e9i 1.78516i −0.450892 0.892578i \(-0.648894\pi\)
0.450892 0.892578i \(-0.351106\pi\)
\(228\) 3.32247e9 1.22948
\(229\) 1.98073e9i 0.720252i 0.932904 + 0.360126i \(0.117266\pi\)
−0.932904 + 0.360126i \(0.882734\pi\)
\(230\) −8.46435e9 −3.02470
\(231\) 3.51949e9i 1.23604i
\(232\) 4.09588e9i 1.41382i
\(233\) 2.97503e9i 1.00941i 0.863291 + 0.504706i \(0.168399\pi\)
−0.863291 + 0.504706i \(0.831601\pi\)
\(234\) 6.87485e8 0.229298
\(235\) 3.50894e9i 1.15055i
\(236\) −1.56185e9 + 4.63338e9i −0.503490 + 1.49365i
\(237\) 6.64455e8 0.210607
\(238\) 2.29854e9i 0.716383i
\(239\) −4.45303e9 −1.36478 −0.682392 0.730987i \(-0.739060\pi\)
−0.682392 + 0.730987i \(0.739060\pi\)
\(240\) −2.67399e8 −0.0805962
\(241\) −6.45336e9 −1.91301 −0.956507 0.291711i \(-0.905776\pi\)
−0.956507 + 0.291711i \(0.905776\pi\)
\(242\) 2.80875e9i 0.818940i
\(243\) 2.23677e8 0.0641500
\(244\) 4.46075e9i 1.25849i
\(245\) 1.11581e10 3.09689
\(246\) 2.42468e9i 0.662087i
\(247\) 2.15516e9i 0.579017i
\(248\) −2.49996e9 −0.660886
\(249\) 4.33319e9i 1.12722i
\(250\) 3.01649e9i 0.772221i
\(251\) −3.67346e9 −0.925508 −0.462754 0.886487i \(-0.653139\pi\)
−0.462754 + 0.886487i \(0.653139\pi\)
\(252\) −3.69125e9 −0.915316
\(253\) 6.23463e9 1.52170
\(254\) 2.51726e8i 0.0604774i
\(255\) 9.51835e8 0.225113
\(256\) −3.63786e9 −0.847005
\(257\) −6.27039e9 −1.43735 −0.718674 0.695347i \(-0.755251\pi\)
−0.718674 + 0.695347i \(0.755251\pi\)
\(258\) −3.39558e9 −0.766365
\(259\) 3.38615e9i 0.752502i
\(260\) 4.69811e9i 1.02809i
\(261\) 2.36454e9 0.509548
\(262\) −2.01668e9 −0.427989
\(263\) −2.37803e9 −0.497044 −0.248522 0.968626i \(-0.579945\pi\)
−0.248522 + 0.968626i \(0.579945\pi\)
\(264\) −3.18761e9 −0.656219
\(265\) 1.03022e10 2.08903
\(266\) 1.89127e10i 3.77770i
\(267\) 1.17119e9i 0.230453i
\(268\) 1.43904e10i 2.78955i
\(269\) 2.51448e9i 0.480218i −0.970746 0.240109i \(-0.922817\pi\)
0.970746 0.240109i \(-0.0771832\pi\)
\(270\) 2.49832e9i 0.470102i
\(271\) −2.01336e9 −0.373288 −0.186644 0.982428i \(-0.559761\pi\)
−0.186644 + 0.982428i \(0.559761\pi\)
\(272\) −1.28632e8 −0.0235003
\(273\) 2.39437e9i 0.431063i
\(274\) 1.60180e10i 2.84188i
\(275\) 9.25019e9i 1.61741i
\(276\) 6.53889e9i 1.12685i
\(277\) 7.95593e9 1.35136 0.675681 0.737194i \(-0.263850\pi\)
0.675681 + 0.737194i \(0.263850\pi\)
\(278\) 3.27437e9i 0.548212i
\(279\) 1.44322e9i 0.238186i
\(280\) 1.50722e10i 2.45213i
\(281\) 8.46663e8 0.135795 0.0678977 0.997692i \(-0.478371\pi\)
0.0678977 + 0.997692i \(0.478371\pi\)
\(282\) −4.43048e9 −0.700575
\(283\) 3.53661e8i 0.0551367i 0.999620 + 0.0275684i \(0.00877639\pi\)
−0.999620 + 0.0275684i \(0.991224\pi\)
\(284\) 1.63579e10 2.51452
\(285\) −7.83183e9 −1.18709
\(286\) 5.65595e9i 0.845359i
\(287\) 8.44468e9 1.24467
\(288\) 2.45861e9i 0.357372i
\(289\) −6.51788e9 −0.934361
\(290\) 2.64102e10i 3.73405i
\(291\) 3.85251e9i 0.537244i
\(292\) 6.47810e9i 0.891078i
