Properties

Label 177.9.c.a.58.5
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 58.5
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.76

$q$-expansion

\(f(q)\) \(=\) \(q-29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} -1363.64i q^{6} -1275.54 q^{7} +9863.29i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} -1363.64i q^{6} -1275.54 q^{7} +9863.29i q^{8} +2187.00 q^{9} +25960.0i q^{10} +12776.2i q^{11} -27790.6 q^{12} +22856.4i q^{13} +37193.6i q^{14} -41634.5 q^{15} +135476. q^{16} -85141.2 q^{17} -63771.1i q^{18} -42936.4 q^{19} +529059. q^{20} -59651.0 q^{21} +372544. q^{22} -240016. i q^{23} +461261. i q^{24} +401984. q^{25} +666475. q^{26} +102276. q^{27} +757997. q^{28} +158660. q^{29} +1.21403e6i q^{30} -826585. i q^{31} -1.42535e6i q^{32} +597485. i q^{33} +2.48265e6i q^{34} +1.13559e6 q^{35} -1.29964e6 q^{36} -899334. i q^{37} +1.25199e6i q^{38} +1.06889e6i q^{39} -8.78115e6i q^{40} -2.13093e6 q^{41} +1.73937e6i q^{42} +2.82120e6i q^{43} -7.59236e6i q^{44} -1.94706e6 q^{45} -6.99866e6 q^{46} +5.83048e6i q^{47} +6.33557e6 q^{48} -4.13780e6 q^{49} -1.17215e7i q^{50} -3.98166e6 q^{51} -1.35826e7i q^{52} +1.29905e7 q^{53} -2.98228e6i q^{54} -1.13745e7i q^{55} -1.25810e7i q^{56} -2.00794e6 q^{57} -4.62640e6i q^{58} +(8.68651e6 - 8.44837e6i) q^{59} +2.47416e7 q^{60} -3.72205e6i q^{61} -2.41025e7 q^{62} -2.78960e6 q^{63} -6.88034e6 q^{64} -2.03488e7i q^{65} +1.74222e7 q^{66} -3.14296e6i q^{67} +5.05958e7 q^{68} -1.12244e7i q^{69} -3.31130e7i q^{70} -1.78522e7 q^{71} +2.15710e7i q^{72} +208529. i q^{73} -2.62238e7 q^{74} +1.87989e7 q^{75} +2.55153e7 q^{76} -1.62966e7i q^{77} +3.11679e7 q^{78} -5.74903e7 q^{79} -1.20612e8 q^{80} +4.78297e6 q^{81} +6.21363e7i q^{82} +4.16878e6i q^{83} +3.54480e7 q^{84} +7.58000e7 q^{85} +8.22638e7 q^{86} +7.41980e6 q^{87} -1.26016e8 q^{88} +4.65731e7i q^{89} +5.67745e7i q^{90} -2.91543e7i q^{91} +1.42631e8i q^{92} -3.86556e7i q^{93} +1.70012e8 q^{94} +3.82257e7 q^{95} -6.66571e7i q^{96} -1.21368e8i q^{97} +1.20655e8i q^{98} +2.79416e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 29.1592i 1.82245i −0.411911 0.911224i \(-0.635139\pi\)
0.411911 0.911224i \(-0.364861\pi\)
\(3\) 46.7654 0.577350
\(4\) −594.257 −2.32132
\(5\) −890.286 −1.42446 −0.712229 0.701947i \(-0.752314\pi\)
−0.712229 + 0.701947i \(0.752314\pi\)
\(6\) 1363.64i 1.05219i
\(7\) −1275.54 −0.531253 −0.265626 0.964076i \(-0.585579\pi\)
−0.265626 + 0.964076i \(0.585579\pi\)
\(8\) 9863.29i 2.40803i
\(9\) 2187.00 0.333333
\(10\) 25960.0i 2.59600i
\(11\) 12776.2i 0.872633i 0.899793 + 0.436317i \(0.143717\pi\)
−0.899793 + 0.436317i \(0.856283\pi\)
\(12\) −27790.6 −1.34021
\(13\) 22856.4i 0.800268i 0.916457 + 0.400134i \(0.131036\pi\)
−0.916457 + 0.400134i \(0.868964\pi\)
\(14\) 37193.6i 0.968181i
\(15\) −41634.5 −0.822411
\(16\) 135476. 2.06719
\(17\) −85141.2 −1.01940 −0.509700 0.860352i \(-0.670243\pi\)
−0.509700 + 0.860352i \(0.670243\pi\)
\(18\) 63771.1i 0.607483i
\(19\) −42936.4 −0.329467 −0.164733 0.986338i \(-0.552676\pi\)
−0.164733 + 0.986338i \(0.552676\pi\)
\(20\) 529059. 3.30662
\(21\) −59651.0 −0.306719
\(22\) 372544. 1.59033
\(23\) 240016.i 0.857686i −0.903379 0.428843i \(-0.858921\pi\)
0.903379 0.428843i \(-0.141079\pi\)
\(24\) 461261.i 1.39028i
\(25\) 401984. 1.02908
\(26\) 666475. 1.45845
\(27\) 102276. 0.192450
\(28\) 757997. 1.23321
\(29\) 158660. 0.224324 0.112162 0.993690i \(-0.464222\pi\)
0.112162 + 0.993690i \(0.464222\pi\)
\(30\) 1.21403e6i 1.49880i
\(31\) 826585.i 0.895036i −0.894275 0.447518i \(-0.852308\pi\)
0.894275 0.447518i \(-0.147692\pi\)
\(32\) 1.42535e6i 1.35932i
\(33\) 597485.i 0.503815i
\(34\) 2.48265e6i 1.85780i
\(35\) 1.13559e6 0.756747
\(36\) −1.29964e6 −0.773772
\(37\) 899334.i 0.479859i −0.970790 0.239930i \(-0.922876\pi\)
0.970790 0.239930i \(-0.0771244\pi\)
\(38\) 1.25199e6i 0.600436i
\(39\) 1.06889e6i 0.462035i
\(40\) 8.78115e6i 3.43014i
\(41\) −2.13093e6 −0.754110 −0.377055 0.926191i \(-0.623063\pi\)
−0.377055 + 0.926191i \(0.623063\pi\)
\(42\) 1.73937e6i 0.558979i
\(43\) 2.82120e6i 0.825201i 0.910912 + 0.412601i \(0.135379\pi\)
−0.910912 + 0.412601i \(0.864621\pi\)
\(44\) 7.59236e6i 2.02566i
\(45\) −1.94706e6 −0.474819
\(46\) −6.99866e6 −1.56309
\(47\) 5.83048e6i 1.19485i 0.801925 + 0.597424i \(0.203809\pi\)
−0.801925 + 0.597424i \(0.796191\pi\)
\(48\) 6.33557e6 1.19349
\(49\) −4.13780e6 −0.717770
