Properties

Label 81.12.c.b.28.1
Level $81$
Weight $12$
Character 81.28
Analytic conductor $62.236$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 81.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(62.2357976253\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 28.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 81.28
Dual form 81.12.c.b.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} +O(q^{10})\) \(q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} -115920. q^{10} +(267306. + 462988. i) q^{11} +(288869. - 500336. i) q^{13} +(200928. - 348018. i) q^{14} +(-493568. - 854885. i) q^{16} +6.90593e6 q^{17} +1.06614e7 q^{19} +(-3.55488e6 - 6.15723e6i) q^{20} +(6.41534e6 - 1.11117e7i) q^{22} +(9.32164e6 - 1.61455e7i) q^{23} +(1.27496e7 + 2.20830e7i) q^{25} -1.38657e7 q^{26} +2.46472e7 q^{28} +(6.42033e7 + 1.11203e8i) q^{29} +(2.64216e7 - 4.57635e7i) q^{31} +(-9.83532e7 + 1.70353e8i) q^{32} +(-8.28712e7 - 1.43537e8i) q^{34} +8.08735e7 q^{35} -1.82213e8 q^{37} +(-1.27937e8 - 2.21593e8i) q^{38} +(-2.04019e8 + 3.53372e8i) q^{40} +(1.54060e8 - 2.66840e8i) q^{41} +(8.56285e6 + 1.48313e7i) q^{43} +7.86949e8 q^{44} -4.47439e8 q^{46} +(1.34367e9 + 2.32731e9i) q^{47} +(8.48483e8 - 1.46961e9i) q^{49} +(3.05991e8 - 5.29991e8i) q^{50} +(-4.25215e8 - 7.36494e8i) q^{52} +1.59606e9 q^{53} +2.58218e9 q^{55} +(-7.07267e8 - 1.22502e9i) q^{56} +(1.54088e9 - 2.66888e9i) q^{58} +(-2.59460e9 + 4.49398e9i) q^{59} +(-3.47824e9 - 6.02449e9i) q^{61} -1.26824e9 q^{62} +2.69930e9 q^{64} +(-1.39524e9 - 2.41662e9i) q^{65} +(7.74091e9 - 1.34077e10i) q^{67} +(5.08277e9 - 8.80361e9i) q^{68} +(-9.70482e8 - 1.68092e9i) q^{70} -9.79149e9 q^{71} +1.46379e9 q^{73} +(2.18656e9 + 3.78723e9i) q^{74} +(7.84681e9 - 1.35911e10i) q^{76} +(-4.47577e9 + 7.75226e9i) q^{77} +(-1.90584e10 - 3.30102e10i) q^{79} -4.76787e9 q^{80} -7.39489e9 q^{82} +(-1.46675e10 - 2.54049e10i) q^{83} +(1.66778e10 - 2.88868e10i) q^{85} +(2.05508e8 - 3.55951e8i) q^{86} +(-2.25820e10 - 3.91132e10i) q^{88} +2.49929e10 q^{89} +9.67365e9 q^{91} +(-1.37214e10 - 2.37662e10i) q^{92} +(3.22482e10 - 5.58555e10i) q^{94} +(2.57473e10 - 4.45957e10i) q^{95} +(-3.75068e10 - 6.49637e10i) q^{97} -4.07272e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 24q^{2} + 1472q^{4} + 4830q^{5} + 16744q^{7} - 168960q^{8} + O(q^{10}) \) \( 2q - 24q^{2} + 1472q^{4} + 4830q^{5} + 16744q^{7} - 168960q^{8} - 231840q^{10} + 534612q^{11} + 577738q^{13} + 401856q^{14} - 987136q^{16} + 13811868q^{17} + 21322840q^{19} - 7109760q^{20} + 12830688q^{22} + 18643272q^{23} + 25499225q^{25} - 27731424q^{26} + 49294336q^{28} + 128406630q^{29} + 52843168q^{31} - 196706304q^{32} - 165742416q^{34} + 161747040q^{35} - 364426628q^{37} - 255874080q^{38} - 408038400q^{40} + 308120442q^{41} + 17125708q^{43} + 1573897728q^{44} - 894877056q^{46} + 2687348496q^{47} + 1696965207q^{49} + 611981400q^{50} - 850430336q^{52} + 3192111396q^{53} + 5164351920q^{55} - 1414533120q^{56} + 3081759120q^{58} - 5189203740q^{59} - 6956478662q^{61} - 2536472064q^{62} + 5398593536q^{64} - 2790474540q^{65} + 15481826884q^{67} + 10165534848q^{68} - 1940964480q^{70} - 19582970544q^{71} + 2927582644q^{73} + 4373119536q^{74} + 15693610240q^{76} - 8951543328q^{77} - 38116845680q^{79} - 9535733760q^{80} - 14789781216q^{82} - 29335099668q^{83} + 33355661220q^{85} + 411016992q^{86} - 45164021760q^{88} + 49985834220q^{89} + 19347290144q^{91} - 27442896384q^{92} + 64496363904q^{94} + 51494658600q^{95} - 75013568546q^{97} - 81454329936q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.0000 20.7846i −0.265165 0.459279i 0.702442 0.711741i \(-0.252093\pi\)
−0.967607 + 0.252462i \(0.918760\pi\)
\(3\) 0 0
\(4\) 736.000 1274.79i 0.359375 0.622456i
\(5\) 2415.00 4182.90i 0.345607 0.598608i −0.639857 0.768494i \(-0.721006\pi\)
0.985464 + 0.169886i \(0.0543398\pi\)
\(6\) 0 0
\(7\) 8372.00 + 14500.7i 0.188274 + 0.326100i 0.944675 0.328008i \(-0.106377\pi\)
−0.756401 + 0.654108i \(0.773044\pi\)
\(8\) −84480.0 −0.911505
\(9\) 0 0
\(10\) −115920. −0.366571
\(11\) 267306. + 462988.i 0.500436 + 0.866781i 1.00000 0.000504048i \(0.000160443\pi\)
−0.499563 + 0.866277i \(0.666506\pi\)
\(12\) 0 0
\(13\) 288869. 500336.i 0.215781 0.373743i −0.737733 0.675092i \(-0.764104\pi\)
0.953514 + 0.301349i \(0.0974371\pi\)
\(14\) 200928. 348018.i 0.0998473 0.172941i
\(15\) 0 0
\(16\) −493568. 854885.i −0.117676 0.203820i
\(17\) 6.90593e6 1.17965 0.589825 0.807531i \(-0.299197\pi\)
0.589825 + 0.807531i \(0.299197\pi\)
\(18\) 0 0
\(19\) 1.06614e7 0.987803 0.493901 0.869518i \(-0.335570\pi\)
0.493901 + 0.869518i \(0.335570\pi\)
\(20\) −3.55488e6 6.15723e6i −0.248405 0.430250i
\(21\) 0 0
\(22\) 6.41534e6 1.11117e7i 0.265397 0.459680i
\(23\) 9.32164e6 1.61455e7i 0.301988 0.523058i −0.674599 0.738185i \(-0.735683\pi\)
0.976586 + 0.215127i \(0.0690166\pi\)
\(24\) 0 0
\(25\) 1.27496e7 + 2.20830e7i 0.261112 + 0.452259i
\(26\) −1.38657e7 −0.228870
\(27\) 0 0
\(28\) 2.46472e7 0.270644
\(29\) 6.42033e7 + 1.11203e8i 0.581257 + 1.00677i 0.995331 + 0.0965237i \(0.0307724\pi\)
