Properties

Label 177.11.c.a.58.16
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 58.16
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.85

$q$-expansion

\(f(q)\) \(=\) \(q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-47.5424i q^{2} +140.296 q^{3} -1236.28 q^{4} -4974.64 q^{5} -6670.02i q^{6} +12474.7 q^{7} +10092.4i q^{8} +19683.0 q^{9} +236507. i q^{10} +91525.3i q^{11} -173446. q^{12} -581654. i q^{13} -593078. i q^{14} -697923. q^{15} -786135. q^{16} +253586. q^{17} -935778. i q^{18} -3.54734e6 q^{19} +6.15006e6 q^{20} +1.75015e6 q^{21} +4.35134e6 q^{22} -7.87195e6i q^{23} +1.41593e6i q^{24} +1.49815e7 q^{25} -2.76532e7 q^{26} +2.76145e6 q^{27} -1.54223e7 q^{28} -3.50297e7 q^{29} +3.31810e7i q^{30} +4.69488e7i q^{31} +4.77094e7i q^{32} +1.28406e7i q^{33} -1.20561e7i q^{34} -6.20573e7 q^{35} -2.43337e7 q^{36} +7.93633e7i q^{37} +1.68649e8i q^{38} -8.16037e7i q^{39} -5.02061e7i q^{40} +9.67573e6 q^{41} -8.32066e7i q^{42} -7.78354e7i q^{43} -1.13151e8i q^{44} -9.79159e7 q^{45} -3.74251e8 q^{46} -4.77102e7i q^{47} -1.10292e8 q^{48} -1.26857e8 q^{49} -7.12255e8i q^{50} +3.55772e7 q^{51} +7.19088e8i q^{52} +6.70282e8 q^{53} -1.31286e8i q^{54} -4.55306e8i q^{55} +1.25900e8i q^{56} -4.97678e8 q^{57} +1.66540e9i q^{58} +(7.02192e8 + 1.34322e8i) q^{59} +8.62830e8 q^{60} -1.29266e9i q^{61} +2.23206e9 q^{62} +2.45540e8 q^{63} +1.46322e9 q^{64} +2.89352e9i q^{65} +6.10475e8 q^{66} +1.73077e9i q^{67} -3.13504e8 q^{68} -1.10440e9i q^{69} +2.95035e9i q^{70} -3.39938e9 q^{71} +1.98649e8i q^{72} +1.89958e7i q^{73} +3.77312e9 q^{74} +2.10184e9 q^{75} +4.38551e9 q^{76} +1.14175e9i q^{77} -3.87964e9 q^{78} +2.81385e9 q^{79} +3.91074e9 q^{80} +3.87420e8 q^{81} -4.60008e8i q^{82} -3.49802e9i q^{83} -2.16368e9 q^{84} -1.26150e9 q^{85} -3.70048e9 q^{86} -4.91453e9 q^{87} -9.23711e8 q^{88} +2.25318e9i q^{89} +4.65516e9i q^{90} -7.25596e9i q^{91} +9.73195e9i q^{92} +6.58674e9i q^{93} -2.26826e9 q^{94} +1.76468e10 q^{95} +6.69344e9i q^{96} +1.06360e10i q^{97} +6.03108e9i q^{98} +1.80149e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 47.5424i 1.48570i −0.669457 0.742850i \(-0.733473\pi\)
0.669457 0.742850i \(-0.266527\pi\)
\(3\) 140.296 0.577350
\(4\) −1236.28 −1.20731
\(5\) −4974.64 −1.59189 −0.795943 0.605371i \(-0.793025\pi\)
−0.795943 + 0.605371i \(0.793025\pi\)
\(6\) 6670.02i 0.857770i
\(7\) 12474.7 0.742233 0.371117 0.928586i \(-0.378975\pi\)
0.371117 + 0.928586i \(0.378975\pi\)
\(8\) 10092.4i 0.307996i
\(9\) 19683.0 0.333333
\(10\) 236507.i 2.36507i
\(11\) 91525.3i 0.568300i 0.958780 + 0.284150i \(0.0917114\pi\)
−0.958780 + 0.284150i \(0.908289\pi\)
\(12\) −173446. −0.697039
\(13\) 581654.i 1.56656i −0.621668 0.783281i \(-0.713545\pi\)
0.621668 0.783281i \(-0.286455\pi\)
\(14\) 593078.i 1.10274i
\(15\) −697923. −0.919076
\(16\) −786135. −0.749717
\(17\) 253586. 0.178600 0.0892999 0.996005i \(-0.471537\pi\)
0.0892999 + 0.996005i \(0.471537\pi\)
\(18\) 935778.i 0.495234i
\(19\) −3.54734e6 −1.43263 −0.716316 0.697776i \(-0.754173\pi\)
−0.716316 + 0.697776i \(0.754173\pi\)
\(20\) 6.15006e6 1.92189
\(21\) 1.75015e6 0.428529
\(22\) 4.35134e6 0.844324
\(23\) 7.87195e6i 1.22305i −0.791226 0.611523i \(-0.790557\pi\)
0.791226 0.611523i \(-0.209443\pi\)
\(24\) 1.41593e6i 0.177821i
\(25\) 1.49815e7 1.53410
\(26\) −2.76532e7 −2.32744
\(27\) 2.76145e6 0.192450
\(28\) −1.54223e7 −0.896103
\(29\) −3.50297e7 −1.70784 −0.853919 0.520406i \(-0.825781\pi\)
−0.853919 + 0.520406i \(0.825781\pi\)
\(30\) 3.31810e7i 1.36547i
\(31\) 4.69488e7i 1.63990i 0.572438 + 0.819948i \(0.305998\pi\)
−0.572438 + 0.819948i \(0.694002\pi\)
\(32\) 4.77094e7i 1.42185i
\(33\) 1.28406e7i 0.328108i
\(34\) 1.20561e7i 0.265346i
\(35\) −6.20573e7 −1.18155
\(36\) −2.43337e7 −0.402436
\(37\) 7.93633e7i 1.14449i 0.820084 + 0.572244i \(0.193927\pi\)
−0.820084 + 0.572244i \(0.806073\pi\)
\(38\) 1.68649e8i 2.12846i
\(39\) 8.16037e7i 0.904455i
\(40\) 5.02061e7i 0.490294i
\(41\) 9.67573e6 0.0835150 0.0417575 0.999128i \(-0.486704\pi\)
0.0417575 + 0.999128i \(0.486704\pi\)
\(42\) 8.32066e7i 0.636665i
\(43\) 7.78354e7i 0.529462i −0.964322 0.264731i \(-0.914717\pi\)
0.964322 0.264731i \(-0.0852832\pi\)
\(44\) 1.13151e8i 0.686113i
\(45\) −9.79159e7 −0.530629
\(46\) −3.74251e8 −1.81708
\(47\) 4.77102e7i 0.208028i −0.994576 0.104014i \(-0.966831\pi\)
0.994576 0.104014i \(-0.0331687\pi\)
\(48\) −1.10292e8 −0.432849
\(49\) −1.26857e8 −0.449090