\(293\) 1.97817e9 0.268407 0.134203 0.990954i \(-0.457152\pi\)
0.134203 + 0.990954i \(0.457152\pi\)
\(294\) 1.40885e10i 1.88571i
\(295\) 3.68163e9 1.09219e10i 0.486130 1.44215i
\(296\) −3.06684e9 −0.399507
\(297\) 1.84020e9i 0.236504i
\(298\) −1.83124e10 −2.32210
\(299\) 4.24152e9 0.530685
\(300\) −9.70161e9 −1.19773
\(301\) 1.18261e10i 1.44071i
\(302\) 9.60620e9 1.15485
\(303\) 6.80683e9i 0.807559i
\(304\) 1.05840e9 0.123924
\(305\) 1.05150e10i 1.21509i
\(306\) 1.20181e9i 0.137073i
\(307\) 1.04677e10 1.17841 0.589205 0.807984i \(-0.299441\pi\)
0.589205 + 0.807984i \(0.299441\pi\)
\(308\) 3.03680e10i 3.37453i
\(309\) 7.38651e9i 0.810225i
\(310\) 1.61197e10 1.74546
\(311\) −7.77197e9 −0.830787 −0.415393 0.909642i \(-0.636356\pi\)
−0.415393 + 0.909642i \(0.636356\pi\)
\(312\) −2.16858e9 −0.228853
\(313\) 3.77331e9i 0.393138i −0.980490 0.196569i \(-0.937020\pi\)
0.980490 0.196569i \(-0.0629799\pi\)
\(314\) −1.89222e10 −1.94649
\(315\) 8.70112e9 0.883757
\(316\) −5.73325e9 −0.574980
\(317\) 2.22856e9 0.220692 0.110346 0.993893i \(-0.464804\pi\)
0.110346 + 0.993893i \(0.464804\pi\)
\(318\) 1.30078e10i 1.27203i
\(319\) 1.94531e10i 1.87857i
\(320\) 2.59972e10 2.47928
\(321\) 1.80732e9 0.170222
\(322\) −3.72217e10 −3.46237
\(323\) −3.76750e9 −0.346133
\(324\) −1.93000e9 −0.175137
\(325\) 6.29305e9i 0.564063i
\(326\) 1.02740e10i 0.909643i
\(327\) 6.43986e9i 0.563230i
\(328\) 7.64835e9i 0.660803i
\(329\) 1.54305e10i 1.31703i
\(330\) 2.05537e10 1.73314
\(331\) −9.97024e9 −0.830603 −0.415302 0.909684i \(-0.636324\pi\)
−0.415302 + 0.909684i \(0.636324\pi\)
\(332\) 3.73889e10i 3.07745i
\(333\) 1.77048e9i 0.143984i
\(334\) 1.55262e10i 1.24761i
\(335\) 3.39216e10i 2.69337i
\(336\) −1.17588e9 −0.0922583
\(337\) 3.14033e9i 0.243476i 0.992562 + 0.121738i \(0.0388467\pi\)
−0.992562 + 0.121738i \(0.961153\pi\)
\(338\) 1.71010e10i 1.31025i
\(339\) 6.33727e9i 0.479848i
\(340\) −8.21291e9 −0.614584
\(341\) −1.18734e10 −0.878127
\(342\) 9.88868e9i 0.722826i
\(343\) 2.49545e10 1.80291
\(344\) 1.07109e10 0.764880
\(345\) 1.54136e10i 1.08800i
\(346\) 2.91738e10 2.03558
\(347\) 1.41172e10i 0.973709i 0.873483 + 0.486855i \(0.161856\pi\)
−0.873483 + 0.486855i \(0.838144\pi\)
\(348\) −2.04025e10 −1.39112
\(349\) 1.18938e10i 0.801712i 0.916141 + 0.400856i \(0.131287\pi\)
−0.916141 + 0.400856i \(0.868713\pi\)
\(350\) 5.52251e10i 3.68014i
\(351\) 1.25192e9i 0.0824796i
\(352\) −2.02270e10 −1.31753
\(353\) 1.21056e10i 0.779629i 0.920893 + 0.389814i \(0.127461\pi\)
−0.920893 + 0.389814i \(0.872539\pi\)
\(354\) −1.37903e10 4.64853e9i −0.878136 0.296007i
\(355\) −3.85594e10 −2.42782
\(356\) 1.01056e10i 0.629164i
\(357\) 4.18567e9 0.257687
\(358\) 4.22524e10 2.57229
\(359\) −2.50527e10 −1.50826 −0.754132 0.656723i \(-0.771942\pi\)
−0.754132 + 0.656723i \(0.771942\pi\)
\(360\) 7.88061e9i 0.469191i
\(361\) 1.40159e10 0.825262
\(362\) 3.26207e10i 1.89958i
