Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [445,2,Mod(1,445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(445, 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("445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 445 = 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 445.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: | \(3.55334288995\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.26266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11962 | 1.49880 | 0.749399 | − | 0.662119i | \(-0.230343\pi\) | ||||
0.749399 | + | 0.662119i | \(0.230343\pi\) | |||||||
\(3\) | −3.29058 | −1.89981 | −0.949907 | − | 0.312532i | \(-0.898823\pi\) | ||||
−0.949907 | + | 0.312532i | \(0.898823\pi\) | |||||||
\(4\) | 2.49279 | 1.24639 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.97477 | −2.84744 | ||||||||
\(7\) | −4.83304 | −1.82672 | −0.913358 | − | 0.407157i | \(-0.866520\pi\) | ||||
−0.913358 | + | 0.407157i | \(0.866520\pi\) | |||||||
\(8\) | 1.04452 | 0.369294 | ||||||||
\(9\) | 7.82788 | 2.60929 | ||||||||
\(10\) | 2.11962 | 0.670283 | ||||||||
\(11\) | −2.21586 | −0.668106 | −0.334053 | − | 0.942554i | \(-0.608417\pi\) | ||||
−0.334053 | + | 0.942554i | \(0.608417\pi\) | |||||||
\(12\) | −8.20270 | −2.36792 | ||||||||
\(13\) | −2.26162 | −0.627261 | −0.313631 | − | 0.949545i | \(-0.601545\pi\) | ||||
−0.313631 | + | 0.949545i | \(0.601545\pi\) | |||||||
\(14\) | −10.2442 | −2.73788 | ||||||||
\(15\) | −3.29058 | −0.849623 | ||||||||
\(16\) | −2.77159 | −0.692896 | ||||||||
\(17\) | −3.10920 | −0.754092 | −0.377046 | − | 0.926194i | \(-0.623060\pi\) | ||||
−0.377046 | + | 0.926194i | \(0.623060\pi\) | |||||||
\(18\) | 16.5921 | 3.91080 | ||||||||
\(19\) | −5.93952 | −1.36262 | −0.681309 | − | 0.731996i | \(-0.738589\pi\) | ||||
−0.681309 | + | 0.731996i | \(0.738589\pi\) | |||||||
\(20\) | 2.49279 | 0.557404 | ||||||||
\(21\) | 15.9035 | 3.47042 | ||||||||
\(22\) | −4.69678 | −1.00136 | ||||||||
\(23\) | 5.79416 | 1.20817 | 0.604083 | − | 0.796921i | \(-0.293540\pi\) | ||||
0.604083 | + | 0.796921i | \(0.293540\pi\) | |||||||
\(24\) | −3.43708 | −0.701590 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.79378 | −0.940138 | ||||||||
\(27\) | −15.8865 | −3.05736 | ||||||||
\(28\) | −12.0477 | −2.27681 | ||||||||
\(29\) | 2.32757 | 0.432220 | 0.216110 | − | 0.976369i | \(-0.430663\pi\) | ||||
0.216110 | + | 0.976369i | \(0.430663\pi\) | |||||||
\(30\) | −6.97477 | −1.27341 | ||||||||
\(31\) | 4.47624 | 0.803956 | 0.401978 | − | 0.915649i | \(-0.368323\pi\) | ||||
0.401978 | + | 0.915649i | \(0.368323\pi\) | |||||||
\(32\) | −7.96375 | −1.40781 | ||||||||
\(33\) | 7.29145 | 1.26928 | ||||||||
\(34\) | −6.59033 | −1.13023 | ||||||||
\(35\) | −4.83304 | −0.816932 | ||||||||
\(36\) | 19.5133 | 3.25221 | ||||||||
\(37\) | −8.23124 | −1.35321 | −0.676604 | − | 0.736347i | \(-0.736549\pi\) | ||||
−0.676604 | + | 0.736347i | \(0.736549\pi\) | |||||||
\(38\) | −12.5895 | −2.04229 | ||||||||
\(39\) | 7.44204 | 1.19168 | ||||||||
\(40\) | 1.04452 | 0.165153 | ||||||||
\(41\) | −0.278075 | −0.0434281 | −0.0217140 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217140 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(42\) | 33.7093 | 5.20146 | ||||||||
\(43\) | −0.176109 | −0.0268564 | −0.0134282 | − | 0.999910i | \(-0.504274\pi\) | ||||
−0.0134282 | + | 0.999910i | \(0.504274\pi\) | |||||||
\(44\) | −5.52366 | −0.832724 | ||||||||
\(45\) | 7.82788 | 1.16691 | ||||||||
\(46\) | 12.2814 | 1.81080 | ||||||||
\(47\) | 1.91855 | 0.279850 | 0.139925 | − | 0.990162i | \(-0.455314\pi\) | ||||
0.139925 | + | 0.990162i | \(0.455314\pi\) | |||||||
\(48\) | 9.12011 | 1.31637 | ||||||||
\(49\) | 16.3583 | 2.33689 | ||||||||
\(50\) | 2.11962 | 0.299759 | ||||||||
\(51\) | 10.2311 | 1.43264 | ||||||||
\(52\) | −5.63775 | −0.781815 | ||||||||
\(53\) | 8.65904 | 1.18941 | 0.594706 | − | 0.803944i | \(-0.297269\pi\) | ||||
0.594706 | + | 0.803944i | \(0.297269\pi\) | |||||||
\(54\) | −33.6734 | −4.58237 | ||||||||
\(55\) | −2.21586 | −0.298786 | ||||||||
\(56\) | −5.04821 | −0.674596 | ||||||||
\(57\) | 19.5444 | 2.58872 | ||||||||
\(58\) | 4.93357 | 0.647810 | ||||||||
\(59\) | 5.39666 | 0.702585 | 0.351292 | − | 0.936266i | \(-0.385742\pi\) | ||||
0.351292 | + | 0.936266i | \(0.385742\pi\) | |||||||
\(60\) | −8.20270 | −1.05896 | ||||||||
\(61\) | −9.69150 | −1.24087 | −0.620434 | − | 0.784258i | \(-0.713044\pi\) | ||||
−0.620434 | + | 0.784258i | \(0.713044\pi\) | |||||||
\(62\) | 9.48792 | 1.20497 | ||||||||
\(63\) | −37.8325 | −4.76644 | ||||||||
\(64\) | −11.3370 | −1.41712 | ||||||||
\(65\) | −2.26162 | −0.280520 | ||||||||
\(66\) | 15.4551 | 1.90239 | ||||||||
\(67\) | 8.06916 | 0.985805 | 0.492903 | − | 0.870084i | \(-0.335936\pi\) | ||||
0.492903 | + | 0.870084i | \(0.335936\pi\) | |||||||
\(68\) | −7.75058 | −0.939896 | ||||||||
\(69\) | −19.0661 | −2.29529 | ||||||||
\(70\) | −10.2442 | −1.22442 | ||||||||
\(71\) | −5.00576 | −0.594075 | −0.297037 | − | 0.954866i | \(-0.595999\pi\) | ||||
−0.297037 | + | 0.954866i | \(0.595999\pi\) | |||||||
\(72\) | 8.17640 | 0.963597 | ||||||||
\(73\) | −9.18909 | −1.07550 | −0.537751 | − | 0.843104i | \(-0.680726\pi\) | ||||
−0.537751 | + | 0.843104i | \(0.680726\pi\) | |||||||
\(74\) | −17.4471 | −2.02818 | ||||||||
\(75\) | −3.29058 | −0.379963 | ||||||||
\(76\) | −14.8060 | −1.69836 | ||||||||
\(77\) | 10.7093 | 1.22044 | ||||||||
\(78\) | 15.7743 | 1.78609 | ||||||||
\(79\) | −1.78949 | −0.201333 | −0.100666 | − | 0.994920i | \(-0.532097\pi\) | ||||
−0.100666 | + | 0.994920i | \(0.532097\pi\) | |||||||
\(80\) | −2.77159 | −0.309873 | ||||||||
\(81\) | 28.7921 | 3.19912 | ||||||||
\(82\) | −0.589414 | −0.0650899 | ||||||||
\(83\) | 13.8879 | 1.52439 | 0.762197 | − | 0.647345i | \(-0.224121\pi\) | ||||
0.762197 | + | 0.647345i | \(0.224121\pi\) | |||||||
\(84\) | 39.6440 | 4.32551 | ||||||||
\(85\) | −3.10920 | −0.337240 | ||||||||
\(86\) | −0.373284 | −0.0402523 | ||||||||
\(87\) | −7.65906 | −0.821137 | ||||||||
\(88\) | −2.31451 | −0.246728 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 16.5921 | 1.74896 | ||||||||
\(91\) | 10.9305 | 1.14583 | ||||||||
\(92\) | 14.4436 | 1.50585 | ||||||||
\(93\) | −14.7294 | −1.52737 | ||||||||
\(94\) | 4.06660 | 0.419438 | ||||||||
\(95\) | −5.93952 | −0.609382 | ||||||||
\(96\) | 26.2053 | 2.67457 | ||||||||
\(97\) | −5.52008 | −0.560479 | −0.280240 | − | 0.959930i | \(-0.590414\pi\) | ||||
−0.280240 | + | 0.959930i | \(0.590414\pi\) | |||||||
\(98\) | 34.6733 | 3.50253 | ||||||||
\(99\) | −17.3455 | −1.74329 | ||||||||
\(100\) | 2.49279 | 0.249279 | ||||||||
\(101\) | −12.8409 | −1.27772 | −0.638860 | − | 0.769323i | \(-0.720594\pi\) | ||||
−0.638860 | + | 0.769323i | \(0.720594\pi\) | |||||||
\(102\) | 21.6860 | 2.14723 | ||||||||
\(103\) | −11.7697 | −1.15970 | −0.579852 | − | 0.814722i | \(-0.696890\pi\) | ||||
−0.579852 | + | 0.814722i | \(0.696890\pi\) | |||||||
\(104\) | −2.36231 | −0.231644 | ||||||||
\(105\) | 15.9035 | 1.55202 | ||||||||
\(106\) | 18.3539 | 1.78269 | ||||||||
\(107\) | −15.4620 | −1.49477 | −0.747383 | − | 0.664393i | \(-0.768690\pi\) | ||||
−0.747383 | + | 0.664393i | \(0.768690\pi\) | |||||||
\(108\) | −39.6017 | −3.81068 | ||||||||
