Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + 5490 x^{8} - 2787 x^{7} - 10540 x^{6} + 1919 x^{5} + 10822 x^{4} + 132 x^{3} + \cdots + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.25035\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 | ||||||||
\(3\) | −1.25035 | −0.721892 | −0.360946 | − | 0.932587i | \(-0.617546\pi\) | ||||
−0.360946 | + | 0.932587i | \(0.617546\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.07514 | −1.37524 | −0.687622 | − | 0.726069i | \(-0.741345\pi\) | ||||
−0.687622 | + | 0.726069i | \(0.741345\pi\) | |||||||
\(6\) | −1.25035 | −0.510455 | ||||||||
\(7\) | −0.487959 | −0.184431 | −0.0922157 | − | 0.995739i | \(-0.529395\pi\) | ||||
−0.0922157 | + | 0.995739i | \(0.529395\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.43661 | −0.478872 | ||||||||
\(10\) | −3.07514 | −0.972444 | ||||||||
\(11\) | −4.26766 | −1.28675 | −0.643374 | − | 0.765552i | \(-0.722466\pi\) | ||||
−0.643374 | + | 0.765552i | \(0.722466\pi\) | |||||||
\(12\) | −1.25035 | −0.360946 | ||||||||
\(13\) | −2.00084 | −0.554932 | −0.277466 | − | 0.960735i | \(-0.589495\pi\) | ||||
−0.277466 | + | 0.960735i | \(0.589495\pi\) | |||||||
\(14\) | −0.487959 | −0.130413 | ||||||||
\(15\) | 3.84501 | 0.992778 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.08581 | 0.990955 | 0.495478 | − | 0.868621i | \(-0.334993\pi\) | ||||
0.495478 | + | 0.868621i | \(0.334993\pi\) | |||||||
\(18\) | −1.43661 | −0.338613 | ||||||||
\(19\) | 8.04310 | 1.84521 | 0.922607 | − | 0.385741i | \(-0.126054\pi\) | ||||
0.922607 | + | 0.385741i | \(0.126054\pi\) | |||||||
\(20\) | −3.07514 | −0.687622 | ||||||||
\(21\) | 0.610122 | 0.133140 | ||||||||
\(22\) | −4.26766 | −0.909868 | ||||||||
\(23\) | −0.0257712 | −0.00537366 | −0.00268683 | − | 0.999996i | \(-0.500855\pi\) | ||||
−0.00268683 | + | 0.999996i | \(0.500855\pi\) | |||||||
\(24\) | −1.25035 | −0.255227 | ||||||||
\(25\) | 4.45648 | 0.891296 | ||||||||
\(26\) | −2.00084 | −0.392396 | ||||||||
\(27\) | 5.54734 | 1.06759 | ||||||||
\(28\) | −0.487959 | −0.0922157 | ||||||||
\(29\) | 9.96727 | 1.85088 | 0.925438 | − | 0.378900i | \(-0.123698\pi\) | ||||
0.925438 | + | 0.378900i | \(0.123698\pi\) | |||||||
\(30\) | 3.84501 | 0.702000 | ||||||||
\(31\) | 0.393455 | 0.0706666 | 0.0353333 | − | 0.999376i | \(-0.488751\pi\) | ||||
0.0353333 | + | 0.999376i | \(0.488751\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.33608 | 0.928893 | ||||||||
\(34\) | 4.08581 | 0.700711 | ||||||||
\(35\) | 1.50054 | 0.253638 | ||||||||
\(36\) | −1.43661 | −0.239436 | ||||||||
\(37\) | 10.0185 | 1.64703 | 0.823514 | − | 0.567297i | \(-0.192011\pi\) | ||||
0.823514 | + | 0.567297i | \(0.192011\pi\) | |||||||
\(38\) | 8.04310 | 1.30476 | ||||||||
\(39\) | 2.50175 | 0.400601 | ||||||||
\(40\) | −3.07514 | −0.486222 | ||||||||
\(41\) | −4.52723 | −0.707034 | −0.353517 | − | 0.935428i | \(-0.615014\pi\) | ||||
−0.353517 | + | 0.935428i | \(0.615014\pi\) | |||||||
\(42\) | 0.610122 | 0.0941439 | ||||||||
\(43\) | −4.16008 | −0.634406 | −0.317203 | − | 0.948358i | \(-0.602744\pi\) | ||||
−0.317203 | + | 0.948358i | \(0.602744\pi\) | |||||||
\(44\) | −4.26766 | −0.643374 | ||||||||
\(45\) | 4.41779 | 0.658565 | ||||||||
\(46\) | −0.0257712 | −0.00379975 | ||||||||
\(47\) | −0.996759 | −0.145392 | −0.0726961 | − | 0.997354i | \(-0.523160\pi\) | ||||
−0.0726961 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(48\) | −1.25035 | −0.180473 | ||||||||
\(49\) | −6.76190 | −0.965985 | ||||||||
\(50\) | 4.45648 | 0.630242 | ||||||||
\(51\) | −5.10871 | −0.715363 | ||||||||
\(52\) | −2.00084 | −0.277466 | ||||||||
\(53\) | −5.88337 | −0.808142 | −0.404071 | − | 0.914728i | \(-0.632405\pi\) | ||||
−0.404071 | + | 0.914728i | \(0.632405\pi\) | |||||||
\(54\) | 5.54734 | 0.754897 | ||||||||
\(55\) | 13.1236 | 1.76959 | ||||||||
\(56\) | −0.487959 | −0.0652063 | ||||||||
\(57\) | −10.0567 | −1.33205 | ||||||||
\(58\) | 9.96727 | 1.30877 | ||||||||
\(59\) | 6.63589 | 0.863919 | 0.431960 | − | 0.901893i | \(-0.357822\pi\) | ||||
0.431960 | + | 0.901893i | \(0.357822\pi\) | |||||||
\(60\) | 3.84501 | 0.496389 | ||||||||
\(61\) | −4.39227 | −0.562373 | −0.281186 | − | 0.959653i | \(-0.590728\pi\) | ||||
−0.281186 | + | 0.959653i | \(0.590728\pi\) | |||||||
\(62\) | 0.393455 | 0.0499688 | ||||||||
\(63\) | 0.701010 | 0.0883189 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.15285 | 0.763167 | ||||||||
\(66\) | 5.33608 | 0.656826 | ||||||||
\(67\) | 11.7016 | 1.42958 | 0.714791 | − | 0.699338i | \(-0.246522\pi\) | ||||
0.714791 | + | 0.699338i | \(0.246522\pi\) | |||||||
\(68\) | 4.08581 | 0.495478 | ||||||||
\(69\) | 0.0322231 | 0.00387920 | ||||||||
\(70\) | 1.50054 | 0.179349 | ||||||||
\(71\) | −0.816623 | −0.0969153 | −0.0484577 | − | 0.998825i | \(-0.515431\pi\) | ||||
−0.0484577 | + | 0.998825i | \(0.515431\pi\) | |||||||
\(72\) | −1.43661 | −0.169307 | ||||||||
\(73\) | 1.75200 | 0.205056 | 0.102528 | − | 0.994730i | \(-0.467307\pi\) | ||||
0.102528 | + | 0.994730i | \(0.467307\pi\) | |||||||
\(74\) | 10.0185 | 1.16462 | ||||||||
\(75\) | −5.57218 | −0.643420 | ||||||||
\(76\) | 8.04310 | 0.922607 | ||||||||
\(77\) | 2.08244 | 0.237316 | ||||||||
\(78\) | 2.50175 | 0.283268 | ||||||||
\(79\) | 1.76038 | 0.198058 | 0.0990292 | − | 0.995085i | \(-0.468426\pi\) | ||||
0.0990292 | + | 0.995085i | \(0.468426\pi\) | |||||||
\(80\) | −3.07514 | −0.343811 | ||||||||
\(81\) | −2.62629 | −0.291810 | ||||||||
\(82\) | −4.52723 | −0.499949 | ||||||||
\(83\) | −17.9525 | −1.97054 | −0.985272 | − | 0.170993i | \(-0.945303\pi\) | ||||
−0.985272 | + | 0.170993i | \(0.945303\pi\) | |||||||
\(84\) | 0.610122 | 0.0665698 | ||||||||
\(85\) | −12.5644 | −1.36281 | ||||||||
\(86\) | −4.16008 | −0.448593 | ||||||||
\(87\) | −12.4626 | −1.33613 | ||||||||
\(88\) | −4.26766 | −0.454934 | ||||||||
\(89\) | 5.54121 | 0.587368 | 0.293684 | − | 0.955903i | \(-0.405119\pi\) | ||||
0.293684 | + | 0.955903i | \(0.405119\pi\) | |||||||
\(90\) | 4.41779 | 0.465676 | ||||||||
\(91\) | 0.976327 | 0.102347 | ||||||||
\(92\) | −0.0257712 | −0.00268683 | ||||||||
\(93\) | −0.491958 | −0.0510137 | ||||||||
\(94\) | −0.996759 | −0.102808 | ||||||||
\(95\) | −24.7337 | −2.53762 | ||||||||
\(96\) | −1.25035 | −0.127614 | ||||||||
\(97\) | 10.5413 | 1.07031 | 0.535155 | − | 0.844754i | \(-0.320253\pi\) | ||||
0.535155 | + | 0.844754i | \(0.320253\pi\) | |||||||
\(98\) | −6.76190 | −0.683055 | ||||||||
\(99\) | 6.13098 | 0.616187 | ||||||||
\(100\) | 4.45648 | 0.445648 | ||||||||
\(101\) | 6.67517 | 0.664204 | 0.332102 | − | 0.943243i | \(-0.392242\pi\) | ||||
0.332102 | + | 0.943243i | \(0.392242\pi\) | |||||||
\(102\) | −5.10871 | −0.505838 | ||||||||
\(103\) | 11.9804 | 1.18047 | 0.590233 | − | 0.807233i | \(-0.299036\pi\) | ||||
0.590233 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(104\) | −2.00084 | −0.196198 | ||||||||
\(105\) | −1.87621 | −0.183099 | ||||||||
\(106\) | −5.88337 | −0.571443 | ||||||||
\(107\) | 7.35926 | 0.711447 | 0.355723 | − | 0.934591i | \(-0.384235\pi\) | ||||
0.355723 | + | 0.934591i | \(0.384235\pi\) | |||||||
\(108\) | 5.54734 | 0.533793 | ||||||||
\(109\) | 7.21073 | 0.690663 | 0.345332 | − | 0.938481i | \(-0.387766\pi\) | ||||