\(50\) 7.12255e8i 2.27922i
\(51\) 3.55772e7 0.103115
\(52\) 7.19088e8i 1.89132i
\(53\) 6.70282e8 1.60280 0.801398 0.598131i \(-0.204090\pi\)
0.801398 + 0.598131i \(0.204090\pi\)
\(54\) 1.31286e8i 0.285923i
\(55\) 4.55306e8i 0.904669i
\(56\) 1.25900e8i 0.228605i
\(57\) −4.97678e8 −0.827131
\(58\) 1.66540e9i 2.53734i
\(59\) 7.02192e8 + 1.34322e8i 0.982191 + 0.187883i
\(60\) 8.62830e8 1.10961
\(61\) 1.29266e9i 1.53051i −0.643727 0.765255i \(-0.722613\pi\)
0.643727 0.765255i \(-0.277387\pi\)
\(62\) 2.23206e9 2.43639
\(63\) 2.45540e8 0.247411
\(64\) 1.46322e9 1.36273
\(65\) 2.89352e9i 2.49379i
\(66\) 6.10475e8 0.487471
\(67\) 1.73077e9i 1.28193i 0.767569 + 0.640966i \(0.221466\pi\)
−0.767569 + 0.640966i \(0.778534\pi\)
\(68\) −3.13504e8 −0.215625
\(69\) 1.10440e9i 0.706126i
\(70\) 2.95035e9i 1.75543i
\(71\) −3.39938e9 −1.88412 −0.942058 0.335451i \(-0.891111\pi\)
−0.942058 + 0.335451i \(0.891111\pi\)
\(72\) 1.98649e8i 0.102665i
\(73\) 1.89958e7i 0.00916311i 0.999990 + 0.00458155i \(0.00145836\pi\)
−0.999990 + 0.00458155i \(0.998542\pi\)
\(74\) 3.77312e9 1.70037
\(75\) 2.10184e9 0.885714
\(76\) 4.38551e9 1.72963
\(77\) 1.14175e9i 0.421811i
\(78\) −3.87964e9 −1.34375
\(79\) 2.81385e9 0.914460 0.457230 0.889348i \(-0.348842\pi\)
0.457230 + 0.889348i \(0.348842\pi\)
\(80\) 3.91074e9 1.19346
\(81\) 3.87420e8 0.111111
\(82\) 4.60008e8i 0.124078i
\(83\) 3.49802e9i 0.888038i −0.896017 0.444019i \(-0.853552\pi\)
0.896017 0.444019i \(-0.146448\pi\)
\(84\) −2.16368e9 −0.517365
\(85\) −1.26150e9 −0.284311
\(86\) −3.70048e9 −0.786622
\(87\) −4.91453e9 −0.986021
\(88\) −9.23711e8 −0.175034
\(89\) 2.25318e9i 0.403503i 0.979437 + 0.201751i \(0.0646633\pi\)
−0.979437 + 0.201751i \(0.935337\pi\)
\(90\) 4.65516e9i 0.788356i
\(91\) 7.25596e9i 1.16275i
\(92\) 9.73195e9i 1.47659i
\(93\) 6.58674e9i 0.946794i
\(94\) −2.26826e9 −0.309067
\(95\) 1.76468e10 2.28059
\(96\) 6.69344e9i 0.820906i
\(97\) 1.06360e10i 1.23857i 0.785167 + 0.619284i \(0.212577\pi\)
−0.785167 + 0.619284i \(0.787423\pi\)
\(98\) 6.03108e9i 0.667213i
\(99\) 1.80149e9i 0.189433i
\(100\) −1.85213e10 −1.85213
\(101\) 1.46879e9i 0.139750i −0.997556 0.0698752i \(-0.977740\pi\)
0.997556 0.0698752i \(-0.0222601\pi\)
\(102\) 1.69142e9i 0.153198i
\(103\) 1.96079e10i 1.69139i 0.533666 + 0.845695i \(0.320814\pi\)
−0.533666 + 0.845695i \(0.679186\pi\)
\(104\) 5.87028e9 0.482495
\(105\) −8.70639e9 −0.682169
\(106\) 3.18668e10i 2.38128i
\(107\) 1.03987e10 0.741416 0.370708 0.928749i \(-0.379115\pi\)
0.370708 + 0.928749i \(0.379115\pi\)
\(108\) −3.41393e9 −0.232346
\(109\) 6.75429e9i 0.438983i 0.975614 + 0.219491i \(0.0704397\pi\)
−0.975614 + 0.219491i \(0.929560\pi\)
\(110\) −2.16463e10 −1.34407
\(111\) 1.11344e10i 0.660770i
\(112\) −9.80682e9 −0.556465
\(113\) 1.66808e10i 0.905367i −0.891671 0.452683i \(-0.850467\pi\)
0.891671 0.452683i \(-0.149533\pi\)
\(114\) 2.36608e10i 1.22887i
\(115\) 3.91601e10i 1.94695i
\(116\) 4.33066e10 2.06188
\(117\) 1.14487e10i 0.522187i
\(118\) 6.38601e9 3.33839e10i 0.279138 1.45924i
\(119\) 3.16342e9 0.132563
\(120\) 7.04372e9i 0.283072i
\(121\) 1.75605e10 0.677035
\(122\) −6.14563e10 −2.27388
\(123\) 1.35747e9 0.0482174
\(124\) 5.80420e10i 1.97986i
\(125\) −2.59469e10 −0.850229
\(126\) 1.16736e10i 0.367579i
\(127\) 4.88844e10 1.47962 0.739812 0.672814i \(-0.234915\pi\)
0.739812 + 0.672814i \(0.234915\pi\)
\(128\) 2.07105e10i 0.602755i
\(129\) 1.09200e10i 0.305685i
\(130\) 1.37565e11 3.70502
\(131\) 3.48703e10i 0.903857i −0.892054 0.451928i \(-0.850736\pi\)
0.892054 0.451928i \(-0.149264\pi\)
\(132\) 1.58747e10i 0.396127i
\(133\) −4.42520e10 −1.06335
\(134\) 8.22849e10 1.90457
\(135\) −1.37372e10 −0.306359
\(136\) 2.55929e9i 0.0550080i
\(137\) −6.88870e10 −1.42736 −0.713681 0.700471i \(-0.752974\pi\)
−0.713681 + 0.700471i \(0.752974\pi\)
\(138\) −5.25060e10 −1.04909
\(139\) 1.14551e10 0.220763 0.110381 0.993889i \(-0.464793\pi\)
0.110381 + 0.993889i \(0.464793\pi\)
\(140\) 7.67203e10 1.42649
\(141\) 6.69355e9i 0.120105i
\(142\) 1.61615e11i 2.79923i
\(143\) 5.32360e10 0.890278
\(144\) −1.54735e10 −0.249906
\(145\) 1.74260e11 2.71868
\(146\) 9.03105e8 0.0136136
\(147\) −1.77975e10 −0.259282
\(148\) 9.81154e10i 1.38175i
\(149\) 1.15357e11i 1.57076i 0.619011 + 0.785382i \(0.287534\pi\)
−0.619011 + 0.785382i \(0.712466\pi\)
\(150\) 9.99266e10i 1.31591i
\(151\) 1.05286e11i 1.34118i 0.741830 + 0.670588i \(0.233958\pi\)