\(363\) −5.11476e9 −0.294577
\(364\) 2.06598e10i 1.17685i
\(365\) 1.52704e10i 0.860355i
\(366\) 1.32765e10 0.739878
\(367\) 9.78687e9i 0.539485i −0.962932 0.269743i \(-0.913061\pi\)
0.962932 0.269743i \(-0.0869386\pi\)
\(368\) 2.08302e9i 0.113580i
\(369\) 4.41537e9 0.238156
\(370\) 1.97750e10 1.05514
\(371\) 4.53035e10 2.39131
\(372\) 1.24528e10i 0.650274i
\(373\) −4.70700e9 −0.243169 −0.121585 0.992581i \(-0.538798\pi\)
−0.121585 + 0.992581i \(0.538798\pi\)
\(374\) 9.88734e9 0.505351
\(375\) 5.49305e9 0.277772
\(376\) 1.39754e10 0.699217
\(377\) 1.32343e10i 0.655141i
\(378\) 1.09863e10i 0.538125i
\(379\) −7.32437e8 −0.0354988 −0.0177494 0.999842i \(-0.505650\pi\)
−0.0177494 + 0.999842i \(0.505650\pi\)
\(380\) 6.75769e10 3.24089
\(381\) 4.58395e8 0.0217541
\(382\) 1.50128e10 0.705030
\(383\) −1.41091e10 −0.655699 −0.327849 0.944730i \(-0.606324\pi\)
−0.327849 + 0.944730i \(0.606324\pi\)
\(384\) 1.93659e10i 0.890663i
\(385\) 7.15843e10i 3.25818i
\(386\) 1.29315e10i 0.582506i
\(387\) 6.18339e9i 0.275666i
\(388\) 3.32414e10i 1.46674i
\(389\) −2.85066e10 −1.24494 −0.622469 0.782645i \(-0.713870\pi\)
−0.622469 + 0.782645i \(0.713870\pi\)
\(390\) 1.39830e10 0.604424
\(391\) 7.41473e9i 0.317240i
\(392\) 4.44404e10i 1.88206i
\(393\) 3.67239e9i 0.153950i
\(394\) 2.42748e10i 1.00733i
\(395\) 1.35146e10 0.555155
\(396\) 1.58781e10i 0.645683i
\(397\) 4.82585e7i 0.00194273i 1.00000 0.000971363i \(0.000309195\pi\)
−1.00000 0.000971363i \(0.999691\pi\)
\(398\) 8.01090e9i 0.319263i
\(399\) −3.44402e10 −1.35886
\(400\) −3.09053e9 −0.120724
\(401\) 3.13170e10i 1.21116i 0.795783 + 0.605581i \(0.207059\pi\)
−0.795783 + 0.605581i \(0.792941\pi\)
\(402\) −4.28303e10 −1.64001
\(403\) −8.07766e9 −0.306243
\(404\) 5.87328e10i 2.20473i
\(405\) 4.54945e9 0.169098
\(406\) 1.16138e11i 4.27436i
\(407\) −1.45658e10 −0.530830
\(408\) 3.79096e9i 0.136807i
\(409\) 3.47833e10i 1.24302i 0.783406 + 0.621510i \(0.213480\pi\)
−0.783406 + 0.621510i \(0.786520\pi\)
\(410\) 4.93165e10i 1.74525i
\(411\) −2.91689e10 −1.02224
\(412\) 6.37345e10i 2.21200i
\(413\) 1.61899e10 4.80289e10i 0.556472 1.65083i
\(414\) −1.94617e10 −0.662490
\(415\) 8.81343e10i 2.97134i
\(416\) −1.37608e10 −0.459483
\(417\) −5.96265e9 −0.197195
\(418\) −8.13543e10 −2.66487
\(419\) 2.76733e9i 0.0897851i 0.998992 + 0.0448926i \(0.0142946\pi\)
−0.998992 + 0.0448926i \(0.985705\pi\)
\(420\) −7.50776e10 −2.41276
\(421\) 5.62314e10i 1.78999i −0.446078 0.894994i \(-0.647180\pi\)
0.446078 0.894994i \(-0.352820\pi\)
\(422\) −1.12648e10 −0.355201
\(423\) 8.06795e9i 0.252001i
\(424\) 4.10314e10i 1.26956i
\(425\) 1.10011e10 0.337194
\(426\) 4.86861e10i 1.47831i
\(427\) 4.62394e10i 1.39092i
\(428\) −1.55945e10 −0.464724
\(429\) −1.02995e10 −0.304080
\(430\) −6.90640e10 −2.02012
\(431\) 4.15179e10i 1.20317i −0.798810 0.601584i \(-0.794537\pi\)
0.798810 0.601584i \(-0.205463\pi\)
\(432\) −6.14818e8 −0.0176527