\(109\) | −7.88060 | −0.754824 | −0.377412 | − | 0.926045i | \(-0.623186\pi\) | ||||
−0.377412 | + | 0.926045i | \(0.623186\pi\) | |||||||
\(110\) | −4.69678 | −0.447820 | ||||||||
\(111\) | 27.0855 | 2.57084 | ||||||||
\(112\) | 13.3952 | 1.26573 | ||||||||
\(113\) | −2.01004 | −0.189088 | −0.0945442 | − | 0.995521i | \(-0.530139\pi\) | ||||
−0.0945442 | + | 0.995521i | \(0.530139\pi\) | |||||||
\(114\) | 41.4268 | 3.87997 | ||||||||
\(115\) | 5.79416 | 0.540308 | ||||||||
\(116\) | 5.80215 | 0.538716 | ||||||||
\(117\) | −17.7037 | −1.63671 | ||||||||
\(118\) | 11.4389 | 1.05303 | ||||||||
\(119\) | 15.0269 | 1.37751 | ||||||||
\(120\) | −3.43708 | −0.313761 | ||||||||
\(121\) | −6.08997 | −0.553634 | ||||||||
\(122\) | −20.5423 | −1.85981 | ||||||||
\(123\) | 0.915028 | 0.0825053 | ||||||||
\(124\) | 11.1583 | 1.00205 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −80.1904 | −7.14393 | ||||||||
\(127\) | −12.0158 | −1.06623 | −0.533113 | − | 0.846044i | \(-0.678978\pi\) | ||||
−0.533113 | + | 0.846044i | \(0.678978\pi\) | |||||||
\(128\) | −8.10252 | −0.716169 | ||||||||
\(129\) | 0.579500 | 0.0510221 | ||||||||
\(130\) | −4.79378 | −0.420442 | ||||||||
\(131\) | −20.6066 | −1.80040 | −0.900202 | − | 0.435472i | \(-0.856581\pi\) | ||||
−0.900202 | + | 0.435472i | \(0.856581\pi\) | |||||||
\(132\) | 18.1760 | 1.58202 | ||||||||
\(133\) | 28.7059 | 2.48912 | ||||||||
\(134\) | 17.1036 | 1.47752 | ||||||||
\(135\) | −15.8865 | −1.36729 | ||||||||
\(136\) | −3.24763 | −0.278482 | ||||||||
\(137\) | 10.9369 | 0.934400 | 0.467200 | − | 0.884152i | \(-0.345263\pi\) | ||||
0.467200 | + | 0.884152i | \(0.345263\pi\) | |||||||
\(138\) | −40.4129 | −3.44018 | ||||||||
\(139\) | −0.432073 | −0.0366479 | −0.0183240 | − | 0.999832i | \(-0.505833\pi\) | ||||
−0.0183240 | + | 0.999832i | \(0.505833\pi\) | |||||||
\(140\) | −12.0477 | −1.01822 | ||||||||
\(141\) | −6.31314 | −0.531663 | ||||||||
\(142\) | −10.6103 | −0.890397 | ||||||||
\(143\) | 5.01144 | 0.419077 | ||||||||
\(144\) | −21.6957 | −1.80797 | ||||||||
\(145\) | 2.32757 | 0.193294 | ||||||||
\(146\) | −19.4774 | −1.61196 | ||||||||
\(147\) | −53.8281 | −4.43966 | ||||||||
\(148\) | −20.5187 | −1.68663 | ||||||||
\(149\) | −13.6417 | −1.11757 | −0.558785 | − | 0.829313i | \(-0.688732\pi\) | ||||
−0.558785 | + | 0.829313i | \(0.688732\pi\) | |||||||
\(150\) | −6.97477 | −0.569487 | ||||||||
\(151\) | 22.3825 | 1.82146 | 0.910730 | − | 0.413002i | \(-0.135520\pi\) | ||||
0.910730 | + | 0.413002i | \(0.135520\pi\) | |||||||
\(152\) | −6.20396 | −0.503207 | ||||||||
\(153\) | −24.3385 | −1.96765 | ||||||||
\(154\) | 22.6997 | 1.82919 | ||||||||
\(155\) | 4.47624 | 0.359540 | ||||||||
\(156\) | 18.5514 | 1.48530 | ||||||||
\(157\) | 11.7366 | 0.936683 | 0.468342 | − | 0.883547i | \(-0.344852\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344852\pi\) | |||||||
\(158\) | −3.79303 | −0.301757 | ||||||||
\(159\) | −28.4932 | −2.25966 | ||||||||
\(160\) | −7.96375 | −0.629590 | ||||||||
\(161\) | −28.0034 | −2.20698 | ||||||||
\(162\) | 61.0283 | 4.79484 | ||||||||
\(163\) | 1.49678 | 0.117237 | 0.0586184 | − | 0.998280i | \(-0.481330\pi\) | ||||
0.0586184 | + | 0.998280i | \(0.481330\pi\) | |||||||
\(164\) | −0.693183 | −0.0541285 | ||||||||
\(165\) | 7.29145 | 0.567638 | ||||||||
\(166\) | 29.4371 | 2.28476 | ||||||||
\(167\) | −0.555849 | −0.0430129 | −0.0215064 | − | 0.999769i | \(-0.506846\pi\) | ||||
−0.0215064 | + | 0.999769i | \(0.506846\pi\) | |||||||
\(168\) | 16.6115 | 1.28161 | ||||||||
\(169\) | −7.88506 | −0.606543 | ||||||||
\(170\) | −6.59033 | −0.505455 | ||||||||
\(171\) | −46.4939 | −3.55547 | ||||||||
\(172\) | −0.439002 | −0.0334736 | ||||||||
\(173\) | 14.0371 | 1.06722 | 0.533611 | − | 0.845730i | \(-0.320835\pi\) | ||||
0.533611 | + | 0.845730i | \(0.320835\pi\) | |||||||
\(174\) | −16.2343 | −1.23072 | ||||||||
\(175\) | −4.83304 | −0.365343 | ||||||||
\(176\) | 6.14144 | 0.462929 | ||||||||
\(177\) | −17.7581 | −1.33478 | ||||||||
\(178\) | 2.11962 | 0.158872 | ||||||||
\(179\) | 9.22570 | 0.689561 | 0.344780 | − | 0.938683i | \(-0.387953\pi\) | ||||
0.344780 | + | 0.938683i | \(0.387953\pi\) | |||||||
\(180\) | 19.5133 | 1.45443 | ||||||||
\(181\) | −10.4704 | −0.778259 | −0.389129 | − | 0.921183i | \(-0.627224\pi\) | ||||
−0.389129 | + | 0.921183i | \(0.627224\pi\) | |||||||
\(182\) | 23.1685 | 1.71737 | ||||||||
\(183\) | 31.8906 | 2.35742 | ||||||||
\(184\) | 6.05213 | 0.446169 | ||||||||
\(185\) | −8.23124 | −0.605173 | ||||||||
\(186\) | −31.2207 | −2.28921 | ||||||||
\(187\) | 6.88955 | 0.503814 | ||||||||
\(188\) | 4.78255 | 0.348803 | ||||||||
\(189\) | 76.7801 | 5.58493 | ||||||||
\(190\) | −12.5895 | −0.913340 | ||||||||
\(191\) | −4.73905 | −0.342906 | −0.171453 | − | 0.985192i | \(-0.554846\pi\) | ||||
−0.171453 | + | 0.985192i | \(0.554846\pi\) | |||||||
\(192\) | 37.3051 | 2.69226 | ||||||||
\(193\) | 1.48587 | 0.106955 | 0.0534775 | − | 0.998569i | \(-0.482969\pi\) | ||||
0.0534775 | + | 0.998569i | \(0.482969\pi\) | |||||||
\(194\) | −11.7005 | −0.840045 | ||||||||
\(195\) | 7.44204 | 0.532936 | ||||||||
\(196\) | 40.7777 | 2.91269 | ||||||||
\(197\) | −4.51312 | −0.321547 | −0.160773 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160773 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(198\) | −36.7658 | −2.61283 | ||||||||
\(199\) | 7.28028 | 0.516085 | 0.258043 | − | 0.966134i | \(-0.416923\pi\) | ||||
0.258043 | + | 0.966134i | \(0.416923\pi\) | |||||||
\(200\) | 1.04452 | 0.0738588 | ||||||||
\(201\) | −26.5522 | −1.87285 | ||||||||
\(202\) | −27.2179 | −1.91504 | ||||||||
\(203\) | −11.2493 | −0.789543 | ||||||||
\(204\) | 25.5039 | 1.78563 | ||||||||
\(205\) | −0.278075 | −0.0194216 | ||||||||
\(206\) | −24.9473 | −1.73816 | ||||||||
\(207\) | 45.3560 | 3.15246 | ||||||||
\(208\) | 6.26828 | 0.434627 | ||||||||
\(209\) | 13.1611 | 0.910374 | ||||||||
\(210\) | 33.7093 | 2.32616 | ||||||||
\(211\) | 14.0051 | 0.964154 | 0.482077 | − | 0.876129i | \(-0.339883\pi\) | ||||
0.482077 | + | 0.876129i | \(0.339883\pi\) | |||||||
\(212\) | 21.5852 | 1.48247 | ||||||||
\(213\) | 16.4718 | 1.12863 | ||||||||
\(214\) | −32.7735 | −2.24035 | ||||||||
\(215\) | −0.176109 | −0.0120105 | ||||||||
\(216\) | −16.5938 | −1.12907 | ||||||||
\(217\) | −21.6338 | −1.46860 | ||||||||
\(218\) | −16.7039 | −1.13133 | ||||||||
\(219\) | 30.2374 | 2.04325 | ||||||||
\(220\) | −5.52366 | −0.372405 | ||||||||
\(221\) | 7.03184 | 0.473013 | ||||||||
\(222\) | 57.4110 | 3.85317 | ||||||||
\(223\) | −8.76611 | −0.587022 | −0.293511 | − | 0.955956i | \(-0.594824\pi\) | ||||
−0.293511 | + | 0.955956i | \(0.594824\pi\) | |||||||
\(224\) | 38.4891 | 2.57166 | ||||||||
\(225\) | 7.82788 | 0.521859 | ||||||||
\(226\) | −4.26051 | −0.283405 | ||||||||
\(227\) | −21.8527 | −1.45042 | −0.725209 | − | 0.688529i | \(-0.758257\pi\) | ||||
−0.725209 | + | 0.688529i | \(0.758257\pi\) | |||||||
\(228\) | 48.7201 | 3.22657 | ||||||||
\(229\) | −20.0211 | −1.32303 | −0.661514 | − | 0.749932i | \(-0.730086\pi\) | ||||
−0.661514 | + | 0.749932i | \(0.730086\pi\) | |||||||
\(230\) | 12.2814 | 0.809812 | ||||||||
\(231\) | −35.2398 | −2.31861 | ||||||||
\(232\) | 2.43120 | 0.159616 | ||||||||