0.345332 | + | 0.938481i | \(0.387766\pi\) | |||||||
\(110\) | 13.1236 | 1.25129 | ||||||||
\(111\) | −12.5266 | −1.18898 | ||||||||
\(112\) | −0.487959 | −0.0461078 | ||||||||
\(113\) | −1.34213 | −0.126257 | −0.0631287 | − | 0.998005i | \(-0.520108\pi\) | ||||
−0.0631287 | + | 0.998005i | \(0.520108\pi\) | |||||||
\(114\) | −10.0567 | −0.941899 | ||||||||
\(115\) | 0.0792499 | 0.00739009 | ||||||||
\(116\) | 9.96727 | 0.925438 | ||||||||
\(117\) | 2.87443 | 0.265741 | ||||||||
\(118\) | 6.63589 | 0.610883 | ||||||||
\(119\) | −1.99371 | −0.182763 | ||||||||
\(120\) | 3.84501 | 0.351000 | ||||||||
\(121\) | 7.21290 | 0.655718 | ||||||||
\(122\) | −4.39227 | −0.397657 | ||||||||
\(123\) | 5.66064 | 0.510403 | ||||||||
\(124\) | 0.393455 | 0.0353333 | ||||||||
\(125\) | 1.67140 | 0.149494 | ||||||||
\(126\) | 0.701010 | 0.0624509 | ||||||||
\(127\) | −10.3758 | −0.920702 | −0.460351 | − | 0.887737i | \(-0.652276\pi\) | ||||
−0.460351 | + | 0.887737i | \(0.652276\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.20157 | 0.457973 | ||||||||
\(130\) | 6.15285 | 0.539641 | ||||||||
\(131\) | 2.44482 | 0.213605 | 0.106803 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106803 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(132\) | 5.33608 | 0.464446 | ||||||||
\(133\) | −3.92471 | −0.340315 | ||||||||
\(134\) | 11.7016 | 1.01087 | ||||||||
\(135\) | −17.0588 | −1.46819 | ||||||||
\(136\) | 4.08581 | 0.350356 | ||||||||
\(137\) | 6.38733 | 0.545707 | 0.272853 | − | 0.962056i | \(-0.412033\pi\) | ||||
0.272853 | + | 0.962056i | \(0.412033\pi\) | |||||||
\(138\) | 0.0322231 | 0.00274301 | ||||||||
\(139\) | 13.8060 | 1.17101 | 0.585504 | − | 0.810670i | \(-0.300897\pi\) | ||||
0.585504 | + | 0.810670i | \(0.300897\pi\) | |||||||
\(140\) | 1.50054 | 0.126819 | ||||||||
\(141\) | 1.24630 | 0.104958 | ||||||||
\(142\) | −0.816623 | −0.0685295 | ||||||||
\(143\) | 8.53889 | 0.714058 | ||||||||
\(144\) | −1.43661 | −0.119718 | ||||||||
\(145\) | −30.6507 | −2.54541 | ||||||||
\(146\) | 1.75200 | 0.144996 | ||||||||
\(147\) | 8.45476 | 0.697337 | ||||||||
\(148\) | 10.0185 | 0.823514 | ||||||||
\(149\) | −12.3706 | −1.01344 | −0.506720 | − | 0.862111i | \(-0.669142\pi\) | ||||
−0.506720 | + | 0.862111i | \(0.669142\pi\) | |||||||
\(150\) | −5.57218 | −0.454966 | ||||||||
\(151\) | 6.20066 | 0.504603 | 0.252301 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252301 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(152\) | 8.04310 | 0.652382 | ||||||||
\(153\) | −5.86974 | −0.474540 | ||||||||
\(154\) | 2.08244 | 0.167808 | ||||||||
\(155\) | −1.20993 | −0.0971838 | ||||||||
\(156\) | 2.50175 | 0.200301 | ||||||||
\(157\) | 0.364004 | 0.0290507 | 0.0145253 | − | 0.999895i | \(-0.495376\pi\) | ||||
0.0145253 | + | 0.999895i | \(0.495376\pi\) | |||||||
\(158\) | 1.76038 | 0.140048 | ||||||||
\(159\) | 7.35629 | 0.583392 | ||||||||
\(160\) | −3.07514 | −0.243111 | ||||||||
\(161\) | 0.0125753 | 0.000991070 0 | ||||||||
\(162\) | −2.62629 | −0.206341 | ||||||||
\(163\) | 20.4860 | 1.60459 | 0.802294 | − | 0.596930i | \(-0.203613\pi\) | ||||
0.802294 | + | 0.596930i | \(0.203613\pi\) | |||||||
\(164\) | −4.52723 | −0.353517 | ||||||||
\(165\) | −16.4092 | −1.27745 | ||||||||
\(166\) | −17.9525 | −1.39339 | ||||||||
\(167\) | 11.4706 | 0.887618 | 0.443809 | − | 0.896121i | \(-0.353627\pi\) | ||||
0.443809 | + | 0.896121i | \(0.353627\pi\) | |||||||
\(168\) | 0.610122 | 0.0470719 | ||||||||
\(169\) | −8.99665 | −0.692050 | ||||||||
\(170\) | −12.5644 | −0.963649 | ||||||||
\(171\) | −11.5548 | −0.883621 | ||||||||
\(172\) | −4.16008 | −0.317203 | ||||||||
\(173\) | −9.37883 | −0.713059 | −0.356530 | − | 0.934284i | \(-0.616040\pi\) | ||||
−0.356530 | + | 0.934284i | \(0.616040\pi\) | |||||||
\(174\) | −12.4626 | −0.944788 | ||||||||
\(175\) | −2.17458 | −0.164383 | ||||||||
\(176\) | −4.26766 | −0.321687 | ||||||||
\(177\) | −8.29721 | −0.623657 | ||||||||
\(178\) | 5.54121 | 0.415332 | ||||||||
\(179\) | −11.3854 | −0.850982 | −0.425491 | − | 0.904963i | \(-0.639899\pi\) | ||||
−0.425491 | + | 0.904963i | \(0.639899\pi\) | |||||||
\(180\) | 4.41779 | 0.329283 | ||||||||
\(181\) | 16.9420 | 1.25929 | 0.629644 | − | 0.776883i | \(-0.283201\pi\) | ||||
0.629644 | + | 0.776883i | \(0.283201\pi\) | |||||||
\(182\) | 0.976327 | 0.0723702 | ||||||||
\(183\) | 5.49189 | 0.405972 | ||||||||
\(184\) | −0.0257712 | −0.00189987 | ||||||||
\(185\) | −30.8082 | −2.26506 | ||||||||
\(186\) | −0.491958 | −0.0360721 | ||||||||
\(187\) | −17.4369 | −1.27511 | ||||||||
\(188\) | −0.996759 | −0.0726961 | ||||||||
\(189\) | −2.70688 | −0.196896 | ||||||||
\(190\) | −24.7337 | −1.79437 | ||||||||
\(191\) | 3.61845 | 0.261822 | 0.130911 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130911 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(192\) | −1.25035 | −0.0902365 | ||||||||
\(193\) | −13.7420 | −0.989172 | −0.494586 | − | 0.869129i | \(-0.664680\pi\) | ||||
−0.494586 | + | 0.869129i | \(0.664680\pi\) | |||||||
\(194\) | 10.5413 | 0.756823 | ||||||||
\(195\) | −7.69324 | −0.550925 | ||||||||
\(196\) | −6.76190 | −0.482993 | ||||||||
\(197\) | −5.57990 | −0.397551 | −0.198776 | − | 0.980045i | \(-0.563697\pi\) | ||||
−0.198776 | + | 0.980045i | \(0.563697\pi\) | |||||||
\(198\) | 6.13098 | 0.435710 | ||||||||
\(199\) | 22.2676 | 1.57850 | 0.789252 | − | 0.614069i | \(-0.210468\pi\) | ||||
0.789252 | + | 0.614069i | \(0.210468\pi\) | |||||||
\(200\) | 4.45648 | 0.315121 | ||||||||
\(201\) | −14.6312 | −1.03200 | ||||||||
\(202\) | 6.67517 | 0.469663 | ||||||||
\(203\) | −4.86362 | −0.341359 | ||||||||
\(204\) | −5.10871 | −0.357682 | ||||||||
\(205\) | 13.9219 | 0.972345 | ||||||||
\(206\) | 11.9804 | 0.834716 | ||||||||
\(207\) | 0.0370232 | 0.00257329 | ||||||||
\(208\) | −2.00084 | −0.138733 | ||||||||
\(209\) | −34.3252 | −2.37432 | ||||||||
\(210\) | −1.87621 | −0.129471 | ||||||||
\(211\) | −21.3358 | −1.46882 | −0.734409 | − | 0.678707i | \(-0.762541\pi\) | ||||
−0.734409 | + | 0.678707i | \(0.762541\pi\) | |||||||
\(212\) | −5.88337 | −0.404071 | ||||||||
\(213\) | 1.02107 | 0.0699624 | ||||||||
\(214\) | 7.35926 | 0.503069 | ||||||||
\(215\) | 12.7928 | 0.872464 | ||||||||
\(216\) | 5.54734 | 0.377449 | ||||||||
\(217\) | −0.191990 | −0.0130331 | ||||||||
\(218\) | 7.21073 | 0.488373 | ||||||||
\(219\) | −2.19062 | −0.148028 | ||||||||
\(220\) | 13.1236 | 0.884796 | ||||||||
\(221\) | −8.17505 | −0.549913 | ||||||||
\(222\) | −12.5266 | −0.840733 | ||||||||
\(223\) | 15.2924 | 1.02405 | 0.512026 | − | 0.858970i | \(-0.328895\pi\) | ||||
0.512026 | + | 0.858970i | \(0.328895\pi\) | |||||||
\(224\) | −0.487959 | −0.0326032 | ||||||||
\(225\) | −6.40225 | −0.426816 | ||||||||
\(226\) | −1.34213 | −0.0892775 | ||||||||
\(227\) | 6.22212 | 0.412976 | 0.206488 | − | 0.978449i | \(-0.433796\pi\) | ||||
0.206488 | + | 0.978449i | \(0.433796\pi\) | |||||||
\(228\) | −10.0567 | −0.666023 | ||||||||
\(229\) | −1.20776 | −0.0798113 | −0.0399056 | − | 0.999203i | \(-0.512706\pi\) | ||||
−0.0399056 | + | 0.999203i | \(0.512706\pi\) | |||||||
\(230\) | 0.0792499 | 0.00522558 | ||||||||
\(231\) | −2.60379 | −0.171317 | ||||||||
\(232\) | 9.96727 | 0.654383 | ||||||||