−0.741830 + 0.670588i \(0.766042\pi\)
\(152\) 3.58012e10i 0.441245i
\(153\) 4.99134e9 0.0595333
\(154\) 5.42817e10 0.626685
\(155\) 2.33554e11i 2.61053i
\(156\) 1.00885e11i 1.09195i
\(157\) 1.54569e10i 0.162041i 0.996712 + 0.0810204i \(0.0258179\pi\)
−0.996712 + 0.0810204i \(0.974182\pi\)
\(158\) 1.33777e11i 1.35861i
\(159\) 9.40380e10 0.925375
\(160\) 2.37337e11i 2.26343i
\(161\) 9.82003e10i 0.907786i
\(162\) 1.84189e10i 0.165078i
\(163\) 1.75392e11 1.52431 0.762153 0.647397i \(-0.224142\pi\)
0.762153 + 0.647397i \(0.224142\pi\)
\(164\) −1.19619e10 −0.100828
\(165\) 6.38776e10i 0.522311i
\(166\) −1.66304e11 −1.31936
\(167\) 5.47488e10 0.421494 0.210747 0.977541i \(-0.432410\pi\)
0.210747 + 0.977541i \(0.432410\pi\)
\(168\) 1.76633e10i 0.131985i
\(169\) −2.00462e11 −1.45412
\(170\) 5.99748e10i 0.422400i
\(171\) −6.98223e10 −0.477544
\(172\) 9.62265e10i 0.639223i
\(173\) 1.16508e11i 0.751841i −0.926652 0.375920i \(-0.877327\pi\)
0.926652 0.375920i \(-0.122673\pi\)
\(174\) 2.33649e11i 1.46493i
\(175\) 1.86889e11 1.13866
\(176\) 7.19513e10i 0.426064i
\(177\) 9.85149e10 + 1.88449e10i 0.567068 + 0.108474i
\(178\) 1.07122e11 0.599485
\(179\) 2.34414e11i 1.27561i −0.770198 0.637805i \(-0.779843\pi\)
0.770198 0.637805i \(-0.220157\pi\)
\(180\) 1.21052e11 0.640632
\(181\) 1.22529e11 0.630736 0.315368 0.948969i \(-0.397872\pi\)
0.315368 + 0.948969i \(0.397872\pi\)
\(182\) −3.44966e11 −1.72751
\(183\) 1.81356e11i 0.883640i
\(184\) 7.94469e10 0.376693
\(185\) 3.94804e11i 1.82189i
\(186\) 3.13149e11 1.40665
\(187\) 2.32096e10i 0.101498i
\(188\) 5.89833e10i 0.251154i
\(189\) 3.44483e10 0.142843
\(190\) 8.38969e11i 3.38827i
\(191\) 4.02313e11i 1.58269i 0.611368 + 0.791347i \(0.290620\pi\)
−0.611368 + 0.791347i \(0.709380\pi\)
\(192\) 2.05284e11 0.786771
\(193\) −1.97970e11 −0.739288 −0.369644 0.929173i \(-0.620520\pi\)
−0.369644 + 0.929173i \(0.620520\pi\)
\(194\) 5.05662e11 1.84014
\(195\) 4.05950e11i 1.43979i
\(196\) 1.56831e11 0.542189
\(197\) −3.75407e11 −1.26523 −0.632617 0.774465i \(-0.718019\pi\)
−0.632617 + 0.774465i \(0.718019\pi\)
\(198\) 8.56473e10 0.281441
\(199\) 2.97679e11 0.953856 0.476928 0.878942i \(-0.341750\pi\)
0.476928 + 0.878942i \(0.341750\pi\)
\(200\) 1.51199e11i 0.472497i
\(201\) 2.42820e11i 0.740124i
\(202\) −6.98299e10 −0.207627
\(203\) −4.36986e11 −1.26761
\(204\) −4.39834e10 −0.124491
\(205\) −4.81333e10 −0.132946
\(206\) 9.32205e11 2.51290
\(207\) 1.54944e11i 0.407682i
\(208\) 4.57259e11i 1.17448i
\(209\) 3.24671e11i 0.814165i
\(210\) 4.13923e11i 1.01350i
\(211\) 3.79905e11i 0.908370i 0.890907 + 0.454185i \(0.150069\pi\)
−0.890907 + 0.454185i \(0.849931\pi\)
\(212\) −8.28658e11 −1.93507
\(213\) −4.76919e11 −1.08779
\(214\) 4.94382e11i 1.10152i
\(215\) 3.87203e11i 0.842843i
\(216\) 2.78697e10i 0.0592738i
\(217\) 5.85673e11i 1.21719i
\(218\) 3.21115e11 0.652197
\(219\) 2.66503e9i 0.00529032i
\(220\) 5.62886e11i 1.09221i
\(221\) 1.47499e11i 0.279788i
\(222\) 5.29354e11 0.981707
\(223\) −9.15378e11 −1.65988 −0.829939 0.557854i \(-0.811625\pi\)
−0.829939 + 0.557854i \(0.811625\pi\)
\(224\) 5.95161e11i 1.05535i
\(225\) 2.94880e11 0.511367
\(226\) −7.93045e11 −1.34510
\(227\) 3.00794e11i 0.499045i 0.968369 + 0.249523i \(0.0802737\pi\)
−0.968369 + 0.249523i \(0.919726\pi\)
\(228\) 6.15270e11 0.998600
\(229\) 5.50473e11i 0.874094i 0.899439 + 0.437047i \(0.143976\pi\)
−0.899439 + 0.437047i \(0.856024\pi\)
\(230\) 1.86177e12 2.89259
\(231\) 1.60183e11i 0.243533i
\(232\) 3.53534e11i 0.526007i
\(233\) 8.38036e11i 1.22035i −0.792268 0.610173i \(-0.791100\pi\)
0.792268 0.610173i \(-0.208900\pi\)
\(234\) −5.44298e11 −0.775814
\(235\) 2.37341e11i 0.331157i
\(236\) −8.68108e11 1.66060e11i −1.18581 0.226833i
\(237\) 3.94772e11 0.527964
\(238\) 1.50396e11i 0.196949i
\(239\) −9.21230e11 −1.18135 −0.590675 0.806909i \(-0.701138\pi\)
−0.590675 + 0.806909i \(0.701138\pi\)
\(240\) 5.48662e11 0.689047
\(241\) 2.06797e11 0.254366 0.127183 0.991879i \(-0.459406\pi\)
0.127183 + 0.991879i \(0.459406\pi\)
\(242\) 8.34871e11i 1.00587i
\(243\) 5.43536e10 0.0641500
\(244\) 1.59810e12i 1.84779i
\(245\) 6.31067e11 0.714900
\(246\) 6.45373e10i 0.0716366i
\(247\) 2.06332e12i 2.24431i
\(248\) −4.73827e11 −0.505081
\(249\) 4.90758e11i 0.512709i
\(250\) 1.23358e12i 1.26319i
\(251\) 7.95542e11 0.798536 0.399268 0.916834i \(-0.369264\pi\)
0.399268 + 0.916834i \(0.369264\pi\)
\(252\) −3.03556e11 −0.298701
\(253\) 7.20482e11 0.695058