\(233\) | 15.3296 | 1.00428 | 0.502139 | − | 0.864787i | \(-0.332547\pi\) | ||||
0.502139 | + | 0.864787i | \(0.332547\pi\) | |||||||
\(234\) | −37.5252 | −2.45310 | ||||||||
\(235\) | 1.91855 | 0.125153 | ||||||||
\(236\) | 13.4527 | 0.875697 | ||||||||
\(237\) | 5.88844 | 0.382495 | ||||||||
\(238\) | 31.8513 | 2.06461 | ||||||||
\(239\) | 7.27188 | 0.470379 | 0.235190 | − | 0.971950i | \(-0.424429\pi\) | ||||
0.235190 | + | 0.971950i | \(0.424429\pi\) | |||||||
\(240\) | 9.12011 | 0.588701 | ||||||||
\(241\) | 4.02887 | 0.259522 | 0.129761 | − | 0.991545i | \(-0.458579\pi\) | ||||
0.129761 | + | 0.991545i | \(0.458579\pi\) | |||||||
\(242\) | −12.9084 | −0.829785 | ||||||||
\(243\) | −47.0831 | −3.02038 | ||||||||
\(244\) | −24.1588 | −1.54661 | ||||||||
\(245\) | 16.3583 | 1.04509 | ||||||||
\(246\) | 1.93951 | 0.123659 | ||||||||
\(247\) | 13.4329 | 0.854718 | ||||||||
\(248\) | 4.67553 | 0.296896 | ||||||||
\(249\) | −45.6992 | −2.89607 | ||||||||
\(250\) | 2.11962 | 0.134057 | ||||||||
\(251\) | −6.99410 | −0.441464 | −0.220732 | − | 0.975335i | \(-0.570845\pi\) | ||||
−0.220732 | + | 0.975335i | \(0.570845\pi\) | |||||||
\(252\) | −94.3083 | −5.94086 | ||||||||
\(253\) | −12.8390 | −0.807183 | ||||||||
\(254\) | −25.4688 | −1.59806 | ||||||||
\(255\) | 10.2311 | 0.640694 | ||||||||
\(256\) | 5.49964 | 0.343727 | ||||||||
\(257\) | −19.3582 | −1.20753 | −0.603767 | − | 0.797161i | \(-0.706334\pi\) | ||||
−0.603767 | + | 0.797161i | \(0.706334\pi\) | |||||||
\(258\) | 1.22832 | 0.0764718 | ||||||||
\(259\) | 39.7819 | 2.47193 | ||||||||
\(260\) | −5.63775 | −0.349638 | ||||||||
\(261\) | 18.2200 | 1.12779 | ||||||||
\(262\) | −43.6781 | −2.69844 | ||||||||
\(263\) | −5.73446 | −0.353602 | −0.176801 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176801 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(264\) | 7.61608 | 0.468737 | ||||||||
\(265\) | 8.65904 | 0.531921 | ||||||||
\(266\) | 60.8456 | 3.73068 | ||||||||
\(267\) | −3.29058 | −0.201380 | ||||||||
\(268\) | 20.1147 | 1.22870 | ||||||||
\(269\) | 5.07725 | 0.309565 | 0.154783 | − | 0.987949i | \(-0.450532\pi\) | ||||
0.154783 | + | 0.987949i | \(0.450532\pi\) | |||||||
\(270\) | −33.6734 | −2.04930 | ||||||||
\(271\) | 14.8909 | 0.904557 | 0.452278 | − | 0.891877i | \(-0.350611\pi\) | ||||
0.452278 | + | 0.891877i | \(0.350611\pi\) | |||||||
\(272\) | 8.61742 | 0.522508 | ||||||||
\(273\) | −35.9677 | −2.17686 | ||||||||
\(274\) | 23.1820 | 1.40048 | ||||||||
\(275\) | −2.21586 | −0.133621 | ||||||||
\(276\) | −47.5278 | −2.86084 | ||||||||
\(277\) | −30.6930 | −1.84417 | −0.922083 | − | 0.386993i | \(-0.873514\pi\) | ||||
−0.922083 | + | 0.386993i | \(0.873514\pi\) | |||||||
\(278\) | −0.915829 | −0.0549278 | ||||||||
\(279\) | 35.0395 | 2.09776 | ||||||||
\(280\) | −5.04821 | −0.301688 | ||||||||
\(281\) | 19.5982 | 1.16913 | 0.584564 | − | 0.811348i | \(-0.301266\pi\) | ||||
0.584564 | + | 0.811348i | \(0.301266\pi\) | |||||||
\(282\) | −13.3815 | −0.796855 | ||||||||
\(283\) | 32.1638 | 1.91194 | 0.955968 | − | 0.293469i | \(-0.0948099\pi\) | ||||
0.955968 | + | 0.293469i | \(0.0948099\pi\) | |||||||
\(284\) | −12.4783 | −0.740451 | ||||||||
\(285\) | 19.5444 | 1.15771 | ||||||||
\(286\) | 10.6223 | 0.628112 | ||||||||
\(287\) | 1.34395 | 0.0793308 | ||||||||
\(288\) | −62.3393 | −3.67338 | ||||||||
\(289\) | −7.33286 | −0.431345 | ||||||||
\(290\) | 4.93357 | 0.289709 | ||||||||
\(291\) | 18.1642 | 1.06481 | ||||||||
\(292\) | −22.9064 | −1.34050 | ||||||||
\(293\) | −22.7569 | −1.32947 | −0.664737 | − | 0.747077i | \(-0.731457\pi\) | ||||
−0.664737 | + | 0.747077i | \(0.731457\pi\) | |||||||
\(294\) | −114.095 | −6.65416 | ||||||||
\(295\) | 5.39666 | 0.314205 | ||||||||
\(296\) | −8.59771 | −0.499732 | ||||||||
\(297\) | 35.2023 | 2.04264 | ||||||||
\(298\) | −28.9152 | −1.67501 | ||||||||
\(299\) | −13.1042 | −0.757836 | ||||||||
\(300\) | −8.20270 | −0.473583 | ||||||||
\(301\) | 0.851142 | 0.0490590 | ||||||||
\(302\) | 47.4423 | 2.73000 | ||||||||
\(303\) | 42.2541 | 2.42743 | ||||||||
\(304\) | 16.4619 | 0.944154 | ||||||||
\(305\) | −9.69150 | −0.554933 | ||||||||
\(306\) | −51.5883 | −2.94911 | ||||||||
\(307\) | 0.883192 | 0.0504064 | 0.0252032 | − | 0.999682i | \(-0.491977\pi\) | ||||
0.0252032 | + | 0.999682i | \(0.491977\pi\) | |||||||
\(308\) | 26.6961 | 1.52115 | ||||||||
\(309\) | 38.7291 | 2.20322 | ||||||||
\(310\) | 9.48792 | 0.538878 | ||||||||
\(311\) | −2.98323 | −0.169163 | −0.0845816 | − | 0.996417i | \(-0.526955\pi\) | ||||
−0.0845816 | + | 0.996417i | \(0.526955\pi\) | |||||||
\(312\) | 7.77337 | 0.440081 | ||||||||
\(313\) | 6.07859 | 0.343582 | 0.171791 | − | 0.985133i | \(-0.445045\pi\) | ||||
0.171791 | + | 0.985133i | \(0.445045\pi\) | |||||||
\(314\) | 24.8771 | 1.40390 | ||||||||
\(315\) | −37.8325 | −2.13162 | ||||||||
\(316\) | −4.46081 | −0.250940 | ||||||||
\(317\) | 2.02998 | 0.114015 | 0.0570075 | − | 0.998374i | \(-0.481844\pi\) | ||||
0.0570075 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(318\) | −60.3948 | −3.38677 | ||||||||
\(319\) | −5.15757 | −0.288769 | ||||||||
\(320\) | −11.3370 | −0.633755 | ||||||||
\(321\) | 50.8788 | 2.83978 | ||||||||
\(322\) | −59.3565 | −3.30781 | ||||||||
\(323\) | 18.4672 | 1.02754 | ||||||||
\(324\) | 71.7726 | 3.98737 | ||||||||
\(325\) | −2.26162 | −0.125452 | ||||||||
\(326\) | 3.17260 | 0.175714 | ||||||||
\(327\) | 25.9317 | 1.43403 | ||||||||
\(328\) | −0.290456 | −0.0160377 | ||||||||
\(329\) | −9.27244 | −0.511206 | ||||||||
\(330\) | 15.4551 | 0.850775 | ||||||||
\(331\) | −12.3999 | −0.681559 | −0.340779 | − | 0.940143i | \(-0.610691\pi\) | ||||
−0.340779 | + | 0.940143i | \(0.610691\pi\) | |||||||
\(332\) | 34.6196 | 1.90000 | ||||||||
\(333\) | −64.4332 | −3.53092 | ||||||||
\(334\) | −1.17819 | −0.0644676 | ||||||||
\(335\) | 8.06916 | 0.440866 | ||||||||
\(336\) | −44.0778 | −2.40464 | ||||||||
\(337\) | 27.1425 | 1.47855 | 0.739274 | − | 0.673405i | \(-0.235169\pi\) | ||||
0.739274 | + | 0.673405i | \(0.235169\pi\) | |||||||
\(338\) | −16.7133 | −0.909085 | ||||||||
\(339\) | 6.61418 | 0.359233 | ||||||||
\(340\) | −7.75058 | −0.420334 | ||||||||
\(341\) | −9.91871 | −0.537128 | ||||||||
\(342\) | −98.5493 | −5.32894 | ||||||||
\(343\) | −45.2288 | −2.44213 | ||||||||
\(344\) | −0.183950 | −0.00991790 | ||||||||
\(345\) | −19.0661 | −1.02649 | ||||||||
\(346\) | 29.7533 | 1.59955 | ||||||||
\(347\) | −17.0635 | −0.916019 | −0.458009 | − | 0.888947i | \(-0.651437\pi\) | ||||
−0.458009 | + | 0.888947i | \(0.651437\pi\) | |||||||
\(348\) | −19.0924 | −1.02346 | ||||||||
\(349\) | 25.3297 | 1.35587 | 0.677933 | − | 0.735124i | \(-0.262876\pi\) | ||||
0.677933 | + | 0.735124i | \(0.262876\pi\) | |||||||
\(350\) | −10.2442 | −0.547576 | ||||||||
\(351\) | 35.9293 | 1.91776 | ||||||||
\(352\) | 17.6465 | 0.940564 | ||||||||
\(353\) | 15.3713 | 0.818132 | 0.409066 | − | 0.912505i | \(-0.365854\pi\) | ||||
0.409066 | + | 0.912505i | \(0.365854\pi\) | |||||||
\(354\) | −37.6404 | −2.00057 | ||||||||
\(355\) | −5.00576 | −0.265678 | ||||||||
\(356\) | 2.49279 | 0.132117 | ||||||||
\(357\) | −49.4471 | −2.61702 | ||||||||
\(358\) | 19.5550 | 1.03351 | ||||||||
\(359\) | −4.81197 | −0.253966 | −0.126983 | − | 0.991905i | \(-0.540529\pi\) | ||||