\(233\) | −25.1341 | −1.64659 | −0.823294 | − | 0.567616i | \(-0.807866\pi\) | ||||
−0.823294 | + | 0.567616i | \(0.807866\pi\) | |||||||
\(234\) | 2.87443 | 0.187907 | ||||||||
\(235\) | 3.06517 | 0.199950 | ||||||||
\(236\) | 6.63589 | 0.431960 | ||||||||
\(237\) | −2.20110 | −0.142977 | ||||||||
\(238\) | −1.99371 | −0.129233 | ||||||||
\(239\) | −23.6571 | −1.53025 | −0.765125 | − | 0.643882i | \(-0.777323\pi\) | ||||
−0.765125 | + | 0.643882i | \(0.777323\pi\) | |||||||
\(240\) | 3.84501 | 0.248194 | ||||||||
\(241\) | −15.1358 | −0.974982 | −0.487491 | − | 0.873128i | \(-0.662088\pi\) | ||||
−0.487491 | + | 0.873128i | \(0.662088\pi\) | |||||||
\(242\) | 7.21290 | 0.463663 | ||||||||
\(243\) | −13.3582 | −0.856930 | ||||||||
\(244\) | −4.39227 | −0.281186 | ||||||||
\(245\) | 20.7938 | 1.32847 | ||||||||
\(246\) | 5.66064 | 0.360909 | ||||||||
\(247\) | −16.0929 | −1.02397 | ||||||||
\(248\) | 0.393455 | 0.0249844 | ||||||||
\(249\) | 22.4470 | 1.42252 | ||||||||
\(250\) | 1.67140 | 0.105709 | ||||||||
\(251\) | 23.0807 | 1.45684 | 0.728419 | − | 0.685132i | \(-0.240256\pi\) | ||||
0.728419 | + | 0.685132i | \(0.240256\pi\) | |||||||
\(252\) | 0.701010 | 0.0441595 | ||||||||
\(253\) | 0.109982 | 0.00691454 | ||||||||
\(254\) | −10.3758 | −0.651035 | ||||||||
\(255\) | 15.7100 | 0.983799 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.54349 | −0.345793 | −0.172897 | − | 0.984940i | \(-0.555313\pi\) | ||||
−0.172897 | + | 0.984940i | \(0.555313\pi\) | |||||||
\(258\) | 5.20157 | 0.323836 | ||||||||
\(259\) | −4.88861 | −0.303763 | ||||||||
\(260\) | 6.15285 | 0.381584 | ||||||||
\(261\) | −14.3191 | −0.886332 | ||||||||
\(262\) | 2.44482 | 0.151042 | ||||||||
\(263\) | 16.2519 | 1.00214 | 0.501068 | − | 0.865408i | \(-0.332941\pi\) | ||||
0.501068 | + | 0.865408i | \(0.332941\pi\) | |||||||
\(264\) | 5.33608 | 0.328413 | ||||||||
\(265\) | 18.0922 | 1.11139 | ||||||||
\(266\) | −3.92471 | −0.240639 | ||||||||
\(267\) | −6.92848 | −0.424016 | ||||||||
\(268\) | 11.7016 | 0.714791 | ||||||||
\(269\) | 13.0504 | 0.795695 | 0.397848 | − | 0.917452i | \(-0.369757\pi\) | ||||
0.397848 | + | 0.917452i | \(0.369757\pi\) | |||||||
\(270\) | −17.0588 | −1.03817 | ||||||||
\(271\) | −8.91362 | −0.541464 | −0.270732 | − | 0.962655i | \(-0.587266\pi\) | ||||
−0.270732 | + | 0.962655i | \(0.587266\pi\) | |||||||
\(272\) | 4.08581 | 0.247739 | ||||||||
\(273\) | −1.22075 | −0.0738834 | ||||||||
\(274\) | 6.38733 | 0.385873 | ||||||||
\(275\) | −19.0187 | −1.14687 | ||||||||
\(276\) | 0.0322231 | 0.00193960 | ||||||||
\(277\) | 31.3497 | 1.88362 | 0.941811 | − | 0.336142i | \(-0.109122\pi\) | ||||
0.941811 | + | 0.336142i | \(0.109122\pi\) | |||||||
\(278\) | 13.8060 | 0.828028 | ||||||||
\(279\) | −0.565243 | −0.0338402 | ||||||||
\(280\) | 1.50054 | 0.0896746 | ||||||||
\(281\) | −11.2573 | −0.671554 | −0.335777 | − | 0.941942i | \(-0.608999\pi\) | ||||
−0.335777 | + | 0.941942i | \(0.608999\pi\) | |||||||
\(282\) | 1.24630 | 0.0742162 | ||||||||
\(283\) | 18.9390 | 1.12580 | 0.562902 | − | 0.826523i | \(-0.309685\pi\) | ||||
0.562902 | + | 0.826523i | \(0.309685\pi\) | |||||||
\(284\) | −0.816623 | −0.0484577 | ||||||||
\(285\) | 30.9258 | 1.83189 | ||||||||
\(286\) | 8.53889 | 0.504915 | ||||||||
\(287\) | 2.20910 | 0.130399 | ||||||||
\(288\) | −1.43661 | −0.0846533 | ||||||||
\(289\) | −0.306124 | −0.0180073 | ||||||||
\(290\) | −30.6507 | −1.79987 | ||||||||
\(291\) | −13.1804 | −0.772648 | ||||||||
\(292\) | 1.75200 | 0.102528 | ||||||||
\(293\) | 22.0162 | 1.28620 | 0.643099 | − | 0.765783i | \(-0.277648\pi\) | ||||
0.643099 | + | 0.765783i | \(0.277648\pi\) | |||||||
\(294\) | 8.45476 | 0.493092 | ||||||||
\(295\) | −20.4063 | −1.18810 | ||||||||
\(296\) | 10.0185 | 0.582312 | ||||||||
\(297\) | −23.6741 | −1.37371 | ||||||||
\(298\) | −12.3706 | −0.716610 | ||||||||
\(299\) | 0.0515639 | 0.00298202 | ||||||||
\(300\) | −5.57218 | −0.321710 | ||||||||
\(301\) | 2.02995 | 0.117004 | ||||||||
\(302\) | 6.20066 | 0.356808 | ||||||||
\(303\) | −8.34633 | −0.479484 | ||||||||
\(304\) | 8.04310 | 0.461304 | ||||||||
\(305\) | 13.5068 | 0.773400 | ||||||||
\(306\) | −5.86974 | −0.335551 | ||||||||
\(307\) | 27.0103 | 1.54156 | 0.770779 | − | 0.637103i | \(-0.219867\pi\) | ||||
0.770779 | + | 0.637103i | \(0.219867\pi\) | |||||||
\(308\) | 2.08244 | 0.118658 | ||||||||
\(309\) | −14.9798 | −0.852170 | ||||||||
\(310\) | −1.20993 | −0.0687193 | ||||||||
\(311\) | 19.1623 | 1.08659 | 0.543296 | − | 0.839541i | \(-0.317176\pi\) | ||||
0.543296 | + | 0.839541i | \(0.317176\pi\) | |||||||
\(312\) | 2.50175 | 0.141634 | ||||||||
\(313\) | −2.27801 | −0.128761 | −0.0643803 | − | 0.997925i | \(-0.520507\pi\) | ||||
−0.0643803 | + | 0.997925i | \(0.520507\pi\) | |||||||
\(314\) | 0.364004 | 0.0205419 | ||||||||
\(315\) | −2.15570 | −0.121460 | ||||||||
\(316\) | 1.76038 | 0.0990292 | ||||||||
\(317\) | −23.8258 | −1.33819 | −0.669095 | − | 0.743177i | \(-0.733318\pi\) | ||||
−0.669095 | + | 0.743177i | \(0.733318\pi\) | |||||||
\(318\) | 7.35629 | 0.412520 | ||||||||
\(319\) | −42.5369 | −2.38161 | ||||||||
\(320\) | −3.07514 | −0.171906 | ||||||||
\(321\) | −9.20168 | −0.513588 | ||||||||
\(322\) | 0.0125753 | 0.000700793 0 | ||||||||
\(323\) | 32.8626 | 1.82853 | ||||||||
\(324\) | −2.62629 | −0.145905 | ||||||||
\(325\) | −8.91669 | −0.494609 | ||||||||
\(326\) | 20.4860 | 1.13461 | ||||||||
\(327\) | −9.01597 | −0.498584 | ||||||||
\(328\) | −4.52723 | −0.249974 | ||||||||
\(329\) | 0.486378 | 0.0268149 | ||||||||
\(330\) | −16.4092 | −0.903297 | ||||||||
\(331\) | 27.3893 | 1.50545 | 0.752727 | − | 0.658333i | \(-0.228738\pi\) | ||||
0.752727 | + | 0.658333i | \(0.228738\pi\) | |||||||
\(332\) | −17.9525 | −0.985272 | ||||||||
\(333\) | −14.3927 | −0.788715 | ||||||||
\(334\) | 11.4706 | 0.627641 | ||||||||
\(335\) | −35.9842 | −1.96602 | ||||||||
\(336\) | 0.610122 | 0.0332849 | ||||||||
\(337\) | −7.97092 | −0.434204 | −0.217102 | − | 0.976149i | \(-0.569660\pi\) | ||||
−0.217102 | + | 0.976149i | \(0.569660\pi\) | |||||||
\(338\) | −8.99665 | −0.489353 | ||||||||
\(339\) | 1.67814 | 0.0911442 | ||||||||
\(340\) | −12.5644 | −0.681403 | ||||||||
\(341\) | −1.67913 | −0.0909301 | ||||||||
\(342\) | −11.5548 | −0.624814 | ||||||||
\(343\) | 6.71525 | 0.362589 | ||||||||
\(344\) | −4.16008 | −0.224297 | ||||||||
\(345\) | −0.0990904 | −0.00533485 | ||||||||
\(346\) | −9.37883 | −0.504209 | ||||||||
\(347\) | 12.4240 | 0.666955 | 0.333478 | − | 0.942758i | \(-0.391778\pi\) | ||||
0.333478 | + | 0.942758i | \(0.391778\pi\) | |||||||
\(348\) | −12.4626 | −0.668066 | ||||||||
\(349\) | 14.3433 | 0.767781 | 0.383890 | − | 0.923379i | \(-0.374584\pi\) | ||||
0.383890 | + | 0.923379i | \(0.374584\pi\) | |||||||
\(350\) | −2.17458 | −0.116236 | ||||||||
\(351\) | −11.0993 | −0.592438 | ||||||||
\(352\) | −4.26766 | −0.227467 | ||||||||
\(353\) | −4.12403 | −0.219500 | −0.109750 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109750 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(354\) | −8.29721 | −0.440992 | ||||||||
\(355\) | 2.51123 | 0.133282 | ||||||||
\(356\) | 5.54121 | 0.293684 | ||||||||
\(357\) | 2.49284 | 0.131935 | ||||||||