\(254\) 2.32408e12i 2.19828i
\(255\) −1.76984e11 −0.164147
\(256\) 5.13708e11 0.467214
\(257\) 1.25101e12 1.11583 0.557913 0.829900i \(-0.311602\pi\)
0.557913 + 0.829900i \(0.311602\pi\)
\(258\) −5.19163e11 −0.454157
\(259\) 9.90034e11i 0.849477i
\(260\) 3.57721e12i 3.01077i
\(261\) −6.89490e11 −0.569279
\(262\) −1.65782e12 −1.34286
\(263\) −2.17127e12 −1.72558 −0.862790 0.505562i \(-0.831285\pi\)
−0.862790 + 0.505562i \(0.831285\pi\)
\(264\) −1.29593e11 −0.101056
\(265\) −3.33442e12 −2.55147
\(266\) 2.10385e12i 1.57982i
\(267\) 3.16113e11i 0.232963i
\(268\) 2.13972e12i 1.54768i
\(269\) 6.00038e10i 0.0426007i 0.999773 + 0.0213004i \(0.00678063\pi\)
−0.999773 + 0.0213004i \(0.993219\pi\)
\(270\) 6.53101e11i 0.455157i
\(271\) 1.84863e12 1.26475 0.632374 0.774663i \(-0.282081\pi\)
0.632374 + 0.774663i \(0.282081\pi\)
\(272\) −1.99353e11 −0.133899
\(273\) 1.01798e12i 0.671317i
\(274\) 3.27505e12i 2.12063i
\(275\) 1.37118e12i 0.871830i
\(276\) 1.36535e12i 0.852511i
\(277\) 1.48046e12 0.907815 0.453908 0.891049i \(-0.350030\pi\)
0.453908 + 0.891049i \(0.350030\pi\)
\(278\) 5.44605e11i 0.327988i
\(279\) 9.24094e11i 0.546632i
\(280\) 6.26307e11i 0.363913i
\(281\) −1.16588e11 −0.0665463 −0.0332731 0.999446i \(-0.510593\pi\)
−0.0332731 + 0.999446i \(0.510593\pi\)
\(282\) −3.18228e11 −0.178440
\(283\) 2.02531e12i 1.11573i 0.829932 + 0.557865i \(0.188379\pi\)
−0.829932 + 0.557865i \(0.811621\pi\)
\(284\) 4.20259e12 2.27471
\(285\) 2.47577e12 1.31670
\(286\) 2.53097e12i 1.32269i
\(287\) 1.20702e11 0.0619876
\(288\) 9.39064e11i 0.473950i
\(289\) −1.95169e12 −0.968102
\(290\) 8.28476e12i 4.03915i
\(291\) 1.49219e12i 0.715088i
\(292\) 2.34841e10i 0.0110627i
\(293\) 4.07698e11 0.188799 0.0943997 0.995534i \(-0.469907\pi\)
0.0943997 + 0.995534i \(0.469907\pi\)
\(294\) 8.46137e11i 0.385216i
\(295\) −3.49316e12 6.68206e11i −1.56354 0.299089i
\(296\) −8.00966e11 −0.352497
\(297\) 2.52742e11i 0.109369i
\(298\) 5.48433e12 2.33369
\(299\) −4.57875e12 −1.91598
\(300\) −2.59847e12 −1.06933
\(301\) 9.70974e11i 0.392984i
\(302\) 5.00555e12 1.99259
\(303\) 2.06066e11i 0.0806849i
\(304\) 2.78869e12 1.07407
\(305\) 6.43054e12i 2.43640i
\(306\) 2.37300e11i 0.0884486i
\(307\) 3.87561e11 0.142118 0.0710589 0.997472i \(-0.477362\pi\)
0.0710589 + 0.997472i \(0.477362\pi\)
\(308\) 1.41153e12i 0.509256i
\(309\) 2.75091e12i 0.976525i
\(310\) −1.11037e13 −3.87846
\(311\) −2.53610e12 −0.871696 −0.435848 0.900020i \(-0.643551\pi\)
−0.435848 + 0.900020i \(0.643551\pi\)
\(312\) 8.23578e11 0.278568
\(313\) 1.19694e12i 0.398427i 0.979956 + 0.199214i \(0.0638388\pi\)
−0.979956 + 0.199214i \(0.936161\pi\)
\(314\) 7.34859e11 0.240744
\(315\) −1.22147e12 −0.393850
\(316\) −3.47871e12 −1.10403
\(317\) 3.26824e12 1.02098 0.510490 0.859884i \(-0.329464\pi\)
0.510490 + 0.859884i \(0.329464\pi\)
\(318\) 4.47079e12i 1.37483i
\(319\) 3.20611e12i 0.970564i
\(320\) −7.27899e12 −2.16931
\(321\) 1.45890e12 0.428057
\(322\) −4.66868e12 −1.34870
\(323\) −8.99556e11 −0.255868
\(324\) −4.78961e11 −0.134145
\(325\) 8.71402e12i 2.40327i
\(326\) 8.33857e12i 2.26466i
\(327\) 9.47601e11i 0.253447i
\(328\) 9.76514e10i 0.0257223i
\(329\) 5.95171e11i 0.154405i
\(330\) −3.03690e12 −0.775998
\(331\) 3.09341e12 0.778571 0.389285 0.921117i \(-0.372722\pi\)
0.389285 + 0.921117i \(0.372722\pi\)
\(332\) 4.32454e12i 1.07213i
\(333\) 1.56211e12i 0.381496i
\(334\) 2.60289e12i 0.626215i
\(335\) 8.60996e12i 2.04069i
\(336\) −1.37586e12 −0.321275
\(337\) 7.64173e11i 0.175809i 0.996129 + 0.0879047i \(0.0280171\pi\)
−0.996129 + 0.0879047i \(0.971983\pi\)
\(338\) 9.53047e12i 2.16038i
\(339\) 2.34025e12i 0.522714i
\(340\) 1.55957e12 0.343250
\(341\) −4.29701e12 −0.931953
\(342\) 3.31952e12i 0.709488i
\(343\) −5.10630e12 −1.07556
\(344\) 7.85546e11 0.163072
\(345\) 5.49402e12i 1.12407i
\(346\) −5.53908e12 −1.11701
\(347\) 3.69950e11i 0.0735353i −0.999324 0.0367677i \(-0.988294\pi\)
0.999324 0.0367677i \(-0.0117061\pi\)
\(348\) 6.07575e12 1.19043
\(349\) 8.71421e11i 0.168306i 0.996453 + 0.0841532i \(0.0268185\pi\)
−0.996453 + 0.0841532i \(0.973181\pi\)
\(350\) 8.88518e12i 1.69171i
\(351\) 1.60621e12i 0.301485i
\(352\) −4.36662e12 −0.808038
\(353\) 5.40604e12i 0.986292i 0.869947 + 0.493146i \(0.164153\pi\)
−0.869947 + 0.493146i \(0.835847\pi\)
\(354\) 8.95932e11 4.68364e12i 0.161161 0.842494i
\(355\) 1.69107e13 2.99930
\(356\) 2.78557e12i 0.487152i
\(357\) 4.43815e11 0.0765351
