Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.39823 | −0.807271 | −0.403635 | − | 0.914920i | \(-0.632254\pi\) | ||||
−0.403635 | + | 0.914920i | \(0.632254\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.539425 | 0.241238 | 0.120619 | − | 0.992699i | \(-0.461512\pi\) | ||||
0.120619 | + | 0.992699i | \(0.461512\pi\) | |||||||
\(6\) | −1.39823 | −0.570827 | ||||||||
\(7\) | 5.05784 | 1.91168 | 0.955842 | − | 0.293883i | \(-0.0949475\pi\) | ||||
0.955842 | + | 0.293883i | \(0.0949475\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.04494 | −0.348314 | ||||||||
\(10\) | 0.539425 | 0.170581 | ||||||||
\(11\) | −1.12561 | −0.339383 | −0.169692 | − | 0.985497i | \(-0.554277\pi\) | ||||
−0.169692 | + | 0.985497i | \(0.554277\pi\) | |||||||
\(12\) | −1.39823 | −0.403635 | ||||||||
\(13\) | −2.68807 | −0.745537 | −0.372768 | − | 0.927924i | \(-0.621591\pi\) | ||||
−0.372768 | + | 0.927924i | \(0.621591\pi\) | |||||||
\(14\) | 5.05784 | 1.35176 | ||||||||
\(15\) | −0.754243 | −0.194745 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.30545 | −1.04423 | −0.522113 | − | 0.852876i | \(-0.674856\pi\) | ||||
−0.522113 | + | 0.852876i | \(0.674856\pi\) | |||||||
\(18\) | −1.04494 | −0.246295 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.539425 | 0.120619 | ||||||||
\(21\) | −7.07204 | −1.54325 | ||||||||
\(22\) | −1.12561 | −0.239980 | ||||||||
\(23\) | 7.92041 | 1.65152 | 0.825760 | − | 0.564022i | \(-0.190747\pi\) | ||||
0.825760 | + | 0.564022i | \(0.190747\pi\) | |||||||
\(24\) | −1.39823 | −0.285413 | ||||||||
\(25\) | −4.70902 | −0.941804 | ||||||||
\(26\) | −2.68807 | −0.527174 | ||||||||
\(27\) | 5.65578 | 1.08845 | ||||||||
\(28\) | 5.05784 | 0.955842 | ||||||||
\(29\) | −0.281706 | −0.0523116 | −0.0261558 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261558 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(30\) | −0.754243 | −0.137705 | ||||||||
\(31\) | −6.56253 | −1.17867 | −0.589333 | − | 0.807890i | \(-0.700609\pi\) | ||||
−0.589333 | + | 0.807890i | \(0.700609\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.57386 | 0.273974 | ||||||||
\(34\) | −4.30545 | −0.738379 | ||||||||
\(35\) | 2.72833 | 0.461171 | ||||||||
\(36\) | −1.04494 | −0.174157 | ||||||||
\(37\) | 1.71537 | 0.282005 | 0.141003 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141003 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 3.75855 | 0.601850 | ||||||||
\(40\) | 0.539425 | 0.0852907 | ||||||||
\(41\) | 0.408032 | 0.0637239 | 0.0318620 | − | 0.999492i | \(-0.489856\pi\) | ||||
0.0318620 | + | 0.999492i | \(0.489856\pi\) | |||||||
\(42\) | −7.07204 | −1.09124 | ||||||||
\(43\) | 5.34809 | 0.815576 | 0.407788 | − | 0.913077i | \(-0.366300\pi\) | ||||
0.407788 | + | 0.913077i | \(0.366300\pi\) | |||||||
\(44\) | −1.12561 | −0.169692 | ||||||||
\(45\) | −0.563668 | −0.0840266 | ||||||||
\(46\) | 7.92041 | 1.16780 | ||||||||
\(47\) | −3.58934 | −0.523559 | −0.261780 | − | 0.965128i | \(-0.584309\pi\) | ||||
−0.261780 | + | 0.965128i | \(0.584309\pi\) | |||||||
\(48\) | −1.39823 | −0.201818 | ||||||||
\(49\) | 18.5817 | 2.65453 | ||||||||
\(50\) | −4.70902 | −0.665956 | ||||||||
\(51\) | 6.02003 | 0.842973 | ||||||||
\(52\) | −2.68807 | −0.372768 | ||||||||
\(53\) | −3.58303 | −0.492167 | −0.246084 | − | 0.969249i | \(-0.579144\pi\) | ||||
−0.246084 | + | 0.969249i | \(0.579144\pi\) | |||||||
\(54\) | 5.65578 | 0.769653 | ||||||||
\(55\) | −0.607181 | −0.0818723 | ||||||||
\(56\) | 5.05784 | 0.675882 | ||||||||
\(57\) | 1.39823 | 0.185201 | ||||||||
\(58\) | −0.281706 | −0.0369899 | ||||||||
\(59\) | 8.94333 | 1.16432 | 0.582161 | − | 0.813074i | \(-0.302207\pi\) | ||||
0.582161 | + | 0.813074i | \(0.302207\pi\) | |||||||
\(60\) | −0.754243 | −0.0973724 | ||||||||
\(61\) | 13.1010 | 1.67741 | 0.838703 | − | 0.544589i | \(-0.183314\pi\) | ||||
0.838703 | + | 0.544589i | \(0.183314\pi\) | |||||||
\(62\) | −6.56253 | −0.833443 | ||||||||
\(63\) | −5.28514 | −0.665865 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.45001 | −0.179852 | ||||||||
\(66\) | 1.57386 | 0.193729 | ||||||||
\(67\) | 7.49995 | 0.916265 | 0.458132 | − | 0.888884i | \(-0.348519\pi\) | ||||
0.458132 | + | 0.888884i | \(0.348519\pi\) | |||||||
\(68\) | −4.30545 | −0.522113 | ||||||||
\(69\) | −11.0746 | −1.33322 | ||||||||
\(70\) | 2.72833 | 0.326097 | ||||||||
\(71\) | 9.98622 | 1.18515 | 0.592573 | − | 0.805517i | \(-0.298112\pi\) | ||||
0.592573 | + | 0.805517i | \(0.298112\pi\) | |||||||
\(72\) | −1.04494 | −0.123147 | ||||||||
\(73\) | −7.18763 | −0.841248 | −0.420624 | − | 0.907235i | \(-0.638189\pi\) | ||||
−0.420624 | + | 0.907235i | \(0.638189\pi\) | |||||||
\(74\) | 1.71537 | 0.199408 | ||||||||
\(75\) | 6.58431 | 0.760291 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −5.69314 | −0.648793 | ||||||||
\(78\) | 3.75855 | 0.425572 | ||||||||
\(79\) | 16.4632 | 1.85226 | 0.926129 | − | 0.377206i | \(-0.123115\pi\) | ||||
0.926129 | + | 0.377206i | \(0.123115\pi\) | |||||||
\(80\) | 0.539425 | 0.0603096 | ||||||||
\(81\) | −4.77328 | −0.530364 | ||||||||
\(82\) | 0.408032 | 0.0450596 | ||||||||
\(83\) | 7.00532 | 0.768933 | 0.384467 | − | 0.923139i | \(-0.374385\pi\) | ||||
0.384467 | + | 0.923139i | \(0.374385\pi\) | |||||||
\(84\) | −7.07204 | −0.771623 | ||||||||
\(85\) | −2.32247 | −0.251907 | ||||||||
\(86\) | 5.34809 | 0.576699 | ||||||||
\(87\) | 0.393892 | 0.0422296 | ||||||||
\(88\) | −1.12561 | −0.119990 | ||||||||
\(89\) | −4.37900 | −0.464173 | −0.232086 | − | 0.972695i | \(-0.574555\pi\) | ||||
−0.232086 | + | 0.972695i | \(0.574555\pi\) | |||||||
\(90\) | −0.563668 | −0.0594158 | ||||||||
\(91\) | −13.5958 | −1.42523 | ||||||||
\(92\) | 7.92041 | 0.825760 | ||||||||
\(93\) | 9.17596 | 0.951503 | ||||||||
\(94\) | −3.58934 | −0.370212 | ||||||||
\(95\) | −0.539425 | −0.0553439 | ||||||||
\(96\) | −1.39823 | −0.142707 | ||||||||
\(97\) | 12.0690 | 1.22542 | 0.612709 | − | 0.790309i | \(-0.290080\pi\) | ||||
0.612709 | + | 0.790309i | \(0.290080\pi\) | |||||||
\(98\) | 18.5817 | 1.87704 | ||||||||
\(99\) | 1.17619 | 0.118212 | ||||||||
\(100\) | −4.70902 | −0.470902 | ||||||||
\(101\) | 1.21217 | 0.120616 | 0.0603079 | − | 0.998180i | \(-0.480792\pi\) | ||||
0.0603079 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(102\) | 6.02003 | 0.596072 | ||||||||
\(103\) | 17.1286 | 1.68773 | 0.843863 | − | 0.536558i | \(-0.180276\pi\) | ||||
0.843863 | + | 0.536558i | \(0.180276\pi\) | |||||||
\(104\) | −2.68807 | −0.263587 | ||||||||
\(105\) | −3.81484 | −0.372290 | ||||||||
\(106\) | −3.58303 | −0.348015 | ||||||||
\(107\) | 5.75691 | 0.556541 | 0.278271 | − | 0.960503i | \(-0.410239\pi\) | ||||
0.278271 | + | 0.960503i | \(0.410239\pi\) | |||||||
\(108\) | 5.65578 | 0.544227 | ||||||||
\(109\) | 1.63885 | 0.156973 | 0.0784865 | − | 0.996915i | \(-0.474991\pi\) | ||||
0.0784865 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(110\) | −0.607181 | −0.0578924 | ||||||||
\(111\) | −2.39849 | −0.227655 | ||||||||
\(112\) | 5.05784 | 0.477921 | ||||||||
\(113\) | −2.73876 | −0.257641 | −0.128821 | − | 0.991668i | \(-0.541119\pi\) | ||||
