Properties

Label 43.11.b.b.42.11
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.11
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.24

$q$-expansion

\(f(q)\) \(=\) \(q-29.9454i q^{2} +271.957i q^{3} +127.271 q^{4} -203.516i q^{5} +8143.86 q^{6} -3479.85i q^{7} -34475.3i q^{8} -14911.3 q^{9} +O(q^{10})\) \(q-29.9454i q^{2} +271.957i q^{3} +127.271 q^{4} -203.516i q^{5} +8143.86 q^{6} -3479.85i q^{7} -34475.3i q^{8} -14911.3 q^{9} -6094.37 q^{10} -186733. q^{11} +34612.1i q^{12} +180877. q^{13} -104206. q^{14} +55347.4 q^{15} -902053. q^{16} +2.31205e6 q^{17} +446527. i q^{18} -1.81781e6i q^{19} -25901.6i q^{20} +946367. q^{21} +5.59179e6i q^{22} +3.25182e6 q^{23} +9.37578e6 q^{24} +9.72421e6 q^{25} -5.41644e6i q^{26} +1.20035e7i q^{27} -442883. i q^{28} +1.93209e6i q^{29} -1.65740e6i q^{30} +1.24335e7 q^{31} -8.29034e6i q^{32} -5.07832e7i q^{33} -6.92353e7i q^{34} -708204. q^{35} -1.89778e6 q^{36} -1.29307e8i q^{37} -5.44351e7 q^{38} +4.91907e7i q^{39} -7.01627e6 q^{40} +5.75466e7 q^{41} -2.83394e7i q^{42} +(-8.81905e7 - 1.17618e8i) q^{43} -2.37656e7 q^{44} +3.03469e6i q^{45} -9.73771e7i q^{46} +2.19743e8 q^{47} -2.45319e8i q^{48} +2.70366e8 q^{49} -2.91196e8i q^{50} +6.28776e8i q^{51} +2.30204e7 q^{52} +2.24365e8 q^{53} +3.59451e8 q^{54} +3.80030e7i q^{55} -1.19969e8 q^{56} +4.94366e8 q^{57} +5.78574e7 q^{58} +4.63656e8 q^{59} +7.04411e6 q^{60} +1.32372e9i q^{61} -3.72327e8i q^{62} +5.18892e7i q^{63} -1.17196e9 q^{64} -3.68113e7i q^{65} -1.52072e9 q^{66} -9.00383e8 q^{67} +2.94256e8 q^{68} +8.84353e8i q^{69} +2.12075e7i q^{70} -5.54119e8i q^{71} +5.14073e8i q^{72} -2.21796e9i q^{73} -3.87215e9 q^{74} +2.64456e9i q^{75} -2.31354e8i q^{76} +6.49801e8i q^{77} +1.47304e9 q^{78} +1.15303e9 q^{79} +1.83582e8i q^{80} -4.14494e9 q^{81} -1.72326e9i q^{82} +1.02782e9 q^{83} +1.20445e8 q^{84} -4.70538e8i q^{85} +(-3.52211e9 + 2.64090e9i) q^{86} -5.25445e8 q^{87} +6.43767e9i q^{88} +6.93215e9i q^{89} +9.08752e7 q^{90} -6.29425e8i q^{91} +4.13861e8 q^{92} +3.38138e9i q^{93} -6.58031e9i q^{94} -3.69953e8 q^{95} +2.25461e9 q^{96} +9.01632e9 q^{97} -8.09623e9i q^{98} +2.78443e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 29.9454i 0.935795i −0.883783 0.467897i \(-0.845012\pi\)
0.883783 0.467897i \(-0.154988\pi\)
\(3\) 271.957i 1.11916i 0.828775 + 0.559581i \(0.189038\pi\)
−0.828775 + 0.559581i \(0.810962\pi\)
\(4\) 127.271 0.124288
\(5\) 203.516i 0.0651250i −0.999470 0.0325625i \(-0.989633\pi\)
0.999470 0.0325625i \(-0.0103668\pi\)
\(6\) 8143.86 1.04731
\(7\) 3479.85i 0.207048i −0.994627 0.103524i \(-0.966988\pi\)
0.994627 0.103524i \(-0.0330118\pi\)
\(8\) 34475.3i 1.05210i
\(9\) −14911.3 −0.252525
\(10\) −6094.37 −0.0609437
\(11\) −186733. −1.15946 −0.579731 0.814808i \(-0.696843\pi\)
−0.579731 + 0.814808i \(0.696843\pi\)
\(12\) 34612.1i 0.139098i
\(13\) 180877. 0.487155 0.243577 0.969881i \(-0.421679\pi\)
0.243577 + 0.969881i \(0.421679\pi\)
\(14\) −104206. −0.193754
\(15\) 55347.4 0.0728855
\(16\) −902053. −0.860265
\(17\) 2.31205e6 1.62837 0.814183 0.580608i \(-0.197185\pi\)
0.814183 + 0.580608i \(0.197185\pi\)
\(18\) 446527.i 0.236311i
\(19\) 1.81781e6i 0.734143i −0.930193 0.367072i \(-0.880360\pi\)
0.930193 0.367072i \(-0.119640\pi\)
\(20\) 25901.6i 0.00809425i
\(21\) 946367. 0.231720
\(22\) 5.59179e6i 1.08502i
\(23\) 3.25182e6 0.505227 0.252614 0.967567i \(-0.418710\pi\)
0.252614 + 0.967567i \(0.418710\pi\)
\(24\) 9.37578e6 1.17747
\(25\) 9.72421e6 0.995759
\(26\) 5.41644e6i 0.455877i
\(27\) 1.20035e7i 0.836546i
\(28\) 442883.i 0.0257335i
\(29\) 1.93209e6i 0.0941972i 0.998890 + 0.0470986i \(0.0149975\pi\)
−0.998890 + 0.0470986i \(0.985002\pi\)
\(30\) 1.65740e6i 0.0682059i
\(31\) 1.24335e7 0.434296 0.217148 0.976139i \(-0.430325\pi\)
0.217148 + 0.976139i \(0.430325\pi\)
\(32\) 8.29034e6i 0.247071i
\(33\) 5.07832e7i 1.29763i
\(34\) 6.92353e7i 1.52382i
\(35\) −708204. −0.0134840
\(36\) −1.89778e6 −0.0313858
\(37\) 1.29307e8i 1.86472i −0.361535 0.932359i \(-0.617747\pi\)
0.361535 0.932359i \(-0.382253\pi\)
\(38\) −5.44351e7 −0.687007
\(39\) 4.91907e7i 0.545205i
\(40\) −7.01627e6 −0.0685182
\(41\) 5.75466e7 0.496707 0.248354 0.968669i \(-0.420111\pi\)
0.248354 + 0.968669i \(0.420111\pi\)
\(42\) 2.83394e7i 0.216842i
\(43\) −8.81905e7 1.17618e8i −0.599901 0.800075i
\(44\) −2.37656e7 −0.144107
\(45\) 3.03469e6i 0.0164457i
\(46\) 9.73771e7i 0.472789i
\(47\) 2.19743e8 0.958134 0.479067 0.877778i \(-0.340975\pi\)
0.479067 + 0.877778i \(0.340975\pi\)