\(358\) | −11.3854 | −0.601735 | ||||||||
\(359\) | −16.4658 | −0.869030 | −0.434515 | − | 0.900665i | \(-0.643080\pi\) | ||||
−0.434515 | + | 0.900665i | \(0.643080\pi\) | |||||||
\(360\) | 4.41779 | 0.232838 | ||||||||
\(361\) | 45.6915 | 2.40482 | ||||||||
\(362\) | 16.9420 | 0.890452 | ||||||||
\(363\) | −9.01868 | −0.473358 | ||||||||
\(364\) | 0.976327 | 0.0511734 | ||||||||
\(365\) | −5.38764 | −0.282002 | ||||||||
\(366\) | 5.49189 | 0.287066 | ||||||||
\(367\) | 14.9541 | 0.780600 | 0.390300 | − | 0.920688i | \(-0.372371\pi\) | ||||
0.390300 | + | 0.920688i | \(0.372371\pi\) | |||||||
\(368\) | −0.0257712 | −0.00134341 | ||||||||
\(369\) | 6.50388 | 0.338579 | ||||||||
\(370\) | −30.8082 | −1.60164 | ||||||||
\(371\) | 2.87084 | 0.149047 | ||||||||
\(372\) | −0.491958 | −0.0255068 | ||||||||
\(373\) | −13.6234 | −0.705393 | −0.352696 | − | 0.935738i | \(-0.614735\pi\) | ||||
−0.352696 | + | 0.935738i | \(0.614735\pi\) | |||||||
\(374\) | −17.4369 | −0.901638 | ||||||||
\(375\) | −2.08984 | −0.107919 | ||||||||
\(376\) | −0.996759 | −0.0514039 | ||||||||
\(377\) | −19.9429 | −1.02711 | ||||||||
\(378\) | −2.70688 | −0.139227 | ||||||||
\(379\) | 8.55606 | 0.439495 | 0.219748 | − | 0.975557i | \(-0.429477\pi\) | ||||
0.219748 | + | 0.975557i | \(0.429477\pi\) | |||||||
\(380\) | −24.7337 | −1.26881 | ||||||||
\(381\) | 12.9734 | 0.664648 | ||||||||
\(382\) | 3.61845 | 0.185136 | ||||||||
\(383\) | −18.9528 | −0.968445 | −0.484222 | − | 0.874945i | \(-0.660897\pi\) | ||||
−0.484222 | + | 0.874945i | \(0.660897\pi\) | |||||||
\(384\) | −1.25035 | −0.0638069 | ||||||||
\(385\) | −6.40380 | −0.326368 | ||||||||
\(386\) | −13.7420 | −0.699451 | ||||||||
\(387\) | 5.97643 | 0.303799 | ||||||||
\(388\) | 10.5413 | 0.535155 | ||||||||
\(389\) | 27.1610 | 1.37712 | 0.688559 | − | 0.725181i | \(-0.258244\pi\) | ||||
0.688559 | + | 0.725181i | \(0.258244\pi\) | |||||||
\(390\) | −7.69324 | −0.389562 | ||||||||
\(391\) | −0.105296 | −0.00532505 | ||||||||
\(392\) | −6.76190 | −0.341527 | ||||||||
\(393\) | −3.05690 | −0.154200 | ||||||||
\(394\) | −5.57990 | −0.281111 | ||||||||
\(395\) | −5.41342 | −0.272379 | ||||||||
\(396\) | 6.13098 | 0.308093 | ||||||||
\(397\) | 17.0314 | 0.854782 | 0.427391 | − | 0.904067i | \(-0.359433\pi\) | ||||
0.427391 | + | 0.904067i | \(0.359433\pi\) | |||||||
\(398\) | 22.2676 | 1.11617 | ||||||||
\(399\) | 4.90727 | 0.245671 | ||||||||
\(400\) | 4.45648 | 0.222824 | ||||||||
\(401\) | −16.0489 | −0.801442 | −0.400721 | − | 0.916200i | \(-0.631240\pi\) | ||||
−0.400721 | + | 0.916200i | \(0.631240\pi\) | |||||||
\(402\) | −14.6312 | −0.729737 | ||||||||
\(403\) | −0.787239 | −0.0392152 | ||||||||
\(404\) | 6.67517 | 0.332102 | ||||||||
\(405\) | 8.07622 | 0.401310 | ||||||||
\(406\) | −4.86362 | −0.241378 | ||||||||
\(407\) | −42.7554 | −2.11931 | ||||||||
\(408\) | −5.10871 | −0.252919 | ||||||||
\(409\) | 0.780928 | 0.0386144 | 0.0193072 | − | 0.999814i | \(-0.493854\pi\) | ||||
0.0193072 | + | 0.999814i | \(0.493854\pi\) | |||||||
\(410\) | 13.9219 | 0.687551 | ||||||||
\(411\) | −7.98643 | −0.393942 | ||||||||
\(412\) | 11.9804 | 0.590233 | ||||||||
\(413\) | −3.23804 | −0.159334 | ||||||||
\(414\) | 0.0370232 | 0.00181959 | ||||||||
\(415\) | 55.2065 | 2.70998 | ||||||||
\(416\) | −2.00084 | −0.0980991 | ||||||||
\(417\) | −17.2624 | −0.845342 | ||||||||
\(418\) | −34.3252 | −1.67890 | ||||||||
\(419\) | 19.4074 | 0.948114 | 0.474057 | − | 0.880494i | \(-0.342789\pi\) | ||||
0.474057 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(420\) | −1.87621 | −0.0915497 | ||||||||
\(421\) | −17.1074 | −0.833765 | −0.416882 | − | 0.908960i | \(-0.636877\pi\) | ||||
−0.416882 | + | 0.908960i | \(0.636877\pi\) | |||||||
\(422\) | −21.3358 | −1.03861 | ||||||||
\(423\) | 1.43196 | 0.0696242 | ||||||||
\(424\) | −5.88337 | −0.285721 | ||||||||
\(425\) | 18.2084 | 0.883235 | ||||||||
\(426\) | 1.02107 | 0.0494709 | ||||||||
\(427\) | 2.14325 | 0.103719 | ||||||||
\(428\) | 7.35926 | 0.355723 | ||||||||
\(429\) | −10.6766 | −0.515473 | ||||||||
\(430\) | 12.7928 | 0.616925 | ||||||||
\(431\) | 9.53381 | 0.459227 | 0.229614 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229614 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(432\) | 5.54734 | 0.266896 | ||||||||
\(433\) | −36.1544 | −1.73747 | −0.868735 | − | 0.495277i | \(-0.835067\pi\) | ||||
−0.868735 | + | 0.495277i | \(0.835067\pi\) | |||||||
\(434\) | −0.191990 | −0.00921582 | ||||||||
\(435\) | 38.3243 | 1.83751 | ||||||||
\(436\) | 7.21073 | 0.345332 | ||||||||
\(437\) | −0.207280 | −0.00991555 | ||||||||
\(438\) | −2.19062 | −0.104672 | ||||||||
\(439\) | −6.91667 | −0.330115 | −0.165057 | − | 0.986284i | \(-0.552781\pi\) | ||||
−0.165057 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(440\) | 13.1236 | 0.625645 | ||||||||
\(441\) | 9.71424 | 0.462583 | ||||||||
\(442\) | −8.17505 | −0.388847 | ||||||||
\(443\) | 23.1969 | 1.10212 | 0.551058 | − | 0.834467i | \(-0.314224\pi\) | ||||
0.551058 | + | 0.834467i | \(0.314224\pi\) | |||||||
\(444\) | −12.5266 | −0.594488 | ||||||||
\(445\) | −17.0400 | −0.807774 | ||||||||
\(446\) | 15.2924 | 0.724114 | ||||||||
\(447\) | 15.4676 | 0.731594 | ||||||||
\(448\) | −0.487959 | −0.0230539 | ||||||||
\(449\) | −8.22895 | −0.388348 | −0.194174 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194174 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(450\) | −6.40225 | −0.301805 | ||||||||
\(451\) | 19.3207 | 0.909774 | ||||||||
\(452\) | −1.34213 | −0.0631287 | ||||||||
\(453\) | −7.75303 | −0.364269 | ||||||||
\(454\) | 6.22212 | 0.292018 | ||||||||
\(455\) | −3.00234 | −0.140752 | ||||||||
\(456\) | −10.0567 | −0.470949 | ||||||||
\(457\) | −28.1009 | −1.31450 | −0.657252 | − | 0.753671i | \(-0.728281\pi\) | ||||
−0.657252 | + | 0.753671i | \(0.728281\pi\) | |||||||
\(458\) | −1.20776 | −0.0564351 | ||||||||
\(459\) | 22.6654 | 1.05793 | ||||||||
\(460\) | 0.0792499 | 0.00369504 | ||||||||
\(461\) | −9.95374 | −0.463592 | −0.231796 | − | 0.972764i | \(-0.574460\pi\) | ||||
−0.231796 | + | 0.972764i | \(0.574460\pi\) | |||||||
\(462\) | −2.60379 | −0.121139 | ||||||||
\(463\) | 2.26105 | 0.105080 | 0.0525399 | − | 0.998619i | \(-0.483268\pi\) | ||||
0.0525399 | + | 0.998619i | \(0.483268\pi\) | |||||||
\(464\) | 9.96727 | 0.462719 | ||||||||
\(465\) | 1.51284 | 0.0701562 | ||||||||
\(466\) | −25.1341 | −1.16431 | ||||||||
\(467\) | −22.1707 | −1.02594 | −0.512970 | − | 0.858407i | \(-0.671455\pi\) | ||||
−0.512970 | + | 0.858407i | \(0.671455\pi\) | |||||||
\(468\) | 2.87443 | 0.132871 | ||||||||
\(469\) | −5.70992 | −0.263660 | ||||||||
\(470\) | 3.06517 | 0.141386 | ||||||||
\(471\) | −0.455134 | −0.0209715 | ||||||||
\(472\) | 6.63589 | 0.305442 | ||||||||
\(473\) | 17.7538 | 0.816321 | ||||||||
\(474\) | −2.20110 | −0.101100 | ||||||||
\(475\) | 35.8439 | 1.64463 | ||||||||
\(476\) | −1.99371 | −0.0913816 | ||||||||
\(477\) | 8.45213 | 0.386996 | ||||||||
\(478\) | −23.6571 | −1.08205 | ||||||||
\(479\) | −7.54080 | −0.344548 | −0.172274 | − | 0.985049i | \(-0.555111\pi\) | ||||
−0.172274 | + | 0.985049i | \(0.555111\pi\) | |||||||
\(480\) | 3.84501 | 0.175500 | ||||||||
\(481\) | −20.0453 | −0.913988 | ||||||||