−0.414073 + 0.910244i \(0.635894\pi\)
\(30\) 0 0
\(31\) 2.64216e7 4.57635e7i 0.165756 0.287098i −0.771167 0.636632i \(-0.780327\pi\)
0.936924 + 0.349534i \(0.113660\pi\)
\(32\) −9.83532e7 + 1.70353e8i −0.518159 + 0.897478i
\(33\) 0 0
\(34\) −8.28712e7 1.43537e8i −0.312802 0.541789i
\(35\) 8.08735e7 0.260275
\(36\) 0 0
\(37\) −1.82213e8 −0.431987 −0.215993 0.976395i \(-0.569299\pi\)
−0.215993 + 0.976395i \(0.569299\pi\)
\(38\) −1.27937e8 2.21593e8i −0.261931 0.453677i
\(39\) 0 0
\(40\) −2.04019e8 + 3.53372e8i −0.315022 + 0.545634i
\(41\) 1.54060e8 2.66840e8i 0.207673 0.359700i −0.743308 0.668949i \(-0.766744\pi\)
0.950981 + 0.309249i \(0.100078\pi\)
\(42\) 0 0
\(43\) 8.56285e6 + 1.48313e7i 0.00888264 + 0.0153852i 0.870433 0.492288i \(-0.163839\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(44\) 7.86949e8 0.719377
\(45\) 0 0
\(46\) −4.47439e8 −0.320306
\(47\) 1.34367e9 + 2.32731e9i 0.854586 + 1.48019i 0.877029 + 0.480438i \(0.159522\pi\)
−0.0224426 + 0.999748i \(0.507144\pi\)
\(48\) 0 0
\(49\) 8.48483e8 1.46961e9i 0.429106 0.743233i
\(50\) 3.05991e8 5.29991e8i 0.138476 0.239847i
\(51\) 0 0
\(52\) −4.25215e8 7.36494e8i −0.155092 0.268628i
\(53\) 1.59606e9 0.524241 0.262120 0.965035i \(-0.415578\pi\)
0.262120 + 0.965035i \(0.415578\pi\)
\(54\) 0 0
\(55\) 2.58218e9 0.691817
\(56\) −7.07267e8 1.22502e9i −0.171613 0.297242i
\(57\) 0 0
\(58\) 1.54088e9 2.66888e9i 0.308258 0.533919i
\(59\) −2.59460e9 + 4.49398e9i −0.472481 + 0.818362i −0.999504 0.0314895i \(-0.989975\pi\)
0.527023 + 0.849851i \(0.323308\pi\)
\(60\) 0 0
\(61\) −3.47824e9 6.02449e9i −0.527285 0.913284i −0.999494 0.0317979i \(-0.989877\pi\)
0.472209 0.881486i \(-0.343457\pi\)
\(62\) −1.26824e9 −0.175811
\(63\) 0 0
\(64\) 2.69930e9 0.314240
\(65\) −1.39524e9 2.41662e9i −0.149150 0.258336i
\(66\) 0 0
\(67\) 7.74091e9 1.34077e10i 0.700456 1.21323i −0.267851 0.963460i \(-0.586313\pi\)
0.968307 0.249765i \(-0.0803533\pi\)
\(68\) 5.08277e9 8.80361e9i 0.423937 0.734280i
\(69\) 0 0
\(70\) −9.70482e8 1.68092e9i −0.0690158 0.119539i
\(71\) −9.79149e9 −0.644062 −0.322031 0.946729i \(-0.604366\pi\)
−0.322031 + 0.946729i \(0.604366\pi\)
\(72\) 0 0
\(73\) 1.46379e9 0.0826425 0.0413212 0.999146i \(-0.486843\pi\)
0.0413212 + 0.999146i \(0.486843\pi\)
\(74\) 2.18656e9 + 3.78723e9i 0.114548 + 0.198403i
\(75\) 0 0
\(76\) 7.84681e9 1.35911e10i 0.354992 0.614864i
\(77\) −4.47577e9 + 7.75226e9i −0.188438 + 0.326385i
\(78\) 0 0
\(79\) −1.90584e10 3.30102e10i −0.696848 1.20698i −0.969554 0.244878i \(-0.921252\pi\)
0.272706 0.962097i \(-0.412081\pi\)
\(80\) −4.76787e9 −0.162678
\(81\) 0 0
\(82\) −7.39489e9 −0.220270
\(83\) −1.46675e10 2.54049e10i −0.408722 0.707927i 0.586025 0.810293i \(-0.300692\pi\)
−0.994747 + 0.102366i \(0.967359\pi\)
\(84\) 0 0
\(85\) 1.66778e10 2.88868e10i 0.407695 0.706149i
\(86\) 2.05508e8 3.55951e8i 0.00471073 0.00815923i
\(87\) 0 0
\(88\) −2.25820e10 3.91132e10i −0.456150 0.790075i
\(89\) 2.49929e10 0.474430 0.237215 0.971457i \(-0.423765\pi\)
0.237215 + 0.971457i \(0.423765\pi\)
\(90\) 0 0
\(91\) 9.67365e9 0.162503
\(92\) −1.37214e10 2.37662e10i −0.217054 0.375948i
\(93\) 0 0
\(94\) 3.22482e10 5.58555e10i 0.453213 0.784987i
\(95\) 2.57473e10 4.45957e10i 0.341391 0.591307i
\(96\) 0 0
\(97\) −3.75068e10 6.49637e10i −0.443471 0.768114i 0.554473 0.832202i \(-0.312920\pi\)
−0.997944 + 0.0640871i \(0.979586\pi\)
\(98\) −4.07272e10 −0.455136
\(99\) 0 0
\(100\) 3.75349e10 0.375349
\(101\) 4.08715e10 + 7.07915e10i 0.386948 + 0.670214i 0.992037 0.125944i \(-0.0401959\pi\)
−0.605089 + 0.796158i \(0.706863\pi\)
\(102\) 0 0
\(103\) 1.12878e11 1.95510e11i 0.959407 1.66174i 0.235463 0.971883i \(-0.424339\pi\)
0.723944 0.689858i \(-0.242327\pi\)
\(104\) −2.44037e10 + 4.22684e10i −0.196685 + 0.340669i
\(105\) 0 0
\(106\) −1.91527e10 3.31734e10i −0.139010 0.240773i
\(107\) −9.02413e10 −0.622006 −0.311003 0.950409i \(-0.600665\pi\)
−0.311003 + 0.950409i \(0.600665\pi\)
\(108\) 0 0
\(109\) 7.34827e10 0.457445 0.228723 0.973492i \(-0.426545\pi\)
0.228723 + 0.973492i \(0.426545\pi\)
\(110\) −3.09861e10 5.36695e10i −0.183446 0.317737i
\(111\) 0 0
\(112\) 8.26430e9 1.43142e10i 0.0443105 0.0767481i
\(113\) −4.25734e10 + 7.37393e10i −0.217374 + 0.376502i −0.954004 0.299793i \(-0.903082\pi\)
0.736630 + 0.676295i \(0.236416\pi\)
\(114\) 0 0
\(115\) −4.50235e10 7.79830e10i −0.208738 0.361545i
\(116\) 1.89015e11 0.835557
\(117\) 0 0
\(118\) 1.24541e11 0.501142
\(119\) 5.78165e10 + 1.00141e11i 0.222097 + 0.384684i
\(120\) 0 0
\(121\) −2.49160e8 + 4.31558e8i −0.000873290 + 0.00151258i
\(122\) −8.34777e10 + 1.44588e11i −0.279635 + 0.484342i
\(123\) 0 0
\(124\) −3.88926e10 6.73639e10i −0.119137 0.206352i
\(125\) 3.59001e11 1.05218
\(126\) 0 0
\(127\) −2.62717e11 −0.705615 −0.352808 0.935696i \(-0.614773\pi\)
−0.352808 + 0.935696i \(0.614773\pi\)
\(128\) 1.69036e11 + 2.92778e11i 0.434834 + 0.753155i
\(129\) 0 0
\(130\) −3.34857e10 + 5.79989e10i −0.0790990 + 0.137003i
