Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −3.11880 | −1.80064 | −0.900320 | − | 0.435229i | \(-0.856667\pi\) | ||||
−0.900320 | + | 0.435229i | \(0.856667\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.57138 | 0.702741 | 0.351370 | − | 0.936237i | \(-0.385716\pi\) | ||||
0.351370 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(6\) | 3.11880 | 1.27324 | ||||||||
\(7\) | 2.57640 | 0.973786 | 0.486893 | − | 0.873462i | \(-0.338130\pi\) | ||||
0.486893 | + | 0.873462i | \(0.338130\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.72691 | 2.24230 | ||||||||
\(10\) | −1.57138 | −0.496913 | ||||||||
\(11\) | −2.27747 | −0.686682 | −0.343341 | − | 0.939211i | \(-0.611559\pi\) | ||||
−0.343341 | + | 0.939211i | \(0.611559\pi\) | |||||||
\(12\) | −3.11880 | −0.900320 | ||||||||
\(13\) | 0.272260 | 0.0755115 | 0.0377557 | − | 0.999287i | \(-0.487979\pi\) | ||||
0.0377557 | + | 0.999287i | \(0.487979\pi\) | |||||||
\(14\) | −2.57640 | −0.688571 | ||||||||
\(15\) | −4.90081 | −1.26538 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.49514 | 0.847695 | 0.423847 | − | 0.905734i | \(-0.360679\pi\) | ||||
0.423847 | + | 0.905734i | \(0.360679\pi\) | |||||||
\(18\) | −6.72691 | −1.58555 | ||||||||
\(19\) | 3.02570 | 0.694144 | 0.347072 | − | 0.937839i | \(-0.387176\pi\) | ||||
0.347072 | + | 0.937839i | \(0.387176\pi\) | |||||||
\(20\) | 1.57138 | 0.351370 | ||||||||
\(21\) | −8.03526 | −1.75344 | ||||||||
\(22\) | 2.27747 | 0.485557 | ||||||||
\(23\) | 1.09989 | 0.229344 | 0.114672 | − | 0.993403i | \(-0.463418\pi\) | ||||
0.114672 | + | 0.993403i | \(0.463418\pi\) | |||||||
\(24\) | 3.11880 | 0.636622 | ||||||||
\(25\) | −2.53078 | −0.506155 | ||||||||
\(26\) | −0.272260 | −0.0533947 | ||||||||
\(27\) | −11.6235 | −2.23694 | ||||||||
\(28\) | 2.57640 | 0.486893 | ||||||||
\(29\) | −7.94298 | −1.47497 | −0.737487 | − | 0.675362i | \(-0.763988\pi\) | ||||
−0.737487 | + | 0.675362i | \(0.763988\pi\) | |||||||
\(30\) | 4.90081 | 0.894761 | ||||||||
\(31\) | 6.65335 | 1.19498 | 0.597489 | − | 0.801877i | \(-0.296165\pi\) | ||||
0.597489 | + | 0.801877i | \(0.296165\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.10296 | 1.23647 | ||||||||
\(34\) | −3.49514 | −0.599411 | ||||||||
\(35\) | 4.04849 | 0.684319 | ||||||||
\(36\) | 6.72691 | 1.12115 | ||||||||
\(37\) | −10.2457 | −1.68437 | −0.842187 | − | 0.539185i | \(-0.818732\pi\) | ||||
−0.842187 | + | 0.539185i | \(0.818732\pi\) | |||||||
\(38\) | −3.02570 | −0.490834 | ||||||||
\(39\) | −0.849126 | −0.135969 | ||||||||
\(40\) | −1.57138 | −0.248456 | ||||||||
\(41\) | −7.55369 | −1.17969 | −0.589844 | − | 0.807517i | \(-0.700811\pi\) | ||||
−0.589844 | + | 0.807517i | \(0.700811\pi\) | |||||||
\(42\) | 8.03526 | 1.23987 | ||||||||
\(43\) | −9.00970 | −1.37397 | −0.686983 | − | 0.726673i | \(-0.741065\pi\) | ||||
−0.686983 | + | 0.726673i | \(0.741065\pi\) | |||||||
\(44\) | −2.27747 | −0.343341 | ||||||||
\(45\) | 10.5705 | 1.57576 | ||||||||
\(46\) | −1.09989 | −0.162171 | ||||||||
\(47\) | 11.7619 | 1.71565 | 0.857823 | − | 0.513945i | \(-0.171817\pi\) | ||||
0.857823 | + | 0.513945i | \(0.171817\pi\) | |||||||
\(48\) | −3.11880 | −0.450160 | ||||||||
\(49\) | −0.362182 | −0.0517403 | ||||||||
\(50\) | 2.53078 | 0.357906 | ||||||||
\(51\) | −10.9006 | −1.52639 | ||||||||
\(52\) | 0.272260 | 0.0377557 | ||||||||
\(53\) | −9.15701 | −1.25781 | −0.628906 | − | 0.777481i | \(-0.716497\pi\) | ||||
−0.628906 | + | 0.777481i | \(0.716497\pi\) | |||||||
\(54\) | 11.6235 | 1.58176 | ||||||||
\(55\) | −3.57875 | −0.482559 | ||||||||
\(56\) | −2.57640 | −0.344285 | ||||||||
\(57\) | −9.43656 | −1.24990 | ||||||||
\(58\) | 7.94298 | 1.04296 | ||||||||
\(59\) | −10.0195 | −1.30443 | −0.652213 | − | 0.758036i | \(-0.726159\pi\) | ||||
−0.652213 | + | 0.758036i | \(0.726159\pi\) | |||||||
\(60\) | −4.90081 | −0.632691 | ||||||||
\(61\) | −5.73379 | −0.734137 | −0.367068 | − | 0.930194i | \(-0.619638\pi\) | ||||
−0.367068 | + | 0.930194i | \(0.619638\pi\) | |||||||
\(62\) | −6.65335 | −0.844976 | ||||||||
\(63\) | 17.3312 | 2.18352 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.427824 | 0.0530650 | ||||||||
\(66\) | −7.10296 | −0.874314 | ||||||||
\(67\) | −2.90990 | −0.355501 | −0.177750 | − | 0.984076i | \(-0.556882\pi\) | ||||
−0.177750 | + | 0.984076i | \(0.556882\pi\) | |||||||
\(68\) | 3.49514 | 0.423847 | ||||||||
\(69\) | −3.43035 | −0.412966 | ||||||||
\(70\) | −4.04849 | −0.483887 | ||||||||
\(71\) | −10.4554 | −1.24083 | −0.620413 | − | 0.784275i | \(-0.713035\pi\) | ||||
−0.620413 | + | 0.784275i | \(0.713035\pi\) | |||||||
\(72\) | −6.72691 | −0.792774 | ||||||||
\(73\) | 2.02729 | 0.237276 | 0.118638 | − | 0.992938i | \(-0.462147\pi\) | ||||
0.118638 | + | 0.992938i | \(0.462147\pi\) | |||||||
\(74\) | 10.2457 | 1.19103 | ||||||||
\(75\) | 7.89299 | 0.911404 | ||||||||
\(76\) | 3.02570 | 0.347072 | ||||||||
\(77\) | −5.86765 | −0.668681 | ||||||||
\(78\) | 0.849126 | 0.0961446 | ||||||||
\(79\) | 15.4765 | 1.74124 | 0.870619 | − | 0.491957i | \(-0.163718\pi\) | ||||
0.870619 | + | 0.491957i | \(0.163718\pi\) | |||||||
\(80\) | 1.57138 | 0.175685 | ||||||||
\(81\) | 16.0706 | 1.78562 | ||||||||
\(82\) | 7.55369 | 0.834165 | ||||||||
\(83\) | 11.0624 | 1.21426 | 0.607128 | − | 0.794604i | \(-0.292321\pi\) | ||||
0.607128 | + | 0.794604i | \(0.292321\pi\) | |||||||
\(84\) | −8.03526 | −0.876719 | ||||||||
\(85\) | 5.49217 | 0.595710 | ||||||||
\(86\) | 9.00970 | 0.971541 | ||||||||
\(87\) | 24.7726 | 2.65590 | ||||||||
\(88\) | 2.27747 | 0.242779 | ||||||||
\(89\) | −9.06665 | −0.961062 | −0.480531 | − | 0.876978i | \(-0.659556\pi\) | ||||
−0.480531 | + | 0.876978i | \(0.659556\pi\) | |||||||
\(90\) | −10.5705 | −1.11423 | ||||||||
\(91\) | 0.701451 | 0.0735320 | ||||||||
\(92\) | 1.09989 | 0.114672 | ||||||||
\(93\) | −20.7505 | −2.15172 | ||||||||
\(94\) | −11.7619 | −1.21314 | ||||||||
\(95\) | 4.75452 | 0.487803 | ||||||||
\(96\) | 3.11880 | 0.318311 | ||||||||
\(97\) | −9.97049 | −1.01235 | −0.506175 | − | 0.862431i | \(-0.668941\pi\) | ||||
−0.506175 | + | 0.862431i | \(0.668941\pi\) | |||||||
\(98\) | 0.362182 | 0.0365859 | ||||||||
\(99\) | −15.3203 | −1.53975 | ||||||||
\(100\) | −2.53078 | −0.253078 | ||||||||
\(101\) | 1.94659 | 0.193693 | 0.0968463 | − | 0.995299i | \(-0.469124\pi\) | ||||
0.0968463 | + | 0.995299i | \(0.469124\pi\) | |||||||
\(102\) | 10.9006 | 1.07932 | ||||||||
\(103\) | 14.7599 | 1.45434 | 0.727168 | − | 0.686459i | \(-0.240836\pi\) | ||||
0.727168 | + | 0.686459i | \(0.240836\pi\) | |||||||
\(104\) | −0.272260 | −0.0266973 | ||||||||
\(105\) | −12.6264 | −1.23221 | ||||||||
\(106\) | 9.15701 | 0.889407 | ||||||||
\(107\) | −8.76868 | −0.847701 | −0.423850 | − | 0.905732i | \(-0.639322\pi\) | ||||
−0.423850 | + | 0.905732i | \(0.639322\pi\) | |||||||
\(108\) | −11.6235 | −1.11847 | ||||||||
\(109\) | 16.3775 | 1.56868 | 0.784341 | − | 0.620331i | \(-0.213002\pi\) | ||||
0.784341 | + | 0.620331i | \(0.213002\pi\) | |||||||
\(110\) | 3.57875 | 0.341221 | ||||||||
\(111\) | 31.9541 | 3.03295 | ||||||||
\(112\) | 2.57640 | 0.243447 | ||||||||
