Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(1,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("735.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.74912\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.665096 | 0.470294 | 0.235147 | − | 0.971960i | \(-0.424443\pi\) | ||||
0.235147 | + | 0.971960i | \(0.424443\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.55765 | −0.778824 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.665096 | 0.271524 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.36618 | −0.836570 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.665096 | −0.210322 | ||||||||
\(11\) | 5.61706 | 1.69361 | 0.846804 | − | 0.531906i | \(-0.178524\pi\) | ||||
0.846804 | + | 0.531906i | \(0.178524\pi\) | |||||||
\(12\) | −1.55765 | −0.449654 | ||||||||
\(13\) | 6.44549 | 1.78766 | 0.893828 | − | 0.448410i | \(-0.148009\pi\) | ||||
0.893828 | + | 0.448410i | \(0.148009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.54156 | 0.385390 | ||||||||
\(17\) | −0.947252 | −0.229742 | −0.114871 | − | 0.993380i | \(-0.536646\pi\) | ||||
−0.114871 | + | 0.993380i | \(0.536646\pi\) | |||||||
\(18\) | 0.665096 | 0.156765 | ||||||||
\(19\) | −6.91245 | −1.58582 | −0.792912 | − | 0.609336i | \(-0.791436\pi\) | ||||
−0.792912 | + | 0.609336i | \(0.791436\pi\) | |||||||
\(20\) | 1.55765 | 0.348301 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.73588 | 0.796493 | ||||||||
\(23\) | 1.53304 | 0.319661 | 0.159830 | − | 0.987145i | \(-0.448905\pi\) | ||||
0.159830 | + | 0.987145i | \(0.448905\pi\) | |||||||
\(24\) | −2.36618 | −0.482994 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.28687 | 0.840724 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.99647 | 1.67060 | 0.835301 | − | 0.549792i | \(-0.185293\pi\) | ||||
0.835301 | + | 0.549792i | \(0.185293\pi\) | |||||||
\(30\) | −0.665096 | −0.121429 | ||||||||
\(31\) | 2.91245 | 0.523091 | 0.261546 | − | 0.965191i | \(-0.415768\pi\) | ||||
0.261546 | + | 0.965191i | \(0.415768\pi\) | |||||||
\(32\) | 5.75764 | 1.01782 | ||||||||
\(33\) | 5.61706 | 0.977805 | ||||||||
\(34\) | −0.630013 | −0.108046 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.55765 | −0.259608 | ||||||||
\(37\) | 6.16804 | 1.01402 | 0.507010 | − | 0.861940i | \(-0.330751\pi\) | ||||
0.507010 | + | 0.861940i | \(0.330751\pi\) | |||||||
\(38\) | −4.59744 | −0.745804 | ||||||||
\(39\) | 6.44549 | 1.03210 | ||||||||
\(40\) | 2.36618 | 0.374125 | ||||||||
\(41\) | −0.118824 | −0.0185573 | −0.00927863 | − | 0.999957i | \(-0.502954\pi\) | ||||
−0.00927863 | + | 0.999957i | \(0.502954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.11529 | 0.780075 | 0.390038 | − | 0.920799i | \(-0.372462\pi\) | ||||
0.390038 | + | 0.920799i | \(0.372462\pi\) | |||||||
\(44\) | −8.74940 | −1.31902 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 1.01962 | 0.150334 | ||||||||
\(47\) | −6.48528 | −0.945976 | −0.472988 | − | 0.881069i | \(-0.656825\pi\) | ||||
−0.472988 | + | 0.881069i | \(0.656825\pi\) | |||||||
\(48\) | 1.54156 | 0.222505 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.665096 | 0.0940588 | ||||||||
\(51\) | −0.947252 | −0.132642 | ||||||||
\(52\) | −10.0398 | −1.39227 | ||||||||
\(53\) | −3.03127 | −0.416377 | −0.208189 | − | 0.978089i | \(-0.566757\pi\) | ||||
−0.208189 | + | 0.978089i | \(0.566757\pi\) | |||||||
\(54\) | 0.665096 | 0.0905081 | ||||||||
\(55\) | −5.61706 | −0.757404 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.91245 | −0.915576 | ||||||||
\(58\) | 5.98352 | 0.785674 | ||||||||
\(59\) | 5.48881 | 0.714582 | 0.357291 | − | 0.933993i | \(-0.383700\pi\) | ||||
0.357291 | + | 0.933993i | \(0.383700\pi\) | |||||||
\(60\) | 1.55765 | 0.201091 | ||||||||
\(61\) | −9.41421 | −1.20537 | −0.602683 | − | 0.797981i | \(-0.705902\pi\) | ||||
−0.602683 | + | 0.797981i | \(0.705902\pi\) | |||||||
\(62\) | 1.93706 | 0.246007 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.746264 | 0.0932829 | ||||||||
\(65\) | −6.44549 | −0.799464 | ||||||||
\(66\) | 3.73588 | 0.459856 | ||||||||
\(67\) | −8.72293 | −1.06568 | −0.532838 | − | 0.846217i | \(-0.678874\pi\) | ||||
−0.532838 | + | 0.846217i | \(0.678874\pi\) | |||||||
\(68\) | 1.47548 | 0.178929 | ||||||||
\(69\) | 1.53304 | 0.184556 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.44902 | −0.171967 | −0.0859833 | − | 0.996297i | \(-0.527403\pi\) | ||||
−0.0859833 | + | 0.996297i | \(0.527403\pi\) | |||||||
\(72\) | −2.36618 | −0.278857 | ||||||||
\(73\) | −7.78510 | −0.911177 | −0.455589 | − | 0.890190i | \(-0.650571\pi\) | ||||
−0.455589 | + | 0.890190i | \(0.650571\pi\) | |||||||
\(74\) | 4.10234 | 0.476887 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 10.7672 | 1.23508 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.28687 | 0.485392 | ||||||||
\(79\) | −11.4325 | −1.28626 | −0.643130 | − | 0.765757i | \(-0.722365\pi\) | ||||
−0.643130 | + | 0.765757i | \(0.722365\pi\) | |||||||
\(80\) | −1.54156 | −0.172352 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.0790296 | −0.00872736 | ||||||||
\(83\) | 7.17157 | 0.787182 | 0.393591 | − | 0.919286i | \(-0.371233\pi\) | ||||