\(482\) | −15.1358 | −0.689417 | ||||||||
\(483\) | −0.0157235 | −0.000715446 0 | ||||||||
\(484\) | 7.21290 | 0.327859 | ||||||||
\(485\) | −32.4161 | −1.47194 | ||||||||
\(486\) | −13.3582 | −0.605941 | ||||||||
\(487\) | 19.2978 | 0.874467 | 0.437233 | − | 0.899348i | \(-0.355958\pi\) | ||||
0.437233 | + | 0.899348i | \(0.355958\pi\) | |||||||
\(488\) | −4.39227 | −0.198829 | ||||||||
\(489\) | −25.6147 | −1.15834 | ||||||||
\(490\) | 20.7938 | 0.939367 | ||||||||
\(491\) | 3.53482 | 0.159524 | 0.0797621 | − | 0.996814i | \(-0.474584\pi\) | ||||
0.0797621 | + | 0.996814i | \(0.474584\pi\) | |||||||
\(492\) | 5.66064 | 0.255201 | ||||||||
\(493\) | 40.7244 | 1.83413 | ||||||||
\(494\) | −16.0929 | −0.724055 | ||||||||
\(495\) | −18.8536 | −0.847407 | ||||||||
\(496\) | 0.393455 | 0.0176667 | ||||||||
\(497\) | 0.398479 | 0.0178742 | ||||||||
\(498\) | 22.4470 | 1.00587 | ||||||||
\(499\) | −0.943200 | −0.0422234 | −0.0211117 | − | 0.999777i | \(-0.506721\pi\) | ||||
−0.0211117 | + | 0.999777i | \(0.506721\pi\) | |||||||
\(500\) | 1.67140 | 0.0747472 | ||||||||
\(501\) | −14.3423 | −0.640765 | ||||||||
\(502\) | 23.0807 | 1.03014 | ||||||||
\(503\) | 37.4162 | 1.66831 | 0.834154 | − | 0.551532i | \(-0.185956\pi\) | ||||
0.834154 | + | 0.551532i | \(0.185956\pi\) | |||||||
\(504\) | 0.701010 | 0.0312255 | ||||||||
\(505\) | −20.5271 | −0.913443 | ||||||||
\(506\) | 0.109982 | 0.00488932 | ||||||||
\(507\) | 11.2490 | 0.499586 | ||||||||
\(508\) | −10.3758 | −0.460351 | ||||||||
\(509\) | −16.5233 | −0.732380 | −0.366190 | − | 0.930540i | \(-0.619338\pi\) | ||||
−0.366190 | + | 0.930540i | \(0.619338\pi\) | |||||||
\(510\) | 15.7100 | 0.695651 | ||||||||
\(511\) | −0.854904 | −0.0378187 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 44.6178 | 1.96992 | ||||||||
\(514\) | −5.54349 | −0.244513 | ||||||||
\(515\) | −36.8415 | −1.62343 | ||||||||
\(516\) | 5.20157 | 0.228987 | ||||||||
\(517\) | 4.25383 | 0.187083 | ||||||||
\(518\) | −4.88861 | −0.214793 | ||||||||
\(519\) | 11.7269 | 0.514752 | ||||||||
\(520\) | 6.15285 | 0.269820 | ||||||||
\(521\) | 15.0883 | 0.661030 | 0.330515 | − | 0.943801i | \(-0.392778\pi\) | ||||
0.330515 | + | 0.943801i | \(0.392778\pi\) | |||||||
\(522\) | −14.3191 | −0.626731 | ||||||||
\(523\) | −9.97432 | −0.436147 | −0.218073 | − | 0.975932i | \(-0.569977\pi\) | ||||
−0.218073 | + | 0.975932i | \(0.569977\pi\) | |||||||
\(524\) | 2.44482 | 0.106803 | ||||||||
\(525\) | 2.71900 | 0.118667 | ||||||||
\(526\) | 16.2519 | 0.708617 | ||||||||
\(527\) | 1.60758 | 0.0700275 | ||||||||
\(528\) | 5.33608 | 0.232223 | ||||||||
\(529\) | −22.9993 | −0.999971 | ||||||||
\(530\) | 18.0922 | 0.785873 | ||||||||
\(531\) | −9.53322 | −0.413706 | ||||||||
\(532\) | −3.92471 | −0.170158 | ||||||||
\(533\) | 9.05824 | 0.392356 | ||||||||
\(534\) | −6.92848 | −0.299825 | ||||||||
\(535\) | −22.6308 | −0.978413 | ||||||||
\(536\) | 11.7016 | 0.505434 | ||||||||
\(537\) | 14.2357 | 0.614317 | ||||||||
\(538\) | 13.0504 | 0.562641 | ||||||||
\(539\) | 28.8575 | 1.24298 | ||||||||
\(540\) | −17.0588 | −0.734096 | ||||||||
\(541\) | −34.5081 | −1.48362 | −0.741810 | − | 0.670610i | \(-0.766032\pi\) | ||||
−0.741810 | + | 0.670610i | \(0.766032\pi\) | |||||||
\(542\) | −8.91362 | −0.382873 | ||||||||
\(543\) | −21.1835 | −0.909071 | ||||||||
\(544\) | 4.08581 | 0.175178 | ||||||||
\(545\) | −22.1740 | −0.949830 | ||||||||
\(546\) | −1.22075 | −0.0522435 | ||||||||
\(547\) | −5.30310 | −0.226744 | −0.113372 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113372 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(548\) | 6.38733 | 0.272853 | ||||||||
\(549\) | 6.31000 | 0.269304 | ||||||||
\(550\) | −19.0187 | −0.810962 | ||||||||
\(551\) | 80.1678 | 3.41526 | ||||||||
\(552\) | 0.0322231 | 0.00137150 | ||||||||
\(553\) | −0.858994 | −0.0365282 | ||||||||
\(554\) | 31.3497 | 1.33192 | ||||||||
\(555\) | 38.5212 | 1.63513 | ||||||||
\(556\) | 13.8060 | 0.585504 | ||||||||
\(557\) | 5.82931 | 0.246996 | 0.123498 | − | 0.992345i | \(-0.460589\pi\) | ||||
0.123498 | + | 0.992345i | \(0.460589\pi\) | |||||||
\(558\) | −0.565243 | −0.0239287 | ||||||||
\(559\) | 8.32364 | 0.352053 | ||||||||
\(560\) | 1.50054 | 0.0634095 | ||||||||
\(561\) | 21.8022 | 0.920491 | ||||||||
\(562\) | −11.2573 | −0.474860 | ||||||||
\(563\) | 13.9047 | 0.586011 | 0.293006 | − | 0.956111i | \(-0.405344\pi\) | ||||
0.293006 | + | 0.956111i | \(0.405344\pi\) | |||||||
\(564\) | 1.24630 | 0.0524788 | ||||||||
\(565\) | 4.12725 | 0.173635 | ||||||||
\(566\) | 18.9390 | 0.796064 | ||||||||
\(567\) | 1.28152 | 0.0538190 | ||||||||
\(568\) | −0.816623 | −0.0342647 | ||||||||
\(569\) | 39.9841 | 1.67622 | 0.838110 | − | 0.545501i | \(-0.183661\pi\) | ||||
0.838110 | + | 0.545501i | \(0.183661\pi\) | |||||||
\(570\) | 30.9258 | 1.29534 | ||||||||
\(571\) | −40.1158 | −1.67879 | −0.839397 | − | 0.543518i | \(-0.817092\pi\) | ||||
−0.839397 | + | 0.543518i | \(0.817092\pi\) | |||||||
\(572\) | 8.53889 | 0.357029 | ||||||||
\(573\) | −4.52434 | −0.189007 | ||||||||
\(574\) | 2.20910 | 0.0922062 | ||||||||
\(575\) | −0.114849 | −0.00478952 | ||||||||
\(576\) | −1.43661 | −0.0598590 | ||||||||
\(577\) | 42.6589 | 1.77591 | 0.887957 | − | 0.459926i | \(-0.152124\pi\) | ||||
0.887957 | + | 0.459926i | \(0.152124\pi\) | |||||||
\(578\) | −0.306124 | −0.0127331 | ||||||||
\(579\) | 17.1824 | 0.714076 | ||||||||
\(580\) | −30.6507 | −1.27270 | ||||||||
\(581\) | 8.76010 | 0.363430 | ||||||||
\(582\) | −13.1804 | −0.546345 | ||||||||
\(583\) | 25.1082 | 1.03987 | ||||||||
\(584\) | 1.75200 | 0.0724982 | ||||||||
\(585\) | −8.83928 | −0.365459 | ||||||||
\(586\) | 22.0162 | 0.909480 | ||||||||
\(587\) | −26.5806 | −1.09710 | −0.548549 | − | 0.836118i | \(-0.684820\pi\) | ||||
−0.548549 | + | 0.836118i | \(0.684820\pi\) | |||||||
\(588\) | 8.45476 | 0.348669 | ||||||||
\(589\) | 3.16460 | 0.130395 | ||||||||
\(590\) | −20.4063 | −0.840113 | ||||||||
\(591\) | 6.97685 | 0.286989 | ||||||||
\(592\) | 10.0185 | 0.411757 | ||||||||
\(593\) | −30.0581 | −1.23434 | −0.617169 | − | 0.786831i | \(-0.711720\pi\) | ||||
−0.617169 | + | 0.786831i | \(0.711720\pi\) | |||||||
\(594\) | −23.6741 | −0.971362 | ||||||||
\(595\) | 6.13094 | 0.251344 | ||||||||
\(596\) | −12.3706 | −0.506720 | ||||||||
\(597\) | −27.8423 | −1.13951 | ||||||||
\(598\) | 0.0515639 | 0.00210860 | ||||||||
\(599\) | 0.721394 | 0.0294753 | 0.0147377 | − | 0.999891i | \(-0.495309\pi\) | ||||
0.0147377 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(600\) | −5.57218 | −0.227483 | ||||||||
\(601\) | 25.1413 | 1.02553 | 0.512767 | − | 0.858528i | \(-0.328621\pi\) | ||||
0.512767 | + | 0.858528i | \(0.328621\pi\) | |||||||
\(602\) | 2.02995 | 0.0827346 | ||||||||
\(603\) | −16.8107 | −0.684587 | ||||||||
\(604\) | 6.20066 | 0.252301 | ||||||||
\(605\) | −22.1807 | −0.901773 | ||||||||
\(606\) | −8.34633 | −0.339046 | ||||||||
\(607\) | −25.5188 | −1.03578 | −0.517889 | − | 0.855448i | \(-0.673282\pi\) | ||||
−0.517889 | + | 0.855448i | \(0.673282\pi\) | |||||||
\(608\) | 8.04310 | 0.326191 | ||||||||
\(609\) | 6.08125 | 0.246425 | ||||||||
\(610\) | 13.5068 | 0.546876 | ||||||||
\(611\) | 1.99435 | 0.0806828 | ||||||||