\(48\) 2.45319e8i 0.962776i
\(49\) 2.70366e8 0.957131
\(50\) 2.91196e8i 0.931826i
\(51\) 6.28776e8i 1.82241i
\(52\) 2.30204e7 0.0605474
\(53\) 2.24365e8 0.536508 0.268254 0.963348i \(-0.413553\pi\)
0.268254 + 0.963348i \(0.413553\pi\)
\(54\) 3.59451e8 0.782836
\(55\) 3.80030e7i 0.0755101i
\(56\) −1.19969e8 −0.217835
\(57\) 4.94366e8 0.821625
\(58\) 5.78574e7 0.0881493
\(59\) 4.63656e8 0.648538 0.324269 0.945965i \(-0.394882\pi\)
0.324269 + 0.945965i \(0.394882\pi\)
\(60\) 7.04411e6 0.00905878
\(61\) 1.32372e9i 1.56729i 0.621212 + 0.783643i \(0.286641\pi\)
−0.621212 + 0.783643i \(0.713359\pi\)
\(62\) 3.72327e8i 0.406412i
\(63\) 5.18892e7i 0.0522846i
\(64\) −1.17196e9 −1.09147
\(65\) 3.68113e7i 0.0317260i
\(66\) −1.52072e9 −1.21431
\(67\) −9.00383e8 −0.666888 −0.333444 0.942770i \(-0.608211\pi\)
−0.333444 + 0.942770i \(0.608211\pi\)
\(68\) 2.94256e8 0.202386
\(69\) 8.84353e8i 0.565432i
\(70\) 2.12075e7i 0.0126182i
\(71\) 5.54119e8i 0.307122i −0.988139 0.153561i \(-0.950926\pi\)
0.988139 0.153561i \(-0.0490742\pi\)
\(72\) 5.14073e8i 0.265682i
\(73\) 2.21796e9i 1.06989i −0.844887 0.534944i \(-0.820333\pi\)
0.844887 0.534944i \(-0.179667\pi\)
\(74\) −3.87215e9 −1.74499
\(75\) 2.64456e9i 1.11442i
\(76\) 2.31354e8i 0.0912450i
\(77\) 6.49801e8i 0.240064i
\(78\) 1.47304e9 0.510200
\(79\) 1.15303e9 0.374718 0.187359 0.982292i \(-0.440007\pi\)
0.187359 + 0.982292i \(0.440007\pi\)
\(80\) 1.83582e8i 0.0560248i
\(81\) −4.14494e9 −1.18876
\(82\) 1.72326e9i 0.464816i
\(83\) 1.02782e9 0.260931 0.130465 0.991453i \(-0.458353\pi\)
0.130465 + 0.991453i \(0.458353\pi\)
\(84\) 1.20445e8 0.0288000
\(85\) 4.70538e8i 0.106047i
\(86\) −3.52211e9 + 2.64090e9i −0.748706 + 0.561384i
\(87\) −5.25445e8 −0.105422
\(88\) 6.43767e9i 1.21987i
\(89\) 6.93215e9i 1.24142i 0.784041 + 0.620709i \(0.213155\pi\)
−0.784041 + 0.620709i \(0.786845\pi\)
\(90\) 9.08752e7 0.0153898
\(91\) 6.29425e8i 0.100864i
\(92\) 4.13861e8 0.0627936
\(93\) 3.38138e9i 0.486047i
\(94\) 6.58031e9i 0.896617i
\(95\) −3.69953e8 −0.0478111
\(96\) 2.25461e9 0.276513
\(97\) 9.01632e9 1.04996 0.524978 0.851116i \(-0.324074\pi\)
0.524978 + 0.851116i \(0.324074\pi\)
\(98\) 8.09623e9i 0.895679i
\(99\) 2.78443e9 0.292793
\(100\) 1.23761e9 0.123761
\(101\) 1.02554e9 0.0975768 0.0487884 0.998809i \(-0.484464\pi\)
0.0487884 + 0.998809i \(0.484464\pi\)
\(102\) 1.88290e10 1.70540
\(103\) −1.17742e10 −1.01566 −0.507828 0.861458i \(-0.669552\pi\)
−0.507828 + 0.861458i \(0.669552\pi\)
\(104\) 6.23579e9i 0.512537i
\(105\) 1.92601e8i 0.0150908i
\(106\) 6.71871e9i 0.502061i
\(107\) −1.00033e10 −0.713222 −0.356611 0.934253i \(-0.616068\pi\)
−0.356611 + 0.934253i \(0.616068\pi\)
\(108\) 1.52770e9i 0.103973i
\(109\) −2.28161e10 −1.48289 −0.741444 0.671015i \(-0.765858\pi\)
−0.741444 + 0.671015i \(0.765858\pi\)
\(110\) 1.13802e9 0.0706619
\(111\) 3.51658e10 2.08692
\(112\) 3.13901e9i 0.178116i
\(113\) 5.09756e9i 0.276675i −0.990385 0.138338i \(-0.955824\pi\)
0.990385 0.138338i \(-0.0441759\pi\)
\(114\) 1.48040e10i 0.768873i
\(115\) 6.61796e8i 0.0329029i
\(116\) 2.45899e8i 0.0117076i
\(117\) −2.69712e9 −0.123019
\(118\) 1.38844e10i 0.606899i
\(119\) 8.04557e9i 0.337149i
\(120\) 1.90812e9i 0.0766830i
\(121\) 8.93167e9 0.344354
\(122\) 3.96395e10 1.46666
\(123\) 1.56502e10i 0.555896i
\(124\) 1.58242e9 0.0539777
\(125\) 3.96649e9i 0.129974i
\(126\) 1.55384e9 0.0489277
\(127\) −4.69853e10 −1.42214 −0.711072 0.703119i \(-0.751790\pi\)
−0.711072 + 0.703119i \(0.751790\pi\)
\(128\) 2.66055e10i 0.774323i
\(129\) 3.19869e10 2.39840e10i 0.895413 0.671386i
\(130\) −1.10233e9 −0.0296890
\(131\) 4.29874e10i 1.11426i −0.830426 0.557128i \(-0.811903\pi\)
0.830426 0.557128i \(-0.188097\pi\)
\(132\) 6.46321e9i 0.161279i
\(133\) −6.32571e9 −0.152003
\(134\) 2.69624e10i 0.624071i
\(135\) 2.44291e9 0.0544801
\(136\) 7.97086e10i 1.71321i
\(137\) 3.02579e10i 0.626954i 0.949596 + 0.313477i \(0.101494\pi\)
−0.949596 + 0.313477i \(0.898506\pi\)
\(138\) 2.64823e10 0.529128
\(139\) −6.74771e10 −1.30042 −0.650208 0.759756i \(-0.725318\pi\)
−0.650208 + 0.759756i \(0.725318\pi\)
\(140\) −9.01336e7 −0.00167589
\(141\) 5.97606e10i 1.07231i
\(142\) −1.65933e10 −0.287403
\(143\) −3.37757e10 −0.564838
\(144\) 1.34508e10 0.217238
\(145\) 3.93211e8 0.00613460
\(146\) −6.64176e10 −1.00120
\(147\) 7.35278e10i 1.07119i
\(148\) 1.64570e10i 0.231762i
\(149\) 6.07433e10i 0.827117i 0.910478 + 0.413558i \(0.135714\pi\)
−0.910478 + 0.413558i \(0.864286\pi\)
\(150\) 7.91925e10 1.04286