\(113\) | 8.31720 | 0.782416 | 0.391208 | − | 0.920302i | \(-0.372057\pi\) | ||||
0.391208 | + | 0.920302i | \(0.372057\pi\) | |||||||
\(114\) | 9.43656 | 0.883815 | ||||||||
\(115\) | 1.72835 | 0.161169 | ||||||||
\(116\) | −7.94298 | −0.737487 | ||||||||
\(117\) | 1.83147 | 0.169320 | ||||||||
\(118\) | 10.0195 | 0.922368 | ||||||||
\(119\) | 9.00485 | 0.825474 | ||||||||
\(120\) | 4.90081 | 0.447380 | ||||||||
\(121\) | −5.81315 | −0.528468 | ||||||||
\(122\) | 5.73379 | 0.519113 | ||||||||
\(123\) | 23.5584 | 2.12419 | ||||||||
\(124\) | 6.65335 | 0.597489 | ||||||||
\(125\) | −11.8337 | −1.05844 | ||||||||
\(126\) | −17.3312 | −1.54398 | ||||||||
\(127\) | 10.5055 | 0.932211 | 0.466106 | − | 0.884729i | \(-0.345657\pi\) | ||||
0.466106 | + | 0.884729i | \(0.345657\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 28.0994 | 2.47402 | ||||||||
\(130\) | −0.427824 | −0.0375226 | ||||||||
\(131\) | 9.40784 | 0.821967 | 0.410983 | − | 0.911643i | \(-0.365185\pi\) | ||||
0.410983 | + | 0.911643i | \(0.365185\pi\) | |||||||
\(132\) | 7.10296 | 0.618233 | ||||||||
\(133\) | 7.79541 | 0.675948 | ||||||||
\(134\) | 2.90990 | 0.251377 | ||||||||
\(135\) | −18.2649 | −1.57199 | ||||||||
\(136\) | −3.49514 | −0.299705 | ||||||||
\(137\) | 2.24860 | 0.192111 | 0.0960554 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960554 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(138\) | 3.43035 | 0.292011 | ||||||||
\(139\) | −10.9625 | −0.929828 | −0.464914 | − | 0.885356i | \(-0.653915\pi\) | ||||
−0.464914 | + | 0.885356i | \(0.653915\pi\) | |||||||
\(140\) | 4.04849 | 0.342160 | ||||||||
\(141\) | −36.6829 | −3.08926 | ||||||||
\(142\) | 10.4554 | 0.877397 | ||||||||
\(143\) | −0.620064 | −0.0518523 | ||||||||
\(144\) | 6.72691 | 0.560576 | ||||||||
\(145\) | −12.4814 | −1.03652 | ||||||||
\(146\) | −2.02729 | −0.167780 | ||||||||
\(147\) | 1.12957 | 0.0931656 | ||||||||
\(148\) | −10.2457 | −0.842187 | ||||||||
\(149\) | −20.6707 | −1.69341 | −0.846703 | − | 0.532065i | \(-0.821416\pi\) | ||||
−0.846703 | + | 0.532065i | \(0.821416\pi\) | |||||||
\(150\) | −7.89299 | −0.644460 | ||||||||
\(151\) | −11.1355 | −0.906196 | −0.453098 | − | 0.891461i | \(-0.649681\pi\) | ||||
−0.453098 | + | 0.891461i | \(0.649681\pi\) | |||||||
\(152\) | −3.02570 | −0.245417 | ||||||||
\(153\) | 23.5115 | 1.90079 | ||||||||
\(154\) | 5.86765 | 0.472829 | ||||||||
\(155\) | 10.4549 | 0.839759 | ||||||||
\(156\) | −0.849126 | −0.0679845 | ||||||||
\(157\) | 15.4422 | 1.23242 | 0.616211 | − | 0.787581i | \(-0.288667\pi\) | ||||
0.616211 | + | 0.787581i | \(0.288667\pi\) | |||||||
\(158\) | −15.4765 | −1.23124 | ||||||||
\(159\) | 28.5589 | 2.26487 | ||||||||
\(160\) | −1.57138 | −0.124228 | ||||||||
\(161\) | 2.83377 | 0.223332 | ||||||||
\(162\) | −16.0706 | −1.26263 | ||||||||
\(163\) | −19.4247 | −1.52146 | −0.760728 | − | 0.649071i | \(-0.775158\pi\) | ||||
−0.760728 | + | 0.649071i | \(0.775158\pi\) | |||||||
\(164\) | −7.55369 | −0.589844 | ||||||||
\(165\) | 11.1614 | 0.868915 | ||||||||
\(166\) | −11.0624 | −0.858609 | ||||||||
\(167\) | −23.0061 | −1.78026 | −0.890132 | − | 0.455703i | \(-0.849388\pi\) | ||||
−0.890132 | + | 0.455703i | \(0.849388\pi\) | |||||||
\(168\) | 8.03526 | 0.619934 | ||||||||
\(169\) | −12.9259 | −0.994298 | ||||||||
\(170\) | −5.49217 | −0.421230 | ||||||||
\(171\) | 20.3536 | 1.55648 | ||||||||
\(172\) | −9.00970 | −0.686983 | ||||||||
\(173\) | 12.6019 | 0.958103 | 0.479051 | − | 0.877787i | \(-0.340981\pi\) | ||||
0.479051 | + | 0.877787i | \(0.340981\pi\) | |||||||
\(174\) | −24.7726 | −1.87800 | ||||||||
\(175\) | −6.52029 | −0.492887 | ||||||||
\(176\) | −2.27747 | −0.171670 | ||||||||
\(177\) | 31.2488 | 2.34880 | ||||||||
\(178\) | 9.06665 | 0.679574 | ||||||||
\(179\) | −4.22919 | −0.316105 | −0.158052 | − | 0.987431i | \(-0.550521\pi\) | ||||
−0.158052 | + | 0.987431i | \(0.550521\pi\) | |||||||
\(180\) | 10.5705 | 0.787879 | ||||||||
\(181\) | 8.10763 | 0.602635 | 0.301318 | − | 0.953524i | \(-0.402574\pi\) | ||||
0.301318 | + | 0.953524i | \(0.402574\pi\) | |||||||
\(182\) | −0.701451 | −0.0519950 | ||||||||
\(183\) | 17.8825 | 1.32192 | ||||||||
\(184\) | −1.09989 | −0.0810853 | ||||||||
\(185\) | −16.0998 | −1.18368 | ||||||||
\(186\) | 20.7505 | 1.52150 | ||||||||
\(187\) | −7.96005 | −0.582096 | ||||||||
\(188\) | 11.7619 | 0.857823 | ||||||||
\(189\) | −29.9467 | −2.17830 | ||||||||
\(190\) | −4.75452 | −0.344929 | ||||||||
\(191\) | 3.58116 | 0.259124 | 0.129562 | − | 0.991571i | \(-0.458643\pi\) | ||||
0.129562 | + | 0.991571i | \(0.458643\pi\) | |||||||
\(192\) | −3.11880 | −0.225080 | ||||||||
\(193\) | −4.77286 | −0.343558 | −0.171779 | − | 0.985135i | \(-0.554952\pi\) | ||||
−0.171779 | + | 0.985135i | \(0.554952\pi\) | |||||||
\(194\) | 9.97049 | 0.715840 | ||||||||
\(195\) | −1.33430 | −0.0955509 | ||||||||
\(196\) | −0.362182 | −0.0258701 | ||||||||
\(197\) | 3.42352 | 0.243915 | 0.121958 | − | 0.992535i | \(-0.461083\pi\) | ||||
0.121958 | + | 0.992535i | \(0.461083\pi\) | |||||||
\(198\) | 15.3203 | 1.08877 | ||||||||
\(199\) | 20.7544 | 1.47124 | 0.735619 | − | 0.677395i | \(-0.236891\pi\) | ||||
0.735619 | + | 0.677395i | \(0.236891\pi\) | |||||||
\(200\) | 2.53078 | 0.178953 | ||||||||
\(201\) | 9.07539 | 0.640129 | ||||||||
\(202\) | −1.94659 | −0.136961 | ||||||||
\(203\) | −20.4643 | −1.43631 | ||||||||
\(204\) | −10.9006 | −0.763196 | ||||||||
\(205\) | −11.8697 | −0.829015 | ||||||||
\(206\) | −14.7599 | −1.02837 | ||||||||
\(207\) | 7.39889 | 0.514259 | ||||||||
\(208\) | 0.272260 | 0.0188779 | ||||||||
\(209\) | −6.89093 | −0.476656 | ||||||||
\(210\) | 12.6264 | 0.871306 | ||||||||
\(211\) | 17.2684 | 1.18881 | 0.594403 | − | 0.804167i | \(-0.297388\pi\) | ||||
0.594403 | + | 0.804167i | \(0.297388\pi\) | |||||||
\(212\) | −9.15701 | −0.628906 | ||||||||
\(213\) | 32.6083 | 2.23428 | ||||||||
\(214\) | 8.76868 | 0.599415 | ||||||||
\(215\) | −14.1576 | −0.965542 | ||||||||
\(216\) | 11.6235 | 0.790878 | ||||||||
\(217\) | 17.1417 | 1.16365 | ||||||||
\(218\) | −16.3775 | −1.10923 | ||||||||
\(219\) | −6.32270 | −0.427249 | ||||||||
\(220\) | −3.57875 | −0.241280 | ||||||||
\(221\) | 0.951587 | 0.0640107 | ||||||||
\(222\) | −31.9541 | −2.14462 | ||||||||
\(223\) | 19.1328 | 1.28123 | 0.640613 | − | 0.767864i | \(-0.278680\pi\) | ||||
0.640613 | + | 0.767864i | \(0.278680\pi\) | |||||||
\(224\) | −2.57640 | −0.172143 | ||||||||
\(225\) | −17.0243 | −1.13495 | ||||||||
\(226\) | −8.31720 | −0.553252 | ||||||||
\(227\) | −9.58723 | −0.636327 | −0.318163 | − | 0.948036i | \(-0.603066\pi\) | ||||
−0.318163 | + | 0.948036i | \(0.603066\pi\) | |||||||
\(228\) | −9.43656 | −0.624952 | ||||||||
\(229\) | −15.4499 | −1.02096 | −0.510478 | − | 0.859891i | \(-0.670532\pi\) | ||||
−0.510478 | + | 0.859891i | \(0.670532\pi\) | |||||||
\(230\) | −1.72835 | −0.113964 | ||||||||
\(231\) | 18.3000 | 1.20405 | ||||||||
\(232\) | 7.94298 | 0.521482 | ||||||||
\(233\) | 12.3262 | 0.807513 | 0.403757 | − | 0.914866i | \(-0.367704\pi\) | ||||
0.403757 | + | 0.914866i | \(0.367704\pi\) | |||||||
\(234\) | −1.83147 | −0.119727 | ||||||||
\(235\) | 18.4823 | 1.20565 | ||||||||
