Properties

Label 43.11.b.b.42.8
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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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 42.8
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.27

$q$-expansion

\(f(q)\) \(=\) \(q-41.3871i q^{2} +57.8259i q^{3} -688.891 q^{4} -4608.97i q^{5} +2393.24 q^{6} -16533.3i q^{7} -13869.2i q^{8} +55705.2 q^{9} +O(q^{10})\) \(q-41.3871i q^{2} +57.8259i q^{3} -688.891 q^{4} -4608.97i q^{5} +2393.24 q^{6} -16533.3i q^{7} -13869.2i q^{8} +55705.2 q^{9} -190752. q^{10} +223001. q^{11} -39835.7i q^{12} +652651. q^{13} -684267. q^{14} +266518. q^{15} -1.27943e6 q^{16} -577282. q^{17} -2.30547e6i q^{18} -2.34685e6i q^{19} +3.17508e6i q^{20} +956055. q^{21} -9.22936e6i q^{22} -4.51196e6 q^{23} +801999. q^{24} -1.14770e7 q^{25} -2.70113e7i q^{26} +6.63576e6i q^{27} +1.13897e7i q^{28} +9.59476e6i q^{29} -1.10304e7i q^{30} +9.38059e6 q^{31} +3.87498e7i q^{32} +1.28952e7i q^{33} +2.38920e7i q^{34} -7.62017e7 q^{35} -3.83748e7 q^{36} +9.20205e7i q^{37} -9.71292e7 q^{38} +3.77401e7i q^{39} -6.39227e7 q^{40} -5.46246e7 q^{41} -3.95683e7i q^{42} +(1.46513e8 + 1.20552e7i) q^{43} -1.53623e8 q^{44} -2.56743e8i q^{45} +1.86737e8i q^{46} -5.77200e7 q^{47} -7.39842e7i q^{48} +9.12383e6 q^{49} +4.74999e8i q^{50} -3.33818e7i q^{51} -4.49605e8 q^{52} -3.80772e8 q^{53} +2.74635e8 q^{54} -1.02780e9i q^{55} -2.29304e8 q^{56} +1.35709e8 q^{57} +3.97099e8 q^{58} +5.64392e8 q^{59} -1.83602e8 q^{60} +6.10423e8i q^{61} -3.88235e8i q^{62} -9.20993e8i q^{63} +2.93605e8 q^{64} -3.00805e9i q^{65} +5.33696e8 q^{66} -1.39619e9 q^{67} +3.97684e8 q^{68} -2.60908e8i q^{69} +3.15377e9i q^{70} +2.86201e9i q^{71} -7.72586e8i q^{72} +2.78136e9i q^{73} +3.80846e9 q^{74} -6.63667e8i q^{75} +1.61672e9i q^{76} -3.68695e9i q^{77} +1.56195e9 q^{78} +3.46213e9 q^{79} +5.89685e9i q^{80} +2.90562e9 q^{81} +2.26075e9i q^{82} +3.22198e9 q^{83} -6.58617e8 q^{84} +2.66067e9i q^{85} +(4.98928e8 - 6.06376e9i) q^{86} -5.54826e8 q^{87} -3.09285e9i q^{88} +7.71319e8i q^{89} -1.06259e10 q^{90} -1.07905e10i q^{91} +3.10824e9 q^{92} +5.42441e8i q^{93} +2.38886e9i q^{94} -1.08166e10 q^{95} -2.24074e9 q^{96} +9.01361e9 q^{97} -3.77609e8i q^{98} +1.24223e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.3871i 1.29335i −0.762767 0.646673i \(-0.776160\pi\)
0.762767 0.646673i \(-0.223840\pi\)
\(3\) 57.8259i 0.237967i 0.992896 + 0.118983i \(0.0379635\pi\)
−0.992896 + 0.118983i \(0.962036\pi\)
\(4\) −688.891 −0.672745
\(5\) 4608.97i 1.47487i −0.675418 0.737435i \(-0.736037\pi\)
0.675418 0.737435i \(-0.263963\pi\)
\(6\) 2393.24 0.307773
\(7\) 16533.3i 0.983718i −0.870675 0.491859i \(-0.836318\pi\)
0.870675 0.491859i \(-0.163682\pi\)
\(8\) 13869.2i 0.423255i
\(9\) 55705.2 0.943372
\(10\) −190752. −1.90752
\(11\) 223001. 1.38466 0.692330 0.721581i \(-0.256584\pi\)
0.692330 + 0.721581i \(0.256584\pi\)
\(12\) 39835.7i 0.160091i
\(13\) 652651. 1.75778 0.878890 0.477025i \(-0.158285\pi\)
0.878890 + 0.477025i \(0.158285\pi\)
\(14\) −684267. −1.27229
\(15\) 266518. 0.350970
\(16\) −1.27943e6 −1.22016
\(17\) −577282. −0.406577 −0.203289 0.979119i \(-0.565163\pi\)
−0.203289 + 0.979119i \(0.565163\pi\)
\(18\) 2.30547e6i 1.22011i
\(19\) 2.34685e6i 0.947801i −0.880578 0.473900i \(-0.842846\pi\)
0.880578 0.473900i \(-0.157154\pi\)
\(20\) 3.17508e6i 0.992211i
\(21\) 956055. 0.234092
\(22\) 9.22936e6i 1.79085i
\(23\) −4.51196e6 −0.701013 −0.350506 0.936560i \(-0.613990\pi\)
−0.350506 + 0.936560i \(0.613990\pi\)
\(24\) 801999. 0.100720
\(25\) −1.14770e7 −1.17524
\(26\) 2.70113e7i 2.27342i
\(27\) 6.63576e6i 0.462458i
\(28\) 1.13897e7i 0.661791i
\(29\) 9.59476e6i 0.467783i 0.972263 + 0.233891i \(0.0751460\pi\)
−0.972263 + 0.233891i \(0.924854\pi\)
\(30\) 1.10304e7i 0.453926i
\(31\) 9.38059e6 0.327659 0.163829 0.986489i \(-0.447615\pi\)
0.163829 + 0.986489i \(0.447615\pi\)
\(32\) 3.87498e7i 1.15483i
\(33\) 1.28952e7i 0.329503i
\(34\) 2.38920e7i 0.525845i
\(35\) −7.62017e7 −1.45086
\(36\) −3.83748e7 −0.634648
\(37\) 9.20205e7i 1.32702i 0.748170 + 0.663508i \(0.230933\pi\)
−0.748170 + 0.663508i \(0.769067\pi\)
\(38\) −9.71292e7 −1.22583
\(39\) 3.77401e7i 0.418293i
\(40\) −6.39227e7 −0.624246
\(41\) −5.46246e7 −0.471486 −0.235743 0.971815i \(-0.575752\pi\)
−0.235743 + 0.971815i \(0.575752\pi\)
\(42\) 3.95683e7i 0.302762i
\(43\) 1.46513e8 + 1.20552e7i 0.996632 + 0.0820032i
\(44\) −1.53623e8 −0.931523
\(45\) 2.56743e8i 1.39135i