\(358\) −1.11446e13 −1.89517
\(359\) −1.06964e13 −1.79377 −0.896885 0.442264i \(-0.854176\pi\)
−0.896885 + 0.442264i \(0.854176\pi\)
\(360\) 9.88207e11i 0.163431i
\(361\) 6.45255e12 1.05243
\(362\) 5.82535e12i 0.937085i
\(363\) 2.46368e12 0.390886
\(364\) 8.97042e12i 1.40380i
\(365\) 9.44972e10i 0.0145866i
\(366\) −8.62209e12 −1.31283
\(367\) 8.00075e12i 1.20171i 0.799358 + 0.600856i \(0.205173\pi\)
−0.799358 + 0.600856i \(0.794827\pi\)
\(368\) 6.18842e12i 0.916939i
\(369\) 1.90447e11 0.0278383
\(370\) −1.87699e13 −2.70679
\(371\) 8.36158e12 1.18965
\(372\) 8.14307e12i 1.14307i
\(373\) −1.08064e12 −0.149670 −0.0748351 0.997196i \(-0.523843\pi\)
−0.0748351 + 0.997196i \(0.523843\pi\)
\(374\) 1.10344e12 0.150796
\(375\) −3.64025e12 −0.490880
\(376\) 4.81511e11 0.0640718
\(377\) 2.03752e13i 2.67543i
\(378\) 1.63775e12i 0.212222i
\(379\) −4.13823e12 −0.529198 −0.264599 0.964359i \(-0.585240\pi\)
−0.264599 + 0.964359i \(0.585240\pi\)
\(380\) −2.18164e13 −2.75337
\(381\) 6.85828e12 0.854261
\(382\) 1.91269e13 2.35141
\(383\) −2.76676e12 −0.335720 −0.167860 0.985811i \(-0.553686\pi\)
−0.167860 + 0.985811i \(0.553686\pi\)
\(384\) 2.90560e12i 0.348001i
\(385\) 5.67981e12i 0.671476i
\(386\) 9.41200e12i 1.09836i
\(387\) 1.53203e12i 0.176487i
\(388\) 1.31491e13i 1.49533i
\(389\) 1.31884e13 1.48062 0.740311 0.672265i \(-0.234678\pi\)
0.740311 + 0.672265i \(0.234678\pi\)
\(390\) 1.92998e13 2.13910
\(391\) 1.99622e12i 0.218436i
\(392\) 1.28029e12i 0.138318i
\(393\) 4.89217e12i 0.521842i
\(394\) 1.78477e13i 1.87976i
\(395\) −1.39979e13 −1.45572
\(396\) 2.22715e12i 0.228704i
\(397\) 6.53060e12i 0.662218i 0.943593 + 0.331109i \(0.107423\pi\)
−0.943593 + 0.331109i \(0.892577\pi\)
\(398\) 1.41524e13i 1.41714i
\(399\) −6.20839e12 −0.613924
\(400\) −1.17775e13 −1.15014
\(401\) 1.79410e13i 1.73032i −0.501500 0.865158i \(-0.667218\pi\)
0.501500 0.865158i \(-0.332782\pi\)
\(402\) 1.15443e13 1.09960
\(403\) 2.73080e13 2.56900
\(404\) 1.81584e12i 0.168722i
\(405\) −1.92728e12 −0.176876
\(406\) 2.07754e13i 1.88330i
\(407\) −7.26375e12 −0.650412
\(408\) 3.59059e11i 0.0317589i
\(409\) 1.13865e13i 0.994889i 0.867496 + 0.497445i \(0.165728\pi\)
−0.867496 + 0.497445i \(0.834272\pi\)
\(410\) 2.28837e12i 0.197519i
\(411\) −9.66458e12 −0.824088
\(412\) 2.42408e13i 2.04203i
\(413\) 8.75965e12 + 1.67563e12i 0.729015 + 0.139453i
\(414\) −7.36639e12 −0.605694
\(415\) 1.74014e13i 1.41366i
\(416\) 2.77504e13 2.22742
\(417\) 1.60711e12 0.127458
\(418\) −1.54357e13 −1.20961
\(419\) 1.39833e12i 0.108278i 0.998533 + 0.0541390i \(0.0172414\pi\)
−0.998533 + 0.0541390i \(0.982759\pi\)
\(420\) 1.07636e13 0.823587
\(421\) 7.96565e12i 0.602297i 0.953577 + 0.301149i \(0.0973700\pi\)
−0.953577 + 0.301149i \(0.902630\pi\)
\(422\) 1.80616e13 1.34957
\(423\) 9.39080e11i 0.0693427i
\(424\) 6.76476e12i 0.493654i
\(425\) 3.79909e12 0.273990
\(426\) 2.26739e13i 1.61614i
\(427\) 1.61256e13i 1.13600i
\(428\) −1.28558e13 −0.895117
\(429\) 7.46881e12 0.514002
\(430\) 1.84086e13 1.25221
\(431\) 5.37574e12i 0.361453i 0.983533 + 0.180726i \(0.0578448\pi\)
−0.983533 + 0.180726i \(0.942155\pi\)
\(432\) −2.17087e12 −0.144283
\(433\) −1.42980e13 −0.939369 −0.469685 0.882834i \(-0.655632\pi\)
−0.469685 + 0.882834i \(0.655632\pi\)
\(434\) 2.78443e13 1.80837
\(435\) 2.44481e13 1.56963
\(436\) 8.35021e12i 0.529987i
\(437\) 2.79245e13i 1.75218i
\(438\) 1.26702e11 0.00785983
\(439\) −9.94179e12 −0.609736 −0.304868 0.952395i \(-0.598612\pi\)
−0.304868 + 0.952395i \(0.598612\pi\)
\(440\) 4.59513e12 0.278634
\(441\) −2.49692e12 −0.149697
\(442\) −7.01248e12 −0.415681
\(443\) 1.00600e13i 0.589630i −0.955554 0.294815i \(-0.904742\pi\)
0.955554 0.294815i \(-0.0952581\pi\)
\(444\) 1.37652e13i 0.797752i
\(445\) 1.12088e13i 0.642331i
\(446\) 4.35193e13i 2.46608i
\(447\) 1.61841e13i 0.906881i
\(448\) 1.82532e13 1.01146
\(449\) 3.03874e13 1.66518 0.832592 0.553886i \(-0.186856\pi\)
0.832592 + 0.553886i \(0.186856\pi\)
\(450\) 1.40193e13i 0.759739i
\(451\) 8.85574e11i 0.0474616i
\(452\) 2.06222e13i 1.09306i
\(453\) 1.47712e13i 0.774329i
\(454\) 1.43005e13 0.741432
\(455\) 3.60958e13i 1.85097i
\(456\) 5.02277e12i 0.254753i
\(457\) 2.85028e13i 1.42990i −0.699173 0.714952i \(-0.746448\pi\)
0.699173 0.714952i \(-0.253552\pi\)
\(458\) 2.61708e13 1.29864
\(459\) 7.00265e11 0.0343715
\(460\) 4.84130e13i 2.35057i
\(461\) −7.52318e12 −0.361324 −0.180662 0.983545i \(-0.557824\pi\)