−0.128821 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(114\) | 1.39823 | 0.130957 | ||||||||
\(115\) | 4.27247 | 0.398410 | ||||||||
\(116\) | −0.281706 | −0.0261558 | ||||||||
\(117\) | 2.80888 | 0.259681 | ||||||||
\(118\) | 8.94333 | 0.823300 | ||||||||
\(119\) | −21.7763 | −1.99623 | ||||||||
\(120\) | −0.754243 | −0.0688527 | ||||||||
\(121\) | −9.73301 | −0.884819 | ||||||||
\(122\) | 13.1010 | 1.18611 | ||||||||
\(123\) | −0.570524 | −0.0514425 | ||||||||
\(124\) | −6.56253 | −0.589333 | ||||||||
\(125\) | −5.23729 | −0.468438 | ||||||||
\(126\) | −5.28514 | −0.470838 | ||||||||
\(127\) | 15.1724 | 1.34633 | 0.673166 | − | 0.739492i | \(-0.264934\pi\) | ||||
0.673166 | + | 0.739492i | \(0.264934\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.47788 | −0.658391 | ||||||||
\(130\) | −1.45001 | −0.127175 | ||||||||
\(131\) | 17.8014 | 1.55531 | 0.777656 | − | 0.628690i | \(-0.216409\pi\) | ||||
0.777656 | + | 0.628690i | \(0.216409\pi\) | |||||||
\(132\) | 1.57386 | 0.136987 | ||||||||
\(133\) | −5.05784 | −0.438570 | ||||||||
\(134\) | 7.49995 | 0.647897 | ||||||||
\(135\) | 3.05087 | 0.262577 | ||||||||
\(136\) | −4.30545 | −0.369190 | ||||||||
\(137\) | −6.31444 | −0.539479 | −0.269740 | − | 0.962933i | \(-0.586938\pi\) | ||||
−0.269740 | + | 0.962933i | \(0.586938\pi\) | |||||||
\(138\) | −11.0746 | −0.942731 | ||||||||
\(139\) | −4.18766 | −0.355193 | −0.177596 | − | 0.984103i | \(-0.556832\pi\) | ||||
−0.177596 | + | 0.984103i | \(0.556832\pi\) | |||||||
\(140\) | 2.72833 | 0.230586 | ||||||||
\(141\) | 5.01874 | 0.422654 | ||||||||
\(142\) | 9.98622 | 0.838025 | ||||||||
\(143\) | 3.02571 | 0.253023 | ||||||||
\(144\) | −1.04494 | −0.0870784 | ||||||||
\(145\) | −0.151960 | −0.0126196 | ||||||||
\(146\) | −7.18763 | −0.594852 | ||||||||
\(147\) | −25.9816 | −2.14293 | ||||||||
\(148\) | 1.71537 | 0.141003 | ||||||||
\(149\) | −13.0258 | −1.06712 | −0.533558 | − | 0.845763i | \(-0.679146\pi\) | ||||
−0.533558 | + | 0.845763i | \(0.679146\pi\) | |||||||
\(150\) | 6.58431 | 0.537607 | ||||||||
\(151\) | −0.626724 | −0.0510021 | −0.0255010 | − | 0.999675i | \(-0.508118\pi\) | ||||
−0.0255010 | + | 0.999675i | \(0.508118\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 4.49895 | 0.363718 | ||||||||
\(154\) | −5.69314 | −0.458766 | ||||||||
\(155\) | −3.54000 | −0.284340 | ||||||||
\(156\) | 3.75855 | 0.300925 | ||||||||
\(157\) | −6.57277 | −0.524564 | −0.262282 | − | 0.964991i | \(-0.584475\pi\) | ||||
−0.262282 | + | 0.964991i | \(0.584475\pi\) | |||||||
\(158\) | 16.4632 | 1.30974 | ||||||||
\(159\) | 5.00992 | 0.397312 | ||||||||
\(160\) | 0.539425 | 0.0426453 | ||||||||
\(161\) | 40.0601 | 3.15718 | ||||||||
\(162\) | −4.77328 | −0.375024 | ||||||||
\(163\) | 7.39921 | 0.579551 | 0.289776 | − | 0.957095i | \(-0.406419\pi\) | ||||
0.289776 | + | 0.957095i | \(0.406419\pi\) | |||||||
\(164\) | 0.408032 | 0.0318620 | ||||||||
\(165\) | 0.848981 | 0.0660931 | ||||||||
\(166\) | 7.00532 | 0.543718 | ||||||||
\(167\) | −15.1677 | −1.17371 | −0.586855 | − | 0.809692i | \(-0.699634\pi\) | ||||
−0.586855 | + | 0.809692i | \(0.699634\pi\) | |||||||
\(168\) | −7.07204 | −0.545620 | ||||||||
\(169\) | −5.77428 | −0.444175 | ||||||||
\(170\) | −2.32247 | −0.178125 | ||||||||
\(171\) | 1.04494 | 0.0799086 | ||||||||
\(172\) | 5.34809 | 0.407788 | ||||||||
\(173\) | −15.7761 | −1.19944 | −0.599719 | − | 0.800211i | \(-0.704721\pi\) | ||||
−0.599719 | + | 0.800211i | \(0.704721\pi\) | |||||||
\(174\) | 0.393892 | 0.0298608 | ||||||||
\(175\) | −23.8175 | −1.80043 | ||||||||
\(176\) | −1.12561 | −0.0848458 | ||||||||
\(177\) | −12.5049 | −0.939923 | ||||||||
\(178\) | −4.37900 | −0.328220 | ||||||||
\(179\) | 0.905811 | 0.0677035 | 0.0338518 | − | 0.999427i | \(-0.489223\pi\) | ||||
0.0338518 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(180\) | −0.563668 | −0.0420133 | ||||||||
\(181\) | −16.8041 | −1.24904 | −0.624518 | − | 0.781010i | \(-0.714705\pi\) | ||||
−0.624518 | + | 0.781010i | \(0.714705\pi\) | |||||||
\(182\) | −13.5958 | −1.00779 | ||||||||
\(183\) | −18.3182 | −1.35412 | ||||||||
\(184\) | 7.92041 | 0.583900 | ||||||||
\(185\) | 0.925314 | 0.0680305 | ||||||||
\(186\) | 9.17596 | 0.672814 | ||||||||
\(187\) | 4.84625 | 0.354393 | ||||||||
\(188\) | −3.58934 | −0.261780 | ||||||||
\(189\) | 28.6060 | 2.08078 | ||||||||
\(190\) | −0.539425 | −0.0391340 | ||||||||
\(191\) | −9.56666 | −0.692219 | −0.346109 | − | 0.938194i | \(-0.612497\pi\) | ||||
−0.346109 | + | 0.938194i | \(0.612497\pi\) | |||||||
\(192\) | −1.39823 | −0.100909 | ||||||||
\(193\) | 19.2576 | 1.38619 | 0.693097 | − | 0.720844i | \(-0.256246\pi\) | ||||
0.693097 | + | 0.720844i | \(0.256246\pi\) | |||||||
\(194\) | 12.0690 | 0.866501 | ||||||||
\(195\) | 2.02746 | 0.145189 | ||||||||
\(196\) | 18.5817 | 1.32727 | ||||||||
\(197\) | 14.0935 | 1.00412 | 0.502060 | − | 0.864833i | \(-0.332576\pi\) | ||||
0.502060 | + | 0.864833i | \(0.332576\pi\) | |||||||
\(198\) | 1.17619 | 0.0835884 | ||||||||
\(199\) | 1.07616 | 0.0762872 | 0.0381436 | − | 0.999272i | \(-0.487856\pi\) | ||||
0.0381436 | + | 0.999272i | \(0.487856\pi\) | |||||||
\(200\) | −4.70902 | −0.332978 | ||||||||
\(201\) | −10.4867 | −0.739674 | ||||||||
\(202\) | 1.21217 | 0.0852882 | ||||||||
\(203\) | −1.42483 | −0.100003 | ||||||||
\(204\) | 6.02003 | 0.421487 | ||||||||
\(205\) | 0.220103 | 0.0153727 | ||||||||
\(206\) | 17.1286 | 1.19340 | ||||||||
\(207\) | −8.27636 | −0.575247 | ||||||||
\(208\) | −2.68807 | −0.186384 | ||||||||
\(209\) | 1.12561 | 0.0778598 | ||||||||
\(210\) | −3.81484 | −0.263249 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −3.58303 | −0.246084 | ||||||||
\(213\) | −13.9631 | −0.956734 | ||||||||
\(214\) | 5.75691 | 0.393534 | ||||||||
\(215\) | 2.88489 | 0.196748 | ||||||||
\(216\) | 5.65578 | 0.384827 | ||||||||
\(217\) | −33.1922 | −2.25324 | ||||||||
\(218\) | 1.63885 | 0.110997 | ||||||||
\(219\) | 10.0500 | 0.679115 | ||||||||
\(220\) | −0.607181 | −0.0409361 | ||||||||
\(221\) | 11.5734 | 0.778509 | ||||||||
\(222\) | −2.39849 | −0.160976 | ||||||||
\(223\) | 9.95413 | 0.666578 | 0.333289 | − | 0.942825i | \(-0.391842\pi\) | ||||
0.333289 | + | 0.942825i | \(0.391842\pi\) | |||||||
\(224\) | 5.05784 | 0.337941 | ||||||||
\(225\) | 4.92065 | 0.328043 | ||||||||
\(226\) | −2.73876 | −0.182180 | ||||||||
\(227\) | 25.9588 | 1.72295 | 0.861474 | − | 0.507801i | \(-0.169542\pi\) | ||||
0.861474 | + | 0.507801i | \(0.169542\pi\) | |||||||
\(228\) | 1.39823 | 0.0926003 | ||||||||
\(229\) | −4.86224 | −0.321306 | −0.160653 | − | 0.987011i | \(-0.551360\pi\) | ||||
−0.160653 | + | 0.987011i | \(0.551360\pi\) | |||||||
\(230\) | 4.27247 | 0.281718 | ||||||||
\(231\) | 7.96034 | 0.523752 | ||||||||
\(232\) | −0.281706 | −0.0184949 | ||||||||
\(233\) | 3.48455 | 0.228280 | 0.114140 | − | 0.993465i | \(-0.463589\pi\) | ||||
0.114140 | + | 0.993465i | \(0.463589\pi\) | |||||||
\(234\) | 2.80888 | 0.183622 | ||||||||
\(235\) | −1.93618 | −0.126303 | ||||||||
\(236\) | 8.94333 | 0.582161 | ||||||||
\(237\) | −23.0195 | −1.49527 | ||||||||
\(238\) | −21.7763 | −1.41155 | ||||||||
\(239\) | −23.5249 | −1.52170 | −0.760848 | − | 0.648930i | \(-0.775217\pi\) | ||||