\(612\) | −5.86974 | −0.237270 | ||||||||
\(613\) | 44.3356 | 1.79070 | 0.895349 | − | 0.445365i | \(-0.146926\pi\) | ||||
0.895349 | + | 0.445365i | \(0.146926\pi\) | |||||||
\(614\) | 27.0103 | 1.09005 | ||||||||
\(615\) | −17.4072 | −0.701928 | ||||||||
\(616\) | 2.08244 | 0.0839040 | ||||||||
\(617\) | −3.80538 | −0.153199 | −0.0765994 | − | 0.997062i | \(-0.524406\pi\) | ||||
−0.0765994 | + | 0.997062i | \(0.524406\pi\) | |||||||
\(618\) | −14.9798 | −0.602575 | ||||||||
\(619\) | −2.83337 | −0.113883 | −0.0569413 | − | 0.998378i | \(-0.518135\pi\) | ||||
−0.0569413 | + | 0.998378i | \(0.518135\pi\) | |||||||
\(620\) | −1.20993 | −0.0485919 | ||||||||
\(621\) | −0.142961 | −0.00573684 | ||||||||
\(622\) | 19.1623 | 0.768336 | ||||||||
\(623\) | −2.70389 | −0.108329 | ||||||||
\(624\) | 2.50175 | 0.100150 | ||||||||
\(625\) | −27.4222 | −1.09689 | ||||||||
\(626\) | −2.27801 | −0.0910475 | ||||||||
\(627\) | 42.9187 | 1.71401 | ||||||||
\(628\) | 0.364004 | 0.0145253 | ||||||||
\(629\) | 40.9336 | 1.63213 | ||||||||
\(630\) | −2.15570 | −0.0858852 | ||||||||
\(631\) | −7.54691 | −0.300438 | −0.150219 | − | 0.988653i | \(-0.547998\pi\) | ||||
−0.150219 | + | 0.988653i | \(0.547998\pi\) | |||||||
\(632\) | 1.76038 | 0.0700242 | ||||||||
\(633\) | 26.6773 | 1.06033 | ||||||||
\(634\) | −23.8258 | −0.946243 | ||||||||
\(635\) | 31.9070 | 1.26619 | ||||||||
\(636\) | 7.35629 | 0.291696 | ||||||||
\(637\) | 13.5294 | 0.536056 | ||||||||
\(638\) | −42.5369 | −1.68405 | ||||||||
\(639\) | 1.17317 | 0.0464100 | ||||||||
\(640\) | −3.07514 | −0.121556 | ||||||||
\(641\) | −31.0501 | −1.22641 | −0.613203 | − | 0.789925i | \(-0.710119\pi\) | ||||
−0.613203 | + | 0.789925i | \(0.710119\pi\) | |||||||
\(642\) | −9.20168 | −0.363161 | ||||||||
\(643\) | 43.4217 | 1.71239 | 0.856193 | − | 0.516656i | \(-0.172823\pi\) | ||||
0.856193 | + | 0.516656i | \(0.172823\pi\) | |||||||
\(644\) | 0.0125753 | 0.000495535 0 | ||||||||
\(645\) | −15.9956 | −0.629825 | ||||||||
\(646\) | 32.8626 | 1.29296 | ||||||||
\(647\) | 11.3056 | 0.444470 | 0.222235 | − | 0.974993i | \(-0.428665\pi\) | ||||
0.222235 | + | 0.974993i | \(0.428665\pi\) | |||||||
\(648\) | −2.62629 | −0.103171 | ||||||||
\(649\) | −28.3197 | −1.11165 | ||||||||
\(650\) | −8.91669 | −0.349741 | ||||||||
\(651\) | 0.240056 | 0.00940852 | ||||||||
\(652\) | 20.4860 | 0.802294 | ||||||||
\(653\) | 23.1531 | 0.906051 | 0.453025 | − | 0.891498i | \(-0.350345\pi\) | ||||
0.453025 | + | 0.891498i | \(0.350345\pi\) | |||||||
\(654\) | −9.01597 | −0.352552 | ||||||||
\(655\) | −7.51818 | −0.293759 | ||||||||
\(656\) | −4.52723 | −0.176759 | ||||||||
\(657\) | −2.51695 | −0.0981955 | ||||||||
\(658\) | 0.486378 | 0.0189610 | ||||||||
\(659\) | −24.1765 | −0.941782 | −0.470891 | − | 0.882191i | \(-0.656068\pi\) | ||||
−0.470891 | + | 0.882191i | \(0.656068\pi\) | |||||||
\(660\) | −16.4092 | −0.638727 | ||||||||
\(661\) | −41.0112 | −1.59515 | −0.797575 | − | 0.603219i | \(-0.793884\pi\) | ||||
−0.797575 | + | 0.603219i | \(0.793884\pi\) | |||||||
\(662\) | 27.3893 | 1.06452 | ||||||||
\(663\) | 10.2217 | 0.396978 | ||||||||
\(664\) | −17.9525 | −0.696693 | ||||||||
\(665\) | 12.0690 | 0.468017 | ||||||||
\(666\) | −14.3927 | −0.557705 | ||||||||
\(667\) | −0.256868 | −0.00994597 | ||||||||
\(668\) | 11.4706 | 0.443809 | ||||||||
\(669\) | −19.1209 | −0.739255 | ||||||||
\(670\) | −35.9842 | −1.39019 | ||||||||
\(671\) | 18.7447 | 0.723631 | ||||||||
\(672\) | 0.610122 | 0.0235360 | ||||||||
\(673\) | 26.5236 | 1.02241 | 0.511204 | − | 0.859459i | \(-0.329200\pi\) | ||||
0.511204 | + | 0.859459i | \(0.329200\pi\) | |||||||
\(674\) | −7.97092 | −0.307028 | ||||||||
\(675\) | 24.7216 | 0.951535 | ||||||||
\(676\) | −8.99665 | −0.346025 | ||||||||
\(677\) | −18.9379 | −0.727843 | −0.363922 | − | 0.931430i | \(-0.618562\pi\) | ||||
−0.363922 | + | 0.931430i | \(0.618562\pi\) | |||||||
\(678\) | 1.67814 | 0.0644487 | ||||||||
\(679\) | −5.14374 | −0.197399 | ||||||||
\(680\) | −12.5644 | −0.481825 | ||||||||
\(681\) | −7.77985 | −0.298125 | ||||||||
\(682\) | −1.67913 | −0.0642973 | ||||||||
\(683\) | −26.2998 | −1.00633 | −0.503166 | − | 0.864190i | \(-0.667832\pi\) | ||||
−0.503166 | + | 0.864190i | \(0.667832\pi\) | |||||||
\(684\) | −11.5548 | −0.441810 | ||||||||
\(685\) | −19.6419 | −0.750480 | ||||||||
\(686\) | 6.71525 | 0.256389 | ||||||||
\(687\) | 1.51013 | 0.0576151 | ||||||||
\(688\) | −4.16008 | −0.158602 | ||||||||
\(689\) | 11.7717 | 0.448464 | ||||||||
\(690\) | −0.0990904 | −0.00377231 | ||||||||
\(691\) | −28.7667 | −1.09434 | −0.547168 | − | 0.837023i | \(-0.684294\pi\) | ||||
−0.547168 | + | 0.837023i | \(0.684294\pi\) | |||||||
\(692\) | −9.37883 | −0.356530 | ||||||||
\(693\) | −2.99167 | −0.113644 | ||||||||
\(694\) | 12.4240 | 0.471609 | ||||||||
\(695\) | −42.4553 | −1.61042 | ||||||||
\(696\) | −12.4626 | −0.472394 | ||||||||
\(697\) | −18.4974 | −0.700639 | ||||||||
\(698\) | 14.3433 | 0.542903 | ||||||||
\(699\) | 31.4265 | 1.18866 | ||||||||
\(700\) | −2.17458 | −0.0821915 | ||||||||
\(701\) | −12.2711 | −0.463473 | −0.231737 | − | 0.972779i | \(-0.574441\pi\) | ||||
−0.231737 | + | 0.972779i | \(0.574441\pi\) | |||||||
\(702\) | −11.0993 | −0.418917 | ||||||||
\(703\) | 80.5796 | 3.03912 | ||||||||
\(704\) | −4.26766 | −0.160843 | ||||||||
\(705\) | −3.83255 | −0.144342 | ||||||||
\(706\) | −4.12403 | −0.155210 | ||||||||
\(707\) | −3.25721 | −0.122500 | ||||||||
\(708\) | −8.29721 | −0.311828 | ||||||||
\(709\) | −12.3020 | −0.462010 | −0.231005 | − | 0.972953i | \(-0.574201\pi\) | ||||
−0.231005 | + | 0.972953i | \(0.574201\pi\) | |||||||
\(710\) | 2.51123 | 0.0942448 | ||||||||
\(711\) | −2.52899 | −0.0948445 | ||||||||
\(712\) | 5.54121 | 0.207666 | ||||||||
\(713\) | −0.0101398 | −0.000379738 0 | ||||||||
\(714\) | 2.49284 | 0.0932924 | ||||||||
\(715\) | −26.2583 | −0.982003 | ||||||||
\(716\) | −11.3854 | −0.425491 | ||||||||
\(717\) | 29.5797 | 1.10467 | ||||||||
\(718\) | −16.4658 | −0.614497 | ||||||||
\(719\) | 9.14406 | 0.341016 | 0.170508 | − | 0.985356i | \(-0.445459\pi\) | ||||
0.170508 | + | 0.985356i | \(0.445459\pi\) | |||||||
\(720\) | 4.41779 | 0.164641 | ||||||||
\(721\) | −5.84596 | −0.217715 | ||||||||
\(722\) | 45.6915 | 1.70046 | ||||||||
\(723\) | 18.9251 | 0.703832 | ||||||||
\(724\) | 16.9420 | 0.629644 | ||||||||
\(725\) | 44.4189 | 1.64968 | ||||||||
\(726\) | −9.01868 | −0.334715 | ||||||||
\(727\) | 0.913119 | 0.0338657 | 0.0169329 | − | 0.999857i | \(-0.494610\pi\) | ||||
0.0169329 | + | 0.999857i | \(0.494610\pi\) | |||||||
\(728\) | 0.976327 | 0.0361851 | ||||||||
\(729\) | 24.5814 | 0.910422 | ||||||||
\(730\) | −5.38764 | −0.199406 | ||||||||
\(731\) | −16.9973 | −0.628668 | ||||||||
\(732\) | 5.49189 | 0.202986 | ||||||||
\(733\) | −17.6523 | −0.652002 | −0.326001 | − | 0.945369i | \(-0.605701\pi\) | ||||
−0.326001 | + | 0.945369i | \(0.605701\pi\) | |||||||
\(734\) | 14.9541 | 0.551967 | ||||||||
\(735\) | −25.9996 | −0.959009 | ||||||||
\(736\) | −0.0257712 | −0.000949937 0 | ||||||||
\(737\) | −49.9386 | −1.83951 | ||||||||
\(738\) | 6.50388 | 0.239411 | ||||||||
\(739\) | 49.7299 | 1.82934 | 0.914671 | − | 0.404198i | \(-0.132449\pi\) | ||||