\(131\) 3.15764e11 5.46920e11i 0.715107 1.23860i −0.247811 0.968808i \(-0.579711\pi\)
0.962918 0.269793i \(-0.0869554\pi\)
\(132\) 0 0
\(133\) 8.92574e10 + 1.54598e11i 0.185977 + 0.322122i
\(134\) −3.71564e11 −0.742946
\(135\) 0 0
\(136\) −5.83413e11 −1.07526
\(137\) −1.48599e11 2.57382e11i −0.263059 0.455632i 0.703994 0.710206i \(-0.251398\pi\)
−0.967053 + 0.254574i \(0.918065\pi\)
\(138\) 0 0
\(139\) −2.98397e11 + 5.16838e11i −0.487767 + 0.844838i −0.999901 0.0140679i \(-0.995522\pi\)
0.512134 + 0.858906i \(0.328855\pi\)
\(140\) 5.95229e10 1.03097e11i 0.0935363 0.162010i
\(141\) 0 0
\(142\) 1.17498e11 + 2.03512e11i 0.170783 + 0.295804i
\(143\) 3.08866e11 0.431938
\(144\) 0 0
\(145\) 6.20204e11 0.803546
\(146\) −1.75655e10 3.04243e10i −0.0219139 0.0379560i
\(147\) 0 0
\(148\) −1.34109e11 + 2.32284e11i −0.155245 + 0.268893i
\(149\) −5.57717e11 + 9.65994e11i −0.622142 + 1.07758i 0.366945 + 0.930243i \(0.380404\pi\)
−0.989086 + 0.147338i \(0.952929\pi\)
\(150\) 0 0
\(151\) 4.12224e11 + 7.13992e11i 0.427326 + 0.740151i 0.996635 0.0819732i \(-0.0261222\pi\)
−0.569308 + 0.822124i \(0.692789\pi\)
\(152\) −9.00677e11 −0.900387
\(153\) 0 0
\(154\) 2.14837e11 0.199869
\(155\) −1.27616e11 2.21038e11i −0.114573 0.198446i
\(156\) 0 0
\(157\) −6.57558e11 + 1.13892e12i −0.550156 + 0.952899i 0.448106 + 0.893980i \(0.352099\pi\)
−0.998263 + 0.0589187i \(0.981235\pi\)
\(158\) −4.57402e11 + 7.92244e11i −0.369559 + 0.640096i
\(159\) 0 0
\(160\) 4.75046e11 + 8.22803e11i 0.358159 + 0.620349i
\(161\) 3.12163e11 0.227425
\(162\) 0 0
\(163\) −3.57833e11 −0.243584 −0.121792 0.992556i \(-0.538864\pi\)
−0.121792 + 0.992556i \(0.538864\pi\)
\(164\) −2.26777e11 3.92789e11i −0.149265 0.258534i
\(165\) 0 0
\(166\) −3.52021e11 + 6.09719e11i −0.216758 + 0.375435i
\(167\) 1.37742e12 2.38576e12i 0.820587 1.42130i −0.0846581 0.996410i \(-0.526980\pi\)
0.905245 0.424889i \(-0.139687\pi\)
\(168\) 0 0
\(169\) 7.29190e11 + 1.26299e12i 0.406877 + 0.704732i
\(170\) −8.00536e11 −0.432426
\(171\) 0 0
\(172\) 2.52090e10 0.0127688
\(173\) −4.75194e11 8.23060e11i −0.233140 0.403811i 0.725590 0.688127i \(-0.241567\pi\)
−0.958731 + 0.284316i \(0.908233\pi\)
\(174\) 0 0
\(175\) −2.13480e11 + 3.69757e11i −0.0983211 + 0.170297i
\(176\) 2.63867e11 4.57032e11i 0.117779 0.203998i
\(177\) 0 0
\(178\) −2.99915e11 5.19468e11i −0.125802 0.217896i
\(179\) −1.68138e12 −0.683873 −0.341936 0.939723i \(-0.611083\pi\)
−0.341936 + 0.939723i \(0.611083\pi\)
\(180\) 0 0
\(181\) −9.96774e11 −0.381386 −0.190693 0.981650i \(-0.561073\pi\)
−0.190693 + 0.981650i \(0.561073\pi\)
\(182\) −1.16084e11 2.01063e11i −0.0430902 0.0746345i
\(183\) 0 0
\(184\) −7.87492e11 + 1.36398e12i −0.275263 + 0.476770i
\(185\) −4.40045e11 + 7.62181e11i −0.149298 + 0.258591i
\(186\) 0 0
\(187\) 1.84600e12 + 3.19736e12i 0.590340 + 1.02250i
\(188\) 3.95578e12 1.22847
\(189\) 0 0
\(190\) −1.23587e12 −0.362100
\(191\) 1.38120e12 + 2.39231e12i 0.393164 + 0.680980i 0.992865 0.119244i \(-0.0380472\pi\)
−0.599701 + 0.800224i \(0.704714\pi\)
\(192\) 0 0
\(193\) −2.72119e12 + 4.71325e12i −0.731466 + 1.26694i 0.224790 + 0.974407i \(0.427830\pi\)
−0.956256 + 0.292530i \(0.905503\pi\)
\(194\) −9.00163e11 + 1.55913e12i −0.235186 + 0.407354i
\(195\) 0 0
\(196\) −1.24897e12 2.16327e12i −0.308420 0.534199i
\(197\) 2.87609e12 0.690619 0.345309 0.938489i \(-0.387774\pi\)
0.345309 + 0.938489i \(0.387774\pi\)
\(198\) 0 0
\(199\) 7.28391e11 0.165452 0.0827262 0.996572i \(-0.473637\pi\)
0.0827262 + 0.996572i \(0.473637\pi\)
\(200\) −1.07709e12 1.86557e12i −0.238005 0.412237i
\(201\) 0 0
\(202\) 9.80916e11 1.69900e12i 0.205210 0.355435i
\(203\) −1.07502e12 + 1.86199e12i −0.218871 + 0.379096i
\(204\) 0 0
\(205\) −7.44111e11 1.28884e12i −0.143546 0.248629i
\(206\) −5.41812e12 −1.01760
\(207\) 0 0
\(208\) −5.70306e11 −0.101569
\(209\) 2.84986e12 + 4.93610e12i 0.494333 + 0.856209i
\(210\) 0 0
\(211\) 3.39658e12 5.88306e12i 0.559099 0.968388i −0.438473 0.898745i \(-0.644480\pi\)
0.997572 0.0696437i \(-0.0221863\pi\)
\(212\) 1.17470e12 2.03463e12i 0.188399 0.326317i
\(213\) 0 0
\(214\) 1.08290e12 + 1.87563e12i 0.164934 + 0.285674i
\(215\) 8.27172e10 0.0122796
\(216\) 0 0
\(217\) 8.84806e11 0.124830
\(218\) −8.81792e11 1.52731e12i −0.121299 0.210095i
\(219\) 0 0
\(220\) 1.90048e12 3.29173e12i 0.248622 0.430625i
\(221\) 1.99491e12 3.45529e12i 0.254546 0.440886i
\(222\) 0 0
\(223\) −3.66743e12 6.35218e12i −0.445333 0.771340i 0.552742 0.833352i \(-0.313582\pi\)
−0.998075 + 0.0620124i \(0.980248\pi\)
\(224\) −3.29365e12 −0.390223
\(225\) 0 0
\(226\) 2.04352e12 0.230560
\(227\) −6.79920e11 1.17766e12i −0.0748713 0.129681i 0.826159 0.563437i \(-0.190521\pi\)
−0.901030 + 0.433756i \(0.857188\pi\)
\(228\) 0 0
\(229\) 5.91221e12 1.02402e13i 0.620375 1.07452i −0.369041 0.929413i \(-0.620314\pi\)
0.989416 0.145108i \(-0.0463530\pi\)
\(230\) −1.08056e12 + 1.87159e12i −0.110700 + 0.191738i
\(231\) 0 0
\(232\) −5.42390e12 9.39446e12i −0.529819 0.917673i
\(233\) 1.75634e13 1.67552 0.837761 0.546038i \(-0.183865\pi\)
0.837761 + 0.546038i \(0.183865\pi\)
