Properties

Label 177.11.c.a.58.4
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.4
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.97

$q$-expansion

\(f(q)\) \(=\) \(q-59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} -8357.61i q^{6} +8815.37 q^{7} +89400.5i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} -8357.61i q^{6} +8815.37 q^{7} +89400.5i q^{8} +19683.0 q^{9} +283782. i q^{10} -307379. i q^{11} -354210. q^{12} -68920.8i q^{13} -525142. i q^{14} -668335. q^{15} +2.74037e6 q^{16} +1.05697e6 q^{17} -1.17254e6i q^{18} +4.26559e6 q^{19} +1.20272e7 q^{20} +1.23676e6 q^{21} -1.83109e7 q^{22} -3.74201e6i q^{23} +1.25425e7i q^{24} +1.29277e7 q^{25} -4.10570e6 q^{26} +2.76145e6 q^{27} -2.22564e7 q^{28} +1.29563e7 q^{29} +3.98136e7i q^{30} -5.38973e7i q^{31} -7.17012e7i q^{32} -4.31241e7i q^{33} -6.29652e7i q^{34} -4.19942e7 q^{35} -4.96943e7 q^{36} -2.46831e7i q^{37} -2.54107e8i q^{38} -9.66932e6i q^{39} -4.25881e8i q^{40} +1.00932e8 q^{41} -7.36754e7i q^{42} -1.57771e8i q^{43} +7.76050e8i q^{44} -9.37648e7 q^{45} -2.22916e8 q^{46} +1.16768e8i q^{47} +3.84463e8 q^{48} -2.04765e8 q^{49} -7.70117e8i q^{50} +1.48289e8 q^{51} +1.74007e8i q^{52} +6.16971e8 q^{53} -1.64503e8i q^{54} +1.46428e9i q^{55} +7.88098e8i q^{56} +5.98446e8 q^{57} -7.71821e8i q^{58} +(-2.89308e8 - 6.53772e8i) q^{59} +1.68737e9 q^{60} +9.65398e7i q^{61} -3.21073e9 q^{62} +1.73513e8 q^{63} -1.46519e9 q^{64} +3.28321e8i q^{65} -2.56896e9 q^{66} +1.44219e9i q^{67} -2.66857e9 q^{68} -5.24990e8i q^{69} +2.50165e9i q^{70} +1.91425e9 q^{71} +1.75967e9i q^{72} +1.00218e9i q^{73} -1.47040e9 q^{74} +1.81370e9 q^{75} -1.07695e10 q^{76} -2.70966e9i q^{77} -5.76013e8 q^{78} +4.68097e8 q^{79} -1.30544e10 q^{80} +3.87420e8 q^{81} -6.01266e9i q^{82} +3.18460e9i q^{83} -3.12249e9 q^{84} -5.03515e9 q^{85} -9.39859e9 q^{86} +1.81771e9 q^{87} +2.74798e10 q^{88} -7.27168e9i q^{89} +5.58569e9i q^{90} -6.07562e8i q^{91} +9.44757e9i q^{92} -7.56159e9i q^{93} +6.95600e9 q^{94} -2.03202e10 q^{95} -1.00594e10i q^{96} +1.55181e10i q^{97} +1.21981e10i q^{98} -6.05014e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 59.5712i 1.86160i −0.365527 0.930801i \(-0.619111\pi\)
0.365527 0.930801i \(-0.380889\pi\)
\(3\) 140.296 0.577350
\(4\) −2524.73 −2.46556
\(5\) −4763.75 −1.52440 −0.762200 0.647342i \(-0.775881\pi\)
−0.762200 + 0.647342i \(0.775881\pi\)
\(6\) 8357.61i 1.07480i
\(7\) 8815.37 0.524506 0.262253 0.964999i \(-0.415535\pi\)
0.262253 + 0.964999i \(0.415535\pi\)
\(8\) 89400.5i 2.72829i
\(9\) 19683.0 0.333333
\(10\) 283782.i 2.83782i
\(11\) 307379.i 1.90858i −0.298879 0.954291i \(-0.596613\pi\)
0.298879 0.954291i \(-0.403387\pi\)
\(12\) −354210. −1.42349
\(13\) 68920.8i 0.185624i −0.995684 0.0928119i \(-0.970414\pi\)
0.995684 0.0928119i \(-0.0295855\pi\)
\(14\) 525142.i 0.976420i
\(15\) −668335. −0.880112
\(16\) 2.74037e6 2.61342
\(17\) 1.05697e6 0.744422 0.372211 0.928148i \(-0.378600\pi\)
0.372211 + 0.928148i \(0.378600\pi\)
\(18\) 1.17254e6i 0.620534i
\(19\) 4.26559e6 1.72271 0.861354 0.508006i \(-0.169617\pi\)
0.861354 + 0.508006i \(0.169617\pi\)
\(20\) 1.20272e7 3.75850
\(21\) 1.23676e6 0.302823
\(22\) −1.83109e7 −3.55302
\(23\) 3.74201e6i 0.581388i −0.956816 0.290694i \(-0.906114\pi\)
0.956816 0.290694i \(-0.0938861\pi\)
\(24\) 1.25425e7i 1.57518i
\(25\) 1.29277e7 1.32379
\(26\) −4.10570e6 −0.345557
\(27\) 2.76145e6 0.192450
\(28\) −2.22564e7 −1.29320
\(29\) 1.29563e7 0.631670 0.315835 0.948814i \(-0.397715\pi\)
0.315835 + 0.948814i \(0.397715\pi\)
\(30\) 3.98136e7i 1.63842i
\(31\) 5.38973e7i 1.88260i −0.337567 0.941302i \(-0.609604\pi\)
0.337567 0.941302i \(-0.390396\pi\)
\(32\) 7.17012e7i 2.13686i
\(33\) 4.31241e7i 1.10192i
\(34\) 6.29652e7i 1.38582i
\(35\) −4.19942e7 −0.799556
\(36\) −4.96943e7 −0.821853
\(37\) 2.46831e7i 0.355952i −0.984035 0.177976i \(-0.943045\pi\)
0.984035 0.177976i \(-0.0569549\pi\)
\(38\) 2.54107e8i 3.20699i
\(39\) 9.66932e6i 0.107170i
\(40\) 4.25881e8i 4.15900i
\(41\) 1.00932e8 0.871186 0.435593 0.900144i \(-0.356539\pi\)
0.435593 + 0.900144i \(0.356539\pi\)
\(42\) 7.36754e7i 0.563736i
\(43\) 1.57771e8i 1.07321i −0.843834 0.536604i \(-0.819707\pi\)
0.843834 0.536604i \(-0.180293\pi\)
\(44\) 7.76050e8i 4.70572i
\(45\) −9.37648e7 −0.508133
\(46\) −2.22916e8 −1.08231
\(47\) 1.16768e8i 0.509136i 0.967055 + 0.254568i \(0.0819333\pi\)
−0.967055 + 0.254568i \(0.918067\pi\)
\(48\) 3.84463e8 1.50886