−0.126983 | + | 0.991905i | \(0.540529\pi\) | |||||||
\(360\) | 8.17640 | 0.430934 | ||||||||
\(361\) | 16.2779 | 0.856730 | ||||||||
\(362\) | −22.1933 | −1.16645 | ||||||||
\(363\) | 20.0395 | 1.05180 | ||||||||
\(364\) | 27.2474 | 1.42815 | ||||||||
\(365\) | −9.18909 | −0.480979 | ||||||||
\(366\) | 67.5959 | 3.53330 | ||||||||
\(367\) | 23.4281 | 1.22294 | 0.611468 | − | 0.791269i | \(-0.290579\pi\) | ||||
0.611468 | + | 0.791269i | \(0.290579\pi\) | |||||||
\(368\) | −16.0590 | −0.837134 | ||||||||
\(369\) | −2.17674 | −0.113317 | ||||||||
\(370\) | −17.4471 | −0.907031 | ||||||||
\(371\) | −41.8495 | −2.17272 | ||||||||
\(372\) | −36.7173 | −1.90370 | ||||||||
\(373\) | 10.4886 | 0.543078 | 0.271539 | − | 0.962427i | \(-0.412467\pi\) | ||||
0.271539 | + | 0.962427i | \(0.412467\pi\) | |||||||
\(374\) | 14.6032 | 0.755115 | ||||||||
\(375\) | −3.29058 | −0.169925 | ||||||||
\(376\) | 2.00397 | 0.103347 | ||||||||
\(377\) | −5.26409 | −0.271115 | ||||||||
\(378\) | 162.745 | 8.37068 | ||||||||
\(379\) | −20.6495 | −1.06069 | −0.530347 | − | 0.847781i | \(-0.677938\pi\) | ||||
−0.530347 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(380\) | −14.8060 | −0.759529 | ||||||||
\(381\) | 39.5388 | 2.02563 | ||||||||
\(382\) | −10.0450 | −0.513946 | ||||||||
\(383\) | 11.8529 | 0.605654 | 0.302827 | − | 0.953046i | \(-0.402070\pi\) | ||||
0.302827 | + | 0.953046i | \(0.402070\pi\) | |||||||
\(384\) | 26.6620 | 1.36059 | ||||||||
\(385\) | 10.7093 | 0.545798 | ||||||||
\(386\) | 3.14947 | 0.160304 | ||||||||
\(387\) | −1.37856 | −0.0700762 | ||||||||
\(388\) | −13.7604 | −0.698578 | ||||||||
\(389\) | −11.8172 | −0.599157 | −0.299578 | − | 0.954072i | \(-0.596846\pi\) | ||||
−0.299578 | + | 0.954072i | \(0.596846\pi\) | |||||||
\(390\) | 15.7743 | 0.798762 | ||||||||
\(391\) | −18.0152 | −0.911068 | ||||||||
\(392\) | 17.0866 | 0.863001 | ||||||||
\(393\) | 67.8075 | 3.42043 | ||||||||
\(394\) | −9.56610 | −0.481933 | ||||||||
\(395\) | −1.78949 | −0.0900388 | ||||||||
\(396\) | −43.2386 | −2.17282 | ||||||||
\(397\) | 36.5070 | 1.83223 | 0.916116 | − | 0.400912i | \(-0.131307\pi\) | ||||
0.916116 | + | 0.400912i | \(0.131307\pi\) | |||||||
\(398\) | 15.4314 | 0.773507 | ||||||||
\(399\) | −94.4590 | −4.72886 | ||||||||
\(400\) | −2.77159 | −0.138579 | ||||||||
\(401\) | 1.45221 | 0.0725197 | 0.0362599 | − | 0.999342i | \(-0.488456\pi\) | ||||
0.0362599 | + | 0.999342i | \(0.488456\pi\) | |||||||
\(402\) | −56.2805 | −2.80702 | ||||||||
\(403\) | −10.1236 | −0.504291 | ||||||||
\(404\) | −32.0097 | −1.59254 | ||||||||
\(405\) | 28.7921 | 1.43069 | ||||||||
\(406\) | −23.8441 | −1.18336 | ||||||||
\(407\) | 18.2393 | 0.904086 | ||||||||
\(408\) | 10.6866 | 0.529064 | ||||||||
\(409\) | 32.3981 | 1.60198 | 0.800992 | − | 0.598674i | \(-0.204306\pi\) | ||||
0.800992 | + | 0.598674i | \(0.204306\pi\) | |||||||
\(410\) | −0.589414 | −0.0291091 | ||||||||
\(411\) | −35.9886 | −1.77519 | ||||||||
\(412\) | −29.3394 | −1.44545 | ||||||||
\(413\) | −26.0822 | −1.28342 | ||||||||
\(414\) | 96.1375 | 4.72490 | ||||||||
\(415\) | 13.8879 | 0.681730 | ||||||||
\(416\) | 18.0110 | 0.883062 | ||||||||
\(417\) | 1.42177 | 0.0696242 | ||||||||
\(418\) | 27.8966 | 1.36447 | ||||||||
\(419\) | −10.4032 | −0.508227 | −0.254114 | − | 0.967174i | \(-0.581784\pi\) | ||||
−0.254114 | + | 0.967174i | \(0.581784\pi\) | |||||||
\(420\) | 39.6440 | 1.93443 | ||||||||
\(421\) | 1.28300 | 0.0625297 | 0.0312648 | − | 0.999511i | \(-0.490046\pi\) | ||||
0.0312648 | + | 0.999511i | \(0.490046\pi\) | |||||||
\(422\) | 29.6856 | 1.44507 | ||||||||
\(423\) | 15.0182 | 0.730211 | ||||||||
\(424\) | 9.04456 | 0.439243 | ||||||||
\(425\) | −3.10920 | −0.150818 | ||||||||
\(426\) | 34.9140 | 1.69159 | ||||||||
\(427\) | 46.8394 | 2.26672 | ||||||||
\(428\) | −38.5434 | −1.86307 | ||||||||
\(429\) | −16.4905 | −0.796169 | ||||||||
\(430\) | −0.373284 | −0.0180014 | ||||||||
\(431\) | −2.37582 | −0.114439 | −0.0572195 | − | 0.998362i | \(-0.518223\pi\) | ||||
−0.0572195 | + | 0.998362i | \(0.518223\pi\) | |||||||
\(432\) | 44.0308 | 2.11843 | ||||||||
\(433\) | 31.3903 | 1.50852 | 0.754262 | − | 0.656574i | \(-0.227995\pi\) | ||||
0.754262 | + | 0.656574i | \(0.227995\pi\) | |||||||
\(434\) | −45.8555 | −2.20113 | ||||||||
\(435\) | −7.65906 | −0.367224 | ||||||||
\(436\) | −19.6447 | −0.940808 | ||||||||
\(437\) | −34.4145 | −1.64627 | ||||||||
\(438\) | 64.0917 | 3.06242 | ||||||||
\(439\) | −8.32745 | −0.397448 | −0.198724 | − | 0.980056i | \(-0.563680\pi\) | ||||
−0.198724 | + | 0.980056i | \(0.563680\pi\) | |||||||
\(440\) | −2.31451 | −0.110340 | ||||||||
\(441\) | 128.051 | 6.09764 | ||||||||
\(442\) | 14.9048 | 0.708950 | ||||||||
\(443\) | −27.1908 | −1.29188 | −0.645938 | − | 0.763390i | \(-0.723534\pi\) | ||||
−0.645938 | + | 0.763390i | \(0.723534\pi\) | |||||||
\(444\) | 67.5184 | 3.20428 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | −18.5808 | −0.879827 | ||||||||
\(447\) | 44.8890 | 2.12318 | ||||||||
\(448\) | 54.7919 | 2.58867 | ||||||||
\(449\) | −20.2755 | −0.956861 | −0.478430 | − | 0.878126i | \(-0.658794\pi\) | ||||
−0.478430 | + | 0.878126i | \(0.658794\pi\) | |||||||
\(450\) | 16.5921 | 0.782161 | ||||||||
\(451\) | 0.616176 | 0.0290146 | ||||||||
\(452\) | −5.01059 | −0.235679 | ||||||||
\(453\) | −73.6512 | −3.46044 | ||||||||
\(454\) | −46.3195 | −2.17388 | ||||||||
\(455\) | 10.9305 | 0.512430 | ||||||||
\(456\) | 20.4146 | 0.956000 | ||||||||
\(457\) | −27.8204 | −1.30138 | −0.650691 | − | 0.759343i | \(-0.725521\pi\) | ||||
−0.650691 | + | 0.759343i | \(0.725521\pi\) | |||||||
\(458\) | −42.4370 | −1.98295 | ||||||||
\(459\) | 49.3944 | 2.30553 | ||||||||
\(460\) | 14.4436 | 0.673437 | ||||||||
\(461\) | 3.25129 | 0.151428 | 0.0757138 | − | 0.997130i | \(-0.475876\pi\) | ||||
0.0757138 | + | 0.997130i | \(0.475876\pi\) | |||||||
\(462\) | −74.6951 | −3.47513 | ||||||||
\(463\) | −13.8292 | −0.642699 | −0.321349 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321349 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(464\) | −6.45107 | −0.299483 | ||||||||
\(465\) | −14.7294 | −0.683059 | ||||||||
\(466\) | 32.4930 | 1.50521 | ||||||||
\(467\) | −19.5627 | −0.905253 | −0.452626 | − | 0.891700i | \(-0.649513\pi\) | ||||
−0.452626 | + | 0.891700i | \(0.649513\pi\) | |||||||
\(468\) | −44.1316 | −2.03998 | ||||||||
\(469\) | −38.9986 | −1.80079 | ||||||||
\(470\) | 4.06660 | 0.187578 | ||||||||
\(471\) | −38.6202 | −1.77952 | ||||||||
\(472\) | 5.63692 | 0.259461 | ||||||||
\(473\) | 0.390233 | 0.0179429 | ||||||||
\(474\) | 12.4812 | 0.573283 | ||||||||
\(475\) | −5.93952 | −0.272524 | ||||||||
\(476\) | 37.4588 | 1.71692 | ||||||||
\(477\) | 67.7820 | 3.10352 | ||||||||
\(478\) | 15.4136 | 0.705003 | ||||||||
\(479\) | 26.2070 | 1.19743 | 0.598714 | − | 0.800963i | \(-0.295679\pi\) | ||||
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(480\) | 26.2053 | 1.19610 | ||||||||
\(481\) | 18.6160 | 0.848815 | ||||||||
\(482\) | 8.53968 | 0.388972 | ||||||||
\(483\) | 92.1473 | 4.19285 | ||||||||
\(484\) | −15.1810 | −0.690046 | ||||||||
\(485\) | −5.52008 | −0.250654 | ||||||||
\(486\) | −99.7982 | −4.52694 | ||||||||
