Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(1,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, 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("637.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4507648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) |
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 | 1.4 | ||
Root | \(1.90903\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.264627 | 0.187119 | 0.0935596 | − | 0.995614i | \(-0.470175\pi\) | ||||
0.0935596 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(3\) | −2.90903 | −1.67953 | −0.839765 | − | 0.542949i | \(-0.817308\pi\) | ||||
−0.839765 | + | 0.542949i | \(0.817308\pi\) | |||||||
\(4\) | −1.92997 | −0.964986 | ||||||||
\(5\) | 1.43515 | 0.641820 | 0.320910 | − | 0.947110i | \(-0.396011\pi\) | ||||
0.320910 | + | 0.947110i | \(0.396011\pi\) | |||||||
\(6\) | −0.769807 | −0.314273 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.03998 | −0.367687 | ||||||||
\(9\) | 5.46247 | 1.82082 | ||||||||
\(10\) | 0.379780 | 0.120097 | ||||||||
\(11\) | 5.50474 | 1.65974 | 0.829871 | − | 0.557955i | \(-0.188414\pi\) | ||||
0.829871 | + | 0.557955i | \(0.188414\pi\) | |||||||
\(12\) | 5.61435 | 1.62072 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.17491 | −1.07796 | ||||||||
\(16\) | 3.58474 | 0.896185 | ||||||||
\(17\) | −4.83072 | −1.17162 | −0.585811 | − | 0.810448i | \(-0.699224\pi\) | ||||
−0.585811 | + | 0.810448i | \(0.699224\pi\) | |||||||
\(18\) | 1.44552 | 0.340711 | ||||||||
\(19\) | −2.82036 | −0.647035 | −0.323518 | − | 0.946222i | \(-0.604865\pi\) | ||||
−0.323518 | + | 0.946222i | \(0.604865\pi\) | |||||||
\(20\) | −2.76981 | −0.619348 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.45670 | 0.310570 | ||||||||
\(23\) | −5.99956 | −1.25100 | −0.625498 | − | 0.780226i | \(-0.715104\pi\) | ||||
−0.625498 | + | 0.780226i | \(0.715104\pi\) | |||||||
\(24\) | 3.02532 | 0.617541 | ||||||||
\(25\) | −2.94033 | −0.588067 | ||||||||
\(26\) | −0.264627 | −0.0518975 | ||||||||
\(27\) | −7.16341 | −1.37860 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.04188 | 0.193472 | 0.0967361 | − | 0.995310i | \(-0.469160\pi\) | ||||
0.0967361 | + | 0.995310i | \(0.469160\pi\) | |||||||
\(30\) | −1.10479 | −0.201706 | ||||||||
\(31\) | −9.20895 | −1.65398 | −0.826988 | − | 0.562219i | \(-0.809948\pi\) | ||||
−0.826988 | + | 0.562219i | \(0.809948\pi\) | |||||||
\(32\) | 3.02857 | 0.535380 | ||||||||
\(33\) | −16.0135 | −2.78759 | ||||||||
\(34\) | −1.27834 | −0.219233 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.5424 | −1.75707 | ||||||||
\(37\) | 0.612497 | 0.100694 | 0.0503470 | − | 0.998732i | \(-0.483967\pi\) | ||||
0.0503470 | + | 0.998732i | \(0.483967\pi\) | |||||||
\(38\) | −0.746342 | −0.121073 | ||||||||
\(39\) | 2.90903 | 0.465818 | ||||||||
\(40\) | −1.49252 | −0.235989 | ||||||||
\(41\) | 10.6196 | 1.65850 | 0.829249 | − | 0.558879i | \(-0.188768\pi\) | ||||
0.829249 | + | 0.558879i | \(0.188768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.43685 | −1.28661 | −0.643304 | − | 0.765611i | \(-0.722437\pi\) | ||||
−0.643304 | + | 0.765611i | \(0.722437\pi\) | |||||||
\(44\) | −10.6240 | −1.60163 | ||||||||
\(45\) | 7.83949 | 1.16864 | ||||||||
\(46\) | −1.58764 | −0.234085 | ||||||||
\(47\) | −2.40922 | −0.351422 | −0.175711 | − | 0.984442i | \(-0.556222\pi\) | ||||
−0.175711 | + | 0.984442i | \(0.556222\pi\) | |||||||
\(48\) | −10.4281 | −1.50517 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.778091 | −0.110039 | ||||||||
\(51\) | 14.0527 | 1.96778 | ||||||||
\(52\) | 1.92997 | 0.267639 | ||||||||
\(53\) | −1.82959 | −0.251313 | −0.125657 | − | 0.992074i | \(-0.540104\pi\) | ||||
−0.125657 | + | 0.992074i | \(0.540104\pi\) | |||||||
\(54\) | −1.89563 | −0.257962 | ||||||||
\(55\) | 7.90015 | 1.06526 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.20452 | 1.08672 | ||||||||
\(58\) | 0.275709 | 0.0362024 | ||||||||
\(59\) | 0.870914 | 0.113383 | 0.0566917 | − | 0.998392i | \(-0.481945\pi\) | ||||
0.0566917 | + | 0.998392i | \(0.481945\pi\) | |||||||
\(60\) | 8.05746 | 1.04021 | ||||||||
\(61\) | 3.33253 | 0.426686 | 0.213343 | − | 0.976977i | \(-0.431565\pi\) | ||||
0.213343 | + | 0.976977i | \(0.431565\pi\) | |||||||
\(62\) | −2.43693 | −0.309491 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.36804 | −0.796005 | ||||||||
\(65\) | −1.43515 | −0.178009 | ||||||||
\(66\) | −4.23759 | −0.521611 | ||||||||
\(67\) | −6.62741 | −0.809667 | −0.404833 | − | 0.914390i | \(-0.632671\pi\) | ||||
−0.404833 | + | 0.914390i | \(0.632671\pi\) | |||||||
\(68\) | 9.32316 | 1.13060 | ||||||||
\(69\) | 17.4529 | 2.10108 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.85856 | −0.813961 | −0.406980 | − | 0.913437i | \(-0.633418\pi\) | ||||
−0.406980 | + | 0.913437i | \(0.633418\pi\) | |||||||
\(72\) | −5.68083 | −0.669493 | ||||||||
\(73\) | −3.14147 | −0.367682 | −0.183841 | − | 0.982956i | \(-0.558853\pi\) | ||||
−0.183841 | + | 0.982956i | \(0.558853\pi\) | |||||||
\(74\) | 0.162083 | 0.0188418 | ||||||||
\(75\) | 8.55353 | 0.987676 | ||||||||
\(76\) | 5.44322 | 0.624380 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.769807 | 0.0871635 | ||||||||
\(79\) | −17.5723 | −1.97704 | −0.988518 | − | 0.151101i | \(-0.951718\pi\) | ||||
−0.988518 | + | 0.151101i | \(0.951718\pi\) | |||||||
\(80\) | 5.14465 | 0.575190 | ||||||||
\(81\) | 4.45118 | 0.494576 | ||||||||
\(82\) | 2.81022 | 0.310337 | ||||||||
\(83\) | −11.4525 | −1.25708 | −0.628538 | − | 0.777779i | \(-0.716346\pi\) | ||||
−0.628538 | + | 0.777779i | \(0.716346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.93283 | −0.751971 | ||||||||
\(86\) | −2.23261 | −0.240749 | ||||||||
\(87\) | −3.03086 | −0.324943 | ||||||||
\(88\) | −5.72479 | −0.610265 | ||||||||
\(89\) | 0.995318 | 0.105503 | 0.0527517 | − | 0.998608i | \(-0.483201\pi\) | ||||
0.0527517 | + | 0.998608i | \(0.483201\pi\) | |||||||
\(90\) | 2.07454 | 0.218675 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.5790 | 1.20719 | ||||||||
\(93\) | 26.7891 | 2.77790 | ||||||||
\(94\) | −0.637545 | −0.0657577 | ||||||||
\(95\) | −4.04765 | −0.415280 | ||||||||
\(96\) | −8.81020 | −0.899188 | ||||||||
\(97\) | −13.5090 | −1.37163 | −0.685817 | − | 0.727774i | \(-0.740555\pi\) | ||||
−0.685817 | + | 0.727774i | \(0.740555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30.0695 | 3.02210 | ||||||||
\(100\) | 5.67477 | 0.567477 | ||||||||
\(101\) | 1.00807 | 0.100306 | 0.0501532 | − | 0.998742i | \(-0.484029\pi\) | ||||
0.0501532 | + | 0.998742i | \(0.484029\pi\) | |||||||
\(102\) | 3.71873 | 0.368209 | ||||||||
\(103\) | 12.7754 | 1.25880 | 0.629401 | − | 0.777081i | \(-0.283300\pi\) | ||||
0.629401 | + | 0.777081i | \(0.283300\pi\) | |||||||
\(104\) | 1.03998 | 0.101978 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.484157 | −0.0470255 | ||||||||
\(107\) | −0.685495 | −0.0662693 | −0.0331347 | − | 0.999451i | \(-0.510549\pi\) | ||||
−0.0331347 | + | 0.999451i | \(0.510549\pi\) | |||||||
\(108\) | 13.8252 | 1.33033 | ||||||||