\(49\) −2.04765e8 −0.724894
\(50\) 7.70117e8i 2.46437i
\(51\) 1.48289e8 0.429792
\(52\) 1.74007e8i 0.457666i
\(53\) 6.16971e8 1.47532 0.737659 0.675174i \(-0.235931\pi\)
0.737659 + 0.675174i \(0.235931\pi\)
\(54\) 1.64503e8i 0.358265i
\(55\) 1.46428e9i 2.90944i
\(56\) 7.88098e8i 1.43100i
\(57\) 5.98446e8 0.994606
\(58\) 7.71821e8i 1.17592i
\(59\) −2.89308e8 6.53772e8i −0.404670 0.914463i
\(60\) 1.68737e9 2.16997
\(61\) 9.65398e7i 0.114303i 0.998366 + 0.0571515i \(0.0182018\pi\)
−0.998366 + 0.0571515i \(0.981798\pi\)
\(62\) −3.21073e9 −3.50466
\(63\) 1.73513e8 0.174835
\(64\) −1.46519e9 −1.36456
\(65\) 3.28321e8i 0.282965i
\(66\) −2.56896e9 −2.05134
\(67\) 1.44219e9i 1.06819i 0.845423 + 0.534097i \(0.179348\pi\)
−0.845423 + 0.534097i \(0.820652\pi\)
\(68\) −2.66857e9 −1.83542
\(69\) 5.24990e8i 0.335664i
\(70\) 2.50165e9i 1.48845i
\(71\) 1.91425e9 1.06098 0.530491 0.847691i \(-0.322008\pi\)
0.530491 + 0.847691i \(0.322008\pi\)
\(72\) 1.75967e9i 0.909429i
\(73\) 1.00218e9i 0.483429i 0.970347 + 0.241714i \(0.0777097\pi\)
−0.970347 + 0.241714i \(0.922290\pi\)
\(74\) −1.47040e9 −0.662640
\(75\) 1.81370e9 0.764292
\(76\) −1.07695e10 −4.24744
\(77\) 2.70966e9i 1.00106i
\(78\) −5.76013e8 −0.199508
\(79\) 4.68097e8 0.152125 0.0760625 0.997103i \(-0.475765\pi\)
0.0760625 + 0.997103i \(0.475765\pi\)
\(80\) −1.30544e10 −3.98390
\(81\) 3.87420e8 0.111111
\(82\) 6.01266e9i 1.62180i
\(83\) 3.18460e9i 0.808472i 0.914655 + 0.404236i \(0.132463\pi\)
−0.914655 + 0.404236i \(0.867537\pi\)
\(84\) −3.12249e9 −0.746629
\(85\) −5.03515e9 −1.13480
\(86\) −9.39859e9 −1.99788
\(87\) 1.81771e9 0.364695
\(88\) 2.74798e10 5.20716
\(89\) 7.27168e9i 1.30222i −0.758983 0.651110i \(-0.774304\pi\)
0.758983 0.651110i \(-0.225696\pi\)
\(90\) 5.58569e9i 0.945941i
\(91\) 6.07562e8i 0.0973607i
\(92\) 9.44757e9i 1.43345i
\(93\) 7.56159e9i 1.08692i
\(94\) 6.95600e9 0.947808
\(95\) −2.03202e10 −2.62609
\(96\) 1.00594e10i 1.23372i
\(97\) 1.55181e10i 1.80709i 0.428495 + 0.903544i \(0.359044\pi\)
−0.428495 + 0.903544i \(0.640956\pi\)
\(98\) 1.21981e10i 1.34946i
\(99\) 6.05014e9i 0.636194i
\(100\) −3.26389e10 −3.26389
\(101\) 6.63900e9i 0.631678i −0.948813 0.315839i \(-0.897714\pi\)
0.948813 0.315839i \(-0.102286\pi\)
\(102\) 8.83377e9i 0.800102i
\(103\) 1.17829e9i 0.101640i 0.998708 + 0.0508202i \(0.0161836\pi\)
−0.998708 + 0.0508202i \(0.983816\pi\)
\(104\) 6.16155e9 0.506435
\(105\) −5.89162e9 −0.461624
\(106\) 3.67537e10i 2.74645i
\(107\) 1.76272e10 1.25679 0.628397 0.777893i \(-0.283711\pi\)
0.628397 + 0.777893i \(0.283711\pi\)
\(108\) −6.97192e9 −0.474497
\(109\) 5.60648e8i 0.0364383i 0.999834 + 0.0182191i \(0.00579966\pi\)
−0.999834 + 0.0182191i \(0.994200\pi\)
\(110\) 8.72287e10 5.41622
\(111\) 3.46294e9i 0.205509i
\(112\) 2.41574e10 1.37075
\(113\) 8.03621e9i 0.436174i −0.975929 0.218087i \(-0.930018\pi\)
0.975929 0.218087i \(-0.0699816\pi\)
\(114\) 3.56502e10i 1.85156i
\(115\) 1.78260e10i 0.886267i
\(116\) −3.27111e10 −1.55742
\(117\) 1.35657e9i 0.0618746i
\(118\) −3.89460e10 + 1.72344e10i −1.70237 + 0.753334i
\(119\) 9.31760e9 0.390454
\(120\) 5.97495e10i 2.40120i
\(121\) −6.85445e10 −2.64269
\(122\) 5.75100e9 0.212786
\(123\) 1.41604e10 0.502979
\(124\) 1.36076e11i 4.64167i
\(125\) −1.50632e10 −0.493590
\(126\) 1.03364e10i 0.325473i
\(127\) −6.34339e10 −1.92001 −0.960003 0.279990i \(-0.909669\pi\)
−0.960003 + 0.279990i \(0.909669\pi\)
\(128\) 1.38611e10i 0.403411i
\(129\) 2.21346e10i 0.619617i
\(130\) 1.95585e10 0.526767
\(131\) 1.65942e10i 0.430130i −0.976600 0.215065i \(-0.931004\pi\)
0.976600 0.215065i \(-0.0689963\pi\)
\(132\) 1.08877e11i 2.71685i
\(133\) 3.76028e10 0.903570
\(134\) 8.59133e10 1.98855
\(135\) −1.31548e10 −0.293371
\(136\) 9.44939e10i 2.03100i
\(137\) 5.76929e9 0.119542 0.0597709 0.998212i \(-0.480963\pi\)
0.0597709 + 0.998212i \(0.480963\pi\)
\(138\) −3.12743e10 −0.624873
\(139\) −7.84083e10 −1.51108 −0.755541 0.655102i \(-0.772626\pi\)
−0.755541 + 0.655102i \(0.772626\pi\)
\(140\) 1.06024e11 1.97135
\(141\) 1.63821e10i 0.293950i
\(142\) 1.14034e11i 1.97512i
\(143\) −2.11848e10 −0.354278
\(144\) 5.39387e10 0.871140
\(145\) −6.17204e10 −0.962917
\(146\) 5.97013e10 0.899952
\(147\) −2.87277e10 −0.418518
\(148\) 6.23182e10i 0.877620i
\(149\) 1.01063e11i 1.37613i −0.725648 0.688066i \(-0.758460\pi\)
0.725648 0.688066i \(-0.241540\pi\)
\(150\) 1.08044e11i 1.42281i