0.393591 | + | 0.919286i | \(0.371233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.947252 | 0.102744 | ||||||||
\(86\) | 3.40216 | 0.366865 | ||||||||
\(87\) | 8.99647 | 0.964523 | ||||||||
\(88\) | −13.2910 | −1.41682 | ||||||||
\(89\) | 0.828427 | 0.0878131 | 0.0439065 | − | 0.999036i | \(-0.486020\pi\) | ||||
0.0439065 | + | 0.999036i | \(0.486020\pi\) | |||||||
\(90\) | −0.665096 | −0.0701073 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.38793 | −0.248959 | ||||||||
\(93\) | 2.91245 | 0.302007 | ||||||||
\(94\) | −4.31333 | −0.444887 | ||||||||
\(95\) | 6.91245 | 0.709202 | ||||||||
\(96\) | 5.75764 | 0.587637 | ||||||||
\(97\) | −7.93430 | −0.805606 | −0.402803 | − | 0.915287i | \(-0.631964\pi\) | ||||
−0.402803 | + | 0.915287i | \(0.631964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.61706 | 0.564536 | ||||||||
\(100\) | −1.55765 | −0.155765 | ||||||||
\(101\) | 1.77568 | 0.176687 | 0.0883433 | − | 0.996090i | \(-0.471843\pi\) | ||||
0.0883433 | + | 0.996090i | \(0.471843\pi\) | |||||||
\(102\) | −0.630013 | −0.0623806 | ||||||||
\(103\) | −0.168043 | −0.0165578 | −0.00827889 | − | 0.999966i | \(-0.502635\pi\) | ||||
−0.00827889 | + | 0.999966i | \(0.502635\pi\) | |||||||
\(104\) | −15.2512 | −1.49550 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.01609 | −0.195820 | ||||||||
\(107\) | 5.70108 | 0.551144 | 0.275572 | − | 0.961280i | \(-0.411133\pi\) | ||||
0.275572 | + | 0.961280i | \(0.411133\pi\) | |||||||
\(108\) | −1.55765 | −0.149885 | ||||||||
\(109\) | −3.65685 | −0.350263 | −0.175132 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175132 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(110\) | −3.73588 | −0.356203 | ||||||||
\(111\) | 6.16804 | 0.585445 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.5791 | −1.65370 | −0.826851 | − | 0.562421i | \(-0.809870\pi\) | ||||
−0.826851 | + | 0.562421i | \(0.809870\pi\) | |||||||
\(114\) | −4.59744 | −0.430590 | ||||||||
\(115\) | −1.53304 | −0.142957 | ||||||||
\(116\) | −14.0133 | −1.30110 | ||||||||
\(117\) | 6.44549 | 0.595885 | ||||||||
\(118\) | 3.65059 | 0.336064 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.36618 | 0.216001 | ||||||||
\(121\) | 20.5514 | 1.86831 | ||||||||
\(122\) | −6.26136 | −0.566877 | ||||||||
\(123\) | −0.118824 | −0.0107140 | ||||||||
\(124\) | −4.53657 | −0.407396 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2869 | −1.26775 | −0.633877 | − | 0.773434i | \(-0.718538\pi\) | ||||
−0.633877 | + | 0.773434i | \(0.718538\pi\) | |||||||
\(128\) | −11.0189 | −0.973946 | ||||||||
\(129\) | 5.11529 | 0.450377 | ||||||||
\(130\) | −4.28687 | −0.375983 | ||||||||
\(131\) | 14.6926 | 1.28369 | 0.641847 | − | 0.766832i | \(-0.278168\pi\) | ||||
0.641847 | + | 0.766832i | \(0.278168\pi\) | |||||||
\(132\) | −8.74940 | −0.761537 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.80159 | −0.501181 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 2.24136 | 0.192195 | ||||||||
\(137\) | 11.4370 | 0.977126 | 0.488563 | − | 0.872529i | \(-0.337521\pi\) | ||||
0.488563 | + | 0.872529i | \(0.337521\pi\) | |||||||
\(138\) | 1.01962 | 0.0867956 | ||||||||
\(139\) | −18.1466 | −1.53917 | −0.769586 | − | 0.638543i | \(-0.779537\pi\) | ||||
−0.769586 | + | 0.638543i | \(0.779537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.48528 | −0.546159 | ||||||||
\(142\) | −0.963735 | −0.0808748 | ||||||||
\(143\) | 36.2047 | 3.02759 | ||||||||
\(144\) | 1.54156 | 0.128463 | ||||||||
\(145\) | −8.99647 | −0.747116 | ||||||||
\(146\) | −5.17784 | −0.428521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.60764 | −0.789743 | ||||||||
\(149\) | −8.23059 | −0.674276 | −0.337138 | − | 0.941455i | \(-0.609459\pi\) | ||||
−0.337138 | + | 0.941455i | \(0.609459\pi\) | |||||||
\(150\) | 0.665096 | 0.0543049 | ||||||||
\(151\) | −9.79453 | −0.797067 | −0.398534 | − | 0.917154i | \(-0.630481\pi\) | ||||
−0.398534 | + | 0.917154i | \(0.630481\pi\) | |||||||
\(152\) | 16.3561 | 1.32665 | ||||||||
\(153\) | −0.947252 | −0.0765807 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.91245 | −0.233934 | ||||||||
\(156\) | −10.0398 | −0.803827 | ||||||||
\(157\) | 8.10234 | 0.646637 | 0.323319 | − | 0.946290i | \(-0.395201\pi\) | ||||
0.323319 | + | 0.946290i | \(0.395201\pi\) | |||||||
\(158\) | −7.60373 | −0.604920 | ||||||||
\(159\) | −3.03127 | −0.240396 | ||||||||
\(160\) | −5.75764 | −0.455181 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.665096 | 0.0522549 | ||||||||
\(163\) | 17.8382 | 1.39720 | 0.698599 | − | 0.715514i | \(-0.253807\pi\) | ||||
0.698599 | + | 0.715514i | \(0.253807\pi\) | |||||||
\(164\) | 0.185086 | 0.0144528 | ||||||||
\(165\) | −5.61706 | −0.437287 | ||||||||
\(166\) | 4.76978 | 0.370207 | ||||||||
\(167\) | 15.5514 | 1.20340 | 0.601700 | − | 0.798722i | \(-0.294490\pi\) | ||||
0.601700 | + | 0.798722i | \(0.294490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5443 | 2.19572 | ||||||||
\(170\) | 0.630013 | 0.0483198 | ||||||||
\(171\) | −6.91245 | −0.528608 | ||||||||
\(172\) | −7.96782 | −0.607541 | ||||||||