\(109\) | −2.90344 | −0.278099 | −0.139050 | − | 0.990285i | \(-0.544405\pi\) | ||||
−0.139050 | + | 0.990285i | \(0.544405\pi\) | |||||||
\(110\) | 2.09059 | 0.199330 | ||||||||
\(111\) | −1.78177 | −0.169119 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0315 | 1.13183 | 0.565915 | − | 0.824464i | \(-0.308523\pi\) | ||||
0.565915 | + | 0.824464i | \(0.308523\pi\) | |||||||
\(114\) | 2.17113 | 0.203345 | ||||||||
\(115\) | −8.61029 | −0.802914 | ||||||||
\(116\) | −2.01080 | −0.186698 | ||||||||
\(117\) | −5.46247 | −0.505006 | ||||||||
\(118\) | 0.230467 | 0.0212162 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.34180 | 0.396350 | ||||||||
\(121\) | 19.3022 | 1.75474 | ||||||||
\(122\) | 0.881875 | 0.0798412 | ||||||||
\(123\) | −30.8927 | −2.78550 | ||||||||
\(124\) | 17.7730 | 1.59606 | ||||||||
\(125\) | −11.3956 | −1.01925 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6659 | 1.39012 | 0.695062 | − | 0.718950i | \(-0.255377\pi\) | ||||
0.695062 | + | 0.718950i | \(0.255377\pi\) | |||||||
\(128\) | −7.74229 | −0.684328 | ||||||||
\(129\) | 24.5431 | 2.16090 | ||||||||
\(130\) | −0.379780 | −0.0333089 | ||||||||
\(131\) | −12.1273 | −1.05957 | −0.529784 | − | 0.848132i | \(-0.677727\pi\) | ||||
−0.529784 | + | 0.848132i | \(0.677727\pi\) | |||||||
\(132\) | 30.9056 | 2.68998 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.75379 | −0.151504 | ||||||||
\(135\) | −10.2806 | −0.884813 | ||||||||
\(136\) | 5.02383 | 0.430790 | ||||||||
\(137\) | 15.9375 | 1.36163 | 0.680815 | − | 0.732456i | \(-0.261626\pi\) | ||||
0.680815 | + | 0.732456i | \(0.261626\pi\) | |||||||
\(138\) | 4.61851 | 0.393153 | ||||||||
\(139\) | 6.64088 | 0.563272 | 0.281636 | − | 0.959521i | \(-0.409123\pi\) | ||||
0.281636 | + | 0.959521i | \(0.409123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00851 | 0.590223 | ||||||||
\(142\) | −1.81496 | −0.152308 | ||||||||
\(143\) | −5.50474 | −0.460330 | ||||||||
\(144\) | 19.5815 | 1.63180 | ||||||||
\(145\) | 1.49526 | 0.124174 | ||||||||
\(146\) | −0.831317 | −0.0688003 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.18210 | −0.0971683 | ||||||||
\(149\) | −19.5502 | −1.60162 | −0.800809 | − | 0.598920i | \(-0.795597\pi\) | ||||
−0.800809 | + | 0.598920i | \(0.795597\pi\) | |||||||
\(150\) | 2.26349 | 0.184813 | ||||||||
\(151\) | 10.6880 | 0.869779 | 0.434890 | − | 0.900484i | \(-0.356787\pi\) | ||||
0.434890 | + | 0.900484i | \(0.356787\pi\) | |||||||
\(152\) | 2.93311 | 0.237906 | ||||||||
\(153\) | −26.3877 | −2.13332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.2163 | −1.06156 | ||||||||
\(156\) | −5.61435 | −0.449508 | ||||||||
\(157\) | 15.0734 | 1.20299 | 0.601496 | − | 0.798876i | \(-0.294572\pi\) | ||||
0.601496 | + | 0.798876i | \(0.294572\pi\) | |||||||
\(158\) | −4.65009 | −0.369942 | ||||||||
\(159\) | 5.32233 | 0.422088 | ||||||||
\(160\) | 4.34646 | 0.343618 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.17790 | 0.0925447 | ||||||||
\(163\) | −23.8135 | −1.86521 | −0.932607 | − | 0.360894i | \(-0.882472\pi\) | ||||
−0.932607 | + | 0.360894i | \(0.882472\pi\) | |||||||
\(164\) | −20.4955 | −1.60043 | ||||||||
\(165\) | −22.9818 | −1.78913 | ||||||||
\(166\) | −3.03064 | −0.235223 | ||||||||
\(167\) | 7.12371 | 0.551249 | 0.275625 | − | 0.961265i | \(-0.411115\pi\) | ||||
0.275625 | + | 0.961265i | \(0.411115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.83461 | −0.140708 | ||||||||
\(171\) | −15.4061 | −1.17814 | ||||||||
\(172\) | 16.2829 | 1.24156 | ||||||||
\(173\) | −11.2367 | −0.854309 | −0.427155 | − | 0.904179i | \(-0.640484\pi\) | ||||
−0.427155 | + | 0.904179i | \(0.640484\pi\) | |||||||
\(174\) | −0.802047 | −0.0608030 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.7331 | 1.48744 | ||||||||
\(177\) | −2.53352 | −0.190431 | ||||||||
\(178\) | 0.263387 | 0.0197417 | ||||||||
\(179\) | −13.1945 | −0.986204 | −0.493102 | − | 0.869972i | \(-0.664137\pi\) | ||||
−0.493102 | + | 0.869972i | \(0.664137\pi\) | |||||||
\(180\) | −15.1300 | −1.12772 | ||||||||
\(181\) | 13.7414 | 1.02139 | 0.510696 | − | 0.859761i | \(-0.329388\pi\) | ||||
0.510696 | + | 0.859761i | \(0.329388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.69443 | −0.716633 | ||||||||
\(184\) | 6.23939 | 0.459974 | ||||||||
\(185\) | 0.879028 | 0.0646274 | ||||||||
\(186\) | 7.08912 | 0.519799 | ||||||||
\(187\) | −26.5919 | −1.94459 | ||||||||
\(188\) | 4.64974 | 0.339117 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.07112 | −0.0777069 | ||||||||
\(191\) | −16.3307 | −1.18165 | −0.590824 | − | 0.806800i | \(-0.701197\pi\) | ||||
−0.590824 | + | 0.806800i | \(0.701197\pi\) | |||||||
\(192\) | 18.5248 | 1.33692 | ||||||||
\(193\) | −14.0533 | −1.01158 | −0.505790 | − | 0.862656i | \(-0.668799\pi\) | ||||
−0.505790 | + | 0.862656i | \(0.668799\pi\) | |||||||
\(194\) | −3.57485 | −0.256659 | ||||||||
\(195\) | 4.17491 | 0.298971 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.46898 | −0.104660 | −0.0523302 | − | 0.998630i | \(-0.516665\pi\) | ||||
−0.0523302 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(198\) | 7.95719 | 0.565493 | ||||||||
\(199\) | 13.3772 | 0.948285 | 0.474142 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474142 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(200\) | 3.05787 | 0.216224 | ||||||||
\(201\) | 19.2794 | 1.35986 | ||||||||
\(202\) | 0.266761 | 0.0187692 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −27.1214 | −1.89888 | ||||||||
\(205\) | 15.2407 | 1.06446 | ||||||||
\(206\) | 3.38072 | 0.235546 | ||||||||
\(207\) | −32.7724 | −2.27784 | ||||||||
\(208\) | −3.58474 | −0.248557 | ||||||||
\(209\) | −15.5254 | −1.07391 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.47044 | 0.238915 | 0.119457 | − | 0.992839i | \(-0.461885\pi\) | ||||
0.119457 | + | 0.992839i | \(0.461885\pi\) | |||||||
\(212\) | 3.53105 | 0.242514 | ||||||||
\(213\) | 19.9518 | 1.36707 | ||||||||
\(214\) | −0.181400 | −0.0124003 | ||||||||
\(215\) | −12.1082 | −0.825771 | ||||||||
\(216\) | 7.44977 | 0.506893 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.768328 | −0.0520378 | ||||||||
\(219\) | 9.13865 | 0.617533 | ||||||||
\(220\) | −15.2471 | −1.02796 | ||||||||
\(221\) | 4.83072 | 0.324950 | ||||||||
\(222\) | −0.471505 | −0.0316453 | ||||||||
\(223\) | 9.91318 | 0.663836 | 0.331918 | − | 0.943308i | \(-0.392304\pi\) | ||||
0.331918 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.0615 | −1.07077 | ||||||||
\(226\) | 3.18386 | 0.211787 | ||||||||
\(227\) | −12.0727 | −0.801292 | −0.400646 | − | 0.916233i | \(-0.631214\pi\) | ||||
−0.400646 | + | 0.916233i | \(0.631214\pi\) | |||||||
\(228\) | −15.8345 | −1.04867 | ||||||||
\(229\) | −4.05171 | −0.267745 | −0.133872 | − | 0.990999i | \(-0.542741\pi\) | ||||
−0.133872 | + | 0.990999i | \(0.542741\pi\) | |||||||
\(230\) | −2.27851 | −0.150241 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.08353 | −0.0711372 | ||||||||
\(233\) | 12.5450 | 0.821850 | 0.410925 | − | 0.911669i | \(-0.365206\pi\) | ||||
0.410925 | + | 0.911669i | \(0.365206\pi\) | |||||||
\(234\) | −1.44552 | −0.0944963 | ||||||||