\(50\) 1.17215e7i 1.87544i
\(51\) −3.98166e6 −0.588550
\(52\) 1.35826e7i 1.85767i
\(53\) 1.29905e7 1.64635 0.823176 0.567787i \(-0.192200\pi\)
0.823176 + 0.567787i \(0.192200\pi\)
\(54\) 2.98228e6i 0.350730i
\(55\) 1.13745e7i 1.24303i
\(56\) 1.25810e7i 1.27927i
\(57\) −2.00794e6 −0.190218
\(58\) 4.62640e6i 0.408819i
\(59\) 8.68651e6 8.44837e6i 0.716865 0.697212i
\(60\) 2.47416e7 1.90908
\(61\) 3.72205e6i 0.268820i −0.990926 0.134410i \(-0.957086\pi\)
0.990926 0.134410i \(-0.0429140\pi\)
\(62\) −2.41025e7 −1.63116
\(63\) −2.78960e6 −0.177084
\(64\) −6.88034e6 −0.410100
\(65\) 2.03488e7i 1.13995i
\(66\) 1.74222e7 0.918177
\(67\) 3.14296e6i 0.155970i −0.996955 0.0779848i \(-0.975151\pi\)
0.996955 0.0779848i \(-0.0248486\pi\)
\(68\) 5.05958e7 2.36635
\(69\) 1.12244e7i 0.495186i
\(70\) 3.31130e7i 1.37913i
\(71\) −1.78522e7 −0.702520 −0.351260 0.936278i \(-0.614247\pi\)
−0.351260 + 0.936278i \(0.614247\pi\)
\(72\) 2.15710e7i 0.802677i
\(73\) 208529.i 0.00734303i 0.999993 + 0.00367152i \(0.00116868\pi\)
−0.999993 + 0.00367152i \(0.998831\pi\)
\(74\) −2.62238e7 −0.874519
\(75\) 1.87989e7 0.594139
\(76\) 2.55153e7 0.764796
\(77\) 1.62966e7i 0.463589i
\(78\) 3.11679e7 0.842034
\(79\) −5.74903e7 −1.47600 −0.738000 0.674801i \(-0.764230\pi\)
−0.738000 + 0.674801i \(0.764230\pi\)
\(80\) −1.20612e8 −2.94463
\(81\) 4.78297e6 0.111111
\(82\) 6.21363e7i 1.37433i
\(83\) 4.16878e6i 0.0878408i 0.999035 + 0.0439204i \(0.0139848\pi\)
−0.999035 + 0.0439204i \(0.986015\pi\)
\(84\) 3.54480e7 0.711992
\(85\) 7.58000e7 1.45209
\(86\) 8.22638e7 1.50389
\(87\) 7.41980e6 0.129514
\(88\) −1.26016e8 −2.10133
\(89\) 4.65731e7i 0.742292i 0.928574 + 0.371146i \(0.121035\pi\)
−0.928574 + 0.371146i \(0.878965\pi\)
\(90\) 5.67745e7i 0.865333i
\(91\) 2.91543e7i 0.425144i
\(92\) 1.42631e8i 1.99096i
\(93\) 3.86556e7i 0.516750i
\(94\) 1.70012e8 2.17755
\(95\) 3.82257e7 0.469311
\(96\) 6.66571e7i 0.784805i
\(97\) 1.21368e8i 1.37094i −0.728101 0.685470i \(-0.759597\pi\)
0.728101 0.685470i \(-0.240403\pi\)
\(98\) 1.20655e8i 1.30810i
\(99\) 2.79416e7i 0.290878i
\(100\) −2.38882e8 −2.38882
\(101\) 1.87669e8i 1.80346i 0.432297 + 0.901731i \(0.357703\pi\)
−0.432297 + 0.901731i \(0.642297\pi\)
\(102\) 1.16102e8i 1.07260i
\(103\) 1.37271e8i 1.21964i −0.792540 0.609819i \(-0.791242\pi\)
0.792540 0.609819i \(-0.208758\pi\)
\(104\) −2.25440e8 −1.92707
\(105\) 5.31065e7 0.436908
\(106\) 3.78792e8i 3.00039i
\(107\) −3.65182e7 −0.278596 −0.139298 0.990251i \(-0.544485\pi\)
−0.139298 + 0.990251i \(0.544485\pi\)
\(108\) −6.07782e7 −0.446738
\(109\) 1.21819e8i 0.862998i −0.902114 0.431499i \(-0.857985\pi\)
0.902114 0.431499i \(-0.142015\pi\)
\(110\) −3.31671e8 −2.26536
\(111\) 4.20577e7i 0.277047i
\(112\) −1.72804e8 −1.09820
\(113\) 1.15797e8i 0.710204i −0.934827 0.355102i \(-0.884446\pi\)
0.934827 0.355102i \(-0.115554\pi\)
\(114\) 5.85498e7i 0.346662i
\(115\) 2.13683e8i 1.22174i
\(116\) −9.42849e7 −0.520727
\(117\) 4.99870e7i 0.266756i
\(118\) −2.46347e8 2.53291e8i −1.27063 1.30645i
\(119\) 1.08601e8 0.541559
\(120\) 4.10654e8i 1.98039i
\(121\) 5.11270e7 0.238511
\(122\) −1.08532e8 −0.489911
\(123\) −9.96539e7 −0.435385
\(124\) 4.91204e8i 2.07766i
\(125\) −1.01127e7 −0.0414216
\(126\) 8.13425e7i 0.322727i
\(127\) −3.04346e7 −0.116991 −0.0584954 0.998288i \(-0.518630\pi\)
−0.0584954 + 0.998288i \(0.518630\pi\)
\(128\) 1.64265e8i 0.611936i
\(129\) 1.31934e8i 0.476430i
\(130\) −5.93353e8 −2.07749
\(131\) 1.54953e8i 0.526155i −0.964775 0.263077i \(-0.915263\pi\)
0.964775 0.263077i \(-0.0847375\pi\)
\(132\) 3.55060e8i 1.16951i
\(133\) 5.47671e7 0.175030
\(134\) −9.16461e7 −0.284246
\(135\) −9.10548e7 −0.274137
\(136\) 8.39773e8i 2.45474i
\(137\) −3.52274e8 −0.999997 −0.499999 0.866026i \(-0.666666\pi\)
−0.499999 + 0.866026i \(0.666666\pi\)
\(138\) −3.27295e8 −0.902450
\(139\) 7.36864e8 1.97391 0.986957 0.160986i \(-0.0514674\pi\)
0.986957 + 0.160986i \(0.0514674\pi\)
\(140\) −6.74834e8 −1.75665
\(141\) 2.72665e8i 0.689846i
\(142\) 5.20556e8i 1.28031i
\(143\) −2.92019e8 −0.698340
\(144\) 2.96285e8 0.689064
\(145\) −1.41253e8 −0.319540
\(146\) 6.08054e6 0.0133823
\(147\) −1.93506e8 −0.414405
\(148\) 5.34435e8i 1.11391i
\(149\) 3.98415e8i 0.808333i 0.914686 + 0.404166i \(0.132438\pi\)
−0.914686 + 0.404166i \(0.867562\pi\)
\(150\) 5.48161e8i 1.08279i
\(151\) 6.37835e8i 1.22688i −0.789743 0.613438i \(-0.789786\pi\)