\(433\) 2.35994e10 0.671351 0.335676 0.941978i \(-0.391035\pi\)
0.335676 + 0.941978i \(0.391035\pi\)
\(434\) 7.08861e10 1.99803
\(435\) 4.80933e10 1.34316
\(436\) 5.55664e10i 1.53768i
\(437\) 6.10094e10i 1.67290i
\(438\) −1.92808e10 −0.523875
\(439\) 2.64779e9 0.0712895 0.0356447 0.999365i \(-0.488652\pi\)
0.0356447 + 0.999365i \(0.488652\pi\)
\(440\) −6.48339e10 −1.72978
\(441\) 2.56553e10 0.678302
\(442\) 6.72651e9 0.176239
\(443\) 2.31302e10i 0.600572i −0.953849 0.300286i \(-0.902918\pi\)
0.953849 0.300286i \(-0.0970821\pi\)
\(444\) 1.52766e10i 0.393092i
\(445\) 2.38213e10i 0.607471i
\(446\) 6.97618e10i 1.76311i
\(447\) 3.33471e10i 0.835271i
\(448\) 1.14322e11 2.83803
\(449\) −2.70386e10 −0.665272 −0.332636 0.943055i \(-0.607938\pi\)
−0.332636 + 0.943055i \(0.607938\pi\)
\(450\) 2.88749e10i 0.704159i
\(451\) 3.63253e10i 0.878018i
\(452\) 5.46811e10i 1.31004i
\(453\) 1.74930e10i 0.415404i
\(454\) −1.21728e11 −2.86529
\(455\) 4.86999e10i 1.13627i
\(456\) 3.11925e10i 0.721425i
\(457\) 5.14489e10i 1.17954i 0.807573 + 0.589768i \(0.200781\pi\)
−0.807573 + 0.589768i \(0.799219\pi\)
\(458\) 5.08673e10 1.15605
\(459\) 2.18851e9 0.0493058
\(460\) 1.32997e11i 2.97036i
\(461\) −3.76966e10 −0.834639 −0.417319 0.908760i \(-0.637030\pi\)
−0.417319 + 0.908760i \(0.637030\pi\)
\(462\) 9.03842e10 1.98392
\(463\) 3.52785e9i 0.0767691i 0.999263 + 0.0383846i \(0.0122212\pi\)
−0.999263 + 0.0383846i \(0.987779\pi\)
\(464\) −6.49938e9 −0.140217
\(465\) 2.93542e10i 0.627853i
\(466\) 7.64019e10 1.62017
\(467\) 1.82138e10i 0.382941i −0.981498 0.191471i \(-0.938674\pi\)
0.981498 0.191471i \(-0.0613257\pi\)
\(468\) 1.08022e10i 0.225179i
\(469\) 1.49169e11i 3.08310i
\(470\) −9.01132e10 −1.84670
\(471\) 3.44575e10i 0.700164i
\(472\) 4.34998e10 + 1.46632e10i 0.876434 + 0.295434i
\(473\) 5.08708e10 1.01631
\(474\) 1.70639e10i 0.338037i
\(475\) −9.05183e10 −1.77812
\(476\) −3.61161e10 −0.703514
\(477\) 2.36873e10 0.457554
\(478\) 1.14358e11i 2.19057i
\(479\) 5.83560e10 1.10852 0.554260 0.832343i \(-0.313001\pi\)
0.554260 + 0.832343i \(0.313001\pi\)
\(480\) 5.00066e10i 0.942025i
\(481\) −9.90932e9 −0.185124
\(482\) 1.65729e11i 3.07051i
\(483\) 6.77811e10i 1.24543i
\(484\) 4.41327e10 0.804228
\(485\) 7.83576e10i 1.41617i
\(486\) 5.74426e9i 0.102965i
\(487\) −4.42685e9 −0.0787007 −0.0393504 0.999225i \(-0.512529\pi\)
−0.0393504 + 0.999225i \(0.512529\pi\)
\(488\) −4.18791e10 −0.738444
\(489\) −1.87091e10 −0.327204
\(490\) 2.86551e11i 4.97071i
\(491\) 1.59957e10 0.275219 0.137610 0.990487i \(-0.456058\pi\)
0.137610 + 0.990487i \(0.456058\pi\)
\(492\) −3.80981e10 −0.650193
\(493\) 2.31352e10 0.391639
\(494\) −5.53467e10 −0.929359
\(495\) 3.74284e10i 0.623420i
\(496\) 3.96695e9i 0.0655436i
\(497\) −1.69564e11 −2.77912
\(498\) 1.11281e11 1.80927
\(499\) −6.22322e10 −1.00372 −0.501860 0.864949i \(-0.667351\pi\)
−0.501860 + 0.864949i \(0.667351\pi\)