\(235\) | −3.45761 | −0.225549 | ||||||||
\(236\) | −1.68084 | −0.109413 | ||||||||
\(237\) | 51.1184 | 3.32049 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3463 | 0.863299 | 0.431649 | − | 0.902042i | \(-0.357932\pi\) | ||||
0.431649 | + | 0.902042i | \(0.357932\pi\) | |||||||
\(240\) | −14.9660 | −0.966049 | ||||||||
\(241\) | −20.3854 | −1.31314 | −0.656568 | − | 0.754267i | \(-0.727993\pi\) | ||||
−0.656568 | + | 0.754267i | \(0.727993\pi\) | |||||||
\(242\) | 5.10787 | 0.328346 | ||||||||
\(243\) | 8.54160 | 0.547944 | ||||||||
\(244\) | −6.43169 | −0.411747 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.17502 | −0.521221 | ||||||||
\(247\) | 2.82036 | 0.179455 | ||||||||
\(248\) | 9.57708 | 0.608145 | ||||||||
\(249\) | 33.3157 | 2.11130 | ||||||||
\(250\) | −3.01558 | −0.190722 | ||||||||
\(251\) | −17.1921 | −1.08515 | −0.542577 | − | 0.840006i | \(-0.682551\pi\) | ||||
−0.542577 | + | 0.840006i | \(0.682551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.0260 | −2.07633 | ||||||||
\(254\) | 4.14561 | 0.260119 | ||||||||
\(255\) | 20.1678 | 1.26296 | ||||||||
\(256\) | 10.6873 | 0.667954 | ||||||||
\(257\) | 7.64695 | 0.477004 | 0.238502 | − | 0.971142i | \(-0.423344\pi\) | ||||
0.238502 | + | 0.971142i | \(0.423344\pi\) | |||||||
\(258\) | 6.49475 | 0.404345 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.76981 | 0.171776 | ||||||||
\(261\) | 5.69124 | 0.352279 | ||||||||
\(262\) | −3.20921 | −0.198266 | ||||||||
\(263\) | −0.101037 | −0.00623022 | −0.00311511 | − | 0.999995i | \(-0.500992\pi\) | ||||
−0.00311511 | + | 0.999995i | \(0.500992\pi\) | |||||||
\(264\) | 16.6536 | 1.02496 | ||||||||
\(265\) | −2.62574 | −0.161298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.89541 | −0.177196 | ||||||||
\(268\) | 12.7907 | 0.781318 | ||||||||
\(269\) | 7.56852 | 0.461461 | 0.230730 | − | 0.973018i | \(-0.425889\pi\) | ||||
0.230730 | + | 0.973018i | \(0.425889\pi\) | |||||||
\(270\) | −2.72052 | −0.165565 | ||||||||
\(271\) | 13.8554 | 0.841653 | 0.420826 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420826 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(272\) | −17.3169 | −1.04999 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.21748 | 0.254787 | ||||||||
\(275\) | −16.1858 | −0.976039 | ||||||||
\(276\) | −33.6837 | −2.02752 | ||||||||
\(277\) | 0.552935 | 0.0332226 | 0.0166113 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166113 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(278\) | 1.75735 | 0.105399 | ||||||||
\(279\) | −50.3036 | −3.01160 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.14667 | 0.0684043 | 0.0342022 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342022 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(282\) | 1.85464 | 0.110442 | ||||||||
\(283\) | 4.05396 | 0.240983 | 0.120491 | − | 0.992714i | \(-0.461553\pi\) | ||||
0.120491 | + | 0.992714i | \(0.461553\pi\) | |||||||
\(284\) | 13.2368 | 0.785461 | ||||||||
\(285\) | 11.7747 | 0.697476 | ||||||||
\(286\) | −1.45670 | −0.0861365 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.5435 | 0.974833 | ||||||||
\(289\) | 6.33588 | 0.372699 | ||||||||
\(290\) | 0.395685 | 0.0232354 | ||||||||
\(291\) | 39.2982 | 2.30370 | ||||||||
\(292\) | 6.06296 | 0.354808 | ||||||||
\(293\) | −15.0649 | −0.880102 | −0.440051 | − | 0.897973i | \(-0.645040\pi\) | ||||
−0.440051 | + | 0.897973i | \(0.645040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.24990 | 0.0727718 | ||||||||
\(296\) | −0.636982 | −0.0370238 | ||||||||
\(297\) | −39.4327 | −2.28812 | ||||||||
\(298\) | −5.17351 | −0.299694 | ||||||||
\(299\) | 5.99956 | 0.346964 | ||||||||
\(300\) | −16.5081 | −0.953094 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.82834 | 0.162752 | ||||||||
\(303\) | −2.93250 | −0.168468 | ||||||||
\(304\) | −10.1103 | −0.579863 | ||||||||
\(305\) | 4.78269 | 0.273856 | ||||||||
\(306\) | −6.98288 | −0.399185 | ||||||||
\(307\) | 19.9408 | 1.13808 | 0.569040 | − | 0.822310i | \(-0.307315\pi\) | ||||
0.569040 | + | 0.822310i | \(0.307315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.1642 | −2.11420 | ||||||||
\(310\) | −3.49737 | −0.198637 | ||||||||
\(311\) | 10.8956 | 0.617833 | 0.308916 | − | 0.951089i | \(-0.400034\pi\) | ||||
0.308916 | + | 0.951089i | \(0.400034\pi\) | |||||||
\(312\) | −3.02532 | −0.171275 | ||||||||
\(313\) | 0.0519190 | 0.00293464 | 0.00146732 | − | 0.999999i | \(-0.499533\pi\) | ||||
0.00146732 | + | 0.999999i | \(0.499533\pi\) | |||||||
\(314\) | 3.98883 | 0.225103 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.9140 | 1.90781 | ||||||||
\(317\) | 16.1010 | 0.904321 | 0.452161 | − | 0.891937i | \(-0.350653\pi\) | ||||
0.452161 | + | 0.891937i | \(0.350653\pi\) | |||||||
\(318\) | 1.40843 | 0.0789808 | ||||||||
\(319\) | 5.73528 | 0.321114 | ||||||||
\(320\) | −9.13912 | −0.510892 | ||||||||
\(321\) | 1.99413 | 0.111301 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6244 | 0.758081 | ||||||||
\(324\) | −8.59066 | −0.477259 | ||||||||
\(325\) | 2.94033 | 0.163100 | ||||||||
\(326\) | −6.30167 | −0.349017 | ||||||||
\(327\) | 8.44621 | 0.467077 | ||||||||
\(328\) | −11.0441 | −0.609808 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.08159 | −0.334781 | ||||||||
\(331\) | 30.7862 | 1.69216 | 0.846081 | − | 0.533054i | \(-0.178956\pi\) | ||||
0.846081 | + | 0.533054i | \(0.178956\pi\) | |||||||
\(332\) | 22.1030 | 1.21306 | ||||||||
\(333\) | 3.34575 | 0.183346 | ||||||||
\(334\) | 1.88512 | 0.103149 | ||||||||
\(335\) | −9.51135 | −0.519661 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.41842 | −0.131740 | −0.0658700 | − | 0.997828i | \(-0.520982\pi\) | ||||
−0.0658700 | + | 0.997828i | \(0.520982\pi\) | |||||||
\(338\) | 0.264627 | 0.0143938 | ||||||||
\(339\) | −35.0001 | −1.90094 | ||||||||
\(340\) | 13.3802 | 0.725642 | ||||||||
\(341\) | −50.6929 | −2.74517 | ||||||||
\(342\) | −4.07687 | −0.220452 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.77411 | 0.473069 | ||||||||
\(345\) | 25.0476 | 1.34852 | ||||||||
\(346\) | −2.97353 | −0.159858 | ||||||||
\(347\) | −0.492527 | −0.0264403 | −0.0132201 | − | 0.999913i | \(-0.504208\pi\) | ||||
−0.0132201 | + | 0.999913i | \(0.504208\pi\) | |||||||
\(348\) | 5.84948 | 0.313565 | ||||||||
\(349\) | 11.9442 | 0.639356 | 0.319678 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319678 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.16341 | 0.382355 | ||||||||
\(352\) | 16.6715 | 0.888593 | ||||||||
\(353\) | −15.5299 | −0.826575 | −0.413288 | − | 0.910601i | \(-0.635620\pi\) | ||||
−0.413288 | + | 0.910601i | \(0.635620\pi\) | |||||||
\(354\) | −0.670436 | −0.0356333 | ||||||||
\(355\) | −9.84308 | −0.522417 | ||||||||
\(356\) | −1.92094 | −0.101809 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.49162 | −0.184538 | ||||||||
\(359\) | −8.50709 | −0.448987 | −0.224493 | − | 0.974476i | \(-0.572073\pi\) | ||||
−0.224493 | + | 0.974476i | \(0.572073\pi\) | |||||||
\(360\) | −8.15287 | −0.429694 | ||||||||
\(361\) | −11.0456 | −0.581345 | ||||||||
