Properties

Label 81.12.c.d.55.1
Level $81$
Weight $12$
Character 81.55
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 55.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 81.55
Dual form 81.12.c.d.28.1

$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

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

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 \(-0.747907\pi\)
0.967607 + 0.252462i \(0.0812402\pi\)
\(3\) 0 0
\(4\) 736.000 + 1274.79i 0.359375 + 0.622456i
\(5\) −2415.00 4182.90i −0.345607 0.598608i 0.639857 0.768494i \(-0.278994\pi\)
−0.985464 + 0.169886i \(0.945660\pi\)
\(6\) 0 0
\(7\) 8372.00 14500.7i 0.188274 0.326100i −0.756401 0.654108i \(-0.773044\pi\)
0.944675 + 0.328008i \(0.106377\pi\)
\(8\) 84480.0 0.911505
\(9\) 0 0
\(10\) −115920. −0.366571
\(11\) −267306. + 462988.i −0.500436 + 0.866781i 0.499563 + 0.866277i \(0.333494\pi\)
−1.00000 0.000504048i \(0.999840\pi\)
\(12\) 0 0
\(13\) 288869. + 500336.i 0.215781 + 0.373743i 0.953514 0.301349i \(-0.0974371\pi\)
−0.737733 + 0.675092i \(0.764104\pi\)
\(14\) −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 \(-0.700803\pi\)
−0.589825 + 0.807531i \(0.700803\pi\)
\(18\) 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 \(-0.264317\pi\)
−0.976586 + 0.215127i \(0.930983\pi\)
\(24\) 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 0.414073 + 0.910244i \(0.364106\pi\)
−0.995331 + 0.0965237i \(0.969228\pi\)
\(30\) 0 0
\(31\) 2.64216e7 + 4.57635e7i 0.165756 + 0.287098i 0.936924 0.349534i \(-0.113660\pi\)
−0.771167 + 0.636632i \(0.780327\pi\)
\(32\) 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 \(-0.233256\pi\)
−0.950981 + 0.309249i \(0.899922\pi\)
\(42\) 0 0
\(43\) 8.56285e6 1.48313e7i 0.00888264 0.0153852i −0.861550 0.507673i \(-0.830506\pi\)
0.870433 + 0.492288i \(0.163839\pi\)
\(44\) −7.86949e8 −0.719377
\(45\) 0 0
\(46\) −4.47439e8 −0.320306
\(47\) −1.34367e9 + 2.32731e9i −0.854586 + 1.48019i 0.0224426 + 0.999748i \(0.492856\pi\)
−0.877029 + 0.480438i \(0.840478\pi\)
\(48\) 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 \(-0.584422\pi\)
−0.262120 + 0.965035i \(0.584422\pi\)
\(54\) 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 \(-0.0100251\pi\)
−0.527023 + 0.849851i \(0.676692\pi\)
\(60\) 0 0
\(61\) −3.47824e9 + 6.02449e9i −0.527285 + 0.913284i 0.472209 + 0.881486i \(0.343457\pi\)
−0.999494 + 0.0317979i \(0.989877\pi\)
\(62\) 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 0.968307 + 0.249765i \(0.0803533\pi\)
−0.267851 + 0.963460i \(0.586313\pi\)
\(68\) −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 \(-0.395634\pi\)
0.322031 + 0.946729i \(0.395634\pi\)
\(72\) 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 0.272706 + 0.962097i \(0.412081\pi\)
−0.969554 + 0.244878i \(0.921252\pi\)
\(80\) 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 \(-0.699308\pi\)
0.994747 + 0.102366i \(0.0326412\pi\)
\(84\) 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 \(-0.576235\pi\)
−0.237215 + 0.971457i \(0.576235\pi\)
\(90\) 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 −0.997944 0.0640871i \(-0.979586\pi\)
0.554473 + 0.832202i \(0.312920\pi\)
\(98\) 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 \(-0.959804\pi\)
0.605089 + 0.796158i \(0.293137\pi\)
\(102\) 0 0
\(103\) 1.12878e11 + 1.95510e11i 0.959407 + 1.66174i 0.723944 + 0.689858i \(0.242327\pi\)
0.235463 + 0.971883i \(0.424339\pi\)
\(104\) 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 \(-0.399335\pi\)
0.311003 + 0.950409i \(0.399335\pi\)
\(108\) 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 \(-0.0969176\pi\)
−0.736630 + 0.676295i \(0.763584\pi\)
\(114\) 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 −0.962918 0.269793i \(-0.913045\pi\)
0.247811 0.968808i \(-0.420289\pi\)
\(132\) 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 \(-0.748602\pi\)