\(46\) 1.86737e8i 0.906652i
\(47\) −5.77200e7 −0.251673 −0.125837 0.992051i \(-0.540161\pi\)
−0.125837 + 0.992051i \(0.540161\pi\)
\(48\) 7.39842e7i 0.290357i
\(49\) 9.12383e6 0.0322996
\(50\) 4.74999e8i 1.52000i
\(51\) 3.33818e7i 0.0967518i
\(52\) −4.49605e8 −1.18254
\(53\) −3.80772e8 −0.910512 −0.455256 0.890361i \(-0.650452\pi\)
−0.455256 + 0.890361i \(0.650452\pi\)
\(54\) 2.74635e8 0.598118
\(55\) 1.02780e9i 2.04219i
\(56\) −2.29304e8 −0.416363
\(57\) 1.35709e8 0.225545
\(58\) 3.97099e8 0.605005
\(59\) 5.64392e8 0.789443 0.394721 0.918801i \(-0.370841\pi\)
0.394721 + 0.918801i \(0.370841\pi\)
\(60\) −1.83602e8 −0.236113
\(61\) 6.10423e8i 0.722739i 0.932423 + 0.361370i \(0.117691\pi\)
−0.932423 + 0.361370i \(0.882309\pi\)
\(62\) 3.88235e8i 0.423776i
\(63\) 9.20993e8i 0.928012i
\(64\) 2.93605e8 0.273441
\(65\) 3.00805e9i 2.59250i
\(66\) 5.33696e8 0.426161
\(67\) −1.39619e9 −1.03412 −0.517061 0.855949i \(-0.672974\pi\)
−0.517061 + 0.855949i \(0.672974\pi\)
\(68\) 3.97684e8 0.273523
\(69\) 2.60908e8i 0.166818i
\(70\) 3.15377e9i 1.87646i
\(71\) 2.86201e9i 1.58628i 0.609040 + 0.793139i \(0.291555\pi\)
−0.609040 + 0.793139i \(0.708445\pi\)
\(72\) 7.72586e8i 0.399286i
\(73\) 2.78136e9i 1.34166i 0.741611 + 0.670830i \(0.234062\pi\)
−0.741611 + 0.670830i \(0.765938\pi\)
\(74\) 3.80846e9 1.71629
\(75\) 6.63667e8i 0.279669i
\(76\) 1.61672e9i 0.637628i
\(77\) 3.68695e9i 1.36211i
\(78\) 1.56195e9 0.540998
\(79\) 3.46213e9 1.12514 0.562572 0.826748i \(-0.309812\pi\)
0.562572 + 0.826748i \(0.309812\pi\)
\(80\) 5.89685e9i 1.79958i
\(81\) 2.90562e9 0.833322
\(82\) 2.26075e9i 0.609795i
\(83\) 3.22198e9 0.817960 0.408980 0.912543i \(-0.365885\pi\)
0.408980 + 0.912543i \(0.365885\pi\)
\(84\) −6.58617e8 −0.157484
\(85\) 2.66067e9i 0.599649i
\(86\) 4.98928e8 6.06376e9i 0.106059 1.28899i
\(87\) −5.54826e8 −0.111317
\(88\) 3.09285e9i 0.586064i
\(89\) 7.71319e8i 0.138129i 0.997612 + 0.0690644i \(0.0220014\pi\)
−0.997612 + 0.0690644i \(0.977999\pi\)
\(90\) −1.06259e10 −1.79950
\(91\) 1.07905e10i 1.72916i
\(92\) 3.10824e9 0.471602
\(93\) 5.42441e8i 0.0779719i
\(94\) 2.38886e9i 0.325500i
\(95\) −1.08166e10 −1.39788
\(96\) −2.24074e9 −0.274812
\(97\) 9.01361e9 1.04964 0.524820 0.851213i \(-0.324133\pi\)
0.524820 + 0.851213i \(0.324133\pi\)
\(98\) 3.77609e8i 0.0417745i
\(99\) 1.24223e10 1.30625
\(100\) 7.90638e9 0.790638
\(101\) −1.63722e10 −1.55775 −0.778877 0.627177i \(-0.784210\pi\)
−0.778877 + 0.627177i \(0.784210\pi\)
\(102\) −1.38158e9 −0.125134
\(103\) 1.12194e10 0.967799 0.483899 0.875124i \(-0.339220\pi\)
0.483899 + 0.875124i \(0.339220\pi\)
\(104\) 9.05175e9i 0.743988i
\(105\) 4.40643e9i 0.345255i
\(106\) 1.57590e10i 1.17761i
\(107\) −1.42067e10 −1.01292 −0.506460 0.862263i \(-0.669046\pi\)
−0.506460 + 0.862263i \(0.669046\pi\)
\(108\) 4.57131e9i 0.311116i
\(109\) −1.56200e10 −1.01519 −0.507596 0.861595i \(-0.669466\pi\)
−0.507596 + 0.861595i \(0.669466\pi\)
\(110\) −4.25378e10 −2.64126
\(111\) −5.32117e9 −0.315785
\(112\) 2.11533e10i 1.20029i
\(113\) 3.16782e10i 1.71937i −0.510826 0.859684i \(-0.670660\pi\)
0.510826 0.859684i \(-0.329340\pi\)
\(114\) 5.61658e9i 0.291708i
\(115\) 2.07955e10i 1.03390i
\(116\) 6.60974e9i 0.314698i
\(117\) 3.63560e10 1.65824
\(118\) 2.33585e10i 1.02102i
\(119\) 9.54439e9i 0.399957i
\(120\) 3.69639e9i 0.148550i
\(121\) 2.37920e10 0.917284
\(122\) 2.52636e10 0.934752
\(123\) 3.15871e9i 0.112198i
\(124\) −6.46220e9 −0.220431
\(125\) 7.88758e9i 0.258460i
\(126\) −3.81172e10 −1.20024
\(127\) −4.98671e9 −0.150937 −0.0754684 0.997148i \(-0.524045\pi\)
−0.0754684 + 0.997148i \(0.524045\pi\)
\(128\) 2.75283e10i 0.801180i
\(129\) −6.97101e8 + 8.47226e9i −0.0195140 + 0.237165i
\(130\) −1.24494e11 −3.35300
\(131\) 4.98746e10i 1.29277i 0.763010 + 0.646387i \(0.223721\pi\)
−0.763010 + 0.646387i \(0.776279\pi\)
\(132\) 8.88340e9i 0.221671i
\(133\) −3.88012e10 −0.932368
\(134\) 5.77844e10i 1.33748i
\(135\) 3.05840e10 0.682065
\(136\) 8.00644e9i 0.172086i
\(137\) 1.51873e10i 0.314686i −0.987544 0.157343i \(-0.949707\pi\)
0.987544 0.157343i \(-0.0502929\pi\)
\(138\) −1.07982e10 −0.215753
\(139\) −2.60375e10 −0.501794 −0.250897 0.968014i \(-0.580726\pi\)
−0.250897 + 0.968014i \(0.580726\pi\)
\(140\) 5.24946e10 0.976056
\(141\) 3.33771e9i 0.0598898i
\(142\) 1.18450e11 2.05161
\(143\) 1.45542e11 2.43393
\(144\) −7.12708e10 −1.15106
\(145\) 4.42220e10 0.689919
\(146\) 1.15112e11 1.73523
\(147\) 5.27593e8i 0.00768622i
\(148\) 6.33920e10i 0.892742i