\(487\) | 28.8600 | 1.30777 | 0.653887 | − | 0.756592i | \(-0.273137\pi\) | ||||
0.653887 | + | 0.756592i | \(0.273137\pi\) | |||||||
\(488\) | −10.1230 | −0.458246 | ||||||||
\(489\) | −4.92526 | −0.222728 | ||||||||
\(490\) | 34.6733 | 1.56638 | ||||||||
\(491\) | −27.5737 | −1.24438 | −0.622192 | − | 0.782865i | \(-0.713758\pi\) | ||||
−0.622192 | + | 0.782865i | \(0.713758\pi\) | |||||||
\(492\) | 2.28097 | 0.102834 | ||||||||
\(493\) | −7.23690 | −0.325933 | ||||||||
\(494\) | 28.4727 | 1.28105 | ||||||||
\(495\) | −17.3455 | −0.779621 | ||||||||
\(496\) | −12.4063 | −0.557058 | ||||||||
\(497\) | 24.1930 | 1.08521 | ||||||||
\(498\) | −96.8648 | −4.34062 | ||||||||
\(499\) | 32.9455 | 1.47484 | 0.737422 | − | 0.675432i | \(-0.236043\pi\) | ||||
0.737422 | + | 0.675432i | \(0.236043\pi\) | |||||||
\(500\) | 2.49279 | 0.111481 | ||||||||
\(501\) | 1.82906 | 0.0817165 | ||||||||
\(502\) | −14.8248 | −0.661665 | ||||||||
\(503\) | −25.6894 | −1.14543 | −0.572717 | − | 0.819753i | \(-0.694110\pi\) | ||||
−0.572717 | + | 0.819753i | \(0.694110\pi\) | |||||||
\(504\) | −39.5168 | −1.76022 | ||||||||
\(505\) | −12.8409 | −0.571414 | ||||||||
\(506\) | −27.2139 | −1.20980 | ||||||||
\(507\) | 25.9464 | 1.15232 | ||||||||
\(508\) | −29.9527 | −1.32894 | ||||||||
\(509\) | 27.1811 | 1.20478 | 0.602390 | − | 0.798202i | \(-0.294215\pi\) | ||||
0.602390 | + | 0.798202i | \(0.294215\pi\) | |||||||
\(510\) | 21.6860 | 0.960270 | ||||||||
\(511\) | 44.4112 | 1.96464 | ||||||||
\(512\) | 27.8622 | 1.23135 | ||||||||
\(513\) | 94.3582 | 4.16602 | ||||||||
\(514\) | −41.0321 | −1.80985 | ||||||||
\(515\) | −11.7697 | −0.518635 | ||||||||
\(516\) | 1.44457 | 0.0635937 | ||||||||
\(517\) | −4.25124 | −0.186969 | ||||||||
\(518\) | 84.3225 | 3.70492 | ||||||||
\(519\) | −46.1902 | −2.02752 | ||||||||
\(520\) | −2.36231 | −0.103594 | ||||||||
\(521\) | 0.901023 | 0.0394745 | 0.0197373 | − | 0.999805i | \(-0.493717\pi\) | ||||
0.0197373 | + | 0.999805i | \(0.493717\pi\) | |||||||
\(522\) | 38.6194 | 1.69033 | ||||||||
\(523\) | 0.0126235 | 0.000551986 0 | 0.000275993 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000275993 | 1.00000i | \(0.499912\pi\) | ||||||||
\(524\) | −51.3678 | −2.24401 | ||||||||
\(525\) | 15.9035 | 0.694084 | ||||||||
\(526\) | −12.1549 | −0.529978 | ||||||||
\(527\) | −13.9175 | −0.606257 | ||||||||
\(528\) | −20.2089 | −0.879478 | ||||||||
\(529\) | 10.5723 | 0.459665 | ||||||||
\(530\) | 18.3539 | 0.797242 | ||||||||
\(531\) | 42.2444 | 1.83325 | ||||||||
\(532\) | 71.5577 | 3.10242 | ||||||||
\(533\) | 0.628902 | 0.0272408 | ||||||||
\(534\) | −6.97477 | −0.301828 | ||||||||
\(535\) | −15.4620 | −0.668480 | ||||||||
\(536\) | 8.42842 | 0.364052 | ||||||||
\(537\) | −30.3578 | −1.31004 | ||||||||
\(538\) | 10.7618 | 0.463976 | ||||||||
\(539\) | −36.2476 | −1.56129 | ||||||||
\(540\) | −39.6017 | −1.70419 | ||||||||
\(541\) | 9.28499 | 0.399193 | 0.199596 | − | 0.979878i | \(-0.436037\pi\) | ||||
0.199596 | + | 0.979878i | \(0.436037\pi\) | |||||||
\(542\) | 31.5630 | 1.35575 | ||||||||
\(543\) | 34.4536 | 1.47855 | ||||||||
\(544\) | 24.7609 | 1.06162 | ||||||||
\(545\) | −7.88060 | −0.337568 | ||||||||
\(546\) | −76.2378 | −3.26267 | ||||||||
\(547\) | −12.6475 | −0.540770 | −0.270385 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270385 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(548\) | 27.2633 | 1.16463 | ||||||||
\(549\) | −75.8639 | −3.23779 | ||||||||
\(550\) | −4.69678 | −0.200271 | ||||||||
\(551\) | −13.8247 | −0.588951 | ||||||||
\(552\) | −19.9150 | −0.847638 | ||||||||
\(553\) | 8.64865 | 0.367778 | ||||||||
\(554\) | −65.0576 | −2.76403 | ||||||||
\(555\) | 27.0855 | 1.14972 | ||||||||
\(556\) | −1.07707 | −0.0456777 | ||||||||
\(557\) | −1.89455 | −0.0802747 | −0.0401374 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401374 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(558\) | 74.2704 | 3.14411 | ||||||||
\(559\) | 0.398292 | 0.0168460 | ||||||||
\(560\) | 13.3952 | 0.566050 | ||||||||
\(561\) | −22.6706 | −0.957153 | ||||||||
\(562\) | 41.5406 | 1.75229 | ||||||||
\(563\) | −39.9171 | −1.68231 | −0.841153 | − | 0.540797i | \(-0.818123\pi\) | ||||
−0.841153 | + | 0.540797i | \(0.818123\pi\) | |||||||
\(564\) | −15.7373 | −0.662661 | ||||||||
\(565\) | −2.01004 | −0.0845629 | ||||||||
\(566\) | 68.1749 | 2.86561 | ||||||||
\(567\) | −139.153 | −5.84389 | ||||||||
\(568\) | −5.22863 | −0.219388 | ||||||||
\(569\) | −12.8214 | −0.537499 | −0.268750 | − | 0.963210i | \(-0.586610\pi\) | ||||
−0.268750 | + | 0.963210i | \(0.586610\pi\) | |||||||
\(570\) | 41.4268 | 1.73518 | ||||||||
\(571\) | −24.0157 | −1.00503 | −0.502513 | − | 0.864570i | \(-0.667591\pi\) | ||||
−0.502513 | + | 0.864570i | \(0.667591\pi\) | |||||||
\(572\) | 12.4924 | 0.522335 | ||||||||
\(573\) | 15.5942 | 0.651457 | ||||||||
\(574\) | 2.84866 | 0.118901 | ||||||||
\(575\) | 5.79416 | 0.241633 | ||||||||
\(576\) | −88.7443 | −3.69768 | ||||||||
\(577\) | −28.5046 | −1.18666 | −0.593331 | − | 0.804959i | \(-0.702187\pi\) | ||||
−0.593331 | + | 0.804959i | \(0.702187\pi\) | |||||||
\(578\) | −15.5429 | −0.646499 | ||||||||
\(579\) | −4.88935 | −0.203195 | ||||||||
\(580\) | 5.80215 | 0.240921 | ||||||||
\(581\) | −67.1207 | −2.78464 | ||||||||
\(582\) | 38.5013 | 1.59593 | ||||||||
\(583\) | −19.1872 | −0.794653 | ||||||||
\(584\) | −9.59820 | −0.397176 | ||||||||
\(585\) | −17.7037 | −0.731959 | ||||||||
\(586\) | −48.2361 | −1.99261 | ||||||||
\(587\) | −2.40697 | −0.0993462 | −0.0496731 | − | 0.998766i | \(-0.515818\pi\) | ||||
−0.0496731 | + | 0.998766i | \(0.515818\pi\) | |||||||
\(588\) | −134.182 | −5.53357 | ||||||||
\(589\) | −26.5867 | −1.09549 | ||||||||
\(590\) | 11.4389 | 0.470930 | ||||||||
\(591\) | 14.8508 | 0.610879 | ||||||||
\(592\) | 22.8136 | 0.937633 | ||||||||
\(593\) | 10.4715 | 0.430013 | 0.215006 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215006 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(594\) | 74.6154 | 3.06151 | ||||||||
\(595\) | 15.0269 | 0.616042 | ||||||||
\(596\) | −34.0058 | −1.39293 | ||||||||
\(597\) | −23.9563 | −0.980466 | ||||||||
\(598\) | −27.7759 | −1.13584 | ||||||||
\(599\) | 9.28858 | 0.379521 | 0.189760 | − | 0.981830i | \(-0.439229\pi\) | ||||
0.189760 | + | 0.981830i | \(0.439229\pi\) | |||||||
\(600\) | −3.43708 | −0.140318 | ||||||||
\(601\) | −18.0877 | −0.737814 | −0.368907 | − | 0.929466i | \(-0.620268\pi\) | ||||
−0.368907 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(602\) | 1.80410 | 0.0735295 | ||||||||
\(603\) | 63.1645 | 2.57226 | ||||||||
\(604\) | 55.7948 | 2.27026 | ||||||||
\(605\) | −6.08997 | −0.247593 | ||||||||
\(606\) | 89.5625 | 3.63823 | ||||||||
\(607\) | −4.08445 | −0.165783 | −0.0828914 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828914 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(608\) | 47.3008 | 1.91830 | ||||||||
\(609\) | 37.0165 | 1.49998 | ||||||||
\(610\) | −20.5423 | −0.831733 | ||||||||
\(611\) | −4.33904 | −0.175539 | ||||||||
\(612\) | −60.6706 | −2.45247 | ||||||||
\(613\) | 20.2800 | 0.819101 | 0.409551 | − | 0.912287i | \(-0.365685\pi\) | ||||
0.409551 | + | 0.912287i | \(0.365685\pi\) | |||||||
\(614\) | 1.87203 | 0.0755490 | ||||||||