0.789743 0.613438i \(-0.210214\pi\)
\(152\) 4.23495e8i 0.793366i
\(153\) −1.86204e8 −0.339800
\(154\) −4.75194e8 −0.844867
\(155\) 7.35897e8i 1.27494i
\(156\) 6.35195e8i 1.07253i
\(157\) 6.02298e8i 0.991318i 0.868517 + 0.495659i \(0.165073\pi\)
−0.868517 + 0.495659i \(0.834927\pi\)
\(158\) 1.67637e9i 2.68993i
\(159\) 6.07506e8 0.950521
\(160\) 1.26897e9i 1.93630i
\(161\) 3.06149e8i 0.455648i
\(162\) 1.39467e8i 0.202494i
\(163\) 8.36185e8 1.18455 0.592273 0.805737i \(-0.298231\pi\)
0.592273 + 0.805737i \(0.298231\pi\)
\(164\) 1.26632e9 1.75053
\(165\) 5.31932e8i 0.717663i
\(166\) 1.21558e8 0.160085
\(167\) 9.61416e8 1.23608 0.618038 0.786148i \(-0.287928\pi\)
0.618038 + 0.786148i \(0.287928\pi\)
\(168\) 5.88355e8i 0.738589i
\(169\) 2.93314e8 0.359572
\(170\) 2.21027e9i 2.64636i
\(171\) −9.39020e7 −0.109822
\(172\) 1.67652e9i 1.91555i
\(173\) 1.32604e9i 1.48038i −0.672400 0.740188i \(-0.734737\pi\)
0.672400 0.740188i \(-0.265263\pi\)
\(174\) 2.16355e8i 0.236032i
\(175\) −5.12746e8 −0.546701
\(176\) 1.73087e9i 1.80390i
\(177\) 4.06228e8 3.95091e8i 0.413882 0.402536i
\(178\) 1.35803e9 1.35279
\(179\) 1.02503e9i 0.998447i 0.866473 + 0.499223i \(0.166381\pi\)
−0.866473 + 0.499223i \(0.833619\pi\)
\(180\) 1.15705e9 1.10221
\(181\) 1.51215e9 1.40890 0.704451 0.709753i \(-0.251193\pi\)
0.704451 + 0.709753i \(0.251193\pi\)
\(182\) −8.50114e8 −0.774804
\(183\) 1.74063e8i 0.155204i
\(184\) 2.36735e9 2.06533
\(185\) 8.00664e8i 0.683539i
\(186\) −1.12716e9 −0.941749
\(187\) 1.08778e9i 0.889562i
\(188\) 3.46480e9i 2.77362i
\(189\) −1.30457e8 −0.102240
\(190\) 1.11463e9i 0.855295i
\(191\) 1.66824e9i 1.25350i 0.779220 + 0.626750i \(0.215615\pi\)
−0.779220 + 0.626750i \(0.784385\pi\)
\(192\) −3.21762e8 −0.236771
\(193\) 1.12322e9 0.809538 0.404769 0.914419i \(-0.367352\pi\)
0.404769 + 0.914419i \(0.367352\pi\)
\(194\) −3.53900e9 −2.49847
\(195\) 9.51618e8i 0.658149i
\(196\) 2.45892e9 1.66617
\(197\) 7.15552e8 0.475090 0.237545 0.971376i \(-0.423657\pi\)
0.237545 + 0.971376i \(0.423657\pi\)
\(198\) 8.14754e8 0.530110
\(199\) 1.62982e8 0.103927 0.0519634 0.998649i \(-0.483452\pi\)
0.0519634 + 0.998649i \(0.483452\pi\)
\(200\) 3.96489e9i 2.47805i
\(201\) 1.46982e8i 0.0900491i
\(202\) 5.47227e9 3.28672
\(203\) −2.02377e8 −0.119173
\(204\) 2.36613e9 1.36621
\(205\) 1.89714e9 1.07420
\(206\) −4.00272e9 −2.22273
\(207\) 5.24915e8i 0.285895i
\(208\) 3.09649e9i 1.65431i
\(209\) 5.48565e8i 0.287504i
\(210\) 1.54854e9i 0.796242i
\(211\) 3.40476e7i 0.0171774i −0.999963 0.00858868i \(-0.997266\pi\)
0.999963 0.00858868i \(-0.00273390\pi\)
\(212\) −7.71970e9 −3.82170
\(213\) −8.34865e8 −0.405600
\(214\) 1.06484e9i 0.507726i
\(215\) 2.51167e9i 1.17546i
\(216\) 1.00878e9i 0.463426i
\(217\) 1.05434e9i 0.475491i
\(218\) −3.55214e9 −1.57277
\(219\) 9.75194e6i 0.00423950i
\(220\) 6.75937e9i 2.88546i
\(221\) 1.94603e9i 0.815792i
\(222\) −1.22637e9 −0.504904
\(223\) −8.46796e8 −0.342420 −0.171210 0.985235i \(-0.554768\pi\)
−0.171210 + 0.985235i \(0.554768\pi\)
\(224\) 1.81809e9i 0.722144i
\(225\) 8.79139e8 0.343026
\(226\) −3.37654e9 −1.29431
\(227\) 9.21542e8i 0.347066i −0.984828 0.173533i \(-0.944482\pi\)
0.984828 0.173533i \(-0.0555183\pi\)
\(228\) 1.19323e9 0.441555
\(229\) 2.37081e9i 0.862095i −0.902329 0.431048i \(-0.858144\pi\)
0.902329 0.431048i \(-0.141856\pi\)
\(230\) 6.23081e9 2.22655
\(231\) 7.62115e8i 0.267653i
\(232\) 1.56491e9i 0.540179i
\(233\) 1.46452e8i 0.0496903i 0.999691 + 0.0248452i \(0.00790928\pi\)
−0.999691 + 0.0248452i \(0.992091\pi\)
\(234\) 1.45758e9 0.486149
\(235\) 5.19079e9i 1.70201i
\(236\) −5.16202e9 + 5.02050e9i −1.66407 + 1.61845i
\(237\) −2.68856e9 −0.852169
\(238\) 3.16671e9i 0.986963i
\(239\) 4.57915e9 1.40344 0.701720 0.712453i \(-0.252416\pi\)
0.701720 + 0.712453i \(0.252416\pi\)
\(240\) −5.64047e9 −1.70008
\(241\) 5.33390e9 1.58116 0.790582 0.612357i \(-0.209778\pi\)
0.790582 + 0.612357i \(0.209778\pi\)
\(242\) 1.49082e9i 0.434675i
\(243\) 2.23677e8 0.0641500
\(244\) 2.21185e9i 0.624017i
\(245\) 3.68383e9 1.02243
\(246\) 2.90583e9i 0.793467i
\(247\) 9.81374e8i 0.263662i
\(248\) 8.15285e9 2.15528
\(249\) 1.94954e8i 0.0507149i
\(250\) 2.94878e8i 0.0754887i
\(251\) 2.14584e9 0.540632 0.270316 0.962772i \(-0.412872\pi\)
0.270316 + 0.962772i \(0.412872\pi\)
\(252\) 1.65774e9 0.411069
\(253\) 3.06650e9 0.748446
\(254\) 8.87446e8i 0.213210i