0.967053 + 0.254574i \(0.0819351\pi\)
\(138\) 0 0
\(139\) −2.98397e11 5.16838e11i −0.487767 0.844838i 0.512134 0.858906i \(-0.328855\pi\)
−0.999901 + 0.0140679i \(0.995522\pi\)
\(140\) −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 0.989086 + 0.147338i \(0.0470705\pi\)
−0.366945 + 0.930243i \(0.619596\pi\)
\(150\) 0 0
\(151\) 4.12224e11 7.13992e11i 0.427326 0.740151i −0.569308 0.822124i \(-0.692789\pi\)
0.996635 + 0.0819732i \(0.0261222\pi\)
\(152\) 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 −0.998263 0.0589187i \(-0.981235\pi\)
0.448106 0.893980i \(-0.352099\pi\)
\(158\) 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 −0.905245 0.424889i \(-0.860313\pi\)
0.0846581 0.996410i \(-0.473020\pi\)
\(168\) 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 \(-0.758433\pi\)
0.958731 + 0.284316i \(0.0917666\pi\)
\(174\) 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 \(-0.388917\pi\)
0.341936 + 0.939723i \(0.388917\pi\)
\(180\) 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 \(-0.961953\pi\)
0.599701 + 0.800224i \(0.295286\pi\)
\(192\) 0 0
\(193\) −2.72119e12 4.71325e12i −0.731466 1.26694i −0.956256 0.292530i \(-0.905503\pi\)
0.224790 0.974407i \(-0.427830\pi\)
\(194\) 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 \(-0.612226\pi\)
−0.345309 + 0.938489i \(0.612226\pi\)
\(198\) 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 0.997572 + 0.0696437i \(0.0221863\pi\)
−0.438473 + 0.898745i \(0.644480\pi\)
\(212\) −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 −0.998075 0.0620124i \(-0.980248\pi\)
0.552742 + 0.833352i \(0.313582\pi\)
\(224\) 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 \(-0.809479\pi\)
0.901030 + 0.433756i \(0.142812\pi\)
\(228\) 0 0
\(229\) 5.91221e12 + 1.02402e13i 0.620375 + 1.07452i 0.989416 + 0.145108i \(0.0463530\pi\)
−0.369041 + 0.929413i \(0.620314\pi\)
\(230\) 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 \(-0.816135\pi\)
−0.837761 + 0.546038i \(0.816135\pi\)
\(234\) 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 \(-0.0709769\pi\)
−0.679132 + 0.734016i \(0.737644\pi\)
\(240\) 0 0
\(241\) 1.15653e11 2.00318e11i 0.00916357 0.0158718i −0.861407 0.507915i \(-0.830416\pi\)
0.870571 + 0.492043i \(0.163750\pi\)
\(242\) −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 \(-0.365081\pi\)
0.411284 + 0.911507i \(0.365081\pi\)
\(252\) 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 −0.978857 0.204546i \(-0.934428\pi\)
0.312286 0.949988i \(-0.398905\pi\)
\(258\) 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 −0.398808 0.917034i \(-0.630576\pi\)
0.993579 0.113139i \(-0.0360907\pi\)
\(264\) 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 \(-0.311099\pi\)
0.559225 + 0.829016i \(0.311099\pi\)
\(270\) 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 −0.674228 0.738523i \(-0.735524\pi\)
0.976694 + 0.214637i \(0.0688569\pi\)
\(278\) −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 \(-0.949919\pi\)
0.629517 + 0.776987i \(0.283253\pi\)
\(282\) 0 0
\(283\) −8.35659e12 1.44740e13i −0.273655 0.473985i 0.696140 0.717906i \(-0.254899\pi\)
−0.969795 + 0.243922i \(0.921566\pi\)
\(284\) 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 \(-0.0617546\pi\)
−0.657583 + 0.753382i \(0.728421\pi\)
\(294\) 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 \(-0.328226\pi\)
−0.999871 + 0.0160451i \(0.994892\pi\)
\(312\) 0 0
\(313\) 4.97404e13 8.61529e13i 0.935870 1.62097i 0.162795 0.986660i \(-0.447949\pi\)
0.773075 0.634315i \(-0.218718\pi\)
\(314\) −3.15628e13 −0.583529
\(315\) 0 0
\(316\) −5.61080e13 −1.00172
\(317\) −4.16846e13 + 7.21999e13i −0.731392 + 1.26681i 0.224897 + 0.974383i \(0.427795\pi\)
−0.956289 + 0.292425i \(0.905538\pi\)
\(318\) 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 −0.557865 0.829931i \(-0.688379\pi\)
