Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(1.98166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.98166 | 1.40125 | 0.700623 | − | 0.713532i | \(-0.252906\pi\) | ||||
0.700623 | + | 0.713532i | \(0.252906\pi\) | |||||||
\(3\) | 1.84905 | 1.06755 | 0.533775 | − | 0.845626i | \(-0.320773\pi\) | ||||
0.533775 | + | 0.845626i | \(0.320773\pi\) | |||||||
\(4\) | 1.92698 | 0.963488 | ||||||||
\(5\) | 2.60057 | 1.16301 | 0.581505 | − | 0.813543i | \(-0.302464\pi\) | ||||
0.581505 | + | 0.813543i | \(0.302464\pi\) | |||||||
\(6\) | 3.66419 | 1.49590 | ||||||||
\(7\) | −2.18138 | −0.824486 | −0.412243 | − | 0.911074i | \(-0.635254\pi\) | ||||
−0.412243 | + | 0.911074i | \(0.635254\pi\) | |||||||
\(8\) | −0.144707 | −0.0511617 | ||||||||
\(9\) | 0.418993 | 0.139664 | ||||||||
\(10\) | 5.15344 | 1.62966 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.56308 | 1.02857 | ||||||||
\(13\) | 0.444418 | 0.123259 | 0.0616297 | − | 0.998099i | \(-0.480370\pi\) | ||||
0.0616297 | + | 0.998099i | \(0.480370\pi\) | |||||||
\(14\) | −4.32276 | −1.15531 | ||||||||
\(15\) | 4.80859 | 1.24157 | ||||||||
\(16\) | −4.14071 | −1.03518 | ||||||||
\(17\) | 6.05961 | 1.46967 | 0.734836 | − | 0.678245i | \(-0.237259\pi\) | ||||
0.734836 | + | 0.678245i | \(0.237259\pi\) | |||||||
\(18\) | 0.830301 | 0.195704 | ||||||||
\(19\) | −1.92163 | −0.440852 | −0.220426 | − | 0.975404i | \(-0.570745\pi\) | ||||
−0.220426 | + | 0.975404i | \(0.570745\pi\) | |||||||
\(20\) | 5.01124 | 1.12055 | ||||||||
\(21\) | −4.03349 | −0.880180 | ||||||||
\(22\) | 1.98166 | 0.422491 | ||||||||
\(23\) | −9.17660 | −1.91345 | −0.956726 | − | 0.290990i | \(-0.906015\pi\) | ||||
−0.956726 | + | 0.290990i | \(0.906015\pi\) | |||||||
\(24\) | −0.267571 | −0.0546177 | ||||||||
\(25\) | 1.76296 | 0.352591 | ||||||||
\(26\) | 0.880686 | 0.172717 | ||||||||
\(27\) | −4.77242 | −0.918452 | ||||||||
\(28\) | −4.20348 | −0.794382 | ||||||||
\(29\) | 10.5575 | 1.96048 | 0.980238 | − | 0.197822i | \(-0.0633868\pi\) | ||||
0.980238 | + | 0.197822i | \(0.0633868\pi\) | |||||||
\(30\) | 9.52898 | 1.73975 | ||||||||
\(31\) | 3.13863 | 0.563715 | 0.281858 | − | 0.959456i | \(-0.409049\pi\) | ||||
0.281858 | + | 0.959456i | \(0.409049\pi\) | |||||||
\(32\) | −7.91607 | −1.39938 | ||||||||
\(33\) | 1.84905 | 0.321879 | ||||||||
\(34\) | 12.0081 | 2.05937 | ||||||||
\(35\) | −5.67284 | −0.958885 | ||||||||
\(36\) | 0.807389 | 0.134565 | ||||||||
\(37\) | −1.07395 | −0.176556 | −0.0882780 | − | 0.996096i | \(-0.528136\pi\) | ||||
−0.0882780 | + | 0.996096i | \(0.528136\pi\) | |||||||
\(38\) | −3.80802 | −0.617742 | ||||||||
\(39\) | 0.821752 | 0.131586 | ||||||||
\(40\) | −0.376321 | −0.0595015 | ||||||||
\(41\) | 1.30812 | 0.204294 | 0.102147 | − | 0.994769i | \(-0.467429\pi\) | ||||
0.102147 | + | 0.994769i | \(0.467429\pi\) | |||||||
\(42\) | −7.99301 | −1.23335 | ||||||||
\(43\) | −12.5238 | −1.90987 | −0.954934 | − | 0.296817i | \(-0.904075\pi\) | ||||
−0.954934 | + | 0.296817i | \(0.904075\pi\) | |||||||
\(44\) | 1.92698 | 0.290503 | ||||||||
\(45\) | 1.08962 | 0.162431 | ||||||||
\(46\) | −18.1849 | −2.68122 | ||||||||
\(47\) | −1.08337 | −0.158025 | −0.0790127 | − | 0.996874i | \(-0.525177\pi\) | ||||
−0.0790127 | + | 0.996874i | \(0.525177\pi\) | |||||||
\(48\) | −7.65639 | −1.10511 | ||||||||
\(49\) | −2.24156 | −0.320223 | ||||||||
\(50\) | 3.49358 | 0.494067 | ||||||||
\(51\) | 11.2045 | 1.56895 | ||||||||
\(52\) | 0.856384 | 0.118759 | ||||||||
\(53\) | −4.16225 | −0.571729 | −0.285864 | − | 0.958270i | \(-0.592281\pi\) | ||||
−0.285864 | + | 0.958270i | \(0.592281\pi\) | |||||||
\(54\) | −9.45731 | −1.28698 | ||||||||
\(55\) | 2.60057 | 0.350661 | ||||||||
\(56\) | 0.315662 | 0.0421821 | ||||||||
\(57\) | −3.55320 | −0.470632 | ||||||||
\(58\) | 20.9213 | 2.74711 | ||||||||
\(59\) | 8.24320 | 1.07317 | 0.536587 | − | 0.843845i | \(-0.319713\pi\) | ||||
0.536587 | + | 0.843845i | \(0.319713\pi\) | |||||||
\(60\) | 9.26603 | 1.19624 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 6.21970 | 0.789903 | ||||||||
\(63\) | −0.913984 | −0.115151 | ||||||||
\(64\) | −7.40554 | −0.925692 | ||||||||
\(65\) | 1.15574 | 0.143352 | ||||||||
\(66\) | 3.66419 | 0.451031 | ||||||||
\(67\) | −10.2859 | −1.25662 | −0.628309 | − | 0.777964i | \(-0.716253\pi\) | ||||
−0.628309 | + | 0.777964i | \(0.716253\pi\) | |||||||
\(68\) | 11.6767 | 1.41601 | ||||||||
\(69\) | −16.9680 | −2.04271 | ||||||||
\(70\) | −11.2416 | −1.34363 | ||||||||
\(71\) | −5.20811 | −0.618089 | −0.309044 | − | 0.951048i | \(-0.600009\pi\) | ||||
−0.309044 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(72\) | −0.0606312 | −0.00714545 | ||||||||
\(73\) | −0.283380 | −0.0331671 | −0.0165835 | − | 0.999862i | \(-0.505279\pi\) | ||||
−0.0165835 | + | 0.999862i | \(0.505279\pi\) | |||||||
\(74\) | −2.12820 | −0.247398 | ||||||||
\(75\) | 3.25980 | 0.376409 | ||||||||
\(76\) | −3.70294 | −0.424756 | ||||||||
\(77\) | −2.18138 | −0.248592 | ||||||||
\(78\) | 1.62843 | 0.184384 | ||||||||
\(79\) | 14.7634 | 1.66101 | 0.830505 | − | 0.557012i | \(-0.188052\pi\) | ||||
0.830505 | + | 0.557012i | \(0.188052\pi\) | |||||||
\(80\) | −10.7682 | −1.20392 | ||||||||
\(81\) | −10.0814 | −1.12016 | ||||||||
\(82\) | 2.59225 | 0.286266 | ||||||||
\(83\) | 15.2641 | 1.67546 | 0.837728 | − | 0.546088i | \(-0.183884\pi\) | ||||
0.837728 | + | 0.546088i | \(0.183884\pi\) | |||||||
\(84\) | −7.77245 | −0.848043 | ||||||||
\(85\) | 15.7584 | 1.70924 | ||||||||
\(86\) | −24.8180 | −2.67619 | ||||||||
\(87\) | 19.5213 | 2.09291 | ||||||||
\(88\) | −0.144707 | −0.0154258 | ||||||||
\(89\) | 16.3022 | 1.72803 | 0.864015 | − | 0.503466i | \(-0.167942\pi\) | ||||
0.864015 | + | 0.503466i | \(0.167942\pi\) | |||||||
\(90\) | 2.15925 | 0.227605 | ||||||||
\(91\) | −0.969447 | −0.101626 | ||||||||
\(92\) | −17.6831 | −1.84359 | ||||||||
\(93\) | 5.80349 | 0.601794 | ||||||||
\(94\) | −2.14687 | −0.221432 | ||||||||
\(95\) | −4.99733 | −0.512716 | ||||||||
\(96\) | −14.6372 | −1.49391 | ||||||||
\(97\) | 4.78591 | 0.485935 | 0.242968 | − | 0.970034i | \(-0.421879\pi\) | ||||
0.242968 | + | 0.970034i | \(0.421879\pi\) | |||||||
\(98\) | −4.44202 | −0.448712 | ||||||||
\(99\) | 0.418993 | 0.0421103 | ||||||||
\(100\) | 3.39718 | 0.339718 | ||||||||
\(101\) | 3.67611 | 0.365786 | 0.182893 | − | 0.983133i | \(-0.441454\pi\) | ||||
0.182893 | + | 0.983133i | \(0.441454\pi\) | |||||||
\(102\) | 22.2036 | 2.19848 | ||||||||
\(103\) | 8.87836 | 0.874811 | 0.437405 | − | 0.899264i | \(-0.355898\pi\) | ||||
0.437405 | + | 0.899264i | \(0.355898\pi\) | |||||||
\(104\) | −0.0643105 | −0.00630616 | ||||||||
\(105\) | −10.4894 | −1.02366 | ||||||||
\(106\) | −8.24816 | −0.801132 | ||||||||
\(107\) | 3.89110 | 0.376167 | 0.188083 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188083 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(108\) | −9.19634 | −0.884918 | ||||||||
\(109\) | −8.52962 | −0.816990 | −0.408495 | − | 0.912761i | \(-0.633946\pi\) | ||||
−0.408495 | + | 0.912761i | \(0.633946\pi\) | |||||||
\(110\) | 5.15344 | 0.491362 | ||||||||
\(111\) | −1.98579 | −0.188483 | ||||||||
\(112\) | 9.03249 | 0.853490 | ||||||||