\(234\) 0 0
\(235\) 1.29799e13 1.18140
\(236\) 3.81925e12 + 6.61514e12i 0.339596 + 0.588197i
\(237\) 0 0
\(238\) 1.38760e12 2.40339e12i 0.117785 0.204009i
\(239\) −3.56979e12 + 6.18306e12i −0.296111 + 0.512879i −0.975243 0.221137i \(-0.929023\pi\)
0.679132 + 0.734016i \(0.262356\pi\)
\(240\) 0 0
\(241\) 1.15653e11 + 2.00318e11i 0.00916357 + 0.0158718i 0.870571 0.492043i \(-0.163750\pi\)
−0.861407 + 0.507915i \(0.830416\pi\)
\(242\) 1.19597e10 0.000926264
\(243\) 0 0
\(244\) −1.02399e13 −0.757972
\(245\) −4.09817e12 7.09824e12i −0.296604 0.513733i
\(246\) 0 0
\(247\) 3.07975e12 5.33429e12i 0.213149 0.369184i
\(248\) −2.23210e12 + 3.86610e12i −0.151087 + 0.261691i
\(249\) 0 0
\(250\) −4.30801e12 7.46170e12i −0.279002 0.483245i
\(251\) −1.29831e13 −0.822567 −0.411284 0.911507i \(-0.634919\pi\)
−0.411284 + 0.911507i \(0.634919\pi\)
\(252\) 0 0
\(253\) 9.96692e12 0.604502
\(254\) 3.15261e12 + 5.46047e12i 0.187105 + 0.324075i
\(255\) 0 0
\(256\) 6.82094e12 1.18142e13i 0.387725 0.671560i
\(257\) 1.19806e13 2.07510e13i 0.666571 1.15453i −0.312286 0.949988i \(-0.601095\pi\)
0.978857 0.204546i \(-0.0655719\pi\)
\(258\) 0 0
\(259\) −1.52549e12 2.64223e12i −0.0813318 0.140871i
\(260\) −4.10758e12 −0.214404
\(261\) 0 0
\(262\) −1.51567e13 −0.758485
\(263\) −1.21369e13 2.10217e13i −0.594771 1.03017i −0.993579 0.113139i \(-0.963909\pi\)
0.398808 0.917034i \(-0.369424\pi\)
\(264\) 0 0
\(265\) 3.85447e12 6.67615e12i 0.181181 0.313815i
\(266\) 2.14218e12 3.71036e12i 0.0986294 0.170831i
\(267\) 0 0
\(268\) −1.13946e13 1.97361e13i −0.503453 0.872006i
\(269\) −2.58377e13 −1.11845 −0.559225 0.829016i \(-0.688901\pi\)
−0.559225 + 0.829016i \(0.688901\pi\)
\(270\) 0 0
\(271\) −3.76793e12 −0.156593 −0.0782964 0.996930i \(-0.524948\pi\)
−0.0782964 + 0.996930i \(0.524948\pi\)
\(272\) −3.40855e12 5.90378e12i −0.138816 0.240437i
\(273\) 0 0
\(274\) −3.56638e12 + 6.17716e12i −0.139508 + 0.241636i
\(275\) −6.81610e12 + 1.18058e13i −0.261340 + 0.452654i
\(276\) 0 0
\(277\) 8.20947e12 + 1.42192e13i 0.302466 + 0.523886i 0.976694 0.214637i \(-0.0688569\pi\)
−0.674228 + 0.738523i \(0.735524\pi\)
\(278\) 1.43230e13 0.517355
\(279\) 0 0
\(280\) −6.83219e12 −0.237242
\(281\) 1.05179e13 + 1.82175e13i 0.358132 + 0.620302i 0.987649 0.156684i \(-0.0500806\pi\)
−0.629517 + 0.776987i \(0.716747\pi\)
\(282\) 0 0
\(283\) −8.35659e12 + 1.44740e13i −0.273655 + 0.473985i −0.969795 0.243922i \(-0.921566\pi\)
0.696140 + 0.717906i \(0.254899\pi\)
\(284\) −7.20653e12 + 1.24821e13i −0.231460 + 0.400900i
\(285\) 0 0
\(286\) −3.70639e12 6.41965e12i −0.114535 0.198380i
\(287\) 5.15917e12 0.156397
\(288\) 0 0
\(289\) 1.34200e13 0.391575
\(290\) −7.44245e12 1.28907e13i −0.213072 0.369052i
\(291\) 0 0
\(292\) 1.07735e12 1.86603e12i 0.0296996 0.0514413i
\(293\) −1.19634e13 + 2.07213e13i −0.323656 + 0.560589i −0.981239 0.192793i \(-0.938245\pi\)
0.657583 + 0.753382i \(0.271579\pi\)
\(294\) 0 0
\(295\) 1.25319e13 + 2.17059e13i 0.326585 + 0.565663i
\(296\) 1.53934e13 0.393758
\(297\) 0 0
\(298\) 2.67704e13 0.659881
\(299\) −5.38546e12 9.32790e12i −0.130326 0.225731i
\(300\) 0 0
\(301\) −1.43376e11 + 2.48335e11i −0.00334474 + 0.00579326i
\(302\) 9.89337e12 1.71358e13i 0.226624 0.392524i
\(303\) 0 0
\(304\) −5.26214e12 9.11429e12i −0.116240 0.201334i
\(305\) −3.35998e13 −0.728933
\(306\) 0 0
\(307\) 1.53111e13 0.320439 0.160219 0.987081i \(-0.448780\pi\)
0.160219 + 0.987081i \(0.448780\pi\)
\(308\) 6.58834e12 + 1.14113e13i 0.135440 + 0.234589i
\(309\) 0 0
\(310\) −3.06279e12 + 5.30491e12i −0.0607614 + 0.105242i
\(311\) 2.49376e13 4.31932e13i 0.486040 0.841846i −0.513831 0.857891i \(-0.671774\pi\)
0.999871 + 0.0160451i \(0.00510753\pi\)
\(312\) 0 0
\(313\) 4.97404e13 + 8.61529e13i 0.935870 + 1.62097i 0.773075 + 0.634315i \(0.218718\pi\)
0.162795 + 0.986660i \(0.447949\pi\)
\(314\) 3.15628e13 0.583529
\(315\) 0 0
\(316\) −5.61080e13 −1.00172
\(317\) 4.16846e13 + 7.21999e13i 0.731392 + 1.26681i 0.956289 + 0.292425i \(0.0944621\pi\)
−0.224897 + 0.974383i \(0.572205\pi\)
\(318\) 0 0
\(319\) −3.43239e13 + 5.94507e13i −0.581765 + 1.00765i
\(320\) 6.51880e12 1.12909e13i 0.108603 0.188106i
\(321\) 0 0
\(322\) −3.74596e12 6.48819e12i −0.0603053 0.104452i
\(323\) 7.36271e13 1.16526
\(324\) 0 0
\(325\) 1.47319e13 0.225372
\(326\) 4.29399e12 + 7.43741e12i 0.0645899 + 0.111873i
\(327\) 0 0
\(328\) −1.30150e13 + 2.25427e13i −0.189295 + 0.327868i
\(329\) −2.24985e13 + 3.89685e13i −0.321792 + 0.557361i
\(330\) 0 0
\(331\) 3.17920e13 + 5.50654e13i 0.439809 + 0.761771i 0.997674 0.0681600i \(-0.0217128\pi\)
−0.557865 + 0.829931i \(0.688379\pi\)
\(332\) −4.31813e13 −0.587538
\(333\) 0 0
\(334\) −6.61160e13 −0.870364
\(335\) −3.73886e13 6.47590e13i −0.484164 0.838597i
\(336\) 0 0
\(337\) −6.05007e13 + 1.04790e14i −0.758221 + 1.31328i 0.185535 + 0.982638i \(0.440598\pi\)
−0.943757 + 0.330640i \(0.892735\pi\)
\(338\) 1.75006e13 3.03118e13i 0.215779 0.373741i
\(339\) 0 0
\(340\) −2.45498e13 4.25214e13i −0.293031 0.507544i
\(341\) 2.82506e13 0.331802