\(173\) | 13.2645 | 1.00848 | 0.504240 | − | 0.863563i | \(-0.331773\pi\) | ||||
0.504240 | + | 0.863563i | \(0.331773\pi\) | |||||||
\(174\) | 5.98352 | 0.453609 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.65903 | 0.652699 | ||||||||
\(177\) | 5.48881 | 0.412564 | ||||||||
\(178\) | 0.550984 | 0.0412980 | ||||||||
\(179\) | −7.89060 | −0.589771 | −0.294886 | − | 0.955533i | \(-0.595282\pi\) | ||||
−0.294886 | + | 0.955533i | \(0.595282\pi\) | |||||||
\(180\) | 1.55765 | 0.116100 | ||||||||
\(181\) | −24.8960 | −1.85050 | −0.925251 | − | 0.379355i | \(-0.876146\pi\) | ||||
−0.925251 | + | 0.379355i | \(0.876146\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.41421 | −0.695919 | ||||||||
\(184\) | −3.62744 | −0.267418 | ||||||||
\(185\) | −6.16804 | −0.453484 | ||||||||
\(186\) | 1.93706 | 0.142032 | ||||||||
\(187\) | −5.32077 | −0.389093 | ||||||||
\(188\) | 10.1018 | 0.736748 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.59744 | 0.333534 | ||||||||
\(191\) | 7.03626 | 0.509126 | 0.254563 | − | 0.967056i | \(-0.418068\pi\) | ||||
0.254563 | + | 0.967056i | \(0.418068\pi\) | |||||||
\(192\) | 0.746264 | 0.0538569 | ||||||||
\(193\) | 8.81510 | 0.634525 | 0.317262 | − | 0.948338i | \(-0.397236\pi\) | ||||
0.317262 | + | 0.948338i | \(0.397236\pi\) | |||||||
\(194\) | −5.27707 | −0.378872 | ||||||||
\(195\) | −6.44549 | −0.461571 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.5130 | 1.60399 | 0.801993 | − | 0.597333i | \(-0.203773\pi\) | ||||
0.801993 | + | 0.597333i | \(0.203773\pi\) | |||||||
\(198\) | 3.73588 | 0.265498 | ||||||||
\(199\) | −8.32167 | −0.589908 | −0.294954 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294954 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(200\) | −2.36618 | −0.167314 | ||||||||
\(201\) | −8.72293 | −0.615268 | ||||||||
\(202\) | 1.18100 | 0.0830946 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.47548 | 0.103305 | ||||||||
\(205\) | 0.118824 | 0.00829906 | ||||||||
\(206\) | −0.111765 | −0.00778702 | ||||||||
\(207\) | 1.53304 | 0.106554 | ||||||||
\(208\) | 9.93610 | 0.688945 | ||||||||
\(209\) | −38.8276 | −2.68576 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.65332 | −0.595719 | −0.297860 | − | 0.954610i | \(-0.596273\pi\) | ||||
−0.297860 | + | 0.954610i | \(0.596273\pi\) | |||||||
\(212\) | 4.72165 | 0.324285 | ||||||||
\(213\) | −1.44902 | −0.0992850 | ||||||||
\(214\) | 3.79177 | 0.259200 | ||||||||
\(215\) | −5.11529 | −0.348860 | ||||||||
\(216\) | −2.36618 | −0.160998 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.43216 | −0.164727 | ||||||||
\(219\) | −7.78510 | −0.526068 | ||||||||
\(220\) | 8.74940 | 0.589884 | ||||||||
\(221\) | −6.10550 | −0.410700 | ||||||||
\(222\) | 4.10234 | 0.275331 | ||||||||
\(223\) | −0.597838 | −0.0400342 | −0.0200171 | − | 0.999800i | \(-0.506372\pi\) | ||||
−0.0200171 | + | 0.999800i | \(0.506372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −11.6918 | −0.777726 | ||||||||
\(227\) | 0.765881 | 0.0508333 | 0.0254167 | − | 0.999677i | \(-0.491909\pi\) | ||||
0.0254167 | + | 0.999677i | \(0.491909\pi\) | |||||||
\(228\) | 10.7672 | 0.713072 | ||||||||
\(229\) | −4.92893 | −0.325713 | −0.162857 | − | 0.986650i | \(-0.552071\pi\) | ||||
−0.162857 | + | 0.986650i | \(0.552071\pi\) | |||||||
\(230\) | −1.01962 | −0.0672316 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.2872 | −1.39758 | ||||||||
\(233\) | 29.0938 | 1.90600 | 0.953000 | − | 0.302971i | \(-0.0979786\pi\) | ||||
0.953000 | + | 0.302971i | \(0.0979786\pi\) | |||||||
\(234\) | 4.28687 | 0.280241 | ||||||||
\(235\) | 6.48528 | 0.423053 | ||||||||
\(236\) | −8.54963 | −0.556534 | ||||||||
\(237\) | −11.4325 | −0.742623 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.1873 | −1.37049 | −0.685245 | − | 0.728313i | \(-0.740305\pi\) | ||||
−0.685245 | + | 0.728313i | \(0.740305\pi\) | |||||||
\(240\) | −1.54156 | −0.0995072 | ||||||||
\(241\) | 0.261489 | 0.0168440 | 0.00842198 | − | 0.999965i | \(-0.497319\pi\) | ||||
0.00842198 | + | 0.999965i | \(0.497319\pi\) | |||||||
\(242\) | 13.6686 | 0.878653 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.6640 | 0.938768 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0790296 | −0.00503875 | ||||||||
\(247\) | −44.5541 | −2.83491 | ||||||||
\(248\) | −6.89137 | −0.437602 | ||||||||
\(249\) | 7.17157 | 0.454480 | ||||||||
\(250\) | −0.665096 | −0.0420644 | ||||||||
\(251\) | 19.7194 | 1.24468 | 0.622339 | − | 0.782748i | \(-0.286183\pi\) | ||||
0.622339 | + | 0.782748i | \(0.286183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.61117 | 0.541379 | ||||||||
\(254\) | −9.50214 | −0.596217 | ||||||||
\(255\) | 0.947252 | 0.0593192 | ||||||||
\(256\) | −8.82118 | −0.551324 | ||||||||
\(257\) | −9.23412 | −0.576009 | −0.288004 | − | 0.957629i | \(-0.592992\pi\) | ||||
−0.288004 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(258\) | 3.40216 | 0.211809 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.0398 | 0.622642 | ||||||||
\(261\) | 8.99647 | 0.556868 | ||||||||
\(262\) | 9.77196 | 0.603714 | ||||||||