\(615\) | 0.915028 | 0.0368975 | ||||||||
\(616\) | 11.1861 | 0.450702 | ||||||||
\(617\) | 3.23902 | 0.130398 | 0.0651990 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651990 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(618\) | 82.0910 | 3.30218 | ||||||||
\(619\) | 2.62101 | 0.105347 | 0.0526737 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526737 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(620\) | 11.1583 | 0.448129 | ||||||||
\(621\) | −92.0490 | −3.69380 | ||||||||
\(622\) | −6.32330 | −0.253541 | ||||||||
\(623\) | −4.83304 | −0.193632 | ||||||||
\(624\) | −20.6263 | −0.825711 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.8843 | 0.514960 | ||||||||
\(627\) | −43.3077 | −1.72954 | ||||||||
\(628\) | 29.2569 | 1.16748 | ||||||||
\(629\) | 25.5926 | 1.02044 | ||||||||
\(630\) | −80.1904 | −3.19486 | ||||||||
\(631\) | −4.84085 | −0.192711 | −0.0963557 | − | 0.995347i | \(-0.530719\pi\) | ||||
−0.0963557 | + | 0.995347i | \(0.530719\pi\) | |||||||
\(632\) | −1.86916 | −0.0743511 | ||||||||
\(633\) | −46.0850 | −1.83171 | ||||||||
\(634\) | 4.30278 | 0.170885 | ||||||||
\(635\) | −12.0158 | −0.476831 | ||||||||
\(636\) | −71.0276 | −2.81643 | ||||||||
\(637\) | −36.9962 | −1.46584 | ||||||||
\(638\) | −10.9321 | −0.432806 | ||||||||
\(639\) | −39.1845 | −1.55012 | ||||||||
\(640\) | −8.10252 | −0.320280 | ||||||||
\(641\) | −41.4377 | −1.63669 | −0.818344 | − | 0.574728i | \(-0.805108\pi\) | ||||
−0.818344 | + | 0.574728i | \(0.805108\pi\) | |||||||
\(642\) | 107.844 | 4.25625 | ||||||||
\(643\) | −26.2789 | −1.03634 | −0.518168 | − | 0.855279i | \(-0.673386\pi\) | ||||
−0.518168 | + | 0.855279i | \(0.673386\pi\) | |||||||
\(644\) | −69.8065 | −2.75076 | ||||||||
\(645\) | 0.579500 | 0.0228178 | ||||||||
\(646\) | 39.1434 | 1.54007 | ||||||||
\(647\) | 32.8680 | 1.29218 | 0.646088 | − | 0.763263i | \(-0.276404\pi\) | ||||
0.646088 | + | 0.763263i | \(0.276404\pi\) | |||||||
\(648\) | 30.0740 | 1.18142 | ||||||||
\(649\) | −11.9582 | −0.469401 | ||||||||
\(650\) | −4.79378 | −0.188028 | ||||||||
\(651\) | 71.1877 | 2.79007 | ||||||||
\(652\) | 3.73115 | 0.146123 | ||||||||
\(653\) | 34.0840 | 1.33381 | 0.666904 | − | 0.745143i | \(-0.267619\pi\) | ||||
0.666904 | + | 0.745143i | \(0.267619\pi\) | |||||||
\(654\) | 54.9653 | 2.14931 | ||||||||
\(655\) | −20.6066 | −0.805165 | ||||||||
\(656\) | 0.770710 | 0.0300912 | ||||||||
\(657\) | −71.9311 | −2.80630 | ||||||||
\(658\) | −19.6540 | −0.766195 | ||||||||
\(659\) | −22.3303 | −0.869864 | −0.434932 | − | 0.900463i | \(-0.643228\pi\) | ||||
−0.434932 | + | 0.900463i | \(0.643228\pi\) | |||||||
\(660\) | 18.1760 | 0.707501 | ||||||||
\(661\) | −4.90059 | −0.190611 | −0.0953055 | − | 0.995448i | \(-0.530383\pi\) | ||||
−0.0953055 | + | 0.995448i | \(0.530383\pi\) | |||||||
\(662\) | −26.2830 | −1.02152 | ||||||||
\(663\) | −23.1388 | −0.898637 | ||||||||
\(664\) | 14.5062 | 0.562950 | ||||||||
\(665\) | 28.7059 | 1.11317 | ||||||||
\(666\) | −136.574 | −5.29213 | ||||||||
\(667\) | 13.4863 | 0.522193 | ||||||||
\(668\) | −1.38561 | −0.0536110 | ||||||||
\(669\) | 28.8455 | 1.11523 | ||||||||
\(670\) | 17.1036 | 0.660768 | ||||||||
\(671\) | 21.4750 | 0.829032 | ||||||||
\(672\) | −126.651 | −4.88568 | ||||||||
\(673\) | 17.8142 | 0.686689 | 0.343344 | − | 0.939210i | \(-0.388440\pi\) | ||||
0.343344 | + | 0.939210i | \(0.388440\pi\) | |||||||
\(674\) | 57.5318 | 2.21604 | ||||||||
\(675\) | −15.8865 | −0.611472 | ||||||||
\(676\) | −19.6558 | −0.755992 | ||||||||
\(677\) | −2.59037 | −0.0995561 | −0.0497780 | − | 0.998760i | \(-0.515851\pi\) | ||||
−0.0497780 | + | 0.998760i | \(0.515851\pi\) | |||||||
\(678\) | 14.0195 | 0.538417 | ||||||||
\(679\) | 26.6788 | 1.02384 | ||||||||
\(680\) | −3.24763 | −0.124541 | ||||||||
\(681\) | 71.9081 | 2.75552 | ||||||||
\(682\) | −21.0239 | −0.805046 | ||||||||
\(683\) | 24.9388 | 0.954257 | 0.477128 | − | 0.878834i | \(-0.341678\pi\) | ||||
0.477128 | + | 0.878834i | \(0.341678\pi\) | |||||||
\(684\) | −115.899 | −4.43152 | ||||||||
\(685\) | 10.9369 | 0.417876 | ||||||||
\(686\) | −95.8678 | −3.66025 | ||||||||
\(687\) | 65.8808 | 2.51351 | ||||||||
\(688\) | 0.488101 | 0.0186087 | ||||||||
\(689\) | −19.5835 | −0.746072 | ||||||||
\(690\) | −40.4129 | −1.53849 | ||||||||
\(691\) | −29.1377 | −1.10845 | −0.554226 | − | 0.832366i | \(-0.686986\pi\) | ||||
−0.554226 | + | 0.832366i | \(0.686986\pi\) | |||||||
\(692\) | 34.9915 | 1.33018 | ||||||||
\(693\) | 83.8314 | 3.18449 | ||||||||
\(694\) | −36.1682 | −1.37293 | ||||||||
\(695\) | −0.432073 | −0.0163894 | ||||||||
\(696\) | −8.00005 | −0.303241 | ||||||||
\(697\) | 0.864593 | 0.0327488 | ||||||||
\(698\) | 53.6893 | 2.03217 | ||||||||
\(699\) | −50.4433 | −1.90794 | ||||||||
\(700\) | −12.0477 | −0.455362 | ||||||||
\(701\) | −37.5559 | −1.41847 | −0.709233 | − | 0.704974i | \(-0.750958\pi\) | ||||
−0.709233 | + | 0.704974i | \(0.750958\pi\) | |||||||
\(702\) | 76.1565 | 2.87434 | ||||||||
\(703\) | 48.8896 | 1.84391 | ||||||||
\(704\) | 25.1211 | 0.946786 | ||||||||
\(705\) | −6.31314 | −0.237767 | ||||||||
\(706\) | 32.5813 | 1.22621 | ||||||||
\(707\) | 62.0607 | 2.33403 | ||||||||
\(708\) | −44.2672 | −1.66366 | ||||||||
\(709\) | −16.0916 | −0.604334 | −0.302167 | − | 0.953255i | \(-0.597710\pi\) | ||||
−0.302167 | + | 0.953255i | \(0.597710\pi\) | |||||||
\(710\) | −10.6103 | −0.398198 | ||||||||
\(711\) | −14.0079 | −0.525337 | ||||||||
\(712\) | 1.04452 | 0.0391451 | ||||||||
\(713\) | 25.9360 | 0.971312 | ||||||||
\(714\) | −104.809 | −3.92238 | ||||||||
\(715\) | 5.01144 | 0.187417 | ||||||||
\(716\) | 22.9977 | 0.859464 | ||||||||
\(717\) | −23.9287 | −0.893633 | ||||||||
\(718\) | −10.1995 | −0.380644 | ||||||||
\(719\) | −3.86290 | −0.144062 | −0.0720310 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720310 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(720\) | −21.6957 | −0.808549 | ||||||||
\(721\) | 56.8834 | 2.11845 | ||||||||
\(722\) | 34.5029 | 1.28406 | ||||||||
\(723\) | −13.2573 | −0.493044 | ||||||||
\(724\) | −26.1005 | −0.970017 | ||||||||
\(725\) | 2.32757 | 0.0864439 | ||||||||
\(726\) | 42.4761 | 1.57644 | ||||||||
\(727\) | −10.4042 | −0.385871 | −0.192935 | − | 0.981211i | \(-0.561801\pi\) | ||||
−0.192935 | + | 0.981211i | \(0.561801\pi\) | |||||||
\(728\) | 11.4172 | 0.423148 | ||||||||
\(729\) | 68.5541 | 2.53904 | ||||||||
\(730\) | −19.4774 | −0.720890 | ||||||||
\(731\) | 0.547558 | 0.0202522 | ||||||||
\(732\) | 79.4965 | 2.93827 | ||||||||
\(733\) | −16.9908 | −0.627569 | −0.313784 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313784 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(734\) | 49.6587 | 1.83293 | ||||||||
\(735\) | −53.8281 | −1.98548 | ||||||||
\(736\) | −46.1432 | −1.70086 | ||||||||
\(737\) | −17.8801 | −0.658623 | ||||||||
\(738\) | −4.61387 | −0.169839 | ||||||||
\(739\) | 10.1630 | 0.373854 | 0.186927 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186927 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(740\) | −20.5187 | −0.754283 | ||||||||
\(741\) | −44.2021 | −1.62381 | ||||||||
\(742\) | −88.7050 | −3.25646 | ||||||||
\(743\) | −25.6666 | −0.941617 | −0.470809 | − | 0.882235i | \(-0.656038\pi\) | ||||