−0.180662 + 0.983545i \(0.557824\pi\)
\(462\) 7.61551e12 0.361817
\(463\) 3.38232e12i 0.158968i −0.996836 0.0794841i \(-0.974673\pi\)
0.996836 0.0794841i \(-0.0253273\pi\)
\(464\) 2.75381e13 1.28040
\(465\) 3.27667e13i 1.50719i
\(466\) −3.98423e13 −1.81307
\(467\) 3.58012e13i 1.61181i 0.592046 + 0.805904i \(0.298320\pi\)
−0.592046 + 0.805904i \(0.701680\pi\)
\(468\) 1.41538e13i 0.630440i
\(469\) 2.15908e13i 0.951492i
\(470\) 1.12838e13 0.492000
\(471\) 2.16854e12i 0.0935543i
\(472\) −1.35564e12 + 7.08681e12i −0.0578672 + 0.302511i
\(473\) 7.12391e12 0.300893
\(474\) 1.87684e13i 0.784396i
\(475\) −5.31443e13 −2.19780
\(476\) −3.91087e12 −0.160044
\(477\) 1.31932e13 0.534265
\(478\) 4.37975e13i 1.75513i
\(479\) −3.00548e13 −1.19189 −0.595945 0.803025i \(-0.703223\pi\)
−0.595945 + 0.803025i \(0.703223\pi\)
\(480\) 3.32975e13i 1.30679i
\(481\) 4.61619e13 1.79291
\(482\) 9.83163e12i 0.377912i
\(483\) 1.37771e13i 0.524110i
\(484\) −2.17098e13 −0.817389
\(485\) 5.29104e13i 1.97166i
\(486\) 2.58410e12i 0.0953077i
\(487\) −4.04542e13 −1.47679 −0.738396 0.674368i \(-0.764416\pi\)
−0.738396 + 0.674368i \(0.764416\pi\)
\(488\) 1.30461e13 0.471391
\(489\) 2.46068e13 0.880059
\(490\) 3.00025e13i 1.06213i
\(491\) −4.42270e13 −1.54982 −0.774908 0.632074i \(-0.782204\pi\)
−0.774908 + 0.632074i \(0.782204\pi\)
\(492\) −1.67821e12 −0.0582132
\(493\) −8.88305e12 −0.305019
\(494\) 9.80954e13 3.33437
\(495\) 8.96179e12i 0.301556i
\(496\) 3.69081e13i 1.22946i
\(497\) −4.24062e13 −1.39845
\(498\) −2.33318e13 −0.761732
\(499\) −5.35177e13 −1.72980 −0.864898 0.501947i \(-0.832617\pi\)
−0.864898 + 0.501947i \(0.832617\pi\)
\(500\) 3.20777e13 1.02649
\(501\) 7.68104e12 0.243350
\(502\) 3.78220e13i 1.18638i
\(503\) 4.96500e13i 1.54198i 0.636846 + 0.770991i \(0.280239\pi\)
−0.636846 + 0.770991i \(0.719761\pi\)
\(504\) 2.47809e12i 0.0762016i
\(505\) 7.30671e12i 0.222467i
\(506\) 3.42535e13i 1.03265i
\(507\) −2.81241e13 −0.839535
\(508\) −6.04348e13 −1.78636
\(509\) 2.10201e13i 0.615240i 0.951509 + 0.307620i \(0.0995326\pi\)
−0.951509 + 0.307620i \(0.900467\pi\)
\(510\) 8.41423e12i 0.243873i
\(511\) 2.36967e11i 0.00680116i
\(512\) 4.56305e13i 1.29690i
\(513\) −9.79579e12 −0.275710
\(514\) 5.94762e13i 1.65778i
\(515\) 9.75421e13i 2.69250i
\(516\) 1.35002e13i 0.369056i
\(517\) 4.36669e12 0.118222
\(518\) 4.70686e13 1.26207
\(519\) 1.63456e13i 0.434075i
\(520\) −2.92026e13 −0.768077
\(521\) 9.13680e12 0.238016 0.119008 0.992893i \(-0.462029\pi\)
0.119008 + 0.992893i \(0.462029\pi\)
\(522\) 3.27800e13i 0.845779i
\(523\) 3.04103e12 0.0777164 0.0388582 0.999245i \(-0.487628\pi\)
0.0388582 + 0.999245i \(0.487628\pi\)
\(524\) 4.31096e13i 1.09123i
\(525\) 2.62199e13 0.657406
\(526\) 1.03227e14i 2.56370i
\(527\) 1.19056e13i 0.292885i
\(528\) 1.00945e13i 0.245988i
\(529\) −2.05410e13 −0.495843
\(530\) 1.58526e14i 3.79072i
\(531\) 1.38213e13 + 2.64387e12i 0.327397 + 0.0626277i
\(532\) 5.47080e13 1.28379
\(533\) 5.62792e12i 0.130831i
\(534\) 1.50288e13 0.346113
\(535\) −5.17301e13 −1.18025
\(536\) −1.74676e13 −0.394830
\(537\) 3.28873e13i 0.736473i
\(538\) 2.85272e12 0.0632919
\(539\) 1.16106e13i 0.255218i
\(540\) 1.69831e13 0.369869
\(541\) 1.97545e12i 0.0426266i −0.999773 0.0213133i \(-0.993215\pi\)
0.999773 0.0213133i \(-0.00678474\pi\)
\(542\) 8.78884e13i 1.87904i
\(543\) 1.71904e13 0.364155
\(544\) 1.20984e13i 0.253942i
\(545\) 3.36002e13i 0.698810i
\(546\) −4.83974e13 −0.997376
\(547\) −1.58960e13 −0.324601 −0.162301 0.986741i \(-0.551891\pi\)
−0.162301 + 0.986741i \(0.551891\pi\)
\(548\) 8.51637e13 1.72326
\(549\) 2.54435e13i 0.510170i
\(550\) 6.51894e13 1.29528
\(551\) 1.24262e14 2.44670
\(552\) 1.11461e13 0.217484
\(553\) 3.51019e13 0.678743
\(554\) 7.03846e13i 1.34874i
\(555\) 5.53895e13i 1.05187i
\(556\) −1.41618e13 −0.266529
\(557\) −8.16098e12 −0.152218 −0.0761091 0.997099i \(-0.524250\pi\)
−0.0761091 + 0.997099i \(0.524250\pi\)
\(558\) 4.39337e13 0.812132
\(559\) −4.52732e13 −0.829435
\(560\) 4.87854e13 0.885829
\(561\) 3.25621e12i 0.0586001i
\(562\) 5.54289e12i 0.0988678i
\(563\) 2.87343e12i 0.0507995i 0.999677 + 0.0253997i \(0.00808585\pi\)
−0.999677 + 0.0253997i \(0.991914\pi\)
\(564\) 8.27512e12i 0.145004i
\(565\) 8.29810e13i 1.44124i
\(566\) 9.62881e13 1.65764
\(567\) 4.83296e12 0.0824704
\(568\) 3.43079e13i 0.580300i
\(569\) 8.08683e12i 0.135587i 0.997699 + 0.0677933i \(0.0215958\pi\)
−0.997699 + 0.0677933i \(0.978404\pi\)