0.997674 + 0.0681600i \(0.0217128\pi\)
\(332\) 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 −0.943757 0.330640i \(-0.892735\pi\)
0.185535 0.982638i \(-0.440598\pi\)
\(338\) −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 0.897643 + 0.440724i \(0.145278\pi\)
−0.0671435 + 0.997743i \(0.521389\pi\)
\(348\) 0 0
\(349\) 1.28215e13 2.22075e13i 0.132556 0.229594i −0.792105 0.610385i \(-0.791015\pi\)
0.924661 + 0.380791i \(0.124348\pi\)
\(350\) −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 \(-0.871925\pi\)
0.799197 + 0.601069i \(0.205258\pi\)
\(354\) 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 \(-0.254354\pi\)
0.697370 + 0.716712i \(0.254354\pi\)
\(360\) 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 −0.271957 0.962309i \(-0.587671\pi\)
0.969363 0.245633i \(-0.0789958\pi\)
\(368\) 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 0.947812 0.318829i \(-0.103290\pi\)
−0.750020 + 0.661415i \(0.769956\pi\)
\(374\) −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 −0.961980 0.273120i \(-0.911945\pi\)
0.244462 0.969659i \(-0.421389\pi\)
\(384\) 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 \(-0.693063\pi\)
0.996563 + 0.0828326i \(0.0263967\pi\)
\(390\) 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 \(-0.0625601\pi\)
−0.659488 + 0.751715i \(0.729227\pi\)
\(402\) 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 0.998077 0.0619816i \(-0.0197420\pi\)
−0.552716 + 0.833369i \(0.686409\pi\)
\(410\) 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 \(-0.211004\pi\)
−0.927057 + 0.374920i \(0.877670\pi\)
\(420\) 0 0
\(421\) −8.55560e13 + 1.48187e14i −0.315282 + 0.546084i −0.979497 0.201457i \(-0.935432\pi\)
0.664216 + 0.747541i \(0.268766\pi\)
\(422\) 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 \(-0.537081\pi\)
−0.116231 + 0.993222i \(0.537081\pi\)
\(432\) 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 −0.843999 0.536345i \(-0.819804\pi\)
0.886488 + 0.462752i \(0.153138\pi\)
\(440\) 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 \(-0.984483\pi\)
0.541605 + 0.840633i \(0.317817\pi\)
\(444\) 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 \(-0.790867\pi\)
−0.791822 + 0.610752i \(0.790867\pi\)
\(450\) 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 −0.987305 0.158838i \(-0.949225\pi\)
0.631210 + 0.775612i \(0.282559\pi\)
\(458\) 2.83786e14 0.658007
\(459\) 0 0
\(460\) −1.32549e14 −0.300061
\(461\) 3.64654e14 6.31599e14i 0.815691 1.41282i −0.0931391 0.995653i \(-0.529690\pi\)
0.908830 0.417166i \(-0.136977\pi\)
\(462\) 0 0
\(463\) −6.10941e13 1.05818e14i −0.133445 0.231134i 0.791557 0.611095i \(-0.209271\pi\)
−0.925003 + 0.379961i \(0.875937\pi\)
\(464\) −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 \(-0.722353\pi\)
−0.643103 + 0.765780i \(0.722353\pi\)
\(468\) 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 −0.211076 + 0.977470i \(0.567697\pi\)
−0.740976 + 0.671532i \(0.765637\pi\)
\(480\) 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 \(-0.0416956\pi\)
−0.608834 + 0.793298i \(0.708362\pi\)
\(492\) 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 0.902719 0.430230i \(-0.141568\pi\)
−0.823950 + 0.566663i \(0.808234\pi\)
\(500\) −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 \(-0.385926\pi\)
0.350753 + 0.936468i \(0.385926\pi\)
\(504\) 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 \(-0.184382\pi\)
−0.892497 + 0.451053i \(0.851049\pi\)
\(510\) 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 \(-0.322450\pi\)
0.529312 + 0.848428i \(0.322450\pi\)
\(522\) 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 −0.982185 0.187915i \(-0.939827\pi\)
0.653832 + 0.756640i \(0.273160\pi\)
\(548\) 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 \(-0.476396\pi\)
0.0740870 + 0.997252i \(0.476396\pi\)