\(342\) 0 0
\(343\) 6.15223e13 0.699705
\(344\) −7.23390e11 1.25295e12i −0.00809657 0.0140237i
\(345\) 0 0
\(346\) −1.14046e13 + 1.97534e13i −0.123641 + 0.214153i
\(347\) −7.78308e13 + 1.34807e14i −0.830499 + 1.43847i 0.0671435 + 0.997743i \(0.478611\pi\)
−0.897643 + 0.440724i \(0.854722\pi\)
\(348\) 0 0
\(349\) 1.28215e13 + 2.22075e13i 0.132556 + 0.229594i 0.924661 0.380791i \(-0.124348\pi\)
−0.792105 + 0.610385i \(0.791015\pi\)
\(350\) 1.02470e13 0.104285
\(351\) 0 0
\(352\) −1.05162e14 −1.03722
\(353\) 1.24549e13 + 2.15725e13i 0.120943 + 0.209479i 0.920140 0.391590i \(-0.128075\pi\)
−0.799197 + 0.601069i \(0.794742\pi\)
\(354\) 0 0
\(355\) −2.36464e13 + 4.09568e13i −0.222592 + 0.385541i
\(356\) 1.83948e13 3.18607e13i 0.170498 0.295312i
\(357\) 0 0
\(358\) 2.01766e13 + 3.49469e13i 0.181339 + 0.314089i
\(359\) −1.57584e14 −1.39474 −0.697370 0.716712i \(-0.745646\pi\)
−0.697370 + 0.716712i \(0.745646\pi\)
\(360\) 0 0
\(361\) −2.82438e12 −0.0242457
\(362\) 1.19613e13 + 2.07176e13i 0.101130 + 0.175163i
\(363\) 0 0
\(364\) 7.11980e12 1.23319e13i 0.0583997 0.101151i
\(365\) 3.53506e12 6.12290e12i 0.0285618 0.0494705i
\(366\) 0 0
\(367\) 8.89506e13 + 1.54067e14i 0.697406 + 1.20794i 0.969363 + 0.245633i \(0.0789958\pi\)
−0.271957 + 0.962309i \(0.587671\pi\)
\(368\) −1.84034e13 −0.142146
\(369\) 0 0
\(370\) 2.11222e13 0.158354
\(371\) 1.33622e13 + 2.31440e13i 0.0987008 + 0.170955i
\(372\) 0 0
\(373\) 2.75809e13 4.77715e13i 0.197792 0.342586i −0.750020 0.661415i \(-0.769956\pi\)
0.947812 + 0.318829i \(0.103290\pi\)
\(374\) 4.43039e13 7.67367e13i 0.313075 0.542262i
\(375\) 0 0
\(376\) −1.13514e14 1.96611e14i −0.778959 1.34920i
\(377\) 7.41854e13 0.501696
\(378\) 0 0
\(379\) 1.46463e14 0.962083 0.481042 0.876698i \(-0.340259\pi\)
0.481042 + 0.876698i \(0.340259\pi\)
\(380\) −3.79001e13 6.56448e13i −0.245375 0.425002i
\(381\) 0 0
\(382\) 3.31488e13 5.74155e13i 0.208507 0.361144i
\(383\) 1.15725e14 2.00441e14i 0.717519 1.24278i −0.244462 0.969659i \(-0.578611\pi\)
0.961980 0.273120i \(-0.0880555\pi\)
\(384\) 0 0
\(385\) 2.16180e13 + 3.74434e13i 0.130251 + 0.225601i
\(386\) 1.30617e14 0.775837
\(387\) 0 0
\(388\) −1.10420e14 −0.637490
\(389\) −7.49358e13 1.29793e14i −0.426547 0.738800i 0.570017 0.821633i \(-0.306937\pi\)
−0.996563 + 0.0828326i \(0.973603\pi\)
\(390\) 0 0
\(391\) 6.43746e13 1.11500e14i 0.356240 0.617025i
\(392\) −7.16798e13 + 1.24153e14i −0.391132 + 0.677461i
\(393\) 0 0
\(394\) −3.45131e13 5.97784e13i −0.183128 0.317187i
\(395\) −1.84104e14 −0.963341
\(396\) 0 0
\(397\) 2.08111e14 1.05912 0.529562 0.848271i \(-0.322356\pi\)
0.529562 + 0.848271i \(0.322356\pi\)
\(398\) −8.74070e12 1.51393e13i −0.0438722 0.0759888i
\(399\) 0 0
\(400\) 1.25856e13 2.17989e13i 0.0614531 0.106440i
\(401\) −6.67040e13 + 1.15535e14i −0.321261 + 0.556440i −0.980748 0.195275i \(-0.937440\pi\)
0.659488 + 0.751715i \(0.270773\pi\)
\(402\) 0 0
\(403\) −1.52648e13 2.64393e13i −0.0715339 0.123900i
\(404\) 1.20326e14 0.556238
\(405\) 0 0
\(406\) 5.16010e13 0.232148
\(407\) −4.87067e13 8.43625e13i −0.216182 0.374438i
\(408\) 0 0
\(409\) 1.03084e14 1.78546e14i 0.445361 0.771388i −0.552716 0.833369i \(-0.686409\pi\)
0.998077 + 0.0619816i \(0.0197420\pi\)
\(410\) −1.78587e13 + 3.09321e13i −0.0761268 + 0.131856i
\(411\) 0 0
\(412\) −1.66156e14 2.87790e14i −0.689574 1.19438i
\(413\) −8.68880e13 −0.355824
\(414\) 0 0
\(415\) −1.41689e14 −0.565028
\(416\) 5.68224e13 + 9.84192e13i 0.223618 + 0.387317i
\(417\) 0 0
\(418\) 6.83967e13 1.18467e14i 0.262159 0.454073i
\(419\) 3.67018e13 6.35693e13i 0.138838 0.240475i −0.788219 0.615395i \(-0.788996\pi\)
0.927057 + 0.374920i \(0.122330\pi\)
\(420\) 0 0
\(421\) −8.55560e13 1.48187e14i −0.315282 0.546084i 0.664216 0.747541i \(-0.268766\pi\)
−0.979497 + 0.201457i \(0.935432\pi\)
\(422\) −1.63036e14 −0.593014
\(423\) 0 0
\(424\) −1.34835e14 −0.477848
\(425\) 8.80480e13 + 1.52504e14i 0.308021 + 0.533508i
\(426\) 0 0
\(427\) 5.82396e13 1.00874e14i 0.198548 0.343895i
\(428\) −6.64176e13 + 1.15039e14i −0.223533 + 0.387171i
\(429\) 0 0
\(430\) −9.92606e11 1.71924e12i −0.00325612 0.00563977i
\(431\) 7.17758e13 0.232463 0.116231 0.993222i \(-0.462919\pi\)
0.116231 + 0.993222i \(0.462919\pi\)
\(432\) 0 0
\(433\) 9.98812e13 0.315356 0.157678 0.987491i \(-0.449599\pi\)
0.157678 + 0.987491i \(0.449599\pi\)
\(434\) −1.06177e13 1.83903e13i −0.0331006 0.0573319i
\(435\) 0 0
\(436\) 5.40832e13 9.36749e13i 0.164394 0.284739i
\(437\) 9.93819e13 1.72134e14i 0.298304 0.516678i
\(438\) 0 0
\(439\) 1.45156e13 + 2.51418e13i 0.0424894 + 0.0735938i 0.886488 0.462752i \(-0.153138\pi\)
−0.843999 + 0.536345i \(0.819804\pi\)
\(440\) −2.18142e14 −0.630594
\(441\) 0 0
\(442\) −9.57557e13 −0.269987
\(443\) 1.64185e14 + 2.84377e14i 0.457207 + 0.791906i 0.998812 0.0487274i \(-0.0155166\pi\)
−0.541605 + 0.840633i \(0.682183\pi\)
\(444\) 0 0
\(445\) 6.03579e13 1.04543e14i 0.163966 0.283998i
\(446\) −8.80184e13 + 1.52452e14i −0.236174 + 0.409065i
\(447\) 0 0
\(448\) 2.25985e13 + 3.91418e13i 0.0591631 + 0.102473i