\(263\) | −17.2524 | −1.06383 | −0.531915 | − | 0.846797i | \(-0.678528\pi\) | ||||
−0.531915 | + | 0.846797i | \(0.678528\pi\) | |||||||
\(264\) | −13.2910 | −0.818002 | ||||||||
\(265\) | 3.03127 | 0.186210 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.828427 | 0.0506989 | ||||||||
\(268\) | 13.5872 | 0.829973 | ||||||||
\(269\) | 11.5210 | 0.702447 | 0.351223 | − | 0.936292i | \(-0.385766\pi\) | ||||
0.351223 | + | 0.936292i | \(0.385766\pi\) | |||||||
\(270\) | −0.665096 | −0.0404765 | ||||||||
\(271\) | −18.2958 | −1.11139 | −0.555694 | − | 0.831387i | \(-0.687547\pi\) | ||||
−0.555694 | + | 0.831387i | \(0.687547\pi\) | |||||||
\(272\) | −1.46024 | −0.0885403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.60668 | 0.459536 | ||||||||
\(275\) | 5.61706 | 0.338721 | ||||||||
\(276\) | −2.38793 | −0.143737 | ||||||||
\(277\) | −14.8776 | −0.893911 | −0.446956 | − | 0.894556i | \(-0.647492\pi\) | ||||
−0.446956 | + | 0.894556i | \(0.647492\pi\) | |||||||
\(278\) | −12.0692 | −0.723863 | ||||||||
\(279\) | 2.91245 | 0.174364 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.5443 | −0.927295 | −0.463648 | − | 0.886020i | \(-0.653460\pi\) | ||||
−0.463648 | + | 0.886020i | \(0.653460\pi\) | |||||||
\(282\) | −4.31333 | −0.256855 | ||||||||
\(283\) | 6.30019 | 0.374508 | 0.187254 | − | 0.982312i | \(-0.440041\pi\) | ||||
0.187254 | + | 0.982312i | \(0.440041\pi\) | |||||||
\(284\) | 2.25706 | 0.133932 | ||||||||
\(285\) | 6.91245 | 0.409458 | ||||||||
\(286\) | 24.0796 | 1.42386 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.75764 | 0.339272 | ||||||||
\(289\) | −16.1027 | −0.947219 | ||||||||
\(290\) | −5.98352 | −0.351364 | ||||||||
\(291\) | −7.93430 | −0.465117 | ||||||||
\(292\) | 12.1264 | 0.709646 | ||||||||
\(293\) | −6.65332 | −0.388691 | −0.194346 | − | 0.980933i | \(-0.562258\pi\) | ||||
−0.194346 | + | 0.980933i | \(0.562258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.48881 | −0.319571 | ||||||||
\(296\) | −14.5947 | −0.848299 | ||||||||
\(297\) | 5.61706 | 0.325935 | ||||||||
\(298\) | −5.47413 | −0.317108 | ||||||||
\(299\) | 9.88118 | 0.571443 | ||||||||
\(300\) | −1.55765 | −0.0899308 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.51430 | −0.374856 | ||||||||
\(303\) | 1.77568 | 0.102010 | ||||||||
\(304\) | −10.6560 | −0.611161 | ||||||||
\(305\) | 9.41421 | 0.539056 | ||||||||
\(306\) | −0.630013 | −0.0360155 | ||||||||
\(307\) | 7.31371 | 0.417415 | 0.208708 | − | 0.977978i | \(-0.433074\pi\) | ||||
0.208708 | + | 0.977978i | \(0.433074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.168043 | −0.00955964 | ||||||||
\(310\) | −1.93706 | −0.110018 | ||||||||
\(311\) | −33.7686 | −1.91484 | −0.957421 | − | 0.288694i | \(-0.906779\pi\) | ||||
−0.957421 | + | 0.288694i | \(0.906779\pi\) | |||||||
\(312\) | −15.2512 | −0.863427 | ||||||||
\(313\) | 17.9702 | 1.01574 | 0.507868 | − | 0.861435i | \(-0.330434\pi\) | ||||
0.507868 | + | 0.861435i | \(0.330434\pi\) | |||||||
\(314\) | 5.38883 | 0.304110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.8079 | 1.00177 | ||||||||
\(317\) | 10.1769 | 0.571594 | 0.285797 | − | 0.958290i | \(-0.407742\pi\) | ||||
0.285797 | + | 0.958290i | \(0.407742\pi\) | |||||||
\(318\) | −2.01609 | −0.113057 | ||||||||
\(319\) | 50.5337 | 2.82934 | ||||||||
\(320\) | −0.746264 | −0.0417174 | ||||||||
\(321\) | 5.70108 | 0.318203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.54783 | 0.364331 | ||||||||
\(324\) | −1.55765 | −0.0865360 | ||||||||
\(325\) | 6.44549 | 0.357531 | ||||||||
\(326\) | 11.8641 | 0.657094 | ||||||||
\(327\) | −3.65685 | −0.202225 | ||||||||
\(328\) | 0.281160 | 0.0155244 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.73588 | −0.205654 | ||||||||
\(331\) | 8.31724 | 0.457157 | 0.228578 | − | 0.973526i | \(-0.426592\pi\) | ||||
0.228578 | + | 0.973526i | \(0.426592\pi\) | |||||||
\(332\) | −11.1708 | −0.613076 | ||||||||
\(333\) | 6.16804 | 0.338007 | ||||||||
\(334\) | 10.3431 | 0.565952 | ||||||||
\(335\) | 8.72293 | 0.476585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0233 | 1.41758 | 0.708790 | − | 0.705420i | \(-0.249241\pi\) | ||||
0.708790 | + | 0.705420i | \(0.249241\pi\) | |||||||
\(338\) | 18.9847 | 1.03263 | ||||||||
\(339\) | −17.5791 | −0.954766 | ||||||||
\(340\) | −1.47548 | −0.0800193 | ||||||||
\(341\) | 16.3594 | 0.885911 | ||||||||
\(342\) | −4.59744 | −0.248601 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.1037 | −0.652587 | ||||||||
\(345\) | −1.53304 | −0.0825360 | ||||||||
\(346\) | 8.82216 | 0.474282 | ||||||||
\(347\) | 9.77069 | 0.524518 | 0.262259 | − | 0.964998i | \(-0.415533\pi\) | ||||
0.262259 | + | 0.964998i | \(0.415533\pi\) | |||||||
\(348\) | −14.0133 | −0.751193 | ||||||||
\(349\) | 19.9809 | 1.06955 | 0.534776 | − | 0.844994i | \(-0.320396\pi\) | ||||
0.534776 | + | 0.844994i | \(0.320396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.44549 | 0.344035 | ||||||||
\(352\) | 32.3410 | 1.72378 | ||||||||
\(353\) | −24.5667 | −1.30755 | −0.653776 | − | 0.756688i | \(-0.726816\pi\) | ||||
−0.653776 | + | 0.756688i | \(0.726816\pi\) | |||||||
\(354\) | 3.65059 | 0.194026 | ||||||||