\(113\) | 9.75866 | 0.918018 | 0.459009 | − | 0.888432i | \(-0.348205\pi\) | ||||
0.459009 | + | 0.888432i | \(0.348205\pi\) | |||||||
\(114\) | −7.04123 | −0.659471 | ||||||||
\(115\) | −23.8644 | −2.22536 | ||||||||
\(116\) | 20.3440 | 1.88890 | ||||||||
\(117\) | 0.186208 | 0.0172149 | ||||||||
\(118\) | 16.3352 | 1.50378 | ||||||||
\(119\) | −13.2183 | −1.21172 | ||||||||
\(120\) | −0.695836 | −0.0635209 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.98166 | −0.179411 | ||||||||
\(123\) | 2.41878 | 0.218094 | ||||||||
\(124\) | 6.04807 | 0.543133 | ||||||||
\(125\) | −8.41815 | −0.752942 | ||||||||
\(126\) | −1.81120 | −0.161355 | ||||||||
\(127\) | −20.5051 | −1.81953 | −0.909765 | − | 0.415123i | \(-0.863739\pi\) | ||||
−0.909765 | + | 0.415123i | \(0.863739\pi\) | |||||||
\(128\) | 1.15688 | 0.102255 | ||||||||
\(129\) | −23.1572 | −2.03888 | ||||||||
\(130\) | 2.29028 | 0.200871 | ||||||||
\(131\) | 13.2639 | 1.15887 | 0.579437 | − | 0.815017i | \(-0.303273\pi\) | ||||
0.579437 | + | 0.815017i | \(0.303273\pi\) | |||||||
\(132\) | 3.56308 | 0.310126 | ||||||||
\(133\) | 4.19181 | 0.363476 | ||||||||
\(134\) | −20.3831 | −1.76083 | ||||||||
\(135\) | −12.4110 | −1.06817 | ||||||||
\(136\) | −0.876869 | −0.0751909 | ||||||||
\(137\) | −9.00446 | −0.769303 | −0.384652 | − | 0.923062i | \(-0.625678\pi\) | ||||
−0.384652 | + | 0.923062i | \(0.625678\pi\) | |||||||
\(138\) | −33.6248 | −2.86233 | ||||||||
\(139\) | 15.4273 | 1.30852 | 0.654262 | − | 0.756268i | \(-0.272979\pi\) | ||||
0.654262 | + | 0.756268i | \(0.272979\pi\) | |||||||
\(140\) | −10.9314 | −0.923874 | ||||||||
\(141\) | −2.00320 | −0.168700 | ||||||||
\(142\) | −10.3207 | −0.866094 | ||||||||
\(143\) | 0.444418 | 0.0371641 | ||||||||
\(144\) | −1.73493 | −0.144577 | ||||||||
\(145\) | 27.4555 | 2.28005 | ||||||||
\(146\) | −0.561562 | −0.0464752 | ||||||||
\(147\) | −4.14477 | −0.341855 | ||||||||
\(148\) | −2.06947 | −0.170110 | ||||||||
\(149\) | 9.29642 | 0.761592 | 0.380796 | − | 0.924659i | \(-0.375650\pi\) | ||||
0.380796 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(150\) | 6.45981 | 0.527442 | ||||||||
\(151\) | −8.26936 | −0.672951 | −0.336475 | − | 0.941692i | \(-0.609235\pi\) | ||||
−0.336475 | + | 0.941692i | \(0.609235\pi\) | |||||||
\(152\) | 0.278074 | 0.0225547 | ||||||||
\(153\) | 2.53893 | 0.205261 | ||||||||
\(154\) | −4.32276 | −0.348338 | ||||||||
\(155\) | 8.16223 | 0.655606 | ||||||||
\(156\) | 1.58350 | 0.126781 | ||||||||
\(157\) | −13.5257 | −1.07946 | −0.539732 | − | 0.841837i | \(-0.681475\pi\) | ||||
−0.539732 | + | 0.841837i | \(0.681475\pi\) | |||||||
\(158\) | 29.2560 | 2.32748 | ||||||||
\(159\) | −7.69621 | −0.610349 | ||||||||
\(160\) | −20.5863 | −1.62749 | ||||||||
\(161\) | 20.0177 | 1.57761 | ||||||||
\(162\) | −19.9780 | −1.56962 | ||||||||
\(163\) | −12.9831 | −1.01692 | −0.508458 | − | 0.861087i | \(-0.669784\pi\) | ||||
−0.508458 | + | 0.861087i | \(0.669784\pi\) | |||||||
\(164\) | 2.52072 | 0.196835 | ||||||||
\(165\) | 4.80859 | 0.374348 | ||||||||
\(166\) | 30.2483 | 2.34772 | ||||||||
\(167\) | −21.3647 | −1.65325 | −0.826624 | − | 0.562755i | \(-0.809742\pi\) | ||||
−0.826624 | + | 0.562755i | \(0.809742\pi\) | |||||||
\(168\) | 0.583675 | 0.0450315 | ||||||||
\(169\) | −12.8025 | −0.984807 | ||||||||
\(170\) | 31.2279 | 2.39507 | ||||||||
\(171\) | −0.805149 | −0.0615713 | ||||||||
\(172\) | −24.1332 | −1.84014 | ||||||||
\(173\) | 13.8496 | 1.05297 | 0.526483 | − | 0.850186i | \(-0.323510\pi\) | ||||
0.526483 | + | 0.850186i | \(0.323510\pi\) | |||||||
\(174\) | 38.6847 | 2.93268 | ||||||||
\(175\) | −3.84569 | −0.290707 | ||||||||
\(176\) | −4.14071 | −0.312118 | ||||||||
\(177\) | 15.2421 | 1.14567 | ||||||||
\(178\) | 32.3054 | 2.42139 | ||||||||
\(179\) | −1.03648 | −0.0774700 | −0.0387350 | − | 0.999250i | \(-0.512333\pi\) | ||||
−0.0387350 | + | 0.999250i | \(0.512333\pi\) | |||||||
\(180\) | 2.09967 | 0.156500 | ||||||||
\(181\) | −13.2287 | −0.983281 | −0.491640 | − | 0.870798i | \(-0.663603\pi\) | ||||
−0.491640 | + | 0.870798i | \(0.663603\pi\) | |||||||
\(182\) | −1.92111 | −0.142402 | ||||||||
\(183\) | −1.84905 | −0.136686 | ||||||||
\(184\) | 1.32792 | 0.0978954 | ||||||||
\(185\) | −2.79288 | −0.205336 | ||||||||
\(186\) | 11.5006 | 0.843262 | ||||||||
\(187\) | 6.05961 | 0.443123 | ||||||||
\(188\) | −2.08762 | −0.152256 | ||||||||
\(189\) | 10.4105 | 0.757250 | ||||||||
\(190\) | −9.90302 | −0.718440 | ||||||||
\(191\) | −8.86840 | −0.641695 | −0.320848 | − | 0.947131i | \(-0.603968\pi\) | ||||
−0.320848 | + | 0.947131i | \(0.603968\pi\) | |||||||
\(192\) | −13.6932 | −0.988223 | ||||||||
\(193\) | 3.17960 | 0.228872 | 0.114436 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114436 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(194\) | 9.48404 | 0.680915 | ||||||||
\(195\) | 2.13702 | 0.153035 | ||||||||
\(196\) | −4.31944 | −0.308532 | ||||||||
\(197\) | 17.0357 | 1.21374 | 0.606871 | − | 0.794801i | \(-0.292425\pi\) | ||||
0.606871 | + | 0.794801i | \(0.292425\pi\) | |||||||
\(198\) | 0.830301 | 0.0590069 | ||||||||
\(199\) | 27.9216 | 1.97931 | 0.989656 | − | 0.143458i | \(-0.0458221\pi\) | ||||
0.989656 | + | 0.143458i | \(0.0458221\pi\) | |||||||
\(200\) | −0.255112 | −0.0180392 | ||||||||
\(201\) | −19.0191 | −1.34150 | ||||||||
\(202\) | 7.28480 | 0.512557 | ||||||||
\(203\) | −23.0299 | −1.61638 | ||||||||
\(204\) | 21.5909 | 1.51166 | ||||||||
\(205\) | 3.40185 | 0.237596 | ||||||||
\(206\) | 17.5939 | 1.22582 | ||||||||
\(207\) | −3.84493 | −0.267241 | ||||||||
\(208\) | −1.84021 | −0.127596 | ||||||||
\(209\) | −1.92163 | −0.132922 | ||||||||
\(210\) | −20.7864 | −1.43440 | ||||||||
\(211\) | 14.8812 | 1.02446 | 0.512232 | − | 0.858847i | \(-0.328819\pi\) | ||||
0.512232 | + | 0.858847i | \(0.328819\pi\) | |||||||
\(212\) | −8.02056 | −0.550854 | ||||||||
\(213\) | −9.63006 | −0.659841 | ||||||||
\(214\) | 7.71084 | 0.527102 | ||||||||
\(215\) | −32.5691 | −2.22120 | ||||||||
\(216\) | 0.690602 | 0.0469895 | ||||||||
\(217\) | −6.84656 | −0.464775 | ||||||||
\(218\) | −16.9028 | −1.14480 | ||||||||
\(219\) | −0.523984 | −0.0354076 | ||||||||
\(220\) | 5.01124 | 0.337857 | ||||||||
\(221\) | 2.69300 | 0.181151 | ||||||||
\(222\) | −3.93515 | −0.264110 | ||||||||
\(223\) | 24.3925 | 1.63344 | 0.816722 | − | 0.577032i | \(-0.195789\pi\) | ||||
0.816722 | + | 0.577032i | \(0.195789\pi\) | |||||||
\(224\) | 17.2680 | 1.15377 | ||||||||
\(225\) | 0.738666 | 0.0492444 | ||||||||
\(226\) | 19.3383 | 1.28637 | ||||||||
\(227\) | −4.57809 | −0.303859 | −0.151929 | − | 0.988391i | \(-0.548549\pi\) | ||||
−0.151929 | + | 0.988391i | \(0.548549\pi\) | |||||||
\(228\) | −6.84693 | −0.453449 | ||||||||
\(229\) | −16.3940 | −1.08335 | −0.541673 | − | 0.840589i | \(-0.682209\pi\) | ||||
−0.541673 | + | 0.840589i | \(0.682209\pi\) | |||||||
\(230\) | −47.2911 | −3.11828 | ||||||||
\(231\) | −4.03349 | −0.265384 | ||||||||
\(232\) | −1.52774 | −0.100301 | ||||||||
\(233\) | 10.0688 | 0.659626 | 0.329813 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329813 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(234\) | 0.369001 | 0.0241223 | ||||||||
\(235\) | −2.81737 | −0.183785 | ||||||||
\(236\) | 15.8845 | 1.03399 | ||||||||