\(255\) 3.54482e9 0.838365
\(256\) −6.55121e9 −1.52532
\(257\) −1.33536e9 −0.306102 −0.153051 0.988218i \(-0.548910\pi\)
−0.153051 + 0.988218i \(0.548910\pi\)
\(258\) 3.84710e9 0.868269
\(259\) 1.14713e9i 0.254927i
\(260\) 1.20924e10i 2.64618i
\(261\) 3.46990e8 0.0747747
\(262\) −4.51829e9 −0.958890
\(263\) 3.46742e9 0.724742 0.362371 0.932034i \(-0.381967\pi\)
0.362371 + 0.932034i \(0.381967\pi\)
\(264\) −5.89317e9 −1.21320
\(265\) −1.15653e10 −2.34516
\(266\) 1.59696e9i 0.318983i
\(267\) 2.17801e9i 0.428563i
\(268\) 1.86773e9i 0.362055i
\(269\) 3.17574e8i 0.0606508i −0.999540 0.0303254i \(-0.990346\pi\)
0.999540 0.0303254i \(-0.00965435\pi\)
\(270\) 2.65508e9i 0.499600i
\(271\) 6.39999e8 0.118659 0.0593297 0.998238i \(-0.481104\pi\)
0.0593297 + 0.998238i \(0.481104\pi\)
\(272\) −1.15346e10 −2.10730
\(273\) 1.36341e9i 0.245457i
\(274\) 1.02720e10i 1.82244i
\(275\) 5.13584e9i 0.898008i
\(276\) 6.67020e9i 1.14948i
\(277\) −8.41688e9 −1.42966 −0.714829 0.699299i \(-0.753496\pi\)
−0.714829 + 0.699299i \(0.753496\pi\)
\(278\) 2.14863e10i 3.59735i
\(279\) 1.80774e9i 0.298345i
\(280\) 1.12007e10i 1.82227i
\(281\) −8.79263e9 −1.41024 −0.705121 0.709087i \(-0.749107\pi\)
−0.705121 + 0.709087i \(0.749107\pi\)
\(282\) 7.95067e9 1.25721
\(283\) 1.03836e9i 0.161884i 0.996719 + 0.0809418i \(0.0257928\pi\)
−0.996719 + 0.0809418i \(0.974207\pi\)
\(284\) 1.06088e10 1.63077
\(285\) 1.78764e9 0.270957
\(286\) 8.51503e9i 1.27269i
\(287\) 2.71809e9 0.400623
\(288\) 3.11725e9i 0.453107i
\(289\) 2.73273e8 0.0391747
\(290\) 4.11882e9i 0.582345i
\(291\) 5.67584e9i 0.791513i
\(292\) 1.23920e8i 0.0170455i
\(293\) 8.39608e9 1.13922 0.569608 0.821916i \(-0.307095\pi\)
0.569608 + 0.821916i \(0.307095\pi\)
\(294\) 5.64247e9i 0.755231i
\(295\) −7.73348e9 + 7.52146e9i −1.02114 + 0.993149i
\(296\) 8.87039e9 1.15552
\(297\) 1.30670e9i 0.167938i
\(298\) 1.16174e10 1.47314
\(299\) 5.48591e9 0.686379
\(300\) −1.11714e10 −1.37918
\(301\) 3.59855e9i 0.438390i
\(302\) −1.85987e10 −2.23592
\(303\) 8.77641e9i 1.04123i
\(304\) −5.81684e9 −0.681071
\(305\) 3.31368e9i 0.382923i
\(306\) 5.42955e9i 0.619267i
\(307\) −3.44203e9 −0.387491 −0.193745 0.981052i \(-0.562064\pi\)
−0.193745 + 0.981052i \(0.562064\pi\)
\(308\) 9.68434e9i 1.07614i
\(309\) 6.41955e9i 0.704159i
\(310\) 2.14581e10 2.32351
\(311\) 5.52302e9 0.590384 0.295192 0.955438i \(-0.404616\pi\)
0.295192 + 0.955438i \(0.404616\pi\)
\(312\) −1.05428e10 −1.11259
\(313\) 7.74206e9i 0.806639i −0.915059 0.403319i \(-0.867856\pi\)
0.915059 0.403319i \(-0.132144\pi\)
\(314\) 1.75625e10 1.80662
\(315\) 2.48354e9 0.252249
\(316\) 3.41640e10 3.42626
\(317\) 5.51270e8 0.0545918 0.0272959 0.999627i \(-0.491310\pi\)
0.0272959 + 0.999627i \(0.491310\pi\)
\(318\) 1.77144e10i 1.73228i
\(319\) 2.02708e9i 0.195753i
\(320\) 6.12547e9 0.584170
\(321\) −1.70779e9 −0.160847
\(322\) 8.92706e9 0.830395
\(323\) 3.65566e9 0.335858
\(324\) −2.84231e9 −0.257924
\(325\) 9.18792e9i 0.823539i
\(326\) 2.43825e10i 2.15877i
\(327\) 5.69692e9i 0.498252i
\(328\) 2.10180e10i 1.81592i
\(329\) 7.43700e9i 0.634767i
\(330\) −1.55107e10 −1.30790
\(331\) −1.83436e10 −1.52818 −0.764088 0.645112i \(-0.776811\pi\)
−0.764088 + 0.645112i \(0.776811\pi\)
\(332\) 2.47732e9i 0.203906i
\(333\) 1.96684e9i 0.159953i
\(334\) 2.80341e10i 2.25268i
\(335\) 2.79813e9i 0.222172i
\(336\) −8.08126e9 −0.634047
\(337\) 2.40138e10i 1.86184i −0.365229 0.930918i \(-0.619009\pi\)
0.365229 0.930918i \(-0.380991\pi\)
\(338\) 8.55278e9i 0.655301i
\(339\) 5.41529e9i 0.410037i
\(340\) −4.50447e10 −3.37076
\(341\) 1.05606e10 0.781039
\(342\) 2.73810e9i 0.200145i
\(343\) 1.26311e10 0.912570
\(344\) −2.78263e10 −1.98711
\(345\) 9.99295e9i 0.705371i
\(346\) −3.86662e10 −2.69791
\(347\) 1.66067e10i 1.14542i 0.819758 + 0.572711i \(0.194108\pi\)
−0.819758 + 0.572711i \(0.805892\pi\)
\(348\) −4.40927e9 −0.300642
\(349\) 1.61798e9i 0.109061i 0.998512 + 0.0545306i \(0.0173662\pi\)
−0.998512 + 0.0545306i \(0.982634\pi\)
\(350\) 1.49512e10i 0.996334i
\(351\) 2.33766e9i 0.154012i
\(352\) 1.82106e10 1.18619
\(353\) 1.39661e10i 0.899449i −0.893167 0.449724i \(-0.851522\pi\)
0.893167 0.449724i \(-0.148478\pi\)
\(354\) −1.15205e10 1.18453e10i −0.733600 0.754279i
\(355\) 1.58936e10 1.00071
\(356\) 2.76764e10i 1.72310i
\(357\) 5.07876e9 0.312669
\(358\) 2.98890e10 1.81962
\(359\) 1.39663e10 0.840819 0.420409 0.907335i \(-0.361886\pi\)