\(500\) −4.73968e10 −0.758349
\(501\) 2.82733e10 0.448773
\(502\) 9.43381e10i 1.48550i
\(503\) 1.08220e11i 1.69058i 0.534311 + 0.845288i \(0.320571\pi\)
−0.534311 + 0.845288i \(0.679429\pi\)
\(504\) 3.46547e10i 0.537082i
\(505\) 1.38447e11i 2.12871i
\(506\) 1.60112e11i 2.44242i
\(507\) 3.11410e10 0.471304
\(508\) −3.95527e9 −0.0593910
\(509\) 5.44215e10i 0.810773i 0.914145 + 0.405386i \(0.132863\pi\)
−0.914145 + 0.405386i \(0.867137\pi\)
\(510\) 2.44441e10i 0.361321i
\(511\) 6.71509e10i 0.984846i
\(512\) 1.25879e10i 0.183178i
\(513\) −1.80074e10 −0.260004
\(514\) 1.61030e11i 2.30704i
\(515\) 1.50237e11i 2.13574i
\(516\) 5.33534e10i 0.752598i
\(517\) 6.63752e10 0.929059
\(518\) 8.69599e10 1.20781
\(519\) 5.31257e10i 0.732209i
\(520\) −4.41075e10 −0.603253
\(521\) −5.92887e10 −0.804676 −0.402338 0.915491i \(-0.631802\pi\)
−0.402338 + 0.915491i \(0.631802\pi\)
\(522\) 6.07239e10i 0.817857i
\(523\) −3.98393e10 −0.532482 −0.266241 0.963906i \(-0.585782\pi\)
−0.266241 + 0.963906i \(0.585782\pi\)
\(524\) 3.16873e10i 0.420300i
\(525\) 1.00565e11 1.32377
\(526\) 6.10703e10i 0.797787i
\(527\) 1.41208e10i 0.183070i
\(528\) 5.05812e9i 0.0650809i
\(529\) −4.17602e10 −0.533261
\(530\) 2.64571e11i 3.35303i
\(531\) 8.46501e9 2.51123e10i 0.106475 0.315870i
\(532\) 2.97168e11 3.70984
\(533\) 2.47127e10i 0.306205i
\(534\) −3.00774e10 −0.369893
\(535\) 3.67597e10 0.448701
\(536\) 1.35102e11 1.63683
\(537\) 7.69421e10i 0.925266i
\(538\) −6.45744e10 −0.770781
\(539\) 2.11067e11i 2.50072i
\(540\) −3.92550e10 −0.461657
\(541\) 1.29570e11i 1.51257i −0.654245 0.756283i \(-0.727013\pi\)
0.654245 0.756283i \(-0.272987\pi\)
\(542\) 5.17051e10i 0.599151i
\(543\) −5.94025e10 −0.683291
\(544\) 2.40556e10i 0.274676i
\(545\) 1.30983e11i 1.48466i
\(546\) 6.14899e10 0.691883
\(547\) 1.30171e11 1.45400 0.727000 0.686637i \(-0.240914\pi\)
0.727000 + 0.686637i \(0.240914\pi\)
\(548\) 2.51684e11 2.79083
\(549\) 2.41767e10i 0.266138i
\(550\) 2.37554e11 2.59604
\(551\) −1.90360e11 −2.06523
\(552\) 6.13893e10 0.661206
\(553\) 5.94300e10 0.635485
\(554\) 2.04316e11i 2.16902i
\(555\) 3.60104e10i 0.379539i
\(556\) 5.14488e10 0.538364
\(557\) −8.74828e10 −0.908870 −0.454435 0.890780i \(-0.650159\pi\)
−0.454435 + 0.890780i \(0.650159\pi\)
\(558\) 3.70634e10 0.382303
\(559\) 3.46083e10 0.354432
\(560\) −2.39166e10 −0.243191
\(561\) 1.80049e10i 0.181777i
\(562\) 2.17432e10i 0.217960i
\(563\) 8.21664e10i 0.817825i 0.912574 + 0.408913i \(0.134092\pi\)
−0.912574 + 0.408913i \(0.865908\pi\)
\(564\) 6.96143e10i 0.687990i
\(565\) 1.28896e11i 1.26487i
\(566\) 9.08237e9 0.0884980
\(567\) 2.00061e10 0.193566
\(568\) 1.53574e11i 1.47545i
\(569\) 1.48678e11i 1.41840i 0.705009 + 0.709198i \(0.250943\pi\)
−0.705009 + 0.709198i \(0.749057\pi\)
\(570\) 2.01129e11i 1.90536i
\(571\) 8.59763e10i 0.808788i −0.914585 0.404394i \(-0.867483\pi\)
0.914585 0.404394i \(-0.132517\pi\)
\(572\) 8.88696e10 0.830174