\(449\) 6.12368e14 1.58364 0.791822 0.610752i \(-0.209133\pi\)
0.791822 + 0.610752i \(0.209133\pi\)
\(450\) 0 0
\(451\) 1.64725e14 0.415708
\(452\) 6.26681e13 + 1.08544e14i 0.156237 + 0.270611i
\(453\) 0 0
\(454\) −1.63181e13 + 2.82637e13i −0.0397065 + 0.0687737i
\(455\) 2.33619e13 4.04639e13i 0.0561623 0.0972759i
\(456\) 0 0
\(457\) −1.51742e14 2.62824e14i −0.356095 0.616774i 0.631210 0.775612i \(-0.282559\pi\)
−0.987305 + 0.158838i \(0.949225\pi\)
\(458\) −2.83786e14 −0.658007
\(459\) 0 0
\(460\) −1.32549e14 −0.300061
\(461\) −3.64654e14 6.31599e14i −0.815691 1.41282i −0.908830 0.417166i \(-0.863023\pi\)
0.0931391 0.995653i \(-0.470310\pi\)
\(462\) 0 0
\(463\) −6.10941e13 + 1.05818e14i −0.133445 + 0.231134i −0.925003 0.379961i \(-0.875937\pi\)
0.791557 + 0.611095i \(0.209271\pi\)
\(464\) 6.33774e13 1.09773e14i 0.136800 0.236944i
\(465\) 0 0
\(466\) −2.10760e14 3.65047e14i −0.444290 0.769532i
\(467\) 6.17381e14 1.28621 0.643103 0.765780i \(-0.277647\pi\)
0.643103 + 0.765780i \(0.277647\pi\)
\(468\) 0 0
\(469\) 2.59228e14 0.527510
\(470\) −1.55759e14 2.69782e14i −0.313267 0.542594i
\(471\) 0 0
\(472\) 2.19192e14 3.79652e14i 0.430669 0.745941i
\(473\) −4.57780e12 + 7.92899e12i −0.00889039 + 0.0153986i
\(474\) 0 0
\(475\) 1.35929e14 + 2.35436e14i 0.257927 + 0.446743i
\(476\) 1.70212e14 0.319265
\(477\) 0 0
\(478\) 1.71350e14 0.314073
\(479\) 5.25419e14 + 9.10052e14i 0.952052 + 1.64900i 0.740976 + 0.671532i \(0.234363\pi\)
0.211076 + 0.977470i \(0.432303\pi\)
\(480\) 0 0
\(481\) −5.26358e13 + 9.11678e13i −0.0932144 + 0.161452i
\(482\) 2.77568e12 4.80762e12i 0.00485972 0.00841728i
\(483\) 0 0
\(484\) 3.66763e11 + 6.35253e11i 0.000627678 + 0.00108717i
\(485\) −3.62316e14 −0.613066
\(486\) 0 0
\(487\) −2.19910e14 −0.363777 −0.181889 0.983319i \(-0.558221\pi\)
−0.181889 + 0.983319i \(0.558221\pi\)
\(488\) 2.93842e14 + 5.08949e14i 0.480623 + 0.832463i
\(489\) 0 0
\(490\) −9.83561e13 + 1.70358e14i −0.157298 + 0.272448i
\(491\) −2.41932e14 + 4.19038e14i −0.382599 + 0.662682i −0.991433 0.130616i \(-0.958304\pi\)
0.608834 + 0.793298i \(0.291638\pi\)
\(492\) 0 0
\(493\) 4.43384e14 + 7.67963e14i 0.685681 + 1.18763i
\(494\) −1.47828e14 −0.226078
\(495\) 0 0
\(496\) −5.21634e13 −0.0780219
\(497\) −8.19743e13 1.41984e14i −0.121260 0.210029i
\(498\) 0 0
\(499\) 5.44389e13 9.42909e13i 0.0787691 0.136432i −0.823950 0.566663i \(-0.808234\pi\)
0.902719 + 0.430230i \(0.141568\pi\)
\(500\) 2.64225e14 4.57651e14i 0.378128 0.654937i
\(501\) 0 0
\(502\) 1.55797e14 + 2.69848e14i 0.218116 + 0.377788i
\(503\) −5.06588e14 −0.701506 −0.350753 0.936468i \(-0.614074\pi\)
−0.350753 + 0.936468i \(0.614074\pi\)
\(504\) 0 0
\(505\) 3.94818e14 0.534927
\(506\) −1.19603e14 2.07158e14i −0.160293 0.277635i
\(507\) 0 0
\(508\) −1.93360e14 + 3.34909e14i −0.253581 + 0.439214i
\(509\) 4.28767e13 7.42646e13i 0.0556254 0.0963461i −0.836872 0.547399i \(-0.815618\pi\)
0.892497 + 0.451053i \(0.148951\pi\)
\(510\) 0 0
\(511\) 1.22549e13 + 2.12260e13i 0.0155594 + 0.0269497i
\(512\) 3.64965e14 0.458423
\(513\) 0 0
\(514\) −5.75069e14 −0.707005
\(515\) −5.45199e14 9.44312e14i −0.663155 1.14862i
\(516\) 0 0
\(517\) −7.18344e14 + 1.24421e15i −0.855332 + 1.48148i
\(518\) −3.66118e13 + 6.34134e13i −0.0431327 + 0.0747081i
\(519\) 0 0
\(520\) 1.17870e14 + 2.04156e14i 0.135951 + 0.235475i
\(521\) −9.27575e14 −1.05862 −0.529312 0.848428i \(-0.677550\pi\)
−0.529312 + 0.848428i \(0.677550\pi\)
\(522\) 0 0
\(523\) −2.18187e13 −0.0243820 −0.0121910 0.999926i \(-0.503881\pi\)
−0.0121910 + 0.999926i \(0.503881\pi\)
\(524\) −4.64805e14 8.05066e14i −0.513983 0.890245i
\(525\) 0 0
\(526\) −2.91285e14 + 5.04520e14i −0.315425 + 0.546332i
\(527\) 1.82466e14 3.16040e14i 0.195534 0.338675i
\(528\) 0 0
\(529\) 3.02619e14 + 5.24152e14i 0.317607 + 0.550112i
\(530\) −1.85015e14 −0.192172
\(531\) 0 0
\(532\) 2.62774e14 0.267343
\(533\) −8.90064e13 1.54164e14i −0.0896235 0.155232i
\(534\) 0 0
\(535\) −2.17933e14 + 3.77470e14i −0.214969 + 0.372338i
\(536\) −6.53952e14 + 1.13268e15i −0.638469 + 1.10586i
\(537\) 0 0
\(538\) 3.10052e14 + 5.37027e14i 0.296574 + 0.513681i
\(539\) 9.07218e14 0.858961
\(540\) 0 0
\(541\) −1.69527e15 −1.57273 −0.786363 0.617765i \(-0.788038\pi\)
−0.786363 + 0.617765i \(0.788038\pi\)
\(542\) 4.52152e13 + 7.83150e13i 0.0415230 + 0.0719199i
\(543\) 0 0
\(544\) −6.79220e14 + 1.17644e15i −0.611247 + 1.05871i
\(545\) 1.77461e14 3.07371e14i 0.158096 0.273831i
\(546\) 0 0
\(547\) −3.76072e14 6.51376e14i −0.328353 0.568724i 0.653832 0.756640i \(-0.273160\pi\)
−0.982185 + 0.187915i \(0.939827\pi\)
\(548\) −4.37477e14 −0.378148
\(549\) 0 0
\(550\) 3.27173e14 0.277193
\(551\) 6.84499e14 + 1.18559e15i 0.574168 + 0.994488i
\(552\) 0 0
\(553\) 3.19114e14 5.52722e14i 0.262396 0.454484i
\(554\) 1.97027e14 3.41261e14i 0.160407 0.277833i
\(555\) 0 0
\(556\) 4.39240e14 + 7.60786e14i 0.350583 + 0.607227i
\(557\) −1.87489e14 −0.148174 −0.0740870 0.997252i \(-0.523604\pi\)
−0.0740870 + 0.997252i \(0.523604\pi\)
\(558\) 0 0