0.420409 + 0.907335i \(0.361886\pi\)
\(360\) 1.92044e10i 1.14338i
\(361\) −1.51400e10 −0.891452
\(362\) 4.40930e10i 2.56765i
\(363\) 2.39097e9 0.137705
\(364\) 1.73251e10i 0.986895i
\(365\) 1.85651e8i 0.0104598i
\(366\) −5.07553e9 −0.282850
\(367\) 2.00449e10i 1.10494i 0.833533 + 0.552470i \(0.186315\pi\)
−0.833533 + 0.552470i \(0.813685\pi\)
\(368\) 3.25163e10i 1.77300i
\(369\) −4.66035e9 −0.251370
\(370\) 2.33467e10 1.24571
\(371\) −1.65699e10 −0.874629
\(372\) 2.29713e10i 1.19954i
\(373\) 2.88197e10 1.48886 0.744430 0.667700i \(-0.232721\pi\)
0.744430 + 0.667700i \(0.232721\pi\)
\(374\) −3.17189e10 −1.62118
\(375\) −4.72924e8 −0.0239148
\(376\) −5.75077e10 −2.87723
\(377\) 3.62641e9i 0.179519i
\(378\) 3.80401e9i 0.186326i
\(379\) 2.19596e10 1.06431 0.532155 0.846647i \(-0.321382\pi\)
0.532155 + 0.846647i \(0.321382\pi\)
\(380\) −2.27159e10 −1.08942
\(381\) −1.42328e9 −0.0675447
\(382\) 4.86444e10 2.28444
\(383\) −1.78028e10 −0.827355 −0.413678 0.910423i \(-0.635756\pi\)
−0.413678 + 0.910423i \(0.635756\pi\)
\(384\) 7.68193e9i 0.353301i
\(385\) 1.45086e10i 0.660363i
\(386\) 3.27523e10i 1.47534i
\(387\) 6.16996e9i 0.275067i
\(388\) 7.21240e10i 3.18239i
\(389\) −3.83303e10 −1.67396 −0.836979 0.547236i \(-0.815680\pi\)
−0.836979 + 0.547236i \(0.815680\pi\)
\(390\) −2.77484e10 −1.19944
\(391\) 2.04352e10i 0.874325i
\(392\) 4.08124e10i 1.72841i
\(393\) 7.24641e9i 0.303776i
\(394\) 2.08649e10i 0.865828i
\(395\) 5.11828e10 2.10250
\(396\) 1.66045e10i 0.675219i
\(397\) 3.53449e10i 1.42287i −0.702753 0.711434i \(-0.748046\pi\)
0.702753 0.711434i \(-0.251954\pi\)
\(398\) 4.75243e9i 0.189401i
\(399\) 2.56120e9 0.101054
\(400\) 5.44590e10 2.12731
\(401\) 2.59132e10i 1.00217i 0.865397 + 0.501087i \(0.167066\pi\)
−0.865397 + 0.501087i \(0.832934\pi\)
\(402\) −4.28587e9 −0.164110
\(403\) 1.88928e10 0.716269
\(404\) 1.11524e11i 4.18641i
\(405\) −4.25821e9 −0.158273
\(406\) 5.90115e9i 0.217186i
\(407\) 1.14901e10 0.418741
\(408\) 3.92723e10i 1.41725i
\(409\) 4.37463e10i 1.56332i 0.623704 + 0.781660i \(0.285627\pi\)
−0.623704 + 0.781660i \(0.714373\pi\)
\(410\) 5.53190e10i 1.95767i
\(411\) −1.64742e10 −0.577349
\(412\) 8.15745e10i 2.83117i
\(413\) −1.10800e10 + 1.07762e10i −0.380837 + 0.370396i
\(414\) −1.53061e10 −0.521030
\(415\) 3.71140e9i 0.125125i
\(416\) 3.25785e10 1.08782
\(417\) 3.44597e10 1.13964
\(418\) −1.59957e10 −0.523960
\(419\) 1.01547e10i 0.329467i 0.986338 + 0.164734i \(0.0526765\pi\)
−0.986338 + 0.164734i \(0.947324\pi\)
\(420\) −3.15589e10 −1.01420
\(421\) 7.44469e9i 0.236983i 0.992955 + 0.118492i \(0.0378059\pi\)
−0.992955 + 0.118492i \(0.962194\pi\)
\(422\) −9.92799e8 −0.0313049
\(423\) 1.27513e10i 0.398283i
\(424\) 1.28129e11i 3.96446i
\(425\) −3.42254e10 −1.04904
\(426\) 2.43440e10i 0.739185i
\(427\) 4.74761e9i 0.142812i
\(428\) 2.17012e10 0.646708
\(429\) −1.36564e10 −0.403187
\(430\) −7.32383e10 −2.14222
\(431\) 4.50007e10i 1.30410i 0.758177 + 0.652049i \(0.226090\pi\)
−0.758177 + 0.652049i \(0.773910\pi\)
\(432\) 1.38559e10 0.397832
\(433\) 4.18729e10 1.19119 0.595596 0.803284i \(-0.296916\pi\)
0.595596 + 0.803284i \(0.296916\pi\)
\(434\) 3.07437e10 0.866557
\(435\) −6.60574e9 −0.184487
\(436\) 7.23919e10i 2.00329i
\(437\) 1.03054e10i 0.282579i
\(438\) 2.84359e8 0.00772627
\(439\) −2.03288e10 −0.547335 −0.273668 0.961824i \(-0.588237\pi\)
−0.273668 + 0.961824i \(0.588237\pi\)
\(440\) 1.12190e11 2.99325
\(441\) −9.04938e9 −0.239257
\(442\) −5.67445e10 −1.48674
\(443\) 3.55878e10i 0.924032i 0.886872 + 0.462016i \(0.152874\pi\)
−0.886872 + 0.462016i \(0.847126\pi\)
\(444\) 2.49931e10i 0.643114i
\(445\) 4.14634e10i 1.05736i
\(446\) 2.46919e10i 0.624043i
\(447\) 1.86320e10i 0.466691i
\(448\) 8.77614e9 0.217867
\(449\) −6.58262e10 −1.61962 −0.809811 0.586691i \(-0.800430\pi\)
−0.809811 + 0.586691i \(0.800430\pi\)
\(450\) 2.56350e10i 0.625148i
\(451\) 2.72253e10i 0.658061i
\(452\) 6.88132e10i 1.64861i
\(453\) 2.98286e10i 0.708337i
\(454\) −2.68714e10 −0.632509
\(455\) 2.59556e10i 0.605600i
\(456\) 1.98049e10i 0.458050i
\(457\) 4.19545e10i 0.961864i 0.876758 + 0.480932i \(0.159702\pi\)
−0.876758 + 0.480932i \(0.840298\pi\)
\(458\) −6.91309e10 −1.57112
\(459\) −8.70789e9 −0.196183
\(460\) 1.26982e11i 2.83604i
\(461\) 1.04144e10 0.230586 0.115293 0.993332i \(-0.463219\pi\)
0.115293 + 0.993332i \(0.463219\pi\)
\(462\) −2.22226e10 −0.487784