\(236\) | −10.0195 | −0.652213 | ||||||||
\(237\) | −48.2680 | −3.13534 | ||||||||
\(238\) | −9.00485 | −0.583698 | ||||||||
\(239\) | −25.2462 | −1.63304 | −0.816520 | − | 0.577317i | \(-0.804100\pi\) | ||||
−0.816520 | + | 0.577317i | \(0.804100\pi\) | |||||||
\(240\) | −4.90081 | −0.316346 | ||||||||
\(241\) | −16.5545 | −1.06637 | −0.533184 | − | 0.845999i | \(-0.679005\pi\) | ||||
−0.533184 | + | 0.845999i | \(0.679005\pi\) | |||||||
\(242\) | 5.81315 | 0.373683 | ||||||||
\(243\) | −15.2505 | −0.978320 | ||||||||
\(244\) | −5.73379 | −0.367068 | ||||||||
\(245\) | −0.569124 | −0.0363600 | ||||||||
\(246\) | −23.5584 | −1.50203 | ||||||||
\(247\) | 0.823779 | 0.0524158 | ||||||||
\(248\) | −6.65335 | −0.422488 | ||||||||
\(249\) | −34.5014 | −2.18644 | ||||||||
\(250\) | 11.8337 | 0.748428 | ||||||||
\(251\) | 23.4094 | 1.47759 | 0.738793 | − | 0.673933i | \(-0.235396\pi\) | ||||
0.738793 | + | 0.673933i | \(0.235396\pi\) | |||||||
\(252\) | 17.3312 | 1.09176 | ||||||||
\(253\) | −2.50497 | −0.157486 | ||||||||
\(254\) | −10.5055 | −0.659173 | ||||||||
\(255\) | −17.1290 | −1.07266 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.81989 | −0.612548 | −0.306274 | − | 0.951943i | \(-0.599082\pi\) | ||||
−0.306274 | + | 0.951943i | \(0.599082\pi\) | |||||||
\(258\) | −28.0994 | −1.74939 | ||||||||
\(259\) | −26.3969 | −1.64022 | ||||||||
\(260\) | 0.427824 | 0.0265325 | ||||||||
\(261\) | −53.4317 | −3.30734 | ||||||||
\(262\) | −9.40784 | −0.581218 | ||||||||
\(263\) | −28.8537 | −1.77919 | −0.889596 | − | 0.456747i | \(-0.849014\pi\) | ||||
−0.889596 | + | 0.456747i | \(0.849014\pi\) | |||||||
\(264\) | −7.10296 | −0.437157 | ||||||||
\(265\) | −14.3891 | −0.883916 | ||||||||
\(266\) | −7.79541 | −0.477967 | ||||||||
\(267\) | 28.2770 | 1.73053 | ||||||||
\(268\) | −2.90990 | −0.177750 | ||||||||
\(269\) | −11.8656 | −0.723461 | −0.361731 | − | 0.932283i | \(-0.617814\pi\) | ||||
−0.361731 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(270\) | 18.2649 | 1.11156 | ||||||||
\(271\) | −4.36320 | −0.265046 | −0.132523 | − | 0.991180i | \(-0.542308\pi\) | ||||
−0.132523 | + | 0.991180i | \(0.542308\pi\) | |||||||
\(272\) | 3.49514 | 0.211924 | ||||||||
\(273\) | −2.18768 | −0.132405 | ||||||||
\(274\) | −2.24860 | −0.135843 | ||||||||
\(275\) | 5.76376 | 0.347568 | ||||||||
\(276\) | −3.43035 | −0.206483 | ||||||||
\(277\) | 18.1159 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(278\) | 10.9625 | 0.657488 | ||||||||
\(279\) | 44.7565 | 2.67950 | ||||||||
\(280\) | −4.04849 | −0.241943 | ||||||||
\(281\) | −28.0924 | −1.67585 | −0.837927 | − | 0.545782i | \(-0.816233\pi\) | ||||
−0.837927 | + | 0.545782i | \(0.816233\pi\) | |||||||
\(282\) | 36.6829 | 2.18444 | ||||||||
\(283\) | 13.8475 | 0.823148 | 0.411574 | − | 0.911376i | \(-0.364979\pi\) | ||||
0.411574 | + | 0.911376i | \(0.364979\pi\) | |||||||
\(284\) | −10.4554 | −0.620413 | ||||||||
\(285\) | −14.8284 | −0.878358 | ||||||||
\(286\) | 0.620064 | 0.0366651 | ||||||||
\(287\) | −19.4613 | −1.14876 | ||||||||
\(288\) | −6.72691 | −0.396387 | ||||||||
\(289\) | −4.78403 | −0.281414 | ||||||||
\(290\) | 12.4814 | 0.732933 | ||||||||
\(291\) | 31.0960 | 1.82288 | ||||||||
\(292\) | 2.02729 | 0.118638 | ||||||||
\(293\) | −15.2879 | −0.893129 | −0.446564 | − | 0.894751i | \(-0.647353\pi\) | ||||
−0.446564 | + | 0.894751i | \(0.647353\pi\) | |||||||
\(294\) | −1.12957 | −0.0658780 | ||||||||
\(295\) | −15.7444 | −0.916673 | ||||||||
\(296\) | 10.2457 | 0.595516 | ||||||||
\(297\) | 26.4721 | 1.53607 | ||||||||
\(298\) | 20.6707 | 1.19742 | ||||||||
\(299\) | 0.299458 | 0.0173181 | ||||||||
\(300\) | 7.89299 | 0.455702 | ||||||||
\(301\) | −23.2126 | −1.33795 | ||||||||
\(302\) | 11.1355 | 0.640777 | ||||||||
\(303\) | −6.07102 | −0.348771 | ||||||||
\(304\) | 3.02570 | 0.173536 | ||||||||
\(305\) | −9.00994 | −0.515908 | ||||||||
\(306\) | −23.5115 | −1.34406 | ||||||||
\(307\) | −18.5486 | −1.05862 | −0.529312 | − | 0.848427i | \(-0.677550\pi\) | ||||
−0.529312 | + | 0.848427i | \(0.677550\pi\) | |||||||
\(308\) | −5.86765 | −0.334341 | ||||||||
\(309\) | −46.0332 | −2.61874 | ||||||||
\(310\) | −10.4549 | −0.593799 | ||||||||
\(311\) | −15.5169 | −0.879880 | −0.439940 | − | 0.898027i | \(-0.645000\pi\) | ||||
−0.439940 | + | 0.898027i | \(0.645000\pi\) | |||||||
\(312\) | 0.849126 | 0.0480723 | ||||||||
\(313\) | −2.30508 | −0.130291 | −0.0651455 | − | 0.997876i | \(-0.520751\pi\) | ||||
−0.0651455 | + | 0.997876i | \(0.520751\pi\) | |||||||
\(314\) | −15.4422 | −0.871454 | ||||||||
\(315\) | 27.2338 | 1.53445 | ||||||||
\(316\) | 15.4765 | 0.870619 | ||||||||
\(317\) | 11.3746 | 0.638864 | 0.319432 | − | 0.947609i | \(-0.396508\pi\) | ||||
0.319432 | + | 0.947609i | \(0.396508\pi\) | |||||||
\(318\) | −28.5589 | −1.60150 | ||||||||
\(319\) | 18.0899 | 1.01284 | ||||||||
\(320\) | 1.57138 | 0.0878426 | ||||||||
\(321\) | 27.3478 | 1.52640 | ||||||||
\(322\) | −2.83377 | −0.157920 | ||||||||
\(323\) | 10.5752 | 0.588422 | ||||||||
\(324\) | 16.0706 | 0.892811 | ||||||||
\(325\) | −0.689030 | −0.0382205 | ||||||||
\(326\) | 19.4247 | 1.07583 | ||||||||
\(327\) | −51.0782 | −2.82463 | ||||||||
\(328\) | 7.55369 | 0.417083 | ||||||||
\(329\) | 30.3032 | 1.67067 | ||||||||
\(330\) | −11.1614 | −0.614416 | ||||||||
\(331\) | −14.3485 | −0.788663 | −0.394332 | − | 0.918968i | \(-0.629024\pi\) | ||||
−0.394332 | + | 0.918968i | \(0.629024\pi\) | |||||||
\(332\) | 11.0624 | 0.607128 | ||||||||
\(333\) | −68.9216 | −3.77688 | ||||||||
\(334\) | 23.0061 | 1.25884 | ||||||||
\(335\) | −4.57254 | −0.249825 | ||||||||
\(336\) | −8.03526 | −0.438360 | ||||||||
\(337\) | −33.0436 | −1.80000 | −0.900000 | − | 0.435890i | \(-0.856434\pi\) | ||||
−0.900000 | + | 0.435890i | \(0.856434\pi\) | |||||||
\(338\) | 12.9259 | 0.703075 | ||||||||
\(339\) | −25.9397 | −1.40885 | ||||||||
\(340\) | 5.49217 | 0.297855 | ||||||||
\(341\) | −15.1528 | −0.820569 | ||||||||
\(342\) | −20.3536 | −1.10060 | ||||||||
\(343\) | −18.9679 | −1.02417 | ||||||||
\(344\) | 9.00970 | 0.485770 | ||||||||
\(345\) | −5.39037 | −0.290208 | ||||||||
\(346\) | −12.6019 | −0.677481 | ||||||||
\(347\) | 1.25935 | 0.0676054 | 0.0338027 | − | 0.999429i | \(-0.489238\pi\) | ||||
0.0338027 | + | 0.999429i | \(0.489238\pi\) | |||||||
\(348\) | 24.7726 | 1.32795 | ||||||||
\(349\) | −5.46754 | −0.292671 | −0.146335 | − | 0.989235i | \(-0.546748\pi\) | ||||
−0.146335 | + | 0.989235i | \(0.546748\pi\) | |||||||
\(350\) | 6.52029 | 0.348524 | ||||||||
\(351\) | −3.16462 | −0.168915 | ||||||||
\(352\) | 2.27747 | 0.121389 | ||||||||
\(353\) | 28.6896 | 1.52699 | 0.763497 | − | 0.645811i | \(-0.223481\pi\) | ||||
0.763497 | + | 0.645811i | \(0.223481\pi\) | |||||||
\(354\) | −31.2488 | −1.66085 | ||||||||
\(355\) | −16.4293 | −0.871979 | ||||||||
\(356\) | −9.06665 | −0.480531 | ||||||||
\(357\) | −28.0843 | −1.48638 | ||||||||
\(358\) | 4.22919 | 0.223520 | ||||||||
\(359\) | 3.40290 | 0.179598 | 0.0897992 | − | 0.995960i | \(-0.471377\pi\) | ||||
0.0897992 | + | 0.995960i | \(0.471377\pi\) | |||||||
\(360\) | −10.5705 | −0.557115 | ||||||||
\(361\) | −9.84512 | −0.518164 | ||||||||