\(559\) 9.89417e12 0.00766681
\(560\) −3.99166e13 6.91375e13i −0.0306280 0.0530493i
\(561\) 0 0
\(562\) 2.52429e14 4.37219e14i 0.189928 0.328965i
\(563\) 1.22486e14 2.12151e14i 0.0912618 0.158070i −0.816781 0.576949i \(-0.804243\pi\)
0.908042 + 0.418878i \(0.137577\pi\)
\(564\) 0 0
\(565\) 2.05630e14 + 3.56161e14i 0.150252 + 0.260244i
\(566\) 4.01116e14 0.290255
\(567\) 0 0
\(568\) 8.27185e14 0.587066
\(569\) 6.76213e14 + 1.17124e15i 0.475298 + 0.823240i 0.999600 0.0282923i \(-0.00900691\pi\)
−0.524302 + 0.851533i \(0.675674\pi\)
\(570\) 0 0
\(571\) −7.16114e14 + 1.24035e15i −0.493723 + 0.855154i −0.999974 0.00723249i \(-0.997698\pi\)
0.506250 + 0.862387i \(0.331031\pi\)
\(572\) 2.27325e14 3.93739e14i 0.155228 0.268862i
\(573\) 0 0
\(574\) −6.19100e13 1.07231e14i −0.0414711 0.0718301i
\(575\) 4.75389e14 0.315410
\(576\) 0 0
\(577\) −8.77659e14 −0.571293 −0.285647 0.958335i \(-0.592208\pi\)
−0.285647 + 0.958335i \(0.592208\pi\)
\(578\) −1.61040e14 2.78930e14i −0.103832 0.179842i
\(579\) 0 0
\(580\) 4.56470e14 7.90630e14i 0.288774 0.500172i
\(581\) 2.45593e14 4.25380e14i 0.153903 0.266568i
\(582\) 0 0
\(583\) 4.26635e14 + 7.38954e14i 0.262349 + 0.454402i
\(584\) −1.23661e14 −0.0753290
\(585\) 0 0
\(586\) 5.74245e14 0.343289
\(587\) −1.21713e15 2.10812e15i −0.720818 1.24849i −0.960672 0.277685i \(-0.910433\pi\)
0.239854 0.970809i \(-0.422900\pi\)
\(588\) 0 0
\(589\) 2.81692e14 4.87904e14i 0.163734 0.283596i
\(590\) 3.00766e14 5.20942e14i 0.173198 0.299988i
\(591\) 0 0
\(592\) 8.99347e13 + 1.55771e14i 0.0508344 + 0.0880478i
\(593\) 3.03318e14 0.169863 0.0849313 0.996387i \(-0.472933\pi\)
0.0849313 + 0.996387i \(0.472933\pi\)
\(594\) 0 0
\(595\) 5.58507e14 0.307033
\(596\) 8.20959e14 + 1.42194e15i 0.447164 + 0.774511i
\(597\) 0 0
\(598\) −1.29251e14 + 2.23870e14i −0.0691159 + 0.119712i
\(599\) −8.50992e14 + 1.47396e15i −0.450898 + 0.780978i −0.998442 0.0557990i \(-0.982229\pi\)
0.547544 + 0.836777i \(0.315563\pi\)
\(600\) 0 0
\(601\) −1.16961e15 2.02582e15i −0.608458 1.05388i −0.991495 0.130147i \(-0.958455\pi\)
0.383036 0.923733i \(-0.374878\pi\)
\(602\) 6.88207e12 0.00354763
\(603\) 0 0
\(604\) 1.21359e15 0.614282
\(605\) 1.20344e12 + 2.08442e12i 0.000603630 + 0.00104552i
\(606\) 0 0
\(607\) 1.24804e15 2.16166e15i 0.614737 1.06476i −0.375694 0.926744i \(-0.622595\pi\)
0.990431 0.138012i \(-0.0440712\pi\)
\(608\) −1.04858e15 + 1.81620e15i −0.511839 + 0.886532i
\(609\) 0 0
\(610\) 4.03198e14 + 6.98359e14i 0.193287 + 0.334784i
\(611\) 1.55258e15 0.737612
\(612\) 0 0
\(613\) 2.47301e15 1.15397 0.576983 0.816756i \(-0.304230\pi\)
0.576983 + 0.816756i \(0.304230\pi\)
\(614\) −1.83733e14 3.18235e14i −0.0849692 0.147171i
\(615\) 0 0
\(616\) 3.78113e14 6.54911e14i 0.171762 0.297501i
\(617\) 1.21684e13 2.10763e13i 0.00547854 0.00948911i −0.863273 0.504737i \(-0.831589\pi\)
0.868752 + 0.495248i \(0.164923\pi\)
\(618\) 0 0
\(619\) −2.11273e15 3.65935e15i −0.934425 1.61847i −0.775656 0.631156i \(-0.782581\pi\)
−0.158769 0.987316i \(-0.550753\pi\)
\(620\) −3.75702e14 −0.164698
\(621\) 0 0
\(622\) −1.19700e15 −0.515523
\(623\) 2.09241e14 + 3.62416e14i 0.0893227 + 0.154711i
\(624\) 0 0
\(625\) 2.44448e14 4.23396e14i 0.102529 0.177585i
\(626\) 1.19377e15 2.06767e15i 0.496320 0.859652i
\(627\) 0 0
\(628\) 9.67926e14 + 1.67650e15i 0.395425 + 0.684896i
\(629\) −1.25835e15 −0.509594
\(630\) 0 0
\(631\) −4.26326e15 −1.69660 −0.848302 0.529513i \(-0.822375\pi\)
−0.848302 + 0.529513i \(0.822375\pi\)
\(632\) 1.61006e15 + 2.78870e15i 0.635180 + 1.10016i
\(633\) 0 0
\(634\) 1.00043e15 1.73280e15i 0.387879 0.671826i
\(635\) −6.34462e14 + 1.09892e15i −0.243865 + 0.422387i
\(636\) 0 0
\(637\) −4.90201e14 8.49052e14i −0.185186 0.320751i
\(638\) 1.64755e15 0.617055
\(639\) 0 0
\(640\) 1.63288e15 0.601126
\(641\) 5.04148e14 + 8.73210e14i 0.184009 + 0.318713i 0.943242 0.332106i \(-0.107759\pi\)
−0.759233 + 0.650819i \(0.774426\pi\)
\(642\) 0 0
\(643\) −1.51991e14 + 2.63256e14i −0.0545328 + 0.0944536i −0.892003 0.452029i \(-0.850700\pi\)
0.837470 + 0.546483i \(0.184034\pi\)
\(644\) 2.29752e14 3.97942e14i 0.0817310 0.141562i
\(645\) 0 0
\(646\) −8.83525e14 1.53031e15i −0.308987 0.535181i
\(647\) −3.43583e15 −1.19140 −0.595700 0.803207i \(-0.703125\pi\)
−0.595700 + 0.803207i \(0.703125\pi\)
\(648\) 0 0
\(649\) −2.77421e15 −0.945788
\(650\) −1.76782e14 3.06196e14i −0.0597607 0.103509i
\(651\) 0 0
\(652\) −2.63365e14 + 4.56161e14i −0.0875379 + 0.151620i
\(653\) −5.92694e14 + 1.02658e15i −0.195347 + 0.338352i −0.947014 0.321191i \(-0.895917\pi\)
0.751667 + 0.659543i \(0.229250\pi\)
\(654\) 0 0
\(655\) −1.52514e15 2.64162e15i −0.494291 0.856138i
\(656\) −3.04157e14 −0.0977522
\(657\) 0 0
\(658\) 1.07993e15 0.341312
\(659\) −1.13255e15 1.96164e15i −0.354967 0.614821i 0.632145 0.774850i \(-0.282175\pi\)
−0.987112 + 0.160029i \(0.948841\pi\)
\(660\) 0 0
\(661\) 2.66506e15 4.61602e15i 0.821484 1.42285i −0.0830931 0.996542i \(-0.526480\pi\)
0.904577 0.426310i \(-0.140187\pi\)
\(662\) 7.63008e14 1.32157e15i 0.233244 0.403990i