\(151\) 7.82666e10i 0.996993i −0.866892 0.498496i \(-0.833886\pi\)
0.866892 0.498496i \(-0.166114\pi\)
\(152\) 3.81346e11i 4.70004i
\(153\) 2.08044e10 0.248141
\(154\) −1.61418e11 −1.86358
\(155\) 2.56753e11i 2.86984i
\(156\) 2.44124e10i 0.264234i
\(157\) 6.29703e9i 0.0660143i 0.999455 + 0.0330071i \(0.0105084\pi\)
−0.999455 + 0.0330071i \(0.989492\pi\)
\(158\) 2.78851e10i 0.283196i
\(159\) 8.65586e10 0.851775
\(160\) 3.41566e11i 3.25743i
\(161\) 3.29872e10i 0.304941i
\(162\) 2.30791e10i 0.206845i
\(163\) 1.18731e11 1.03187 0.515936 0.856627i \(-0.327444\pi\)
0.515936 + 0.856627i \(0.327444\pi\)
\(164\) −2.54827e11 −2.14796
\(165\) 2.05432e11i 1.67977i
\(166\) 1.89711e11 1.50505
\(167\) 1.46766e11 1.12991 0.564953 0.825123i \(-0.308894\pi\)
0.564953 + 0.825123i \(0.308894\pi\)
\(168\) 1.10567e11i 0.826189i
\(169\) 1.33108e11 0.965544
\(170\) 2.99950e11i 2.11254i
\(171\) 8.39597e10 0.574236
\(172\) 3.98328e11i 2.64606i
\(173\) 2.48584e11i 1.60414i 0.597228 + 0.802071i \(0.296269\pi\)
−0.597228 + 0.802071i \(0.703731\pi\)
\(174\) 1.08283e11i 0.678916i
\(175\) 1.13962e11 0.694337
\(176\) 8.42333e11i 4.98793i
\(177\) −4.05888e10 9.17216e10i −0.233636 0.527965i
\(178\) −4.33183e11 −2.42422
\(179\) 1.83522e11i 0.998672i −0.866408 0.499336i \(-0.833577\pi\)
0.866408 0.499336i \(-0.166423\pi\)
\(180\) 2.36731e11 1.25283
\(181\) 2.33072e11 1.19977 0.599885 0.800086i \(-0.295213\pi\)
0.599885 + 0.800086i \(0.295213\pi\)
\(182\) −3.61932e10 −0.181247
\(183\) 1.35442e10i 0.0659928i
\(184\) 3.34537e11 1.58619
\(185\) 1.17584e11i 0.542613i
\(186\) −4.50453e11 −2.02341
\(187\) 3.24891e11i 1.42079i
\(188\) 2.94807e11i 1.25531i
\(189\) 2.43432e10 0.100941
\(190\) 1.21050e12i 4.88874i
\(191\) 6.46864e10i 0.254476i −0.991872 0.127238i \(-0.959389\pi\)
0.991872 0.127238i \(-0.0406111\pi\)
\(192\) −2.05560e11 −0.787831
\(193\) −3.39025e11 −1.26604 −0.633018 0.774137i \(-0.718184\pi\)
−0.633018 + 0.774137i \(0.718184\pi\)
\(194\) 9.24431e11 3.36408
\(195\) 4.60622e10i 0.163370i
\(196\) 5.16976e11 1.78727
\(197\) −1.17018e11 −0.394385 −0.197192 0.980365i \(-0.563182\pi\)
−0.197192 + 0.980365i \(0.563182\pi\)
\(198\) −3.60414e11 −1.18434
\(199\) −9.16201e9 −0.0293579 −0.0146790 0.999892i \(-0.504673\pi\)
−0.0146790 + 0.999892i \(0.504673\pi\)
\(200\) 1.15574e12i 3.61169i
\(201\) 2.02334e11i 0.616722i
\(202\) −3.95493e11 −1.17593
\(203\) 1.14214e11 0.331314
\(204\) −3.74391e11 −1.05968
\(205\) −4.80816e11 −1.32804
\(206\) 7.01923e10 0.189214
\(207\) 7.36540e10i 0.193796i
\(208\) 1.88869e11i 0.485113i
\(209\) 1.31115e12i 3.28793i
\(210\) 3.50971e11i 0.859359i
\(211\) 3.54835e11i 0.848425i 0.905563 + 0.424213i \(0.139449\pi\)
−0.905563 + 0.424213i \(0.860551\pi\)
\(212\) −1.55769e12 −3.63748
\(213\) 2.68562e11 0.612558
\(214\) 1.05007e12i 2.33965i
\(215\) 7.51579e11i 1.63600i
\(216\) 2.46875e11i 0.525059i
\(217\) 4.75125e11i 0.987436i
\(218\) 3.33985e10 0.0678336
\(219\) 1.40602e11i 0.279108i
\(220\) 3.69691e12i 7.17340i
\(221\) 7.28474e10i 0.138182i
\(222\) −2.06292e11 −0.382576
\(223\) 1.19156e11 0.216068 0.108034 0.994147i \(-0.465544\pi\)
0.108034 + 0.994147i \(0.465544\pi\)
\(224\) 6.32072e11i 1.12080i
\(225\) 2.54455e11 0.441264
\(226\) −4.78727e11 −0.811981
\(227\) 6.14134e10i 0.101891i −0.998701 0.0509453i \(-0.983777\pi\)
0.998701 0.0509453i \(-0.0162234\pi\)
\(228\) −1.51092e12 −2.45226
\(229\) 8.61736e11i 1.36835i −0.729318 0.684175i \(-0.760163\pi\)
0.729318 0.684175i \(-0.239837\pi\)
\(230\) 1.06192e12 1.64988
\(231\) 3.80155e11i 0.577963i
\(232\) 1.15830e12i 1.72338i
\(233\) 6.75198e10i 0.0983222i −0.998791 0.0491611i \(-0.984345\pi\)
0.998791 0.0491611i \(-0.0156548\pi\)
\(234\) −8.08124e10 −0.115186
\(235\) 5.56252e11i 0.776127i
\(236\) 7.30426e11 + 1.65060e12i 0.997737 + 2.25466i
\(237\) 6.56722e10 0.0878294
\(238\) 5.55061e11i 0.726869i
\(239\) 2.58785e11 0.331857 0.165928 0.986138i \(-0.446938\pi\)
0.165928 + 0.986138i \(0.446938\pi\)
\(240\) −1.83149e12 −2.30010
\(241\) −1.33896e12 −1.64696 −0.823478 0.567348i \(-0.807969\pi\)
−0.823478 + 0.567348i \(0.807969\pi\)
\(242\) 4.08328e12i 4.91963i
\(243\) 5.43536e10 0.0641500
\(244\) 2.43737e11i 0.281821i
\(245\) 9.75447e11 1.10503
\(246\) 8.43553e11i 0.936347i
\(247\) 2.93988e11i 0.319775i
\(248\) 4.81845e12 5.13628
\(249\) 4.46787e11i 0.466771i
\(250\) 8.97332e11i 0.918868i
\(251\) −1.54586e12 −1.55168 −0.775838 0.630932i \(-0.782673\pi\)
−0.775838 + 0.630932i \(0.782673\pi\)