−0.760848 | + | 0.648930i | \(0.775217\pi\) | |||||||
\(240\) | −0.754243 | −0.0486862 | ||||||||
\(241\) | 14.2840 | 0.920116 | 0.460058 | − | 0.887889i | \(-0.347829\pi\) | ||||
0.460058 | + | 0.887889i | \(0.347829\pi\) | |||||||
\(242\) | −9.73301 | −0.625662 | ||||||||
\(243\) | −10.2932 | −0.660307 | ||||||||
\(244\) | 13.1010 | 0.838703 | ||||||||
\(245\) | 10.0235 | 0.640375 | ||||||||
\(246\) | −0.570524 | −0.0363753 | ||||||||
\(247\) | 2.68807 | 0.171038 | ||||||||
\(248\) | −6.56253 | −0.416721 | ||||||||
\(249\) | −9.79507 | −0.620738 | ||||||||
\(250\) | −5.23729 | −0.331235 | ||||||||
\(251\) | −5.37276 | −0.339126 | −0.169563 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169563 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(252\) | −5.28514 | −0.332933 | ||||||||
\(253\) | −8.91526 | −0.560498 | ||||||||
\(254\) | 15.1724 | 0.952000 | ||||||||
\(255\) | 3.24736 | 0.203358 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.19233 | −0.136754 | −0.0683770 | − | 0.997660i | \(-0.521782\pi\) | ||||
−0.0683770 | + | 0.997660i | \(0.521782\pi\) | |||||||
\(258\) | −7.47788 | −0.465552 | ||||||||
\(259\) | 8.67606 | 0.539104 | ||||||||
\(260\) | −1.45001 | −0.0899260 | ||||||||
\(261\) | 0.294367 | 0.0182208 | ||||||||
\(262\) | 17.8014 | 1.09977 | ||||||||
\(263\) | 31.8437 | 1.96357 | 0.981785 | − | 0.189998i | \(-0.0608481\pi\) | ||||
0.981785 | + | 0.189998i | \(0.0608481\pi\) | |||||||
\(264\) | 1.57386 | 0.0968645 | ||||||||
\(265\) | −1.93278 | −0.118730 | ||||||||
\(266\) | −5.05784 | −0.310116 | ||||||||
\(267\) | 6.12287 | 0.374713 | ||||||||
\(268\) | 7.49995 | 0.458132 | ||||||||
\(269\) | 17.6913 | 1.07866 | 0.539330 | − | 0.842095i | \(-0.318678\pi\) | ||||
0.539330 | + | 0.842095i | \(0.318678\pi\) | |||||||
\(270\) | 3.05087 | 0.185670 | ||||||||
\(271\) | 8.78563 | 0.533689 | 0.266845 | − | 0.963740i | \(-0.414019\pi\) | ||||
0.266845 | + | 0.963740i | \(0.414019\pi\) | |||||||
\(272\) | −4.30545 | −0.261056 | ||||||||
\(273\) | 19.0101 | 1.15055 | ||||||||
\(274\) | −6.31444 | −0.381469 | ||||||||
\(275\) | 5.30050 | 0.319632 | ||||||||
\(276\) | −11.0746 | −0.666612 | ||||||||
\(277\) | −21.3490 | −1.28274 | −0.641368 | − | 0.767233i | \(-0.721633\pi\) | ||||
−0.641368 | + | 0.767233i | \(0.721633\pi\) | |||||||
\(278\) | −4.18766 | −0.251159 | ||||||||
\(279\) | 6.85746 | 0.410546 | ||||||||
\(280\) | 2.72833 | 0.163049 | ||||||||
\(281\) | 0.534356 | 0.0318770 | 0.0159385 | − | 0.999873i | \(-0.494926\pi\) | ||||
0.0159385 | + | 0.999873i | \(0.494926\pi\) | |||||||
\(282\) | 5.01874 | 0.298862 | ||||||||
\(283\) | −11.9700 | −0.711541 | −0.355771 | − | 0.934573i | \(-0.615782\pi\) | ||||
−0.355771 | + | 0.934573i | \(0.615782\pi\) | |||||||
\(284\) | 9.98622 | 0.592573 | ||||||||
\(285\) | 0.754243 | 0.0446775 | ||||||||
\(286\) | 3.02571 | 0.178914 | ||||||||
\(287\) | 2.06376 | 0.121820 | ||||||||
\(288\) | −1.04494 | −0.0615737 | ||||||||
\(289\) | 1.53693 | 0.0904077 | ||||||||
\(290\) | −0.151960 | −0.00892338 | ||||||||
\(291\) | −16.8752 | −0.989244 | ||||||||
\(292\) | −7.18763 | −0.420624 | ||||||||
\(293\) | −16.8883 | −0.986625 | −0.493313 | − | 0.869852i | \(-0.664214\pi\) | ||||
−0.493313 | + | 0.869852i | \(0.664214\pi\) | |||||||
\(294\) | −25.9816 | −1.51528 | ||||||||
\(295\) | 4.82426 | 0.280879 | ||||||||
\(296\) | 1.71537 | 0.0997039 | ||||||||
\(297\) | −6.36618 | −0.369403 | ||||||||
\(298\) | −13.0258 | −0.754565 | ||||||||
\(299\) | −21.2906 | −1.23127 | ||||||||
\(300\) | 6.58431 | 0.380145 | ||||||||
\(301\) | 27.0498 | 1.55912 | ||||||||
\(302\) | −0.626724 | −0.0360639 | ||||||||
\(303\) | −1.69490 | −0.0973696 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 7.06699 | 0.404655 | ||||||||
\(306\) | 4.49895 | 0.257188 | ||||||||
\(307\) | −19.8836 | −1.13482 | −0.567408 | − | 0.823437i | \(-0.692054\pi\) | ||||
−0.567408 | + | 0.823437i | \(0.692054\pi\) | |||||||
\(308\) | −5.69314 | −0.324397 | ||||||||
\(309\) | −23.9497 | −1.36245 | ||||||||
\(310\) | −3.54000 | −0.201058 | ||||||||
\(311\) | 8.70171 | 0.493428 | 0.246714 | − | 0.969088i | \(-0.420649\pi\) | ||||
0.246714 | + | 0.969088i | \(0.420649\pi\) | |||||||
\(312\) | 3.75855 | 0.212786 | ||||||||
\(313\) | −23.2841 | −1.31610 | −0.658049 | − | 0.752975i | \(-0.728618\pi\) | ||||
−0.658049 | + | 0.752975i | \(0.728618\pi\) | |||||||
\(314\) | −6.57277 | −0.370923 | ||||||||
\(315\) | −2.85094 | −0.160632 | ||||||||
\(316\) | 16.4632 | 0.926129 | ||||||||
\(317\) | −1.08251 | −0.0607997 | −0.0303998 | − | 0.999538i | \(-0.509678\pi\) | ||||
−0.0303998 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(318\) | 5.00992 | 0.280942 | ||||||||
\(319\) | 0.317091 | 0.0177537 | ||||||||
\(320\) | 0.539425 | 0.0301548 | ||||||||
\(321\) | −8.04951 | −0.449280 | ||||||||
\(322\) | 40.0601 | 2.23246 | ||||||||
\(323\) | 4.30545 | 0.239562 | ||||||||
\(324\) | −4.77328 | −0.265182 | ||||||||
\(325\) | 12.6582 | 0.702149 | ||||||||
\(326\) | 7.39921 | 0.409804 | ||||||||
\(327\) | −2.29149 | −0.126720 | ||||||||
\(328\) | 0.408032 | 0.0225298 | ||||||||
\(329\) | −18.1543 | −1.00088 | ||||||||
\(330\) | 0.848981 | 0.0467349 | ||||||||
\(331\) | 29.4757 | 1.62013 | 0.810064 | − | 0.586341i | \(-0.199432\pi\) | ||||
0.810064 | + | 0.586341i | \(0.199432\pi\) | |||||||
\(332\) | 7.00532 | 0.384467 | ||||||||
\(333\) | −1.79246 | −0.0982262 | ||||||||
\(334\) | −15.1677 | −0.829938 | ||||||||
\(335\) | 4.04566 | 0.221038 | ||||||||
\(336\) | −7.07204 | −0.385812 | ||||||||
\(337\) | −8.97516 | −0.488908 | −0.244454 | − | 0.969661i | \(-0.578609\pi\) | ||||
−0.244454 | + | 0.969661i | \(0.578609\pi\) | |||||||
\(338\) | −5.77428 | −0.314079 | ||||||||
\(339\) | 3.82943 | 0.207986 | ||||||||
\(340\) | −2.32247 | −0.125954 | ||||||||
\(341\) | 7.38683 | 0.400019 | ||||||||
\(342\) | 1.04494 | 0.0565039 | ||||||||
\(343\) | 58.5785 | 3.16294 | ||||||||
\(344\) | 5.34809 | 0.288350 | ||||||||
\(345\) | −5.97391 | −0.321625 | ||||||||
\(346\) | −15.7761 | −0.848131 | ||||||||
\(347\) | 26.4970 | 1.42244 | 0.711218 | − | 0.702971i | \(-0.248144\pi\) | ||||
0.711218 | + | 0.702971i | \(0.248144\pi\) | |||||||
\(348\) | 0.393892 | 0.0211148 | ||||||||
\(349\) | −4.60150 | −0.246312 | −0.123156 | − | 0.992387i | \(-0.539302\pi\) | ||||
−0.123156 | + | 0.992387i | \(0.539302\pi\) | |||||||
\(350\) | −23.8175 | −1.27310 | ||||||||
\(351\) | −15.2031 | −0.811483 | ||||||||
\(352\) | −1.12561 | −0.0599950 | ||||||||
\(353\) | −3.77583 | −0.200967 | −0.100484 | − | 0.994939i | \(-0.532039\pi\) | ||||
−0.100484 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(354\) | −12.5049 | −0.664626 | ||||||||
\(355\) | 5.38682 | 0.285903 | ||||||||
\(356\) | −4.37900 | −0.232086 | ||||||||
\(357\) | 30.4484 | 1.61150 | ||||||||
\(358\) | 0.905811 | 0.0478736 | ||||||||
\(359\) | −21.5307 | −1.13635 | −0.568173 | − | 0.822909i | \(-0.692350\pi\) | ||||
−0.568173 | + | 0.822909i | \(0.692350\pi\) | |||||||
\(360\) | −0.563668 | −0.0297079 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.8041 | −0.883203 | ||||||||
\(363\) | 13.6090 | 0.714289 | ||||||||