\(149\) 9.55286e10i 1.30078i −0.759603 0.650388i \(-0.774607\pi\)
0.759603 0.650388i \(-0.225393\pi\)
\(150\) −2.74672e10 −0.361708
\(151\) 1.25033e11i 1.59272i 0.604824 + 0.796360i \(0.293244\pi\)
−0.604824 + 0.796360i \(0.706756\pi\)
\(152\) −3.25489e10 −0.401161
\(153\) −3.21576e10 −0.383554
\(154\) −1.52592e11 −1.76169
\(155\) 4.32349e10i 0.483254i
\(156\) 2.59988e10i 0.281404i
\(157\) 9.09771e10i 0.953748i −0.878972 0.476874i \(-0.841770\pi\)
0.878972 0.476874i \(-0.158230\pi\)
\(158\) 1.43288e11i 1.45520i
\(159\) 2.20185e10i 0.216671i
\(160\) 1.78597e11 1.70323
\(161\) 7.45977e10i 0.689598i
\(162\) 1.20255e11i 1.07777i
\(163\) 1.78007e11i 1.54703i 0.633776 + 0.773517i \(0.281504\pi\)
−0.633776 + 0.773517i \(0.718496\pi\)
\(164\) 3.76303e10 0.317190
\(165\) 5.94337e10 0.485974
\(166\) 1.33348e11i 1.05791i
\(167\) 5.39108e10 0.415043 0.207522 0.978230i \(-0.433460\pi\)
0.207522 + 0.978230i \(0.433460\pi\)
\(168\) 1.32597e10i 0.0990805i
\(169\) 2.88095e11 2.08979
\(170\) 1.10118e11 0.775554
\(171\) 1.30732e11i 0.894129i
\(172\) −1.00932e11 8.30469e9i −0.670479 0.0551672i
\(173\) −2.11497e11 −1.36481 −0.682407 0.730972i \(-0.739067\pi\)
−0.682407 + 0.730972i \(0.739067\pi\)
\(174\) 2.29626e10i 0.143971i
\(175\) 1.89753e11i 1.15611i
\(176\) −2.85314e11 −1.68951
\(177\) 3.26365e10i 0.187861i
\(178\) 3.19227e10 0.178648
\(179\) 1.44297e10i 0.0785220i 0.999229 + 0.0392610i \(0.0125004\pi\)
−0.999229 + 0.0392610i \(0.987500\pi\)
\(180\) 1.76868e11i 0.936024i
\(181\) 2.16492e11 1.11442 0.557211 0.830371i \(-0.311871\pi\)
0.557211 + 0.830371i \(0.311871\pi\)
\(182\) −4.46588e11 −2.23640
\(183\) −3.52983e10 −0.171988
\(184\) 6.25773e10i 0.296707i
\(185\) 4.24120e11 1.95718
\(186\) 2.24501e10 0.100845
\(187\) −1.28734e11 −0.562971
\(188\) 3.97627e10 0.169312
\(189\) 1.09711e11 0.454928
\(190\) 4.47666e11i 1.80795i
\(191\) 1.17486e11i 0.462188i 0.972931 + 0.231094i \(0.0742305\pi\)
−0.972931 + 0.231094i \(0.925769\pi\)
\(192\) 1.69780e10i 0.0650698i
\(193\) −3.90134e11 −1.45689 −0.728445 0.685104i \(-0.759757\pi\)
−0.728445 + 0.685104i \(0.759757\pi\)
\(194\) 3.73047e11i 1.35755i
\(195\) 1.73943e11 0.616928
\(196\) −6.28532e9 −0.0217294
\(197\) −1.50033e11 −0.505658 −0.252829 0.967511i \(-0.581361\pi\)
−0.252829 + 0.967511i \(0.581361\pi\)
\(198\) 5.14123e11i 1.68943i
\(199\) 2.20399e11i 0.706227i 0.935581 + 0.353113i \(0.114877\pi\)
−0.935581 + 0.353113i \(0.885123\pi\)
\(200\) 1.59177e11i 0.497427i
\(201\) 8.07362e10i 0.246087i
\(202\) 6.77596e11i 2.01472i
\(203\) 1.58634e11 0.460166
\(204\) 2.29964e10i 0.0650893i
\(205\) 2.51763e11i 0.695381i
\(206\) 4.64340e11i 1.25170i
\(207\) −2.51339e11 −0.661316
\(208\) −8.35021e11 −2.14477
\(209\) 5.23349e11i 1.31238i
\(210\) −1.82369e11 −0.446535
\(211\) 1.56284e11i 0.373682i −0.982390 0.186841i \(-0.940175\pi\)
0.982390 0.186841i \(-0.0598249\pi\)
\(212\) 2.62310e11 0.612542
\(213\) −1.65498e11 −0.377481
\(214\) 5.87975e11i 1.31006i
\(215\) 5.55619e10 6.75276e11i 0.120944 1.46990i
\(216\) 9.20327e10 0.195737
\(217\) 1.55093e11i 0.322324i
\(218\) 6.46466e11i 1.31299i
\(219\) −1.60835e11 −0.319271
\(220\) 7.08045e11i 1.37388i
\(221\) −3.76764e11 −0.714673
\(222\) 2.20228e11i 0.408420i
\(223\) 8.73734e11i 1.58436i −0.610285 0.792182i \(-0.708945\pi\)
0.610285 0.792182i \(-0.291055\pi\)
\(224\) 6.40664e11 1.13603
\(225\) −6.39327e11 −1.10869
\(226\) −1.31107e12 −2.22374
\(227\) 1.30562e11i 0.216614i −0.994117 0.108307i \(-0.965457\pi\)
0.994117 0.108307i \(-0.0345430\pi\)
\(228\) −9.34884e10 −0.151734
\(229\) 5.94053e11 0.943295 0.471648 0.881787i \(-0.343659\pi\)
0.471648 + 0.881787i \(0.343659\pi\)
\(230\) 8.60664e11 1.33719
\(231\) 2.13201e11 0.324138
\(232\) 1.33072e11 0.197991
\(233\) 9.83403e11i 1.43203i −0.698085 0.716015i \(-0.745964\pi\)
0.698085 0.716015i \(-0.254036\pi\)
\(234\) 1.50467e12i 2.14468i
\(235\) 2.66030e11i 0.371185i
\(236\) −3.88804e11 −0.531093
\(237\) 2.00201e11i 0.267747i
\(238\) 3.95015e11 0.517283
\(239\) 1.42825e12 1.83154 0.915769 0.401705i \(-0.131582\pi\)
0.915769 + 0.401705i \(0.131582\pi\)
\(240\) −3.40991e11 −0.428239
\(241\) 1.07910e12i 1.32732i 0.748036 + 0.663658i \(0.230997\pi\)
−0.748036 + 0.663658i \(0.769003\pi\)
\(242\) 9.84681e11i 1.18637i
\(243\) 5.59855e11i 0.660761i
\(244\) 4.20515e11i 0.486219i
\(245\) 4.20514e10i 0.0476377i
\(246\) −1.30730e11 −0.145111
\(247\) 1.53167e12i 1.66602i
\(248\) 1.30101e11i 0.138683i
\(249\) 1.86314e11i 0.194647i
\(250\) 3.26444e11 0.334279