\(362\) | −8.10763 | −0.426127 | ||||||||
\(363\) | 18.1301 | 0.951581 | ||||||||
\(364\) | 0.701451 | 0.0367660 | ||||||||
\(365\) | 3.18563 | 0.166744 | ||||||||
\(366\) | −17.8825 | −0.934735 | ||||||||
\(367\) | −15.4357 | −0.805735 | −0.402868 | − | 0.915258i | \(-0.631987\pi\) | ||||
−0.402868 | + | 0.915258i | \(0.631987\pi\) | |||||||
\(368\) | 1.09989 | 0.0573360 | ||||||||
\(369\) | −50.8130 | −2.64522 | ||||||||
\(370\) | 16.0998 | 0.836987 | ||||||||
\(371\) | −23.5921 | −1.22484 | ||||||||
\(372\) | −20.7505 | −1.07586 | ||||||||
\(373\) | 31.0288 | 1.60661 | 0.803304 | − | 0.595569i | \(-0.203073\pi\) | ||||
0.803304 | + | 0.595569i | \(0.203073\pi\) | |||||||
\(374\) | 7.96005 | 0.411604 | ||||||||
\(375\) | 36.9069 | 1.90586 | ||||||||
\(376\) | −11.7619 | −0.606572 | ||||||||
\(377\) | −2.16256 | −0.111377 | ||||||||
\(378\) | 29.9467 | 1.54029 | ||||||||
\(379\) | 0.478507 | 0.0245793 | 0.0122896 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122896 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(380\) | 4.75452 | 0.243902 | ||||||||
\(381\) | −32.7645 | −1.67858 | ||||||||
\(382\) | −3.58116 | −0.183228 | ||||||||
\(383\) | −23.3872 | −1.19503 | −0.597515 | − | 0.801858i | \(-0.703845\pi\) | ||||
−0.597515 | + | 0.801858i | \(0.703845\pi\) | |||||||
\(384\) | 3.11880 | 0.159156 | ||||||||
\(385\) | −9.22029 | −0.469910 | ||||||||
\(386\) | 4.77286 | 0.242932 | ||||||||
\(387\) | −60.6074 | −3.08085 | ||||||||
\(388\) | −9.97049 | −0.506175 | ||||||||
\(389\) | 24.8239 | 1.25862 | 0.629310 | − | 0.777155i | \(-0.283338\pi\) | ||||
0.629310 | + | 0.777155i | \(0.283338\pi\) | |||||||
\(390\) | 1.33430 | 0.0675647 | ||||||||
\(391\) | 3.84428 | 0.194414 | ||||||||
\(392\) | 0.362182 | 0.0182929 | ||||||||
\(393\) | −29.3412 | −1.48007 | ||||||||
\(394\) | −3.42352 | −0.172474 | ||||||||
\(395\) | 24.3193 | 1.22364 | ||||||||
\(396\) | −15.3203 | −0.769874 | ||||||||
\(397\) | 28.6504 | 1.43792 | 0.718960 | − | 0.695051i | \(-0.244618\pi\) | ||||
0.718960 | + | 0.695051i | \(0.244618\pi\) | |||||||
\(398\) | −20.7544 | −1.04032 | ||||||||
\(399\) | −24.3123 | −1.21714 | ||||||||
\(400\) | −2.53078 | −0.126539 | ||||||||
\(401\) | 16.2022 | 0.809098 | 0.404549 | − | 0.914516i | \(-0.367429\pi\) | ||||
0.404549 | + | 0.914516i | \(0.367429\pi\) | |||||||
\(402\) | −9.07539 | −0.452639 | ||||||||
\(403\) | 1.81144 | 0.0902345 | ||||||||
\(404\) | 1.94659 | 0.0968463 | ||||||||
\(405\) | 25.2529 | 1.25483 | ||||||||
\(406\) | 20.4643 | 1.01562 | ||||||||
\(407\) | 23.3341 | 1.15663 | ||||||||
\(408\) | 10.9006 | 0.539661 | ||||||||
\(409\) | −1.44491 | −0.0714460 | −0.0357230 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357230 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(410\) | 11.8697 | 0.586202 | ||||||||
\(411\) | −7.01293 | −0.345923 | ||||||||
\(412\) | 14.7599 | 0.727168 | ||||||||
\(413\) | −25.8142 | −1.27023 | ||||||||
\(414\) | −7.39889 | −0.363636 | ||||||||
\(415\) | 17.3832 | 0.853308 | ||||||||
\(416\) | −0.272260 | −0.0133487 | ||||||||
\(417\) | 34.1899 | 1.67429 | ||||||||
\(418\) | 6.89093 | 0.337047 | ||||||||
\(419\) | −32.9567 | −1.61004 | −0.805021 | − | 0.593246i | \(-0.797846\pi\) | ||||
−0.805021 | + | 0.593246i | \(0.797846\pi\) | |||||||
\(420\) | −12.6264 | −0.616106 | ||||||||
\(421\) | 35.1379 | 1.71252 | 0.856259 | − | 0.516546i | \(-0.172783\pi\) | ||||
0.856259 | + | 0.516546i | \(0.172783\pi\) | |||||||
\(422\) | −17.2684 | −0.840613 | ||||||||
\(423\) | 79.1211 | 3.84700 | ||||||||
\(424\) | 9.15701 | 0.444704 | ||||||||
\(425\) | −8.84541 | −0.429065 | ||||||||
\(426\) | −32.6083 | −1.57988 | ||||||||
\(427\) | −14.7725 | −0.714892 | ||||||||
\(428\) | −8.76868 | −0.423850 | ||||||||
\(429\) | 1.93385 | 0.0933674 | ||||||||
\(430\) | 14.1576 | 0.682741 | ||||||||
\(431\) | 3.44601 | 0.165989 | 0.0829943 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829943 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(432\) | −11.6235 | −0.559235 | ||||||||
\(433\) | 22.6597 | 1.08896 | 0.544479 | − | 0.838775i | \(-0.316727\pi\) | ||||
0.544479 | + | 0.838775i | \(0.316727\pi\) | |||||||
\(434\) | −17.1417 | −0.822826 | ||||||||
\(435\) | 38.9270 | 1.86641 | ||||||||
\(436\) | 16.3775 | 0.784341 | ||||||||
\(437\) | 3.32796 | 0.159198 | ||||||||
\(438\) | 6.32270 | 0.302110 | ||||||||
\(439\) | −27.4365 | −1.30947 | −0.654736 | − | 0.755858i | \(-0.727220\pi\) | ||||
−0.654736 | + | 0.755858i | \(0.727220\pi\) | |||||||
\(440\) | 3.57875 | 0.170610 | ||||||||
\(441\) | −2.43637 | −0.116017 | ||||||||
\(442\) | −0.951587 | −0.0452624 | ||||||||
\(443\) | 10.7107 | 0.508879 | 0.254439 | − | 0.967089i | \(-0.418109\pi\) | ||||
0.254439 | + | 0.967089i | \(0.418109\pi\) | |||||||
\(444\) | 31.9541 | 1.51648 | ||||||||
\(445\) | −14.2471 | −0.675378 | ||||||||
\(446\) | −19.1328 | −0.905964 | ||||||||
\(447\) | 64.4677 | 3.04922 | ||||||||
\(448\) | 2.57640 | 0.121723 | ||||||||
\(449\) | −23.3758 | −1.10317 | −0.551586 | − | 0.834118i | \(-0.685977\pi\) | ||||
−0.551586 | + | 0.834118i | \(0.685977\pi\) | |||||||
\(450\) | 17.0243 | 0.802534 | ||||||||
\(451\) | 17.2033 | 0.810070 | ||||||||
\(452\) | 8.31720 | 0.391208 | ||||||||
\(453\) | 34.7295 | 1.63173 | ||||||||
\(454\) | 9.58723 | 0.449951 | ||||||||
\(455\) | 1.10224 | 0.0516739 | ||||||||
\(456\) | 9.43656 | 0.441907 | ||||||||
\(457\) | 11.1400 | 0.521108 | 0.260554 | − | 0.965459i | \(-0.416095\pi\) | ||||
0.260554 | + | 0.965459i | \(0.416095\pi\) | |||||||
\(458\) | 15.4499 | 0.721925 | ||||||||
\(459\) | −40.6257 | −1.89624 | ||||||||
\(460\) | 1.72835 | 0.0805847 | ||||||||
\(461\) | −22.5473 | −1.05013 | −0.525067 | − | 0.851061i | \(-0.675960\pi\) | ||||
−0.525067 | + | 0.851061i | \(0.675960\pi\) | |||||||
\(462\) | −18.3000 | −0.851395 | ||||||||
\(463\) | 21.6006 | 1.00387 | 0.501933 | − | 0.864907i | \(-0.332622\pi\) | ||||
0.501933 | + | 0.864907i | \(0.332622\pi\) | |||||||
\(464\) | −7.94298 | −0.368743 | ||||||||
\(465\) | −32.6068 | −1.51210 | ||||||||
\(466\) | −12.3262 | −0.570998 | ||||||||
\(467\) | 20.3649 | 0.942376 | 0.471188 | − | 0.882033i | \(-0.343825\pi\) | ||||
0.471188 | + | 0.882033i | \(0.343825\pi\) | |||||||
\(468\) | 1.83147 | 0.0846598 | ||||||||
\(469\) | −7.49705 | −0.346182 | ||||||||
\(470\) | −18.4823 | −0.852526 | ||||||||
\(471\) | −48.1611 | −2.21915 | ||||||||
\(472\) | 10.0195 | 0.461184 | ||||||||
\(473\) | 20.5193 | 0.943477 | ||||||||
\(474\) | 48.2680 | 2.21702 | ||||||||
\(475\) | −7.65738 | −0.351345 | ||||||||
\(476\) | 9.00485 | 0.412737 | ||||||||
\(477\) | −61.5984 | −2.82040 | ||||||||
\(478\) | 25.2462 | 1.15473 | ||||||||
\(479\) | −2.02262 | −0.0924158 | −0.0462079 | − | 0.998932i | \(-0.514714\pi\) | ||||
−0.0462079 | + | 0.998932i | \(0.514714\pi\) | |||||||
\(480\) | 4.90081 | 0.223690 | ||||||||
\(481\) | −2.78949 | −0.127190 | ||||||||
\(482\) | 16.5545 | 0.754037 | ||||||||
\(483\) | −8.83795 | −0.402140 | ||||||||
\(484\) | −5.81315 | −0.264234 | ||||||||
\(485\) | −15.6674 | −0.711420 | ||||||||
\(486\) | 15.2505 | 0.691777 | ||||||||