\(237\) | 27.2982 | 1.77321 | ||||||||
\(238\) | −26.1943 | −1.69792 | ||||||||
\(239\) | 8.26608 | 0.534688 | 0.267344 | − | 0.963601i | \(-0.413854\pi\) | ||||
0.267344 | + | 0.963601i | \(0.413854\pi\) | |||||||
\(240\) | −19.9110 | −1.28525 | ||||||||
\(241\) | 1.52656 | 0.0983343 | 0.0491672 | − | 0.998791i | \(-0.484343\pi\) | ||||
0.0491672 | + | 0.998791i | \(0.484343\pi\) | |||||||
\(242\) | 1.98166 | 0.127386 | ||||||||
\(243\) | −4.32382 | −0.277373 | ||||||||
\(244\) | −1.92698 | −0.123362 | ||||||||
\(245\) | −5.82934 | −0.372423 | ||||||||
\(246\) | 4.79320 | 0.305603 | ||||||||
\(247\) | −0.854008 | −0.0543392 | ||||||||
\(248\) | −0.454182 | −0.0288406 | ||||||||
\(249\) | 28.2242 | 1.78863 | ||||||||
\(250\) | −16.6819 | −1.05506 | ||||||||
\(251\) | 21.1073 | 1.33228 | 0.666142 | − | 0.745825i | \(-0.267945\pi\) | ||||
0.666142 | + | 0.745825i | \(0.267945\pi\) | |||||||
\(252\) | −1.76123 | −0.110947 | ||||||||
\(253\) | −9.17660 | −0.576928 | ||||||||
\(254\) | −40.6341 | −2.54961 | ||||||||
\(255\) | 29.1382 | 1.82470 | ||||||||
\(256\) | 17.1036 | 1.06898 | ||||||||
\(257\) | 8.94976 | 0.558271 | 0.279135 | − | 0.960252i | \(-0.409952\pi\) | ||||
0.279135 | + | 0.960252i | \(0.409952\pi\) | |||||||
\(258\) | −45.8898 | −2.85697 | ||||||||
\(259\) | 2.34269 | 0.145568 | ||||||||
\(260\) | 2.22708 | 0.138118 | ||||||||
\(261\) | 4.42351 | 0.273808 | ||||||||
\(262\) | 26.2846 | 1.62387 | ||||||||
\(263\) | −29.0355 | −1.79041 | −0.895204 | − | 0.445657i | \(-0.852970\pi\) | ||||
−0.895204 | + | 0.445657i | \(0.852970\pi\) | |||||||
\(264\) | −0.267571 | −0.0164678 | ||||||||
\(265\) | −10.8242 | −0.664926 | ||||||||
\(266\) | 8.30675 | 0.509320 | ||||||||
\(267\) | 30.1436 | 1.84476 | ||||||||
\(268\) | −19.8206 | −1.21074 | ||||||||
\(269\) | −0.271779 | −0.0165706 | −0.00828532 | − | 0.999966i | \(-0.502637\pi\) | ||||
−0.00828532 | + | 0.999966i | \(0.502637\pi\) | |||||||
\(270\) | −24.5944 | −1.49677 | ||||||||
\(271\) | −9.91921 | −0.602549 | −0.301275 | − | 0.953537i | \(-0.597412\pi\) | ||||
−0.301275 | + | 0.953537i | \(0.597412\pi\) | |||||||
\(272\) | −25.0911 | −1.52137 | ||||||||
\(273\) | −1.79256 | −0.108491 | ||||||||
\(274\) | −17.8438 | −1.07798 | ||||||||
\(275\) | 1.76296 | 0.106310 | ||||||||
\(276\) | −32.6969 | −1.96812 | ||||||||
\(277\) | −2.47418 | −0.148659 | −0.0743295 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743295 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(278\) | 30.5716 | 1.83356 | ||||||||
\(279\) | 1.31506 | 0.0787308 | ||||||||
\(280\) | 0.820900 | 0.0490581 | ||||||||
\(281\) | −12.2927 | −0.733321 | −0.366660 | − | 0.930355i | \(-0.619499\pi\) | ||||
−0.366660 | + | 0.930355i | \(0.619499\pi\) | |||||||
\(282\) | −3.96967 | −0.236390 | ||||||||
\(283\) | 12.7133 | 0.755725 | 0.377862 | − | 0.925862i | \(-0.376659\pi\) | ||||
0.377862 | + | 0.925862i | \(0.376659\pi\) | |||||||
\(284\) | −10.0359 | −0.595521 | ||||||||
\(285\) | −9.24033 | −0.547350 | ||||||||
\(286\) | 0.880686 | 0.0520761 | ||||||||
\(287\) | −2.85351 | −0.168437 | ||||||||
\(288\) | −3.31678 | −0.195443 | ||||||||
\(289\) | 19.7189 | 1.15994 | ||||||||
\(290\) | 54.4074 | 3.19491 | ||||||||
\(291\) | 8.84939 | 0.518760 | ||||||||
\(292\) | −0.546066 | −0.0319561 | ||||||||
\(293\) | −10.1272 | −0.591637 | −0.295818 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295818 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(294\) | −8.21352 | −0.479022 | ||||||||
\(295\) | 21.4370 | 1.24811 | ||||||||
\(296\) | 0.155408 | 0.00903290 | ||||||||
\(297\) | −4.77242 | −0.276924 | ||||||||
\(298\) | 18.4223 | 1.06718 | ||||||||
\(299\) | −4.07825 | −0.235851 | ||||||||
\(300\) | 6.28156 | 0.362666 | ||||||||
\(301\) | 27.3193 | 1.57466 | ||||||||
\(302\) | −16.3871 | −0.942969 | ||||||||
\(303\) | 6.79731 | 0.390496 | ||||||||
\(304\) | 7.95692 | 0.456361 | ||||||||
\(305\) | −2.60057 | −0.148908 | ||||||||
\(306\) | 5.03130 | 0.287620 | ||||||||
\(307\) | −4.15427 | −0.237097 | −0.118548 | − | 0.992948i | \(-0.537824\pi\) | ||||
−0.118548 | + | 0.992948i | \(0.537824\pi\) | |||||||
\(308\) | −4.20348 | −0.239515 | ||||||||
\(309\) | 16.4165 | 0.933904 | ||||||||
\(310\) | 16.1748 | 0.918665 | ||||||||
\(311\) | 10.2275 | 0.579948 | 0.289974 | − | 0.957035i | \(-0.406353\pi\) | ||||
0.289974 | + | 0.957035i | \(0.406353\pi\) | |||||||
\(312\) | −0.118913 | −0.00673214 | ||||||||
\(313\) | −8.72686 | −0.493271 | −0.246636 | − | 0.969108i | \(-0.579325\pi\) | ||||
−0.246636 | + | 0.969108i | \(0.579325\pi\) | |||||||
\(314\) | −26.8033 | −1.51260 | ||||||||
\(315\) | −2.37688 | −0.133922 | ||||||||
\(316\) | 28.4487 | 1.60036 | ||||||||
\(317\) | −0.569591 | −0.0319914 | −0.0159957 | − | 0.999872i | \(-0.505092\pi\) | ||||
−0.0159957 | + | 0.999872i | \(0.505092\pi\) | |||||||
\(318\) | −15.2513 | −0.855249 | ||||||||
\(319\) | 10.5575 | 0.591106 | ||||||||
\(320\) | −19.2586 | −1.07659 | ||||||||
\(321\) | 7.19485 | 0.401577 | ||||||||
\(322\) | 39.6682 | 2.21062 | ||||||||
\(323\) | −11.6443 | −0.647908 | ||||||||
\(324\) | −19.4267 | −1.07926 | ||||||||
\(325\) | 0.783490 | 0.0434602 | ||||||||
\(326\) | −25.7281 | −1.42495 | ||||||||
\(327\) | −15.7717 | −0.872178 | ||||||||
\(328\) | −0.189294 | −0.0104520 | ||||||||
\(329\) | 2.36324 | 0.130290 | ||||||||
\(330\) | 9.52898 | 0.524553 | ||||||||
\(331\) | −20.0001 | −1.09930 | −0.549652 | − | 0.835394i | \(-0.685240\pi\) | ||||
−0.549652 | + | 0.835394i | \(0.685240\pi\) | |||||||
\(332\) | 29.4136 | 1.61428 | ||||||||
\(333\) | −0.449976 | −0.0246586 | ||||||||
\(334\) | −42.3375 | −2.31661 | ||||||||
\(335\) | −26.7491 | −1.46146 | ||||||||
\(336\) | 16.7015 | 0.911143 | ||||||||
\(337\) | 27.7992 | 1.51432 | 0.757161 | − | 0.653229i | \(-0.226586\pi\) | ||||
0.757161 | + | 0.653229i | \(0.226586\pi\) | |||||||
\(338\) | −25.3702 | −1.37996 | ||||||||
\(339\) | 18.0443 | 0.980030 | ||||||||
\(340\) | 30.3661 | 1.64684 | ||||||||
\(341\) | 3.13863 | 0.169966 | ||||||||
\(342\) | −1.59553 | −0.0862765 | ||||||||
\(343\) | 20.1594 | 1.08851 | ||||||||
\(344\) | 1.81229 | 0.0977121 | ||||||||
\(345\) | −44.1264 | −2.37569 | ||||||||
\(346\) | 27.4452 | 1.47546 | ||||||||
\(347\) | 14.0784 | 0.755770 | 0.377885 | − | 0.925853i | \(-0.376651\pi\) | ||||
0.377885 | + | 0.925853i | \(0.376651\pi\) | |||||||
\(348\) | 37.6172 | 2.01649 | ||||||||
\(349\) | 26.9981 | 1.44517 | 0.722586 | − | 0.691281i | \(-0.242953\pi\) | ||||
0.722586 | + | 0.691281i | \(0.242953\pi\) | |||||||
\(350\) | −7.62084 | −0.407351 | ||||||||
\(351\) | −2.12095 | −0.113208 | ||||||||
\(352\) | −7.91607 | −0.421928 | ||||||||
\(353\) | −7.06670 | −0.376122 | −0.188061 | − | 0.982157i | \(-0.560220\pi\) | ||||
−0.188061 | + | 0.982157i | \(0.560220\pi\) | |||||||
\(354\) | 30.2047 | 1.60536 | ||||||||
\(355\) | −13.5440 | −0.718843 | ||||||||
\(356\) | 31.4140 | 1.66494 | ||||||||
\(357\) | −24.4414 | −1.29358 | ||||||||
\(358\) | −2.05395 | −0.108554 | ||||||||
\(359\) | −1.11238 | −0.0587090 | −0.0293545 | − | 0.999569i | \(-0.509345\pi\) | ||||
−0.0293545 | + | 0.999569i | \(0.509345\pi\) | |||||||
\(360\) | −0.157676 | −0.00831023 | ||||||||
\(361\) | −15.3073 | −0.805649 | ||||||||