\(362\) | 3.63635 | 0.191122 | ||||||||
\(363\) | −56.1507 | −2.94715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.50850 | −0.235985 | ||||||||
\(366\) | −2.56540 | −0.134096 | ||||||||
\(367\) | −5.19084 | −0.270960 | −0.135480 | − | 0.990780i | \(-0.543258\pi\) | ||||
−0.135480 | + | 0.990780i | \(0.543258\pi\) | |||||||
\(368\) | −21.5069 | −1.12112 | ||||||||
\(369\) | 58.0091 | 3.01983 | ||||||||
\(370\) | 0.232614 | 0.0120930 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −51.7023 | −2.68064 | ||||||||
\(373\) | −10.1427 | −0.525169 | −0.262585 | − | 0.964909i | \(-0.584575\pi\) | ||||
−0.262585 | + | 0.964909i | \(0.584575\pi\) | |||||||
\(374\) | −7.03692 | −0.363870 | ||||||||
\(375\) | 33.1502 | 1.71187 | ||||||||
\(376\) | 2.50553 | 0.129213 | ||||||||
\(377\) | −1.04188 | −0.0536595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.63670 | −0.186805 | −0.0934024 | − | 0.995628i | \(-0.529774\pi\) | ||||
−0.0934024 | + | 0.995628i | \(0.529774\pi\) | |||||||
\(380\) | 7.81186 | 0.400740 | ||||||||
\(381\) | −45.5726 | −2.33476 | ||||||||
\(382\) | −4.32154 | −0.221109 | ||||||||
\(383\) | −4.60281 | −0.235192 | −0.117596 | − | 0.993061i | \(-0.537519\pi\) | ||||
−0.117596 | + | 0.993061i | \(0.537519\pi\) | |||||||
\(384\) | 22.5226 | 1.14935 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.71888 | −0.189286 | ||||||||
\(387\) | −46.0861 | −2.34269 | ||||||||
\(388\) | 26.0721 | 1.32361 | ||||||||
\(389\) | 19.6104 | 0.994286 | 0.497143 | − | 0.867669i | \(-0.334382\pi\) | ||||
0.497143 | + | 0.867669i | \(0.334382\pi\) | |||||||
\(390\) | 1.10479 | 0.0559433 | ||||||||
\(391\) | 28.9822 | 1.46569 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.2788 | 1.77958 | ||||||||
\(394\) | −0.388731 | −0.0195840 | ||||||||
\(395\) | −25.2189 | −1.26890 | ||||||||
\(396\) | −58.0333 | −2.91628 | ||||||||
\(397\) | 19.8635 | 0.996919 | 0.498459 | − | 0.866913i | \(-0.333899\pi\) | ||||
0.498459 | + | 0.866913i | \(0.333899\pi\) | |||||||
\(398\) | 3.53996 | 0.177442 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.5403 | −0.527017 | ||||||||
\(401\) | −15.1117 | −0.754644 | −0.377322 | − | 0.926082i | \(-0.623155\pi\) | ||||
−0.377322 | + | 0.926082i | \(0.623155\pi\) | |||||||
\(402\) | 5.10183 | 0.254456 | ||||||||
\(403\) | 9.20895 | 0.458731 | ||||||||
\(404\) | −1.94554 | −0.0967943 | ||||||||
\(405\) | 6.38813 | 0.317429 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.37164 | 0.167126 | ||||||||
\(408\) | −14.6145 | −0.723525 | ||||||||
\(409\) | 35.2443 | 1.74272 | 0.871360 | − | 0.490644i | \(-0.163238\pi\) | ||||
0.871360 | + | 0.490644i | \(0.163238\pi\) | |||||||
\(410\) | 4.03310 | 0.199181 | ||||||||
\(411\) | −46.3626 | −2.28690 | ||||||||
\(412\) | −24.6563 | −1.21473 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.67246 | −0.426228 | ||||||||
\(415\) | −16.4361 | −0.806816 | ||||||||
\(416\) | −3.02857 | −0.148488 | ||||||||
\(417\) | −19.3185 | −0.946033 | ||||||||
\(418\) | −4.10842 | −0.200950 | ||||||||
\(419\) | −1.50468 | −0.0735084 | −0.0367542 | − | 0.999324i | \(-0.511702\pi\) | ||||
−0.0367542 | + | 0.999324i | \(0.511702\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5079 | −1.19444 | −0.597221 | − | 0.802077i | \(-0.703728\pi\) | ||||
−0.597221 | + | 0.802077i | \(0.703728\pi\) | |||||||
\(422\) | 0.918370 | 0.0447056 | ||||||||
\(423\) | −13.1603 | −0.639877 | ||||||||
\(424\) | 1.90272 | 0.0924045 | ||||||||
\(425\) | 14.2039 | 0.688992 | ||||||||
\(426\) | 5.27977 | 0.255806 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.32299 | 0.0639490 | ||||||||
\(429\) | 16.0135 | 0.773138 | ||||||||
\(430\) | −3.20414 | −0.154518 | ||||||||
\(431\) | 41.0655 | 1.97805 | 0.989027 | − | 0.147732i | \(-0.0471974\pi\) | ||||
0.989027 | + | 0.147732i | \(0.0471974\pi\) | |||||||
\(432\) | −25.6790 | −1.23548 | ||||||||
\(433\) | −6.65603 | −0.319869 | −0.159934 | − | 0.987128i | \(-0.551128\pi\) | ||||
−0.159934 | + | 0.987128i | \(0.551128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.34975 | −0.208555 | ||||||||
\(436\) | 5.60357 | 0.268362 | ||||||||
\(437\) | 16.9209 | 0.809438 | ||||||||
\(438\) | 2.41833 | 0.115552 | ||||||||
\(439\) | −8.22990 | −0.392792 | −0.196396 | − | 0.980525i | \(-0.562924\pi\) | ||||
−0.196396 | + | 0.980525i | \(0.562924\pi\) | |||||||
\(440\) | −8.21596 | −0.391681 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.27834 | 0.0608043 | ||||||||
\(443\) | 17.6856 | 0.840266 | 0.420133 | − | 0.907463i | \(-0.361983\pi\) | ||||
0.420133 | + | 0.907463i | \(0.361983\pi\) | |||||||
\(444\) | 3.43878 | 0.163197 | ||||||||
\(445\) | 1.42843 | 0.0677143 | ||||||||
\(446\) | 2.62329 | 0.124216 | ||||||||
\(447\) | 56.8723 | 2.68997 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.5250 | −0.685477 | −0.342738 | − | 0.939431i | \(-0.611354\pi\) | ||||
−0.342738 | + | 0.939431i | \(0.611354\pi\) | |||||||
\(450\) | −4.25030 | −0.200361 | ||||||||
\(451\) | 58.4580 | 2.75268 | ||||||||
\(452\) | −23.2205 | −1.09220 | ||||||||
\(453\) | −31.0918 | −1.46082 | ||||||||
\(454\) | −3.19475 | −0.149937 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.53250 | −0.399571 | ||||||||
\(457\) | 3.78919 | 0.177251 | 0.0886255 | − | 0.996065i | \(-0.471753\pi\) | ||||
0.0886255 | + | 0.996065i | \(0.471753\pi\) | |||||||
\(458\) | −1.07219 | −0.0501002 | ||||||||
\(459\) | 34.6045 | 1.61520 | ||||||||
\(460\) | 16.6176 | 0.774801 | ||||||||
\(461\) | −13.1107 | −0.610627 | −0.305314 | − | 0.952252i | \(-0.598761\pi\) | ||||
−0.305314 | + | 0.952252i | \(0.598761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3027 | 0.711176 | 0.355588 | − | 0.934643i | \(-0.384281\pi\) | ||||
0.355588 | + | 0.934643i | \(0.384281\pi\) | |||||||
\(464\) | 3.73487 | 0.173387 | ||||||||
\(465\) | 38.4465 | 1.78292 | ||||||||
\(466\) | 3.31974 | 0.153784 | ||||||||
\(467\) | −30.7738 | −1.42404 | −0.712022 | − | 0.702158i | \(-0.752220\pi\) | ||||
−0.712022 | + | 0.702158i | \(0.752220\pi\) | |||||||
\(468\) | 10.5424 | 0.487324 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.914975 | −0.0422046 | ||||||||
\(471\) | −43.8491 | −2.02046 | ||||||||
\(472\) | −0.905729 | −0.0416896 | ||||||||
\(473\) | −46.4427 | −2.13544 | ||||||||
\(474\) | 13.5273 | 0.621328 | ||||||||
\(475\) | 8.29280 | 0.380500 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.99407 | −0.457597 | ||||||||
\(478\) | 3.53178 | 0.161540 | ||||||||
\(479\) | 1.71740 | 0.0784699 | 0.0392350 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392350 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(480\) | −12.6440 | −0.577117 | ||||||||
\(481\) | −0.612497 | −0.0279275 | ||||||||
\(482\) | −5.39451 | −0.245713 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.2527 | −1.69330 | ||||||||
\(485\) | −19.3875 | −0.880342 | ||||||||
\(486\) | 2.26033 | 0.102531 | ||||||||
\(487\) | 22.6805 | 1.02775 | 0.513877 | − | 0.857864i | \(-0.328209\pi\) | ||||
0.513877 | + | 0.857864i | \(0.328209\pi\) | |||||||
\(488\) | −3.46575 | −0.156887 | ||||||||