\(251\) −1.49606e11 −0.150169 −0.0750846 0.997177i \(-0.523923\pi\)
−0.0750846 + 0.997177i \(0.523923\pi\)
\(252\) 6.34463e11i 0.624315i
\(253\) −1.00617e12 −0.970664
\(254\) 2.06385e11i 0.195214i
\(255\) −1.53856e11 −0.142696
\(256\) 1.43997e12 1.30964
\(257\) 2.14576e12i 1.91389i 0.290273 + 0.956944i \(0.406254\pi\)
−0.290273 + 0.956944i \(0.593746\pi\)
\(258\) 3.50642e11 + 2.88510e10i 0.306737 + 0.0252384i
\(259\) 1.52141e12 1.30541
\(260\) 2.07222e12i 1.74409i
\(261\) 5.34478e11i 0.441293i
\(262\) 2.06416e12 1.67200
\(263\) 4.92321e11i 0.391264i −0.980677 0.195632i \(-0.937324\pi\)
0.980677 0.195632i \(-0.0626758\pi\)
\(264\) 1.78847e11 0.139464
\(265\) 1.75497e12i 1.34289i
\(266\) 1.60587e12i 1.20588i
\(267\) −4.46022e10 −0.0328700
\(268\) 9.61825e11 0.695700
\(269\) 2.36892e10 0.0168186 0.00840930 0.999965i \(-0.497323\pi\)
0.00840930 + 0.999965i \(0.497323\pi\)
\(270\) 1.26578e12i 0.882146i
\(271\) −8.95184e11 −0.612444 −0.306222 0.951960i \(-0.599065\pi\)
−0.306222 + 0.951960i \(0.599065\pi\)
\(272\) 7.38591e11 0.496089
\(273\) 6.23971e11 0.411482
\(274\) −6.28558e11 −0.406998
\(275\) −2.55938e12 −1.62731
\(276\) 1.79737e11i 0.112226i
\(277\) 1.22921e12i 0.753752i −0.926264 0.376876i \(-0.876998\pi\)
0.926264 0.376876i \(-0.123002\pi\)
\(278\) 1.07762e12i 0.648994i
\(279\) 5.22547e11 0.309104
\(280\) 1.05686e12i 0.614081i
\(281\) −1.42026e12 −0.810653 −0.405327 0.914172i \(-0.632842\pi\)
−0.405327 + 0.914172i \(0.632842\pi\)
\(282\) −1.38138e11 −0.0774582
\(283\) 3.23709e11 0.178329 0.0891646 0.996017i \(-0.471580\pi\)
0.0891646 + 0.996017i \(0.471580\pi\)
\(284\) 1.97161e12i 1.06716i
\(285\) 6.25477e11i 0.332650i
\(286\) 6.02355e12i 3.14791i
\(287\) 9.03127e11i 0.463809i
\(288\) 2.15856e12i 1.08944i
\(289\) −1.68274e12 −0.834695
\(290\) 1.83022e12i 0.892304i
\(291\) 5.21220e11i 0.249779i
\(292\) 1.91605e12i 0.902595i
\(293\) 3.98890e12 1.84720 0.923602 0.383354i \(-0.125231\pi\)
0.923602 + 0.383354i \(0.125231\pi\)
\(294\) 2.18356e10 0.00994094
\(295\) 2.60126e12i 1.16433i
\(296\) 1.27625e12 0.561665
\(297\) 1.47978e12i 0.640347i
\(298\) −3.95365e12 −1.68235
\(299\) −2.94473e12 −1.23223
\(300\) 4.57194e11i 0.188146i
\(301\) 1.99312e11 2.42236e12i 0.0806680 0.980405i
\(302\) 5.17474e12 2.05994
\(303\) 9.46734e11i 0.370694i
\(304\) 3.00263e12i 1.15647i
\(305\) 2.81342e12 1.06595
\(306\) 1.33091e12i 0.496068i
\(307\) −4.96244e12 −1.81972 −0.909858 0.414920i \(-0.863810\pi\)
−0.909858 + 0.414920i \(0.863810\pi\)
\(308\) 2.53991e12i 0.916355i
\(309\) 6.48774e11i 0.230304i
\(310\) −1.78937e12 −0.625015
\(311\) 1.69678e12 0.583209 0.291605 0.956539i \(-0.405811\pi\)
0.291605 + 0.956539i \(0.405811\pi\)
\(312\) 5.23426e11 0.177044
\(313\) 3.31526e12i 1.10356i −0.833990 0.551779i \(-0.813949\pi\)
0.833990 0.551779i \(-0.186051\pi\)
\(314\) −3.76528e12 −1.23353
\(315\) −4.24483e12 −1.36870
\(316\) −2.38503e12 −0.756935
\(317\) 3.73328e10 0.0116626 0.00583129 0.999983i \(-0.498144\pi\)
0.00583129 + 0.999983i \(0.498144\pi\)
\(318\) −9.11281e11 −0.280231
\(319\) 2.13964e12i 0.647720i
\(320\) 1.35322e12i 0.403290i
\(321\) 8.21517e11i 0.241041i
\(322\) 3.08738e12 0.891890
\(323\) 1.35479e12i 0.385354i
\(324\) −2.00165e12 −0.560613
\(325\) −7.49047e12 −2.06582
\(326\) 7.36720e12 2.00085
\(327\) 9.03240e11i 0.241582i
\(328\) 7.57599e11i 0.199559i
\(329\) 9.54304e11i 0.247575i
\(330\) 2.45979e12i 0.628533i
\(331\) 2.77022e12i 0.697228i 0.937266 + 0.348614i \(0.113348\pi\)
−0.937266 + 0.348614i \(0.886652\pi\)
\(332\) −2.21959e12 −0.550278
\(333\) 5.12602e12i 1.25187i
\(334\) 2.23121e12i 0.536795i
\(335\) 6.43502e12i 1.52520i
\(336\) −1.22321e12 −0.285630
\(337\) −3.25059e12 −0.747846 −0.373923 0.927460i \(-0.621988\pi\)
−0.373923 + 0.927460i \(0.621988\pi\)
\(338\) 1.19234e13i 2.70282i
\(339\) 1.83182e12 0.409152
\(340\) 1.83291e12i 0.403410i
\(341\) 2.09188e12 0.453696
\(342\) −5.41060e12 −1.15642
\(343\) 4.82111e12i 1.01549i
\(344\) 1.67196e11 2.03202e12i 0.0347082 0.421829i
\(345\) −1.20252e12 −0.246034
\(346\) 8.75324e12i 1.76518i
\(347\) 8.79337e12i 1.74787i 0.486047 + 0.873933i \(0.338438\pi\)
−0.486047 + 0.873933i \(0.661562\pi\)
\(348\) 3.82214e11 0.0748877
\(349\) 1.71043e12i 0.330353i −0.986264 0.165177i \(-0.947181\pi\)
0.986264 0.165177i \(-0.0528194\pi\)
\(350\) 7.85332e12 1.49525
\(351\) 4.33084e12i 0.812899i
\(352\) 8.64124e12i 1.59905i
\(353\) −1.03009e13 −1.87932 −0.939661 0.342106i \(-0.888860\pi\)
−0.939661 + 0.342106i \(0.888860\pi\)