\(570\) 1.17704e14i 1.95622i
\(571\) 2.30233e13i 0.379304i 0.981851 + 0.189652i \(0.0607360\pi\)
−0.981851 + 0.189652i \(0.939264\pi\)
\(572\) −6.58148e13 −1.07484
\(573\) 5.64429e13i 0.913768i
\(574\) 5.73846e12i 0.0920950i
\(575\) 1.17933e14i 1.87628i
\(576\) 2.88005e13 0.454243
\(577\) −7.83551e13 −1.22515 −0.612573 0.790414i \(-0.709866\pi\)
−0.612573 + 0.790414i \(0.709866\pi\)
\(578\) 9.27880e13i 1.43831i
\(579\) −2.77745e13 −0.426828
\(580\) −2.15435e14 −3.28228
\(581\) 4.36368e13i 0.659132i
\(582\) 7.09424e13 1.06241
\(583\) 6.13478e13i 0.910869i
\(584\) −1.91713e11 −0.00282220
\(585\) 5.69532e13i 0.831263i
\(586\) 1.93830e13i 0.280499i
\(587\) 1.36868e13i 0.196386i −0.995167 0.0981929i \(-0.968694\pi\)
0.995167 0.0981929i \(-0.0313062\pi\)
\(588\) 2.20027e13 0.313033
\(589\) 1.66543e14i 2.34937i
\(590\) −3.17681e13 + 1.66073e14i −0.444356 + 2.32295i
\(591\) −5.26681e13 −0.730483
\(592\) 6.23903e13i 0.858042i
\(593\) −1.74570e13 −0.238066 −0.119033 0.992890i \(-0.537979\pi\)
−0.119033 + 0.992890i \(0.537979\pi\)
\(594\) 1.20160e13 0.162490
\(595\) −1.57369e13 −0.211025
\(596\) 1.42613e14i 1.89639i
\(597\) 4.17632e13 0.550709
\(598\) 2.17685e14i 2.84657i
\(599\) −7.08734e13 −0.919071 −0.459536 0.888159i \(-0.651984\pi\)
−0.459536 + 0.888159i \(0.651984\pi\)
\(600\) 2.12126e13i 0.272796i
\(601\) 1.17177e14i 1.49442i −0.664590 0.747208i \(-0.731394\pi\)
0.664590 0.747208i \(-0.268606\pi\)
\(602\) −4.61625e13 −0.583857
\(603\) 3.40667e13i 0.427311i
\(604\) 1.30163e14i 1.61921i
\(605\) −8.73575e13 −1.07776
\(606\) −9.79686e12 −0.119874
\(607\) −1.78667e11 −0.00216821 −0.00108411 0.999999i \(-0.500345\pi\)
−0.00108411 + 0.999999i \(0.500345\pi\)
\(608\) 1.69241e14i 2.03699i
\(609\) −6.13074e13 −0.731857
\(610\) 3.05723e14 3.61976
\(611\) −2.77508e13 −0.325889
\(612\) −6.17070e12 −0.0718749
\(613\) 3.48149e13i 0.402219i 0.979569 + 0.201109i \(0.0644547\pi\)
−0.979569 + 0.201109i \(0.935545\pi\)
\(614\) 1.84256e13i 0.211144i
\(615\) −6.75292e12 −0.0767566
\(616\) −1.15230e13 −0.129916
\(617\) −8.79881e13 −0.984006 −0.492003 0.870593i \(-0.663735\pi\)
−0.492003 + 0.870593i \(0.663735\pi\)
\(618\) 1.30785e14 1.45082
\(619\) −8.43433e12 −0.0928105 −0.0464053 0.998923i \(-0.514777\pi\)
−0.0464053 + 0.998923i \(0.514777\pi\)
\(620\) 2.88738e14i 3.15171i
\(621\) 2.17380e13i 0.235375i
\(622\) 1.20572e14i 1.29508i
\(623\) 2.81078e13i 0.299493i
\(624\) 6.41516e13i 0.678086i
\(625\) −1.72266e13 −0.180634
\(626\) 5.69052e13 0.591944
\(627\) 4.55501e13i 0.470058i
\(628\) 1.91091e13i 0.195633i
\(629\) 2.01254e13i 0.204405i
\(630\) 5.80718e13i 0.585144i
\(631\) 3.67916e13 0.367791 0.183896 0.982946i \(-0.441129\pi\)
0.183896 + 0.982946i \(0.441129\pi\)
\(632\) 2.83985e13i 0.281650i
\(633\) 5.32992e13i 0.524448i
\(634\) 1.55380e14i 1.51687i
\(635\) −2.43182e14 −2.35539
\(636\) −1.16257e14 −1.11721
\(637\) 7.37867e13i 0.703527i
\(638\) −1.52426e14 −1.44197
\(639\) −6.69099e13 −0.628038
\(640\) 1.03027e14i 0.959518i
\(641\) −1.03346e13 −0.0955000 −0.0477500 0.998859i \(-0.515205\pi\)
−0.0477500 + 0.998859i \(0.515205\pi\)
\(642\) 6.93598e13i 0.635965i
\(643\) −5.05738e13 −0.460120 −0.230060 0.973176i \(-0.573892\pi\)
−0.230060 + 0.973176i \(0.573892\pi\)
\(644\) 1.21403e14i 1.09598i
\(645\) 5.43231e13i 0.486616i
\(646\) 4.27671e13i 0.380143i
\(647\) −1.17517e14 −1.03652 −0.518261 0.855222i \(-0.673421\pi\)
−0.518261 + 0.855222i \(0.673421\pi\)
\(648\) 3.91000e12i 0.0342218i
\(649\) −1.22939e13 + 6.42684e13i −0.106774 + 0.558180i
\(650\) −4.14286e14 −3.57053
\(651\) 8.21677e13i 0.702742i
\(652\) −2.16834e14 −1.84031
\(653\) 4.49008e13 0.378171 0.189086 0.981961i \(-0.439448\pi\)
0.189086 + 0.981961i \(0.439448\pi\)
\(654\) 4.50512e13 0.376546
\(655\) 1.73468e14i 1.43884i
\(656\) −7.60643e12 −0.0626126
\(657\) 3.73894e11i 0.00305437i
\(658\) −2.82959e13 −0.229400
\(659\) 1.77691e14i 1.42968i 0.699287 + 0.714841i \(0.253501\pi\)
−0.699287 + 0.714841i \(0.746499\pi\)
\(660\) 7.89708e13i 0.630590i
\(661\) 1.37183e14 1.08716 0.543580 0.839358i \(-0.317069\pi\)
0.543580 + 0.839358i \(0.317069\pi\)
\(662\) 1.47068e14i 1.15672i
\(663\) 2.06936e13i 0.161536i
\(664\) 3.53034e13 0.273512
\(665\) 2.20138e14 1.69273
\(666\) 7.42664e13 0.566789
\(667\) 2.75752e14i 2.08877i
\(668\) −6.76849e13 −0.508873
\(669\) −1.28424e14 −0.958331
\(670\) −4.09338e14 −3.03185
\(671\) 1.18311e14 0.869789
\(672\) 8.34988e13i 0.609304i