\(489\) | 69.2741 | 3.13268 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.1366 | −0.592846 | −0.296423 | − | 0.955057i | \(-0.595794\pi\) | ||||
−0.296423 | + | 0.955057i | \(0.595794\pi\) | |||||||
\(492\) | 59.6220 | 2.68797 | ||||||||
\(493\) | −5.03303 | −0.226676 | ||||||||
\(494\) | 0.746342 | 0.0335795 | ||||||||
\(495\) | 43.1543 | 1.93964 | ||||||||
\(496\) | −33.0117 | −1.48227 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.81622 | 0.395064 | ||||||||
\(499\) | 14.0395 | 0.628495 | 0.314248 | − | 0.949341i | \(-0.398248\pi\) | ||||
0.314248 | + | 0.949341i | \(0.398248\pi\) | |||||||
\(500\) | 21.9932 | 0.983566 | ||||||||
\(501\) | −20.7231 | −0.925840 | ||||||||
\(502\) | −4.54948 | −0.203053 | ||||||||
\(503\) | −0.367865 | −0.0164023 | −0.00820114 | − | 0.999966i | \(-0.502611\pi\) | ||||
−0.00820114 | + | 0.999966i | \(0.502611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.44673 | 0.0643786 | ||||||||
\(506\) | −8.73957 | −0.388521 | ||||||||
\(507\) | −2.90903 | −0.129195 | ||||||||
\(508\) | −30.2348 | −1.34145 | ||||||||
\(509\) | −41.2319 | −1.82757 | −0.913787 | − | 0.406194i | \(-0.866856\pi\) | ||||
−0.913787 | + | 0.406194i | \(0.866856\pi\) | |||||||
\(510\) | 5.33694 | 0.236324 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.3127 | 0.809315 | ||||||||
\(513\) | 20.2034 | 0.892002 | ||||||||
\(514\) | 2.02359 | 0.0892566 | ||||||||
\(515\) | 18.3347 | 0.807925 | ||||||||
\(516\) | −47.3675 | −2.08524 | ||||||||
\(517\) | −13.2622 | −0.583269 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.6879 | 1.43484 | ||||||||
\(520\) | 1.49252 | 0.0654515 | ||||||||
\(521\) | −1.04099 | −0.0456065 | −0.0228032 | − | 0.999740i | \(-0.507259\pi\) | ||||
−0.0228032 | + | 0.999740i | \(0.507259\pi\) | |||||||
\(522\) | 1.50605 | 0.0659182 | ||||||||
\(523\) | 20.0209 | 0.875451 | 0.437726 | − | 0.899109i | \(-0.355784\pi\) | ||||
0.437726 | + | 0.899109i | \(0.355784\pi\) | |||||||
\(524\) | 23.4054 | 1.02247 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0267371 | −0.00116579 | ||||||||
\(527\) | 44.4859 | 1.93784 | ||||||||
\(528\) | −57.4042 | −2.49820 | ||||||||
\(529\) | 12.9947 | 0.564989 | ||||||||
\(530\) | −0.694840 | −0.0301819 | ||||||||
\(531\) | 4.75735 | 0.206451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.6196 | −0.459985 | ||||||||
\(534\) | −0.766203 | −0.0331568 | ||||||||
\(535\) | −0.983791 | −0.0425330 | ||||||||
\(536\) | 6.89234 | 0.297704 | ||||||||
\(537\) | 38.3833 | 1.65636 | ||||||||
\(538\) | 2.00283 | 0.0863481 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.8413 | 0.853832 | ||||||||
\(541\) | −9.78749 | −0.420797 | −0.210399 | − | 0.977616i | \(-0.567476\pi\) | ||||
−0.210399 | + | 0.977616i | \(0.567476\pi\) | |||||||
\(542\) | 3.66649 | 0.157489 | ||||||||
\(543\) | −39.9743 | −1.71546 | ||||||||
\(544\) | −14.6302 | −0.627263 | ||||||||
\(545\) | −4.16689 | −0.178490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.56174 | −0.109532 | −0.0547660 | − | 0.998499i | \(-0.517441\pi\) | ||||
−0.0547660 | + | 0.998499i | \(0.517441\pi\) | |||||||
\(548\) | −30.7589 | −1.31395 | ||||||||
\(549\) | 18.2038 | 0.776921 | ||||||||
\(550\) | −4.28319 | −0.182636 | ||||||||
\(551\) | −2.93848 | −0.125183 | ||||||||
\(552\) | −18.1506 | −0.772541 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.146321 | 0.00621660 | ||||||||
\(555\) | −2.55712 | −0.108544 | ||||||||
\(556\) | −12.8167 | −0.543550 | ||||||||
\(557\) | −27.4442 | −1.16285 | −0.581424 | − | 0.813601i | \(-0.697504\pi\) | ||||
−0.581424 | + | 0.813601i | \(0.697504\pi\) | |||||||
\(558\) | −13.3117 | −0.563528 | ||||||||
\(559\) | 8.43685 | 0.356841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 77.3567 | 3.26600 | ||||||||
\(562\) | 0.303438 | 0.0127998 | ||||||||
\(563\) | −0.162708 | −0.00685734 | −0.00342867 | − | 0.999994i | \(-0.501091\pi\) | ||||
−0.00342867 | + | 0.999994i | \(0.501091\pi\) | |||||||
\(564\) | −13.5262 | −0.569557 | ||||||||
\(565\) | 17.2671 | 0.726431 | ||||||||
\(566\) | 1.07278 | 0.0450925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.13273 | 0.299283 | ||||||||
\(569\) | −12.3901 | −0.519419 | −0.259709 | − | 0.965687i | \(-0.583627\pi\) | ||||
−0.259709 | + | 0.965687i | \(0.583627\pi\) | |||||||
\(570\) | 3.11591 | 0.130511 | ||||||||
\(571\) | −21.8122 | −0.912810 | −0.456405 | − | 0.889772i | \(-0.650863\pi\) | ||||
−0.456405 | + | 0.889772i | \(0.650863\pi\) | |||||||
\(572\) | 10.6240 | 0.444212 | ||||||||
\(573\) | 47.5066 | 1.98462 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.6407 | 0.735669 | ||||||||
\(576\) | −34.7852 | −1.44939 | ||||||||
\(577\) | −6.06583 | −0.252524 | −0.126262 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126262 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(578\) | 1.67664 | 0.0697391 | ||||||||
\(579\) | 40.8816 | 1.69898 | ||||||||
\(580\) | −2.88581 | −0.119827 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.3993 | 0.431067 | ||||||||
\(583\) | −10.0714 | −0.417115 | ||||||||
\(584\) | 3.26705 | 0.135192 | ||||||||
\(585\) | −7.83949 | −0.324123 | ||||||||
\(586\) | −3.98658 | −0.164684 | ||||||||
\(587\) | −20.5820 | −0.849510 | −0.424755 | − | 0.905308i | \(-0.639640\pi\) | ||||
−0.424755 | + | 0.905308i | \(0.639640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.9726 | 1.07018 | ||||||||
\(590\) | 0.330756 | 0.0136170 | ||||||||
\(591\) | 4.27331 | 0.175781 | ||||||||
\(592\) | 2.19564 | 0.0902404 | ||||||||
\(593\) | 24.0397 | 0.987190 | 0.493595 | − | 0.869692i | \(-0.335682\pi\) | ||||
0.493595 | + | 0.869692i | \(0.335682\pi\) | |||||||
\(594\) | −10.4349 | −0.428151 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 37.7314 | 1.54554 | ||||||||
\(597\) | −38.9147 | −1.59267 | ||||||||
\(598\) | 1.58764 | 0.0649236 | ||||||||
\(599\) | 32.2523 | 1.31779 | 0.658896 | − | 0.752234i | \(-0.271024\pi\) | ||||
0.658896 | + | 0.752234i | \(0.271024\pi\) | |||||||
\(600\) | −8.89546 | −0.363156 | ||||||||
\(601\) | −5.21454 | −0.212705 | −0.106353 | − | 0.994328i | \(-0.533917\pi\) | ||||
−0.106353 | + | 0.994328i | \(0.533917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.2020 | −1.47426 | ||||||||
\(604\) | −20.6276 | −0.839325 | ||||||||
\(605\) | 27.7016 | 1.12623 | ||||||||
\(606\) | −0.776017 | −0.0315235 | ||||||||
\(607\) | −9.07048 | −0.368160 | −0.184080 | − | 0.982911i | \(-0.558930\pi\) | ||||
−0.184080 | + | 0.982911i | \(0.558930\pi\) | |||||||
\(608\) | −8.54165 | −0.346410 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.26563 | 0.0512437 | ||||||||
\(611\) | 2.40922 | 0.0974668 | ||||||||
\(612\) | 50.9275 | 2.05862 | ||||||||
\(613\) | 20.0920 | 0.811507 | 0.405754 | − | 0.913983i | \(-0.367009\pi\) | ||||
0.405754 | + | 0.913983i | \(0.367009\pi\) | |||||||
\(614\) | 5.27686 | 0.212957 | ||||||||
\(615\) | −44.3357 | −1.78779 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9556 | −0.521572 | −0.260786 | − | 0.965397i | \(-0.583982\pi\) | ||||
−0.260786 | + | 0.965397i | \(0.583982\pi\) | |||||||
\(618\) | −9.83463 | −0.395607 | ||||||||