\(151\) 4.24289e10i 0.540477i −0.962793 0.270238i \(-0.912898\pi\)
0.962793 0.270238i \(-0.0871025\pi\)
\(152\) −6.26696e10 −0.772394
\(153\) −3.44757e10 −0.411203
\(154\) 1.94586e10 0.224651
\(155\) 2.53042e9i 0.0282835i
\(156\) 6.26054e9i 0.0677624i
\(157\) 6.74501e10i 0.707105i 0.935415 + 0.353553i \(0.115027\pi\)
−0.935415 + 0.353553i \(0.884973\pi\)
\(158\) 3.45279e10i 0.350659i
\(159\) 6.10175e10i 0.600439i
\(160\) −1.68721e9 −0.0160905
\(161\) 1.13158e10i 0.104606i
\(162\) 1.24122e11i 1.11243i
\(163\) 4.69429e10i 0.407973i 0.978974 + 0.203987i \(0.0653899\pi\)
−0.978974 + 0.203987i \(0.934610\pi\)
\(164\) 7.32400e9 0.0617346
\(165\) −1.03352e10 −0.0845080
\(166\) 3.07784e10i 0.244178i
\(167\) 2.47736e10 0.190725 0.0953623 0.995443i \(-0.469599\pi\)
0.0953623 + 0.995443i \(0.469599\pi\)
\(168\) 3.26263e10i 0.243793i
\(169\) −1.05142e11 −0.762680
\(170\) −1.40905e10 −0.0992386
\(171\) 2.71060e10i 0.185389i
\(172\) −1.12241e10 1.49693e10i −0.0745603 0.0994395i
\(173\) 1.71294e11 1.10538 0.552690 0.833387i \(-0.313601\pi\)
0.552690 + 0.833387i \(0.313601\pi\)
\(174\) 1.57347e10i 0.0986534i
\(175\) 3.38388e10i 0.206169i
\(176\) 1.68443e11 0.997445
\(177\) 1.26094e11i 0.725820i
\(178\) 2.07586e11 1.16171
\(179\) 2.81260e11i 1.53054i 0.643712 + 0.765268i \(0.277394\pi\)
−0.643712 + 0.765268i \(0.722606\pi\)
\(180\) 3.86227e8i 0.00204400i
\(181\) −9.21860e10 −0.474539 −0.237270 0.971444i \(-0.576252\pi\)
−0.237270 + 0.971444i \(0.576252\pi\)
\(182\) −1.88484e10 −0.0943882
\(183\) −3.59995e11 −1.75405
\(184\) 1.12107e11i 0.531551i
\(185\) −2.63160e10 −0.121440
\(186\) 1.01257e11 0.454841
\(187\) −4.31735e11 −1.88803
\(188\) 2.79669e10 0.119084
\(189\) 4.17704e10 0.173205
\(190\) 1.10784e10i 0.0447414i
\(191\) 1.41848e11i 0.558029i −0.960287 0.279015i \(-0.909992\pi\)
0.960287 0.279015i \(-0.0900078\pi\)
\(192\) 3.18722e11i 1.22154i
\(193\) 3.49463e11 1.30501 0.652507 0.757783i \(-0.273717\pi\)
0.652507 + 0.757783i \(0.273717\pi\)
\(194\) 2.69998e11i 0.982543i
\(195\) 1.00111e10 0.0355065
\(196\) 3.44097e10 0.118960
\(197\) −7.75830e10 −0.261478 −0.130739 0.991417i \(-0.541735\pi\)
−0.130739 + 0.991417i \(0.541735\pi\)
\(198\) 8.33811e10i 0.273994i
\(199\) 5.02411e11i 1.60988i −0.593356 0.804940i \(-0.702197\pi\)
0.593356 0.804940i \(-0.297803\pi\)
\(200\) 3.35245e11i 1.04764i
\(201\) 2.44865e11i 0.746357i
\(202\) 3.07103e10i 0.0913119i
\(203\) 6.72339e9 0.0195033
\(204\) 8.00248e10i 0.226503i
\(205\) 1.17116e10i 0.0323481i
\(206\) 3.52585e11i 0.950446i
\(207\) −4.84889e10 −0.127582
\(208\) −1.63161e11 −0.419082
\(209\) 3.39445e11i 0.851212i
\(210\) −5.76751e9 −0.0141219
\(211\) 6.06724e11i 1.45070i −0.688378 0.725352i \(-0.741677\pi\)
0.688378 0.725352i \(-0.258323\pi\)
\(212\) 2.85551e10 0.0666814
\(213\) 1.50696e11 0.343720
\(214\) 2.99553e11i 0.667430i
\(215\) −2.39370e10 + 1.79481e10i −0.0521049 + 0.0390685i
\(216\) 4.13825e11 0.880133
\(217\) 4.32667e10i 0.0899199i
\(218\) 6.83237e11i 1.38768i
\(219\) 6.03187e11 1.19738
\(220\) 4.83667e9i 0.00938498i
\(221\) 4.18197e11 0.793266
\(222\) 1.05306e12i 1.95293i
\(223\) 3.47401e11i 0.629951i 0.949100 + 0.314976i \(0.101996\pi\)
−0.949100 + 0.314976i \(0.898004\pi\)
\(224\) −2.88491e10 −0.0511555
\(225\) −1.45001e11 −0.251454
\(226\) −1.52649e11 −0.258911
\(227\) 2.92541e11i 0.485352i 0.970107 + 0.242676i \(0.0780252\pi\)
−0.970107 + 0.242676i \(0.921975\pi\)
\(228\) 6.29183e10 0.102118
\(229\) 3.34745e11 0.531540 0.265770 0.964036i \(-0.414374\pi\)
0.265770 + 0.964036i \(0.414374\pi\)
\(230\) −1.98178e10 −0.0307904
\(231\) −1.76718e11 −0.268671
\(232\) 6.66095e10 0.0991052
\(233\) 9.55518e11i 1.39142i 0.718321 + 0.695711i \(0.244911\pi\)
−0.718321 + 0.695711i \(0.755089\pi\)
\(234\) 8.07664e10i 0.115120i
\(235\) 4.47212e10i 0.0623985i
\(236\) 5.90098e10 0.0806054
\(237\) 3.13573e11i 0.419370i
\(238\) −2.40928e11 −0.315503
\(239\) 1.01652e12 1.30355 0.651773 0.758414i \(-0.274026\pi\)
0.651773 + 0.758414i \(0.274026\pi\)
\(240\) −4.99263e10 −0.0627008
\(241\) 4.87485e11i 0.599620i 0.953999 + 0.299810i \(0.0969233\pi\)
−0.953999 + 0.299810i \(0.903077\pi\)
\(242\) 2.67463e11i 0.322245i
\(243\) 4.18446e11i 0.493865i
\(244\) 1.68471e11i 0.194795i
\(245\) 5.50237e10i 0.0623332i
\(246\) 4.68651e11 0.520205
\(247\) 3.28800e11i 0.357641i
\(248\) 4.28649e11i 0.456924i
\(249\) 2.79521e11i 0.292024i
\(250\) −1.18778e11 −0.121629
\(251\) −1.82489e12 −1.83176 −0.915880 0.401453i \(-0.868505\pi\)