\(252\) −4.38073e11 −0.431066
\(253\) −1.15022e12 −1.10963
\(254\) 3.77883e12i 3.57428i
\(255\) −7.06412e11 −0.655175
\(256\) −6.74631e11 −0.613573
\(257\) 1.34163e12 1.19665 0.598324 0.801254i \(-0.295834\pi\)
0.598324 + 0.801254i \(0.295834\pi\)
\(258\) −1.31859e12 −1.15348
\(259\) 2.17591e11i 0.186699i
\(260\) 8.28923e11i 0.697666i
\(261\) 2.55018e11 0.210557
\(262\) −9.88536e11 −0.800730
\(263\) −1.31680e12 −1.04650 −0.523252 0.852178i \(-0.675281\pi\)
−0.523252 + 0.852178i \(0.675281\pi\)
\(264\) 3.85531e12 3.00635
\(265\) −2.93909e12 −2.24897
\(266\) 2.24004e12i 1.68209i
\(267\) 1.02019e12i 0.751837i
\(268\) 3.64116e12i 2.63369i
\(269\) 1.94110e12i 1.37812i −0.724703 0.689061i \(-0.758023\pi\)
0.724703 0.689061i \(-0.241977\pi\)
\(270\) 7.83650e11i 0.546139i
\(271\) 9.78319e11 0.669321 0.334660 0.942339i \(-0.391378\pi\)
0.334660 + 0.942339i \(0.391378\pi\)
\(272\) 2.89650e12 1.94549
\(273\) 8.52386e10i 0.0562112i
\(274\) 3.43684e11i 0.222539i
\(275\) 3.97369e12i 2.52657i
\(276\) 1.32546e12i 0.827600i
\(277\) −1.22302e11 −0.0749957 −0.0374978 0.999297i \(-0.511939\pi\)
−0.0374978 + 0.999297i \(0.511939\pi\)
\(278\) 4.67088e12i 2.81303i
\(279\) 1.06086e12i 0.627534i
\(280\) 3.75430e12i 2.18142i
\(281\) −2.67988e12 −1.52962 −0.764811 0.644254i \(-0.777168\pi\)
−0.764811 + 0.644254i \(0.777168\pi\)
\(282\) 9.75900e11 0.547217
\(283\) 2.07320e12i 1.14211i 0.820910 + 0.571057i \(0.193466\pi\)
−0.820910 + 0.571057i \(0.806534\pi\)
\(284\) −4.83298e12 −2.61591
\(285\) −2.85085e12 −1.51618
\(286\) 1.26201e12i 0.659525i
\(287\) 8.89755e11 0.456942
\(288\) 1.41129e12i 0.712287i
\(289\) −8.98802e11 −0.445836
\(290\) 3.67676e12i 1.79257i
\(291\) 2.17713e12i 1.04332i
\(292\) 2.53024e12i 1.19192i
\(293\) −1.16615e11 −0.0540027 −0.0270014 0.999635i \(-0.508596\pi\)
−0.0270014 + 0.999635i \(0.508596\pi\)
\(294\) 1.71134e12i 0.779113i
\(295\) 1.37819e12 + 3.11440e12i 0.616878 + 1.39401i
\(296\) 2.20668e12 0.971138
\(297\) 8.48811e11i 0.367307i
\(298\) −6.02044e12 −2.56181
\(299\) −2.57902e11 −0.107919
\(300\) −4.57911e12 −1.88441
\(301\) 1.39081e12i 0.562903i
\(302\) −4.66244e12 −1.85600
\(303\) 9.31426e11i 0.364699i
\(304\) 1.16893e13 4.50216
\(305\) 4.59891e11i 0.174243i
\(306\) 1.23934e12i 0.461939i
\(307\) −1.00943e12 −0.370155 −0.185077 0.982724i \(-0.559254\pi\)
−0.185077 + 0.982724i \(0.559254\pi\)
\(308\) 6.84116e12i 2.46818i
\(309\) 1.65310e11i 0.0586822i
\(310\) 1.52951e13 5.34250
\(311\) 4.42123e12 1.51964 0.759821 0.650133i \(-0.225287\pi\)
0.759821 + 0.650133i \(0.225287\pi\)
\(312\) 8.64442e11 0.292390
\(313\) 1.33939e12i 0.445847i 0.974836 + 0.222924i \(0.0715600\pi\)
−0.974836 + 0.222924i \(0.928440\pi\)
\(314\) 3.75122e11 0.122892
\(315\) −8.26571e11 −0.266519
\(316\) −1.18182e12 −0.375073
\(317\) 2.96670e12 0.926782 0.463391 0.886154i \(-0.346632\pi\)
0.463391 + 0.886154i \(0.346632\pi\)
\(318\) 5.15641e12i 1.58567i
\(319\) 3.98249e12i 1.20559i
\(320\) 6.97979e12 2.08014
\(321\) 2.47303e12 0.725611
\(322\) −1.96509e12 −0.567679
\(323\) 4.50862e12 1.28242
\(324\) −9.78133e11 −0.273951
\(325\) 8.90985e11i 0.245727i
\(326\) 7.07294e12i 1.92093i
\(327\) 7.86568e10i 0.0210377i
\(328\) 9.02339e12i 2.37684i
\(329\) 1.02935e12i 0.267045i
\(330\) 1.22379e13 3.12706
\(331\) 4.58261e12 1.15338 0.576691 0.816962i \(-0.304344\pi\)
0.576691 + 0.816962i \(0.304344\pi\)
\(332\) 8.04027e12i 1.99333i
\(333\) 4.85838e11i 0.118651i
\(334\) 8.74301e12i 2.10343i
\(335\) 6.87025e12i 1.62835i
\(336\) 3.38919e12 0.791405
\(337\) 4.93314e12i 1.13494i 0.823393 + 0.567471i \(0.192078\pi\)
−0.823393 + 0.567471i \(0.807922\pi\)
\(338\) 7.92943e12i 1.79746i
\(339\) 1.12745e12i 0.251825i
\(340\) 1.27124e13 2.79791
\(341\) −1.65669e13 −3.59310
\(342\) 5.00158e12i 1.06900i
\(343\) −4.29520e12 −0.904716
\(344\) 1.41048e13 2.92802
\(345\) 2.50092e12i 0.511686i
\(346\) 1.48085e13 2.98627
\(347\) 6.30374e12i 1.25300i 0.779421 + 0.626500i \(0.215513\pi\)
−0.779421 + 0.626500i \(0.784487\pi\)
\(348\) −4.58924e12 −0.899176
\(349\) 1.03542e12i 0.199981i 0.994988 + 0.0999905i \(0.0318812\pi\)
−0.994988 + 0.0999905i \(0.968119\pi\)
\(350\) 6.78886e12i 1.29258i
\(351\) 1.90321e11i 0.0357233i
\(352\) −2.20394e13 −4.07838
\(353\) 3.93173e12i 0.717315i 0.933469 + 0.358657i \(0.116765\pi\)
−0.933469 + 0.358657i \(0.883235\pi\)
\(354\) −5.46397e12 + 2.41793e12i −0.982861 + 0.434937i
\(355\) −9.11902e12 −1.61736