\(619\) | 44.3644 | 1.78316 | 0.891578 | − | 0.452866i | \(-0.149598\pi\) | ||||
0.891578 | + | 0.452866i | \(0.149598\pi\) | |||||||
\(620\) | 25.5070 | 1.02439 | ||||||||
\(621\) | 42.9773 | 1.72462 | ||||||||
\(622\) | 2.88327 | 0.115608 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 10.4281 | 0.417459 | ||||||||
\(625\) | −1.65276 | −0.0661105 | ||||||||
\(626\) | 0.0137392 | 0.000549127 0 | ||||||||
\(627\) | 45.1638 | 1.80367 | ||||||||
\(628\) | −29.0913 | −1.16087 | ||||||||
\(629\) | −2.95880 | −0.117975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.61717 | 0.263426 | 0.131713 | − | 0.991288i | \(-0.457952\pi\) | ||||
0.131713 | + | 0.991288i | \(0.457952\pi\) | |||||||
\(632\) | 18.2747 | 0.726930 | ||||||||
\(633\) | −10.0956 | −0.401265 | ||||||||
\(634\) | 4.26075 | 0.169216 | ||||||||
\(635\) | 22.4830 | 0.892210 | ||||||||
\(636\) | −10.2719 | −0.407309 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.51771 | 0.0600866 | ||||||||
\(639\) | −37.4647 | −1.48208 | ||||||||
\(640\) | −11.1114 | −0.439216 | ||||||||
\(641\) | 18.9567 | 0.748744 | 0.374372 | − | 0.927279i | \(-0.377858\pi\) | ||||
0.374372 | + | 0.927279i | \(0.377858\pi\) | |||||||
\(642\) | 0.527699 | 0.0208266 | ||||||||
\(643\) | −13.4019 | −0.528517 | −0.264259 | − | 0.964452i | \(-0.585127\pi\) | ||||
−0.264259 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35.2231 | 1.38691 | ||||||||
\(646\) | 3.60537 | 0.141851 | ||||||||
\(647\) | −42.7588 | −1.68102 | −0.840511 | − | 0.541794i | \(-0.817745\pi\) | ||||
−0.840511 | + | 0.541794i | \(0.817745\pi\) | |||||||
\(648\) | −4.62912 | −0.181849 | ||||||||
\(649\) | 4.79416 | 0.188187 | ||||||||
\(650\) | 0.778091 | 0.0305192 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 45.9593 | 1.79991 | ||||||||
\(653\) | 10.9852 | 0.429884 | 0.214942 | − | 0.976627i | \(-0.431044\pi\) | ||||
0.214942 | + | 0.976627i | \(0.431044\pi\) | |||||||
\(654\) | 2.23509 | 0.0873990 | ||||||||
\(655\) | −17.4046 | −0.680052 | ||||||||
\(656\) | 38.0684 | 1.48632 | ||||||||
\(657\) | −17.1602 | −0.669483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.7614 | −0.691884 | −0.345942 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345942 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(660\) | 44.3542 | 1.72649 | ||||||||
\(661\) | −8.18255 | −0.318264 | −0.159132 | − | 0.987257i | \(-0.550870\pi\) | ||||
−0.159132 | + | 0.987257i | \(0.550870\pi\) | |||||||
\(662\) | 8.14685 | 0.316636 | ||||||||
\(663\) | −14.0527 | −0.545763 | ||||||||
\(664\) | 11.9103 | 0.462210 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.885374 | 0.0343076 | ||||||||
\(667\) | −6.25082 | −0.242033 | ||||||||
\(668\) | −13.7486 | −0.531948 | ||||||||
\(669\) | −28.8378 | −1.11493 | ||||||||
\(670\) | −2.51696 | −0.0972385 | ||||||||
\(671\) | 18.3447 | 0.708189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.30129 | 0.358539 | 0.179269 | − | 0.983800i | \(-0.442627\pi\) | ||||
0.179269 | + | 0.983800i | \(0.442627\pi\) | |||||||
\(674\) | −0.639979 | −0.0246511 | ||||||||
\(675\) | 21.0628 | 0.810708 | ||||||||
\(676\) | −1.92997 | −0.0742297 | ||||||||
\(677\) | 41.1552 | 1.58172 | 0.790862 | − | 0.611994i | \(-0.209633\pi\) | ||||
0.790862 | + | 0.611994i | \(0.209633\pi\) | |||||||
\(678\) | −9.26195 | −0.355703 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.20997 | 0.276490 | ||||||||
\(681\) | 35.1198 | 1.34579 | ||||||||
\(682\) | −13.4147 | −0.513675 | ||||||||
\(683\) | 39.2842 | 1.50317 | 0.751583 | − | 0.659638i | \(-0.229291\pi\) | ||||
0.751583 | + | 0.659638i | \(0.229291\pi\) | |||||||
\(684\) | 29.7334 | 1.13689 | ||||||||
\(685\) | 22.8727 | 0.873921 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.7866 | 0.449685 | ||||||||
\(688\) | −30.2439 | −1.15304 | ||||||||
\(689\) | 1.82959 | 0.0697017 | ||||||||
\(690\) | 6.62827 | 0.252334 | ||||||||
\(691\) | 3.03355 | 0.115402 | 0.0577009 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0577009 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(692\) | 21.6865 | 0.824397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.130336 | −0.00494748 | ||||||||
\(695\) | 9.53069 | 0.361520 | ||||||||
\(696\) | 3.15202 | 0.119477 | ||||||||
\(697\) | −51.3002 | −1.94313 | ||||||||
\(698\) | 3.16074 | 0.119636 | ||||||||
\(699\) | −36.4938 | −1.38032 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.2320 | −0.990767 | −0.495384 | − | 0.868674i | \(-0.664972\pi\) | ||||
−0.495384 | + | 0.868674i | \(0.664972\pi\) | |||||||
\(702\) | 1.89563 | 0.0715459 | ||||||||
\(703\) | −1.72746 | −0.0651525 | ||||||||
\(704\) | −35.0544 | −1.32116 | ||||||||
\(705\) | 10.0583 | 0.378817 | ||||||||
\(706\) | −4.10963 | −0.154668 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.88962 | 0.183763 | ||||||||
\(709\) | −7.87770 | −0.295853 | −0.147927 | − | 0.988998i | \(-0.547260\pi\) | ||||
−0.147927 | + | 0.988998i | \(0.547260\pi\) | |||||||
\(710\) | −2.60474 | −0.0977542 | ||||||||
\(711\) | −95.9881 | −3.59984 | ||||||||
\(712\) | −1.03511 | −0.0387922 | ||||||||
\(713\) | 55.2497 | 2.06912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.90015 | −0.295449 | ||||||||
\(716\) | 25.4650 | 0.951673 | ||||||||
\(717\) | −38.8247 | −1.44994 | ||||||||
\(718\) | −2.25120 | −0.0840141 | ||||||||
\(719\) | −45.6656 | −1.70304 | −0.851519 | − | 0.524323i | \(-0.824318\pi\) | ||||
−0.851519 | + | 0.524323i | \(0.824318\pi\) | |||||||
\(720\) | 28.1025 | 1.04732 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.92295 | −0.108781 | ||||||||
\(723\) | 59.3017 | 2.20545 | ||||||||
\(724\) | −26.5206 | −0.985630 | ||||||||
\(725\) | −3.06348 | −0.113775 | ||||||||
\(726\) | −14.8590 | −0.551468 | ||||||||
\(727\) | −37.5947 | −1.39431 | −0.697155 | − | 0.716921i | \(-0.745551\pi\) | ||||
−0.697155 | + | 0.716921i | \(0.745551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.2013 | −1.41486 | ||||||||
\(730\) | −1.19307 | −0.0441574 | ||||||||
\(731\) | 40.7561 | 1.50742 | ||||||||
\(732\) | 18.7100 | 0.691541 | ||||||||
\(733\) | −53.1810 | −1.96429 | −0.982143 | − | 0.188138i | \(-0.939755\pi\) | ||||
−0.982143 | + | 0.188138i | \(0.939755\pi\) | |||||||
\(734\) | −1.37363 | −0.0507018 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.1701 | −0.669758 | ||||||||
\(737\) | −36.4822 | −1.34384 | ||||||||
\(738\) | 15.3508 | 0.565069 | ||||||||
\(739\) | 41.9633 | 1.54364 | 0.771822 | − | 0.635839i | \(-0.219346\pi\) | ||||
0.771822 | + | 0.635839i | \(0.219346\pi\) | |||||||
\(740\) | −1.69650 | −0.0623646 | ||||||||
\(741\) | −8.20452 | −0.301401 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.5424 | −1.41398 | −0.706991 | − | 0.707222i | \(-0.749948\pi\) | ||||
−0.706991 | + | 0.707222i | \(0.749948\pi\) | |||||||
\(744\) | −27.8600 | −1.02140 | ||||||||
\(745\) | −28.0576 | −1.02795 | ||||||||
\(746\) | −2.68403 | −0.0982693 | ||||||||
\(747\) | −62.5590 | −2.28891 | ||||||||
\(748\) | 51.3216 | 1.87650 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.77242 | 0.320323 | ||||||||
\(751\) | 36.2434 | 1.32254 | 0.661270 | − | 0.750148i | \(-0.270018\pi\) | ||||