\(354\) 1.35073e12 0.242969
\(355\) 1.31909e13 2.33956
\(356\) 5.31355e11i 0.0929254i
\(357\) −5.51913e11 −0.0951765
\(358\) 5.97202e11 0.101556
\(359\) 5.05095e12 0.847034 0.423517 0.905888i \(-0.360795\pi\)
0.423517 + 0.905888i \(0.360795\pi\)
\(360\) −3.56083e12 −0.588896
\(361\) 6.23369e11 0.101674
\(362\) 8.95999e12i 1.44133i
\(363\) 1.37579e12i 0.218283i
\(364\) 7.43348e12i 1.16328i
\(365\) 1.28192e13 1.97878
\(366\) 1.46089e12i 0.222440i
\(367\) −4.47428e12 −0.672037 −0.336018 0.941855i \(-0.609080\pi\)
−0.336018 + 0.941855i \(0.609080\pi\)
\(368\) 5.77273e12 0.855347
\(369\) −3.04287e12 −0.444787
\(370\) 1.75531e13i 2.53131i
\(371\) 6.29543e12i 0.895687i
\(372\) 3.73683e11i 0.0524551i
\(373\) 8.44273e12i 1.16933i −0.811273 0.584667i \(-0.801225\pi\)
0.811273 0.584667i \(-0.198775\pi\)
\(374\) 5.32794e12i 0.728117i
\(375\) −4.56107e11 −0.0615049
\(376\) 8.00530e11i 0.106522i
\(377\) 6.26203e12i 0.822259i
\(378\) 4.54063e12i 0.588379i
\(379\) 5.87700e12 0.751553 0.375777 0.926710i \(-0.377376\pi\)
0.375777 + 0.926710i \(0.377376\pi\)
\(380\) 7.45142e12 0.940418
\(381\) 2.88361e11i 0.0359179i
\(382\) 4.86240e12 0.597769
\(383\) 1.11495e13i 1.35288i −0.736496 0.676442i \(-0.763521\pi\)
0.736496 0.676442i \(-0.236479\pi\)
\(384\) −1.59185e12 −0.190654
\(385\) −1.69930e13 −2.00894
\(386\) 1.61465e13i 1.88426i
\(387\) 8.16155e12 + 6.71535e11i 0.940195 + 0.0773596i
\(388\) −6.20939e12 −0.706139
\(389\) 1.73137e13i 1.94375i −0.235495 0.971876i \(-0.575671\pi\)
0.235495 0.971876i \(-0.424329\pi\)
\(390\) 7.19900e12i 0.797901i
\(391\) 2.60467e12 0.285016
\(392\) 1.26540e11i 0.0136709i
\(393\) −2.88404e12 −0.307637
\(394\) 6.20944e12i 0.653991i
\(395\) 1.59569e13i 1.65944i
\(396\) −8.55761e12 −0.878772
\(397\) −4.73758e12 −0.480401 −0.240201 0.970723i \(-0.577213\pi\)
−0.240201 + 0.970723i \(0.577213\pi\)
\(398\) 9.12167e12 0.913396
\(399\) 2.24372e12i 0.221873i
\(400\) 1.46840e13 1.43398
\(401\) −7.21764e11 −0.0696103 −0.0348051 0.999394i \(-0.511081\pi\)
−0.0348051 + 0.999394i \(0.511081\pi\)
\(402\) −3.34143e12 −0.318275
\(403\) 6.12226e12 0.575952
\(404\) 1.12786e13 1.04797
\(405\) 1.33919e13i 1.22904i
\(406\) 6.56538e12i 0.595154i
\(407\) 2.05207e13i 1.83747i
\(408\) −4.62979e11 −0.0409506
\(409\) 5.76963e12i 0.504117i 0.967712 + 0.252059i \(0.0811076\pi\)
−0.967712 + 0.252059i \(0.918892\pi\)
\(410\) 1.04197e13 0.899368
\(411\) 8.78219e11 0.0748848
\(412\) −7.72897e12 −0.651081
\(413\) 9.33128e12i 0.776589i
\(414\) 1.04022e13i 0.855310i
\(415\) 1.48500e13i 1.20638i
\(416\) 2.52901e13i 2.02994i
\(417\) 1.50564e12i 0.119410i
\(418\) −2.16599e13 −1.69736
\(419\) 1.13276e13i 0.877138i −0.898698 0.438569i \(-0.855486\pi\)
0.898698 0.438569i \(-0.144514\pi\)
\(420\) 3.03555e12i 0.232269i
\(421\) 3.42831e12i 0.259221i −0.991565 0.129610i \(-0.958627\pi\)
0.991565 0.129610i \(-0.0413727\pi\)
\(422\) −6.46814e12 −0.483300
\(423\) −3.21530e12 −0.237421
\(424\) 5.28100e12i 0.385378i
\(425\) 6.62545e12 0.477827
\(426\) 6.84949e12i 0.488214i
\(427\) 1.00923e13 0.710971
\(428\) 9.78689e12 0.681437
\(429\) 8.41609e12i 0.579194i
\(430\) −2.79477e13 2.29955e12i −1.90109 0.156423i
\(431\) −3.30836e11 −0.0222447 −0.0111223 0.999938i \(-0.503540\pi\)
−0.0111223 + 0.999938i \(0.503540\pi\)
\(432\) 8.48999e12i 0.564272i
\(433\) 1.76261e13i 1.15802i 0.815320 + 0.579010i \(0.196561\pi\)
−0.815320 + 0.579010i \(0.803439\pi\)
\(434\) −6.41883e12 −0.416876
\(435\) 2.55718e12i 0.164178i
\(436\) 1.07605e13 0.682965
\(437\) 1.05889e13i 0.664420i
\(438\) 6.65647e12i 0.412927i
\(439\) 1.04849e13 0.643047 0.321524 0.946902i \(-0.395805\pi\)
0.321524 + 0.946902i \(0.395805\pi\)
\(440\) −1.42548e13 −0.864368
\(441\) 5.08244e11 0.0304705
\(442\) 1.55931e13i 0.924320i
\(443\) 2.43587e13 1.42770 0.713849 0.700300i \(-0.246950\pi\)
0.713849 + 0.700300i \(0.246950\pi\)
\(444\) 3.66570e12 0.212443
\(445\) 3.55499e12 0.203722
\(446\) −3.61613e13 −2.04913
\(447\) 5.52403e12 0.309541
\(448\) 4.85427e12i 0.268989i
\(449\) 1.91626e12i 0.105008i 0.998621 + 0.0525041i \(0.0167202\pi\)
−0.998621 + 0.0525041i \(0.983280\pi\)
\(450\) 2.64599e13i 1.43392i
\(451\) −1.21813e13 −0.652848
\(452\) 2.18228e13i 1.15670i
\(453\) −7.23013e12 −0.379014
\(454\) −5.40357e12 −0.280157
\(455\) −4.97331e13 −2.55029
\(456\) 1.88217e12i 0.0954629i
\(457\) 2.13528e13i 1.07121i −0.844469 0.535604i \(-0.820084\pi\)
0.844469 0.535604i \(-0.179916\pi\)
\(458\) 2.45861e13i 1.22001i