−0.470809 | + | 0.882235i | \(0.656038\pi\) | |||||||
\(744\) | −15.3852 | −0.564048 | ||||||||
\(745\) | −13.6417 | −0.499793 | ||||||||
\(746\) | 22.2318 | 0.813964 | ||||||||
\(747\) | 108.713 | 3.97759 | ||||||||
\(748\) | 17.1742 | 0.627950 | ||||||||
\(749\) | 74.7284 | 2.73051 | ||||||||
\(750\) | −6.97477 | −0.254682 | ||||||||
\(751\) | −1.88134 | −0.0686510 | −0.0343255 | − | 0.999411i | \(-0.510928\pi\) | ||||
−0.0343255 | + | 0.999411i | \(0.510928\pi\) | |||||||
\(752\) | −5.31744 | −0.193907 | ||||||||
\(753\) | 23.0146 | 0.838699 | ||||||||
\(754\) | −11.1579 | −0.406346 | ||||||||
\(755\) | 22.3825 | 0.814582 | ||||||||
\(756\) | 191.397 | 6.96102 | ||||||||
\(757\) | 11.6427 | 0.423161 | 0.211580 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211580 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(758\) | −43.7691 | −1.58977 | ||||||||
\(759\) | 42.2478 | 1.53350 | ||||||||
\(760\) | −6.20396 | −0.225041 | ||||||||
\(761\) | 20.9113 | 0.758035 | 0.379017 | − | 0.925390i | \(-0.376262\pi\) | ||||
0.379017 | + | 0.925390i | \(0.376262\pi\) | |||||||
\(762\) | 83.8071 | 3.03601 | ||||||||
\(763\) | 38.0872 | 1.37885 | ||||||||
\(764\) | −11.8134 | −0.427395 | ||||||||
\(765\) | −24.3385 | −0.879959 | ||||||||
\(766\) | 25.1236 | 0.907753 | ||||||||
\(767\) | −12.2052 | −0.440704 | ||||||||
\(768\) | −18.0970 | −0.653018 | ||||||||
\(769\) | −21.0699 | −0.759800 | −0.379900 | − | 0.925028i | \(-0.624042\pi\) | ||||
−0.379900 | + | 0.925028i | \(0.624042\pi\) | |||||||
\(770\) | 22.6997 | 0.818040 | ||||||||
\(771\) | 63.6997 | 2.29409 | ||||||||
\(772\) | 3.70395 | 0.133308 | ||||||||
\(773\) | 4.26541 | 0.153416 | 0.0767080 | − | 0.997054i | \(-0.475559\pi\) | ||||
0.0767080 | + | 0.997054i | \(0.475559\pi\) | |||||||
\(774\) | −2.92203 | −0.105030 | ||||||||
\(775\) | 4.47624 | 0.160791 | ||||||||
\(776\) | −5.76584 | −0.206982 | ||||||||
\(777\) | −130.905 | −4.69620 | ||||||||
\(778\) | −25.0480 | −0.898015 | ||||||||
\(779\) | 1.65163 | 0.0591759 | ||||||||
\(780\) | 18.5514 | 0.664248 | ||||||||
\(781\) | 11.0921 | 0.396905 | ||||||||
\(782\) | −38.1854 | −1.36551 | ||||||||
\(783\) | −36.9770 | −1.32145 | ||||||||
\(784\) | −45.3383 | −1.61923 | ||||||||
\(785\) | 11.7366 | 0.418898 | ||||||||
\(786\) | 143.726 | 5.12654 | ||||||||
\(787\) | 46.9571 | 1.67384 | 0.836920 | − | 0.547325i | \(-0.184354\pi\) | ||||
0.836920 | + | 0.547325i | \(0.184354\pi\) | |||||||
\(788\) | −11.2503 | −0.400774 | ||||||||
\(789\) | 18.8697 | 0.671778 | ||||||||
\(790\) | −3.79303 | −0.134950 | ||||||||
\(791\) | 9.71458 | 0.345411 | ||||||||
\(792\) | −18.1177 | −0.643786 | ||||||||
\(793\) | 21.9185 | 0.778349 | ||||||||
\(794\) | 77.3809 | 2.74615 | ||||||||
\(795\) | −28.4932 | −1.01055 | ||||||||
\(796\) | 18.1482 | 0.643245 | ||||||||
\(797\) | −36.9401 | −1.30849 | −0.654243 | − | 0.756284i | \(-0.727013\pi\) | ||||
−0.654243 | + | 0.756284i | \(0.727013\pi\) | |||||||
\(798\) | −200.217 | −7.08761 | ||||||||
\(799\) | −5.96517 | −0.211033 | ||||||||
\(800\) | −7.96375 | −0.281561 | ||||||||
\(801\) | 7.82788 | 0.276585 | ||||||||
\(802\) | 3.07813 | 0.108692 | ||||||||
\(803\) | 20.3617 | 0.718549 | ||||||||
\(804\) | −66.1890 | −2.33431 | ||||||||
\(805\) | −28.0034 | −0.986990 | ||||||||
\(806\) | −21.4581 | −0.755829 | ||||||||
\(807\) | −16.7071 | −0.588116 | ||||||||
\(808\) | −13.4126 | −0.471855 | ||||||||
\(809\) | 17.3676 | 0.610613 | 0.305306 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305306 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(810\) | 61.0283 | 2.14432 | ||||||||
\(811\) | −44.5363 | −1.56388 | −0.781941 | − | 0.623352i | \(-0.785770\pi\) | ||||
−0.781941 | + | 0.623352i | \(0.785770\pi\) | |||||||
\(812\) | −28.0420 | −0.984081 | ||||||||
\(813\) | −48.9996 | −1.71849 | ||||||||
\(814\) | 38.6603 | 1.35504 | ||||||||
\(815\) | 1.49678 | 0.0524299 | ||||||||
\(816\) | −28.3563 | −0.992668 | ||||||||
\(817\) | 1.04600 | 0.0365950 | ||||||||
\(818\) | 68.6717 | 2.40105 | ||||||||
\(819\) | 85.5628 | 2.98980 | ||||||||
\(820\) | −0.693183 | −0.0242070 | ||||||||
\(821\) | −17.7581 | −0.619761 | −0.309880 | − | 0.950776i | \(-0.600289\pi\) | ||||
−0.309880 | + | 0.950776i | \(0.600289\pi\) | |||||||
\(822\) | −76.2821 | −2.66064 | ||||||||
\(823\) | −27.7787 | −0.968304 | −0.484152 | − | 0.874984i | \(-0.660872\pi\) | ||||
−0.484152 | + | 0.874984i | \(0.660872\pi\) | |||||||
\(824\) | −12.2937 | −0.428272 | ||||||||
\(825\) | 7.29145 | 0.253856 | ||||||||
\(826\) | −55.2844 | −1.92359 | ||||||||
\(827\) | −28.8725 | −1.00400 | −0.501998 | − | 0.864869i | \(-0.667401\pi\) | ||||
−0.501998 | + | 0.864869i | \(0.667401\pi\) | |||||||
\(828\) | 113.063 | 3.92921 | ||||||||
\(829\) | 41.4440 | 1.43941 | 0.719704 | − | 0.694281i | \(-0.244277\pi\) | ||||
0.719704 | + | 0.694281i | \(0.244277\pi\) | |||||||
\(830\) | 29.4371 | 1.02178 | ||||||||
\(831\) | 100.998 | 3.50357 | ||||||||
\(832\) | 25.6399 | 0.888904 | ||||||||
\(833\) | −50.8611 | −1.76223 | ||||||||
\(834\) | 3.01361 | 0.104353 | ||||||||
\(835\) | −0.555849 | −0.0192360 | ||||||||
\(836\) | 32.8079 | 1.13468 | ||||||||
\(837\) | −71.1118 | −2.45798 | ||||||||
\(838\) | −22.0507 | −0.761730 | ||||||||
\(839\) | −15.0790 | −0.520583 | −0.260292 | − | 0.965530i | \(-0.583819\pi\) | ||||
−0.260292 | + | 0.965530i | \(0.583819\pi\) | |||||||
\(840\) | 16.6115 | 0.573152 | ||||||||
\(841\) | −23.5824 | −0.813186 | ||||||||
\(842\) | 2.71948 | 0.0937193 | ||||||||
\(843\) | −64.4892 | −2.22113 | ||||||||
\(844\) | 34.9118 | 1.20172 | ||||||||
\(845\) | −7.88506 | −0.271254 | ||||||||
\(846\) | 31.8329 | 1.09444 | ||||||||
\(847\) | 29.4331 | 1.01133 | ||||||||
\(848\) | −23.9993 | −0.824139 | ||||||||
\(849\) | −105.837 | −3.63233 | ||||||||
\(850\) | −6.59033 | −0.226046 | ||||||||
\(851\) | −47.6931 | −1.63490 | ||||||||
\(852\) | 41.0608 | 1.40672 | ||||||||
\(853\) | 36.1724 | 1.23852 | 0.619260 | − | 0.785186i | \(-0.287433\pi\) | ||||
0.619260 | + | 0.785186i | \(0.287433\pi\) | |||||||
\(854\) | 99.2816 | 3.39735 | ||||||||
\(855\) | −46.4939 | −1.59006 | ||||||||
\(856\) | −16.1504 | −0.552009 | ||||||||
\(857\) | 14.1138 | 0.482117 | 0.241058 | − | 0.970511i | \(-0.422505\pi\) | ||||
0.241058 | + | 0.970511i | \(0.422505\pi\) | |||||||
\(858\) | −34.9536 | −1.19330 | ||||||||
\(859\) | −3.04904 | −0.104032 | −0.0520159 | − | 0.998646i | \(-0.516565\pi\) | ||||
−0.0520159 | + | 0.998646i | \(0.516565\pi\) | |||||||
\(860\) | −0.439002 | −0.0149699 | ||||||||
\(861\) | −4.42237 | −0.150714 | ||||||||
\(862\) | −5.03582 | −0.171521 | ||||||||
\(863\) | −44.3700 | −1.51037 | −0.755187 | − | 0.655510i | \(-0.772454\pi\) | ||||
−0.755187 | + | 0.655510i | \(0.772454\pi\) | |||||||
\(864\) | 126.516 | 4.30417 | ||||||||
\(865\) | 14.0371 | 0.477276 | ||||||||
\(866\) | 66.5356 | 2.26097 | ||||||||
\(867\) | 24.1293 | 0.819475 | ||||||||
\(868\) | −53.9285 | −1.83045 | ||||||||
\(869\) | 3.96525 | 0.134512 | ||||||||
\(870\) | −16.2343 | −0.550394 | ||||||||
\(871\) | −18.2494 | −0.618358 | ||||||||
\(872\) | −8.23146 | −0.278752 | ||||||||
\(873\) | −43.2105 | −1.46246 | ||||||||
\(874\) | −72.9457 | −2.46742 | ||||||||
\(875\) | −4.83304 | −0.163386 | ||||||||