\(463\) 5.76532e10i 1.25458i 0.778785 + 0.627291i \(0.215836\pi\)
−0.778785 + 0.627291i \(0.784164\pi\)
\(464\) 2.14946e10 0.463721
\(465\) 3.44145e10i 0.736088i
\(466\) 4.27042e9 0.0905580
\(467\) 5.62245e10i 1.18211i 0.806631 + 0.591055i \(0.201289\pi\)
−0.806631 + 0.591055i \(0.798711\pi\)
\(468\) 2.97052e10i 0.619225i
\(469\) 4.00897e9i 0.0828593i
\(470\) −1.51359e11 −3.10183
\(471\) 2.81667e10i 0.572338i
\(472\) 8.33287e10 + 8.56776e10i 1.67891 + 1.72623i
\(473\) −3.60443e10 −0.720098
\(474\) 7.83961e10i 1.55303i
\(475\) −1.72598e10 −0.339047
\(476\) −6.45368e10 −1.25713
\(477\) 2.84102e10 0.548784
\(478\) 1.33524e11i 2.55769i
\(479\) −2.26275e10 −0.429828 −0.214914 0.976633i \(-0.568947\pi\)
−0.214914 + 0.976633i \(0.568947\pi\)
\(480\) 5.93439e10i 1.11792i
\(481\) 2.05556e10 0.384016
\(482\) 1.55532e11i 2.88159i
\(483\) 1.43172e10i 0.263069i
\(484\) −3.03826e10 −0.553660
\(485\) 1.08053e11i 1.95285i
\(486\) 6.52224e9i 0.116910i
\(487\) −7.63144e10 −1.35672 −0.678360 0.734729i \(-0.737309\pi\)
−0.678360 + 0.734729i \(0.737309\pi\)
\(488\) 3.67116e10 0.647328
\(489\) 3.91045e10 0.683898
\(490\) 1.07417e11i 1.86333i
\(491\) 5.10608e10 0.878540 0.439270 0.898355i \(-0.355237\pi\)
0.439270 + 0.898355i \(0.355237\pi\)
\(492\) 5.92200e10 1.01067
\(493\) −1.35085e10 −0.228676
\(494\) −2.86161e10 −0.480509
\(495\) 2.48760e10i 0.414343i
\(496\) 1.11982e11i 1.85021i
\(497\) 2.27712e10 0.373216
\(498\) 5.68471e9 0.0924253
\(499\) 1.13655e11 1.83309 0.916547 0.399927i \(-0.130965\pi\)
0.916547 + 0.399927i \(0.130965\pi\)
\(500\) 6.00954e9 0.0961527
\(501\) 4.49610e10 0.713649
\(502\) 6.25708e10i 0.985274i
\(503\) 8.60576e10i 1.34437i −0.740385 0.672183i \(-0.765357\pi\)
0.740385 0.672183i \(-0.234643\pi\)
\(504\) 2.75147e10i 0.426424i
\(505\) 1.67079e11i 2.56896i
\(506\) 8.94165e10i 1.36400i
\(507\) 1.37169e10 0.207599
\(508\) 1.80859e10 0.271573
\(509\) 4.60652e10i 0.686281i 0.939284 + 0.343140i \(0.111491\pi\)
−0.939284 + 0.343140i \(0.888509\pi\)
\(510\) 1.03364e11i 1.52788i
\(511\) 2.65987e8i 0.00390101i
\(512\) 1.48976e11i 2.16788i
\(513\) −4.39136e9 −0.0634059
\(514\) 3.89380e10i 0.557854i
\(515\) 1.22211e11i 1.73732i
\(516\) 7.84029e10i 1.10594i
\(517\) −7.44915e10 −1.04266
\(518\) 3.34495e10 0.464591
\(519\) 6.20127e10i 0.854695i
\(520\) 2.00706e11 2.74503
\(521\) −1.14549e11 −1.55468 −0.777341 0.629079i \(-0.783432\pi\)
−0.777341 + 0.629079i \(0.783432\pi\)
\(522\) 1.01179e10i 0.136273i
\(523\) 1.09614e11 1.46508 0.732538 0.680726i \(-0.238335\pi\)
0.732538 + 0.680726i \(0.238335\pi\)
\(524\) 9.20816e10i 1.22137i
\(525\) −2.39788e10 −0.315638
\(526\) 1.01107e11i 1.32080i
\(527\) 7.03765e10i 0.912399i
\(528\) 8.09446e10i 1.04148i
\(529\) 2.07034e10 0.264374
\(530\) 3.37233e11i 4.27393i
\(531\) 1.89974e10 1.84766e10i 0.238955 0.232404i
\(532\) −3.25457e10 −0.406300
\(533\) 4.87056e10i 0.603490i
\(534\) 6.35089e10 0.781033
\(535\) 3.25116e10 0.396847
\(536\) 3.09999e10 0.375579
\(537\) 4.79359e10i 0.576453i
\(538\) −9.26020e9 −0.110533
\(539\) 5.28655e10i 0.626350i
\(540\) 5.41099e10 0.636359
\(541\) 8.07139e10i 0.942235i −0.882071 0.471117i \(-0.843851\pi\)
0.882071 0.471117i \(-0.156149\pi\)
\(542\) 1.86618e10i 0.216250i
\(543\) 7.07163e10 0.813429
\(544\) 1.21356e11i 1.38569i
\(545\) 1.08454e11i 1.22930i
\(546\) −3.97559e10 −0.447333
\(547\) −5.62430e10 −0.628231 −0.314116 0.949385i \(-0.601708\pi\)
−0.314116 + 0.949385i \(0.601708\pi\)
\(548\) 2.09342e11 2.32131
\(549\) 8.14011e9i 0.0896068i
\(550\) 1.49757e11 1.63657
\(551\) −6.81230e9 −0.0739073
\(552\) 1.10710e11 1.19242
\(553\) 7.33311e10 0.784129
\(554\) 2.45429e11i 2.60548i
\(555\) 3.74434e10i 0.394642i
\(556\) −4.37887e11 −4.58208
\(557\) 5.95234e9 0.0618396 0.0309198 0.999522i \(-0.490156\pi\)
0.0309198 + 0.999522i \(0.490156\pi\)
\(558\) −5.27122e10 −0.543719
\(559\) −6.44826e10 −0.660382
\(560\) 1.53845e11 1.56434
\(561\) 5.08706e10i 0.513589i
\(562\) 2.56386e11i 2.57009i
\(563\) 9.63638e10i 0.959137i 0.877505 + 0.479568i \(0.159207\pi\)
−0.877505 + 0.479568i \(0.840793\pi\)
\(564\) 1.62033e11i 1.60135i
\(565\) 1.03092e11i 1.01166i
\(566\) 3.02778e10 0.295025
\(567\) −6.10086e9 −0.0590281
\(568\) 1.76082e11i 1.69169i
\(569\) 1.91921e11i 1.83094i −0.402388 0.915469i \(-0.631820\pi\)
0.402388 0.915469i \(-0.368180\pi\)
\(570\) 5.21261e10i 0.493805i
\(571\) 1.35989e9i 0.0127926i 0.999980 + 0.00639632i \(0.00203603\pi\)