\(558\) 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 \(-0.195757\pi\)
−0.908042 + 0.418878i \(0.862423\pi\)
\(564\) 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 \(-0.990993\pi\)
0.524302 + 0.851533i \(0.324326\pi\)
\(570\) 0 0
\(571\) −7.16114e14 1.24035e15i −0.493723 0.855154i 0.506250 0.862387i \(-0.331031\pi\)
−0.999974 + 0.00723249i \(0.997698\pi\)
\(572\) −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 −0.239854 0.970809i \(-0.577100\pi\)
0.960672 0.277685i \(-0.0895671\pi\)
\(588\) 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 \(-0.527067\pi\)
−0.0849313 + 0.996387i \(0.527067\pi\)
\(594\) 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 \(-0.0177706\pi\)
−0.547544 + 0.836777i \(0.684437\pi\)
\(600\) 0 0
\(601\) −1.16961e15 + 2.02582e15i −0.608458 + 1.05388i 0.383036 + 0.923733i \(0.374878\pi\)
−0.991495 + 0.130147i \(0.958455\pi\)
\(602\) −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 0.990431 + 0.138012i \(0.0440712\pi\)
−0.375694 + 0.926744i \(0.622595\pi\)
\(608\) 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 \(-0.168411\pi\)
−0.868752 + 0.495248i \(0.835077\pi\)
\(618\) 0 0
\(619\) −2.11273e15 + 3.65935e15i −0.934425 + 1.61847i −0.158769 + 0.987316i \(0.550753\pi\)
−0.775656 + 0.631156i \(0.782581\pi\)
\(620\) 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 \(-0.892241\pi\)
0.759233 + 0.650819i \(0.225574\pi\)
\(642\) 0 0
\(643\) −1.51991e14 2.63256e14i −0.0545328 0.0944536i 0.837470 0.546483i \(-0.184034\pi\)
−0.892003 + 0.452029i \(0.850700\pi\)
\(644\) −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 \(-0.296875\pi\)
0.595700 + 0.803207i \(0.296875\pi\)
\(648\) 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 \(-0.104083\pi\)
−0.751667 + 0.659543i \(0.770750\pi\)
\(654\) 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 \(-0.717825\pi\)
0.987112 + 0.160029i \(0.0511587\pi\)
\(660\) 0 0
\(661\) 2.66506e15 + 4.61602e15i 0.821484 + 1.42285i 0.904577 + 0.426310i \(0.140187\pi\)
−0.0830931 + 0.996542i \(0.526480\pi\)
\(662\) −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 0.318249 + 0.948007i \(0.396905\pi\)
−0.980123 + 0.198392i \(0.936428\pi\)
\(674\) −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 \(-0.772180\pi\)
0.945562 + 0.325442i \(0.105513\pi\)
\(678\) 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 \(-0.627587\pi\)
−0.390180 + 0.920739i \(0.627587\pi\)
\(684\) 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 −0.651143 0.758955i \(-0.725710\pi\)
0.982846 + 0.184429i \(0.0590436\pi\)
\(692\) 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 \(-0.279359\pi\)
0.638974 + 0.769228i \(0.279359\pi\)
\(702\) 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 −0.900299 0.435271i \(-0.856652\pi\)
0.827106 + 0.562047i \(0.189986\pi\)
\(710\) −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 \(-0.108696\pi\)
0.942260 + 0.334882i \(0.108696\pi\)
\(720\) 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 −0.956337 0.292268i \(-0.905590\pi\)
0.731280 + 0.682078i \(0.238923\pi\)
\(728\) 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 −0.971639 0.236469i \(-0.924010\pi\)
0.281032 0.959698i \(-0.409323\pi\)
\(734\) −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 \(-0.201881\pi\)
−0.915933 + 0.401330i \(0.868548\pi\)
\(744\) 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 −0.999711 0.0240276i \(-0.992351\pi\)
0.479047 0.877789i \(-0.340982\pi\)
\(752\) −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 0.998277 + 0.0586734i \(0.0186871\pi\)
−0.448326 + 0.893870i \(0.647980\pi\)
\(762\) 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 0.768918 0.639348i \(-0.220796\pi\)
−0.938150 + 0.346228i \(0.887462\pi\)
\(770\) −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 \(-0.758729\pi\)
−0.726229 + 0.687453i \(0.758729\pi\)