\(356\) 1.83590e13i 3.21070i
\(357\) 1.30722e12 0.225428
\(358\) −1.09326e13 −1.85913
\(359\) −8.10572e11 −0.135931 −0.0679656 0.997688i \(-0.521651\pi\)
−0.0679656 + 0.997688i \(0.521651\pi\)
\(360\) 8.38262e12i 1.38633i
\(361\) 1.20642e13 1.96772
\(362\) 1.38844e13i 2.23349i
\(363\) −9.61652e12 −1.52576
\(364\) 1.53393e12i 0.240049i
\(365\) 4.77414e12i 0.736939i
\(366\) 8.06842e11 0.122852
\(367\) 5.56208e12i 0.835424i −0.908579 0.417712i \(-0.862832\pi\)
0.908579 0.417712i \(-0.137168\pi\)
\(368\) 1.02545e13i 1.51941i
\(369\) 1.98665e12 0.290395
\(370\) 7.00463e12 1.01013
\(371\) 5.43883e12 0.773812
\(372\) 1.90910e13i 2.67987i
\(373\) −1.16740e13 −1.61687 −0.808433 0.588589i \(-0.799684\pi\)
−0.808433 + 0.588589i \(0.799684\pi\)
\(374\) −1.93542e13 −2.64495
\(375\) −2.11330e12 −0.284974
\(376\) −1.04391e13 −1.38907
\(377\) 8.92956e11i 0.117253i
\(378\) 1.45015e12i 0.187912i
\(379\) −8.15197e12 −1.04248 −0.521239 0.853411i \(-0.674530\pi\)
−0.521239 + 0.853411i \(0.674530\pi\)
\(380\) 5.13031e13 6.47479
\(381\) −8.89952e12 −1.10852
\(382\) −3.85345e12 −0.473732
\(383\) −3.46373e11 −0.0420291 −0.0210146 0.999779i \(-0.506690\pi\)
−0.0210146 + 0.999779i \(0.506690\pi\)
\(384\) 1.94466e12i 0.232909i
\(385\) 1.29081e13i 1.52602i
\(386\) 2.01962e13i 2.35685i
\(387\) 3.10540e12i 0.357736i
\(388\) 3.91790e13i 4.45548i
\(389\) −4.90715e12 −0.550911 −0.275455 0.961314i \(-0.588829\pi\)
−0.275455 + 0.961314i \(0.588829\pi\)
\(390\) 2.74398e12 0.304129
\(391\) 3.95520e12i 0.432798i
\(392\) 1.83060e13i 1.97772i
\(393\) 2.32810e12i 0.248335i
\(394\) 6.97089e12i 0.734187i
\(395\) −2.22990e12 −0.231899
\(396\) 1.52750e13i 1.56857i
\(397\) 1.52710e13i 1.54852i 0.632870 + 0.774258i \(0.281877\pi\)
−0.632870 + 0.774258i \(0.718123\pi\)
\(398\) 5.45792e11i 0.0546528i
\(399\) 5.27552e12 0.521676
\(400\) 3.54266e13 3.45963
\(401\) 1.28285e13i 1.23724i 0.785691 + 0.618619i \(0.212308\pi\)
−0.785691 + 0.618619i \(0.787692\pi\)
\(402\) 1.20533e13 1.14809
\(403\) −3.71465e12 −0.349456
\(404\) 1.67617e13i 1.55744i
\(405\) −1.84557e12 −0.169378
\(406\) 6.80388e12i 0.616775i
\(407\) −7.58707e12 −0.679363
\(408\) 1.32571e13i 1.17260i
\(409\) 3.71099e12i 0.324245i 0.986771 + 0.162122i \(0.0518339\pi\)
−0.986771 + 0.162122i \(0.948166\pi\)
\(410\) 2.86428e13i 2.47227i
\(411\) 8.09409e11 0.0690175
\(412\) 2.97487e12i 0.250601i
\(413\) −2.55036e12 5.76324e12i −0.212252 0.479641i
\(414\) −4.38766e12 −0.360771
\(415\) 1.51706e13i 1.23243i
\(416\) −4.94170e12 −0.396652
\(417\) −1.10004e13 −0.872423
\(418\) −7.81071e13 −6.12081
\(419\) 1.91177e13i 1.48035i −0.672412 0.740177i \(-0.734742\pi\)
0.672412 0.740177i \(-0.265258\pi\)
\(420\) 1.48748e13 1.13816
\(421\) 3.47260e12i 0.262570i −0.991345 0.131285i \(-0.958090\pi\)
0.991345 0.131285i \(-0.0419102\pi\)
\(422\) 2.11379e13 1.57943
\(423\) 2.29834e12i 0.169712i
\(424\) 5.51575e13i 4.02509i
\(425\) 1.36642e13 0.985461
\(426\) 1.59986e13i 1.14034i
\(427\) 8.51034e11i 0.0599525i
\(428\) −4.45039e13 −3.09870
\(429\) −2.97215e12 −0.204543
\(430\) 4.47725e13 3.04557
\(431\) 8.12194e12i 0.546102i −0.962000 0.273051i \(-0.911967\pi\)
0.962000 0.273051i \(-0.0880327\pi\)
\(432\) 7.56739e12 0.502953
\(433\) −3.57079e12 −0.234598 −0.117299 0.993097i \(-0.537424\pi\)
−0.117299 + 0.993097i \(0.537424\pi\)
\(434\) −2.83038e13 −1.83821
\(435\) −8.65913e12 −0.555940
\(436\) 1.41549e12i 0.0898407i
\(437\) 1.59619e13i 1.00156i
\(438\) 8.37585e12 0.519587
\(439\) −6.08525e12 −0.373212 −0.186606 0.982435i \(-0.559749\pi\)
−0.186606 + 0.982435i \(0.559749\pi\)
\(440\) −1.30907e14 −7.93779
\(441\) −4.03038e12 −0.241631
\(442\) −4.33961e12 −0.257241
\(443\) 8.84077e12i 0.518169i −0.965855 0.259084i \(-0.916579\pi\)
0.965855 0.259084i \(-0.0834208\pi\)
\(444\) 8.74301e12i 0.506694i
\(445\) 3.46404e13i 1.98510i
\(446\) 7.09825e12i 0.402232i
\(447\) 1.41787e13i 0.794511i
\(448\) −1.29162e13 −0.715721
\(449\) 2.04538e13 1.12084 0.560419 0.828209i \(-0.310640\pi\)
0.560419 + 0.828209i \(0.310640\pi\)
\(450\) 1.51582e13i 0.821458i
\(451\) 3.10245e13i 1.66273i
\(452\) 2.02893e13i 1.07541i
\(453\) 1.09805e13i 0.575614i
\(454\) −3.65847e12 −0.189680
\(455\) 2.89427e12i 0.148417i
\(456\) 5.35014e13i 2.71357i
\(457\) 2.70573e12i 0.135739i −0.997694 0.0678693i \(-0.978380\pi\)
0.997694 0.0678693i \(-0.0216201\pi\)
\(458\) −5.13347e13 −2.54732
\(459\) 2.91878e12 0.143264
\(460\) 4.50059e13i 2.18514i