\(364\) | −13.5958 | −0.712615 | ||||||||
\(365\) | −3.87719 | −0.202941 | ||||||||
\(366\) | −18.3182 | −0.957508 | ||||||||
\(367\) | −21.8841 | −1.14234 | −0.571170 | − | 0.820832i | \(-0.693510\pi\) | ||||
−0.571170 | + | 0.820832i | \(0.693510\pi\) | |||||||
\(368\) | 7.92041 | 0.412880 | ||||||||
\(369\) | −0.426370 | −0.0221959 | ||||||||
\(370\) | 0.925314 | 0.0481048 | ||||||||
\(371\) | −18.1224 | −0.940867 | ||||||||
\(372\) | 9.17596 | 0.475751 | ||||||||
\(373\) | 13.7549 | 0.712203 | 0.356102 | − | 0.934447i | \(-0.384106\pi\) | ||||
0.356102 | + | 0.934447i | \(0.384106\pi\) | |||||||
\(374\) | 4.84625 | 0.250593 | ||||||||
\(375\) | 7.32296 | 0.378156 | ||||||||
\(376\) | −3.58934 | −0.185106 | ||||||||
\(377\) | 0.757247 | 0.0390002 | ||||||||
\(378\) | 28.6060 | 1.47133 | ||||||||
\(379\) | −5.18809 | −0.266494 | −0.133247 | − | 0.991083i | \(-0.542540\pi\) | ||||
−0.133247 | + | 0.991083i | \(0.542540\pi\) | |||||||
\(380\) | −0.539425 | −0.0276719 | ||||||||
\(381\) | −21.2145 | −1.08685 | ||||||||
\(382\) | −9.56666 | −0.489473 | ||||||||
\(383\) | 32.9761 | 1.68500 | 0.842499 | − | 0.538697i | \(-0.181083\pi\) | ||||
0.842499 | + | 0.538697i | \(0.181083\pi\) | |||||||
\(384\) | −1.39823 | −0.0713533 | ||||||||
\(385\) | −3.07102 | −0.156514 | ||||||||
\(386\) | 19.2576 | 0.980188 | ||||||||
\(387\) | −5.58844 | −0.284076 | ||||||||
\(388\) | 12.0690 | 0.612709 | ||||||||
\(389\) | 11.2758 | 0.571707 | 0.285854 | − | 0.958273i | \(-0.407723\pi\) | ||||
0.285854 | + | 0.958273i | \(0.407723\pi\) | |||||||
\(390\) | 2.02746 | 0.102664 | ||||||||
\(391\) | −34.1010 | −1.72456 | ||||||||
\(392\) | 18.5817 | 0.938519 | ||||||||
\(393\) | −24.8905 | −1.25556 | ||||||||
\(394\) | 14.0935 | 0.710020 | ||||||||
\(395\) | 8.88069 | 0.446836 | ||||||||
\(396\) | 1.17619 | 0.0591059 | ||||||||
\(397\) | −15.9178 | −0.798893 | −0.399446 | − | 0.916757i | \(-0.630798\pi\) | ||||
−0.399446 | + | 0.916757i | \(0.630798\pi\) | |||||||
\(398\) | 1.07616 | 0.0539432 | ||||||||
\(399\) | 7.07204 | 0.354045 | ||||||||
\(400\) | −4.70902 | −0.235451 | ||||||||
\(401\) | 30.8843 | 1.54229 | 0.771143 | − | 0.636662i | \(-0.219685\pi\) | ||||
0.771143 | + | 0.636662i | \(0.219685\pi\) | |||||||
\(402\) | −10.4867 | −0.523028 | ||||||||
\(403\) | 17.6406 | 0.878739 | ||||||||
\(404\) | 1.21217 | 0.0603079 | ||||||||
\(405\) | −2.57483 | −0.127944 | ||||||||
\(406\) | −1.42483 | −0.0707129 | ||||||||
\(407\) | −1.93083 | −0.0957078 | ||||||||
\(408\) | 6.02003 | 0.298036 | ||||||||
\(409\) | 35.8549 | 1.77291 | 0.886455 | − | 0.462814i | \(-0.153160\pi\) | ||||
0.886455 | + | 0.462814i | \(0.153160\pi\) | |||||||
\(410\) | 0.220103 | 0.0108701 | ||||||||
\(411\) | 8.82907 | 0.435506 | ||||||||
\(412\) | 17.1286 | 0.843863 | ||||||||
\(413\) | 45.2339 | 2.22581 | ||||||||
\(414\) | −8.27636 | −0.406761 | ||||||||
\(415\) | 3.77885 | 0.185496 | ||||||||
\(416\) | −2.68807 | −0.131794 | ||||||||
\(417\) | 5.85533 | 0.286737 | ||||||||
\(418\) | 1.12561 | 0.0550552 | ||||||||
\(419\) | −25.3099 | −1.23647 | −0.618234 | − | 0.785994i | \(-0.712152\pi\) | ||||
−0.618234 | + | 0.785994i | \(0.712152\pi\) | |||||||
\(420\) | −3.81484 | −0.186145 | ||||||||
\(421\) | 35.4253 | 1.72653 | 0.863263 | − | 0.504755i | \(-0.168417\pi\) | ||||
0.863263 | + | 0.504755i | \(0.168417\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 3.75065 | 0.182363 | ||||||||
\(424\) | −3.58303 | −0.174007 | ||||||||
\(425\) | 20.2745 | 0.983456 | ||||||||
\(426\) | −13.9631 | −0.676513 | ||||||||
\(427\) | 66.2625 | 3.20667 | ||||||||
\(428\) | 5.75691 | 0.278271 | ||||||||
\(429\) | −4.23065 | −0.204258 | ||||||||
\(430\) | 2.88489 | 0.139122 | ||||||||
\(431\) | 31.1751 | 1.50165 | 0.750825 | − | 0.660501i | \(-0.229656\pi\) | ||||
0.750825 | + | 0.660501i | \(0.229656\pi\) | |||||||
\(432\) | 5.65578 | 0.272114 | ||||||||
\(433\) | −28.5507 | −1.37206 | −0.686030 | − | 0.727574i | \(-0.740648\pi\) | ||||
−0.686030 | + | 0.727574i | \(0.740648\pi\) | |||||||
\(434\) | −33.1922 | −1.59328 | ||||||||
\(435\) | 0.212475 | 0.0101874 | ||||||||
\(436\) | 1.63885 | 0.0784865 | ||||||||
\(437\) | −7.92041 | −0.378885 | ||||||||
\(438\) | 10.0500 | 0.480207 | ||||||||
\(439\) | −25.6159 | −1.22258 | −0.611291 | − | 0.791406i | \(-0.709350\pi\) | ||||
−0.611291 | + | 0.791406i | \(0.709350\pi\) | |||||||
\(440\) | −0.607181 | −0.0289462 | ||||||||
\(441\) | −19.4168 | −0.924610 | ||||||||
\(442\) | 11.5734 | 0.550489 | ||||||||
\(443\) | 16.4574 | 0.781915 | 0.390957 | − | 0.920409i | \(-0.372144\pi\) | ||||
0.390957 | + | 0.920409i | \(0.372144\pi\) | |||||||
\(444\) | −2.39849 | −0.113827 | ||||||||
\(445\) | −2.36214 | −0.111976 | ||||||||
\(446\) | 9.95413 | 0.471342 | ||||||||
\(447\) | 18.2131 | 0.861452 | ||||||||
\(448\) | 5.05784 | 0.238960 | ||||||||
\(449\) | −6.37899 | −0.301043 | −0.150522 | − | 0.988607i | \(-0.548095\pi\) | ||||
−0.150522 | + | 0.988607i | \(0.548095\pi\) | |||||||
\(450\) | 4.92065 | 0.231962 | ||||||||
\(451\) | −0.459284 | −0.0216268 | ||||||||
\(452\) | −2.73876 | −0.128821 | ||||||||
\(453\) | 0.876307 | 0.0411725 | ||||||||
\(454\) | 25.9588 | 1.21831 | ||||||||
\(455\) | −7.33393 | −0.343820 | ||||||||
\(456\) | 1.39823 | 0.0654783 | ||||||||
\(457\) | −17.7167 | −0.828750 | −0.414375 | − | 0.910106i | \(-0.636000\pi\) | ||||
−0.414375 | + | 0.910106i | \(0.636000\pi\) | |||||||
\(458\) | −4.86224 | −0.227198 | ||||||||
\(459\) | −24.3507 | −1.13659 | ||||||||
\(460\) | 4.27247 | 0.199205 | ||||||||
\(461\) | −11.1057 | −0.517242 | −0.258621 | − | 0.965979i | \(-0.583268\pi\) | ||||
−0.258621 | + | 0.965979i | \(0.583268\pi\) | |||||||
\(462\) | 7.96034 | 0.370348 | ||||||||
\(463\) | −20.2349 | −0.940397 | −0.470199 | − | 0.882561i | \(-0.655818\pi\) | ||||
−0.470199 | + | 0.882561i | \(0.655818\pi\) | |||||||
\(464\) | −0.281706 | −0.0130779 | ||||||||
\(465\) | 4.94975 | 0.229539 | ||||||||
\(466\) | 3.48455 | 0.161418 | ||||||||
\(467\) | −33.9185 | −1.56956 | −0.784781 | − | 0.619773i | \(-0.787225\pi\) | ||||
−0.784781 | + | 0.619773i | \(0.787225\pi\) | |||||||
\(468\) | 2.80888 | 0.129840 | ||||||||
\(469\) | 37.9335 | 1.75161 | ||||||||
\(470\) | −1.93618 | −0.0893094 | ||||||||
\(471\) | 9.19027 | 0.423465 | ||||||||
\(472\) | 8.94333 | 0.411650 | ||||||||
\(473\) | −6.01984 | −0.276793 | ||||||||
\(474\) | −23.0195 | −1.05732 | ||||||||
\(475\) | 4.70902 | 0.216065 | ||||||||
\(476\) | −21.7763 | −0.998114 | ||||||||
\(477\) | 3.74406 | 0.171429 | ||||||||
\(478\) | −23.5249 | −1.07600 | ||||||||
\(479\) | 15.7058 | 0.717614 | 0.358807 | − | 0.933412i | \(-0.383184\pi\) | ||||
0.358807 | + | 0.933412i | \(0.383184\pi\) | |||||||
\(480\) | −0.754243 | −0.0344263 | ||||||||
\(481\) | −4.61104 | −0.210245 | ||||||||
\(482\) | 14.2840 | 0.650620 | ||||||||
\(483\) | −56.0135 | −2.54870 | ||||||||
\(484\) | −9.73301 | −0.442410 | ||||||||
\(485\) | 6.51031 | 0.295618 | ||||||||
\(486\) | −10.2932 | −0.466908 | ||||||||
\(487\) | −17.2930 | −0.783618 | −0.391809 | − | 0.920046i | \(-0.628151\pi\) | ||||
−0.391809 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(488\) | 13.1010 | 0.593053 | ||||||||