−0.999980 + 0.00639632i \(0.997964\pi\)
\(572\) 1.73534e11 1.62107
\(573\) 7.80157e10i 0.723708i
\(574\) 7.92572e10i 0.730114i
\(575\) 9.64825e10i 0.882627i
\(576\) −1.50473e10 −0.136700
\(577\) 2.20647e10 0.199065 0.0995327 0.995034i \(-0.468265\pi\)
0.0995327 + 0.995034i \(0.468265\pi\)
\(578\) 7.96841e9i 0.0713938i
\(579\) 5.25280e10 0.467387
\(580\) 8.39405e10 0.741754
\(581\) 5.31743e9i 0.0466657i
\(582\) −1.65503e11 −1.44249
\(583\) 1.65970e11i 1.43666i
\(584\) −2.05678e9 −0.0176822
\(585\) 4.45028e10i 0.379982i
\(586\) 2.44823e11i 2.07616i
\(587\) 7.62512e10i 0.642236i −0.947039 0.321118i \(-0.895941\pi\)
0.947039 0.321118i \(-0.104059\pi\)
\(588\) 1.14992e11 0.961965
\(589\) 3.54906e10i 0.294885i
\(590\) 2.19320e11 + 2.25502e11i 1.80996 + 1.86098i
\(591\) 3.34631e10 0.274294
\(592\) 1.21838e11i 0.991962i
\(593\) −1.64770e11 −1.33248 −0.666239 0.745739i \(-0.732097\pi\)
−0.666239 + 0.745739i \(0.732097\pi\)
\(594\) 3.81023e10 0.306059
\(595\) −9.66858e10 −0.771427
\(596\) 2.36761e11i 1.87640i
\(597\) 7.62192e9 0.0600022
\(598\) 1.59965e11i 1.25089i
\(599\) 1.81857e11 1.41261 0.706304 0.707909i \(-0.250361\pi\)
0.706304 + 0.707909i \(0.250361\pi\)
\(600\) 1.85419e11i 1.43070i
\(601\) 2.62909e10i 0.201515i −0.994911 0.100758i \(-0.967873\pi\)
0.994911 0.100758i \(-0.0321266\pi\)
\(602\) −1.04931e11 −0.798944
\(603\) 6.87366e9i 0.0519899i
\(604\) 3.79038e11i 2.84797i
\(605\) −4.55177e10 −0.339749
\(606\) 2.55913e11 1.89759
\(607\) 1.28964e11 0.949977 0.474989 0.879992i \(-0.342452\pi\)
0.474989 + 0.879992i \(0.342452\pi\)
\(608\) 6.11995e10i 0.447851i
\(609\) −9.46424e9 −0.0688044
\(610\) 9.66243e10 0.697858
\(611\) −1.33264e11 −0.956199
\(612\) 1.10653e11 0.788783
\(613\) 8.23122e10i 0.582938i 0.956580 + 0.291469i \(0.0941440\pi\)
−0.956580 + 0.291469i \(0.905856\pi\)
\(614\) 1.00367e11i 0.706181i
\(615\) 8.87205e10 0.620188
\(616\) 1.60738e11 1.11634
\(617\) −1.13854e10 −0.0785614 −0.0392807 0.999228i \(-0.512507\pi\)
−0.0392807 + 0.999228i \(0.512507\pi\)
\(618\) −1.87189e11 −1.28329
\(619\) 8.04699e10 0.548114 0.274057 0.961713i \(-0.411634\pi\)
0.274057 + 0.961713i \(0.411634\pi\)
\(620\) 4.37312e11i 2.95954i
\(621\) 2.45478e10i 0.165062i
\(622\) 1.61047e11i 1.07594i
\(623\) 5.94057e10i 0.394345i
\(624\) 1.44809e11i 0.955115i
\(625\) −1.48022e11 −0.970076
\(626\) −2.25752e11 −1.47006
\(627\) 2.56539e10i 0.165990i
\(628\) 3.57920e11i 2.30116i
\(629\) 7.65704e10i 0.489168i
\(630\) 7.24181e10i 0.459711i
\(631\) −5.81751e10 −0.366961 −0.183480 0.983023i \(-0.558736\pi\)
−0.183480 + 0.983023i \(0.558736\pi\)
\(632\) 5.67044e11i 3.55425i
\(633\) 1.59225e9i 0.00991736i
\(634\) 1.60746e10i 0.0994908i
\(635\) 2.70955e10 0.166649
\(636\) −3.61015e11 −2.20646
\(637\) 9.45755e10i 0.574408i
\(638\) 5.91079e10 0.356749
\(639\) −3.90428e10 −0.234173
\(640\) 1.46243e11i 0.871676i
\(641\) −2.09645e11 −1.24180 −0.620901 0.783889i \(-0.713233\pi\)
−0.620901 + 0.783889i \(0.713233\pi\)
\(642\) 4.97976e10i 0.293136i
\(643\) −1.94489e11 −1.13776 −0.568880 0.822420i \(-0.692623\pi\)
−0.568880 + 0.822420i \(0.692623\pi\)
\(644\) 1.81931e11i 1.05770i
\(645\) 1.17459e11i 0.678654i
\(646\) 1.06596e11i 0.612084i
\(647\) −5.57482e10 −0.318137 −0.159068 0.987268i \(-0.550849\pi\)
−0.159068 + 0.987268i \(0.550849\pi\)
\(648\) 4.71758e10i 0.267559i
\(649\) 1.07938e11 + 1.10981e11i 0.608410 + 0.625560i
\(650\) 2.67912e11 1.50086
\(651\) 4.93066e10i 0.274525i
\(652\) −4.96909e11 −2.74971
\(653\) 3.92742e9 0.0216000 0.0108000 0.999942i \(-0.496562\pi\)
0.0108000 + 0.999942i \(0.496562\pi\)
\(654\) −1.66117e11 −0.908038
\(655\) 1.37952e11i 0.749485i
\(656\) −2.88690e11 −1.55889
\(657\) 4.56053e8i 0.00244768i
\(658\) −2.16857e11 −1.15683
\(659\) 2.60169e10i 0.137947i −0.997618 0.0689737i \(-0.978028\pi\)
0.997618 0.0689737i \(-0.0219724\pi\)
\(660\) 3.16104e11i 1.66592i
\(661\) 1.77345e10 0.0928994 0.0464497 0.998921i \(-0.485209\pi\)
0.0464497 + 0.998921i \(0.485209\pi\)
\(662\) 5.34885e11i 2.78502i
\(663\) 9.10066e10i 0.470998i
\(664\) −4.11179e10 −0.211523
\(665\) −4.87583e10 −0.249323
\(666\) −5.73515e10 −0.291506
\(667\) 3.80809e10i 0.192400i
\(668\) −5.71328e11 −2.86932
\(669\) −3.96007e10 −0.197696
\(670\) 8.15913e10 0.404897
\(671\) 4.75537e10 0.234582
\(672\) 8.50237e10i 0.416930i
\(673\) 2.86465e11i 1.39640i 0.715901 + 0.698201i \(0.246016\pi\)