\(573\) 2.73384e10i 0.253603i
\(574\) 2.16868e11i 1.99778i
\(575\) 1.78147e11i 1.62970i
\(576\) 5.97741e10 0.543029
\(577\) −1.13285e11 −1.02204 −0.511021 0.859568i \(-0.670732\pi\)
−0.511021 + 0.859568i \(0.670732\pi\)
\(578\) 1.67386e11i 1.49971i
\(579\) −2.35484e10 −0.209531
\(580\) −4.14973e11 −3.66697
\(581\) 3.87568e11i 3.40129i
\(582\) 9.89364e10 0.862311
\(583\) 1.94876e11i 1.68688i
\(584\) 6.08186e10 0.522860
\(585\) 2.54632e10i 0.217415i
\(586\) 5.08015e10i 0.430810i
\(587\) 2.73783e10i 0.230597i −0.993331 0.115299i \(-0.963217\pi\)
0.993331 0.115299i \(-0.0367825\pi\)
\(588\) −2.21367e11 −1.85184
\(589\) 1.16188e11i 0.965383i
\(590\) −2.80487e11 9.45481e10i −2.31475 0.780270i
\(591\) −4.42046e10 −0.362341
\(592\) 4.86648e9i 0.0396213i
\(593\) 2.13025e11 1.72271 0.861355 0.508004i \(-0.169616\pi\)
0.861355 + 0.508004i \(0.169616\pi\)
\(594\) 4.72582e10 0.379604
\(595\) 8.51338e10 0.679257
\(596\) 2.87735e11i 2.28038i
\(597\) −1.45879e10 −0.114841
\(598\) 1.08927e11i 0.851783i
\(599\) −9.11473e10 −0.708005 −0.354003 0.935244i \(-0.615180\pi\)
−0.354003 + 0.935244i \(0.615180\pi\)
\(600\) 9.10821e10i 0.702794i
\(601\) 2.68033e10i 0.205443i −0.994710 0.102721i \(-0.967245\pi\)
0.994710 0.102721i \(-0.0327550\pi\)
\(602\) −3.03707e11 −2.31243
\(603\) 7.79943e10i 0.589921i
\(604\) 1.50938e11i 1.13410i
\(605\) −1.04031e11 −0.776499
\(606\) 1.74806e11 1.29618
\(607\) 7.40206e10 0.545253 0.272626 0.962120i \(-0.412108\pi\)
0.272626 + 0.962120i \(0.412108\pi\)
\(608\) 1.97933e11i 1.44845i
\(609\) 2.11489e11 1.53751
\(610\) 2.70036e11 1.95030
\(611\) 4.51561e10 0.324005
\(612\) −1.88836e10 −0.134610
\(613\) 3.05315e10i 0.216225i −0.994139 0.108113i \(-0.965519\pi\)
0.994139 0.108113i \(-0.0344807\pi\)
\(614\) 2.68820e11i 1.89142i
\(615\) 8.98058e10 0.627775
\(616\) −2.85105e11 −1.98008
\(617\) 1.70239e11 1.17468 0.587338 0.809342i \(-0.300176\pi\)
0.587338 + 0.809342i \(0.300176\pi\)
\(618\) −1.89693e11 −1.30046
\(619\) −4.59600e10 −0.313052 −0.156526 0.987674i \(-0.550030\pi\)
−0.156526 + 0.987674i \(0.550030\pi\)
\(620\) 2.53283e11i 1.71411i
\(621\) 3.54399e10i 0.238301i
\(622\) 1.99592e11i 1.33347i
\(623\) 1.04753e11i 0.695371i
\(624\) 3.44112e9i 0.0226966i
\(625\) −8.91006e10 −0.583929
\(626\) −9.69024e10 −0.631011
\(627\) 1.48147e11i 0.958567i
\(628\) 2.97317e11i 1.91153i
\(629\) 1.73228e10i 0.110666i
\(630\) 2.23454e11i 1.41849i
\(631\) 2.58454e11 1.63029 0.815147 0.579254i \(-0.196656\pi\)
0.815147 + 0.579254i \(0.196656\pi\)
\(632\) 5.38258e10i 0.337382i
\(633\) 2.05133e10i 0.127768i
\(634\) 5.72317e10i 0.354225i
\(635\) 9.32347e9 0.0573433
\(636\) −2.04386e11 −1.24917
\(637\) 1.43592e11i 0.872113i
\(638\) 4.99576e11 3.01522
\(639\) −8.86579e10 −0.531758
\(640\) 3.93891e11i 2.34777i
\(641\) −1.62707e11 −0.963770 −0.481885 0.876234i \(-0.660048\pi\)
−0.481885 + 0.876234i \(0.660048\pi\)