\(487\) | −27.9143 | −1.26492 | −0.632458 | − | 0.774595i | \(-0.717954\pi\) | ||||
−0.632458 | + | 0.774595i | \(0.717954\pi\) | |||||||
\(488\) | 5.73379 | 0.259556 | ||||||||
\(489\) | 60.5816 | 2.73959 | ||||||||
\(490\) | 0.569124 | 0.0257104 | ||||||||
\(491\) | 13.4879 | 0.608700 | 0.304350 | − | 0.952560i | \(-0.401561\pi\) | ||||
0.304350 | + | 0.952560i | \(0.401561\pi\) | |||||||
\(492\) | 23.5584 | 1.06210 | ||||||||
\(493\) | −27.7618 | −1.25033 | ||||||||
\(494\) | −0.823779 | −0.0370636 | ||||||||
\(495\) | −24.0740 | −1.08204 | ||||||||
\(496\) | 6.65335 | 0.298744 | ||||||||
\(497\) | −26.9372 | −1.20830 | ||||||||
\(498\) | 34.5014 | 1.54605 | ||||||||
\(499\) | −37.4379 | −1.67595 | −0.837975 | − | 0.545709i | \(-0.816260\pi\) | ||||
−0.837975 | + | 0.545709i | \(0.816260\pi\) | |||||||
\(500\) | −11.8337 | −0.529218 | ||||||||
\(501\) | 71.7514 | 3.20561 | ||||||||
\(502\) | −23.4094 | −1.04481 | ||||||||
\(503\) | 14.2126 | 0.633708 | 0.316854 | − | 0.948474i | \(-0.397373\pi\) | ||||
0.316854 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(504\) | −17.3312 | −0.771992 | ||||||||
\(505\) | 3.05882 | 0.136116 | ||||||||
\(506\) | 2.50497 | 0.111360 | ||||||||
\(507\) | 40.3132 | 1.79037 | ||||||||
\(508\) | 10.5055 | 0.466106 | ||||||||
\(509\) | −10.3235 | −0.457583 | −0.228791 | − | 0.973475i | \(-0.573477\pi\) | ||||
−0.228791 | + | 0.973475i | \(0.573477\pi\) | |||||||
\(510\) | 17.1290 | 0.758484 | ||||||||
\(511\) | 5.22310 | 0.231056 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −35.1692 | −1.55276 | ||||||||
\(514\) | 9.81989 | 0.433137 | ||||||||
\(515\) | 23.1934 | 1.02202 | ||||||||
\(516\) | 28.0994 | 1.23701 | ||||||||
\(517\) | −26.7873 | −1.17810 | ||||||||
\(518\) | 26.3969 | 1.15981 | ||||||||
\(519\) | −39.3027 | −1.72520 | ||||||||
\(520\) | −0.427824 | −0.0187613 | ||||||||
\(521\) | −7.17528 | −0.314355 | −0.157177 | − | 0.987570i | \(-0.550239\pi\) | ||||
−0.157177 | + | 0.987570i | \(0.550239\pi\) | |||||||
\(522\) | 53.4317 | 2.33864 | ||||||||
\(523\) | −10.1334 | −0.443104 | −0.221552 | − | 0.975149i | \(-0.571112\pi\) | ||||
−0.221552 | + | 0.975149i | \(0.571112\pi\) | |||||||
\(524\) | 9.40784 | 0.410983 | ||||||||
\(525\) | 20.3355 | 0.887512 | ||||||||
\(526\) | 28.8537 | 1.25808 | ||||||||
\(527\) | 23.2544 | 1.01298 | ||||||||
\(528\) | 7.10296 | 0.309117 | ||||||||
\(529\) | −21.7902 | −0.947401 | ||||||||
\(530\) | 14.3891 | 0.625023 | ||||||||
\(531\) | −67.4002 | −2.92492 | ||||||||
\(532\) | 7.79541 | 0.337974 | ||||||||
\(533\) | −2.05657 | −0.0890800 | ||||||||
\(534\) | −28.2770 | −1.22367 | ||||||||
\(535\) | −13.7789 | −0.595714 | ||||||||
\(536\) | 2.90990 | 0.125688 | ||||||||
\(537\) | 13.1900 | 0.569191 | ||||||||
\(538\) | 11.8656 | 0.511564 | ||||||||
\(539\) | 0.824857 | 0.0355291 | ||||||||
\(540\) | −18.2649 | −0.785995 | ||||||||
\(541\) | 39.3072 | 1.68995 | 0.844974 | − | 0.534808i | \(-0.179616\pi\) | ||||
0.844974 | + | 0.534808i | \(0.179616\pi\) | |||||||
\(542\) | 4.36320 | 0.187416 | ||||||||
\(543\) | −25.2861 | −1.08513 | ||||||||
\(544\) | −3.49514 | −0.149853 | ||||||||
\(545\) | 25.7352 | 1.10238 | ||||||||
\(546\) | 2.18768 | 0.0936242 | ||||||||
\(547\) | −27.9640 | −1.19565 | −0.597827 | − | 0.801625i | \(-0.703969\pi\) | ||||
−0.597827 | + | 0.801625i | \(0.703969\pi\) | |||||||
\(548\) | 2.24860 | 0.0960554 | ||||||||
\(549\) | −38.5707 | −1.64616 | ||||||||
\(550\) | −5.76376 | −0.245767 | ||||||||
\(551\) | −24.0331 | −1.02384 | ||||||||
\(552\) | 3.43035 | 0.146005 | ||||||||
\(553\) | 39.8735 | 1.69559 | ||||||||
\(554\) | −18.1159 | −0.769670 | ||||||||
\(555\) | 50.2120 | 2.13138 | ||||||||
\(556\) | −10.9625 | −0.464914 | ||||||||
\(557\) | 18.9856 | 0.804447 | 0.402224 | − | 0.915541i | \(-0.368237\pi\) | ||||
0.402224 | + | 0.915541i | \(0.368237\pi\) | |||||||
\(558\) | −44.7565 | −1.89469 | ||||||||
\(559\) | −2.45298 | −0.103750 | ||||||||
\(560\) | 4.04849 | 0.171080 | ||||||||
\(561\) | 24.8258 | 1.04815 | ||||||||
\(562\) | 28.0924 | 1.18501 | ||||||||
\(563\) | 39.5150 | 1.66536 | 0.832679 | − | 0.553756i | \(-0.186806\pi\) | ||||
0.832679 | + | 0.553756i | \(0.186806\pi\) | |||||||
\(564\) | −36.6829 | −1.54463 | ||||||||
\(565\) | 13.0694 | 0.549836 | ||||||||
\(566\) | −13.8475 | −0.582054 | ||||||||
\(567\) | 41.4042 | 1.73881 | ||||||||
\(568\) | 10.4554 | 0.438698 | ||||||||
\(569\) | −17.9652 | −0.753141 | −0.376571 | − | 0.926388i | \(-0.622897\pi\) | ||||
−0.376571 | + | 0.926388i | \(0.622897\pi\) | |||||||
\(570\) | 14.8284 | 0.621093 | ||||||||
\(571\) | 3.03513 | 0.127016 | 0.0635082 | − | 0.997981i | \(-0.479771\pi\) | ||||
0.0635082 | + | 0.997981i | \(0.479771\pi\) | |||||||
\(572\) | −0.620064 | −0.0259262 | ||||||||
\(573\) | −11.1689 | −0.466588 | ||||||||
\(574\) | 19.4613 | 0.812299 | ||||||||
\(575\) | −2.78359 | −0.116084 | ||||||||
\(576\) | 6.72691 | 0.280288 | ||||||||
\(577\) | 2.82364 | 0.117550 | 0.0587749 | − | 0.998271i | \(-0.481281\pi\) | ||||
0.0587749 | + | 0.998271i | \(0.481281\pi\) | |||||||
\(578\) | 4.78403 | 0.198989 | ||||||||
\(579\) | 14.8856 | 0.618625 | ||||||||
\(580\) | −12.4814 | −0.518262 | ||||||||
\(581\) | 28.5011 | 1.18243 | ||||||||
\(582\) | −31.0960 | −1.28897 | ||||||||
\(583\) | 20.8548 | 0.863716 | ||||||||
\(584\) | −2.02729 | −0.0838898 | ||||||||
\(585\) | 2.87793 | 0.118988 | ||||||||
\(586\) | 15.2879 | 0.631537 | ||||||||
\(587\) | −25.2865 | −1.04369 | −0.521843 | − | 0.853041i | \(-0.674755\pi\) | ||||
−0.521843 | + | 0.853041i | \(0.674755\pi\) | |||||||
\(588\) | 1.12957 | 0.0465828 | ||||||||
\(589\) | 20.1311 | 0.829486 | ||||||||
\(590\) | 15.7444 | 0.648186 | ||||||||
\(591\) | −10.6773 | −0.439204 | ||||||||
\(592\) | −10.2457 | −0.421094 | ||||||||
\(593\) | 0.413543 | 0.0169822 | 0.00849109 | − | 0.999964i | \(-0.497297\pi\) | ||||
0.00849109 | + | 0.999964i | \(0.497297\pi\) | |||||||
\(594\) | −26.4721 | −1.08616 | ||||||||
\(595\) | 14.1500 | 0.580094 | ||||||||
\(596\) | −20.6707 | −0.846703 | ||||||||
\(597\) | −64.7287 | −2.64917 | ||||||||
\(598\) | −0.299458 | −0.0122457 | ||||||||
\(599\) | 10.4742 | 0.427965 | 0.213982 | − | 0.976838i | \(-0.431356\pi\) | ||||
0.213982 | + | 0.976838i | \(0.431356\pi\) | |||||||
\(600\) | −7.89299 | −0.322230 | ||||||||
\(601\) | 34.2647 | 1.39769 | 0.698844 | − | 0.715274i | \(-0.253698\pi\) | ||||
0.698844 | + | 0.715274i | \(0.253698\pi\) | |||||||
\(602\) | 23.2126 | 0.946073 | ||||||||
\(603\) | −19.5746 | −0.797140 | ||||||||
\(604\) | −11.1355 | −0.453098 | ||||||||
\(605\) | −9.13465 | −0.371376 | ||||||||
\(606\) | 6.07102 | 0.246618 | ||||||||
\(607\) | 4.29781 | 0.174443 | 0.0872213 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872213 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(608\) | −3.02570 | −0.122708 | ||||||||
\(609\) | 63.8239 | 2.58628 | ||||||||
\(610\) | 9.00994 | 0.364802 | ||||||||
\(611\) | 3.20229 | 0.129551 | ||||||||
\(612\) | 23.5115 | 0.950395 | ||||||||
\(613\) | −36.4900 | −1.47382 | −0.736908 | − | 0.675993i | \(-0.763715\pi\) | ||||
−0.736908 | + | 0.675993i | \(0.763715\pi\) | |||||||
\(614\) | 18.5486 | 0.748561 | ||||||||