\(461\) −6.63428e11 −0.0318632 −0.0159316 0.999873i \(-0.505071\pi\)
−0.0159316 + 0.999873i \(0.505071\pi\)
\(462\) −2.26463e13 −1.07594
\(463\) 2.63519e13i 1.23853i −0.785182 0.619266i \(-0.787430\pi\)
0.785182 0.619266i \(-0.212570\pi\)
\(464\) 3.55050e13 1.65082
\(465\) 3.60215e13i 1.65690i
\(466\) −4.02224e12 −0.183037
\(467\) 4.60839e12i 0.207475i 0.994605 + 0.103737i \(0.0330801\pi\)
−0.994605 + 0.103737i \(0.966920\pi\)
\(468\) 3.42497e12i 0.152555i
\(469\) 1.27135e13i 0.560273i
\(470\) −3.31366e13 −1.44484
\(471\) 8.83449e11i 0.0381134i
\(472\) 5.84475e13 2.58643e13i 2.49492 1.10405i
\(473\) −4.84954e13 −2.04830
\(474\) 3.91218e12i 0.163503i
\(475\) 5.51442e13 2.28051
\(476\) −2.35245e13 −0.962686
\(477\) 1.21438e13 0.491772
\(478\) 1.54162e13i 0.617785i
\(479\) 4.03658e13 1.60080 0.800399 0.599468i \(-0.204621\pi\)
0.800399 + 0.599468i \(0.204621\pi\)
\(480\) 4.79204e13i 1.88068i
\(481\) −1.70118e12 −0.0660731
\(482\) 7.97634e13i 3.06598i
\(483\) 4.62797e12i 0.176058i
\(484\) 1.73056e14 6.51570
\(485\) 7.39242e13i 2.75472i
\(486\) 3.23791e12i 0.119422i
\(487\) 1.09680e13 0.400391 0.200196 0.979756i \(-0.435842\pi\)
0.200196 + 0.979756i \(0.435842\pi\)
\(488\) −8.63071e12 −0.311851
\(489\) 1.66575e13 0.595751
\(490\) 5.81086e13i 2.05712i
\(491\) −2.14337e13 −0.751085 −0.375542 0.926805i \(-0.622544\pi\)
−0.375542 + 0.926805i \(0.622544\pi\)
\(492\) −3.57512e13 −1.24013
\(493\) 1.36944e13 0.470229
\(494\) −1.75132e13 −0.595294
\(495\) 2.88213e13i 0.969814i
\(496\) 1.47699e14i 4.92004i
\(497\) 1.68749e13 0.556491
\(498\) 2.66157e13 0.868942
\(499\) −3.10709e13 −1.00427 −0.502136 0.864789i \(-0.667452\pi\)
−0.502136 + 0.864789i \(0.667452\pi\)
\(500\) 3.80305e13 1.21697
\(501\) 2.05907e13 0.652351
\(502\) 9.20887e13i 2.88860i
\(503\) 2.00583e13i 0.622952i −0.950254 0.311476i \(-0.899177\pi\)
0.950254 0.311476i \(-0.100823\pi\)
\(504\) 1.55121e13i 0.477000i
\(505\) 3.16265e13i 0.962930i
\(506\) 6.85198e13i 2.06568i
\(507\) 1.86746e13 0.557457
\(508\) 1.60153e14 4.73389
\(509\) 2.00516e13i 0.586894i 0.955975 + 0.293447i \(0.0948024\pi\)
−0.955975 + 0.293447i \(0.905198\pi\)
\(510\) 4.20819e13i 1.21967i
\(511\) 8.83461e12i 0.253561i
\(512\) 5.43824e13i 1.54564i
\(513\) 1.17792e13 0.331535
\(514\) 7.99224e13i 2.22768i
\(515\) 5.61308e12i 0.154941i
\(516\) 5.58839e13i 1.52770i
\(517\) 3.58920e13 0.971728
\(518\) −1.29621e13 −0.347559
\(519\) 3.48754e13i 0.926152i
\(520\) −2.93521e13 −0.772009
\(521\) −2.12115e13 −0.552564 −0.276282 0.961077i \(-0.589102\pi\)
−0.276282 + 0.961077i \(0.589102\pi\)
\(522\) 1.51918e13i 0.391972i
\(523\) 3.90091e13 0.996913 0.498457 0.866915i \(-0.333900\pi\)
0.498457 + 0.866915i \(0.333900\pi\)
\(524\) 4.18959e13i 1.06051i
\(525\) 1.59884e13 0.400876
\(526\) 7.84434e13i 1.94817i
\(527\) 5.69680e13i 1.40145i
\(528\) 1.18176e14i 2.87978i
\(529\) 2.74239e13 0.661988
\(530\) 1.75086e14i 4.18669i
\(531\) −5.69445e12 1.28682e13i −0.134890 0.304821i
\(532\) −9.49369e13 −2.22780
\(533\) 6.95633e12i 0.161713i
\(534\) −6.07739e13 −1.39962
\(535\) −8.39715e13 −1.91586
\(536\) −1.28933e14 −2.91434
\(537\) 2.57474e13i 0.576583i
\(538\) −1.15634e14 −2.56551
\(539\) 6.29403e13i 1.38352i
\(540\) 3.32125e13 0.723323
\(541\) 2.97252e13i 0.641415i −0.947178 0.320707i \(-0.896079\pi\)
0.947178 0.320707i \(-0.103921\pi\)
\(542\) 5.82797e13i 1.24601i
\(543\) 3.26992e13 0.692688
\(544\) 7.57862e13i 1.59073i
\(545\) 2.67079e12i 0.0555465i
\(546\) −5.07777e12 −0.104643
\(547\) 1.57133e12 0.0320871 0.0160436 0.999871i \(-0.494893\pi\)
0.0160436 + 0.999871i \(0.494893\pi\)
\(548\) −1.45659e13 −0.294737
\(549\) 1.90019e12i 0.0381010i
\(550\) −2.36718e14 −4.70346
\(551\) 5.52662e13 1.08818
\(552\) 4.69343e13 0.915788
\(553\) 4.12645e12 0.0797904
\(554\) 7.28571e12i 0.139612i
\(555\) 1.64966e13i 0.313278i
\(556\) 1.97960e14 3.72566
\(557\) 1.01564e14 1.89436 0.947181 0.320699i \(-0.103918\pi\)
0.947181 + 0.320699i \(0.103918\pi\)
\(558\) −6.31968e13 −1.16822
\(559\) −1.08737e13 −0.199213
\(560\) −1.15080e14 −2.08958
\(561\) 4.55810e13i 0.820294i
\(562\) 1.59644e14i 2.84755i
\(563\) 2.62954e13i 0.464877i −0.972611 0.232438i \(-0.925330\pi\)
0.972611 0.232438i \(-0.0746704\pi\)
\(564\) 4.13603e13i 0.724751i
\(565\) 3.82825e13i 0.664903i
\(566\) 1.23503e14 2.12616
\(567\) 3.41525e12 0.0582784
\(568\) 1.71135e14i 2.89466i
\(569\) 9.01712e13i 1.51184i 0.654662 + 0.755921i \(0.272811\pi\)