\(362\) | −26.2148 | −1.37782 | ||||||||
\(363\) | 1.84905 | 0.0970501 | ||||||||
\(364\) | −1.86810 | −0.0979151 | ||||||||
\(365\) | −0.736949 | −0.0385737 | ||||||||
\(366\) | −3.66419 | −0.191530 | ||||||||
\(367\) | −15.6511 | −0.816979 | −0.408489 | − | 0.912763i | \(-0.633944\pi\) | ||||
−0.408489 | + | 0.912763i | \(0.633944\pi\) | |||||||
\(368\) | 37.9977 | 1.98076 | ||||||||
\(369\) | 0.548092 | 0.0285325 | ||||||||
\(370\) | −5.53453 | −0.287727 | ||||||||
\(371\) | 9.07946 | 0.471382 | ||||||||
\(372\) | 11.1832 | 0.579822 | ||||||||
\(373\) | −8.11997 | −0.420436 | −0.210218 | − | 0.977655i | \(-0.567417\pi\) | ||||
−0.210218 | + | 0.977655i | \(0.567417\pi\) | |||||||
\(374\) | 12.0081 | 0.620924 | ||||||||
\(375\) | −15.5656 | −0.803804 | ||||||||
\(376\) | 0.156771 | 0.00808484 | ||||||||
\(377\) | 4.69194 | 0.241647 | ||||||||
\(378\) | 20.6300 | 1.06109 | ||||||||
\(379\) | 35.5452 | 1.82583 | 0.912917 | − | 0.408145i | \(-0.133824\pi\) | ||||
0.912917 | + | 0.408145i | \(0.133824\pi\) | |||||||
\(380\) | −9.62975 | −0.493996 | ||||||||
\(381\) | −37.9149 | −1.94244 | ||||||||
\(382\) | −17.5742 | −0.899172 | ||||||||
\(383\) | 25.4279 | 1.29931 | 0.649653 | − | 0.760231i | \(-0.274914\pi\) | ||||
0.649653 | + | 0.760231i | \(0.274914\pi\) | |||||||
\(384\) | 2.13914 | 0.109163 | ||||||||
\(385\) | −5.67284 | −0.289115 | ||||||||
\(386\) | 6.30088 | 0.320706 | ||||||||
\(387\) | −5.24740 | −0.266740 | ||||||||
\(388\) | 9.22233 | 0.468193 | ||||||||
\(389\) | −2.40965 | −0.122174 | −0.0610872 | − | 0.998132i | \(-0.519457\pi\) | ||||
−0.0610872 | + | 0.998132i | \(0.519457\pi\) | |||||||
\(390\) | 4.23485 | 0.214440 | ||||||||
\(391\) | −55.6066 | −2.81215 | ||||||||
\(392\) | 0.324370 | 0.0163832 | ||||||||
\(393\) | 24.5257 | 1.23716 | ||||||||
\(394\) | 33.7589 | 1.70075 | ||||||||
\(395\) | 38.3932 | 1.93177 | ||||||||
\(396\) | 0.807389 | 0.0405728 | ||||||||
\(397\) | 8.86157 | 0.444750 | 0.222375 | − | 0.974961i | \(-0.428619\pi\) | ||||
0.222375 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(398\) | 55.3312 | 2.77350 | ||||||||
\(399\) | 7.75088 | 0.388029 | ||||||||
\(400\) | −7.29990 | −0.364995 | ||||||||
\(401\) | −23.3978 | −1.16843 | −0.584214 | − | 0.811600i | \(-0.698597\pi\) | ||||
−0.584214 | + | 0.811600i | \(0.698597\pi\) | |||||||
\(402\) | −37.6894 | −1.87978 | ||||||||
\(403\) | 1.39487 | 0.0694832 | ||||||||
\(404\) | 7.08378 | 0.352431 | ||||||||
\(405\) | −26.2174 | −1.30275 | ||||||||
\(406\) | −45.6375 | −2.26495 | ||||||||
\(407\) | −1.07395 | −0.0532337 | ||||||||
\(408\) | −1.62138 | −0.0802700 | ||||||||
\(409\) | −18.4508 | −0.912336 | −0.456168 | − | 0.889894i | \(-0.650778\pi\) | ||||
−0.456168 | + | 0.889894i | \(0.650778\pi\) | |||||||
\(410\) | 6.74132 | 0.332930 | ||||||||
\(411\) | −16.6497 | −0.821270 | ||||||||
\(412\) | 17.1084 | 0.842870 | ||||||||
\(413\) | −17.9816 | −0.884816 | ||||||||
\(414\) | −7.61933 | −0.374470 | ||||||||
\(415\) | 39.6954 | 1.94857 | ||||||||
\(416\) | −3.51805 | −0.172486 | ||||||||
\(417\) | 28.5258 | 1.39692 | ||||||||
\(418\) | −3.80802 | −0.186256 | ||||||||
\(419\) | −22.7893 | −1.11333 | −0.556665 | − | 0.830737i | \(-0.687919\pi\) | ||||
−0.556665 | + | 0.830737i | \(0.687919\pi\) | |||||||
\(420\) | −20.2128 | −0.986283 | ||||||||
\(421\) | 16.9851 | 0.827802 | 0.413901 | − | 0.910322i | \(-0.364166\pi\) | ||||
0.413901 | + | 0.910322i | \(0.364166\pi\) | |||||||
\(422\) | 29.4895 | 1.43553 | ||||||||
\(423\) | −0.453923 | −0.0220705 | ||||||||
\(424\) | 0.602307 | 0.0292506 | ||||||||
\(425\) | 10.6828 | 0.518194 | ||||||||
\(426\) | −19.0835 | −0.924599 | ||||||||
\(427\) | 2.18138 | 0.105565 | ||||||||
\(428\) | 7.49806 | 0.362432 | ||||||||
\(429\) | 0.821752 | 0.0396746 | ||||||||
\(430\) | −64.5409 | −3.11244 | ||||||||
\(431\) | −26.8912 | −1.29531 | −0.647653 | − | 0.761936i | \(-0.724249\pi\) | ||||
−0.647653 | + | 0.761936i | \(0.724249\pi\) | |||||||
\(432\) | 19.7612 | 0.950762 | ||||||||
\(433\) | −4.94690 | −0.237733 | −0.118866 | − | 0.992910i | \(-0.537926\pi\) | ||||
−0.118866 | + | 0.992910i | \(0.537926\pi\) | |||||||
\(434\) | −13.5676 | −0.651264 | ||||||||
\(435\) | 50.7666 | 2.43407 | ||||||||
\(436\) | −16.4364 | −0.787160 | ||||||||
\(437\) | 17.6340 | 0.843550 | ||||||||
\(438\) | −1.03836 | −0.0496147 | ||||||||
\(439\) | −16.1331 | −0.769989 | −0.384995 | − | 0.922919i | \(-0.625797\pi\) | ||||
−0.384995 | + | 0.922919i | \(0.625797\pi\) | |||||||
\(440\) | −0.376321 | −0.0179404 | ||||||||
\(441\) | −0.939199 | −0.0447237 | ||||||||
\(442\) | 5.33662 | 0.253837 | ||||||||
\(443\) | 19.9786 | 0.949213 | 0.474607 | − | 0.880198i | \(-0.342590\pi\) | ||||
0.474607 | + | 0.880198i | \(0.342590\pi\) | |||||||
\(444\) | −3.82656 | −0.181601 | ||||||||
\(445\) | 42.3950 | 2.00972 | ||||||||
\(446\) | 48.3377 | 2.28886 | ||||||||
\(447\) | 17.1896 | 0.813038 | ||||||||
\(448\) | 16.1543 | 0.763220 | ||||||||
\(449\) | 3.49232 | 0.164813 | 0.0824064 | − | 0.996599i | \(-0.473739\pi\) | ||||
0.0824064 | + | 0.996599i | \(0.473739\pi\) | |||||||
\(450\) | 1.46378 | 0.0690035 | ||||||||
\(451\) | 1.30812 | 0.0615969 | ||||||||
\(452\) | 18.8047 | 0.884499 | ||||||||
\(453\) | −15.2905 | −0.718409 | ||||||||
\(454\) | −9.07222 | −0.425780 | ||||||||
\(455\) | −2.52111 | −0.118192 | ||||||||
\(456\) | 0.514172 | 0.0240783 | ||||||||
\(457\) | −8.64120 | −0.404218 | −0.202109 | − | 0.979363i | \(-0.564780\pi\) | ||||
−0.202109 | + | 0.979363i | \(0.564780\pi\) | |||||||
\(458\) | −32.4873 | −1.51803 | ||||||||
\(459\) | −28.9190 | −1.34982 | ||||||||
\(460\) | −45.9861 | −2.14411 | ||||||||
\(461\) | 3.04671 | 0.141899 | 0.0709497 | − | 0.997480i | \(-0.477397\pi\) | ||||
0.0709497 | + | 0.997480i | \(0.477397\pi\) | |||||||
\(462\) | −7.99301 | −0.371868 | ||||||||
\(463\) | −8.03359 | −0.373353 | −0.186676 | − | 0.982421i | \(-0.559772\pi\) | ||||
−0.186676 | + | 0.982421i | \(0.559772\pi\) | |||||||
\(464\) | −43.7155 | −2.02944 | ||||||||
\(465\) | 15.0924 | 0.699893 | ||||||||
\(466\) | 19.9528 | 0.924298 | ||||||||
\(467\) | 12.0195 | 0.556195 | 0.278098 | − | 0.960553i | \(-0.410296\pi\) | ||||
0.278098 | + | 0.960553i | \(0.410296\pi\) | |||||||
\(468\) | 0.358818 | 0.0165864 | ||||||||
\(469\) | 22.4374 | 1.03606 | ||||||||
\(470\) | −5.58307 | −0.257528 | ||||||||
\(471\) | −25.0096 | −1.15238 | ||||||||
\(472\) | −1.19285 | −0.0549054 | ||||||||
\(473\) | −12.5238 | −0.575847 | ||||||||
\(474\) | 54.0958 | 2.48470 | ||||||||
\(475\) | −3.38775 | −0.155441 | ||||||||
\(476\) | −25.4714 | −1.16748 | ||||||||
\(477\) | −1.74395 | −0.0798500 | ||||||||
\(478\) | 16.3806 | 0.749230 | ||||||||
\(479\) | −21.3120 | −0.973768 | −0.486884 | − | 0.873467i | \(-0.661867\pi\) | ||||
−0.486884 | + | 0.873467i | \(0.661867\pi\) | |||||||
\(480\) | −38.0651 | −1.73743 | ||||||||
\(481\) | −0.477282 | −0.0217622 | ||||||||
\(482\) | 3.02512 | 0.137791 | ||||||||
\(483\) | 37.0137 | 1.68418 | ||||||||
\(484\) | 1.92698 | 0.0875899 | ||||||||
\(485\) | 12.4461 | 0.565147 | ||||||||
\(486\) | −8.56835 | −0.388668 | ||||||||
\(487\) | −37.5771 | −1.70278 | −0.851391 | − | 0.524532i | \(-0.824240\pi\) | ||||