\(615\) | 37.0192 | 1.49276 | ||||||||
\(616\) | 5.86765 | 0.236415 | ||||||||
\(617\) | −9.12631 | −0.367411 | −0.183706 | − | 0.982981i | \(-0.558809\pi\) | ||||
−0.183706 | + | 0.982981i | \(0.558809\pi\) | |||||||
\(618\) | 46.0332 | 1.85173 | ||||||||
\(619\) | 31.1512 | 1.25207 | 0.626035 | − | 0.779795i | \(-0.284677\pi\) | ||||
0.626035 | + | 0.779795i | \(0.284677\pi\) | |||||||
\(620\) | 10.4549 | 0.419880 | ||||||||
\(621\) | −12.7846 | −0.513029 | ||||||||
\(622\) | 15.5169 | 0.622169 | ||||||||
\(623\) | −23.3593 | −0.935869 | ||||||||
\(624\) | −0.849126 | −0.0339922 | ||||||||
\(625\) | −5.94128 | −0.237651 | ||||||||
\(626\) | 2.30508 | 0.0921297 | ||||||||
\(627\) | 21.4914 | 0.858286 | ||||||||
\(628\) | 15.4422 | 0.616211 | ||||||||
\(629\) | −35.8099 | −1.42784 | ||||||||
\(630\) | −27.2338 | −1.08502 | ||||||||
\(631\) | −27.4566 | −1.09303 | −0.546515 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546515 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(632\) | −15.4765 | −0.615621 | ||||||||
\(633\) | −53.8567 | −2.14061 | ||||||||
\(634\) | −11.3746 | −0.451745 | ||||||||
\(635\) | 16.5081 | 0.655103 | ||||||||
\(636\) | 28.5589 | 1.13243 | ||||||||
\(637\) | −0.0986078 | −0.00390698 | ||||||||
\(638\) | −18.0899 | −0.716184 | ||||||||
\(639\) | −70.3325 | −2.78231 | ||||||||
\(640\) | −1.57138 | −0.0621141 | ||||||||
\(641\) | −9.93186 | −0.392285 | −0.196142 | − | 0.980575i | \(-0.562841\pi\) | ||||
−0.196142 | + | 0.980575i | \(0.562841\pi\) | |||||||
\(642\) | −27.3478 | −1.07933 | ||||||||
\(643\) | 30.8635 | 1.21714 | 0.608569 | − | 0.793501i | \(-0.291744\pi\) | ||||
0.608569 | + | 0.793501i | \(0.291744\pi\) | |||||||
\(644\) | 2.83377 | 0.111666 | ||||||||
\(645\) | 44.1548 | 1.73859 | ||||||||
\(646\) | −10.5752 | −0.416077 | ||||||||
\(647\) | −13.1275 | −0.516096 | −0.258048 | − | 0.966132i | \(-0.583079\pi\) | ||||
−0.258048 | + | 0.966132i | \(0.583079\pi\) | |||||||
\(648\) | −16.0706 | −0.631313 | ||||||||
\(649\) | 22.8190 | 0.895725 | ||||||||
\(650\) | 0.689030 | 0.0270260 | ||||||||
\(651\) | −53.4614 | −2.09532 | ||||||||
\(652\) | −19.4247 | −0.760728 | ||||||||
\(653\) | −5.48671 | −0.214711 | −0.107356 | − | 0.994221i | \(-0.534238\pi\) | ||||
−0.107356 | + | 0.994221i | \(0.534238\pi\) | |||||||
\(654\) | 51.0782 | 1.99731 | ||||||||
\(655\) | 14.7833 | 0.577630 | ||||||||
\(656\) | −7.55369 | −0.294922 | ||||||||
\(657\) | 13.6374 | 0.532045 | ||||||||
\(658\) | −30.3032 | −1.18134 | ||||||||
\(659\) | −30.1775 | −1.17555 | −0.587774 | − | 0.809025i | \(-0.699996\pi\) | ||||
−0.587774 | + | 0.809025i | \(0.699996\pi\) | |||||||
\(660\) | 11.1614 | 0.434458 | ||||||||
\(661\) | −18.5785 | −0.722620 | −0.361310 | − | 0.932446i | \(-0.617670\pi\) | ||||
−0.361310 | + | 0.932446i | \(0.617670\pi\) | |||||||
\(662\) | 14.3485 | 0.557669 | ||||||||
\(663\) | −2.96781 | −0.115260 | ||||||||
\(664\) | −11.0624 | −0.429305 | ||||||||
\(665\) | 12.2495 | 0.475016 | ||||||||
\(666\) | 68.9216 | 2.67066 | ||||||||
\(667\) | −8.73644 | −0.338276 | ||||||||
\(668\) | −23.0061 | −0.890132 | ||||||||
\(669\) | −59.6713 | −2.30703 | ||||||||
\(670\) | 4.57254 | 0.176653 | ||||||||
\(671\) | 13.0585 | 0.504118 | ||||||||
\(672\) | 8.03526 | 0.309967 | ||||||||
\(673\) | 40.9287 | 1.57768 | 0.788842 | − | 0.614596i | \(-0.210681\pi\) | ||||
0.788842 | + | 0.614596i | \(0.210681\pi\) | |||||||
\(674\) | 33.0436 | 1.27279 | ||||||||
\(675\) | 29.4165 | 1.13224 | ||||||||
\(676\) | −12.9259 | −0.497149 | ||||||||
\(677\) | −34.2455 | −1.31616 | −0.658080 | − | 0.752948i | \(-0.728631\pi\) | ||||
−0.658080 | + | 0.752948i | \(0.728631\pi\) | |||||||
\(678\) | 25.9397 | 0.996207 | ||||||||
\(679\) | −25.6879 | −0.985813 | ||||||||
\(680\) | −5.49217 | −0.210615 | ||||||||
\(681\) | 29.9007 | 1.14580 | ||||||||
\(682\) | 15.1528 | 0.580230 | ||||||||
\(683\) | −23.3249 | −0.892504 | −0.446252 | − | 0.894907i | \(-0.647241\pi\) | ||||
−0.446252 | + | 0.894907i | \(0.647241\pi\) | |||||||
\(684\) | 20.3536 | 0.778241 | ||||||||
\(685\) | 3.53340 | 0.135004 | ||||||||
\(686\) | 18.9679 | 0.724198 | ||||||||
\(687\) | 48.1851 | 1.83837 | ||||||||
\(688\) | −9.00970 | −0.343492 | ||||||||
\(689\) | −2.49309 | −0.0949792 | ||||||||
\(690\) | 5.39037 | 0.205208 | ||||||||
\(691\) | −18.0107 | −0.685161 | −0.342581 | − | 0.939488i | \(-0.611301\pi\) | ||||
−0.342581 | + | 0.939488i | \(0.611301\pi\) | |||||||
\(692\) | 12.6019 | 0.479051 | ||||||||
\(693\) | −39.4712 | −1.49939 | ||||||||
\(694\) | −1.25935 | −0.0478042 | ||||||||
\(695\) | −17.2262 | −0.653428 | ||||||||
\(696\) | −24.7726 | −0.939001 | ||||||||
\(697\) | −26.4012 | −1.00002 | ||||||||
\(698\) | 5.46754 | 0.206949 | ||||||||
\(699\) | −38.4428 | −1.45404 | ||||||||
\(700\) | −6.52029 | −0.246444 | ||||||||
\(701\) | −10.0324 | −0.378918 | −0.189459 | − | 0.981889i | \(-0.560673\pi\) | ||||
−0.189459 | + | 0.981889i | \(0.560673\pi\) | |||||||
\(702\) | 3.16462 | 0.119441 | ||||||||
\(703\) | −31.0003 | −1.16920 | ||||||||
\(704\) | −2.27747 | −0.0858352 | ||||||||
\(705\) | −57.6427 | −2.17095 | ||||||||
\(706\) | −28.6896 | −1.07975 | ||||||||
\(707\) | 5.01518 | 0.188615 | ||||||||
\(708\) | 31.2488 | 1.17440 | ||||||||
\(709\) | 41.6972 | 1.56597 | 0.782986 | − | 0.622039i | \(-0.213696\pi\) | ||||
0.782986 | + | 0.622039i | \(0.213696\pi\) | |||||||
\(710\) | 16.4293 | 0.616582 | ||||||||
\(711\) | 104.109 | 3.90439 | ||||||||
\(712\) | 9.06665 | 0.339787 | ||||||||
\(713\) | 7.31799 | 0.274061 | ||||||||
\(714\) | 28.0843 | 1.05103 | ||||||||
\(715\) | −0.974353 | −0.0364387 | ||||||||
\(716\) | −4.22919 | −0.158052 | ||||||||
\(717\) | 78.7378 | 2.94052 | ||||||||
\(718\) | −3.40290 | −0.126995 | ||||||||
\(719\) | −18.8814 | −0.704159 | −0.352080 | − | 0.935970i | \(-0.614525\pi\) | ||||
−0.352080 | + | 0.935970i | \(0.614525\pi\) | |||||||
\(720\) | 10.5705 | 0.393940 | ||||||||
\(721\) | 38.0274 | 1.41621 | ||||||||
\(722\) | 9.84512 | 0.366398 | ||||||||
\(723\) | 51.6302 | 1.92015 | ||||||||
\(724\) | 8.10763 | 0.301318 | ||||||||
\(725\) | 20.1019 | 0.746566 | ||||||||
\(726\) | −18.1301 | −0.672869 | ||||||||
\(727\) | 13.2857 | 0.492739 | 0.246369 | − | 0.969176i | \(-0.420762\pi\) | ||||
0.246369 | + | 0.969176i | \(0.420762\pi\) | |||||||
\(728\) | −0.701451 | −0.0259975 | ||||||||
\(729\) | −0.648523 | −0.0240194 | ||||||||
\(730\) | −3.18563 | −0.117906 | ||||||||
\(731\) | −31.4901 | −1.16470 | ||||||||
\(732\) | 17.8825 | 0.660958 | ||||||||
\(733\) | −3.01860 | −0.111495 | −0.0557473 | − | 0.998445i | \(-0.517754\pi\) | ||||
−0.0557473 | + | 0.998445i | \(0.517754\pi\) | |||||||
\(734\) | 15.4357 | 0.569741 | ||||||||
\(735\) | 1.77498 | 0.0654713 | ||||||||
\(736\) | −1.09989 | −0.0405427 | ||||||||
\(737\) | 6.62719 | 0.244116 | ||||||||
\(738\) | 50.8130 | 1.87045 | ||||||||
\(739\) | −35.8354 | −1.31822 | −0.659112 | − | 0.752044i | \(-0.729068\pi\) | ||||
−0.659112 | + | 0.752044i | \(0.729068\pi\) | |||||||
\(740\) | −16.0998 | −0.591839 | ||||||||
\(741\) | −2.56920 | −0.0943820 | ||||||||
\(742\) | 23.5921 | 0.866093 | ||||||||