\(355\) | 1.44902 | 0.0769058 | ||||||||
\(356\) | −1.29040 | −0.0683909 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.24801 | −0.277366 | ||||||||
\(359\) | −4.03979 | −0.213212 | −0.106606 | − | 0.994301i | \(-0.533998\pi\) | ||||
−0.106606 | + | 0.994301i | \(0.533998\pi\) | |||||||
\(360\) | 2.36618 | 0.124708 | ||||||||
\(361\) | 28.7819 | 1.51484 | ||||||||
\(362\) | −16.5582 | −0.870280 | ||||||||
\(363\) | 20.5514 | 1.07867 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.78510 | 0.407491 | ||||||||
\(366\) | −6.26136 | −0.327286 | ||||||||
\(367\) | −5.27001 | −0.275092 | −0.137546 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137546 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(368\) | 2.36327 | 0.123194 | ||||||||
\(369\) | −0.118824 | −0.00618575 | ||||||||
\(370\) | −4.10234 | −0.213271 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.53657 | −0.235210 | ||||||||
\(373\) | −27.3066 | −1.41388 | −0.706942 | − | 0.707271i | \(-0.749926\pi\) | ||||
−0.706942 | + | 0.707271i | \(0.749926\pi\) | |||||||
\(374\) | −3.53882 | −0.182988 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 15.3453 | 0.791375 | ||||||||
\(377\) | 57.9866 | 2.98646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1984 | −0.626590 | −0.313295 | − | 0.949656i | \(-0.601433\pi\) | ||||
−0.313295 | + | 0.949656i | \(0.601433\pi\) | |||||||
\(380\) | −10.7672 | −0.552343 | ||||||||
\(381\) | −14.2869 | −0.731938 | ||||||||
\(382\) | 4.67979 | 0.239439 | ||||||||
\(383\) | −13.4818 | −0.688885 | −0.344443 | − | 0.938807i | \(-0.611932\pi\) | ||||
−0.344443 | + | 0.938807i | \(0.611932\pi\) | |||||||
\(384\) | −11.0189 | −0.562308 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.86289 | 0.298413 | ||||||||
\(387\) | 5.11529 | 0.260025 | ||||||||
\(388\) | 12.3588 | 0.627425 | ||||||||
\(389\) | −33.0331 | −1.67485 | −0.837423 | − | 0.546556i | \(-0.815939\pi\) | ||||
−0.837423 | + | 0.546556i | \(0.815939\pi\) | |||||||
\(390\) | −4.28687 | −0.217074 | ||||||||
\(391\) | −1.45217 | −0.0734395 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.6926 | 0.741142 | ||||||||
\(394\) | 14.9733 | 0.754345 | ||||||||
\(395\) | 11.4325 | 0.575233 | ||||||||
\(396\) | −8.74940 | −0.439674 | ||||||||
\(397\) | 21.0363 | 1.05578 | 0.527890 | − | 0.849313i | \(-0.322983\pi\) | ||||
0.527890 | + | 0.849313i | \(0.322983\pi\) | |||||||
\(398\) | −5.53471 | −0.277430 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.54156 | 0.0770780 | ||||||||
\(401\) | 6.82137 | 0.340643 | 0.170321 | − | 0.985389i | \(-0.445519\pi\) | ||||
0.170321 | + | 0.985389i | \(0.445519\pi\) | |||||||
\(402\) | −5.80159 | −0.289357 | ||||||||
\(403\) | 18.7721 | 0.935107 | ||||||||
\(404\) | −2.76588 | −0.137608 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.6463 | 1.71735 | ||||||||
\(408\) | 2.24136 | 0.110964 | ||||||||
\(409\) | −13.7869 | −0.681720 | −0.340860 | − | 0.940114i | \(-0.610718\pi\) | ||||
−0.340860 | + | 0.940114i | \(0.610718\pi\) | |||||||
\(410\) | 0.0790296 | 0.00390300 | ||||||||
\(411\) | 11.4370 | 0.564144 | ||||||||
\(412\) | 0.261752 | 0.0128956 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.01962 | 0.0501115 | ||||||||
\(415\) | −7.17157 | −0.352039 | ||||||||
\(416\) | 37.1108 | 1.81951 | ||||||||
\(417\) | −18.1466 | −0.888641 | ||||||||
\(418\) | −25.8241 | −1.26310 | ||||||||
\(419\) | −1.89450 | −0.0925525 | −0.0462763 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462763 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.81138 | −0.234492 | −0.117246 | − | 0.993103i | \(-0.537407\pi\) | ||||
−0.117246 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(422\) | −5.75529 | −0.280163 | ||||||||
\(423\) | −6.48528 | −0.315325 | ||||||||
\(424\) | 7.17253 | 0.348329 | ||||||||
\(425\) | −0.947252 | −0.0459484 | ||||||||
\(426\) | −0.963735 | −0.0466931 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.88027 | −0.429244 | ||||||||
\(429\) | 36.2047 | 1.74798 | ||||||||
\(430\) | −3.40216 | −0.164067 | ||||||||
\(431\) | −18.4196 | −0.887240 | −0.443620 | − | 0.896215i | \(-0.646306\pi\) | ||||
−0.443620 | + | 0.896215i | \(0.646306\pi\) | |||||||
\(432\) | 1.54156 | 0.0741683 | ||||||||
\(433\) | 14.7627 | 0.709451 | 0.354726 | − | 0.934970i | \(-0.384574\pi\) | ||||
0.354726 | + | 0.934970i | \(0.384574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.99647 | −0.431348 | ||||||||
\(436\) | 5.69609 | 0.272793 | ||||||||
\(437\) | −10.5970 | −0.506925 | ||||||||
\(438\) | −5.17784 | −0.247407 | ||||||||
\(439\) | −18.5434 | −0.885028 | −0.442514 | − | 0.896762i | \(-0.645913\pi\) | ||||
−0.442514 | + | 0.896762i | \(0.645913\pi\) | |||||||
\(440\) | 13.2910 | 0.633622 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.06074 | −0.193150 | ||||||||
\(443\) | −26.1068 | −1.24037 | −0.620185 | − | 0.784456i | \(-0.712943\pi\) | ||||
−0.620185 | + | 0.784456i | \(0.712943\pi\) | |||||||
\(444\) | −9.60764 | −0.455958 | ||||||||
\(445\) | −0.828427 | −0.0392712 | ||||||||
\(446\) | −0.397620 | −0.0188278 | ||||||||