−0.915880 + 0.401453i \(0.868505\pi\)
\(252\) 6.60398e9i 0.00649834i
\(253\) −6.07220e11 −0.585792
\(254\) 1.40700e12i 1.33084i
\(255\) 1.27966e11 0.118684
\(256\) −4.03372e11 −0.366865
\(257\) 2.84410e11i 0.253676i 0.991923 + 0.126838i \(0.0404828\pi\)
−0.991923 + 0.126838i \(0.959517\pi\)
\(258\) −7.18210e11 9.57862e11i −0.628280 0.837923i
\(259\) −4.49968e11 −0.386085
\(260\) 4.68500e9i 0.00394315i
\(261\) 2.88101e10i 0.0237871i
\(262\) −1.28728e12 −1.04272
\(263\) 3.79504e11i 0.301604i 0.988564 + 0.150802i \(0.0481856\pi\)
−0.988564 + 0.150802i \(0.951814\pi\)
\(264\) −1.75077e12 −1.36524
\(265\) 4.56618e10i 0.0349401i
\(266\) 1.89426e11i 0.142243i
\(267\) −1.88524e12 −1.38935
\(268\) −1.14592e11 −0.0828861
\(269\) 4.04745e11 0.287356 0.143678 0.989625i \(-0.454107\pi\)
0.143678 + 0.989625i \(0.454107\pi\)
\(270\) 7.31539e10i 0.0509822i
\(271\) 2.37135e12 1.62237 0.811183 0.584793i \(-0.198824\pi\)
0.811183 + 0.584793i \(0.198824\pi\)
\(272\) −2.08559e12 −1.40083
\(273\) 1.71176e11 0.112883
\(274\) 9.06085e11 0.586700
\(275\) −1.81583e12 −1.15455
\(276\) 1.12552e11i 0.0702763i
\(277\) 2.24997e12i 1.37968i −0.723964 0.689838i \(-0.757682\pi\)
0.723964 0.689838i \(-0.242318\pi\)
\(278\) 2.02063e12i 1.21692i
\(279\) −1.85400e11 −0.109670
\(280\) 2.44155e10i 0.0141865i
\(281\) −7.18647e11 −0.410189 −0.205094 0.978742i \(-0.565750\pi\)
−0.205094 + 0.978742i \(0.565750\pi\)
\(282\) 1.78956e12 1.00346
\(283\) 2.12573e12 1.17105 0.585527 0.810653i \(-0.300888\pi\)
0.585527 + 0.810653i \(0.300888\pi\)
\(284\) 7.05231e10i 0.0381715i
\(285\) 1.00611e11i 0.0535084i
\(286\) 1.01143e12i 0.528572i
\(287\) 2.00253e11i 0.102842i
\(288\) 1.23620e11i 0.0623917i
\(289\) 3.32957e12 1.65158
\(290\) 1.17749e10i 0.00574072i
\(291\) 2.45205e12i 1.17507i
\(292\) 2.82281e11i 0.132974i
\(293\) 3.97847e12 1.84237 0.921187 0.389121i \(-0.127221\pi\)
0.921187 + 0.389121i \(0.127221\pi\)
\(294\) 2.20182e12 1.00241
\(295\) 9.43612e10i 0.0422361i
\(296\) −4.45789e12 −1.96187
\(297\) 2.24145e12i 0.969944i
\(298\) 1.81898e12 0.774012
\(299\) 5.88179e11 0.246124
\(300\) 3.36575e11i 0.138508i
\(301\) −4.09292e11 + 3.06889e11i −0.165653 + 0.124208i
\(302\) −1.27055e12 −0.505775
\(303\) 2.78903e11i 0.109204i
\(304\) 1.63976e12i 0.631557i
\(305\) 2.69399e11 0.102070
\(306\) 1.03239e12i 0.384802i
\(307\) 2.68118e11 0.0983183 0.0491591 0.998791i \(-0.484346\pi\)
0.0491591 + 0.998791i \(0.484346\pi\)
\(308\) 8.27007e10i 0.0298370i
\(309\) 3.20208e12i 1.13668i
\(310\) −7.57744e10 −0.0264676
\(311\) −1.56641e12 −0.538399 −0.269199 0.963084i \(-0.586759\pi\)
−0.269199 + 0.963084i \(0.586759\pi\)
\(312\) 1.69586e12 0.573612
\(313\) 2.16661e11i 0.0721205i −0.999350 0.0360602i \(-0.988519\pi\)
0.999350 0.0360602i \(-0.0114808\pi\)
\(314\) 2.01982e12 0.661706
\(315\) 1.05603e10 0.00340504
\(316\) 1.46747e11 0.0465729
\(317\) −4.92724e11 −0.153924 −0.0769622 0.997034i \(-0.524522\pi\)
−0.0769622 + 0.997034i \(0.524522\pi\)
\(318\) 1.82720e12 0.561888
\(319\) 3.60785e11i 0.109218i
\(320\) 2.38512e11i 0.0710822i
\(321\) 2.72046e12i 0.798211i
\(322\) −3.38857e11 −0.0978898
\(323\) 4.20287e12i 1.19545i
\(324\) −5.27529e11 −0.147748
\(325\) 1.75889e12 0.485089
\(326\) 1.40572e12 0.381779
\(327\) 6.20497e12i 1.65959i
\(328\) 1.98394e12i 0.522587i
\(329\) 7.64673e11i 0.198379i
\(330\) 3.09491e11i 0.0790822i
\(331\) 9.92385e11i 0.249770i 0.992171 + 0.124885i \(0.0398562\pi\)
−0.992171 + 0.124885i \(0.960144\pi\)
\(332\) 1.30811e11 0.0324305
\(333\) 1.92814e12i 0.470887i
\(334\) 7.41856e11i 0.178479i
\(335\) 1.83242e11i 0.0434311i
\(336\) −8.53673e11 −0.199340
\(337\) −5.53124e12 −1.27254 −0.636272 0.771465i \(-0.719524\pi\)
−0.636272 + 0.771465i \(0.719524\pi\)
\(338\) 3.14852e12i 0.713712i
\(339\) 1.38632e12 0.309645
\(340\) 5.98857e10i 0.0131804i
\(341\) −2.32174e12 −0.503550
\(342\) 8.11701e11 0.173486
\(343\) 1.92380e12i 0.405219i
\(344\) −4.05491e12 + 3.04039e12i −0.841761 + 0.631157i
\(345\) 1.79980e11 0.0368237
\(346\) 5.12947e12i 1.03441i
\(347\) 1.35809e12i 0.269948i −0.990849 0.134974i \(-0.956905\pi\)
0.990849 0.134974i \(-0.0430951\pi\)
\(348\) −6.68738e10 −0.0131027
\(349\) 5.27222e12i 1.01828i −0.860684 0.509139i \(-0.829964\pi\)
0.860684 0.509139i \(-0.170036\pi\)
\(350\) −1.01332e12 −0.192932
\(351\) 2.17116e12i 0.407527i
\(352\) 1.54808e12i 0.286470i
\(353\) −7.41122e12 −1.35212 −0.676062 0.736845i \(-0.736315\pi\)
−0.676062 + 0.736845i \(0.736315\pi\)
\(354\) 3.77595e12 0.679218
\(355\) −1.12772e11 −0.0200013