−0.715901 + 0.698201i \(0.753984\pi\)
\(674\) −7.00222e11 −3.39310
\(675\) 4.11133e10 0.198046
\(676\) −1.74304e11 −0.834680
\(677\) 2.56441e11 1.22077 0.610384 0.792105i \(-0.291015\pi\)
0.610384 + 0.792105i \(0.291015\pi\)
\(678\) −1.57905e11 −0.747271
\(679\) 1.54810e11i 0.728316i
\(680\) 7.47638e11i 3.49668i
\(681\) 4.30962e10i 0.200378i
\(682\) 3.07939e11i 1.42340i
\(683\) 1.79075e11i 0.822909i −0.911430 0.411454i \(-0.865021\pi\)
0.911430 0.411454i \(-0.134979\pi\)
\(684\) 5.58019e10 0.254932
\(685\) 3.13625e11 1.42445
\(686\) 3.68314e11i 1.66311i
\(687\) 1.10872e11i 0.497731i
\(688\) 3.82203e11i 1.70585i
\(689\) 2.96917e11i 1.31752i
\(690\) 2.91386e11 1.28550
\(691\) 4.39431e11i 1.92743i −0.266933 0.963715i \(-0.586010\pi\)
0.266933 0.963715i \(-0.413990\pi\)
\(692\) 7.88008e11i 3.43642i
\(693\) 3.56406e10i 0.154530i
\(694\) 4.84237e11 2.08747
\(695\) −6.56020e11 −2.81176
\(696\) 7.31837e10i 0.311873i
\(697\) 1.81430e11 0.768739
\(698\) 4.71788e10 0.198758
\(699\) 6.84889e9i 0.0286887i
\(700\) 3.04703e11 1.26907
\(701\) 2.08687e11i 0.864216i 0.901822 + 0.432108i \(0.142230\pi\)
−0.901822 + 0.432108i \(0.857770\pi\)
\(702\) 6.81643e10 0.280678
\(703\) 3.86142e10i 0.158098i
\(704\) 8.79047e10i 0.357867i
\(705\) 2.42749e11i 0.982656i
\(706\) −4.07240e11 −1.63920
\(707\) 2.39379e11i 0.958095i
\(708\) −2.41404e11 + 2.34786e11i −0.960752 + 0.934412i
\(709\) 3.22930e11 1.27798 0.638989 0.769216i \(-0.279353\pi\)
0.638989 + 0.769216i \(0.279353\pi\)
\(710\) 4.63443e11i 1.82374i
\(711\) −1.25731e11 −0.492000
\(712\) −4.59364e11 −1.78746
\(713\) −1.98393e11 −0.767661
\(714\) 1.48092e11i 0.569823i
\(715\) 2.59980e11 0.994756
\(716\) 6.09132e11i 2.31771i
\(717\) 2.14146e11 0.810276
\(718\) 4.07245e11i 1.53235i
\(719\) 3.22948e11i 1.20842i 0.796826 + 0.604209i \(0.206511\pi\)
−0.796826 + 0.604209i \(0.793489\pi\)
\(720\) −2.63778e11 −0.981543
\(721\) 1.75095e11i 0.647937i
\(722\) 4.41471e11i 1.62462i
\(723\) 2.49442e11 0.912885
\(724\) −8.98606e11 −3.27051
\(725\) 6.37788e10 0.230847
\(726\) 6.97188e10i 0.250959i
\(727\) 1.06099e11 0.379818 0.189909 0.981802i \(-0.439181\pi\)
0.189909 + 0.981802i \(0.439181\pi\)
\(728\) 2.87557e11 1.02376
\(729\) 1.04604e10 0.0370370
\(730\) −5.41342e9 −0.0190625
\(731\) 2.40200e11i 0.841209i
\(732\) 1.03438e11i 0.360277i
\(733\) 2.17378e10 0.0753009 0.0376504 0.999291i \(-0.488013\pi\)
0.0376504 + 0.999291i \(0.488013\pi\)
\(734\) 5.84491e11 2.01370
\(735\) 1.72276e11 0.590302
\(736\) −3.42107e11 −1.16587
\(737\) 4.01552e10 0.136104
\(738\) 1.35892e11i 0.458109i
\(739\) 3.55658e11i 1.19249i −0.802802 0.596246i \(-0.796658\pi\)
0.802802 0.596246i \(-0.203342\pi\)
\(740\) 4.75800e11i 1.58671i
\(741\) 4.58943e10i 0.152225i
\(742\) 4.83164e11i 1.59397i
\(743\) 5.31380e11 1.74361 0.871806 0.489851i \(-0.162949\pi\)
0.871806 + 0.489851i \(0.162949\pi\)
\(744\) 3.81271e11 1.24435
\(745\) 3.54703e11i 1.15144i
\(746\) 8.40358e11i 2.71337i
\(747\) 9.11712e9i 0.0292803i
\(748\) 6.46423e11i 2.06495i
\(749\) 4.65803e10 0.148005
\(750\) 1.37901e10i 0.0435834i
\(751\) 4.24872e11i 1.33567i −0.744311 0.667834i \(-0.767222\pi\)
0.744311 0.667834i \(-0.232778\pi\)
\(752\) 7.89888e11i 2.46998i
\(753\) 1.00351e11 0.312134
\(754\) 1.05743e11 0.327165
\(755\) 5.67856e11i 1.74763i
\(756\) 7.75249e10 0.237331
\(757\) −2.31078e11 −0.703680 −0.351840 0.936060i \(-0.614444\pi\)
−0.351840 + 0.936060i \(0.614444\pi\)
\(758\) 6.40325e11i 1.93965i
\(759\) 1.43406e11 0.432115
\(760\) 3.77031e11i 1.13012i
\(761\) 6.45763e11 1.92546 0.962730 0.270465i \(-0.0871775\pi\)
0.962730 + 0.270465i \(0.0871775\pi\)
\(762\) 4.15017e10i 0.123097i
\(763\) 1.55385e11i 0.458470i
\(764\) 9.91362e11i 2.90977i
\(765\) 1.65775e11 0.484030
\(766\) 5.19113e11i 1.50781i
\(767\) 1.93100e11 + 1.98543e11i 0.557956 + 0.573684i
\(768\) −3.06370e11 −0.880645
\(769\) 2.79860e11i 0.800268i −0.916457 0.400134i \(-0.868964\pi\)
0.916457 0.400134i \(-0.131036\pi\)
\(770\) 4.23059e11 1.20348
\(771\) −6.24486e10 −0.176728
\(772\) −6.67484e11 −1.87919
\(773\) 4.82350e11i 1.35096i 0.737376 + 0.675482i \(0.236065\pi\)
−0.737376 + 0.675482i \(0.763935\pi\)
\(774\) 1.79911e11 0.501295
\(775\) 3.32274e11i 0.921063i
\(776\) 1.19709e12 3.30127
\(777\) 5.36462e10i 0.147182i
\(778\) 1.11768e12i 3.05070i
\(779\) 9.14947e10 0.248454
\(780\) 5.65506e11i 1.52777i
\(781\) 2.28084e11i 0.613042i
\(782\) 5.95875e11 1.59341