\(489\) | −10.3458 | −0.467855 | ||||||||
\(490\) | 10.0235 | 0.452814 | ||||||||
\(491\) | 25.0354 | 1.12983 | 0.564917 | − | 0.825148i | \(-0.308908\pi\) | ||||
0.564917 | + | 0.825148i | \(0.308908\pi\) | |||||||
\(492\) | −0.570524 | −0.0257212 | ||||||||
\(493\) | 1.21287 | 0.0546251 | ||||||||
\(494\) | 2.68807 | 0.120942 | ||||||||
\(495\) | 0.634468 | 0.0285172 | ||||||||
\(496\) | −6.56253 | −0.294667 | ||||||||
\(497\) | 50.5087 | 2.26562 | ||||||||
\(498\) | −9.79507 | −0.438928 | ||||||||
\(499\) | 32.2250 | 1.44259 | 0.721295 | − | 0.692628i | \(-0.243547\pi\) | ||||
0.721295 | + | 0.692628i | \(0.243547\pi\) | |||||||
\(500\) | −5.23729 | −0.234219 | ||||||||
\(501\) | 21.2080 | 0.947501 | ||||||||
\(502\) | −5.37276 | −0.239798 | ||||||||
\(503\) | −15.4035 | −0.686808 | −0.343404 | − | 0.939188i | \(-0.611580\pi\) | ||||
−0.343404 | + | 0.939188i | \(0.611580\pi\) | |||||||
\(504\) | −5.28514 | −0.235419 | ||||||||
\(505\) | 0.653877 | 0.0290971 | ||||||||
\(506\) | −8.91526 | −0.396332 | ||||||||
\(507\) | 8.07379 | 0.358570 | ||||||||
\(508\) | 15.1724 | 0.673166 | ||||||||
\(509\) | −29.0628 | −1.28818 | −0.644092 | − | 0.764948i | \(-0.722765\pi\) | ||||
−0.644092 | + | 0.764948i | \(0.722765\pi\) | |||||||
\(510\) | 3.24736 | 0.143795 | ||||||||
\(511\) | −36.3538 | −1.60820 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.65578 | −0.249709 | ||||||||
\(514\) | −2.19233 | −0.0966997 | ||||||||
\(515\) | 9.23958 | 0.407144 | ||||||||
\(516\) | −7.47788 | −0.329195 | ||||||||
\(517\) | 4.04019 | 0.177687 | ||||||||
\(518\) | 8.67606 | 0.381204 | ||||||||
\(519\) | 22.0587 | 0.968272 | ||||||||
\(520\) | −1.45001 | −0.0635873 | ||||||||
\(521\) | −19.6781 | −0.862113 | −0.431057 | − | 0.902325i | \(-0.641859\pi\) | ||||
−0.431057 | + | 0.902325i | \(0.641859\pi\) | |||||||
\(522\) | 0.294367 | 0.0128841 | ||||||||
\(523\) | 28.6016 | 1.25066 | 0.625330 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625330 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(524\) | 17.8014 | 0.777656 | ||||||||
\(525\) | 33.3024 | 1.45344 | ||||||||
\(526\) | 31.8437 | 1.38845 | ||||||||
\(527\) | 28.2547 | 1.23079 | ||||||||
\(528\) | 1.57386 | 0.0684935 | ||||||||
\(529\) | 39.7329 | 1.72752 | ||||||||
\(530\) | −1.93278 | −0.0839545 | ||||||||
\(531\) | −9.34525 | −0.405549 | ||||||||
\(532\) | −5.05784 | −0.219285 | ||||||||
\(533\) | −1.09682 | −0.0475085 | ||||||||
\(534\) | 6.12287 | 0.264962 | ||||||||
\(535\) | 3.10542 | 0.134259 | ||||||||
\(536\) | 7.49995 | 0.323948 | ||||||||
\(537\) | −1.26654 | −0.0546551 | ||||||||
\(538\) | 17.6913 | 0.762728 | ||||||||
\(539\) | −20.9157 | −0.900904 | ||||||||
\(540\) | 3.05087 | 0.131288 | ||||||||
\(541\) | −17.0969 | −0.735052 | −0.367526 | − | 0.930013i | \(-0.619795\pi\) | ||||
−0.367526 | + | 0.930013i | \(0.619795\pi\) | |||||||
\(542\) | 8.78563 | 0.377375 | ||||||||
\(543\) | 23.4960 | 1.00831 | ||||||||
\(544\) | −4.30545 | −0.184595 | ||||||||
\(545\) | 0.884035 | 0.0378679 | ||||||||
\(546\) | 19.0101 | 0.813559 | ||||||||
\(547\) | −20.2406 | −0.865426 | −0.432713 | − | 0.901532i | \(-0.642444\pi\) | ||||
−0.432713 | + | 0.901532i | \(0.642444\pi\) | |||||||
\(548\) | −6.31444 | −0.269740 | ||||||||
\(549\) | −13.6897 | −0.584264 | ||||||||
\(550\) | 5.30050 | 0.226014 | ||||||||
\(551\) | 0.281706 | 0.0120011 | ||||||||
\(552\) | −11.0746 | −0.471366 | ||||||||
\(553\) | 83.2684 | 3.54093 | ||||||||
\(554\) | −21.3490 | −0.907031 | ||||||||
\(555\) | −1.29381 | −0.0549190 | ||||||||
\(556\) | −4.18766 | −0.177596 | ||||||||
\(557\) | 11.4566 | 0.485431 | 0.242716 | − | 0.970097i | \(-0.421962\pi\) | ||||
0.242716 | + | 0.970097i | \(0.421962\pi\) | |||||||
\(558\) | 6.85746 | 0.290300 | ||||||||
\(559\) | −14.3760 | −0.608042 | ||||||||
\(560\) | 2.72833 | 0.115293 | ||||||||
\(561\) | −6.77619 | −0.286091 | ||||||||
\(562\) | 0.534356 | 0.0225405 | ||||||||
\(563\) | −13.9464 | −0.587772 | −0.293886 | − | 0.955840i | \(-0.594949\pi\) | ||||
−0.293886 | + | 0.955840i | \(0.594949\pi\) | |||||||
\(564\) | 5.01874 | 0.211327 | ||||||||
\(565\) | −1.47736 | −0.0621530 | ||||||||
\(566\) | −11.9700 | −0.503136 | ||||||||
\(567\) | −24.1425 | −1.01389 | ||||||||
\(568\) | 9.98622 | 0.419013 | ||||||||
\(569\) | 34.4070 | 1.44242 | 0.721208 | − | 0.692718i | \(-0.243587\pi\) | ||||
0.721208 | + | 0.692718i | \(0.243587\pi\) | |||||||
\(570\) | 0.754243 | 0.0315918 | ||||||||
\(571\) | 46.0927 | 1.92892 | 0.964461 | − | 0.264226i | \(-0.0851165\pi\) | ||||
0.964461 | + | 0.264226i | \(0.0851165\pi\) | |||||||
\(572\) | 3.02571 | 0.126511 | ||||||||
\(573\) | 13.3764 | 0.558808 | ||||||||
\(574\) | 2.06376 | 0.0861397 | ||||||||
\(575\) | −37.2974 | −1.55541 | ||||||||
\(576\) | −1.04494 | −0.0435392 | ||||||||
\(577\) | −20.1814 | −0.840162 | −0.420081 | − | 0.907487i | \(-0.637998\pi\) | ||||
−0.420081 | + | 0.907487i | \(0.637998\pi\) | |||||||
\(578\) | 1.53693 | 0.0639279 | ||||||||
\(579\) | −26.9267 | −1.11903 | ||||||||
\(580\) | −0.151960 | −0.00630978 | ||||||||
\(581\) | 35.4318 | 1.46996 | ||||||||
\(582\) | −16.8752 | −0.699501 | ||||||||
\(583\) | 4.03308 | 0.167033 | ||||||||
\(584\) | −7.18763 | −0.297426 | ||||||||
\(585\) | 1.51518 | 0.0626449 | ||||||||
\(586\) | −16.8883 | −0.697649 | ||||||||
\(587\) | −31.7581 | −1.31080 | −0.655399 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655399 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(588\) | −25.9816 | −1.07146 | ||||||||
\(589\) | 6.56253 | 0.270405 | ||||||||
\(590\) | 4.82426 | 0.198612 | ||||||||
\(591\) | −19.7060 | −0.810597 | ||||||||
\(592\) | 1.71537 | 0.0705013 | ||||||||
\(593\) | 11.8103 | 0.484992 | 0.242496 | − | 0.970152i | \(-0.422034\pi\) | ||||
0.242496 | + | 0.970152i | \(0.422034\pi\) | |||||||
\(594\) | −6.36618 | −0.261207 | ||||||||
\(595\) | −11.7467 | −0.481567 | ||||||||
\(596\) | −13.0258 | −0.533558 | ||||||||
\(597\) | −1.50473 | −0.0615844 | ||||||||
\(598\) | −21.2906 | −0.870638 | ||||||||
\(599\) | −16.9161 | −0.691173 | −0.345586 | − | 0.938387i | \(-0.612320\pi\) | ||||
−0.345586 | + | 0.938387i | \(0.612320\pi\) | |||||||
\(600\) | 6.58431 | 0.268803 | ||||||||
\(601\) | 26.4584 | 1.07926 | 0.539629 | − | 0.841903i | \(-0.318564\pi\) | ||||
0.539629 | + | 0.841903i | \(0.318564\pi\) | |||||||
\(602\) | 27.0498 | 1.10247 | ||||||||
\(603\) | −7.83700 | −0.319147 | ||||||||
\(604\) | −0.626724 | −0.0255010 | ||||||||
\(605\) | −5.25023 | −0.213452 | ||||||||
\(606\) | −1.69490 | −0.0688507 | ||||||||
\(607\) | 32.0869 | 1.30237 | 0.651184 | − | 0.758920i | \(-0.274273\pi\) | ||||
0.651184 | + | 0.758920i | \(0.274273\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 1.99224 | 0.0807296 | ||||||||
\(610\) | 7.06699 | 0.286134 | ||||||||
\(611\) | 9.64840 | 0.390332 | ||||||||
\(612\) | 4.49895 | 0.181859 | ||||||||
\(613\) | −16.5732 | −0.669385 | −0.334693 | − | 0.942327i | \(-0.608632\pi\) | ||||
−0.334693 | + | 0.942327i | \(0.608632\pi\) | |||||||
\(614\) | −19.8836 | −0.802436 | ||||||||
\(615\) | −0.307755 | −0.0124099 | ||||||||
\(616\) | −5.69314 | −0.229383 | ||||||||