\(642\) 4.64138e10i 0.273217i
\(643\) 3.41504e11 1.99780 0.998901 0.0468767i \(-0.0149268\pi\)
0.998901 + 0.0468767i \(0.0149268\pi\)
\(644\) 5.84849e11i 3.40017i
\(645\) 1.25766e11i 0.726649i
\(646\) 9.67532e10i 0.555565i
\(647\) 1.73298e11 0.988954 0.494477 0.869191i \(-0.335360\pi\)
0.494477 + 0.869191i \(0.335360\pi\)
\(648\) 1.81195e10i 0.102765i
\(649\) 2.06600e11 + 6.96418e10i 1.16453 + 0.392546i
\(650\) 1.61612e11 0.905358
\(651\) 1.29084e11i 0.718702i
\(652\) 1.61432e11 0.893303
\(653\) 2.36255e11 1.29936 0.649679 0.760209i \(-0.274903\pi\)
0.649679 + 0.760209i \(0.274903\pi\)
\(654\) 1.65382e11 0.904020
\(655\) 7.46941e10i 0.405809i
\(656\) −1.21365e10 −0.0655355
\(657\) 3.51104e10i 0.188441i
\(658\) −3.96270e11 −2.11392
\(659\) 1.18417e11i 0.627871i −0.949444 0.313936i \(-0.898352\pi\)
0.949444 0.313936i \(-0.101648\pi\)
\(660\) 3.22951e11i 1.70201i
\(661\) 7.70053e10 0.403380 0.201690 0.979449i \(-0.435357\pi\)
0.201690 + 0.979449i \(0.435357\pi\)
\(662\) 2.56046e11i 1.33317i
\(663\) 1.22490e10i 0.0633940i
\(664\) −3.51020e11 −1.80576
\(665\) −7.00492e11 −3.58193
\(666\) 4.54677e10 0.231103
\(667\) 3.74643e11i 1.89284i
\(668\) −2.43957e11 −1.22520
\(669\) 1.27037e11 0.634199
\(670\) −8.71140e11 −4.32304
\(671\) −1.98902e11 −0.981180
\(672\) 2.19903e11i 1.07833i
\(673\) 2.12639e11i 1.03653i −0.855220 0.518265i \(-0.826578\pi\)
0.855220 0.518265i \(-0.173422\pi\)
\(674\) 8.06468e10 0.390794
\(675\) 5.25814e10 0.253290
\(676\) −2.68700e11 −1.28671
\(677\) −3.86837e11 −1.84150 −0.920752 0.390148i \(-0.872424\pi\)
−0.920752 + 0.390148i \(0.872424\pi\)
\(678\) −1.62748e11 −0.770186
\(679\) 3.44575e11i 1.62108i
\(680\) 7.71057e10i 0.360621i
\(681\) 2.21669e11i 1.03066i
\(682\) 3.04921e11i 1.40945i
\(683\) 2.43065e11i 1.11696i −0.829516 0.558482i \(-0.811384\pi\)
0.829516 0.558482i \(-0.188616\pi\)
\(684\) 1.55377e11 0.709841
\(685\) −5.93278e11 −2.69461
\(686\) 6.40858e11i 2.89378i
\(687\) 9.26298e10i 0.415838i
\(688\) 1.69962e10i 0.0758573i
\(689\) 1.32577e11i 0.588291i
\(690\) −3.95838e11 −1.74631
\(691\) 1.98105e11i 0.868926i 0.900690 + 0.434463i \(0.143062\pi\)
−0.900690 + 0.434463i \(0.856938\pi\)
\(692\) 4.58395e11i 1.99901i
\(693\) 1.64590e11i 0.713628i
\(694\) 3.62543e11 1.56287
\(695\) −1.21277e11 −0.519801
\(696\) 1.91545e11i 0.816272i
\(697\) 4.32010e10 0.183047
\(698\) 3.05444e11 1.28680
\(699\) 1.39129e11i 0.582784i
\(700\) −8.67729e11 −3.61403
\(701\) 2.21452e11i 0.917079i −0.888674 0.458539i \(-0.848373\pi\)
0.888674 0.458539i \(-0.151627\pi\)
\(702\) 3.21505e10 0.132385
\(703\) 1.42534e11i 0.583576i
\(704\) 4.91762e11i 2.00200i
\(705\) 1.64097e11i 0.664269i
\(706\) 3.10885e11 1.25135
\(707\) 6.08815e11i 2.43673i
\(708\) −7.30404e10 + 2.16682e11i −0.290690 + 0.862362i
\(709\) 3.27105e11 1.29450 0.647250 0.762278i \(-0.275919\pi\)
0.647250 + 0.762278i \(0.275919\pi\)
\(710\) 9.90245e11i 3.89681i