\(876\) | 75.3754 | 2.54670 | ||||||||
\(877\) | −39.0474 | −1.31854 | −0.659268 | − | 0.751908i | \(-0.729134\pi\) | ||||
−0.659268 | + | 0.751908i | \(0.729134\pi\) | |||||||
\(878\) | −17.6510 | −0.595693 | ||||||||
\(879\) | 74.8834 | 2.52575 | ||||||||
\(880\) | 6.14144 | 0.207028 | ||||||||
\(881\) | 8.96712 | 0.302110 | 0.151055 | − | 0.988525i | \(-0.451733\pi\) | ||||
0.151055 | + | 0.988525i | \(0.451733\pi\) | |||||||
\(882\) | 271.418 | 9.13913 | ||||||||
\(883\) | 6.30062 | 0.212033 | 0.106016 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106016 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(884\) | 17.5289 | 0.589560 | ||||||||
\(885\) | −17.7581 | −0.596932 | ||||||||
\(886\) | −57.6343 | −1.93626 | ||||||||
\(887\) | 51.6559 | 1.73443 | 0.867217 | − | 0.497931i | \(-0.165907\pi\) | ||||
0.867217 | + | 0.497931i | \(0.165907\pi\) | |||||||
\(888\) | 28.2914 | 0.949397 | ||||||||
\(889\) | 58.0726 | 1.94769 | ||||||||
\(890\) | 2.11962 | 0.0710498 | ||||||||
\(891\) | −63.7993 | −2.13736 | ||||||||
\(892\) | −21.8520 | −0.731660 | ||||||||
\(893\) | −11.3953 | −0.381329 | ||||||||
\(894\) | 95.1476 | 3.18221 | ||||||||
\(895\) | 9.22570 | 0.308381 | ||||||||
\(896\) | 39.1598 | 1.30824 | ||||||||
\(897\) | 43.1204 | 1.43975 | ||||||||
\(898\) | −42.9764 | −1.43414 | ||||||||
\(899\) | 10.4188 | 0.347486 | ||||||||
\(900\) | 19.5133 | 0.650442 | ||||||||
\(901\) | −26.9227 | −0.896926 | ||||||||
\(902\) | 1.30606 | 0.0434870 | ||||||||
\(903\) | −2.80075 | −0.0932030 | ||||||||
\(904\) | −2.09953 | −0.0698292 | ||||||||
\(905\) | −10.4704 | −0.348048 | ||||||||
\(906\) | −156.113 | −5.18649 | ||||||||
\(907\) | −30.5492 | −1.01437 | −0.507185 | − | 0.861837i | \(-0.669314\pi\) | ||||
−0.507185 | + | 0.861837i | \(0.669314\pi\) | |||||||
\(908\) | −54.4742 | −1.80779 | ||||||||
\(909\) | −100.517 | −3.33395 | ||||||||
\(910\) | 23.1685 | 0.768029 | ||||||||
\(911\) | 13.9379 | 0.461784 | 0.230892 | − | 0.972979i | \(-0.425836\pi\) | ||||
0.230892 | + | 0.972979i | \(0.425836\pi\) | |||||||
\(912\) | −54.1691 | −1.79372 | ||||||||
\(913\) | −30.7736 | −1.01846 | ||||||||
\(914\) | −58.9686 | −1.95051 | ||||||||
\(915\) | 31.8906 | 1.05427 | ||||||||
\(916\) | −49.9082 | −1.64901 | ||||||||
\(917\) | 99.5923 | 3.28883 | ||||||||
\(918\) | 104.697 | 3.45553 | ||||||||
\(919\) | 21.5909 | 0.712217 | 0.356108 | − | 0.934445i | \(-0.384103\pi\) | ||||
0.356108 | + | 0.934445i | \(0.384103\pi\) | |||||||
\(920\) | 6.05213 | 0.199533 | ||||||||
\(921\) | −2.90621 | −0.0957628 | ||||||||
\(922\) | 6.89150 | 0.226959 | ||||||||
\(923\) | 11.3211 | 0.372640 | ||||||||
\(924\) | −87.8454 | −2.88990 | ||||||||
\(925\) | −8.23124 | −0.270641 | ||||||||
\(926\) | −29.3127 | −0.963275 | ||||||||
\(927\) | −92.1319 | −3.02601 | ||||||||
\(928\) | −18.5362 | −0.608481 | ||||||||
\(929\) | −34.8126 | −1.14216 | −0.571082 | − | 0.820893i | \(-0.693476\pi\) | ||||
−0.571082 | + | 0.820893i | \(0.693476\pi\) | |||||||
\(930\) | −31.2207 | −1.02377 | ||||||||
\(931\) | −97.1601 | −3.18429 | ||||||||
\(932\) | 38.2135 | 1.25172 | ||||||||
\(933\) | 9.81653 | 0.321379 | ||||||||
\(934\) | −41.4654 | −1.35679 | ||||||||
\(935\) | 6.88955 | 0.225312 | ||||||||
\(936\) | −18.4919 | −0.604427 | ||||||||
\(937\) | 29.3529 | 0.958918 | 0.479459 | − | 0.877564i | \(-0.340833\pi\) | ||||
0.479459 | + | 0.877564i | \(0.340833\pi\) | |||||||
\(938\) | −82.6622 | −2.69901 | ||||||||
\(939\) | −20.0021 | −0.652743 | ||||||||
\(940\) | 4.78255 | 0.155989 | ||||||||
\(941\) | 39.9726 | 1.30307 | 0.651534 | − | 0.758619i | \(-0.274126\pi\) | ||||
0.651534 | + | 0.758619i | \(0.274126\pi\) | |||||||
\(942\) | −81.8601 | −2.66715 | ||||||||
\(943\) | −1.61121 | −0.0524683 | ||||||||
\(944\) | −14.9573 | −0.486819 | ||||||||
\(945\) | 76.7801 | 2.49766 | ||||||||
\(946\) | 0.827145 | 0.0268928 | ||||||||
\(947\) | 57.0642 | 1.85434 | 0.927168 | − | 0.374646i | \(-0.122236\pi\) | ||||
0.927168 | + | 0.374646i | \(0.122236\pi\) | |||||||
\(948\) | 14.6786 | 0.476739 | ||||||||
\(949\) | 20.7822 | 0.674620 | ||||||||
\(950\) | −12.5895 | −0.408458 | ||||||||
\(951\) | −6.67980 | −0.216607 | ||||||||
\(952\) | 15.6959 | 0.508707 | ||||||||
\(953\) | 47.9488 | 1.55321 | 0.776607 | − | 0.629985i | \(-0.216939\pi\) | ||||
0.776607 | + | 0.629985i | \(0.216939\pi\) | |||||||
\(954\) | 143.672 | 4.65155 | ||||||||
\(955\) | −4.73905 | −0.153352 | ||||||||
\(956\) | 18.1273 | 0.586278 | ||||||||
\(957\) | 16.9714 | 0.548607 | ||||||||
\(958\) | 55.5488 | 1.79470 | ||||||||
\(959\) | −52.8583 | −1.70688 | ||||||||
\(960\) | 37.3051 | 1.20402 | ||||||||
\(961\) | −10.9633 | −0.353655 | ||||||||
\(962\) | 39.4587 | 1.27220 | ||||||||
\(963\) | −121.035 | −3.90029 | ||||||||
\(964\) | 10.0431 | 0.323467 | ||||||||
\(965\) | 1.48587 | 0.0478317 | ||||||||
\(966\) | 195.317 | 6.28423 | ||||||||
\(967\) | −22.9873 | −0.739222 | −0.369611 | − | 0.929187i | \(-0.620509\pi\) | ||||
−0.369611 | + | 0.929187i | \(0.620509\pi\) | |||||||
\(968\) | −6.36111 | −0.204454 | ||||||||
\(969\) | −60.7676 | −1.95214 | ||||||||
\(970\) | −11.7005 | −0.375679 | ||||||||
\(971\) | 4.86938 | 0.156266 | 0.0781330 | − | 0.996943i | \(-0.475104\pi\) | ||||
0.0781330 | + | 0.996943i | \(0.475104\pi\) | |||||||
\(972\) | −117.368 | −3.76458 | ||||||||
\(973\) | 2.08822 | 0.0669454 | ||||||||
\(974\) | 61.1723 | 1.96009 | ||||||||
\(975\) | 7.44204 | 0.238336 | ||||||||
\(976\) | 26.8608 | 0.859794 | ||||||||
\(977\) | 5.28623 | 0.169121 | 0.0845607 | − | 0.996418i | \(-0.473051\pi\) | ||||
0.0845607 | + | 0.996418i | \(0.473051\pi\) | |||||||
\(978\) | −10.4397 | −0.333824 | ||||||||
\(979\) | −2.21586 | −0.0708191 | ||||||||
\(980\) | 40.7777 | 1.30259 | ||||||||
\(981\) | −61.6884 | −1.96956 | ||||||||
\(982\) | −58.4458 | −1.86508 | ||||||||
\(983\) | 21.4830 | 0.685202 | 0.342601 | − | 0.939481i | \(-0.388692\pi\) | ||||
0.342601 | + | 0.939481i | \(0.388692\pi\) | |||||||
\(984\) | 0.955767 | 0.0304687 | ||||||||
\(985\) | −4.51312 | −0.143800 | ||||||||
\(986\) | −15.3395 | −0.488508 | ||||||||
\(987\) | 30.5117 | 0.971197 | ||||||||
\(988\) | 33.4855 | 1.06532 | ||||||||
\(989\) | −1.02040 | −0.0324470 | ||||||||
\(990\) | −36.7658 | −1.16849 | ||||||||
\(991\) | −39.9796 | −1.26999 | −0.634997 | − | 0.772514i | \(-0.718999\pi\) | ||||
−0.634997 | + | 0.772514i | \(0.718999\pi\) | |||||||
\(992\) | −35.6476 | −1.13181 | ||||||||
\(993\) | 40.8027 | 1.29484 | ||||||||
\(994\) | 51.2800 | 1.62650 | ||||||||
\(995\) | 7.28028 | 0.230800 | ||||||||
\(996\) | −113.918 | −3.60964 | ||||||||
\(997\) | −40.8157 | −1.29265 | −0.646323 | − | 0.763064i | \(-0.723694\pi\) | ||||
−0.646323 | + | 0.763064i | \(0.723694\pi\) | |||||||
\(998\) | 69.8320 | 2.21049 | ||||||||
\(999\) | 130.766 | 4.13724 |
(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 | 445.2.a.f.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 4005.2.a.o.1.1 | 7 | |||
4.3 | odd | 2 | 7120.2.a.bj.1.7 | 7 | |||
5.4 | even | 2 | 2225.2.a.k.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.f.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2225.2.a.k.1.1 | 7 | 5.4 | even | 2 | |||
4005.2.a.o.1.1 | 7 | 3.2 | odd | 2 | |||
7120.2.a.bj.1.7 | 7 | 4.3 | odd | 2 |