\(356\) 8.82259e11i 0.154293i
\(357\) 2.18805e12 0.377325
\(358\) 8.42247e12 1.43227
\(359\) −6.00592e12 −1.00718 −0.503591 0.863942i \(-0.667988\pi\)
−0.503591 + 0.863942i \(0.667988\pi\)
\(360\) 1.04622e11 0.0173026
\(361\) 2.82663e12 0.461034
\(362\) 2.76055e12i 0.444071i
\(363\) 2.42902e12i 0.385389i
\(364\) 8.01074e10i 0.0125362i
\(365\) −4.51389e11 −0.0696765
\(366\) 1.07802e13i 1.64143i
\(367\) 9.10870e11 0.136813 0.0684063 0.997658i \(-0.478209\pi\)
0.0684063 + 0.997658i \(0.478209\pi\)
\(368\) −2.93331e12 −0.434629
\(369\) −8.58097e11 −0.125431
\(370\) 7.88043e11i 0.113643i
\(371\) 7.80756e11i 0.111083i
\(372\) 4.30350e11i 0.0604098i
\(373\) 1.18703e13i 1.64406i 0.569443 + 0.822031i \(0.307159\pi\)
−0.569443 + 0.822031i \(0.692841\pi\)
\(374\) 1.29285e13i 1.76681i
\(375\) 1.07871e12 0.145462
\(376\) 7.57572e12i 1.00806i
\(377\) 3.49471e11i 0.0458886i
\(378\) 1.25083e12i 0.162084i
\(379\) 6.13117e12 0.784056 0.392028 0.919953i \(-0.371774\pi\)
0.392028 + 0.919953i \(0.371774\pi\)
\(380\) −4.70842e10 −0.00594234
\(381\) 1.27780e13i 1.59161i
\(382\) −4.24771e12 −0.522201
\(383\) 1.63650e13i 1.98574i 0.119205 + 0.992870i \(0.461965\pi\)
−0.119205 + 0.992870i \(0.538035\pi\)
\(384\) −7.23555e12 −0.866594
\(385\) 1.32245e11 0.0156342
\(386\) 1.04648e13i 1.22123i
\(387\) 1.31504e12 + 1.75384e12i 0.151490 + 0.202039i
\(388\) 1.14751e12 0.130497
\(389\) 7.49710e12i 0.841677i 0.907136 + 0.420839i \(0.138264\pi\)
−0.907136 + 0.420839i \(0.861736\pi\)
\(390\) 2.99786e11i 0.0332268i
\(391\) 7.51836e12 0.822695
\(392\) 9.32095e12i 1.00700i
\(393\) 1.16907e13 1.24703
\(394\) 2.32326e12i 0.244690i
\(395\) 2.34659e11i 0.0244035i
\(396\) 3.54377e11 0.0363906
\(397\) −1.07340e13 −1.08845 −0.544227 0.838938i \(-0.683177\pi\)
−0.544227 + 0.838938i \(0.683177\pi\)
\(398\) −1.50449e13 −1.50652
\(399\) 1.72032e12i 0.170116i
\(400\) −8.77175e12 −0.856616
\(401\) −8.46435e12 −0.816341 −0.408171 0.912906i \(-0.633833\pi\)
−0.408171 + 0.912906i \(0.633833\pi\)
\(402\) −7.33259e12 −0.698437
\(403\) 2.24894e12 0.211569
\(404\) 1.30521e11 0.0121276
\(405\) 8.43560e11i 0.0774178i
\(406\) 2.01335e11i 0.0182511i
\(407\) 2.41458e13i 2.16207i
\(408\) 2.16773e13 1.91736
\(409\) 6.90427e12i 0.603255i 0.953426 + 0.301628i \(0.0975299\pi\)
−0.953426 + 0.301628i \(0.902470\pi\)
\(410\) −3.50710e11 −0.0302711
\(411\) −8.22882e12 −0.701663
\(412\) −1.49852e12 −0.126234
\(413\) 1.61345e12i 0.134278i
\(414\) 1.45202e12i 0.119391i
\(415\) 2.09177e11i 0.0169931i
\(416\) 1.49953e12i 0.120362i
\(417\) 1.83508e13i 1.45538i
\(418\) 1.01648e13 0.796560
\(419\) 3.78990e12i 0.293466i 0.989176 + 0.146733i \(0.0468758\pi\)
−0.989176 + 0.146733i \(0.953124\pi\)
\(420\) 2.45124e10i 0.00187560i
\(421\) 2.61396e12i 0.197646i 0.995105 + 0.0988229i \(0.0315077\pi\)
−0.995105 + 0.0988229i \(0.968492\pi\)
\(422\) −1.81686e13 −1.35756
\(423\) −3.27667e12 −0.241953
\(424\) 7.73505e12i 0.564461i
\(425\) 2.24828e13 1.62146
\(426\) 4.51266e12i 0.321651i
\(427\) 4.60636e12 0.324503
\(428\) −1.27313e12 −0.0886448
\(429\) 9.18551e12i 0.632145i
\(430\) 5.37465e11 + 7.16805e11i 0.0365601 + 0.0487595i
\(431\) 5.30690e12 0.356824 0.178412 0.983956i \(-0.442904\pi\)
0.178412 + 0.983956i \(0.442904\pi\)
\(432\) 1.08278e13i 0.719651i
\(433\) 9.50518e12i 0.624484i 0.950003 + 0.312242i \(0.101080\pi\)
−0.950003 + 0.312242i \(0.898920\pi\)
\(434\) −1.29564e12 −0.0841465
\(435\) 1.06936e11i 0.00686561i
\(436\) −2.90382e12 −0.184305
\(437\) 5.91119e12i 0.370909i
\(438\) 1.80627e13i 1.12050i
\(439\) 2.23920e13 1.37332 0.686658 0.726980i \(-0.259077\pi\)
0.686658 + 0.726980i \(0.259077\pi\)
\(440\) 1.31017e12 0.0794443
\(441\) −4.03152e12 −0.241699
\(442\) 1.25231e13i 0.742335i
\(443\) −1.73807e12 −0.101870 −0.0509352 0.998702i \(-0.516220\pi\)
−0.0509352 + 0.998702i \(0.516220\pi\)
\(444\) 4.47558e12 0.259379
\(445\) 1.41080e12 0.0808473
\(446\) 1.04031e13 0.589505
\(447\) −1.65195e13 −0.925678
\(448\) 4.07824e12i 0.225987i
\(449\) 1.71473e13i 0.939647i −0.882760 0.469823i \(-0.844318\pi\)
0.882760 0.469823i \(-0.155682\pi\)
\(450\) 4.34212e12i 0.235309i
\(451\) −1.07458e13 −0.575913
\(452\) 6.48770e11i 0.0343874i
\(453\) 1.15388e13 0.604881
\(454\) 8.76025e12 0.454190
\(455\) −1.28098e11 −0.00656878
\(456\) 1.70434e13i 0.864435i
\(457\) 2.13148e13i 1.06930i −0.845073 0.534651i \(-0.820443\pi\)
0.845073 0.534651i \(-0.179557\pi\)
\(458\) 1.00241e13i 0.497413i
\(459\) 2.77527e13i 1.36220i
\(460\) 8.42272e10i 0.00408944i