−0.851391 | + | 0.524532i | \(0.824240\pi\) | |||||||
\(488\) | 0.144707 | 0.00655058 | ||||||||
\(489\) | −24.0064 | −1.08561 | ||||||||
\(490\) | −11.5518 | −0.521856 | ||||||||
\(491\) | −34.9908 | −1.57911 | −0.789557 | − | 0.613677i | \(-0.789690\pi\) | ||||
−0.789557 | + | 0.613677i | \(0.789690\pi\) | |||||||
\(492\) | 4.66093 | 0.210131 | ||||||||
\(493\) | 63.9743 | 2.88126 | ||||||||
\(494\) | −1.69235 | −0.0761426 | ||||||||
\(495\) | 1.08962 | 0.0489747 | ||||||||
\(496\) | −12.9962 | −0.583546 | ||||||||
\(497\) | 11.3609 | 0.509605 | ||||||||
\(498\) | 55.9307 | 2.50631 | ||||||||
\(499\) | 33.3039 | 1.49089 | 0.745445 | − | 0.666568i | \(-0.232237\pi\) | ||||
0.745445 | + | 0.666568i | \(0.232237\pi\) | |||||||
\(500\) | −16.2216 | −0.725451 | ||||||||
\(501\) | −39.5044 | −1.76493 | ||||||||
\(502\) | 41.8276 | 1.86686 | ||||||||
\(503\) | 5.22511 | 0.232976 | 0.116488 | − | 0.993192i | \(-0.462836\pi\) | ||||
0.116488 | + | 0.993192i | \(0.462836\pi\) | |||||||
\(504\) | 0.132260 | 0.00589132 | ||||||||
\(505\) | 9.55997 | 0.425413 | ||||||||
\(506\) | −18.1849 | −0.808417 | ||||||||
\(507\) | −23.6725 | −1.05133 | ||||||||
\(508\) | −39.5128 | −1.75310 | ||||||||
\(509\) | −22.3134 | −0.989026 | −0.494513 | − | 0.869170i | \(-0.664654\pi\) | ||||
−0.494513 | + | 0.869170i | \(0.664654\pi\) | |||||||
\(510\) | 57.7419 | 2.55686 | ||||||||
\(511\) | 0.618160 | 0.0273458 | ||||||||
\(512\) | 31.5798 | 1.39564 | ||||||||
\(513\) | 9.17082 | 0.404902 | ||||||||
\(514\) | 17.7354 | 0.782274 | ||||||||
\(515\) | 23.0888 | 1.01741 | ||||||||
\(516\) | −44.6235 | −1.96444 | ||||||||
\(517\) | −1.08337 | −0.0476465 | ||||||||
\(518\) | 4.64242 | 0.203976 | ||||||||
\(519\) | 25.6086 | 1.12409 | ||||||||
\(520\) | −0.167244 | −0.00733412 | ||||||||
\(521\) | 6.24416 | 0.273562 | 0.136781 | − | 0.990601i | \(-0.456324\pi\) | ||||
0.136781 | + | 0.990601i | \(0.456324\pi\) | |||||||
\(522\) | 8.76589 | 0.383673 | ||||||||
\(523\) | −12.1521 | −0.531372 | −0.265686 | − | 0.964060i | \(-0.585598\pi\) | ||||
−0.265686 | + | 0.964060i | \(0.585598\pi\) | |||||||
\(524\) | 25.5593 | 1.11656 | ||||||||
\(525\) | −7.11087 | −0.310344 | ||||||||
\(526\) | −57.5386 | −2.50880 | ||||||||
\(527\) | 19.0189 | 0.828476 | ||||||||
\(528\) | −7.65639 | −0.333202 | ||||||||
\(529\) | 61.2099 | 2.66130 | ||||||||
\(530\) | −21.4499 | −0.931725 | ||||||||
\(531\) | 3.45384 | 0.149884 | ||||||||
\(532\) | 8.07753 | 0.350205 | ||||||||
\(533\) | 0.581352 | 0.0251812 | ||||||||
\(534\) | 59.7344 | 2.58496 | ||||||||
\(535\) | 10.1191 | 0.437486 | ||||||||
\(536\) | 1.48844 | 0.0642907 | ||||||||
\(537\) | −1.91650 | −0.0827031 | ||||||||
\(538\) | −0.538573 | −0.0232195 | ||||||||
\(539\) | −2.24156 | −0.0965510 | ||||||||
\(540\) | −23.9157 | −1.02917 | ||||||||
\(541\) | −16.4664 | −0.707946 | −0.353973 | − | 0.935256i | \(-0.615170\pi\) | ||||
−0.353973 | + | 0.935256i | \(0.615170\pi\) | |||||||
\(542\) | −19.6565 | −0.844319 | ||||||||
\(543\) | −24.4605 | −1.04970 | ||||||||
\(544\) | −47.9683 | −2.05663 | ||||||||
\(545\) | −22.1819 | −0.950167 | ||||||||
\(546\) | −3.55224 | −0.152022 | ||||||||
\(547\) | 5.93546 | 0.253782 | 0.126891 | − | 0.991917i | \(-0.459500\pi\) | ||||
0.126891 | + | 0.991917i | \(0.459500\pi\) | |||||||
\(548\) | −17.3514 | −0.741215 | ||||||||
\(549\) | −0.418993 | −0.0178822 | ||||||||
\(550\) | 3.49358 | 0.148967 | ||||||||
\(551\) | −20.2876 | −0.864281 | ||||||||
\(552\) | 2.45539 | 0.104508 | ||||||||
\(553\) | −32.2046 | −1.36948 | ||||||||
\(554\) | −4.90298 | −0.208308 | ||||||||
\(555\) | −5.16417 | −0.219207 | ||||||||
\(556\) | 29.7280 | 1.26075 | ||||||||
\(557\) | 11.3990 | 0.482990 | 0.241495 | − | 0.970402i | \(-0.422362\pi\) | ||||
0.241495 | + | 0.970402i | \(0.422362\pi\) | |||||||
\(558\) | 2.60601 | 0.110321 | ||||||||
\(559\) | −5.56583 | −0.235409 | ||||||||
\(560\) | 23.4896 | 0.992617 | ||||||||
\(561\) | 11.2045 | 0.473056 | ||||||||
\(562\) | −24.3599 | −1.02756 | ||||||||
\(563\) | −26.2922 | −1.10808 | −0.554042 | − | 0.832489i | \(-0.686915\pi\) | ||||
−0.554042 | + | 0.832489i | \(0.686915\pi\) | |||||||
\(564\) | −3.86013 | −0.162541 | ||||||||
\(565\) | 25.3781 | 1.06766 | ||||||||
\(566\) | 25.1934 | 1.05896 | ||||||||
\(567\) | 21.9915 | 0.923554 | ||||||||
\(568\) | 0.753650 | 0.0316225 | ||||||||
\(569\) | −40.8755 | −1.71359 | −0.856795 | − | 0.515658i | \(-0.827548\pi\) | ||||
−0.856795 | + | 0.515658i | \(0.827548\pi\) | |||||||
\(570\) | −18.3112 | −0.766971 | ||||||||
\(571\) | 3.13722 | 0.131288 | 0.0656442 | − | 0.997843i | \(-0.479090\pi\) | ||||
0.0656442 | + | 0.997843i | \(0.479090\pi\) | |||||||
\(572\) | 0.856384 | 0.0358072 | ||||||||
\(573\) | −16.3981 | −0.685042 | ||||||||
\(574\) | −5.65469 | −0.236022 | ||||||||
\(575\) | −16.1779 | −0.674667 | ||||||||
\(576\) | −3.10287 | −0.129286 | ||||||||
\(577\) | 35.1099 | 1.46164 | 0.730822 | − | 0.682569i | \(-0.239137\pi\) | ||||
0.730822 | + | 0.682569i | \(0.239137\pi\) | |||||||
\(578\) | 39.0762 | 1.62535 | ||||||||
\(579\) | 5.87924 | 0.244333 | ||||||||
\(580\) | 52.9060 | 2.19680 | ||||||||
\(581\) | −33.2969 | −1.38139 | ||||||||
\(582\) | 17.5365 | 0.726911 | ||||||||
\(583\) | −4.16225 | −0.172383 | ||||||||
\(584\) | 0.0410071 | 0.00169688 | ||||||||
\(585\) | 0.484247 | 0.0200211 | ||||||||
\(586\) | −20.0686 | −0.829028 | ||||||||
\(587\) | −11.7853 | −0.486430 | −0.243215 | − | 0.969972i | \(-0.578202\pi\) | ||||
−0.243215 | + | 0.969972i | \(0.578202\pi\) | |||||||
\(588\) | −7.98687 | −0.329373 | ||||||||
\(589\) | −6.03129 | −0.248515 | ||||||||
\(590\) | 42.4809 | 1.74891 | ||||||||
\(591\) | 31.4998 | 1.29573 | ||||||||
\(592\) | 4.44691 | 0.182767 | ||||||||
\(593\) | −14.0578 | −0.577284 | −0.288642 | − | 0.957437i | \(-0.593204\pi\) | ||||
−0.288642 | + | 0.957437i | \(0.593204\pi\) | |||||||
\(594\) | −9.45731 | −0.388038 | ||||||||
\(595\) | −34.3752 | −1.40925 | ||||||||
\(596\) | 17.9140 | 0.733785 | ||||||||
\(597\) | 51.6286 | 2.11302 | ||||||||
\(598\) | −8.08170 | −0.330485 | ||||||||
\(599\) | −23.2077 | −0.948243 | −0.474121 | − | 0.880460i | \(-0.657234\pi\) | ||||
−0.474121 | + | 0.880460i | \(0.657234\pi\) | |||||||
\(600\) | −0.471716 | −0.0192577 | ||||||||
\(601\) | −9.72040 | −0.396503 | −0.198252 | − | 0.980151i | \(-0.563526\pi\) | ||||
−0.198252 | + | 0.980151i | \(0.563526\pi\) | |||||||
\(602\) | 54.1376 | 2.20648 | ||||||||
\(603\) | −4.30970 | −0.175505 | ||||||||
\(604\) | −15.9349 | −0.648380 | ||||||||
\(605\) | 2.60057 | 0.105728 | ||||||||
\(606\) | 13.4700 | 0.547180 | ||||||||
\(607\) | −26.1875 | −1.06292 | −0.531459 | − | 0.847084i | \(-0.678356\pi\) | ||||
−0.531459 | + | 0.847084i | \(0.678356\pi\) | |||||||
\(608\) | 15.2118 | 0.616919 | ||||||||
\(609\) | −42.5835 | −1.72557 | ||||||||
\(610\) | −5.15344 | −0.208657 | ||||||||
\(611\) | −0.481468 | −0.0194781 | ||||||||
\(612\) | 4.89246 | 0.197766 | ||||||||
\(613\) | −1.59718 | −0.0645094 | −0.0322547 | − | 0.999480i | \(-0.510269\pi\) | ||||
−0.0322547 | + | 0.999480i | \(0.510269\pi\) | |||||||
\(614\) | −8.23234 | −0.332230 | ||||||||
\(615\) | 6.29021 | 0.253646 | ||||||||
\(616\) | 0.315662 | 0.0127184 | ||||||||