\(673\) 2.51484e14i 1.82153i −0.412929 0.910763i \(-0.635494\pi\)
0.412929 0.910763i \(-0.364506\pi\)
\(674\) 3.63306e13 0.261200
\(675\) 4.13705e13 0.295238
\(676\) 2.47828e14 1.75557
\(677\) 1.43537e14 1.00930 0.504650 0.863324i \(-0.331621\pi\)
0.504650 + 0.863324i \(0.331621\pi\)
\(678\) −1.11261e14 −0.776596
\(679\) 1.32681e14i 0.919307i
\(680\) 1.27316e13i 0.0875665i
\(681\) 4.22002e13i 0.288124i
\(682\) 2.04290e14i 1.38460i
\(683\) 7.42403e13i 0.499501i 0.968310 + 0.249750i \(0.0803486\pi\)
−0.968310 + 0.249750i \(0.919651\pi\)
\(684\) 8.63200e13 0.576542
\(685\) 3.42688e14 2.27220
\(686\) 2.42766e14i 1.59796i
\(687\) 7.72292e13i 0.504659i
\(688\) 6.11892e13i 0.396947i
\(689\) 3.89872e14i 2.51088i
\(690\) 2.61199e14 1.67004
\(691\) 1.72147e14i 1.09272i −0.837549 0.546362i \(-0.816012\pi\)
0.837549 0.546362i \(-0.183988\pi\)
\(692\) 1.44037e14i 0.907702i
\(693\) 2.24731e13i 0.140604i
\(694\) −1.75883e13 −0.109251
\(695\) −5.69852e13 −0.351429
\(696\) 4.95995e13i 0.303690i
\(697\) 2.45363e12 0.0149158
\(698\) 4.14295e13 0.250053
\(699\) 1.17573e14i 0.704568i
\(700\) −2.31048e14 −1.37471
\(701\) 2.95827e14i 1.74762i −0.486265 0.873811i \(-0.661641\pi\)
0.486265 0.873811i \(-0.338359\pi\)
\(702\) −7.63630e13 −0.447917
\(703\) 2.81528e14i 1.63963i
\(704\) 1.33921e14i 0.774439i
\(705\) 3.32981e13i 0.191194i
\(706\) 2.57016e14 1.46533
\(707\) 1.83227e13i 0.103727i
\(708\) −1.21792e14 2.32976e13i −0.684626 0.130962i
\(709\) −1.50979e13 −0.0842723 −0.0421361 0.999112i \(-0.513416\pi\)
−0.0421361 + 0.999112i \(0.513416\pi\)
\(710\) 8.03975e14i 4.45606i
\(711\) 5.53849e13 0.304820
\(712\) −2.27401e13 −0.124277
\(713\) 3.69579e14 2.00567
\(714\) 2.11000e13i 0.113708i
\(715\) −2.64830e14 −1.41722
\(716\) 2.89801e14i 1.54005i
\(717\) −1.29245e14 −0.682053
\(718\) 5.08534e14i 2.66501i
\(719\) 8.37386e13i 0.435794i −0.975972 0.217897i \(-0.930080\pi\)
0.975972 0.217897i \(-0.0699197\pi\)
\(720\) 7.69752e13 0.397821
\(721\) 2.44602e14i 1.25541i
\(722\) 3.06770e14i 1.56360i
\(723\) 2.90128e13 0.146858
\(724\) −1.51481e14 −0.761492
\(725\) −5.24796e14 −2.62000
\(726\) 1.17129e14i 0.580740i
\(727\) −2.86584e14 −1.41117 −0.705586 0.708624i \(-0.749316\pi\)
−0.705586 + 0.708624i \(0.749316\pi\)
\(728\) 7.32301e13 0.358124
\(729\) 7.62560e12 0.0370370
\(730\) −4.49263e12 −0.0216714
\(731\) 1.97380e13i 0.0945618i
\(732\) 2.24207e14i 1.06682i
\(733\) −6.41426e13 −0.303128 −0.151564 0.988447i \(-0.548431\pi\)
−0.151564 + 0.988447i \(0.548431\pi\)
\(734\) 3.80375e14 1.78538
\(735\) 8.85363e13 0.412748
\(736\) 3.75566e14 1.73899
\(737\) −1.58409e14 −0.728522
\(738\) 9.05433e12i 0.0413594i
\(739\) 4.93707e13i 0.223999i −0.993708 0.112000i \(-0.964274\pi\)
0.993708 0.112000i \(-0.0357256\pi\)
\(740\) 4.88089e14i 2.19958i
\(741\) 2.89476e14i 1.29575i
\(742\) 3.97530e14i 1.76746i
\(743\) 3.80616e13 0.168090 0.0840451 0.996462i \(-0.473216\pi\)
0.0840451 + 0.996462i \(0.473216\pi\)
\(744\) −6.64760e13 −0.291609
\(745\) 5.73858e14i 2.50048i
\(746\) 5.13761e13i 0.222365i
\(747\) 6.88515e13i 0.296013i
\(748\) 2.86936e13i 0.122540i
\(749\) 1.29721e14 0.550304
\(750\) 1.73066e14i 0.729301i
\(751\) 5.78775e13i 0.242276i −0.992636 0.121138i \(-0.961346\pi\)
0.992636 0.121138i \(-0.0386543\pi\)
\(752\) 3.75067e13i 0.155962i
\(753\) 1.11611e14 0.461035
\(754\) 9.68685e14 3.97490
\(755\) 5.23760e14i 2.13500i
\(756\) −4.25878e13 −0.172455
\(757\) −1.62750e14 −0.654700 −0.327350 0.944903i \(-0.606156\pi\)
−0.327350 + 0.944903i \(0.606156\pi\)
\(758\) 1.96741e14i 0.786230i
\(759\) 1.01081e14 0.401292
\(760\) 1.78098e14i 0.702411i
\(761\) −3.92113e14 −1.53634 −0.768171 0.640245i \(-0.778833\pi\)
−0.768171 + 0.640245i \(0.778833\pi\)
\(762\) 3.26059e14i 1.26918i
\(763\) 8.42578e13i 0.325827i
\(764\) 4.97372e14i 1.91080i
\(765\) −2.48301e13 −0.0947702
\(766\) 1.31538e14i 0.498780i
\(767\) 7.81291e13 4.08433e14i 0.294331 1.53866i
\(768\) 7.20712e13 0.269746
\(769\) 1.65204e14i 0.614313i 0.951659 + 0.307157i \(0.0993775\pi\)
−0.951659 + 0.307157i \(0.900622\pi\)
\(770\) −2.70032e14 −0.997612
\(771\) 1.75512e14 0.644222
\(772\) 2.44747e14 0.892548
\(773\) 4.04252e14i 1.46472i 0.680918 + 0.732360i \(0.261581\pi\)
−0.680918 + 0.732360i \(0.738419\pi\)
\(774\) −7.28366e13 −0.262207
\(775\) 7.03362e14i 2.51577i
\(776\) −1.07343e14 −0.381474
\(777\) 1.38898e14i 0.490446i
\(778\) 6.27009e14i 2.19976i
\(779\) −3.43231e13 −0.119646
\(780\) </