\(461\) −2.53916e13 −1.21951 −0.609754 0.792590i \(-0.708732\pi\)
−0.609754 + 0.792590i \(0.708732\pi\)
\(462\) 5.29189e12i 0.251421i
\(463\) 1.86225e13i 0.875254i 0.899157 + 0.437627i \(0.144181\pi\)
−0.899157 + 0.437627i \(0.855819\pi\)
\(464\) 1.74285e12i 0.0810346i
\(465\) 6.88163e11 0.0316539
\(466\) 2.86134e13 1.30209
\(467\) 2.68346e13i 1.20812i 0.796938 + 0.604062i \(0.206452\pi\)
−0.796938 + 0.604062i \(0.793548\pi\)
\(468\) −3.43264e11 −0.0152897
\(469\) 3.13320e12i 0.138078i
\(470\) −1.33920e12 −0.0583922
\(471\) −1.83435e13 −0.791366
\(472\) 1.59847e13i 0.682329i
\(473\) 1.64680e13 + 2.19631e13i 0.695563 + 0.927657i
\(474\) 9.39009e12 0.392444
\(475\) 1.76768e13i 0.731029i
\(476\) 1.02397e12i 0.0419035i
\(477\) −3.34558e12 −0.135482
\(478\) 3.04401e13i 1.21985i
\(479\) −7.59261e12 −0.301102 −0.150551 0.988602i \(-0.548105\pi\)
−0.150551 + 0.988602i \(0.548105\pi\)
\(480\) 4.58849e11i 0.0180079i
\(481\) 2.33887e13i 0.908406i
\(482\) 1.45980e13 0.561121
\(483\) 3.07741e12 0.117071
\(484\) 1.13674e12 0.0427991
\(485\) 1.83496e12i 0.0683784i
\(486\) −1.25306e13 −0.462156
\(487\) −2.06304e13 −0.753116 −0.376558 0.926393i \(-0.622892\pi\)
−0.376558 + 0.926393i \(0.622892\pi\)
\(488\) 4.56358e13 1.64895
\(489\) −1.27664e13 −0.456588
\(490\) −1.64771e12 −0.0583311
\(491\) 5.74792e10i 0.00201420i 0.999999 + 0.00100710i \(0.000320570\pi\)
−0.999999 + 0.00100710i \(0.999679\pi\)
\(492\) 1.99181e12i 0.0690911i
\(493\) 4.46709e12i 0.153388i
\(494\) −9.84607e12 −0.334679
\(495\) 5.66676e11i 0.0190682i
\(496\) −1.12157e13 −0.373609
\(497\) −1.92825e12 −0.0635889
\(498\) 8.37039e12 0.273274
\(499\) 3.88299e13i 1.25506i −0.778594 0.627528i \(-0.784067\pi\)
0.778594 0.627528i \(-0.215933\pi\)
\(500\) 5.04818e11i 0.0161542i
\(501\) 6.73734e12i 0.213452i
\(502\) 5.46472e13i 1.71415i
\(503\) 5.96465e13i 1.85244i 0.376978 + 0.926222i \(0.376963\pi\)
−0.376978 + 0.926222i \(0.623037\pi\)
\(504\) 1.78890e12 0.0550088
\(505\) 2.08714e11i 0.00635469i
\(506\) 1.81835e13i 0.548182i
\(507\) 2.85940e13i 0.853563i
\(508\) −5.97986e12 −0.176755
\(509\) 9.68042e12 0.283338 0.141669 0.989914i \(-0.454753\pi\)
0.141669 + 0.989914i \(0.454753\pi\)
\(510\) 3.83199e12i 0.111064i
\(511\) −7.71815e12 −0.221518
\(512\) 3.93232e13i 1.11763i
\(513\) 2.18201e13 0.614145
\(514\) 8.51677e12 0.237388
\(515\) 2.39624e12i 0.0661446i
\(516\) 4.07100e12 3.05246e12i 0.111289 0.0834451i
\(517\) −4.10333e13 −1.11092
\(518\) 1.34745e13i 0.361297i
\(519\) 4.65845e13i 1.23710i
\(520\) −1.26908e12 −0.0333790
\(521\) 2.61386e13i 0.680916i −0.940260 0.340458i \(-0.889418\pi\)
0.940260 0.340458i \(-0.110582\pi\)
\(522\) −8.62731e11 −0.0222599
\(523\) 4.15936e12i 0.106296i 0.998587 + 0.0531482i \(0.0169256\pi\)
−0.998587 + 0.0531482i \(0.983074\pi\)
\(524\) 5.47104e12i 0.138489i
\(525\) 9.20267e12 0.230737
\(526\) 1.13644e13 0.282239
\(527\) 2.87469e13 0.707193
\(528\) 4.58091e13i 1.11630i
\(529\) −3.08522e13 −0.744745
\(530\) −1.36736e12 −0.0326967
\(531\) −6.91373e12 −0.163772
\(532\) −8.05077e11 −0.0188921
\(533\) 1.04089e13 0.241973
\(534\) 5.64544e13i 1.30014i
\(535\) 2.03583e12i 0.0464486i
\(536\) 3.10410e13i 0.701635i
\(537\) −7.64906e13 −1.71292
\(538\) 1.21203e13i 0.268906i
\(539\) −5.04861e13 −1.10976
\(540\) 3.10910e11 0.00677121
\(541\) 2.48861e13 0.536995 0.268497 0.963280i \(-0.413473\pi\)
0.268497 + 0.963280i \(0.413473\pi\)
\(542\) 7.10110e13i 1.51820i
\(543\) 2.50706e13i 0.531086i
\(544\) 1.91677e13i 0.402323i
\(545\) 4.64343e12i 0.0965731i
\(546\) 5.12595e12i 0.105636i
\(547\) −8.18220e13 −1.67083 −0.835417 0.549616i \(-0.814774\pi\)
−0.835417 + 0.549616i \(0.814774\pi\)
\(548\) 3.85094e12i 0.0779227i
\(549\) 1.97385e13i 0.395779i
\(550\) 5.43757e13i 1.08042i
\(551\) 3.51218e12 0.0691542
\(552\) 3.04883e13 0.594892
\(553\) 4.01236e12i 0.0775844i
\(554\) −6.73762e13 −1.29109
\(555\) 7.15680e12i 0.135911i
\(556\) −8.58786e12 −0.161626
\(557\) 4.67918e13 0.872758 0.436379 0.899763i \(-0.356261\pi\)
0.436379 + 0.899763i \(0.356261\pi\)
\(558\) 5.55190e12i 0.102629i
\(559\) −1.59516e13 2.12744e13i −0.292244 0.389760i
\(560\) 6.38837e11 0.0115998
\(561\) 1.17413e14i 2.11301i
\(562\) 2.15202e13i 0.383853i
\(563\) −5.92155e13 −1.04687 −0.523436 0.852065i \(-0.675350\pi\)
−0.523436 + 0.852065i \(0.675350\pi\)
\(564\) 7.60578e12i 0.133275i
\(565\) −1.03743e12 −0.0180185
\(566\) 6.36560e13i 1.09587i
\(567\) 1.44237e13i 0.246129i
\(568\) −1.91034e13 −0.323124
\(569\) 1.03745e14 1.73943 0.869714 0.493556i \(-0.164303\pi\)