0.661270 | + | 0.750148i | \(0.270018\pi\) | |||||||
\(752\) | −8.63644 | −0.314939 | ||||||||
\(753\) | 50.0123 | 1.82255 | ||||||||
\(754\) | −0.275709 | −0.0100407 | ||||||||
\(755\) | 15.3390 | 0.558242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4752 | 0.707837 | 0.353919 | − | 0.935276i | \(-0.384849\pi\) | ||||
0.353919 | + | 0.935276i | \(0.384849\pi\) | |||||||
\(758\) | −0.962368 | −0.0349548 | ||||||||
\(759\) | 96.0738 | 3.48726 | ||||||||
\(760\) | 4.20946 | 0.152693 | ||||||||
\(761\) | 51.9059 | 1.88159 | 0.940793 | − | 0.338981i | \(-0.110082\pi\) | ||||
0.940793 | + | 0.338981i | \(0.110082\pi\) | |||||||
\(762\) | −12.0597 | −0.436878 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 31.5178 | 1.14028 | ||||||||
\(765\) | −37.8704 | −1.36921 | ||||||||
\(766\) | −1.21803 | −0.0440090 | ||||||||
\(767\) | −0.870914 | −0.0314469 | ||||||||
\(768\) | −31.0896 | −1.12185 | ||||||||
\(769\) | 7.31376 | 0.263741 | 0.131870 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131870 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.2452 | −0.801142 | ||||||||
\(772\) | 27.1225 | 0.976161 | ||||||||
\(773\) | 14.1844 | 0.510178 | 0.255089 | − | 0.966918i | \(-0.417895\pi\) | ||||
0.255089 | + | 0.966918i | \(0.417895\pi\) | |||||||
\(774\) | −12.1956 | −0.438362 | ||||||||
\(775\) | 27.0774 | 0.972649 | ||||||||
\(776\) | 14.0491 | 0.504332 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.18943 | 0.186050 | ||||||||
\(779\) | −29.9510 | −1.07311 | ||||||||
\(780\) | −8.05746 | −0.288503 | ||||||||
\(781\) | −37.7546 | −1.35097 | ||||||||
\(782\) | 7.66946 | 0.274259 | ||||||||
\(783\) | −7.46341 | −0.266721 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.6327 | 0.772104 | ||||||||
\(786\) | 9.33569 | 0.332993 | ||||||||
\(787\) | −31.2777 | −1.11493 | −0.557465 | − | 0.830201i | \(-0.688226\pi\) | ||||
−0.557465 | + | 0.830201i | \(0.688226\pi\) | |||||||
\(788\) | 2.83509 | 0.100996 | ||||||||
\(789\) | 0.293921 | 0.0104639 | ||||||||
\(790\) | −6.67360 | −0.237436 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −31.2715 | −1.11119 | ||||||||
\(793\) | −3.33253 | −0.118342 | ||||||||
\(794\) | 5.25640 | 0.186543 | ||||||||
\(795\) | 7.63836 | 0.270905 | ||||||||
\(796\) | −25.8176 | −0.915082 | ||||||||
\(797\) | −20.2422 | −0.717017 | −0.358509 | − | 0.933526i | \(-0.616715\pi\) | ||||
−0.358509 | + | 0.933526i | \(0.616715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6383 | 0.411733 | ||||||||
\(800\) | −8.90500 | −0.314839 | ||||||||
\(801\) | 5.43689 | 0.192103 | ||||||||
\(802\) | −3.99897 | −0.141208 | ||||||||
\(803\) | −17.2930 | −0.610257 | ||||||||
\(804\) | −37.2086 | −1.31225 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.43693 | 0.0858373 | ||||||||
\(807\) | −22.0171 | −0.775037 | ||||||||
\(808\) | −1.04836 | −0.0368813 | ||||||||
\(809\) | 7.88265 | 0.277139 | 0.138570 | − | 0.990353i | \(-0.455750\pi\) | ||||
0.138570 | + | 0.990353i | \(0.455750\pi\) | |||||||
\(810\) | 1.69047 | 0.0593970 | ||||||||
\(811\) | 5.99962 | 0.210675 | 0.105338 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105338 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.3057 | −1.41358 | ||||||||
\(814\) | 0.892226 | 0.0312725 | ||||||||
\(815\) | −34.1760 | −1.19713 | ||||||||
\(816\) | 50.3754 | 1.76349 | ||||||||
\(817\) | 23.7950 | 0.832480 | ||||||||
\(818\) | 9.32659 | 0.326096 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.4142 | −1.02719 | ||||||||
\(821\) | −19.1692 | −0.669011 | −0.334505 | − | 0.942394i | \(-0.608569\pi\) | ||||
−0.334505 | + | 0.942394i | \(0.608569\pi\) | |||||||
\(822\) | −12.2688 | −0.427923 | ||||||||
\(823\) | −30.3735 | −1.05875 | −0.529376 | − | 0.848387i | \(-0.677574\pi\) | ||||
−0.529376 | + | 0.848387i | \(0.677574\pi\) | |||||||
\(824\) | −13.2861 | −0.462845 | ||||||||
\(825\) | 47.0850 | 1.63929 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.6870 | −0.510717 | −0.255359 | − | 0.966846i | \(-0.582193\pi\) | ||||
−0.255359 | + | 0.966846i | \(0.582193\pi\) | |||||||
\(828\) | 63.2499 | 2.19809 | ||||||||
\(829\) | 34.9985 | 1.21555 | 0.607774 | − | 0.794110i | \(-0.292062\pi\) | ||||
0.607774 | + | 0.794110i | \(0.292062\pi\) | |||||||
\(830\) | −4.34943 | −0.150971 | ||||||||
\(831\) | −1.60851 | −0.0557985 | ||||||||
\(832\) | 6.36804 | 0.220772 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.11220 | −0.177021 | ||||||||
\(835\) | 10.2236 | 0.353803 | ||||||||
\(836\) | 29.9635 | 1.03631 | ||||||||
\(837\) | 65.9675 | 2.28017 | ||||||||
\(838\) | −0.398178 | −0.0137548 | ||||||||
\(839\) | −27.6333 | −0.954008 | −0.477004 | − | 0.878901i | \(-0.658277\pi\) | ||||
−0.477004 | + | 0.878901i | \(0.658277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9145 | −0.962568 | ||||||||
\(842\) | −6.48544 | −0.223503 | ||||||||
\(843\) | −3.33569 | −0.114887 | ||||||||
\(844\) | −6.69785 | −0.230550 | ||||||||
\(845\) | 1.43515 | 0.0493708 | ||||||||
\(846\) | −3.48257 | −0.119733 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.55859 | −0.225223 | ||||||||
\(849\) | −11.7931 | −0.404738 | ||||||||
\(850\) | 3.75874 | 0.128924 | ||||||||
\(851\) | −3.67472 | −0.125968 | ||||||||
\(852\) | −38.5064 | −1.31921 | ||||||||
\(853\) | −32.6336 | −1.11735 | −0.558676 | − | 0.829386i | \(-0.688690\pi\) | ||||
−0.558676 | + | 0.829386i | \(0.688690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.1102 | −0.756152 | ||||||||
\(856\) | 0.712898 | 0.0243664 | ||||||||
\(857\) | 18.8742 | 0.644730 | 0.322365 | − | 0.946616i | \(-0.395522\pi\) | ||||
0.322365 | + | 0.946616i | \(0.395522\pi\) | |||||||
\(858\) | 4.23759 | 0.144669 | ||||||||
\(859\) | −15.8242 | −0.539915 | −0.269957 | − | 0.962872i | \(-0.587010\pi\) | ||||
−0.269957 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(860\) | 23.3684 | 0.796857 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.8670 | 0.370132 | ||||||||
\(863\) | 52.3212 | 1.78104 | 0.890518 | − | 0.454948i | \(-0.150342\pi\) | ||||
0.890518 | + | 0.454948i | \(0.150342\pi\) | |||||||
\(864\) | −21.6949 | −0.738075 | ||||||||
\(865\) | −16.1264 | −0.548313 | ||||||||
\(866\) | −1.76136 | −0.0598536 | ||||||||
\(867\) | −18.4313 | −0.625959 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −96.7309 | −3.28137 | ||||||||
\(870\) | −1.15106 | −0.0390246 | ||||||||
\(871\) | 6.62741 | 0.224561 | ||||||||
\(872\) | 3.01951 | 0.102253 | ||||||||
\(873\) | −73.7927 | −2.49750 | ||||||||
\(874\) | 4.47773 | 0.151461 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.6373 | −0.595911 | ||||||||
\(877\) | −54.0162 | −1.82400 | −0.911999 | − | 0.410193i | \(-0.865461\pi\) | ||||
−0.911999 | + | 0.410193i | \(0.865461\pi\) | |||||||
\(878\) | −2.17785 | −0.0734989 | ||||||||
\(879\) | 43.8243 | 1.47816 | ||||||||
\(880\) | 28.3200 | 0.954667 | ||||||||
\(881\) | 42.0823 | 1.41779 | 0.708895 | − | 0.705314i | \(-0.249194\pi\) | ||||
0.708895 | + | 0.705314i | \(0.249194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5314 | 1.22938 | 0.614689 | − | 0.788769i | \(-0.289281\pi\) | ||||