\(459\) 3.83070e12i 0.188025i
\(460\) 1.43258e13i 0.695552i
\(461\) 2.01606e13 0.968275 0.484138 0.874992i \(-0.339133\pi\)
0.484138 + 0.874992i \(0.339133\pi\)
\(462\) 8.82378e12i 0.419223i
\(463\) 2.86432e13i 1.34622i −0.739542 0.673110i \(-0.764958\pi\)
0.739542 0.673110i \(-0.235042\pi\)
\(464\) 1.22758e13i 0.570770i
\(465\) 2.50010e12 0.114998
\(466\) −4.07002e13 −1.85211
\(467\) 1.24624e13i 0.561070i 0.959844 + 0.280535i \(0.0905119\pi\)
−0.959844 + 0.280535i \(0.909488\pi\)
\(468\) −2.50453e13 −1.11557
\(469\) 2.30838e13i 1.01728i
\(470\) 1.10102e13 0.480071
\(471\) 5.26083e12 0.226960
\(472\) 7.82766e12i 0.334135i
\(473\) 3.26726e13 + 2.68831e12i 1.38000 + 0.113547i
\(474\) 8.28573e12 0.346289
\(475\) 2.69347e13i 1.11390i
\(476\) 6.57504e12i 0.269069i
\(477\) −2.12110e13 −0.858951
\(478\) 5.91113e13i 2.36881i
\(479\) −2.65412e13 −1.05255 −0.526275 0.850314i \(-0.676412\pi\)
−0.526275 + 0.850314i \(0.676412\pi\)
\(480\) 1.03275e13i 0.405312i
\(481\) 6.00573e13i 2.33260i
\(482\) 4.46606e13 1.71668
\(483\) −4.31368e12 −0.164101
\(484\) −1.63901e13 −0.617098
\(485\) 4.15435e13i 1.54808i
\(486\) 2.31708e13 0.854592
\(487\) 4.21082e13 1.53717 0.768584 0.639749i \(-0.220962\pi\)
0.768584 + 0.639749i \(0.220962\pi\)
\(488\) 8.46608e12 0.305903
\(489\) −1.02934e13 −0.368142
\(490\) −1.74039e12 −0.0616120
\(491\) 2.85436e12i 0.100023i 0.998749 + 0.0500116i \(0.0159258\pi\)
−0.998749 + 0.0500116i \(0.984074\pi\)
\(492\) 2.17601e12i 0.0754805i
\(493\) 5.53888e12i 0.190190i
\(494\) −6.33915e13 −2.15475
\(495\) 5.72540e13i 1.92655i
\(496\) −1.20018e13 −0.399796
\(497\) 4.73186e13 1.56045
\(498\) 7.71098e12 0.251746
\(499\) 2.05715e12i 0.0664909i 0.999447 + 0.0332455i \(0.0105843\pi\)
−0.999447 + 0.0332455i \(0.989416\pi\)
\(500\) 5.43368e12i 0.173878i
\(501\) 3.11744e12i 0.0987665i
\(502\) 6.19176e12i 0.194221i
\(503\) 1.19595e13i 0.371428i −0.982604 0.185714i \(-0.940540\pi\)
0.982604 0.185714i \(-0.0594598\pi\)
\(504\) −1.27734e13 −0.392785
\(505\) 7.54588e13i 2.29749i
\(506\) 4.16425e13i 1.25541i
\(507\) 1.66594e13i 0.497300i
\(508\) 3.43529e12 0.101542
\(509\) −3.54611e12 −0.103792 −0.0518960 0.998652i \(-0.516526\pi\)
−0.0518960 + 0.998652i \(0.516526\pi\)
\(510\) 6.36764e12i 0.184556i
\(511\) 4.59852e13 1.31982
\(512\) 3.14071e13i 0.892643i
\(513\) 1.55731e13 0.438318
\(514\) 8.88069e13 2.47532
\(515\) 5.17101e13i 1.42738i
\(516\) 4.80226e11 5.83646e12i 0.0131280 0.159552i
\(517\) −1.28716e13 −0.348482
\(518\) 6.29666e13i 1.68834i
\(519\) 1.22300e13i 0.324780i
\(520\) −4.17193e13 −1.09729
\(521\) 1.30995e13i 0.341244i 0.985337 + 0.170622i \(0.0545777\pi\)
−0.985337 + 0.170622i \(0.945422\pi\)
\(522\) 2.21205e13 0.570745
\(523\) 9.28471e12i 0.237279i −0.992937 0.118640i \(-0.962147\pi\)
0.992937 0.118640i \(-0.0378533\pi\)
\(524\) 3.43581e13i 0.869707i
\(525\) −1.09726e13 −0.275115
\(526\) −2.03757e13 −0.506040
\(527\) −5.41524e12 −0.133219
\(528\) 1.64985e13i 0.402046i
\(529\) −2.10688e13 −0.508581
\(530\) 7.26330e13 1.73682
\(531\) 3.14395e13 0.744738
\(532\) 2.67298e13 0.627246
\(533\) −3.56508e13 −0.828768
\(534\) 1.84596e12i 0.0425124i
\(535\) 6.54784e13i 1.49393i
\(536\) 1.93641e13i 0.437697i
\(537\) −8.34409e11 −0.0186856
\(538\) 9.80428e11i 0.0217523i
\(539\) 2.03462e12 0.0447239
\(540\) −2.10690e13 −0.458856
\(541\) −4.80610e13 −1.03707 −0.518533 0.855057i \(-0.673522\pi\)
−0.518533 + 0.855057i \(0.673522\pi\)
\(542\) 3.70491e13i 0.792102i
\(543\) 1.25189e13i 0.265195i
\(544\) 2.23695e13i 0.469529i
\(545\) 7.19920e13i 1.49728i
\(546\) 2.58243e13i 0.532189i
\(547\) 9.25834e13 1.89059 0.945293 0.326223i \(-0.105776\pi\)
0.945293 + 0.326223i \(0.105776\pi\)
\(548\) 1.04624e13i 0.211703i
\(549\) 3.40037e13i 0.681812i
\(550\) 1.05925e14i 2.10468i
\(551\) 2.25175e13 0.443365
\(552\) −3.61859e12 −0.0706063
\(553\) 5.72406e13i 1.10682i
\(554\) −5.08736e13 −0.974863
\(555\) 2.45251e13i 0.465742i
\(556\) 1.79370e13 0.337579
\(557\) −7.83003e13 −1.46045 −0.730226 0.683206i \(-0.760585\pi\)
−0.730226 + 0.683206i \(0.760585\pi\)
\(558\) 2.16267e13i 0.399779i
\(559\) 9.56221e13 + 7.86782e12i 1.75186 + 0.144144i
\(560\) 9.74947e13 1.77028
\(561\) 7.44418e12i 0.133968i
\(562\) 5.87803e13i 1.04846i
\(563\) 8.52093e13 1.50642 0.753208 0.657782i \(-0.228505\pi\)
0.753208 + 0.657782i \(0.228505\pi\)
\(564\) 2.29932e12i 0.0402905i
\(565\) −1.46004e14 −2.53584
\(566\) 1.33974e13i 0.230641i
\(567\) 4.80395e13i 0.819754i
\(568\) 3.96938e13 0.671399