0.869714 + 0.493556i \(0.164303\pi\)
\(570\) −3.01284e12 −0.0500729
\(571\) 5.54780e12i 0.0913988i −0.998955 0.0456994i \(-0.985448\pi\)
0.998955 0.0456994i \(-0.0145516\pi\)
\(572\) −4.29865e12 −0.0702025
\(573\) 3.85765e13 0.624525
\(574\) −5.99668e12 −0.0962390
\(575\) 3.16213e13 0.503085
\(576\) 1.74755e13 0.275624
\(577\) 1.06287e14i 1.66189i 0.556355 + 0.830945i \(0.312200\pi\)
−0.556355 + 0.830945i \(0.687800\pi\)
\(578\) 9.97055e13i 1.54554i
\(579\) 9.50388e13i 1.46052i
\(580\) 5.00443e10 0.000762456
\(581\) 3.57665e12i 0.0540251i
\(582\) 7.34276e13 1.09963
\(583\) −4.18963e13 −0.622061
\(584\) −7.64647e13 −1.12563
\(585\) 5.48906e11i 0.00801159i
\(586\) 1.19137e14i 1.72408i
\(587\) 5.54347e13i 0.795411i −0.917513 0.397705i \(-0.869807\pi\)
0.917513 0.397705i \(-0.130193\pi\)
\(588\) 9.35793e12i 0.133135i
\(589\) 2.26018e13i 0.318835i
\(590\) −2.82569e12 −0.0395243
\(591\) 2.10992e13i 0.292637i
\(592\) 1.16642e14i 1.60415i
\(593\) 1.23403e14i 1.68288i 0.540349 + 0.841441i \(0.318292\pi\)
−0.540349 + 0.841441i \(0.681708\pi\)
\(594\) −6.71212e13 −0.907669
\(595\) −1.63740e12 −0.0219569
\(596\) 7.73084e12i 0.102801i
\(597\) 1.36634e14 1.80172
\(598\) 1.76133e13i 0.230321i
\(599\) 5.75412e13 0.746182 0.373091 0.927795i \(-0.378298\pi\)
0.373091 + 0.927795i \(0.378298\pi\)
\(600\) 9.11721e13 1.17248
\(601\) 1.12470e14i 1.43437i −0.696881 0.717187i \(-0.745429\pi\)
0.696881 0.717187i \(-0.254571\pi\)
\(602\) 9.18994e12 + 1.22564e13i 0.116233 + 0.155018i
\(603\) 1.34259e13 0.168406
\(604\) 5.39996e12i 0.0671747i
\(605\) 1.81773e12i 0.0224261i
\(606\) 8.35187e12 0.102193
\(607\) 1.14155e13i 0.138532i 0.997598 + 0.0692659i \(0.0220657\pi\)
−0.997598 + 0.0692659i \(0.977934\pi\)
\(608\) −1.50703e13 −0.181386
\(609\) 1.82847e12i 0.0218274i
\(610\) 8.06726e12i 0.0955161i
\(611\) 3.97465e13 0.466760
\(612\) −4.38775e12 −0.0511075
\(613\) 1.42106e14 1.64177 0.820883 0.571096i \(-0.193482\pi\)
0.820883 + 0.571096i \(0.193482\pi\)
\(614\) 8.02892e12i 0.0920058i
\(615\) 3.18506e12 0.0362027
\(616\) 2.24021e13 0.252572
\(617\) 6.74557e13 0.754384 0.377192 0.926135i \(-0.376890\pi\)
0.377192 + 0.926135i \(0.376890\pi\)
\(618\) −9.58877e13 −1.06370
\(619\) 2.48391e13 0.273327 0.136664 0.990618i \(-0.456362\pi\)
0.136664 + 0.990618i \(0.456362\pi\)
\(620\) 3.22048e11i 0.00351530i
\(621\) 3.90333e13i 0.422646i
\(622\) 4.69069e13i 0.503831i
\(623\) 2.41228e13 0.257032
\(624\) 4.43726e13i 0.469021i
\(625\) 9.41557e13 0.987294
\(626\) −6.48800e12 −0.0674900
\(627\) −9.23142e13 −0.952644
\(628\) 8.58442e12i 0.0878846i
\(629\) 2.98964e14i 3.03644i
\(630\) 3.16232e11i 0.00318642i
\(631\) 6.71070e13i 0.670843i 0.942068 + 0.335422i \(0.108879\pi\)
−0.942068 + 0.335422i \(0.891121\pi\)
\(632\) 3.97510e13i 0.394242i
\(633\) 1.65003e14 1.62357
\(634\) 1.47548e13i 0.144042i
\(635\) 9.56225e12i 0.0926172i
\(636\) 7.76575e12i 0.0746273i
\(637\) 4.89030e13 0.466271
\(638\) −1.08039e13 −0.102206
\(639\) 8.26265e12i 0.0775560i
\(640\) 5.41465e12 0.0504278
\(641\) 1.30587e14i 1.20673i 0.797465 + 0.603365i \(0.206174\pi\)
−0.797465 + 0.603365i \(0.793826\pi\)
\(642\) −8.14655e13 −0.746962
\(643\) −8.09113e13 −0.736130 −0.368065 0.929800i \(-0.619980\pi\)
−0.368065 + 0.929800i \(0.619980\pi\)
\(644\) 1.44017e12i 0.0130013i
\(645\) −4.88111e12 6.50984e12i −0.0437240 0.0583138i
\(646\) −1.25857e14 −1.11870
\(647\) 8.55615e13i 0.754669i −0.926077 0.377335i \(-0.876841\pi\)
0.926077 0.377335i \(-0.123159\pi\)
\(648\) 1.42898e14i 1.25069i
\(649\) −8.65797e13 −0.751956
\(650\) 5.26706e13i 0.453943i
\(651\) 1.17667e13 0.100635
\(652\) 5.97445e12i 0.0507061i
\(653\) 1.61973e14i 1.36420i −0.731259 0.682100i \(-0.761067\pi\)
0.731259 0.682100i \(-0.238933\pi\)
\(654\) −1.85811e14 −1.55304
\(655\) −8.74862e12 −0.0725660
\(656\) −5.19101e13 −0.427300
\(657\) 3.30727e13i 0.270173i
\(658\) −2.28985e13 −0.185642
\(659\) −8.60337e13 −0.692216 −0.346108 0.938195i \(-0.612497\pi\)
−0.346108 + 0.938195i \(0.612497\pi\)
\(660\) −1.31536e12 −0.0105033
\(661\) −1.67477e14 −1.32723 −0.663617 0.748073i \(-0.730979\pi\)
−0.663617 + 0.748073i \(0.730979\pi\)
\(662\) 2.97174e13 0.233734
\(663\) 1.13731e14i 0.887794i
\(664\) 3.54343e13i 0.274526i
\(665\) 1.28738e12i 0.00989917i
\(666\) 5.77390e13 0.440654
\(667\) 6.28281e12i 0.0475910i
\(668\) 3.15295e12 0.0237047
\(669\) −9.44780e13 −0.705018
\(670\) 5.48726e12 0.0406426
\(671\) 2.47182e14i 1.81721i
\(672\) 7.84571e12i 0.0572514i