−0.654662 + 0.755921i \(0.727189\pi\)
\(570\) 1.69828e14i 2.82252i
\(571\) 9.16721e13i 1.51028i −0.655565 0.755138i \(-0.727570\pi\)
0.655565 0.755138i \(-0.272430\pi\)
\(572\) 5.34860e13 0.873494
\(573\) 9.07525e12i 0.146922i
\(574\) 5.30038e13i 0.850644i
\(575\) 4.83755e13i 0.769637i
\(576\) −2.88393e13 −0.454855
\(577\) −9.46419e13 −1.47980 −0.739902 0.672714i \(-0.765128\pi\)
−0.739902 + 0.672714i \(0.765128\pi\)
\(578\) 5.35427e13i 0.829968i
\(579\) −4.75640e13 −0.730946
\(580\) 1.55827e14 2.37413
\(581\) 2.80734e13i 0.424048i
\(582\) 1.29694e14 1.94225
\(583\) 1.89644e14i 2.81576i
\(584\) −8.95956e13 −1.31893
\(585\) 6.46235e12i 0.0943216i
\(586\) 6.94689e12i 0.100532i
\(587\) 3.82820e13i 0.549292i 0.961545 + 0.274646i \(0.0885607\pi\)
−0.961545 + 0.274646i \(0.911439\pi\)
\(588\) 7.25297e13 1.03188
\(589\) 2.29904e14i 3.24317i
\(590\) 1.85529e14 8.21006e13i 2.59508 1.14838i
\(591\) −1.64171e13 −0.227698
\(592\) 6.76409e13i 0.930252i
\(593\) −1.13813e14 −1.55209 −0.776044 0.630678i \(-0.782777\pi\)
−0.776044 + 0.630678i \(0.782777\pi\)
\(594\) −5.05647e13 −0.683779
\(595\) −4.43867e13 −0.595207
\(596\) 2.55157e14i 3.39294i
\(597\) −1.28539e12 −0.0169498
\(598\) 1.53636e13i 0.200903i
\(599\) −2.06483e13 −0.267763 −0.133881 0.990997i \(-0.542744\pi\)
−0.133881 + 0.990997i \(0.542744\pi\)
\(600\) 1.62146e14i 2.08521i
\(601\) 1.03016e14i 1.31380i 0.753976 + 0.656902i \(0.228133\pi\)
−0.753976 + 0.656902i \(0.771867\pi\)
\(602\) −8.28520e13 −1.04790
\(603\) 2.83867e13i 0.356065i
\(604\) 1.97602e14i 2.45814i
\(605\) 3.26528e14 4.02851
\(606\) −5.54862e13 −0.678925
\(607\) 9.74616e13 1.18274 0.591371 0.806400i \(-0.298587\pi\)
0.591371 + 0.806400i \(0.298587\pi\)
\(608\) 3.05848e14i 3.68119i
\(609\) 1.60238e13 0.191284
\(610\) −2.73963e13 −0.324371
\(611\) 8.04773e12 0.0945078
\(612\) −5.25255e13 −0.611805
\(613\) 1.46820e14i 1.69622i 0.529820 + 0.848110i \(0.322260\pi\)
−0.529820 + 0.848110i \(0.677740\pi\)
\(614\) 6.01329e13i 0.689081i
\(615\) −6.74566e13 −0.766741
\(616\) 2.42245e14 2.73118
\(617\) −5.74060e13 −0.641995 −0.320997 0.947080i \(-0.604018\pi\)
−0.320997 + 0.947080i \(0.604018\pi\)
\(618\) 9.84771e12 0.109243
\(619\) 1.74878e14 1.92434 0.962170 0.272448i \(-0.0878334\pi\)
0.962170 + 0.272448i \(0.0878334\pi\)
\(620\) 6.48233e14i 7.07576i
\(621\) 1.03334e13i 0.111888i
\(622\) 2.63378e14i 2.82897i
\(623\) 6.41025e13i 0.683022i
\(624\) 2.64975e13i 0.280080i
\(625\) −5.44896e13 −0.571365
\(626\) 7.97892e13 0.829990
\(627\) 1.83950e14i 1.89829i
\(628\) 1.58983e13i 0.162762i
\(629\) 2.60894e13i 0.264978i
\(630\) 4.92399e13i 0.496151i
\(631\) −4.23221e13 −0.423078 −0.211539 0.977370i \(-0.567848\pi\)
−0.211539 + 0.977370i \(0.567848\pi\)
\(632\) 4.18481e13i 0.415040i
\(633\) 4.97819e13i 0.489839i
\(634\) 1.76730e14i 1.72530i
\(635\) 3.02183e14 2.92686
\(636\) −2.18537e14 −2.10010
\(637\) 1.41125e13i 0.134558i
\(638\) −2.37242e14 −2.24433
\(639\) 3.76783e13 0.353661
\(640\) 6.60308e13i 0.614959i
\(641\) −1.07607e14 −0.994379 −0.497190 0.867642i \(-0.665635\pi\)
−0.497190 + 0.867642i \(0.665635\pi\)
\(642\) 1.47321e14i 1.35080i
\(643\) −4.82800e13 −0.439251 −0.219625 0.975584i \(-0.570483\pi\)
−0.219625 + 0.975584i \(0.570483\pi\)
\(644\) 8.32838e13i 0.751850i
\(645\) 1.05444e14i 0.944543i
\(646\) 2.68584e14i 2.38736i
\(647\) 1.99080e14 1.75593 0.877963 0.478728i \(-0.158902\pi\)
0.877963 + 0.478728i \(0.158902\pi\)
\(648\) 3.46356e13i 0.303143i
\(649\) −2.00956e14 + 8.89273e13i −1.74533 + 0.772345i
\(650\) −5.30771e13 −0.457446
\(651\) 6.66582e13i 0.570096i
\(652\) −2.99764e14 −2.54414
\(653\) −1.58076e14 −1.33138 −0.665689 0.746229i \(-0.731862\pi\)
−0.665689 + 0.746229i \(0.731862\pi\)
\(654\) 4.68568e12 0.0391637
\(655\) 7.90505e13i 0.655689i
\(656\) 2.76592e14 2.27678
\(657\) 1.97260e13i 0.161143i
\(658\) 6.13197e13 0.497131
\(659\) 4.18691e13i 0.336874i 0.985712 + 0.168437i \(0.0538719\pi\)
−0.985712 + 0.168437i \(0.946128\pi\)
\(660\) 5.18661e14i 4.14156i
\(661\) 1.58756e14 1.25812 0.629062 0.777355i \(-0.283439\pi\)
0.629062 + 0.777355i \(0.283439\pi\)
\(662\) 2.72992e14i 2.14714i
\(663\) 1.02202e13i 0.0797797i
\(664\) −2.84705e14 −2.20574
\(665\) −1.79130e14 −1.37740
\(666\) −2.89420e13 −0.220880
\(667\) 4.84825e13i 0.367245i
\(668\) −3.70544e14 −2.78585
\(669\) 1.67171e13 0.124747
\(670\) −4.09269e14 −3.03134
\(671\) 2.96743e13 0.218156
\(672\) 8.86773e13i 0.647092i