\(743\) | 40.7369 | 1.49449 | 0.747245 | − | 0.664548i | \(-0.231376\pi\) | ||||
0.747245 | + | 0.664548i | \(0.231376\pi\) | |||||||
\(744\) | 20.7505 | 0.760749 | ||||||||
\(745\) | −32.4814 | −1.19003 | ||||||||
\(746\) | −31.0288 | −1.13604 | ||||||||
\(747\) | 74.4158 | 2.72273 | ||||||||
\(748\) | −7.96005 | −0.291048 | ||||||||
\(749\) | −22.5916 | −0.825479 | ||||||||
\(750\) | −36.9069 | −1.34765 | ||||||||
\(751\) | −36.7976 | −1.34276 | −0.671381 | − | 0.741112i | \(-0.734299\pi\) | ||||
−0.671381 | + | 0.741112i | \(0.734299\pi\) | |||||||
\(752\) | 11.7619 | 0.428911 | ||||||||
\(753\) | −73.0091 | −2.66060 | ||||||||
\(754\) | 2.16256 | 0.0787557 | ||||||||
\(755\) | −17.4981 | −0.636821 | ||||||||
\(756\) | −29.9467 | −1.08915 | ||||||||
\(757\) | 14.3783 | 0.522587 | 0.261293 | − | 0.965259i | \(-0.415851\pi\) | ||||
0.261293 | + | 0.965259i | \(0.415851\pi\) | |||||||
\(758\) | −0.478507 | −0.0173802 | ||||||||
\(759\) | 7.81251 | 0.283576 | ||||||||
\(760\) | −4.75452 | −0.172464 | ||||||||
\(761\) | −2.38705 | −0.0865306 | −0.0432653 | − | 0.999064i | \(-0.513776\pi\) | ||||
−0.0432653 | + | 0.999064i | \(0.513776\pi\) | |||||||
\(762\) | 32.7645 | 1.18693 | ||||||||
\(763\) | 42.1950 | 1.52756 | ||||||||
\(764\) | 3.58116 | 0.129562 | ||||||||
\(765\) | 36.9453 | 1.33576 | ||||||||
\(766\) | 23.3872 | 0.845014 | ||||||||
\(767\) | −2.72791 | −0.0984991 | ||||||||
\(768\) | −3.11880 | −0.112540 | ||||||||
\(769\) | 49.9662 | 1.80183 | 0.900913 | − | 0.434000i | \(-0.142898\pi\) | ||||
0.900913 | + | 0.434000i | \(0.142898\pi\) | |||||||
\(770\) | 9.22029 | 0.332276 | ||||||||
\(771\) | 30.6263 | 1.10298 | ||||||||
\(772\) | −4.77286 | −0.171779 | ||||||||
\(773\) | 50.3248 | 1.81006 | 0.905028 | − | 0.425352i | \(-0.139850\pi\) | ||||
0.905028 | + | 0.425352i | \(0.139850\pi\) | |||||||
\(774\) | 60.6074 | 2.17849 | ||||||||
\(775\) | −16.8381 | −0.604844 | ||||||||
\(776\) | 9.97049 | 0.357920 | ||||||||
\(777\) | 82.3265 | 2.95345 | ||||||||
\(778\) | −24.8239 | −0.889978 | ||||||||
\(779\) | −22.8552 | −0.818873 | ||||||||
\(780\) | −1.33430 | −0.0477755 | ||||||||
\(781\) | 23.8118 | 0.852053 | ||||||||
\(782\) | −3.84428 | −0.137471 | ||||||||
\(783\) | 92.3251 | 3.29943 | ||||||||
\(784\) | −0.362182 | −0.0129351 | ||||||||
\(785\) | 24.2655 | 0.866073 | ||||||||
\(786\) | 29.3412 | 1.04656 | ||||||||
\(787\) | −7.70296 | −0.274581 | −0.137290 | − | 0.990531i | \(-0.543839\pi\) | ||||
−0.137290 | + | 0.990531i | \(0.543839\pi\) | |||||||
\(788\) | 3.42352 | 0.121958 | ||||||||
\(789\) | 89.9888 | 3.20369 | ||||||||
\(790\) | −24.3193 | −0.865244 | ||||||||
\(791\) | 21.4284 | 0.761906 | ||||||||
\(792\) | 15.3203 | 0.544383 | ||||||||
\(793\) | −1.56108 | −0.0554357 | ||||||||
\(794\) | −28.6504 | −1.01676 | ||||||||
\(795\) | 44.8767 | 1.59161 | ||||||||
\(796\) | 20.7544 | 0.735619 | ||||||||
\(797\) | 5.59061 | 0.198030 | 0.0990148 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990148 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(798\) | 24.3123 | 0.860647 | ||||||||
\(799\) | 41.1093 | 1.45434 | ||||||||
\(800\) | 2.53078 | 0.0894765 | ||||||||
\(801\) | −60.9905 | −2.15499 | ||||||||
\(802\) | −16.2022 | −0.572118 | ||||||||
\(803\) | −4.61708 | −0.162933 | ||||||||
\(804\) | 9.07539 | 0.320064 | ||||||||
\(805\) | 4.45291 | 0.156944 | ||||||||
\(806\) | −1.81144 | −0.0638054 | ||||||||
\(807\) | 37.0066 | 1.30269 | ||||||||
\(808\) | −1.94659 | −0.0684807 | ||||||||
\(809\) | −19.8905 | −0.699311 | −0.349656 | − | 0.936878i | \(-0.613701\pi\) | ||||
−0.349656 | + | 0.936878i | \(0.613701\pi\) | |||||||
\(810\) | −25.2529 | −0.887298 | ||||||||
\(811\) | 45.3870 | 1.59375 | 0.796877 | − | 0.604141i | \(-0.206484\pi\) | ||||
0.796877 | + | 0.604141i | \(0.206484\pi\) | |||||||
\(812\) | −20.4643 | −0.718155 | ||||||||
\(813\) | 13.6080 | 0.477252 | ||||||||
\(814\) | −23.3341 | −0.817860 | ||||||||
\(815\) | −30.5234 | −1.06919 | ||||||||
\(816\) | −10.9006 | −0.381598 | ||||||||
\(817\) | −27.2607 | −0.953730 | ||||||||
\(818\) | 1.44491 | 0.0505199 | ||||||||
\(819\) | 4.71860 | 0.164881 | ||||||||
\(820\) | −11.8697 | −0.414507 | ||||||||
\(821\) | −44.4262 | −1.55048 | −0.775242 | − | 0.631664i | \(-0.782372\pi\) | ||||
−0.775242 | + | 0.631664i | \(0.782372\pi\) | |||||||
\(822\) | 7.01293 | 0.244604 | ||||||||
\(823\) | −41.5587 | −1.44864 | −0.724322 | − | 0.689462i | \(-0.757847\pi\) | ||||
−0.724322 | + | 0.689462i | \(0.757847\pi\) | |||||||
\(824\) | −14.7599 | −0.514186 | ||||||||
\(825\) | −17.9760 | −0.625844 | ||||||||
\(826\) | 25.8142 | 0.898189 | ||||||||
\(827\) | −34.3142 | −1.19322 | −0.596611 | − | 0.802530i | \(-0.703487\pi\) | ||||
−0.596611 | + | 0.802530i | \(0.703487\pi\) | |||||||
\(828\) | 7.39889 | 0.257129 | ||||||||
\(829\) | 23.7097 | 0.823472 | 0.411736 | − | 0.911303i | \(-0.364923\pi\) | ||||
0.411736 | + | 0.911303i | \(0.364923\pi\) | |||||||
\(830\) | −17.3832 | −0.603380 | ||||||||
\(831\) | −56.4998 | −1.95996 | ||||||||
\(832\) | 0.272260 | 0.00943893 | ||||||||
\(833\) | −1.26587 | −0.0438600 | ||||||||
\(834\) | −34.1899 | −1.18390 | ||||||||
\(835\) | −36.1512 | −1.25106 | ||||||||
\(836\) | −6.89093 | −0.238328 | ||||||||
\(837\) | −77.3351 | −2.67309 | ||||||||
\(838\) | 32.9567 | 1.13847 | ||||||||
\(839\) | −14.8177 | −0.511564 | −0.255782 | − | 0.966735i | \(-0.582333\pi\) | ||||
−0.255782 | + | 0.966735i | \(0.582333\pi\) | |||||||
\(840\) | 12.6264 | 0.435653 | ||||||||
\(841\) | 34.0909 | 1.17555 | ||||||||
\(842\) | −35.1379 | −1.21093 | ||||||||
\(843\) | 87.6147 | 3.01761 | ||||||||
\(844\) | 17.2684 | 0.594403 | ||||||||
\(845\) | −20.3114 | −0.698734 | ||||||||
\(846\) | −79.1211 | −2.72024 | ||||||||
\(847\) | −14.9770 | −0.514615 | ||||||||
\(848\) | −9.15701 | −0.314453 | ||||||||
\(849\) | −43.1876 | −1.48219 | ||||||||
\(850\) | 8.84541 | 0.303395 | ||||||||
\(851\) | −11.2691 | −0.386301 | ||||||||
\(852\) | 32.6083 | 1.11714 | ||||||||
\(853\) | −44.7255 | −1.53137 | −0.765686 | − | 0.643215i | \(-0.777600\pi\) | ||||
−0.765686 | + | 0.643215i | \(0.777600\pi\) | |||||||
\(854\) | 14.7725 | 0.505505 | ||||||||
\(855\) | 31.9832 | 1.09380 | ||||||||
\(856\) | 8.76868 | 0.299707 | ||||||||
\(857\) | −45.9644 | −1.57012 | −0.785058 | − | 0.619422i | \(-0.787367\pi\) | ||||
−0.785058 | + | 0.619422i | \(0.787367\pi\) | |||||||
\(858\) | −1.93385 | −0.0660207 | ||||||||
\(859\) | −20.9376 | −0.714382 | −0.357191 | − | 0.934031i | \(-0.616265\pi\) | ||||
−0.357191 | + | 0.934031i | \(0.616265\pi\) | |||||||
\(860\) | −14.1576 | −0.482771 | ||||||||
\(861\) | 60.6959 | 2.06851 | ||||||||
\(862\) | −3.44601 | −0.117372 | ||||||||
\(863\) | 27.1193 | 0.923152 | 0.461576 | − | 0.887101i | \(-0.347284\pi\) | ||||
0.461576 | + | 0.887101i | \(0.347284\pi\) | |||||||
\(864\) | 11.6235 | 0.395439 | ||||||||
\(865\) | 19.8023 | 0.673298 | ||||||||
\(866\) | −22.6597 | −0.770010 | ||||||||
\(867\) | 14.9204 | 0.506724 | ||||||||
\(868\) | 17.1417 | 0.581826 | ||||||||
\(869\) | −35.2471 | −1.19568 | ||||||||
\(870\) | −38.9270 | −1.31975 | ||||||||
\(871\) | −0.792250 | −0.0268444 | ||||||||
\(872\) | −16.3775 | −0.554613 | ||||||||