\(663\) 0 0
\(664\) 1.23911e15 + 2.14621e15i 0.372552 + 0.645279i
\(665\) 8.62227e14 0.257100
\(666\) 0 0
\(667\) 2.39392e15 0.702130
\(668\) −2.02756e15 3.51183e15i −0.589797 1.02156i
\(669\) 0 0
\(670\) −8.97327e14 + 1.55422e15i −0.256767 + 0.444733i
\(671\) 1.85951e15 3.22076e15i 0.527745 0.914082i
\(672\) 0 0
\(673\) −2.37060e15 4.10600e15i −0.661874 1.14640i −0.980123 0.198392i \(-0.936428\pi\)
0.318249 0.948007i \(-0.396905\pi\)
\(674\) 2.90403e15 0.804215
\(675\) 0 0
\(676\) 2.14673e15 0.584886
\(677\) −7.06536e14 1.22376e15i −0.190940 0.330717i 0.754622 0.656160i \(-0.227820\pi\)
−0.945562 + 0.325442i \(0.894487\pi\)
\(678\) 0 0
\(679\) 6.28014e14 1.08775e15i 0.166988 0.289232i
\(680\) −1.40894e15 + 2.44036e15i −0.371616 + 0.643658i
\(681\) 0 0
\(682\) −3.39007e14 5.87178e14i −0.0879822 0.152390i
\(683\) 3.03116e15 0.780359 0.390180 0.920739i \(-0.372413\pi\)
0.390180 + 0.920739i \(0.372413\pi\)
\(684\) 0 0
\(685\) −1.43547e15 −0.363660
\(686\) −7.38268e14 1.27872e15i −0.185537 0.321360i
\(687\) 0 0
\(688\) 8.45270e12 1.46405e13i 0.00209054 0.00362093i
\(689\) 4.61051e14 7.98564e14i 0.113121 0.195931i
\(690\) 0 0
\(691\) 1.37366e15 + 2.37924e15i 0.331703 + 0.574526i 0.982846 0.184429i \(-0.0590436\pi\)
−0.651143 + 0.758955i \(0.725710\pi\)
\(692\) −1.39897e15 −0.335139
\(693\) 0 0
\(694\) 3.73588e15 0.880878
\(695\) 1.44126e15 + 2.49633e15i 0.337151 + 0.583963i
\(696\) 0 0
\(697\) 1.06393e15 1.84278e15i 0.244981 0.424320i
\(698\) 3.07716e14 5.32980e14i 0.0702984 0.121760i
\(699\) 0 0
\(700\) 3.14242e14 + 5.44283e14i 0.0706683 + 0.122401i
\(701\) −5.72747e15 −1.27795 −0.638974 0.769228i \(-0.720641\pi\)
−0.638974 + 0.769228i \(0.720641\pi\)
\(702\) 0 0
\(703\) −1.94265e15 −0.426718
\(704\) 7.21538e14 + 1.24974e15i 0.157257 + 0.272377i
\(705\) 0 0
\(706\) 2.98918e14 5.17741e14i 0.0641395 0.111093i
\(707\) −6.84352e14 + 1.18533e15i −0.145704 + 0.252368i
\(708\) 0 0
\(709\) −3.49163e14 6.04768e14i −0.0731938 0.126775i 0.827106 0.562047i \(-0.189986\pi\)
−0.900299 + 0.435271i \(0.856652\pi\)
\(710\) 1.13503e15 0.236095
\(711\) 0 0
\(712\) −2.11140e15 −0.432445
\(713\) −4.92585e14 8.53182e14i −0.100113 0.173400i
\(714\) 0 0
\(715\) 7.45911e14 1.29196e15i 0.149281 0.258562i
\(716\) −1.23750e15 + 2.14341e15i −0.245767 + 0.425681i
\(717\) 0 0
\(718\) 1.89101e15 + 3.27533e15i 0.369836 + 0.640575i
\(719\) −9.70979e15 −1.88452 −0.942260 0.334882i \(-0.891304\pi\)
−0.942260 + 0.334882i \(0.891304\pi\)
\(720\) 0 0
\(721\) 3.78004e15 0.722525
\(722\) 3.38926e13 + 5.87037e13i 0.00642910 + 0.0111355i
\(723\) 0 0
\(724\) −7.33626e14 + 1.27068e15i −0.137061 + 0.237396i
\(725\) −1.63713e15 + 2.83560e15i −0.303547 + 0.525758i
\(726\) 0 0
\(727\) −1.23234e15 2.13448e15i −0.225057 0.389810i 0.731280 0.682078i \(-0.238923\pi\)
−0.956337 + 0.292268i \(0.905590\pi\)
\(728\) −8.17230e14 −0.148123
\(729\) 0 0
\(730\) −1.69683e14 −0.0302944
\(731\) 5.91345e13 + 1.02424e14i 0.0104784 + 0.0181491i
\(732\) 0 0
\(733\) −3.95643e15 + 6.85273e15i −0.690607 + 1.19617i 0.281032 + 0.959698i \(0.409323\pi\)
−0.971639 + 0.236469i \(0.924010\pi\)
\(734\) 2.13481e15 3.69761e15i 0.369855 0.640608i
\(735\) 0 0
\(736\) 1.83362e15 + 3.17593e15i 0.312955 + 0.542055i
\(737\) 8.27677e15 1.40213
\(738\) 0 0
\(739\) −8.40694e15 −1.40312 −0.701558 0.712613i \(-0.747512\pi\)
−0.701558 + 0.712613i \(0.747512\pi\)
\(740\) 6.47746e14 + 1.12193e15i 0.107308 + 0.185862i
\(741\) 0 0
\(742\) 3.20692e14 5.55455e14i 0.0523440 0.0906625i
\(743\) 6.81435e14 1.18028e15i 0.110404 0.191226i −0.805529 0.592556i \(-0.798119\pi\)
0.915933 + 0.401330i \(0.131452\pi\)
\(744\) 0 0
\(745\) 2.69377e15 + 4.66575e15i 0.430033 + 0.744838i
\(746\) −1.32388e15 −0.209790
\(747\) 0 0
\(748\) 5.43462e15 0.848614
\(749\) −7.55500e14 1.30856e15i −0.117107 0.202836i
\(750\) 0 0
\(751\) −3.40861e15 + 5.90389e15i −0.520664 + 0.901817i 0.479047 + 0.877789i \(0.340982\pi\)
−0.999711 + 0.0240276i \(0.992351\pi\)
\(752\) 1.32639e15 2.29737e15i 0.201128 0.348364i
\(753\) 0 0
\(754\) −8.90225e14 1.54191e15i −0.133032 0.230419i
\(755\) 3.98208e15 0.590747
\(756\) 0 0
\(757\) −6.67049e14 −0.0975282 −0.0487641 0.998810i \(-0.515528\pi\)
−0.0487641 + 0.998810i \(0.515528\pi\)
\(758\) −1.75756e15 3.04418e15i −0.255111 0.441865i
\(759\) 0 0
\(760\) −2.17513e15 + 3.76744e15i −0.311180 + 0.538979i
\(761\) −3.87204e15 + 6.70657e15i −0.549951 + 0.952544i 0.448326 + 0.893870i \(0.352020\pi\)
−0.998277 + 0.0586734i \(0.981313\pi\)
\(762\) 0 0
\(763\) 6.15197e14 + 1.06555e15i 0.0861250 + 0.149173i
\(764\) 4.06626e15 0.565173
\(765\) 0 0
\(766\) −5.55479e15 −0.761043
\(767\) 1.49900e15 + 2.59634e15i 0.203905 + 0.353173i
\(768\) 0 0
\(769\) −1.26206e15 + 2.18594e15i −0.169232 + 0.293119i −0.938150 0.346228i \(-0.887462\pi\)
0.768918 + 0.639348i \(0.220796\pi\)
\(770\) 5.18831e14 8.98642e14i 0.0690760 0.119643i
\(771\) 0 0
\(772\) 4.00560e15 + 6.93790e15i 0.525741 + 0.910611i
\(773\) 1.11453e16 1.45246 0.726229 0.687453i \(-0.241271\pi\)
0.726229 + 0.687453i \(0.241271\pi\)