\(617\) | −4.95280 | −0.199392 | −0.0996962 | − | 0.995018i | \(-0.531787\pi\) | ||||
−0.0996962 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(618\) | 32.5320 | 1.30863 | ||||||||
\(619\) | 19.6334 | 0.789132 | 0.394566 | − | 0.918868i | \(-0.370895\pi\) | ||||
0.394566 | + | 0.918868i | \(0.370895\pi\) | |||||||
\(620\) | 15.7284 | 0.631669 | ||||||||
\(621\) | 43.7945 | 1.75741 | ||||||||
\(622\) | 20.2674 | 0.812649 | ||||||||
\(623\) | −35.5614 | −1.42474 | ||||||||
\(624\) | −3.40264 | −0.136215 | ||||||||
\(625\) | −30.7068 | −1.22827 | ||||||||
\(626\) | −17.2937 | −0.691194 | ||||||||
\(627\) | −3.55320 | −0.141901 | ||||||||
\(628\) | −26.0636 | −1.04005 | ||||||||
\(629\) | −6.50771 | −0.259479 | ||||||||
\(630\) | −4.71016 | −0.187657 | ||||||||
\(631\) | 15.1352 | 0.602521 | 0.301261 | − | 0.953542i | \(-0.402593\pi\) | ||||
0.301261 | + | 0.953542i | \(0.402593\pi\) | |||||||
\(632\) | −2.13636 | −0.0849800 | ||||||||
\(633\) | 27.5161 | 1.09367 | ||||||||
\(634\) | −1.12874 | −0.0448278 | ||||||||
\(635\) | −53.3248 | −2.11613 | ||||||||
\(636\) | −14.8304 | −0.588065 | ||||||||
\(637\) | −0.996192 | −0.0394706 | ||||||||
\(638\) | 20.9213 | 0.828284 | ||||||||
\(639\) | −2.18216 | −0.0863249 | ||||||||
\(640\) | 3.00856 | 0.118924 | ||||||||
\(641\) | −40.4127 | −1.59621 | −0.798104 | − | 0.602520i | \(-0.794163\pi\) | ||||
−0.798104 | + | 0.602520i | \(0.794163\pi\) | |||||||
\(642\) | 14.2577 | 0.562708 | ||||||||
\(643\) | −16.3198 | −0.643589 | −0.321794 | − | 0.946810i | \(-0.604286\pi\) | ||||
−0.321794 | + | 0.946810i | \(0.604286\pi\) | |||||||
\(644\) | 38.5736 | 1.52001 | ||||||||
\(645\) | −60.2220 | −2.37124 | ||||||||
\(646\) | −23.0751 | −0.907878 | ||||||||
\(647\) | −22.2041 | −0.872933 | −0.436466 | − | 0.899721i | \(-0.643770\pi\) | ||||
−0.436466 | + | 0.899721i | \(0.643770\pi\) | |||||||
\(648\) | 1.45885 | 0.0573092 | ||||||||
\(649\) | 8.24320 | 0.323574 | ||||||||
\(650\) | 1.55261 | 0.0608984 | ||||||||
\(651\) | −12.6596 | −0.496171 | ||||||||
\(652\) | −25.0182 | −0.979787 | ||||||||
\(653\) | 15.9029 | 0.622327 | 0.311163 | − | 0.950356i | \(-0.399281\pi\) | ||||
0.311163 | + | 0.950356i | \(0.399281\pi\) | |||||||
\(654\) | −31.2542 | −1.22214 | ||||||||
\(655\) | 34.4937 | 1.34778 | ||||||||
\(656\) | −5.41655 | −0.211481 | ||||||||
\(657\) | −0.118734 | −0.00463226 | ||||||||
\(658\) | 4.68314 | 0.182568 | ||||||||
\(659\) | 2.35249 | 0.0916402 | 0.0458201 | − | 0.998950i | \(-0.485410\pi\) | ||||
0.0458201 | + | 0.998950i | \(0.485410\pi\) | |||||||
\(660\) | 9.26603 | 0.360680 | ||||||||
\(661\) | −31.3644 | −1.21994 | −0.609968 | − | 0.792426i | \(-0.708818\pi\) | ||||
−0.609968 | + | 0.792426i | \(0.708818\pi\) | |||||||
\(662\) | −39.6333 | −1.54039 | ||||||||
\(663\) | 4.97950 | 0.193388 | ||||||||
\(664\) | −2.20883 | −0.0857191 | ||||||||
\(665\) | 10.9011 | 0.422727 | ||||||||
\(666\) | −0.891700 | −0.0345527 | ||||||||
\(667\) | −96.8818 | −3.75128 | ||||||||
\(668\) | −41.1692 | −1.59289 | ||||||||
\(669\) | 45.1030 | 1.74378 | ||||||||
\(670\) | −53.0076 | −2.04786 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 31.9294 | 1.23170 | ||||||||
\(673\) | −33.8125 | −1.30338 | −0.651688 | − | 0.758487i | \(-0.725939\pi\) | ||||
−0.651688 | + | 0.758487i | \(0.725939\pi\) | |||||||
\(674\) | 55.0886 | 2.12194 | ||||||||
\(675\) | −8.41357 | −0.323838 | ||||||||
\(676\) | −24.6701 | −0.948850 | ||||||||
\(677\) | 19.5191 | 0.750180 | 0.375090 | − | 0.926988i | \(-0.377612\pi\) | ||||
0.375090 | + | 0.926988i | \(0.377612\pi\) | |||||||
\(678\) | 35.7576 | 1.37326 | ||||||||
\(679\) | −10.4399 | −0.400647 | ||||||||
\(680\) | −2.28036 | −0.0874477 | ||||||||
\(681\) | −8.46513 | −0.324384 | ||||||||
\(682\) | 6.21970 | 0.238165 | ||||||||
\(683\) | −34.3022 | −1.31254 | −0.656268 | − | 0.754528i | \(-0.727866\pi\) | ||||
−0.656268 | + | 0.754528i | \(0.727866\pi\) | |||||||
\(684\) | −1.55150 | −0.0593232 | ||||||||
\(685\) | −23.4167 | −0.894707 | ||||||||
\(686\) | 39.9491 | 1.52526 | ||||||||
\(687\) | −30.3133 | −1.15653 | ||||||||
\(688\) | 51.8577 | 1.97705 | ||||||||
\(689\) | −1.84978 | −0.0704710 | ||||||||
\(690\) | −87.4436 | −3.32892 | ||||||||
\(691\) | −11.5937 | −0.441046 | −0.220523 | − | 0.975382i | \(-0.570776\pi\) | ||||
−0.220523 | + | 0.975382i | \(0.570776\pi\) | |||||||
\(692\) | 26.6879 | 1.01452 | ||||||||
\(693\) | −0.913984 | −0.0347194 | ||||||||
\(694\) | 27.8987 | 1.05902 | ||||||||
\(695\) | 40.1197 | 1.52183 | ||||||||
\(696\) | −2.82488 | −0.107077 | ||||||||
\(697\) | 7.92670 | 0.300245 | ||||||||
\(698\) | 53.5010 | 2.02504 | ||||||||
\(699\) | 18.6176 | 0.704184 | ||||||||
\(700\) | −7.41055 | −0.280092 | ||||||||
\(701\) | 6.50743 | 0.245782 | 0.122891 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122891 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(702\) | −4.20300 | −0.158632 | ||||||||
\(703\) | 2.06373 | 0.0778352 | ||||||||
\(704\) | −7.40554 | −0.279107 | ||||||||
\(705\) | −5.20947 | −0.196200 | ||||||||
\(706\) | −14.0038 | −0.527040 | ||||||||
\(707\) | −8.01900 | −0.301586 | ||||||||
\(708\) | 29.3712 | 1.10384 | ||||||||
\(709\) | 3.54453 | 0.133118 | 0.0665588 | − | 0.997783i | \(-0.478798\pi\) | ||||
0.0665588 | + | 0.997783i | \(0.478798\pi\) | |||||||
\(710\) | −26.8397 | −1.00728 | ||||||||
\(711\) | 6.18574 | 0.231984 | ||||||||
\(712\) | −2.35904 | −0.0884089 | ||||||||
\(713\) | −28.8020 | −1.07864 | ||||||||
\(714\) | −48.4345 | −1.81262 | ||||||||
\(715\) | 1.15574 | 0.0432222 | ||||||||
\(716\) | −1.99727 | −0.0746414 | ||||||||
\(717\) | 15.2844 | 0.570807 | ||||||||
\(718\) | −2.20435 | −0.0822657 | ||||||||
\(719\) | −40.7391 | −1.51931 | −0.759656 | − | 0.650325i | \(-0.774633\pi\) | ||||
−0.759656 | + | 0.650325i | \(0.774633\pi\) | |||||||
\(720\) | −4.51180 | −0.168145 | ||||||||
\(721\) | −19.3671 | −0.721269 | ||||||||
\(722\) | −30.3339 | −1.12891 | ||||||||
\(723\) | 2.82269 | 0.104977 | ||||||||
\(724\) | −25.4914 | −0.947380 | ||||||||
\(725\) | 18.6124 | 0.691247 | ||||||||
\(726\) | 3.66419 | 0.135991 | ||||||||
\(727\) | −34.3861 | −1.27531 | −0.637654 | − | 0.770323i | \(-0.720095\pi\) | ||||
−0.637654 | + | 0.770323i | \(0.720095\pi\) | |||||||
\(728\) | 0.140286 | 0.00519934 | ||||||||
\(729\) | 22.2493 | 0.824048 | ||||||||
\(730\) | −1.46038 | −0.0540512 | ||||||||
\(731\) | −75.8897 | −2.80688 | ||||||||
\(732\) | −3.56308 | −0.131695 | ||||||||
\(733\) | 24.0134 | 0.886956 | 0.443478 | − | 0.896285i | \(-0.353744\pi\) | ||||
0.443478 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(734\) | −31.0151 | −1.14479 | ||||||||
\(735\) | −10.7788 | −0.397580 | ||||||||
\(736\) | 72.6426 | 2.67764 | ||||||||
\(737\) | −10.2859 | −0.378885 | ||||||||
\(738\) | 1.08613 | 0.0399811 | ||||||||
\(739\) | 49.5917 | 1.82426 | 0.912131 | − | 0.409899i | \(-0.134436\pi\) | ||||
0.912131 | + | 0.409899i | \(0.134436\pi\) | |||||||
\(740\) | −5.38181 | −0.197839 | ||||||||
\(741\) | −1.57910 | −0.0580099 | ||||||||
\(742\) | 17.9924 | 0.660522 | ||||||||
\(743\) | −13.9582 | −0.512075 | −0.256038 | − | 0.966667i | \(-0.582417\pi\) | ||||
−0.256038 | + | 0.966667i | \(0.582417\pi\) | |||||||
\(744\) | −0.839807 | −0.0307888 | ||||||||