\(617\) | −46.6098 | −1.87644 | −0.938220 | − | 0.346038i | \(-0.887527\pi\) | ||||
−0.938220 | + | 0.346038i | \(0.887527\pi\) | |||||||
\(618\) | −23.9497 | −0.963399 | ||||||||
\(619\) | 6.72091 | 0.270136 | 0.135068 | − | 0.990836i | \(-0.456875\pi\) | ||||
0.135068 | + | 0.990836i | \(0.456875\pi\) | |||||||
\(620\) | −3.54000 | −0.142170 | ||||||||
\(621\) | 44.7960 | 1.79760 | ||||||||
\(622\) | 8.70171 | 0.348907 | ||||||||
\(623\) | −22.1483 | −0.887352 | ||||||||
\(624\) | 3.75855 | 0.150463 | ||||||||
\(625\) | 20.7200 | 0.828799 | ||||||||
\(626\) | −23.2841 | −0.930621 | ||||||||
\(627\) | −1.57386 | −0.0628540 | ||||||||
\(628\) | −6.57277 | −0.262282 | ||||||||
\(629\) | −7.38545 | −0.294477 | ||||||||
\(630\) | −2.85094 | −0.113584 | ||||||||
\(631\) | 18.7172 | 0.745120 | 0.372560 | − | 0.928008i | \(-0.378480\pi\) | ||||
0.372560 | + | 0.928008i | \(0.378480\pi\) | |||||||
\(632\) | 16.4632 | 0.654872 | ||||||||
\(633\) | 1.39823 | 0.0555748 | ||||||||
\(634\) | −1.08251 | −0.0429919 | ||||||||
\(635\) | 8.18437 | 0.324787 | ||||||||
\(636\) | 5.00992 | 0.198656 | ||||||||
\(637\) | −49.9490 | −1.97905 | ||||||||
\(638\) | 0.317091 | 0.0125537 | ||||||||
\(639\) | −10.4350 | −0.412803 | ||||||||
\(640\) | 0.539425 | 0.0213227 | ||||||||
\(641\) | −32.6567 | −1.28986 | −0.644930 | − | 0.764241i | \(-0.723114\pi\) | ||||
−0.644930 | + | 0.764241i | \(0.723114\pi\) | |||||||
\(642\) | −8.04951 | −0.317689 | ||||||||
\(643\) | 23.2928 | 0.918577 | 0.459289 | − | 0.888287i | \(-0.348104\pi\) | ||||
0.459289 | + | 0.888287i | \(0.348104\pi\) | |||||||
\(644\) | 40.0601 | 1.57859 | ||||||||
\(645\) | −4.03376 | −0.158829 | ||||||||
\(646\) | 4.30545 | 0.169396 | ||||||||
\(647\) | −44.0611 | −1.73222 | −0.866110 | − | 0.499854i | \(-0.833387\pi\) | ||||
−0.866110 | + | 0.499854i | \(0.833387\pi\) | |||||||
\(648\) | −4.77328 | −0.187512 | ||||||||
\(649\) | −10.0667 | −0.395151 | ||||||||
\(650\) | 12.6582 | 0.496495 | ||||||||
\(651\) | 46.4105 | 1.81897 | ||||||||
\(652\) | 7.39921 | 0.289776 | ||||||||
\(653\) | 30.8368 | 1.20674 | 0.603368 | − | 0.797463i | \(-0.293825\pi\) | ||||
0.603368 | + | 0.797463i | \(0.293825\pi\) | |||||||
\(654\) | −2.29149 | −0.0896043 | ||||||||
\(655\) | 9.60251 | 0.375201 | ||||||||
\(656\) | 0.408032 | 0.0159310 | ||||||||
\(657\) | 7.51065 | 0.293018 | ||||||||
\(658\) | −18.1543 | −0.707728 | ||||||||
\(659\) | −43.5281 | −1.69562 | −0.847808 | − | 0.530304i | \(-0.822078\pi\) | ||||
−0.847808 | + | 0.530304i | \(0.822078\pi\) | |||||||
\(660\) | 0.848981 | 0.0330465 | ||||||||
\(661\) | 44.1234 | 1.71620 | 0.858101 | − | 0.513482i | \(-0.171645\pi\) | ||||
0.858101 | + | 0.513482i | \(0.171645\pi\) | |||||||
\(662\) | 29.4757 | 1.14560 | ||||||||
\(663\) | −16.1823 | −0.628467 | ||||||||
\(664\) | 7.00532 | 0.271859 | ||||||||
\(665\) | −2.72833 | −0.105800 | ||||||||
\(666\) | −1.79246 | −0.0694564 | ||||||||
\(667\) | −2.23123 | −0.0863936 | ||||||||
\(668\) | −15.1677 | −0.586855 | ||||||||
\(669\) | −13.9182 | −0.538109 | ||||||||
\(670\) | 4.04566 | 0.156298 | ||||||||
\(671\) | −14.7465 | −0.569283 | ||||||||
\(672\) | −7.07204 | −0.272810 | ||||||||
\(673\) | 23.0409 | 0.888163 | 0.444081 | − | 0.895986i | \(-0.353530\pi\) | ||||
0.444081 | + | 0.895986i | \(0.353530\pi\) | |||||||
\(674\) | −8.97516 | −0.345710 | ||||||||
\(675\) | −26.6332 | −1.02511 | ||||||||
\(676\) | −5.77428 | −0.222088 | ||||||||
\(677\) | 33.9101 | 1.30327 | 0.651636 | − | 0.758532i | \(-0.274083\pi\) | ||||
0.651636 | + | 0.758532i | \(0.274083\pi\) | |||||||
\(678\) | 3.82943 | 0.147069 | ||||||||
\(679\) | 61.0429 | 2.34261 | ||||||||
\(680\) | −2.32247 | −0.0890627 | ||||||||
\(681\) | −36.2965 | −1.39089 | ||||||||
\(682\) | 7.38683 | 0.282856 | ||||||||
\(683\) | −37.2066 | −1.42367 | −0.711836 | − | 0.702346i | \(-0.752136\pi\) | ||||
−0.711836 | + | 0.702346i | \(0.752136\pi\) | |||||||
\(684\) | 1.04494 | 0.0399543 | ||||||||
\(685\) | −3.40617 | −0.130143 | ||||||||
\(686\) | 58.5785 | 2.23654 | ||||||||
\(687\) | 6.79855 | 0.259381 | ||||||||
\(688\) | 5.34809 | 0.203894 | ||||||||
\(689\) | 9.63144 | 0.366929 | ||||||||
\(690\) | −5.97391 | −0.227423 | ||||||||
\(691\) | 37.3225 | 1.41982 | 0.709908 | − | 0.704295i | \(-0.248737\pi\) | ||||
0.709908 | + | 0.704295i | \(0.248737\pi\) | |||||||
\(692\) | −15.7761 | −0.599719 | ||||||||
\(693\) | 5.94899 | 0.225984 | ||||||||
\(694\) | 26.4970 | 1.00581 | ||||||||
\(695\) | −2.25893 | −0.0856861 | ||||||||
\(696\) | 0.393892 | 0.0149304 | ||||||||
\(697\) | −1.75676 | −0.0665422 | ||||||||
\(698\) | −4.60150 | −0.174169 | ||||||||
\(699\) | −4.87221 | −0.184284 | ||||||||
\(700\) | −23.8175 | −0.900215 | ||||||||
\(701\) | 38.9177 | 1.46990 | 0.734951 | − | 0.678120i | \(-0.237205\pi\) | ||||
0.734951 | + | 0.678120i | \(0.237205\pi\) | |||||||
\(702\) | −15.2031 | −0.573805 | ||||||||
\(703\) | −1.71537 | −0.0646964 | ||||||||
\(704\) | −1.12561 | −0.0424229 | ||||||||
\(705\) | 2.70724 | 0.101960 | ||||||||
\(706\) | −3.77583 | −0.142105 | ||||||||
\(707\) | 6.13097 | 0.230579 | ||||||||
\(708\) | −12.5049 | −0.469962 | ||||||||
\(709\) | −41.1852 | −1.54674 | −0.773371 | − | 0.633954i | \(-0.781431\pi\) | ||||
−0.773371 | + | 0.633954i | \(0.781431\pi\) | |||||||
\(710\) | 5.38682 | 0.202164 | ||||||||
\(711\) | −17.2031 | −0.645167 | ||||||||
\(712\) | −4.37900 | −0.164110 | ||||||||
\(713\) | −51.9780 | −1.94659 | ||||||||
\(714\) | 30.4484 | 1.13950 | ||||||||
\(715\) | 1.63215 | 0.0610388 | ||||||||
\(716\) | 0.905811 | 0.0338518 | ||||||||
\(717\) | 32.8933 | 1.22842 | ||||||||
\(718\) | −21.5307 | −0.803518 | ||||||||
\(719\) | −18.1056 | −0.675226 | −0.337613 | − | 0.941285i | \(-0.609619\pi\) | ||||
−0.337613 | + | 0.941285i | \(0.609619\pi\) | |||||||
\(720\) | −0.563668 | −0.0210067 | ||||||||
\(721\) | 86.6334 | 3.22640 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −19.9724 | −0.742783 | ||||||||
\(724\) | −16.8041 | −0.624518 | ||||||||
\(725\) | 1.32656 | 0.0492673 | ||||||||
\(726\) | 13.6090 | 0.505078 | ||||||||
\(727\) | −25.9544 | −0.962594 | −0.481297 | − | 0.876557i | \(-0.659834\pi\) | ||||
−0.481297 | + | 0.876557i | \(0.659834\pi\) | |||||||
\(728\) | −13.5958 | −0.503895 | ||||||||
\(729\) | 28.7121 | 1.06341 | ||||||||
\(730\) | −3.87719 | −0.143501 | ||||||||
\(731\) | −23.0259 | −0.851645 | ||||||||
\(732\) | −18.3182 | −0.677061 | ||||||||
\(733\) | 9.40335 | 0.347321 | 0.173660 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173660 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(734\) | −21.8841 | −0.807757 | ||||||||
\(735\) | −14.0151 | −0.516956 | ||||||||
\(736\) | 7.92041 | 0.291950 | ||||||||
\(737\) | −8.44199 | −0.310965 | ||||||||
\(738\) | −0.426370 | −0.0156949 | ||||||||
\(739\) | 37.2029 | 1.36853 | 0.684266 | − | 0.729232i | \(-0.260123\pi\) | ||||
0.684266 | + | 0.729232i | \(0.260123\pi\) | |||||||
\(740\) | 0.925314 | 0.0340152 | ||||||||
\(741\) | −3.75855 | −0.138074 | ||||||||
\(742\) | −18.1224 | −0.665294 | ||||||||
\(743\) | −30.6366 | −1.12395 | −0.561975 | − | 0.827154i | \(-0.689958\pi\) | ||||