\(569\) −5.42162e13 −0.909009 −0.454504 0.890744i \(-0.650184\pi\)
−0.454504 + 0.890744i \(0.650184\pi\)
\(570\) −2.58867e13 −0.430231
\(571\) 7.67443e13i 1.26434i 0.774828 + 0.632172i \(0.217837\pi\)
−0.774828 + 0.632172i \(0.782163\pi\)
\(572\) −1.00262e14 −1.63741
\(573\) −6.79372e12 −0.109985
\(574\) 3.73778e13 0.599866
\(575\) 5.17836e13 0.823860
\(576\) 1.63553e13 0.257957
\(577\) 1.18461e14i 1.85223i 0.377240 + 0.926115i \(0.376873\pi\)
−0.377240 + 0.926115i \(0.623127\pi\)
\(578\) 6.96437e13i 1.07955i
\(579\) 2.25598e13i 0.346691i
\(580\) −3.04641e13 −0.464139
\(581\) 5.32700e13i 0.804641i
\(582\) 2.15718e13 0.323051
\(583\) −8.49125e13 −1.26075
\(584\) 3.85752e13 0.567864
\(585\) 1.67564e14i 2.44569i
\(586\) 1.65089e14i 2.38907i
\(587\) 5.26291e13i 0.755154i −0.925978 0.377577i \(-0.876757\pi\)
0.925978 0.377577i \(-0.123243\pi\)
\(588\) 3.63454e11i 0.00517086i
\(589\) 2.20148e13i 0.310555i
\(590\) −1.07659e14 −1.50588
\(591\) 8.67582e12i 0.120330i
\(592\) 1.17734e14i 1.61917i
\(593\) 1.12040e14i 1.52791i −0.645267 0.763957i \(-0.723254\pi\)
0.645267 0.763957i \(-0.276746\pi\)
\(594\) 6.12438e13 0.828190
\(595\) 4.39898e13 0.589885
\(596\) 6.58088e13i 0.875089i
\(597\) −1.27448e13 −0.168058
\(598\) 1.21874e14i 1.59369i
\(599\) −2.65090e13 −0.343764 −0.171882 0.985118i \(-0.554985\pi\)
−0.171882 + 0.985118i \(0.554985\pi\)
\(600\) −9.20453e12 −0.118371
\(601\) 5.75764e13i 0.734298i 0.930162 + 0.367149i \(0.119666\pi\)
−0.930162 + 0.367149i \(0.880334\pi\)
\(602\) −1.00254e14 8.24895e12i −1.26800 0.104332i
\(603\) −7.77752e13 −0.975562
\(604\) 8.61339e13i 1.07149i
\(605\) 1.09657e14i 1.35288i
\(606\) −3.91826e13 −0.479435
\(607\) 7.18754e13i 0.872241i 0.899888 + 0.436121i \(0.143648\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(608\) 9.09399e13 1.09455
\(609\) 9.17313e12i 0.109504i
\(610\) 1.16439e14i 1.37864i
\(611\) −3.76710e13 −0.442386
\(612\) 2.21530e13 0.258034
\(613\) −4.70443e13 −0.543507 −0.271753 0.962367i \(-0.587603\pi\)
−0.271753 + 0.962367i \(0.587603\pi\)
\(614\) 2.05381e14i 2.35352i
\(615\) −1.45584e13 −0.165477
\(616\) −5.11351e13 −0.576521
\(617\) −5.09966e13 −0.570316 −0.285158 0.958481i \(-0.592046\pi\)
−0.285158 + 0.958481i \(0.592046\pi\)
\(618\) 2.68509e13 0.297863
\(619\) −4.92566e13 −0.542014 −0.271007 0.962577i \(-0.587357\pi\)
−0.271007 + 0.962577i \(0.587357\pi\)
\(620\) 2.97841e13i 0.325107i
\(621\) 2.99403e13i 0.324189i
\(622\) 7.02249e13i 0.754292i
\(623\) 1.27525e13 0.135880
\(624\) 4.82859e13i 0.510384i
\(625\) −7.57262e13 −0.794047
\(626\) −1.37209e14 −1.42728
\(627\) 3.02631e13 0.312303
\(628\) 6.26733e13i 0.641629i
\(629\) 5.31217e13i 0.539534i
\(630\) 1.75681e14i 1.77020i
\(631\) 9.10936e13i 0.910629i 0.890331 + 0.455314i \(0.150473\pi\)
−0.890331 + 0.455314i \(0.849527\pi\)
\(632\) 4.80170e13i 0.476223i
\(633\) 9.03726e12 0.0889238
\(634\) 1.54510e12i 0.0150838i
\(635\) 2.29836e13i 0.222612i
\(636\) 1.51683e13i 0.145765i
\(637\) 5.95468e12 0.0567755
\(638\) 8.85535e13 0.837727
\(639\) 1.59429e14i 1.49645i
\(640\) 1.26877e14 1.18164
\(641\) 5.43369e13i 0.502117i 0.967972 + 0.251058i \(0.0807786\pi\)
−0.967972 + 0.251058i \(0.919221\pi\)
\(642\) −3.40002e13 −0.311750
\(643\) −1.67473e14 −1.52367 −0.761835 0.647772i \(-0.775701\pi\)
−0.761835 + 0.647772i \(0.775701\pi\)
\(644\) 5.13897e13i 0.463924i
\(645\) 3.90484e13 + 3.21292e12i 0.349788 + 0.0287807i
\(646\) 5.60709e13 0.498396
\(647\) 1.83630e14i 1.61966i −0.586667 0.809828i \(-0.699560\pi\)
0.586667 0.809828i \(-0.300440\pi\)
\(648\) 4.02986e13i 0.352707i
\(649\) 1.25860e14 1.09311
\(650\) 3.10008e14i 2.67182i
\(651\) 8.96837e12 0.0767023
\(652\) 1.22628e14i 1.04076i
\(653\) 1.76238e14i 1.48434i −0.670210 0.742172i \(-0.733796\pi\)
0.670210 0.742172i \(-0.266204\pi\)
\(654\) −3.73824e13 −0.312449
\(655\) 2.29870e14 1.90667
\(656\) 6.98883e13 0.575288
\(657\) 1.54936e14i 1.26569i
\(658\) 3.94958e13 0.320200
\(659\) −1.92062e14 −1.54531 −0.772653 0.634829i \(-0.781070\pi\)
−0.772653 + 0.634829i \(0.781070\pi\)
\(660\) −4.09433e13 −0.326937
\(661\) −8.62903e13 −0.683841 −0.341920 0.939729i \(-0.611077\pi\)
−0.341920 + 0.939729i \(0.611077\pi\)
\(662\) 1.14652e14 0.901758
\(663\) 2.17867e13i 0.170068i
\(664\) 4.46862e13i 0.346205i
\(665\) 1.78834e14i 1.37512i
\(666\) 2.12151e14 1.61910
\(667\) 4.32912e13i 0.327922i
\(668\) −3.71387e13 −0.279218
\(669\) 5.05245e13 0.377026
\(670\) 2.66327e14 1.97261
\(671\) 1.36125e14i 1.00075i
\(672\) 3.70470e13i 0.270337i