\(745\) | 24.1760 | 0.885739 | ||||||||
\(746\) | −16.0910 | −0.589134 | ||||||||
\(747\) | 6.39555 | 0.234001 | ||||||||
\(748\) | 11.6767 | 0.426944 | ||||||||
\(749\) | −8.48799 | −0.310144 | ||||||||
\(750\) | −30.8457 | −1.12633 | ||||||||
\(751\) | 6.81173 | 0.248564 | 0.124282 | − | 0.992247i | \(-0.460337\pi\) | ||||
0.124282 | + | 0.992247i | \(0.460337\pi\) | |||||||
\(752\) | 4.48592 | 0.163584 | ||||||||
\(753\) | 39.0286 | 1.42228 | ||||||||
\(754\) | 9.29783 | 0.338607 | ||||||||
\(755\) | −21.5050 | −0.782648 | ||||||||
\(756\) | 20.0607 | 0.729602 | ||||||||
\(757\) | 21.4347 | 0.779057 | 0.389529 | − | 0.921014i | \(-0.372638\pi\) | ||||
0.389529 | + | 0.921014i | \(0.372638\pi\) | |||||||
\(758\) | 70.4385 | 2.55844 | ||||||||
\(759\) | −16.9680 | −0.615899 | ||||||||
\(760\) | 0.723149 | 0.0262314 | ||||||||
\(761\) | 25.6533 | 0.929931 | 0.464965 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464965 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(762\) | −75.1345 | −2.72184 | ||||||||
\(763\) | 18.6064 | 0.673596 | ||||||||
\(764\) | −17.0892 | −0.618266 | ||||||||
\(765\) | 6.60267 | 0.238720 | ||||||||
\(766\) | 50.3895 | 1.82065 | ||||||||
\(767\) | 3.66343 | 0.132279 | ||||||||
\(768\) | 31.6255 | 1.14119 | ||||||||
\(769\) | 46.6407 | 1.68191 | 0.840953 | − | 0.541108i | \(-0.181995\pi\) | ||||
0.840953 | + | 0.541108i | \(0.181995\pi\) | |||||||
\(770\) | −11.2416 | −0.405121 | ||||||||
\(771\) | 16.5486 | 0.595982 | ||||||||
\(772\) | 6.12701 | 0.220516 | ||||||||
\(773\) | −25.4354 | −0.914849 | −0.457425 | − | 0.889248i | \(-0.651228\pi\) | ||||
−0.457425 | + | 0.889248i | \(0.651228\pi\) | |||||||
\(774\) | −10.3986 | −0.373769 | ||||||||
\(775\) | 5.53328 | 0.198761 | ||||||||
\(776\) | −0.692555 | −0.0248613 | ||||||||
\(777\) | 4.33176 | 0.155401 | ||||||||
\(778\) | −4.77512 | −0.171196 | ||||||||
\(779\) | −2.51372 | −0.0900635 | ||||||||
\(780\) | 4.11799 | 0.147448 | ||||||||
\(781\) | −5.20811 | −0.186361 | ||||||||
\(782\) | −110.193 | −3.94051 | ||||||||
\(783\) | −50.3847 | −1.80060 | ||||||||
\(784\) | 9.28168 | 0.331488 | ||||||||
\(785\) | −35.1744 | −1.25543 | ||||||||
\(786\) | 48.6015 | 1.73356 | ||||||||
\(787\) | 3.14255 | 0.112020 | 0.0560099 | − | 0.998430i | \(-0.482162\pi\) | ||||
0.0560099 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(788\) | 32.8273 | 1.16943 | ||||||||
\(789\) | −53.6882 | −1.91135 | ||||||||
\(790\) | 76.0822 | 2.70688 | ||||||||
\(791\) | −21.2874 | −0.756892 | ||||||||
\(792\) | −0.0606312 | −0.00215444 | ||||||||
\(793\) | −0.444418 | −0.0157818 | ||||||||
\(794\) | 17.5606 | 0.623203 | ||||||||
\(795\) | −20.0145 | −0.709842 | ||||||||
\(796\) | 53.8044 | 1.90705 | ||||||||
\(797\) | −24.9086 | −0.882309 | −0.441155 | − | 0.897431i | \(-0.645431\pi\) | ||||
−0.441155 | + | 0.897431i | \(0.645431\pi\) | |||||||
\(798\) | 15.3596 | 0.543725 | ||||||||
\(799\) | −6.56479 | −0.232245 | ||||||||
\(800\) | −13.9557 | −0.493408 | ||||||||
\(801\) | 6.83050 | 0.241344 | ||||||||
\(802\) | −46.3664 | −1.63725 | ||||||||
\(803\) | −0.283380 | −0.0100003 | ||||||||
\(804\) | −36.6494 | −1.29252 | ||||||||
\(805\) | 52.0573 | 1.83478 | ||||||||
\(806\) | 2.76415 | 0.0973630 | ||||||||
\(807\) | −0.502533 | −0.0176900 | ||||||||
\(808\) | −0.531959 | −0.0187142 | ||||||||
\(809\) | −7.32785 | −0.257634 | −0.128817 | − | 0.991668i | \(-0.541118\pi\) | ||||
−0.128817 | + | 0.991668i | \(0.541118\pi\) | |||||||
\(810\) | −51.9540 | −1.82548 | ||||||||
\(811\) | 0.404969 | 0.0142204 | 0.00711019 | − | 0.999975i | \(-0.497737\pi\) | ||||
0.00711019 | + | 0.999975i | \(0.497737\pi\) | |||||||
\(812\) | −44.3781 | −1.55737 | ||||||||
\(813\) | −18.3411 | −0.643252 | ||||||||
\(814\) | −2.12820 | −0.0745934 | ||||||||
\(815\) | −33.7635 | −1.18268 | ||||||||
\(816\) | −46.3948 | −1.62414 | ||||||||
\(817\) | 24.0662 | 0.841970 | ||||||||
\(818\) | −36.5633 | −1.27841 | ||||||||
\(819\) | −0.406191 | −0.0141935 | ||||||||
\(820\) | 6.55530 | 0.228921 | ||||||||
\(821\) | −2.92173 | −0.101969 | −0.0509846 | − | 0.998699i | \(-0.516236\pi\) | ||||
−0.0509846 | + | 0.998699i | \(0.516236\pi\) | |||||||
\(822\) | −32.9941 | −1.15080 | ||||||||
\(823\) | 33.2014 | 1.15733 | 0.578665 | − | 0.815566i | \(-0.303574\pi\) | ||||
0.578665 | + | 0.815566i | \(0.303574\pi\) | |||||||
\(824\) | −1.28476 | −0.0447568 | ||||||||
\(825\) | 3.25980 | 0.113492 | ||||||||
\(826\) | −35.6334 | −1.23984 | ||||||||
\(827\) | 37.3203 | 1.29775 | 0.648877 | − | 0.760894i | \(-0.275239\pi\) | ||||
0.648877 | + | 0.760894i | \(0.275239\pi\) | |||||||
\(828\) | −7.40908 | −0.257483 | ||||||||
\(829\) | −18.7158 | −0.650027 | −0.325014 | − | 0.945709i | \(-0.605369\pi\) | ||||
−0.325014 | + | 0.945709i | \(0.605369\pi\) | |||||||
\(830\) | 78.6628 | 2.73043 | ||||||||
\(831\) | −4.57489 | −0.158701 | ||||||||
\(832\) | −3.29116 | −0.114100 | ||||||||
\(833\) | −13.5830 | −0.470623 | ||||||||
\(834\) | 56.5285 | 1.95742 | ||||||||
\(835\) | −55.5603 | −1.92274 | ||||||||
\(836\) | −3.70294 | −0.128069 | ||||||||
\(837\) | −14.9789 | −0.517745 | ||||||||
\(838\) | −45.1606 | −1.56005 | ||||||||
\(839\) | −0.337085 | −0.0116375 | −0.00581874 | − | 0.999983i | \(-0.501852\pi\) | ||||
−0.00581874 | + | 0.999983i | \(0.501852\pi\) | |||||||
\(840\) | 1.51789 | 0.0523720 | ||||||||
\(841\) | 82.4605 | 2.84347 | ||||||||
\(842\) | 33.6587 | 1.15995 | ||||||||
\(843\) | −22.7298 | −0.782857 | ||||||||
\(844\) | 28.6758 | 0.987060 | ||||||||
\(845\) | −33.2938 | −1.14534 | ||||||||
\(846\) | −0.899521 | −0.0309262 | ||||||||
\(847\) | −2.18138 | −0.0749532 | ||||||||
\(848\) | 17.2347 | 0.591841 | ||||||||
\(849\) | 23.5075 | 0.806774 | ||||||||
\(850\) | 21.1698 | 0.726117 | ||||||||
\(851\) | 9.85519 | 0.337832 | ||||||||
\(852\) | −18.5569 | −0.635749 | ||||||||
\(853\) | −3.30841 | −0.113278 | −0.0566389 | − | 0.998395i | \(-0.518038\pi\) | ||||
−0.0566389 | + | 0.998395i | \(0.518038\pi\) | |||||||
\(854\) | 4.32276 | 0.147922 | ||||||||
\(855\) | −2.09385 | −0.0716080 | ||||||||
\(856\) | −0.563070 | −0.0192453 | ||||||||
\(857\) | 10.2920 | 0.351568 | 0.175784 | − | 0.984429i | \(-0.443754\pi\) | ||||
0.175784 | + | 0.984429i | \(0.443754\pi\) | |||||||
\(858\) | 1.62843 | 0.0555938 | ||||||||
\(859\) | 34.1456 | 1.16503 | 0.582517 | − | 0.812819i | \(-0.302068\pi\) | ||||
0.582517 | + | 0.812819i | \(0.302068\pi\) | |||||||
\(860\) | −62.7599 | −2.14010 | ||||||||
\(861\) | −5.27629 | −0.179815 | ||||||||
\(862\) | −53.2893 | −1.81504 | ||||||||
\(863\) | −40.4513 | −1.37698 | −0.688489 | − | 0.725247i | \(-0.741726\pi\) | ||||
−0.688489 | + | 0.725247i | \(0.741726\pi\) | |||||||
\(864\) | 37.7788 | 1.28526 | ||||||||
\(865\) | 36.0168 | 1.22461 | ||||||||
\(866\) | −9.80307 | −0.333122 | ||||||||
\(867\) | 36.4613 | 1.23829 | ||||||||
\(868\) | −13.1932 | −0.447805 | ||||||||
\(869\) | 14.7634 | 0.500813 | ||||||||
\(870\) | 100.602 | 3.41073 | ||||||||
\(871\) | −4.57123 | −0.154890 | ||||||||
\(872\) | 1.23430 | 0.0417986 | ||||||||
\(873\) | 2.00526 | 0.0678678 | ||||||||
\(874\) | 34.9447 | 1.18202 | ||||||||
\(875\) | 18.3632 | 0.620790 | ||||||||
\(876\) | −1.00970 | −0.0341148 | ||||||||