−0.561975 | + | 0.827154i | \(0.689958\pi\) | |||||||
\(744\) | 9.17596 | 0.336407 | ||||||||
\(745\) | −7.02646 | −0.257430 | ||||||||
\(746\) | 13.7549 | 0.503604 | ||||||||
\(747\) | −7.32014 | −0.267830 | ||||||||
\(748\) | 4.84625 | 0.177196 | ||||||||
\(749\) | 29.1175 | 1.06393 | ||||||||
\(750\) | 7.32296 | 0.267397 | ||||||||
\(751\) | −47.7664 | −1.74302 | −0.871511 | − | 0.490376i | \(-0.836860\pi\) | ||||
−0.871511 | + | 0.490376i | \(0.836860\pi\) | |||||||
\(752\) | −3.58934 | −0.130890 | ||||||||
\(753\) | 7.51238 | 0.273766 | ||||||||
\(754\) | 0.757247 | 0.0275773 | ||||||||
\(755\) | −0.338071 | −0.0123037 | ||||||||
\(756\) | 28.6060 | 1.04039 | ||||||||
\(757\) | 35.6625 | 1.29617 | 0.648087 | − | 0.761566i | \(-0.275569\pi\) | ||||
0.648087 | + | 0.761566i | \(0.275569\pi\) | |||||||
\(758\) | −5.18809 | −0.188440 | ||||||||
\(759\) | 12.4656 | 0.452474 | ||||||||
\(760\) | −0.539425 | −0.0195670 | ||||||||
\(761\) | −19.2845 | −0.699061 | −0.349531 | − | 0.936925i | \(-0.613659\pi\) | ||||
−0.349531 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(762\) | −21.2145 | −0.768522 | ||||||||
\(763\) | 8.28901 | 0.300082 | ||||||||
\(764\) | −9.56666 | −0.346109 | ||||||||
\(765\) | 2.42685 | 0.0877428 | ||||||||
\(766\) | 32.9761 | 1.19147 | ||||||||
\(767\) | −24.0403 | −0.868045 | ||||||||
\(768\) | −1.39823 | −0.0504544 | ||||||||
\(769\) | 33.9307 | 1.22357 | 0.611787 | − | 0.791023i | \(-0.290451\pi\) | ||||
0.611787 | + | 0.791023i | \(0.290451\pi\) | |||||||
\(770\) | −3.07102 | −0.110672 | ||||||||
\(771\) | 3.06540 | 0.110398 | ||||||||
\(772\) | 19.2576 | 0.693097 | ||||||||
\(773\) | 7.83486 | 0.281801 | 0.140900 | − | 0.990024i | \(-0.455000\pi\) | ||||
0.140900 | + | 0.990024i | \(0.455000\pi\) | |||||||
\(774\) | −5.58844 | −0.200872 | ||||||||
\(775\) | 30.9031 | 1.11007 | ||||||||
\(776\) | 12.0690 | 0.433251 | ||||||||
\(777\) | −12.1312 | −0.435203 | ||||||||
\(778\) | 11.2758 | 0.404258 | ||||||||
\(779\) | −0.408032 | −0.0146193 | ||||||||
\(780\) | 2.02746 | 0.0725947 | ||||||||
\(781\) | −11.2406 | −0.402219 | ||||||||
\(782\) | −34.1010 | −1.21945 | ||||||||
\(783\) | −1.59327 | −0.0569388 | ||||||||
\(784\) | 18.5817 | 0.663633 | ||||||||
\(785\) | −3.54552 | −0.126545 | ||||||||
\(786\) | −24.8905 | −0.887814 | ||||||||
\(787\) | 22.4427 | 0.799994 | 0.399997 | − | 0.916516i | \(-0.369011\pi\) | ||||
0.399997 | + | 0.916516i | \(0.369011\pi\) | |||||||
\(788\) | 14.0935 | 0.502060 | ||||||||
\(789\) | −44.5250 | −1.58513 | ||||||||
\(790\) | 8.88069 | 0.315961 | ||||||||
\(791\) | −13.8522 | −0.492529 | ||||||||
\(792\) | 1.17619 | 0.0417942 | ||||||||
\(793\) | −35.2163 | −1.25057 | ||||||||
\(794\) | −15.9178 | −0.564902 | ||||||||
\(795\) | 2.70248 | 0.0958469 | ||||||||
\(796\) | 1.07616 | 0.0381436 | ||||||||
\(797\) | 23.3320 | 0.826461 | 0.413230 | − | 0.910627i | \(-0.364400\pi\) | ||||
0.413230 | + | 0.910627i | \(0.364400\pi\) | |||||||
\(798\) | 7.07204 | 0.250348 | ||||||||
\(799\) | 15.4537 | 0.546714 | ||||||||
\(800\) | −4.70902 | −0.166489 | ||||||||
\(801\) | 4.57580 | 0.161678 | ||||||||
\(802\) | 30.8843 | 1.09056 | ||||||||
\(803\) | 8.09044 | 0.285505 | ||||||||
\(804\) | −10.4867 | −0.369837 | ||||||||
\(805\) | 21.6095 | 0.761633 | ||||||||
\(806\) | 17.6406 | 0.621362 | ||||||||
\(807\) | −24.7366 | −0.870771 | ||||||||
\(808\) | 1.21217 | 0.0426441 | ||||||||
\(809\) | 15.6008 | 0.548496 | 0.274248 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274248 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(810\) | −2.57483 | −0.0904702 | ||||||||
\(811\) | −33.6213 | −1.18060 | −0.590301 | − | 0.807183i | \(-0.700991\pi\) | ||||
−0.590301 | + | 0.807183i | \(0.700991\pi\) | |||||||
\(812\) | −1.42483 | −0.0500016 | ||||||||
\(813\) | −12.2844 | −0.430832 | ||||||||
\(814\) | −1.93083 | −0.0676756 | ||||||||
\(815\) | 3.99132 | 0.139810 | ||||||||
\(816\) | 6.02003 | 0.210743 | ||||||||
\(817\) | −5.34809 | −0.187106 | ||||||||
\(818\) | 35.8549 | 1.25364 | ||||||||
\(819\) | 14.2068 | 0.496427 | ||||||||
\(820\) | 0.220103 | 0.00768633 | ||||||||
\(821\) | 44.3042 | 1.54623 | 0.773114 | − | 0.634268i | \(-0.218698\pi\) | ||||
0.773114 | + | 0.634268i | \(0.218698\pi\) | |||||||
\(822\) | 8.82907 | 0.307949 | ||||||||
\(823\) | 15.8968 | 0.554128 | 0.277064 | − | 0.960852i | \(-0.410639\pi\) | ||||
0.277064 | + | 0.960852i | \(0.410639\pi\) | |||||||
\(824\) | 17.1286 | 0.596701 | ||||||||
\(825\) | −7.41135 | −0.258030 | ||||||||
\(826\) | 45.2339 | 1.57389 | ||||||||
\(827\) | −50.4230 | −1.75338 | −0.876689 | − | 0.481057i | \(-0.840253\pi\) | ||||
−0.876689 | + | 0.481057i | \(0.840253\pi\) | |||||||
\(828\) | −8.27636 | −0.287623 | ||||||||
\(829\) | −14.0581 | −0.488258 | −0.244129 | − | 0.969743i | \(-0.578502\pi\) | ||||
−0.244129 | + | 0.969743i | \(0.578502\pi\) | |||||||
\(830\) | 3.77885 | 0.131166 | ||||||||
\(831\) | 29.8509 | 1.03552 | ||||||||
\(832\) | −2.68807 | −0.0931921 | ||||||||
\(833\) | −80.0028 | −2.77193 | ||||||||
\(834\) | 5.85533 | 0.202753 | ||||||||
\(835\) | −8.18183 | −0.283144 | ||||||||
\(836\) | 1.12561 | 0.0389299 | ||||||||
\(837\) | −37.1162 | −1.28292 | ||||||||
\(838\) | −25.3099 | −0.874315 | ||||||||
\(839\) | 38.3912 | 1.32541 | 0.662706 | − | 0.748880i | \(-0.269408\pi\) | ||||
0.662706 | + | 0.748880i | \(0.269408\pi\) | |||||||
\(840\) | −3.81484 | −0.131624 | ||||||||
\(841\) | −28.9206 | −0.997263 | ||||||||
\(842\) | 35.4253 | 1.22084 | ||||||||
\(843\) | −0.747155 | −0.0257334 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −3.11479 | −0.107152 | ||||||||
\(846\) | 3.75065 | 0.128950 | ||||||||
\(847\) | −49.2280 | −1.69149 | ||||||||
\(848\) | −3.58303 | −0.123042 | ||||||||
\(849\) | 16.7368 | 0.574407 | ||||||||
\(850\) | 20.2745 | 0.695409 | ||||||||
\(851\) | 13.5864 | 0.465737 | ||||||||
\(852\) | −13.9631 | −0.478367 | ||||||||
\(853\) | −42.4341 | −1.45292 | −0.726458 | − | 0.687211i | \(-0.758835\pi\) | ||||
−0.726458 | + | 0.687211i | \(0.758835\pi\) | |||||||
\(854\) | 66.2625 | 2.26746 | ||||||||
\(855\) | 0.563668 | 0.0192770 | ||||||||
\(856\) | 5.75691 | 0.196767 | ||||||||
\(857\) | 20.3091 | 0.693746 | 0.346873 | − | 0.937912i | \(-0.387244\pi\) | ||||
0.346873 | + | 0.937912i | \(0.387244\pi\) | |||||||
\(858\) | −4.23065 | −0.144432 | ||||||||
\(859\) | 10.8351 | 0.369690 | 0.184845 | − | 0.982768i | \(-0.440822\pi\) | ||||
0.184845 | + | 0.982768i | \(0.440822\pi\) | |||||||
\(860\) | 2.88489 | 0.0983741 | ||||||||
\(861\) | −2.88562 | −0.0983417 | ||||||||
\(862\) | 31.1751 | 1.06183 | ||||||||
\(863\) | 2.34439 | 0.0798040 | 0.0399020 | − | 0.999204i | \(-0.487295\pi\) | ||||
0.0399020 | + | 0.999204i | \(0.487295\pi\) | |||||||
\(864\) | 5.65578 | 0.192413 | ||||||||
\(865\) | −8.51005 | −0.289351 | ||||||||
\(866\) | −28.5507 | −0.970192 | ||||||||
\(867\) | −2.14899 | −0.0729835 | ||||||||
\(868\) | −33.1922 | −1.12662 | ||||||||
\(869\) | −18.5311 | −0.628626 | ||||||||
\(870\) | 0.212475 | 0.00720358 | ||||||||
\(871\) | −20.1604 | −0.683109 | ||||||||
\(872\) | 1.63885 | 0.0554983 | ||||||||
\(873\) | −12.6114 | −0.426830 | ||||||||