0.914671 | + | 0.404198i | \(0.132449\pi\) | |||||||
\(740\) | −30.8082 | −1.13253 | ||||||||
\(741\) | 20.1219 | 0.739195 | ||||||||
\(742\) | 2.87084 | 0.105392 | ||||||||
\(743\) | 50.3686 | 1.84784 | 0.923922 | − | 0.382580i | \(-0.124964\pi\) | ||||
0.923922 | + | 0.382580i | \(0.124964\pi\) | |||||||
\(744\) | −0.491958 | −0.0180361 | ||||||||
\(745\) | 38.0413 | 1.39373 | ||||||||
\(746\) | −13.6234 | −0.498788 | ||||||||
\(747\) | 25.7909 | 0.943638 | ||||||||
\(748\) | −17.4369 | −0.637555 | ||||||||
\(749\) | −3.59102 | −0.131213 | ||||||||
\(750\) | −2.08984 | −0.0763102 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | −0.996759 | −0.0363481 | ||||||||
\(753\) | −28.8590 | −1.05168 | ||||||||
\(754\) | −19.9429 | −0.726277 | ||||||||
\(755\) | −19.0679 | −0.693952 | ||||||||
\(756\) | −2.70688 | −0.0984481 | ||||||||
\(757\) | −25.7409 | −0.935567 | −0.467784 | − | 0.883843i | \(-0.654947\pi\) | ||||
−0.467784 | + | 0.883843i | \(0.654947\pi\) | |||||||
\(758\) | 8.55606 | 0.310770 | ||||||||
\(759\) | −0.137517 | −0.00499155 | ||||||||
\(760\) | −24.7337 | −0.897184 | ||||||||
\(761\) | 34.9639 | 1.26744 | 0.633719 | − | 0.773563i | \(-0.281527\pi\) | ||||
0.633719 | + | 0.773563i | \(0.281527\pi\) | |||||||
\(762\) | 12.9734 | 0.469977 | ||||||||
\(763\) | −3.51855 | −0.127380 | ||||||||
\(764\) | 3.61845 | 0.130911 | ||||||||
\(765\) | 18.0503 | 0.652609 | ||||||||
\(766\) | −18.9528 | −0.684794 | ||||||||
\(767\) | −13.2773 | −0.479417 | ||||||||
\(768\) | −1.25035 | −0.0451183 | ||||||||
\(769\) | −12.4021 | −0.447232 | −0.223616 | − | 0.974677i | \(-0.571786\pi\) | ||||
−0.223616 | + | 0.974677i | \(0.571786\pi\) | |||||||
\(770\) | −6.40380 | −0.230777 | ||||||||
\(771\) | 6.93132 | 0.249626 | ||||||||
\(772\) | −13.7420 | −0.494586 | ||||||||
\(773\) | −19.5835 | −0.704370 | −0.352185 | − | 0.935930i | \(-0.614561\pi\) | ||||
−0.352185 | + | 0.935930i | \(0.614561\pi\) | |||||||
\(774\) | 5.97643 | 0.214818 | ||||||||
\(775\) | 1.75342 | 0.0629849 | ||||||||
\(776\) | 10.5413 | 0.378412 | ||||||||
\(777\) | 6.11249 | 0.219284 | ||||||||
\(778\) | 27.1610 | 0.973769 | ||||||||
\(779\) | −36.4130 | −1.30463 | ||||||||
\(780\) | −7.69324 | −0.275462 | ||||||||
\(781\) | 3.48507 | 0.124706 | ||||||||
\(782\) | −0.105296 | −0.00376538 | ||||||||
\(783\) | 55.2918 | 1.97597 | ||||||||
\(784\) | −6.76190 | −0.241496 | ||||||||
\(785\) | −1.11936 | −0.0399518 | ||||||||
\(786\) | −3.05690 | −0.109036 | ||||||||
\(787\) | −10.2413 | −0.365064 | −0.182532 | − | 0.983200i | \(-0.558429\pi\) | ||||
−0.182532 | + | 0.983200i | \(0.558429\pi\) | |||||||
\(788\) | −5.57990 | −0.198776 | ||||||||
\(789\) | −20.3207 | −0.723434 | ||||||||
\(790\) | −5.41342 | −0.192601 | ||||||||
\(791\) | 0.654907 | 0.0232858 | ||||||||
\(792\) | 6.13098 | 0.217855 | ||||||||
\(793\) | 8.78822 | 0.312079 | ||||||||
\(794\) | 17.0314 | 0.604422 | ||||||||
\(795\) | −22.6216 | −0.802306 | ||||||||
\(796\) | 22.2676 | 0.789252 | ||||||||
\(797\) | −8.14107 | −0.288372 | −0.144186 | − | 0.989551i | \(-0.546056\pi\) | ||||
−0.144186 | + | 0.989551i | \(0.546056\pi\) | |||||||
\(798\) | 4.90727 | 0.173716 | ||||||||
\(799\) | −4.07257 | −0.144077 | ||||||||
\(800\) | 4.45648 | 0.157560 | ||||||||
\(801\) | −7.96059 | −0.281274 | ||||||||
\(802\) | −16.0489 | −0.566705 | ||||||||
\(803\) | −7.47693 | −0.263855 | ||||||||
\(804\) | −14.6312 | −0.516002 | ||||||||
\(805\) | −0.0386707 | −0.00136296 | ||||||||
\(806\) | −0.787239 | −0.0277293 | ||||||||
\(807\) | −16.3176 | −0.574406 | ||||||||
\(808\) | 6.67517 | 0.234832 | ||||||||
\(809\) | −46.5791 | −1.63763 | −0.818817 | − | 0.574055i | \(-0.805370\pi\) | ||||
−0.818817 | + | 0.574055i | \(0.805370\pi\) | |||||||
\(810\) | 8.07622 | 0.283769 | ||||||||
\(811\) | −40.6312 | −1.42675 | −0.713377 | − | 0.700780i | \(-0.752835\pi\) | ||||
−0.713377 | + | 0.700780i | \(0.752835\pi\) | |||||||
\(812\) | −4.86362 | −0.170680 | ||||||||
\(813\) | 11.1452 | 0.390879 | ||||||||
\(814\) | −42.7554 | −1.49858 | ||||||||
\(815\) | −62.9973 | −2.20670 | ||||||||
\(816\) | −5.10871 | −0.178841 | ||||||||
\(817\) | −33.4600 | −1.17062 | ||||||||
\(818\) | 0.780928 | 0.0273045 | ||||||||
\(819\) | −1.40261 | −0.0490110 | ||||||||
\(820\) | 13.9219 | 0.486172 | ||||||||
\(821\) | 30.0352 | 1.04824 | 0.524119 | − | 0.851645i | \(-0.324395\pi\) | ||||
0.524119 | + | 0.851645i | \(0.324395\pi\) | |||||||
\(822\) | −7.98643 | −0.278559 | ||||||||
\(823\) | −25.6172 | −0.892958 | −0.446479 | − | 0.894794i | \(-0.647322\pi\) | ||||
−0.446479 | + | 0.894794i | \(0.647322\pi\) | |||||||
\(824\) | 11.9804 | 0.417358 | ||||||||
\(825\) | 23.7801 | 0.827919 | ||||||||
\(826\) | −3.23804 | −0.112666 | ||||||||
\(827\) | 17.0234 | 0.591961 | 0.295980 | − | 0.955194i | \(-0.404354\pi\) | ||||
0.295980 | + | 0.955194i | \(0.404354\pi\) | |||||||
\(828\) | 0.0370232 | 0.00128665 | ||||||||
\(829\) | −26.2810 | −0.912776 | −0.456388 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456388 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(830\) | 55.2065 | 1.91624 | ||||||||
\(831\) | −39.1983 | −1.35977 | ||||||||
\(832\) | −2.00084 | −0.0693665 | ||||||||
\(833\) | −27.6278 | −0.957248 | ||||||||
\(834\) | −17.2624 | −0.597747 | ||||||||
\(835\) | −35.2736 | −1.22069 | ||||||||
\(836\) | −34.3252 | −1.18716 | ||||||||
\(837\) | 2.18263 | 0.0754427 | ||||||||
\(838\) | 19.4074 | 0.670418 | ||||||||
\(839\) | 12.7311 | 0.439526 | 0.219763 | − | 0.975553i | \(-0.429472\pi\) | ||||
0.219763 | + | 0.975553i | \(0.429472\pi\) | |||||||
\(840\) | −1.87621 | −0.0647354 | ||||||||
\(841\) | 70.3464 | 2.42574 | ||||||||
\(842\) | −17.1074 | −0.589561 | ||||||||
\(843\) | 14.0756 | 0.484790 | ||||||||
\(844\) | −21.3358 | −0.734409 | ||||||||
\(845\) | 27.6660 | 0.951738 | ||||||||
\(846\) | 1.43196 | 0.0492318 | ||||||||
\(847\) | −3.51960 | −0.120935 | ||||||||
\(848\) | −5.88337 | −0.202036 | ||||||||
\(849\) | −23.6804 | −0.812710 | ||||||||
\(850\) | 18.2084 | 0.624541 | ||||||||
\(851\) | −0.258188 | −0.00885056 | ||||||||
\(852\) | 1.02107 | 0.0349812 | ||||||||
\(853\) | 43.7636 | 1.49844 | 0.749219 | − | 0.662322i | \(-0.230429\pi\) | ||||
0.749219 | + | 0.662322i | \(0.230429\pi\) | |||||||
\(854\) | 2.14325 | 0.0733405 | ||||||||
\(855\) | 35.5327 | 1.21519 | ||||||||
\(856\) | 7.35926 | 0.251534 | ||||||||
\(857\) | 35.2258 | 1.20329 | 0.601645 | − | 0.798763i | \(-0.294512\pi\) | ||||
0.601645 | + | 0.798763i | \(0.294512\pi\) | |||||||
\(858\) | −10.6766 | −0.364494 | ||||||||
\(859\) | 28.9699 | 0.988439 | 0.494220 | − | 0.869337i | \(-0.335454\pi\) | ||||
0.494220 | + | 0.869337i | \(0.335454\pi\) | |||||||
\(860\) | 12.7928 | 0.436232 | ||||||||
\(861\) | −2.76216 | −0.0941342 | ||||||||
\(862\) | 9.53381 | 0.324723 | ||||||||
\(863\) | 47.5013 | 1.61696 | 0.808481 | − | 0.588522i | \(-0.200290\pi\) | ||||
0.808481 | + | 0.588522i | \(0.200290\pi\) | |||||||
\(864\) | 5.54734 | 0.188724 | ||||||||
\(865\) | 28.8412 | 0.980631 | ||||||||
\(866\) | −36.1544 | −1.22858 | ||||||||
\(867\) | 0.382763 | 0.0129993 | ||||||||
\(868\) | −0.191990 | −0.00651657 | ||||||||
\(869\) | −7.51270 | −0.254851 | ||||||||