\(447\) | −8.23059 | −0.389294 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.7631 | 1.87654 | 0.938268 | − | 0.345908i | \(-0.112429\pi\) | ||||
0.938268 | + | 0.345908i | \(0.112429\pi\) | |||||||
\(450\) | 0.665096 | 0.0313529 | ||||||||
\(451\) | −0.667444 | −0.0314287 | ||||||||
\(452\) | 27.3820 | 1.28794 | ||||||||
\(453\) | −9.79453 | −0.460187 | ||||||||
\(454\) | 0.509384 | 0.0239066 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.3561 | 0.765943 | ||||||||
\(457\) | −8.22173 | −0.384596 | −0.192298 | − | 0.981337i | \(-0.561594\pi\) | ||||
−0.192298 | + | 0.981337i | \(0.561594\pi\) | |||||||
\(458\) | −3.27821 | −0.153181 | ||||||||
\(459\) | −0.947252 | −0.0442139 | ||||||||
\(460\) | 2.38793 | 0.111338 | ||||||||
\(461\) | −9.91155 | −0.461627 | −0.230813 | − | 0.972998i | \(-0.574139\pi\) | ||||
−0.230813 | + | 0.972998i | \(0.574139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7285 | −0.777437 | −0.388719 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388719 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(464\) | 13.8686 | 0.643833 | ||||||||
\(465\) | −2.91245 | −0.135062 | ||||||||
\(466\) | 19.3502 | 0.896380 | ||||||||
\(467\) | −28.7784 | −1.33171 | −0.665853 | − | 0.746083i | \(-0.731932\pi\) | ||||
−0.665853 | + | 0.746083i | \(0.731932\pi\) | |||||||
\(468\) | −10.0398 | −0.464090 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.31333 | 0.198959 | ||||||||
\(471\) | 8.10234 | 0.373336 | ||||||||
\(472\) | −12.9875 | −0.597798 | ||||||||
\(473\) | 28.7329 | 1.32114 | ||||||||
\(474\) | −7.60373 | −0.349251 | ||||||||
\(475\) | −6.91245 | −0.317165 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.03127 | −0.138792 | ||||||||
\(478\) | −14.0916 | −0.644533 | ||||||||
\(479\) | 14.2173 | 0.649603 | 0.324802 | − | 0.945782i | \(-0.394702\pi\) | ||||
0.324802 | + | 0.945782i | \(0.394702\pi\) | |||||||
\(480\) | −5.75764 | −0.262799 | ||||||||
\(481\) | 39.7560 | 1.81272 | ||||||||
\(482\) | 0.173915 | 0.00792161 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.0118 | −1.45508 | ||||||||
\(485\) | 7.93430 | 0.360278 | ||||||||
\(486\) | 0.665096 | 0.0301694 | ||||||||
\(487\) | −9.56394 | −0.433383 | −0.216692 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216692 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(488\) | 22.2757 | 1.00837 | ||||||||
\(489\) | 17.8382 | 0.806672 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0800 | −1.13184 | −0.565921 | − | 0.824459i | \(-0.691479\pi\) | ||||
−0.565921 | + | 0.824459i | \(0.691479\pi\) | |||||||
\(492\) | 0.185086 | 0.00834434 | ||||||||
\(493\) | −8.52192 | −0.383808 | ||||||||
\(494\) | −29.6328 | −1.33324 | ||||||||
\(495\) | −5.61706 | −0.252468 | ||||||||
\(496\) | 4.48971 | 0.201594 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.76978 | 0.213739 | ||||||||
\(499\) | 3.68903 | 0.165144 | 0.0825718 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825718 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(500\) | 1.55765 | 0.0696601 | ||||||||
\(501\) | 15.5514 | 0.694783 | ||||||||
\(502\) | 13.1153 | 0.585364 | ||||||||
\(503\) | −41.8445 | −1.86575 | −0.932877 | − | 0.360195i | \(-0.882710\pi\) | ||||
−0.932877 | + | 0.360195i | \(0.882710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.77568 | −0.0790167 | ||||||||
\(506\) | 5.72725 | 0.254607 | ||||||||
\(507\) | 28.5443 | 1.26770 | ||||||||
\(508\) | 22.2539 | 0.987357 | ||||||||
\(509\) | 5.44958 | 0.241548 | 0.120774 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120774 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(510\) | 0.630013 | 0.0278975 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.1710 | 0.714662 | ||||||||
\(513\) | −6.91245 | −0.305192 | ||||||||
\(514\) | −6.14158 | −0.270893 | ||||||||
\(515\) | 0.168043 | 0.00740486 | ||||||||
\(516\) | −7.96782 | −0.350764 | ||||||||
\(517\) | −36.4282 | −1.60211 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.2645 | 0.582246 | ||||||||
\(520\) | 15.2512 | 0.668808 | ||||||||
\(521\) | −15.5817 | −0.682648 | −0.341324 | − | 0.939946i | \(-0.610875\pi\) | ||||
−0.341324 | + | 0.939946i | \(0.610875\pi\) | |||||||
\(522\) | 5.98352 | 0.261891 | ||||||||
\(523\) | −4.08845 | −0.178776 | −0.0893878 | − | 0.995997i | \(-0.528491\pi\) | ||||
−0.0893878 | + | 0.995997i | \(0.528491\pi\) | |||||||
\(524\) | −22.8858 | −0.999772 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.4745 | −0.500313 | ||||||||
\(527\) | −2.75882 | −0.120176 | ||||||||
\(528\) | 8.65903 | 0.376836 | ||||||||
\(529\) | −20.6498 | −0.897817 | ||||||||
\(530\) | 2.01609 | 0.0875733 | ||||||||
\(531\) | 5.48881 | 0.238194 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.765881 | −0.0331740 | ||||||||
\(534\) | 0.550984 | 0.0238434 | ||||||||
\(535\) | −5.70108 | −0.246479 | ||||||||
\(536\) | 20.6400 | 0.891512 | ||||||||
\(537\) | −7.89060 | −0.340505 | ||||||||
\(538\) | 7.66256 | 0.330357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.55765 | 0.0670305 | ||||||||
\(541\) | −27.6764 | −1.18990 | −0.594952 | − | 0.803761i | \(-0.702829\pi\) | ||||
−0.594952 | + | 0.803761i | \(0.702829\pi\) | |||||||