\(874\) | −7.92041 | −0.267912 | ||||||||
\(875\) | −26.4894 | −0.895504 | ||||||||
\(876\) | 10.0500 | 0.339558 | ||||||||
\(877\) | 8.53605 | 0.288242 | 0.144121 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144121 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(878\) | −25.6159 | −0.864496 | ||||||||
\(879\) | 23.6138 | 0.796474 | ||||||||
\(880\) | −0.607181 | −0.0204681 | ||||||||
\(881\) | 11.7352 | 0.395369 | 0.197685 | − | 0.980266i | \(-0.436658\pi\) | ||||
0.197685 | + | 0.980266i | \(0.436658\pi\) | |||||||
\(882\) | −19.4168 | −0.653798 | ||||||||
\(883\) | −37.5958 | −1.26520 | −0.632600 | − | 0.774479i | \(-0.718012\pi\) | ||||
−0.632600 | + | 0.774479i | \(0.718012\pi\) | |||||||
\(884\) | 11.5734 | 0.389254 | ||||||||
\(885\) | −6.74544 | −0.226746 | ||||||||
\(886\) | 16.4574 | 0.552897 | ||||||||
\(887\) | −41.5645 | −1.39560 | −0.697800 | − | 0.716292i | \(-0.745838\pi\) | ||||
−0.697800 | + | 0.716292i | \(0.745838\pi\) | |||||||
\(888\) | −2.39849 | −0.0804880 | ||||||||
\(889\) | 76.7394 | 2.57376 | ||||||||
\(890\) | −2.36214 | −0.0791792 | ||||||||
\(891\) | 5.37283 | 0.179997 | ||||||||
\(892\) | 9.95413 | 0.333289 | ||||||||
\(893\) | 3.58934 | 0.120113 | ||||||||
\(894\) | 18.2131 | 0.609139 | ||||||||
\(895\) | 0.488618 | 0.0163327 | ||||||||
\(896\) | 5.05784 | 0.168971 | ||||||||
\(897\) | 29.7693 | 0.993967 | ||||||||
\(898\) | −6.37899 | −0.212870 | ||||||||
\(899\) | 1.84871 | 0.0616579 | ||||||||
\(900\) | 4.92065 | 0.164022 | ||||||||
\(901\) | 15.4266 | 0.513934 | ||||||||
\(902\) | −0.459284 | −0.0152925 | ||||||||
\(903\) | −37.8219 | −1.25863 | ||||||||
\(904\) | −2.73876 | −0.0910900 | ||||||||
\(905\) | −9.06455 | −0.301316 | ||||||||
\(906\) | 0.876307 | 0.0291133 | ||||||||
\(907\) | −21.7421 | −0.721934 | −0.360967 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360967 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(908\) | 25.9588 | 0.861474 | ||||||||
\(909\) | −1.26665 | −0.0420121 | ||||||||
\(910\) | −7.33393 | −0.243118 | ||||||||
\(911\) | −39.8011 | −1.31867 | −0.659335 | − | 0.751849i | \(-0.729162\pi\) | ||||
−0.659335 | + | 0.751849i | \(0.729162\pi\) | |||||||
\(912\) | 1.39823 | 0.0463002 | ||||||||
\(913\) | −7.88523 | −0.260963 | ||||||||
\(914\) | −17.7167 | −0.586015 | ||||||||
\(915\) | −9.88131 | −0.326666 | ||||||||
\(916\) | −4.86224 | −0.160653 | ||||||||
\(917\) | 90.0364 | 2.97326 | ||||||||
\(918\) | −24.3507 | −0.803692 | ||||||||
\(919\) | 36.8996 | 1.21721 | 0.608603 | − | 0.793475i | \(-0.291730\pi\) | ||||
0.608603 | + | 0.793475i | \(0.291730\pi\) | |||||||
\(920\) | 4.27247 | 0.140859 | ||||||||
\(921\) | 27.8019 | 0.916104 | ||||||||
\(922\) | −11.1057 | −0.365745 | ||||||||
\(923\) | −26.8437 | −0.883570 | ||||||||
\(924\) | 7.96034 | 0.261876 | ||||||||
\(925\) | −8.07771 | −0.265594 | ||||||||
\(926\) | −20.2349 | −0.664961 | ||||||||
\(927\) | −17.8983 | −0.587858 | ||||||||
\(928\) | −0.281706 | −0.00924747 | ||||||||
\(929\) | −15.8960 | −0.521532 | −0.260766 | − | 0.965402i | \(-0.583975\pi\) | ||||
−0.260766 | + | 0.965402i | \(0.583975\pi\) | |||||||
\(930\) | 4.94975 | 0.162309 | ||||||||
\(931\) | −18.5817 | −0.608991 | ||||||||
\(932\) | 3.48455 | 0.114140 | ||||||||
\(933\) | −12.1670 | −0.398330 | ||||||||
\(934\) | −33.9185 | −1.10985 | ||||||||
\(935\) | 2.61419 | 0.0854931 | ||||||||
\(936\) | 2.80888 | 0.0918110 | ||||||||
\(937\) | 22.0247 | 0.719515 | 0.359758 | − | 0.933046i | \(-0.382859\pi\) | ||||
0.359758 | + | 0.933046i | \(0.382859\pi\) | |||||||
\(938\) | 37.9335 | 1.23857 | ||||||||
\(939\) | 32.5567 | 1.06245 | ||||||||
\(940\) | −1.93618 | −0.0631513 | ||||||||
\(941\) | 14.5777 | 0.475220 | 0.237610 | − | 0.971361i | \(-0.423636\pi\) | ||||
0.237610 | + | 0.971361i | \(0.423636\pi\) | |||||||
\(942\) | 9.19027 | 0.299435 | ||||||||
\(943\) | 3.23178 | 0.105241 | ||||||||
\(944\) | 8.94333 | 0.291081 | ||||||||
\(945\) | 15.4308 | 0.501964 | ||||||||
\(946\) | −6.01984 | −0.195722 | ||||||||
\(947\) | −18.5352 | −0.602314 | −0.301157 | − | 0.953575i | \(-0.597373\pi\) | ||||
−0.301157 | + | 0.953575i | \(0.597373\pi\) | |||||||
\(948\) | −23.0195 | −0.747637 | ||||||||
\(949\) | 19.3208 | 0.627181 | ||||||||
\(950\) | 4.70902 | 0.152781 | ||||||||
\(951\) | 1.51360 | 0.0490818 | ||||||||
\(952\) | −21.7763 | −0.705774 | ||||||||
\(953\) | −45.5710 | −1.47619 | −0.738094 | − | 0.674698i | \(-0.764274\pi\) | ||||
−0.738094 | + | 0.674698i | \(0.764274\pi\) | |||||||
\(954\) | 3.74406 | 0.121218 | ||||||||
\(955\) | −5.16050 | −0.166990 | ||||||||
\(956\) | −23.5249 | −0.760848 | ||||||||
\(957\) | −0.443367 | −0.0143320 | ||||||||
\(958\) | 15.7058 | 0.507430 | ||||||||
\(959\) | −31.9374 | −1.03131 | ||||||||
\(960\) | −0.754243 | −0.0243431 | ||||||||
\(961\) | 12.0669 | 0.389254 | ||||||||
\(962\) | −4.61104 | −0.148666 | ||||||||
\(963\) | −6.01563 | −0.193851 | ||||||||
\(964\) | 14.2840 | 0.460058 | ||||||||
\(965\) | 10.3881 | 0.334403 | ||||||||
\(966\) | −56.0135 | −1.80220 | ||||||||
\(967\) | −5.76318 | −0.185331 | −0.0926657 | − | 0.995697i | \(-0.529539\pi\) | ||||
−0.0926657 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(968\) | −9.73301 | −0.312831 | ||||||||
\(969\) | −6.02003 | −0.193391 | ||||||||
\(970\) | 6.51031 | 0.209033 | ||||||||
\(971\) | −5.30424 | −0.170221 | −0.0851106 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851106 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(972\) | −10.2932 | −0.330154 | ||||||||
\(973\) | −21.1805 | −0.679016 | ||||||||
\(974\) | −17.2930 | −0.554102 | ||||||||
\(975\) | −17.6991 | −0.566825 | ||||||||
\(976\) | 13.1010 | 0.419352 | ||||||||
\(977\) | −61.5062 | −1.96776 | −0.983879 | − | 0.178834i | \(-0.942768\pi\) | ||||
−0.983879 | + | 0.178834i | \(0.942768\pi\) | |||||||
\(978\) | −10.3458 | −0.330823 | ||||||||
\(979\) | 4.92903 | 0.157532 | ||||||||
\(980\) | 10.0235 | 0.320188 | ||||||||
\(981\) | −1.71250 | −0.0546758 | ||||||||
\(982\) | 25.0354 | 0.798913 | ||||||||
\(983\) | −9.58788 | −0.305806 | −0.152903 | − | 0.988241i | \(-0.548862\pi\) | ||||
−0.152903 | + | 0.988241i | \(0.548862\pi\) | |||||||
\(984\) | −0.570524 | −0.0181877 | ||||||||
\(985\) | 7.60239 | 0.242232 | ||||||||
\(986\) | 1.21287 | 0.0386258 | ||||||||
\(987\) | 25.3840 | 0.807981 | ||||||||
\(988\) | 2.68807 | 0.0855189 | ||||||||
\(989\) | 42.3590 | 1.34694 | ||||||||
\(990\) | 0.634468 | 0.0201647 | ||||||||
\(991\) | 11.9546 | 0.379752 | 0.189876 | − | 0.981808i | \(-0.439191\pi\) | ||||
0.189876 | + | 0.981808i | \(0.439191\pi\) | |||||||
\(992\) | −6.56253 | −0.208361 | ||||||||
\(993\) | −41.2139 | −1.30788 | ||||||||
\(994\) | 50.5087 | 1.60204 | ||||||||
\(995\) | 0.580510 | 0.0184034 | ||||||||
\(996\) | −9.79507 | −0.310369 | ||||||||
\(997\) | −36.0288 | −1.14104 | −0.570522 | − | 0.821283i | \(-0.693259\pi\) | ||||
−0.570522 | + | 0.821283i | \(0.693259\pi\) | |||||||
\(998\) | 32.2250 | 1.02007 | ||||||||
\(999\) | 9.70175 | 0.306950 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.j.1.14 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.14 | ✓ | 47 | 1.1 | even | 1 | trivial |