\(877\) | 52.6517 | 1.77792 | 0.888960 | − | 0.457984i | \(-0.151428\pi\) | ||||
0.888960 | + | 0.457984i | \(0.151428\pi\) | |||||||
\(878\) | −31.9703 | −1.07894 | ||||||||
\(879\) | −18.7257 | −0.631602 | ||||||||
\(880\) | −10.7682 | −0.362996 | ||||||||
\(881\) | 3.36425 | 0.113344 | 0.0566722 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566722 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(882\) | −1.86117 | −0.0626689 | ||||||||
\(883\) | −7.82221 | −0.263238 | −0.131619 | − | 0.991300i | \(-0.542018\pi\) | ||||
−0.131619 | + | 0.991300i | \(0.542018\pi\) | |||||||
\(884\) | 5.18935 | 0.174537 | ||||||||
\(885\) | 39.6382 | 1.33242 | ||||||||
\(886\) | 39.5909 | 1.33008 | ||||||||
\(887\) | 26.2867 | 0.882619 | 0.441310 | − | 0.897355i | \(-0.354514\pi\) | ||||
0.441310 | + | 0.897355i | \(0.354514\pi\) | |||||||
\(888\) | 0.287357 | 0.00964308 | ||||||||
\(889\) | 44.7294 | 1.50018 | ||||||||
\(890\) | 84.0125 | 2.81611 | ||||||||
\(891\) | −10.0814 | −0.337740 | ||||||||
\(892\) | 47.0038 | 1.57380 | ||||||||
\(893\) | 2.08183 | 0.0696659 | ||||||||
\(894\) | 34.0639 | 1.13927 | ||||||||
\(895\) | −2.69543 | −0.0900983 | ||||||||
\(896\) | −2.52361 | −0.0843079 | ||||||||
\(897\) | −7.54089 | −0.251783 | ||||||||
\(898\) | 6.92059 | 0.230943 | ||||||||
\(899\) | 33.1361 | 1.10515 | ||||||||
\(900\) | 1.42339 | 0.0474464 | ||||||||
\(901\) | −25.2216 | −0.840254 | ||||||||
\(902\) | 2.59225 | 0.0863124 | ||||||||
\(903\) | 50.5148 | 1.68103 | ||||||||
\(904\) | −1.41215 | −0.0469673 | ||||||||
\(905\) | −34.4021 | −1.14356 | ||||||||
\(906\) | −30.3005 | −1.00667 | ||||||||
\(907\) | 20.4355 | 0.678551 | 0.339275 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339275 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(908\) | −8.82187 | −0.292764 | ||||||||
\(909\) | 1.54026 | 0.0510873 | ||||||||
\(910\) | −4.99599 | −0.165615 | ||||||||
\(911\) | −8.55567 | −0.283462 | −0.141731 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141731 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(912\) | 14.7128 | 0.487188 | ||||||||
\(913\) | 15.2641 | 0.505169 | ||||||||
\(914\) | −17.1239 | −0.566409 | ||||||||
\(915\) | −4.80859 | −0.158967 | ||||||||
\(916\) | −31.5909 | −1.04379 | ||||||||
\(917\) | −28.9337 | −0.955474 | ||||||||
\(918\) | −57.3076 | −1.89143 | ||||||||
\(919\) | −48.6802 | −1.60581 | −0.802905 | − | 0.596106i | \(-0.796714\pi\) | ||||
−0.802905 | + | 0.596106i | \(0.796714\pi\) | |||||||
\(920\) | 3.45334 | 0.113853 | ||||||||
\(921\) | −7.68145 | −0.253113 | ||||||||
\(922\) | 6.03754 | 0.198836 | ||||||||
\(923\) | −2.31458 | −0.0761853 | ||||||||
\(924\) | −7.77245 | −0.255695 | ||||||||
\(925\) | −1.89333 | −0.0622522 | ||||||||
\(926\) | −15.9198 | −0.523159 | ||||||||
\(927\) | 3.71997 | 0.122180 | ||||||||
\(928\) | −83.5738 | −2.74345 | ||||||||
\(929\) | 10.0819 | 0.330778 | 0.165389 | − | 0.986228i | \(-0.447112\pi\) | ||||
0.165389 | + | 0.986228i | \(0.447112\pi\) | |||||||
\(930\) | 29.9080 | 0.980721 | ||||||||
\(931\) | 4.30746 | 0.141171 | ||||||||
\(932\) | 19.4023 | 0.635542 | ||||||||
\(933\) | 18.9112 | 0.619124 | ||||||||
\(934\) | 23.8185 | 0.779366 | ||||||||
\(935\) | 15.7584 | 0.515356 | ||||||||
\(936\) | −0.0269456 | −0.000880745 0 | ||||||||
\(937\) | −4.03470 | −0.131808 | −0.0659039 | − | 0.997826i | \(-0.520993\pi\) | ||||
−0.0659039 | + | 0.997826i | \(0.520993\pi\) | |||||||
\(938\) | 44.4633 | 1.45178 | ||||||||
\(939\) | −16.1364 | −0.526592 | ||||||||
\(940\) | −5.42901 | −0.177075 | ||||||||
\(941\) | −14.9304 | −0.486716 | −0.243358 | − | 0.969937i | \(-0.578249\pi\) | ||||
−0.243358 | + | 0.969937i | \(0.578249\pi\) | |||||||
\(942\) | −49.5606 | −1.61477 | ||||||||
\(943\) | −12.0041 | −0.390907 | ||||||||
\(944\) | −34.1328 | −1.11093 | ||||||||
\(945\) | 27.0731 | 0.880690 | ||||||||
\(946\) | −24.8180 | −0.806903 | ||||||||
\(947\) | 18.6683 | 0.606639 | 0.303319 | − | 0.952889i | \(-0.401905\pi\) | ||||
0.303319 | + | 0.952889i | \(0.401905\pi\) | |||||||
\(948\) | 52.6031 | 1.70847 | ||||||||
\(949\) | −0.125939 | −0.00408816 | ||||||||
\(950\) | −6.71338 | −0.217811 | ||||||||
\(951\) | −1.05320 | −0.0341525 | ||||||||
\(952\) | 1.91279 | 0.0619938 | ||||||||
\(953\) | 27.8528 | 0.902239 | 0.451120 | − | 0.892463i | \(-0.351025\pi\) | ||||
0.451120 | + | 0.892463i | \(0.351025\pi\) | |||||||
\(954\) | −3.45592 | −0.111890 | ||||||||
\(955\) | −23.0629 | −0.746298 | ||||||||
\(956\) | 15.9286 | 0.515166 | ||||||||
\(957\) | 19.5213 | 0.631035 | ||||||||
\(958\) | −42.2331 | −1.36449 | ||||||||
\(959\) | 19.6422 | 0.634279 | ||||||||
\(960\) | −35.6102 | −1.14931 | ||||||||
\(961\) | −21.1490 | −0.682225 | ||||||||
\(962\) | −0.945811 | −0.0304942 | ||||||||
\(963\) | 1.63034 | 0.0525370 | ||||||||
\(964\) | 2.94164 | 0.0947440 | ||||||||
\(965\) | 8.26876 | 0.266181 | ||||||||
\(966\) | 73.3486 | 2.35995 | ||||||||
\(967\) | −46.3423 | −1.49027 | −0.745134 | − | 0.666915i | \(-0.767614\pi\) | ||||
−0.745134 | + | 0.666915i | \(0.767614\pi\) | |||||||
\(968\) | −0.144707 | −0.00465106 | ||||||||
\(969\) | −21.5310 | −0.691675 | ||||||||
\(970\) | 24.6639 | 0.791910 | ||||||||
\(971\) | −15.7597 | −0.505752 | −0.252876 | − | 0.967499i | \(-0.581377\pi\) | ||||
−0.252876 | + | 0.967499i | \(0.581377\pi\) | |||||||
\(972\) | −8.33191 | −0.267246 | ||||||||
\(973\) | −33.6528 | −1.07886 | ||||||||
\(974\) | −74.4650 | −2.38601 | ||||||||
\(975\) | 1.44871 | 0.0463960 | ||||||||
\(976\) | 4.14071 | 0.132541 | ||||||||
\(977\) | −10.4959 | −0.335792 | −0.167896 | − | 0.985805i | \(-0.553697\pi\) | ||||
−0.167896 | + | 0.985805i | \(0.553697\pi\) | |||||||
\(978\) | −47.5726 | −1.52120 | ||||||||
\(979\) | 16.3022 | 0.521021 | ||||||||
\(980\) | −11.2330 | −0.358825 | ||||||||
\(981\) | −3.57385 | −0.114104 | ||||||||
\(982\) | −69.3400 | −2.21273 | ||||||||
\(983\) | 36.0894 | 1.15107 | 0.575537 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575537 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(984\) | −0.350015 | −0.0111581 | ||||||||
\(985\) | 44.3024 | 1.41159 | ||||||||
\(986\) | 126.775 | 4.03735 | ||||||||
\(987\) | 4.36975 | 0.139091 | ||||||||
\(988\) | −1.64565 | −0.0523552 | ||||||||
\(989\) | 114.926 | 3.65444 | ||||||||
\(990\) | 2.15925 | 0.0686256 | ||||||||
\(991\) | 11.9025 | 0.378094 | 0.189047 | − | 0.981968i | \(-0.439460\pi\) | ||||
0.189047 | + | 0.981968i | \(0.439460\pi\) | |||||||
\(992\) | −24.8456 | −0.788850 | ||||||||
\(993\) | −36.9812 | −1.17356 | ||||||||
\(994\) | 22.5134 | 0.714082 | ||||||||
\(995\) | 72.6122 | 2.30196 | ||||||||
\(996\) | 54.3873 | 1.72333 | ||||||||
\(997\) | −20.2428 | −0.641097 | −0.320549 | − | 0.947232i | \(-0.603867\pi\) | ||||
−0.320549 | + | 0.947232i | \(0.603867\pi\) | |||||||
\(998\) | 65.9971 | 2.08910 | ||||||||
\(999\) | 5.12533 | 0.162158 |
(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 | 671.2.a.c.1.14 | ✓ | 19 | |
3.2 | odd | 2 | 6039.2.a.k.1.6 | 19 | |||
11.10 | odd | 2 | 7381.2.a.i.1.6 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.c.1.14 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6039.2.a.k.1.6 | 19 | 3.2 | odd | 2 | |||
7381.2.a.i.1.6 | 19 | 11.10 | odd | 2 |