\(542\) | −12.1684 | −0.522679 | ||||||||
\(543\) | −24.8960 | −1.06839 | ||||||||
\(544\) | −5.45393 | −0.233835 | ||||||||
\(545\) | 3.65685 | 0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1421 | 0.433646 | 0.216823 | − | 0.976211i | \(-0.430430\pi\) | ||||
0.216823 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(548\) | −17.8148 | −0.761009 | ||||||||
\(549\) | −9.41421 | −0.401789 | ||||||||
\(550\) | 3.73588 | 0.159299 | ||||||||
\(551\) | −62.1876 | −2.64928 | ||||||||
\(552\) | −3.62744 | −0.154394 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.89506 | −0.420401 | ||||||||
\(555\) | −6.16804 | −0.261819 | ||||||||
\(556\) | 28.2660 | 1.19874 | ||||||||
\(557\) | −28.0714 | −1.18943 | −0.594713 | − | 0.803938i | \(-0.702734\pi\) | ||||
−0.594713 | + | 0.803938i | \(0.702734\pi\) | |||||||
\(558\) | 1.93706 | 0.0820022 | ||||||||
\(559\) | 32.9706 | 1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.32077 | −0.224643 | ||||||||
\(562\) | −10.3385 | −0.436101 | ||||||||
\(563\) | 4.67037 | 0.196833 | 0.0984163 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984163 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(564\) | 10.1018 | 0.425362 | ||||||||
\(565\) | 17.5791 | 0.739558 | ||||||||
\(566\) | 4.19023 | 0.176129 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.42863 | 0.143862 | ||||||||
\(569\) | 19.9311 | 0.835557 | 0.417778 | − | 0.908549i | \(-0.362809\pi\) | ||||
0.417778 | + | 0.908549i | \(0.362809\pi\) | |||||||
\(570\) | 4.59744 | 0.192566 | ||||||||
\(571\) | 41.9070 | 1.75375 | 0.876877 | − | 0.480714i | \(-0.159622\pi\) | ||||
0.876877 | + | 0.480714i | \(0.159622\pi\) | |||||||
\(572\) | −56.3941 | −2.35796 | ||||||||
\(573\) | 7.03626 | 0.293944 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.53304 | 0.0639321 | ||||||||
\(576\) | 0.746264 | 0.0310943 | ||||||||
\(577\) | 44.5965 | 1.85658 | 0.928288 | − | 0.371862i | \(-0.121281\pi\) | ||||
0.928288 | + | 0.371862i | \(0.121281\pi\) | |||||||
\(578\) | −10.7099 | −0.445471 | ||||||||
\(579\) | 8.81510 | 0.366343 | ||||||||
\(580\) | 14.0133 | 0.581872 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.27707 | −0.218742 | ||||||||
\(583\) | −17.0268 | −0.705180 | ||||||||
\(584\) | 18.4209 | 0.762264 | ||||||||
\(585\) | −6.44549 | −0.266488 | ||||||||
\(586\) | −4.42510 | −0.182799 | ||||||||
\(587\) | 23.5872 | 0.973550 | 0.486775 | − | 0.873527i | \(-0.338173\pi\) | ||||
0.486775 | + | 0.873527i | \(0.338173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1322 | −0.829531 | ||||||||
\(590\) | −3.65059 | −0.150292 | ||||||||
\(591\) | 22.5130 | 0.926062 | ||||||||
\(592\) | 9.50841 | 0.390793 | ||||||||
\(593\) | 30.3627 | 1.24685 | 0.623424 | − | 0.781884i | \(-0.285741\pi\) | ||||
0.623424 | + | 0.781884i | \(0.285741\pi\) | |||||||
\(594\) | 3.73588 | 0.153285 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.8204 | 0.525142 | ||||||||
\(597\) | −8.32167 | −0.340583 | ||||||||
\(598\) | 6.57193 | 0.268746 | ||||||||
\(599\) | −12.5339 | −0.512123 | −0.256061 | − | 0.966661i | \(-0.582425\pi\) | ||||
−0.256061 | + | 0.966661i | \(0.582425\pi\) | |||||||
\(600\) | −2.36618 | −0.0965988 | ||||||||
\(601\) | −20.4107 | −0.832569 | −0.416285 | − | 0.909234i | \(-0.636668\pi\) | ||||
−0.416285 | + | 0.909234i | \(0.636668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.72293 | −0.355225 | ||||||||
\(604\) | 15.2564 | 0.620775 | ||||||||
\(605\) | −20.5514 | −0.835531 | ||||||||
\(606\) | 1.18100 | 0.0479747 | ||||||||
\(607\) | 30.4253 | 1.23492 | 0.617462 | − | 0.786601i | \(-0.288161\pi\) | ||||
0.617462 | + | 0.786601i | \(0.288161\pi\) | |||||||
\(608\) | −39.7994 | −1.61408 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.26136 | 0.253515 | ||||||||
\(611\) | −41.8008 | −1.69108 | ||||||||
\(612\) | 1.47548 | 0.0596429 | ||||||||
\(613\) | 2.42900 | 0.0981065 | 0.0490533 | − | 0.998796i | \(-0.484380\pi\) | ||||
0.0490533 | + | 0.998796i | \(0.484380\pi\) | |||||||
\(614\) | 4.86432 | 0.196308 | ||||||||
\(615\) | 0.118824 | 0.00479146 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2324 | −1.05608 | −0.528039 | − | 0.849220i | \(-0.677072\pi\) | ||||
−0.528039 | + | 0.849220i | \(0.677072\pi\) | |||||||
\(618\) | −0.111765 | −0.00449584 | ||||||||
\(619\) | 28.3772 | 1.14057 | 0.570287 | − | 0.821445i | \(-0.306832\pi\) | ||||
0.570287 | + | 0.821445i | \(0.306832\pi\) | |||||||
\(620\) | 4.53657 | 0.182193 | ||||||||
\(621\) | 1.53304 | 0.0615187 | ||||||||
\(622\) | −22.4594 | −0.900539 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.93610 | 0.397762 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.9519 | 0.477694 | ||||||||
\(627\) | −38.8276 | −1.55063 | ||||||||
\(628\) | −12.6206 | −0.503616 | ||||||||
\(629\) | −5.84269 | −0.232963 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.96429 | −0.356863 | −0.178431 | − | 0.983952i | \(-0.557102\pi\) | ||||
−0.178431 | + | 0.983952i | \(0.557102\pi\) | |||||||
\(632\) | 27.0514 | 1.07605 | ||||||||
\(633\) | −8.65332 | −0.343939 | ||||||||
\(634\) | 6.76864 | 0.268817 | ||||||||