\(673\) 9.34892e13i 0.677152i −0.940939 0.338576i \(-0.890055\pi\)
0.940939 0.338576i \(-0.109945\pi\)
\(674\) 1.34532e14i 0.967224i
\(675\) 7.61585e13i 0.543500i
\(676\) −1.98466e14 −1.40589
\(677\) 2.15946e13i 0.151845i −0.997114 0.0759227i \(-0.975810\pi\)
0.997114 0.0759227i \(-0.0241902\pi\)
\(678\) 7.58138e13i 0.529175i
\(679\) 1.49025e14i 1.03255i
\(680\) 3.69014e13 0.253804
\(681\) 7.54985e12 0.0515469
\(682\) 8.65769e13i 0.586786i
\(683\) 9.87064e13 0.664113 0.332056 0.943260i \(-0.392258\pi\)
0.332056 + 0.943260i \(0.392258\pi\)
\(684\) 9.00597e13i 0.601520i
\(685\) −6.99978e13 −0.464121
\(686\) −1.99532e14 −1.31338
\(687\) 3.43516e13i 0.224473i
\(688\) −1.87454e14 1.54237e13i −1.21605 0.100057i
\(689\) −2.48511e14 −1.60048
\(690\) 4.97687e13i 0.318208i
\(691\) 1.90466e14i 1.20900i 0.796605 + 0.604500i \(0.206627\pi\)
−0.796605 + 0.604500i \(0.793373\pi\)
\(692\) 1.45698e14 0.918172
\(693\) 2.05382e14i 1.28498i
\(694\) 3.63932e14 2.26060
\(695\) 1.20006e14i 0.740081i
\(696\) 7.69499e12i 0.0471153i
\(697\) 3.15338e13 0.191695
\(698\) −7.07897e13 −0.427261
\(699\) 5.68662e13 0.340775
\(700\) 1.30719e14i 0.777765i
\(701\) −2.16231e14 −1.27740 −0.638701 0.769455i \(-0.720528\pi\)
−0.638701 + 0.769455i \(0.720528\pi\)
\(702\) 1.79241e14 1.05136
\(703\) 2.15958e14 1.25775
\(704\) 6.54742e13 0.378623
\(705\) −1.53834e13 −0.0883297
\(706\) 4.26324e14i 2.43061i
\(707\) 2.70686e14i 1.53239i
\(708\) 2.24829e13i 0.126382i
\(709\) 2.91700e14 1.62819 0.814096 0.580730i \(-0.197233\pi\)
0.814096 + 0.580730i \(0.197233\pi\)
\(710\) 5.45934e14i 3.02585i
\(711\) 1.92859e14 1.06143
\(712\) 1.06976e13 0.0584636
\(713\) −4.23248e13 −0.229693
\(714\) 2.28421e13i 0.123096i
\(715\) 6.70798e14i 3.58973i
\(716\) 9.94047e12i 0.0528253i
\(717\) 8.25901e13i 0.435845i
\(718\) 2.09044e14i 1.09551i
\(719\) −1.88232e13 −0.0979601 −0.0489800 0.998800i \(-0.515597\pi\)
−0.0489800 + 0.998800i \(0.515597\pi\)
\(720\) 3.28485e14i 1.69767i
\(721\) 1.85495e14i 0.952041i
\(722\) 2.57994e13i 0.131499i
\(723\) −6.23996e13 −0.315857
\(724\) −1.49140e14 −0.749722
\(725\) 1.10119e14i 0.549758i
\(726\) 5.69401e13 0.282316
\(727\) 3.32311e14i 1.63634i 0.574979 + 0.818168i \(0.305010\pi\)
−0.574979 + 0.818168i \(0.694990\pi\)
\(728\) −1.49656e14 −0.731874
\(729\) 1.39200e14 0.676083
\(730\) 5.30549e14i 2.55924i
\(731\) −8.45794e13 6.95923e12i −0.405208 0.0333407i
\(732\) 2.43166e13 0.115704
\(733\) 1.30904e14i 0.618631i 0.950960 + 0.309315i \(0.100100\pi\)
−0.950960 + 0.309315i \(0.899900\pi\)
\(734\) 1.85178e14i 0.869176i
\(735\) 2.43166e12 0.0113362
\(736\) 1.74837e14i 0.809553i
\(737\) −3.11353e14 −1.43191
\(738\) 1.25936e14i 0.575263i
\(739\) 1.81148e14i 0.821885i −0.911661 0.410942i \(-0.865200\pi\)
0.911661 0.410942i \(-0.134800\pi\)
\(740\) −2.92172e14 −1.31668
\(741\) 8.85704e13 0.396458
\(742\) 2.60550e14 1.15843
\(743\) 6.15807e12i 0.0271957i 0.999908 + 0.0135979i \(0.00432847\pi\)
−0.999908 + 0.0135979i \(0.995672\pi\)
\(744\) 7.52323e12 0.0330019
\(745\) −4.40289e14 −1.91847
\(746\) −3.49420e14 −1.51235
\(747\) 1.79481e14 0.771640
\(748\) 8.86839e13 0.378736
\(749\) 2.34885e14i 0.996428i
\(750\) 1.88769e13i 0.0795472i
\(751\) 3.33417e14i 1.39569i −0.716251 0.697843i \(-0.754143\pi\)
0.716251 0.697843i \(-0.245857\pi\)
\(752\) 7.38486e13 0.307081
\(753\) 8.65111e12i 0.0357353i
\(754\) 2.59167e14 1.06347
\(755\) 5.76272e14 2.34905
\(756\) −7.55791e13 −0.306050
\(757\) 5.95588e13i 0.239589i 0.992799 + 0.119794i \(0.0382236\pi\)
−0.992799 + 0.119794i \(0.961776\pi\)
\(758\) 2.43232e14i 0.972019i
\(759\) 5.81827e13i 0.230986i
\(760\) 1.50017e14i 0.591660i
\(761\) 1.10350e14i 0.432363i −0.976353 0.216182i \(-0.930640\pi\)
0.976353 0.216182i \(-0.0693603\pi\)
\(762\) −1.19344e13 −0.0464543
\(763\) 2.58251e14i 0.998662i
\(764\) 8.09349e13i 0.310935i
\(765\) 1.48213e14i 0.565692i
\(766\) −4.61444e14 −1.74975
\(767\) 3.68351e14 1.38767
\(768\) 8.32675e13i 0.311652i
\(769\) −1.86002e14 −0.691650 −0.345825 0.938299i \(-0.612401\pi\)
−0.345825 + 0.938299i \(0.612401\pi\)
\(770\) 7.03293e14i 2.59826i
\(771\) −1.24081e14 −0.455441
\(772\) 2.68759e14 0.980115
\(773\) 2.76888e14i 1.00324i 0.865087 + 0.501622i \(0.167263\pi\)
−0.865087 + 0.501622i \(0.832737\pi\)
\(774\) 2.77929e13 3.37783e14i 0.100053 1.21600i
\(775\) −1.07661e14 −0.385079
\(776\) 1.25012e14i 0.444265i
\(777\) 8.79767e13i 0.310644i
\(778\) −7.16561e14 −2.51394
\(779\) 1.28196e14i 0.446875i
\(780\) −1.19828e14