\(870\) | 38.3243 | 1.29931 | ||||||||
\(871\) | −23.4131 | −0.793321 | ||||||||
\(872\) | 7.21073 | 0.244186 | ||||||||
\(873\) | −15.1438 | −0.512541 | ||||||||
\(874\) | −0.207280 | −0.00701135 | ||||||||
\(875\) | −0.815574 | −0.0275714 | ||||||||
\(876\) | −2.19062 | −0.0740142 | ||||||||
\(877\) | 32.3786 | 1.09335 | 0.546674 | − | 0.837345i | \(-0.315894\pi\) | ||||
0.546674 | + | 0.837345i | \(0.315894\pi\) | |||||||
\(878\) | −6.91667 | −0.233426 | ||||||||
\(879\) | −27.5280 | −0.928497 | ||||||||
\(880\) | 13.1236 | 0.442398 | ||||||||
\(881\) | −9.73501 | −0.327981 | −0.163990 | − | 0.986462i | \(-0.552437\pi\) | ||||
−0.163990 | + | 0.986462i | \(0.552437\pi\) | |||||||
\(882\) | 9.71424 | 0.327095 | ||||||||
\(883\) | 25.1596 | 0.846687 | 0.423344 | − | 0.905969i | \(-0.360856\pi\) | ||||
0.423344 | + | 0.905969i | \(0.360856\pi\) | |||||||
\(884\) | −8.17505 | −0.274957 | ||||||||
\(885\) | 25.5151 | 0.857680 | ||||||||
\(886\) | 23.1969 | 0.779314 | ||||||||
\(887\) | 31.6471 | 1.06261 | 0.531303 | − | 0.847182i | \(-0.321702\pi\) | ||||
0.531303 | + | 0.847182i | \(0.321702\pi\) | |||||||
\(888\) | −12.5266 | −0.420366 | ||||||||
\(889\) | 5.06296 | 0.169806 | ||||||||
\(890\) | −17.0400 | −0.571182 | ||||||||
\(891\) | 11.2081 | 0.375486 | ||||||||
\(892\) | 15.2924 | 0.512026 | ||||||||
\(893\) | −8.01704 | −0.268280 | ||||||||
\(894\) | 15.4676 | 0.517315 | ||||||||
\(895\) | 35.0116 | 1.17031 | ||||||||
\(896\) | −0.487959 | −0.0163016 | ||||||||
\(897\) | −0.0644731 | −0.00215269 | ||||||||
\(898\) | −8.22895 | −0.274603 | ||||||||
\(899\) | 3.92167 | 0.130795 | ||||||||
\(900\) | −6.40225 | −0.213408 | ||||||||
\(901\) | −24.0383 | −0.800833 | ||||||||
\(902\) | 19.3207 | 0.643308 | ||||||||
\(903\) | −2.53816 | −0.0844646 | ||||||||
\(904\) | −1.34213 | −0.0446387 | ||||||||
\(905\) | −52.0990 | −1.73183 | ||||||||
\(906\) | −7.75303 | −0.257577 | ||||||||
\(907\) | 14.5931 | 0.484557 | 0.242279 | − | 0.970207i | \(-0.422105\pi\) | ||||
0.242279 | + | 0.970207i | \(0.422105\pi\) | |||||||
\(908\) | 6.22212 | 0.206488 | ||||||||
\(909\) | −9.58965 | −0.318069 | ||||||||
\(910\) | −3.00234 | −0.0995266 | ||||||||
\(911\) | −16.9317 | −0.560972 | −0.280486 | − | 0.959858i | \(-0.590496\pi\) | ||||
−0.280486 | + | 0.959858i | \(0.590496\pi\) | |||||||
\(912\) | −10.0567 | −0.333011 | ||||||||
\(913\) | 76.6152 | 2.53559 | ||||||||
\(914\) | −28.1009 | −0.929494 | ||||||||
\(915\) | −16.8883 | −0.558311 | ||||||||
\(916\) | −1.20776 | −0.0399056 | ||||||||
\(917\) | −1.19298 | −0.0393955 | ||||||||
\(918\) | 22.6654 | 0.748070 | ||||||||
\(919\) | −40.9232 | −1.34993 | −0.674966 | − | 0.737849i | \(-0.735842\pi\) | ||||
−0.674966 | + | 0.737849i | \(0.735842\pi\) | |||||||
\(920\) | 0.0792499 | 0.00261279 | ||||||||
\(921\) | −33.7724 | −1.11284 | ||||||||
\(922\) | −9.95374 | −0.327809 | ||||||||
\(923\) | 1.63393 | 0.0537814 | ||||||||
\(924\) | −2.60379 | −0.0856585 | ||||||||
\(925\) | 44.6471 | 1.46799 | ||||||||
\(926\) | 2.26105 | 0.0743026 | ||||||||
\(927\) | −17.2113 | −0.565292 | ||||||||
\(928\) | 9.96727 | 0.327192 | ||||||||
\(929\) | 22.5424 | 0.739591 | 0.369796 | − | 0.929113i | \(-0.379428\pi\) | ||||
0.369796 | + | 0.929113i | \(0.379428\pi\) | |||||||
\(930\) | 1.51284 | 0.0496080 | ||||||||
\(931\) | −54.3866 | −1.78245 | ||||||||
\(932\) | −25.1341 | −0.823294 | ||||||||
\(933\) | −23.9596 | −0.784402 | ||||||||
\(934\) | −22.1707 | −0.725449 | ||||||||
\(935\) | 53.6208 | 1.75359 | ||||||||
\(936\) | 2.87443 | 0.0939537 | ||||||||
\(937\) | −36.6526 | −1.19739 | −0.598693 | − | 0.800978i | \(-0.704313\pi\) | ||||
−0.598693 | + | 0.800978i | \(0.704313\pi\) | |||||||
\(938\) | −5.70992 | −0.186436 | ||||||||
\(939\) | 2.84831 | 0.0929512 | ||||||||
\(940\) | 3.06517 | 0.0999749 | ||||||||
\(941\) | 12.0701 | 0.393473 | 0.196737 | − | 0.980456i | \(-0.436966\pi\) | ||||
0.196737 | + | 0.980456i | \(0.436966\pi\) | |||||||
\(942\) | −0.455134 | −0.0148291 | ||||||||
\(943\) | 0.116672 | 0.00379936 | ||||||||
\(944\) | 6.63589 | 0.215980 | ||||||||
\(945\) | 8.32402 | 0.270780 | ||||||||
\(946\) | 17.7538 | 0.577226 | ||||||||
\(947\) | 45.2139 | 1.46925 | 0.734627 | − | 0.678472i | \(-0.237357\pi\) | ||||
0.734627 | + | 0.678472i | \(0.237357\pi\) | |||||||
\(948\) | −2.20110 | −0.0714884 | ||||||||
\(949\) | −3.50546 | −0.113792 | ||||||||
\(950\) | 35.8439 | 1.16293 | ||||||||
\(951\) | 29.7907 | 0.966029 | ||||||||
\(952\) | −1.99371 | −0.0646166 | ||||||||
\(953\) | −57.9368 | −1.87676 | −0.938378 | − | 0.345611i | \(-0.887672\pi\) | ||||
−0.938378 | + | 0.345611i | \(0.887672\pi\) | |||||||
\(954\) | 8.45213 | 0.273648 | ||||||||
\(955\) | −11.1272 | −0.360069 | ||||||||
\(956\) | −23.6571 | −0.765125 | ||||||||
\(957\) | 53.1862 | 1.71926 | ||||||||
\(958\) | −7.54080 | −0.243632 | ||||||||
\(959\) | −3.11676 | −0.100645 | ||||||||
\(960\) | 3.84501 | 0.124097 | ||||||||
\(961\) | −30.8452 | −0.995006 | ||||||||
\(962\) | −20.0453 | −0.646287 | ||||||||
\(963\) | −10.5724 | −0.340692 | ||||||||
\(964\) | −15.1358 | −0.487491 | ||||||||
\(965\) | 42.2586 | 1.36035 | ||||||||
\(966\) | −0.0157235 | −0.000505897 0 | ||||||||
\(967\) | −28.2229 | −0.907587 | −0.453793 | − | 0.891107i | \(-0.649930\pi\) | ||||
−0.453793 | + | 0.891107i | \(0.649930\pi\) | |||||||
\(968\) | 7.21290 | 0.231831 | ||||||||
\(969\) | −41.0899 | −1.32000 | ||||||||
\(970\) | −32.4161 | −1.04082 | ||||||||
\(971\) | 7.15962 | 0.229763 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(972\) | −13.3582 | −0.428465 | ||||||||
\(973\) | −6.73676 | −0.215971 | ||||||||
\(974\) | 19.2978 | 0.618341 | ||||||||
\(975\) | 11.1490 | 0.357054 | ||||||||
\(976\) | −4.39227 | −0.140593 | ||||||||
\(977\) | 22.7509 | 0.727865 | 0.363933 | − | 0.931425i | \(-0.381434\pi\) | ||||
0.363933 | + | 0.931425i | \(0.381434\pi\) | |||||||
\(978\) | −25.6147 | −0.819069 | ||||||||
\(979\) | −23.6480 | −0.755794 | ||||||||
\(980\) | 20.7938 | 0.664233 | ||||||||
\(981\) | −10.3590 | −0.330739 | ||||||||
\(982\) | 3.53482 | 0.112801 | ||||||||
\(983\) | 24.8512 | 0.792631 | 0.396315 | − | 0.918114i | \(-0.370289\pi\) | ||||
0.396315 | + | 0.918114i | \(0.370289\pi\) | |||||||
\(984\) | 5.66064 | 0.180455 | ||||||||
\(985\) | 17.1590 | 0.546730 | ||||||||
\(986\) | 40.7244 | 1.29693 | ||||||||
\(987\) | −0.608145 | −0.0193575 | ||||||||
\(988\) | −16.0929 | −0.511984 | ||||||||
\(989\) | 0.107210 | 0.00340908 | ||||||||
\(990\) | −18.8536 | −0.599207 | ||||||||
\(991\) | −2.89525 | −0.0919706 | −0.0459853 | − | 0.998942i | \(-0.514643\pi\) | ||||
−0.0459853 | + | 0.998942i | \(0.514643\pi\) | |||||||
\(992\) | 0.393455 | 0.0124922 | ||||||||
\(993\) | −34.2464 | −1.08678 | ||||||||
\(994\) | 0.398479 | 0.0126390 | ||||||||
\(995\) | −68.4758 | −2.17083 | ||||||||
\(996\) | 22.4470 | 0.711260 | ||||||||
\(997\) | 46.6409 | 1.47713 | 0.738565 | − | 0.674182i | \(-0.235504\pi\) | ||||
0.738565 | + | 0.674182i | \(0.235504\pi\) | |||||||
\(998\) | −0.943200 | −0.0298565 | ||||||||
\(999\) | 55.5759 | 1.75834 |
(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 | 1502.2.a.g.1.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.g.1.3 | ✓ | 16 | 1.1 | even | 1 | trivial |