\(673\) 1.29737e13i 0.0939697i 0.998896 + 0.0469849i \(0.0149613\pi\)
−0.998896 + 0.0469849i \(0.985039\pi\)
\(674\) 2.93873e14 2.11281
\(675\) 3.56991e13 0.254764
\(676\) −3.36063e14 −2.38061
\(677\) −1.52016e14 −1.06892 −0.534462 0.845192i \(-0.679486\pi\)
−0.534462 + 0.845192i \(0.679486\pi\)
\(678\) −6.71636e13 −0.468798
\(679\) 1.36798e14i 0.947828i
\(680\) 4.50145e14i 3.09605i
\(681\) 8.61606e12i 0.0588265i
\(682\) 9.86911e14i 6.68892i
\(683\) 2.93309e14i 1.97343i 0.162451 + 0.986717i \(0.448060\pi\)
−0.162451 + 0.986717i \(0.551940\pi\)
\(684\) −2.11976e14 −1.41581
\(685\) −2.74834e13 −0.182229
\(686\) 2.55870e14i 1.68422i
\(687\) 1.20898e14i 0.790017i
\(688\) 4.32350e14i 2.80474i
\(689\) 4.25221e13i 0.273854i
\(690\) 1.48983e14 0.952556
\(691\) 2.21613e13i 0.140671i 0.997523 + 0.0703356i \(0.0224070\pi\)
−0.997523 + 0.0703356i \(0.977593\pi\)
\(692\) 6.27608e14i 3.95511i
\(693\) 5.33342e13i 0.333687i
\(694\) 3.75522e14 2.33259
\(695\) 3.73517e14 2.30349
\(696\) 1.62505e14i 0.994991i
\(697\) 1.06683e14 0.648530
\(698\) 6.16812e13 0.372285
\(699\) 9.47277e12i 0.0567664i
\(700\) −2.87724e14 −1.71193
\(701\) 1.12954e14i 0.667285i 0.942700 + 0.333643i \(0.108278\pi\)
−0.942700 + 0.333643i \(0.891722\pi\)
\(702\) −1.13377e13 −0.0665026
\(703\) 1.05288e14i 0.613201i
\(704\) 4.50368e14i 2.60438i
\(705\) 7.80401e13i 0.448097i
\(706\) 2.34218e14 1.33535
\(707\) 5.85252e13i 0.331319i
\(708\) 1.02476e14 + 2.31573e14i 0.576044 + 1.30173i
\(709\) 2.71154e14 1.51351 0.756755 0.653698i \(-0.226783\pi\)
0.756755 + 0.653698i \(0.226783\pi\)
\(710\) 5.43232e14i 3.01088i
\(711\) 9.21356e12 0.0507083
\(712\) 6.50091e14 3.55283
\(713\) −2.01684e14 −1.09452
\(714\) 7.78729e13i 0.419658i
\(715\) 1.00919e14 0.540061
\(716\) 4.63344e14i 2.46228i
\(717\) 3.63066e13 0.191597
\(718\) 4.82868e13i 0.253050i
\(719\) 3.12625e13i 0.162697i −0.996686 0.0813485i \(-0.974077\pi\)
0.996686 0.0813485i \(-0.0259227\pi\)
\(720\) −2.56950e14 −1.32797
\(721\) 1.03871e13i 0.0533110i
\(722\) 7.18681e14i 3.66311i
\(723\) −1.87851e14 −0.950870
\(724\) −5.88445e14 −2.95810
\(725\) 1.67494e14 0.836200
\(726\) 5.72868e14i 2.84035i
\(727\) 1.46683e13 0.0722284 0.0361142 0.999348i \(-0.488502\pi\)
0.0361142 + 0.999348i \(0.488502\pi\)
\(728\) 5.43163e13 0.265628
\(729\) 7.62560e12 0.0370370
\(730\) −2.84402e14 −1.37189
\(731\) 1.66759e14i 0.798919i
\(732\) 3.41954e13i 0.162709i
\(733\) −1.72116e14 −0.813393 −0.406696 0.913563i \(-0.633319\pi\)
−0.406696 + 0.913563i \(0.633319\pi\)
\(734\) −3.31340e14 −1.55523
\(735\) 1.36851e14 0.637988
\(736\) −2.68307e14 −1.24235
\(737\) 4.43300e14 2.03873
\(738\) 1.18347e14i 0.540600i
\(739\) 1.77557e14i 0.805595i −0.915289 0.402797i \(-0.868038\pi\)
0.915289 0.402797i \(-0.131962\pi\)
\(740\) 2.96868e14i 1.33784i
\(741\) 4.12454e13i 0.184622i
\(742\) 3.23998e14i 1.44053i
\(743\) 2.33449e14 1.03097 0.515487 0.856897i \(-0.327611\pi\)
0.515487 + 0.856897i \(0.327611\pi\)
\(744\) 6.76009e14 2.96543
\(745\) 4.81438e14i 2.09778i
\(746\) 6.95432e14i 3.00996i
\(747\) 6.26825e13i 0.269491i
\(748\) 8.20264e14i 3.50304i
\(749\) 1.55390e14 0.659196
\(750\) 1.25892e14i 0.530508i
\(751\) 8.63557e13i 0.361486i −0.983530 0.180743i \(-0.942150\pi\)
0.983530 0.180743i \(-0.0578502\pi\)
\(752\) 3.19987e14i 1.33059i
\(753\) −2.16878e14 −0.895861
\(754\) −5.31945e13 −0.218278
\(755\) 3.72843e14i 1.51981i
\(756\) −6.14600e13 −0.248876
\(757\) −1.30911e14 −0.526621 −0.263311 0.964711i \(-0.584814\pi\)
−0.263311 + 0.964711i \(0.584814\pi\)
\(758\) 4.85623e14i 1.94068i
\(759\) −1.61371e14 −0.640643
\(760\) 1.81664e15i 7.16474i
\(761\) 3.64240e14 1.42713 0.713566 0.700588i \(-0.247079\pi\)
0.713566 + 0.700588i \(0.247079\pi\)
\(762\) 5.30156e14i 2.06361i
\(763\) 4.94232e12i 0.0191121i
\(764\) 1.63316e14i 0.627425i
\(765\) −9.91069e13 −0.378266
\(766\) 2.06339e13i 0.0782415i
\(767\) −4.50585e13 + 1.99394e13i −0.169746 + 0.0751163i
\(768\) −9.46481e13 −0.354247
\(769\) 1.91581e14i 0.712393i −0.934411 0.356197i \(-0.884073\pi\)
0.934411 0.356197i \(-0.115927\pi\)
\(770\) 7.68953e14 2.84084
\(771\) 1.88225e14 0.690885
\(772\) 8.55948e14 3.12148
\(773\) 2.83544e14i 1.02736i 0.857982 + 0.513680i \(0.171718\pi\)
−0.857982 + 0.513680i \(0.828282\pi\)
\(774\) −1.84992e14 −0.665961
\(775\) 6.96767e14i 2.49218i
\(776\) −1.38732e15 −4.93025
\(777\) 3.05271e13i 0.107791i
\(778\) 2.92325e14i 1.02558i
\(779\) 4.30536e14 1.50080