0.614689 | + | 0.788769i | \(0.289281\pi\) | |||||||
\(884\) | −9.32316 | −0.313572 | ||||||||
\(885\) | −3.63599 | −0.122222 | ||||||||
\(886\) | 4.68007 | 0.157230 | ||||||||
\(887\) | 11.4648 | 0.384950 | 0.192475 | − | 0.981302i | \(-0.438349\pi\) | ||||
0.192475 | + | 0.981302i | \(0.438349\pi\) | |||||||
\(888\) | 1.85300 | 0.0621827 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.378001 | 0.0126706 | ||||||||
\(891\) | 24.5026 | 0.820869 | ||||||||
\(892\) | −19.1322 | −0.640592 | ||||||||
\(893\) | 6.79488 | 0.227382 | ||||||||
\(894\) | 15.0499 | 0.503345 | ||||||||
\(895\) | −18.9361 | −0.632965 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.4529 | −0.582736 | ||||||||
\(898\) | −3.84370 | −0.128266 | ||||||||
\(899\) | −9.59462 | −0.319999 | ||||||||
\(900\) | 30.9982 | 1.03327 | ||||||||
\(901\) | 8.83823 | 0.294444 | ||||||||
\(902\) | 15.4695 | 0.515079 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5125 | −0.416159 | ||||||||
\(905\) | 19.7211 | 0.655550 | ||||||||
\(906\) | −8.22772 | −0.273348 | ||||||||
\(907\) | −5.04665 | −0.167571 | −0.0837856 | − | 0.996484i | \(-0.526701\pi\) | ||||
−0.0837856 | + | 0.996484i | \(0.526701\pi\) | |||||||
\(908\) | 23.2999 | 0.773236 | ||||||||
\(909\) | 5.50653 | 0.182640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.5236 | 1.57453 | 0.787263 | − | 0.616618i | \(-0.211497\pi\) | ||||
0.787263 | + | 0.616618i | \(0.211497\pi\) | |||||||
\(912\) | 29.4111 | 0.973898 | ||||||||
\(913\) | −63.0431 | −2.08642 | ||||||||
\(914\) | 1.00272 | 0.0331671 | ||||||||
\(915\) | −13.9130 | −0.459950 | ||||||||
\(916\) | 7.81969 | 0.258370 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.15726 | 0.302235 | ||||||||
\(919\) | −45.6698 | −1.50651 | −0.753254 | − | 0.657730i | \(-0.771517\pi\) | ||||
−0.753254 | + | 0.657730i | \(0.771517\pi\) | |||||||
\(920\) | 8.95449 | 0.295221 | ||||||||
\(921\) | −58.0084 | −1.91144 | ||||||||
\(922\) | −3.46945 | −0.114260 | ||||||||
\(923\) | 6.85856 | 0.225752 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.80095 | −0.0592148 | ||||||||
\(926\) | 4.04950 | 0.133075 | ||||||||
\(927\) | 69.7855 | 2.29206 | ||||||||
\(928\) | 3.15540 | 0.103581 | ||||||||
\(929\) | 44.4449 | 1.45819 | 0.729095 | − | 0.684412i | \(-0.239941\pi\) | ||||
0.729095 | + | 0.684412i | \(0.239941\pi\) | |||||||
\(930\) | 10.1740 | 0.333618 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.2115 | −0.793074 | ||||||||
\(933\) | −31.6957 | −1.03767 | ||||||||
\(934\) | −8.14357 | −0.266466 | ||||||||
\(935\) | −38.1634 | −1.24808 | ||||||||
\(936\) | 5.68083 | 0.185684 | ||||||||
\(937\) | −46.9796 | −1.53476 | −0.767379 | − | 0.641194i | \(-0.778439\pi\) | ||||
−0.767379 | + | 0.641194i | \(0.778439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.151034 | −0.00492881 | ||||||||
\(940\) | 6.67309 | 0.217652 | ||||||||
\(941\) | −35.5654 | −1.15940 | −0.579699 | − | 0.814830i | \(-0.696830\pi\) | ||||
−0.579699 | + | 0.814830i | \(0.696830\pi\) | |||||||
\(942\) | −11.6036 | −0.378067 | ||||||||
\(943\) | −63.7128 | −2.07477 | ||||||||
\(944\) | 3.12200 | 0.101613 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2900 | −0.399581 | ||||||||
\(947\) | −22.3592 | −0.726576 | −0.363288 | − | 0.931677i | \(-0.618346\pi\) | ||||
−0.363288 | + | 0.931677i | \(0.618346\pi\) | |||||||
\(948\) | −98.6570 | −3.20423 | ||||||||
\(949\) | 3.14147 | 0.101977 | ||||||||
\(950\) | 2.19450 | 0.0711989 | ||||||||
\(951\) | −46.8383 | −1.51884 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.7684 | −1.51498 | −0.757488 | − | 0.652849i | \(-0.773574\pi\) | ||||
−0.757488 | + | 0.652849i | \(0.773574\pi\) | |||||||
\(954\) | −2.64470 | −0.0856252 | ||||||||
\(955\) | −23.4371 | −0.758406 | ||||||||
\(956\) | −25.7579 | −0.833071 | ||||||||
\(957\) | −16.6841 | −0.539321 | ||||||||
\(958\) | 0.454469 | 0.0146832 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 26.5860 | 0.858059 | ||||||||
\(961\) | 53.8048 | 1.73564 | ||||||||
\(962\) | −0.162083 | −0.00522577 | ||||||||
\(963\) | −3.74450 | −0.120665 | ||||||||
\(964\) | 39.3432 | 1.26716 | ||||||||
\(965\) | −20.1687 | −0.649253 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.22976 | 0.264651 | 0.132326 | − | 0.991206i | \(-0.457756\pi\) | ||||
0.132326 | + | 0.991206i | \(0.457756\pi\) | |||||||
\(968\) | −20.0738 | −0.645196 | ||||||||
\(969\) | −39.6338 | −1.27322 | ||||||||
\(970\) | −5.13046 | −0.164729 | ||||||||
\(971\) | 23.6326 | 0.758407 | 0.379204 | − | 0.925313i | \(-0.376198\pi\) | ||||
0.379204 | + | 0.925313i | \(0.376198\pi\) | |||||||
\(972\) | −16.4850 | −0.528758 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.00187 | 0.192312 | ||||||||
\(975\) | −8.55353 | −0.273932 | ||||||||
\(976\) | 11.9462 | 0.382390 | ||||||||
\(977\) | −26.6428 | −0.852379 | −0.426190 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426190 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(978\) | 18.3318 | 0.586185 | ||||||||
\(979\) | 5.47897 | 0.175109 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.8600 | −0.506370 | ||||||||
\(982\) | −3.47629 | −0.110933 | ||||||||
\(983\) | −43.6302 | −1.39159 | −0.695793 | − | 0.718242i | \(-0.744947\pi\) | ||||
−0.695793 | + | 0.718242i | \(0.744947\pi\) | |||||||
\(984\) | 32.1276 | 1.02419 | ||||||||
\(985\) | −2.10821 | −0.0671732 | ||||||||
\(986\) | −1.33187 | −0.0424155 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.44322 | −0.173172 | ||||||||
\(989\) | 50.6174 | 1.60954 | ||||||||
\(990\) | 11.4198 | 0.362945 | ||||||||
\(991\) | −7.60816 | −0.241681 | −0.120841 | − | 0.992672i | \(-0.538559\pi\) | ||||
−0.120841 | + | 0.992672i | \(0.538559\pi\) | |||||||
\(992\) | −27.8899 | −0.885506 | ||||||||
\(993\) | −89.5581 | −2.84204 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.1983 | 0.608628 | ||||||||
\(996\) | −64.2984 | −2.03737 | ||||||||
\(997\) | −19.4356 | −0.615532 | −0.307766 | − | 0.951462i | \(-0.599581\pi\) | ||||
−0.307766 | + | 0.951462i | \(0.599581\pi\) | |||||||
\(998\) | 3.71523 | 0.117604 | ||||||||
\(999\) | −4.38757 | −0.138817 |
(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 | 637.2.a.m.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 5733.2.a.bu.1.3 | 6 | |||
7.2 | even | 3 | 637.2.e.o.508.3 | 12 | |||
7.3 | odd | 6 | 637.2.e.n.79.3 | 12 | |||
7.4 | even | 3 | 637.2.e.o.79.3 | 12 | |||
7.5 | odd | 6 | 637.2.e.n.508.3 | 12 | |||
7.6 | odd | 2 | 637.2.a.n.1.4 | yes | 6 | ||
13.12 | even | 2 | 8281.2.a.cc.1.3 | 6 | |||
21.20 | even | 2 | 5733.2.a.br.1.3 | 6 | |||
91.90 | odd | 2 | 8281.2.a.cd.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.m.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
637.2.a.n.1.4 | yes | 6 | 7.6 | odd | 2 | ||
637.2.e.n.79.3 | 12 | 7.3 | odd | 6 | |||
637.2.e.n.508.3 | 12 | 7.5 | odd | 6 | |||
637.2.e.o.79.3 | 12 | 7.4 | even | 3 | |||
637.2.e.o.508.3 | 12 | 7.2 | even | 3 | |||
5733.2.a.br.1.3 | 6 | 21.20 | even | 2 | |||
5733.2.a.bu.1.3 | 6 | 3.2 | odd | 2 | |||
8281.2.a.cc.1.3 | 6 | 13.12 | even | 2 | |||
8281.2.a.cd.1.3 | 6 | 91.90 | odd | 2 |