\(711\) 3.10735e10 0.121594
\(712\) 9.48753e10 0.369176
\(713\) 2.28667e11 0.884800
\(714\) 1.07492e11i 0.413604i
\(715\) −2.09486e11 −0.801550
\(716\) 6.63895e11i 2.52608i
\(717\) −2.08247e11 −0.787958
\(718\) 6.43380e11i 2.42086i
\(719\) 1.19003e11i 0.445291i −0.974899 0.222646i \(-0.928531\pi\)
0.974899 0.222646i \(-0.0714693\pi\)
\(720\) −1.25050e10 −0.0465322
\(721\) 6.60662e11i 2.44477i
\(722\) 3.59943e11i 1.32460i
\(723\) −3.01794e11 −1.10448
\(724\) 5.12555e11 1.86546
\(725\) 5.55850e11 2.01190
\(726\) 1.31352e11i 0.472815i
\(727\) −1.19400e9 −0.00427432 −0.00213716 0.999998i \(-0.500680\pi\)
−0.00213716 + 0.999998i \(0.500680\pi\)
\(728\) −1.93962e11 −0.690542
\(729\) 1.04604e10 0.0370370
\(730\) −3.92158e11 −1.38092
\(731\) 6.04997e10i 0.211877i
\(732\) 2.08609e11i 0.726587i
\(733\) 3.01012e11 1.04272 0.521361 0.853336i \(-0.325425\pi\)
0.521361 + 0.853336i \(0.325425\pi\)
\(734\) −2.51337e11 −0.865908
\(735\) 5.21812e11 1.78799
\(736\) 3.89548e11 1.32755
\(737\) 6.41660e11 2.17488
\(738\) 1.13391e11i 0.382256i
\(739\) 4.50964e11i 1.51204i 0.654547 + 0.756022i \(0.272860\pi\)
−0.654547 + 0.756022i \(0.727140\pi\)
\(740\) 3.10716e11i 1.03618i
\(741\) 1.00787e11i 0.334296i
\(742\) 1.16344e12i 3.83821i
\(743\) −4.32552e11 −1.41933 −0.709664 0.704540i \(-0.751153\pi\)
−0.709664 + 0.704540i \(0.751153\pi\)
\(744\) −1.16912e11 −0.381562
\(745\) 6.78258e11i 2.20176i
\(746\) 1.20881e11i 0.390302i
\(747\) 2.02643e11i 0.650803i
\(748\) 1.55356e11i 0.496273i
\(749\) 1.61650e11 0.513627
\(750\) 1.41067e11i 0.445842i
\(751\) 8.66836e10i 0.272507i 0.990674 + 0.136253i \(0.0435061\pi\)
−0.990674 + 0.136253i \(0.956494\pi\)
\(752\) 2.21762e10i 0.0693452i
\(753\) −1.71791e11 −0.534342
\(754\) 3.39870e11 1.05154
\(755\) 3.55796e11i 1.09500i
\(756\) −1.72623e11 −0.528458
\(757\) −2.29030e11 −0.697442 −0.348721 0.937227i \(-0.613384\pi\)
−0.348721 + 0.937227i \(0.613384\pi\)
\(758\) 1.88097e10i 0.0569779i
\(759\) 2.91565e11 0.878553
\(760\) 6.34436e11i 1.90166i
\(761\) −3.30547e11 −0.985585 −0.492793 0.870147i \(-0.664024\pi\)
−0.492793 + 0.870147i \(0.664024\pi\)
\(762\) 1.17721e10i 0.0349167i
\(763\) 5.75993e11i 1.69949i
\(764\) 2.35890e11i 0.692365i
\(765\) 4.45129e10 0.129969
\(766\) 3.62336e11i 1.05244i
\(767\) 1.40553e11 + 4.73784e10i 0.406124 + 0.136899i
\(768\) −1.70126e11 −0.489018
\(769\) 5.16985e11i 1.47834i −0.673522 0.739168i \(-0.735219\pi\)
0.673522 0.739168i \(-0.264781\pi\)
\(770\) 1.83836e12 5.22958
\(771\) −2.93237e11 −0.829854
\(772\) 2.03188e11 0.572042
\(773\) 3.80459e11i 1.06559i −0.846245 0.532794i \(-0.821142\pi\)
0.846245 0.532794i \(-0.178858\pi\)
\(774\) −1.58796e11 −0.442461
\(775\) 3.39268e11i 0.940451i
\(776\) −3.12082e11 −0.860640
\(777\) 1.58355e11i 0.434457i
\(778\) 7.32080e11i 1.99821i
\(779\) −3.55464e11 −0.965263
\(780\) 2.19709e11i 0.593567i
\(781\) 7.29390e11i 1.96045i
\(782\) −1.90418e11 −0.509191