\(873\) | −67.0706 | −2.27000 | ||||||||
\(874\) | −3.32796 | −0.112570 | ||||||||
\(875\) | −30.4883 | −1.03069 | ||||||||
\(876\) | −6.32270 | −0.213624 | ||||||||
\(877\) | 41.1367 | 1.38909 | 0.694544 | − | 0.719451i | \(-0.255606\pi\) | ||||
0.694544 | + | 0.719451i | \(0.255606\pi\) | |||||||
\(878\) | 27.4365 | 0.925936 | ||||||||
\(879\) | 47.6799 | 1.60820 | ||||||||
\(880\) | −3.57875 | −0.120640 | ||||||||
\(881\) | 25.4253 | 0.856600 | 0.428300 | − | 0.903637i | \(-0.359113\pi\) | ||||
0.428300 | + | 0.903637i | \(0.359113\pi\) | |||||||
\(882\) | 2.43637 | 0.0820367 | ||||||||
\(883\) | −22.5281 | −0.758131 | −0.379066 | − | 0.925370i | \(-0.623755\pi\) | ||||
−0.379066 | + | 0.925370i | \(0.623755\pi\) | |||||||
\(884\) | 0.951587 | 0.0320053 | ||||||||
\(885\) | 49.1036 | 1.65060 | ||||||||
\(886\) | −10.7107 | −0.359832 | ||||||||
\(887\) | −10.1145 | −0.339612 | −0.169806 | − | 0.985477i | \(-0.554314\pi\) | ||||
−0.169806 | + | 0.985477i | \(0.554314\pi\) | |||||||
\(888\) | −31.9541 | −1.07231 | ||||||||
\(889\) | 27.0663 | 0.907774 | ||||||||
\(890\) | 14.2471 | 0.477564 | ||||||||
\(891\) | −36.6002 | −1.22615 | ||||||||
\(892\) | 19.1328 | 0.640613 | ||||||||
\(893\) | 35.5879 | 1.19090 | ||||||||
\(894\) | −64.4677 | −2.15612 | ||||||||
\(895\) | −6.64565 | −0.222140 | ||||||||
\(896\) | −2.57640 | −0.0860714 | ||||||||
\(897\) | −0.933949 | −0.0311836 | ||||||||
\(898\) | 23.3758 | 0.780060 | ||||||||
\(899\) | −52.8474 | −1.76256 | ||||||||
\(900\) | −17.0243 | −0.567477 | ||||||||
\(901\) | −32.0050 | −1.06624 | ||||||||
\(902\) | −17.2033 | −0.572806 | ||||||||
\(903\) | 72.3953 | 2.40916 | ||||||||
\(904\) | −8.31720 | −0.276626 | ||||||||
\(905\) | 12.7401 | 0.423496 | ||||||||
\(906\) | −34.7295 | −1.15381 | ||||||||
\(907\) | −7.25000 | −0.240732 | −0.120366 | − | 0.992730i | \(-0.538407\pi\) | ||||
−0.120366 | + | 0.992730i | \(0.538407\pi\) | |||||||
\(908\) | −9.58723 | −0.318163 | ||||||||
\(909\) | 13.0945 | 0.434318 | ||||||||
\(910\) | −1.10224 | −0.0365390 | ||||||||
\(911\) | 23.8429 | 0.789950 | 0.394975 | − | 0.918692i | \(-0.370753\pi\) | ||||
0.394975 | + | 0.918692i | \(0.370753\pi\) | |||||||
\(912\) | −9.43656 | −0.312476 | ||||||||
\(913\) | −25.1942 | −0.833808 | ||||||||
\(914\) | −11.1400 | −0.368479 | ||||||||
\(915\) | 28.1002 | 0.928964 | ||||||||
\(916\) | −15.4499 | −0.510478 | ||||||||
\(917\) | 24.2383 | 0.800420 | ||||||||
\(918\) | 40.6257 | 1.34085 | ||||||||
\(919\) | 52.3672 | 1.72743 | 0.863717 | − | 0.503977i | \(-0.168130\pi\) | ||||
0.863717 | + | 0.503977i | \(0.168130\pi\) | |||||||
\(920\) | −1.72835 | −0.0569820 | ||||||||
\(921\) | 57.8494 | 1.90620 | ||||||||
\(922\) | 22.5473 | 0.742557 | ||||||||
\(923\) | −2.84659 | −0.0936966 | ||||||||
\(924\) | 18.3000 | 0.602027 | ||||||||
\(925\) | 25.9295 | 0.852555 | ||||||||
\(926\) | −21.6006 | −0.709840 | ||||||||
\(927\) | 99.2885 | 3.26106 | ||||||||
\(928\) | 7.94298 | 0.260741 | ||||||||
\(929\) | −43.7670 | −1.43595 | −0.717974 | − | 0.696070i | \(-0.754930\pi\) | ||||
−0.717974 | + | 0.696070i | \(0.754930\pi\) | |||||||
\(930\) | 32.6068 | 1.06922 | ||||||||
\(931\) | −1.09585 | −0.0359152 | ||||||||
\(932\) | 12.3262 | 0.403757 | ||||||||
\(933\) | 48.3940 | 1.58435 | ||||||||
\(934\) | −20.3649 | −0.666360 | ||||||||
\(935\) | −12.5082 | −0.409063 | ||||||||
\(936\) | −1.83147 | −0.0598635 | ||||||||
\(937\) | 28.3684 | 0.926756 | 0.463378 | − | 0.886161i | \(-0.346637\pi\) | ||||
0.463378 | + | 0.886161i | \(0.346637\pi\) | |||||||
\(938\) | 7.49705 | 0.244787 | ||||||||
\(939\) | 7.18910 | 0.234607 | ||||||||
\(940\) | 18.4823 | 0.602827 | ||||||||
\(941\) | −22.7228 | −0.740743 | −0.370371 | − | 0.928884i | \(-0.620770\pi\) | ||||
−0.370371 | + | 0.928884i | \(0.620770\pi\) | |||||||
\(942\) | 48.1611 | 1.56917 | ||||||||
\(943\) | −8.30826 | −0.270554 | ||||||||
\(944\) | −10.0195 | −0.326106 | ||||||||
\(945\) | −47.0575 | −1.53078 | ||||||||
\(946\) | −20.5193 | −0.667139 | ||||||||
\(947\) | −35.7751 | −1.16253 | −0.581267 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581267 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(948\) | −48.2680 | −1.56767 | ||||||||
\(949\) | 0.551950 | 0.0179171 | ||||||||
\(950\) | 7.65738 | 0.248438 | ||||||||
\(951\) | −35.4752 | −1.15036 | ||||||||
\(952\) | −9.00485 | −0.291849 | ||||||||
\(953\) | 37.2108 | 1.20538 | 0.602688 | − | 0.797977i | \(-0.294097\pi\) | ||||
0.602688 | + | 0.797977i | \(0.294097\pi\) | |||||||
\(954\) | 61.5984 | 1.99432 | ||||||||
\(955\) | 5.62735 | 0.182097 | ||||||||
\(956\) | −25.2462 | −0.816520 | ||||||||
\(957\) | −56.4186 | −1.82376 | ||||||||
\(958\) | 2.02262 | 0.0653479 | ||||||||
\(959\) | 5.79329 | 0.187075 | ||||||||
\(960\) | −4.90081 | −0.158173 | ||||||||
\(961\) | 13.2671 | 0.427970 | ||||||||
\(962\) | 2.78949 | 0.0899366 | ||||||||
\(963\) | −58.9862 | −1.90080 | ||||||||
\(964\) | −16.5545 | −0.533184 | ||||||||
\(965\) | −7.49997 | −0.241432 | ||||||||
\(966\) | 8.83795 | 0.284356 | ||||||||
\(967\) | 39.4358 | 1.26817 | 0.634085 | − | 0.773263i | \(-0.281377\pi\) | ||||
0.634085 | + | 0.773263i | \(0.281377\pi\) | |||||||
\(968\) | 5.81315 | 0.186842 | ||||||||
\(969\) | −32.9821 | −1.05954 | ||||||||
\(970\) | 15.6674 | 0.503050 | ||||||||
\(971\) | 17.2603 | 0.553911 | 0.276955 | − | 0.960883i | \(-0.410675\pi\) | ||||
0.276955 | + | 0.960883i | \(0.410675\pi\) | |||||||
\(972\) | −15.2505 | −0.489160 | ||||||||
\(973\) | −28.2438 | −0.905454 | ||||||||
\(974\) | 27.9143 | 0.894431 | ||||||||
\(975\) | 2.14895 | 0.0688214 | ||||||||
\(976\) | −5.73379 | −0.183534 | ||||||||
\(977\) | −5.50737 | −0.176196 | −0.0880982 | − | 0.996112i | \(-0.528079\pi\) | ||||
−0.0880982 | + | 0.996112i | \(0.528079\pi\) | |||||||
\(978\) | −60.5816 | −1.93719 | ||||||||
\(979\) | 20.6490 | 0.659944 | ||||||||
\(980\) | −0.569124 | −0.0181800 | ||||||||
\(981\) | 110.170 | 3.51746 | ||||||||
\(982\) | −13.4879 | −0.430416 | ||||||||
\(983\) | 32.8004 | 1.04617 | 0.523086 | − | 0.852280i | \(-0.324781\pi\) | ||||
0.523086 | + | 0.852280i | \(0.324781\pi\) | |||||||
\(984\) | −23.5584 | −0.751016 | ||||||||
\(985\) | 5.37963 | 0.171409 | ||||||||
\(986\) | 27.7618 | 0.884115 | ||||||||
\(987\) | −94.5098 | −3.00828 | ||||||||
\(988\) | 0.823779 | 0.0262079 | ||||||||
\(989\) | −9.90972 | −0.315111 | ||||||||
\(990\) | 24.0740 | 0.765121 | ||||||||
\(991\) | −4.37186 | −0.138877 | −0.0694383 | − | 0.997586i | \(-0.522121\pi\) | ||||
−0.0694383 | + | 0.997586i | \(0.522121\pi\) | |||||||
\(992\) | −6.65335 | −0.211244 | ||||||||
\(993\) | 44.7500 | 1.42010 | ||||||||
\(994\) | 26.9372 | 0.854397 | ||||||||
\(995\) | 32.6129 | 1.03390 | ||||||||
\(996\) | −34.5014 | −1.09322 | ||||||||
\(997\) | −34.1601 | −1.08186 | −0.540931 | − | 0.841067i | \(-0.681928\pi\) | ||||
−0.540931 | + | 0.841067i | \(0.681928\pi\) | |||||||
\(998\) | 37.4379 | 1.18508 | ||||||||
\(999\) | 119.090 | 3.76785 |
(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 | 4006.2.a.g.1.2 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.2 | ✓ | 40 | 1.1 | even | 1 | trivial |