\(673\) 2.30784e14i 1.67159i −0.549039 0.835797i \(-0.685006\pi\)
0.549039 0.835797i \(-0.314994\pi\)
\(674\) 1.65635e14i 1.19084i
\(675\) 1.16725e14i 0.832998i
\(676\) −1.33815e13 −0.0947919
\(677\) 8.43691e13i 0.593253i 0.954994 + 0.296627i \(0.0958617\pi\)
−0.954994 + 0.296627i \(0.904138\pi\)
\(678\) 4.15138e13i 0.289764i
\(679\) 3.13754e13i 0.217391i
\(680\) −1.62219e13 −0.111573
\(681\) −7.95583e13 −0.543188
\(682\) 6.95256e13i 0.471219i
\(683\) 1.33475e14 0.898038 0.449019 0.893522i \(-0.351773\pi\)
0.449019 + 0.893522i \(0.351773\pi\)
\(684\) 3.44980e12i 0.0230416i
\(685\) 6.15795e12 0.0408304
\(686\) −5.76091e13 −0.379202
\(687\) 9.10360e13i 0.594880i
\(688\) 7.95525e13 + 1.06097e14i 0.516073 + 0.688276i
\(689\) 4.05825e13 0.261362
\(690\) 5.38957e12i 0.0344595i
\(691\) 2.31962e14i 1.47240i 0.676764 + 0.736200i \(0.263382\pi\)
−0.676764 + 0.736200i \(0.736618\pi\)
\(692\) 2.18007e13 0.137385
\(693\) 9.68941e12i 0.0606221i
\(694\) −4.06685e13 −0.252616
\(695\) 1.37327e13i 0.0846897i
\(696\) 1.81149e13i 0.110915i
\(697\) 1.33050e14 0.808821
\(698\) −1.57879e14 −0.952900
\(699\) −2.59859e14 −1.55723
\(700\) 4.30668e12i 0.0256243i
\(701\) 5.99175e13 0.353968 0.176984 0.984214i \(-0.443366\pi\)
0.176984 + 0.984214i \(0.443366\pi\)
\(702\) 6.50164e13 0.381362
\(703\) −2.35055e14 −1.36897
\(704\) 2.18843e14 1.26552
\(705\) 1.21622e13 0.0698341
\(706\) 2.21932e14i 1.26531i
\(707\) 3.56873e12i 0.0202030i
\(708\) 1.60481e13i 0.0902106i
\(709\) 2.44977e14 1.36740 0.683698 0.729765i \(-0.260370\pi\)
0.683698 + 0.729765i \(0.260370\pi\)
\(710\) 3.37700e12i 0.0187171i
\(711\) −1.71932e13 −0.0946256
\(712\) 2.38988e14 1.30610
\(713\) 4.04315e13 0.219418
\(714\) 6.55220e13i 0.353099i
\(715\) 6.87388e12i 0.0367851i
\(716\) 3.57962e13i 0.190227i
\(717\) 2.76449e14i 1.45888i
\(718\) 1.79850e14i 0.942515i
\(719\) 1.12367e14 0.584785 0.292392 0.956298i \(-0.405549\pi\)
0.292392 + 0.956298i \(0.405549\pi\)
\(720\) 2.73745e12i 0.0141476i
\(721\) 4.09726e13i 0.210289i
\(722\) 8.46447e13i 0.431433i
\(723\) −1.32575e14 −0.671072
\(724\) −1.17326e13 −0.0589794
\(725\) 1.87881e13i 0.0937977i
\(726\) 7.27382e13 0.360645
\(727\) 2.03887e14i 1.00396i 0.864878 + 0.501982i \(0.167396\pi\)
−0.864878 + 0.501982i \(0.832604\pi\)
\(728\) −2.16996e13 −0.106119
\(729\) −1.30955e14 −0.636041
\(730\) 1.35170e13i 0.0652029i
\(731\) −2.03901e14 2.71938e14i −0.976858 1.30281i
\(732\) −4.58169e13 −0.218007
\(733\) 1.40792e14i 0.665362i −0.943039 0.332681i \(-0.892047\pi\)
0.943039 0.332681i \(-0.107953\pi\)
\(734\) 2.72764e13i 0.128028i
\(735\) 1.49641e13 0.0697610
\(736\) 2.69587e13i 0.124827i
\(737\) 1.68131e14 0.773233
\(738\) 2.56961e13i 0.117378i
\(739\) 5.06958e13i 0.230012i −0.993365 0.115006i \(-0.963311\pi\)
0.993365 0.115006i \(-0.0366887\pi\)
\(740\) −3.34925e12 −0.0150935
\(741\) 8.94194e13 0.400259
\(742\) −2.33801e13 −0.103951
\(743\) 3.77080e14i 1.66529i 0.553810 + 0.832643i \(0.313173\pi\)
−0.553810 + 0.832643i \(0.686827\pi\)
\(744\) 1.16574e14 0.511372
\(745\) 1.23622e13 0.0538660
\(746\) 3.55462e14 1.53850
\(747\) −1.53261e13 −0.0658915
\(748\) −5.49472e13 −0.234659
\(749\) 3.48100e13i 0.147671i
\(750\) 3.23025e13i 0.136122i
\(751\) 3.16255e14i 1.32385i 0.749571 + 0.661923i \(0.230260\pi\)
−0.749571 + 0.661923i \(0.769740\pi\)
\(752\) −1.98220e14 −0.824249
\(753\) 4.96291e14i 2.05004i
\(754\) 1.04651e13 0.0429423
\(755\) −8.63494e12 −0.0351985
\(756\) 5.31615e12 0.0215273
\(757\) 1.69500e14i 0.681853i −0.940090 0.340927i \(-0.889259\pi\)
0.940090 0.340927i \(-0.110741\pi\)
\(758\) 1.83601e14i 0.733716i
\(759\) 1.65138e14i 0.655597i
\(760\) 1.27542e13i 0.0503022i
\(761\) 4.88591e14i 1.91435i −0.289507 0.957176i \(-0.593491\pi\)
0.289507 0.957176i \(-0.406509\pi\)
\(762\) −3.82642e14 −1.48942
\(763\) 7.93964e13i 0.307028i
\(764\) 1.80531e13i 0.0693562i
\(765\) 7.01635e12i 0.0267796i
\(766\) 4.90057e14 1.85824
\(767\) 8.38647e13 0.315938
\(768\) 1.09700e14i 0.410582i
\(769\) −5.11989e14 −1.90383 −0.951917 0.306356i \(-0.900890\pi\)
−0.951917 + 0.306356i \(0.900890\pi\)
\(770\) 3.96013e12i 0.0146304i
\(771\) −7.73470e13 −0.283904
\(772\) 4.44764e13 0.162197
\(773\) 1.45115e14i 0.525792i −0.964824 0.262896i \(-0.915322\pi\)
0.964824 0.262896i \(-0.0846777\pi\)
\(774\) 5.25194e13 3.93794e13i 0.189067 0.141763i
\(775\) 1.20906e14 0.432454
\(776\) 3.10840e14i 1.10466i
\(777\) 1.22372e14i 0.432092i
\(778\) 2.24504e14 0.787637
\(779\) 1.04609e14i 0.364654i
\(780\) 1.27412e12