\(635\) | 14.2869 | 0.566957 | ||||||||
\(636\) | 4.72165 | 0.187226 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 33.6098 | 1.33062 | ||||||||
\(639\) | −1.44902 | −0.0573222 | ||||||||
\(640\) | 11.0189 | 0.435562 | ||||||||
\(641\) | −18.2565 | −0.721088 | −0.360544 | − | 0.932742i | \(-0.617409\pi\) | ||||
−0.360544 | + | 0.932742i | \(0.617409\pi\) | |||||||
\(642\) | 3.79177 | 0.149649 | ||||||||
\(643\) | −5.10197 | −0.201202 | −0.100601 | − | 0.994927i | \(-0.532077\pi\) | ||||
−0.100601 | + | 0.994927i | \(0.532077\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.11529 | −0.201415 | ||||||||
\(646\) | 4.35493 | 0.171343 | ||||||||
\(647\) | 13.8338 | 0.543861 | 0.271931 | − | 0.962317i | \(-0.412338\pi\) | ||||
0.271931 | + | 0.962317i | \(0.412338\pi\) | |||||||
\(648\) | −2.36618 | −0.0929522 | ||||||||
\(649\) | 30.8310 | 1.21022 | ||||||||
\(650\) | 4.28687 | 0.168145 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.7857 | −1.08817 | ||||||||
\(653\) | 4.37089 | 0.171046 | 0.0855231 | − | 0.996336i | \(-0.472744\pi\) | ||||
0.0855231 | + | 0.996336i | \(0.472744\pi\) | |||||||
\(654\) | −2.43216 | −0.0951050 | ||||||||
\(655\) | −14.6926 | −0.574086 | ||||||||
\(656\) | −0.183175 | −0.00715178 | ||||||||
\(657\) | −7.78510 | −0.303726 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.3365 | −1.92188 | −0.960938 | − | 0.276764i | \(-0.910738\pi\) | ||||
−0.960938 | + | 0.276764i | \(0.910738\pi\) | |||||||
\(660\) | 8.74940 | 0.340570 | ||||||||
\(661\) | −6.77268 | −0.263427 | −0.131713 | − | 0.991288i | \(-0.542048\pi\) | ||||
−0.131713 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(662\) | 5.53176 | 0.214998 | ||||||||
\(663\) | −6.10550 | −0.237118 | ||||||||
\(664\) | −16.9692 | −0.658533 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.10234 | 0.158962 | ||||||||
\(667\) | 13.7919 | 0.534026 | ||||||||
\(668\) | −24.2235 | −0.937236 | ||||||||
\(669\) | −0.597838 | −0.0231138 | ||||||||
\(670\) | 5.80159 | 0.224135 | ||||||||
\(671\) | −52.8802 | −2.04142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.5649 | 1.02400 | 0.512000 | − | 0.858985i | \(-0.328905\pi\) | ||||
0.512000 | + | 0.858985i | \(0.328905\pi\) | |||||||
\(674\) | 17.3080 | 0.666679 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −44.4619 | −1.71007 | ||||||||
\(677\) | 35.3522 | 1.35869 | 0.679347 | − | 0.733817i | \(-0.262263\pi\) | ||||
0.679347 | + | 0.733817i | \(0.262263\pi\) | |||||||
\(678\) | −11.6918 | −0.449020 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.24136 | −0.0859524 | ||||||||
\(681\) | 0.765881 | 0.0293486 | ||||||||
\(682\) | 10.8806 | 0.416639 | ||||||||
\(683\) | −39.2265 | −1.50096 | −0.750481 | − | 0.660892i | \(-0.770178\pi\) | ||||
−0.750481 | + | 0.660892i | \(0.770178\pi\) | |||||||
\(684\) | 10.7672 | 0.411693 | ||||||||
\(685\) | −11.4370 | −0.436984 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.92893 | −0.188050 | ||||||||
\(688\) | 7.88553 | 0.300633 | ||||||||
\(689\) | −19.5380 | −0.744340 | ||||||||
\(690\) | −1.01962 | −0.0388162 | ||||||||
\(691\) | −42.3324 | −1.61040 | −0.805200 | − | 0.593003i | \(-0.797942\pi\) | ||||
−0.805200 | + | 0.593003i | \(0.797942\pi\) | |||||||
\(692\) | −20.6614 | −0.785428 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.49844 | 0.246678 | ||||||||
\(695\) | 18.1466 | 0.688339 | ||||||||
\(696\) | −21.2872 | −0.806891 | ||||||||
\(697\) | 0.112557 | 0.00426338 | ||||||||
\(698\) | 13.2892 | 0.503004 | ||||||||
\(699\) | 29.0938 | 1.10043 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.49062 | 0.207378 | 0.103689 | − | 0.994610i | \(-0.466935\pi\) | ||||
0.103689 | + | 0.994610i | \(0.466935\pi\) | |||||||
\(702\) | 4.28687 | 0.161797 | ||||||||
\(703\) | −42.6363 | −1.60806 | ||||||||
\(704\) | 4.19181 | 0.157985 | ||||||||
\(705\) | 6.48528 | 0.244250 | ||||||||
\(706\) | −16.3392 | −0.614934 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.54963 | −0.321315 | ||||||||
\(709\) | 5.78195 | 0.217146 | 0.108573 | − | 0.994089i | \(-0.465372\pi\) | ||||
0.108573 | + | 0.994089i | \(0.465372\pi\) | |||||||
\(710\) | 0.963735 | 0.0361683 | ||||||||
\(711\) | −11.4325 | −0.428753 | ||||||||
\(712\) | −1.96021 | −0.0734618 | ||||||||
\(713\) | 4.46489 | 0.167212 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.2047 | −1.35398 | ||||||||
\(716\) | 12.2908 | 0.459328 | ||||||||
\(717\) | −21.1873 | −0.791253 | ||||||||
\(718\) | −2.68685 | −0.100272 | ||||||||
\(719\) | 46.7614 | 1.74390 | 0.871952 | − | 0.489591i | \(-0.162854\pi\) | ||||
0.871952 | + | 0.489591i | \(0.162854\pi\) | |||||||
\(720\) | −1.54156 | −0.0574505 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.1428 | 0.712420 | ||||||||
\(723\) | 0.261489 | 0.00972486 | ||||||||
\(724\) | 38.7791 | 1.44122 | ||||||||
\(725\) | 8.99647 | 0.334121 | ||||||||
\(726\) | 13.6686 | 0.507290 | ||||||||
\(727\) | −3.32783 | −0.123422 | −0.0617111 | − | 0.998094i | \(-0.519656\pi\) | ||||
−0.0617111 | + | 0.998094i | \(0.519656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.17784 | 0.191640 | ||||||||
\(731\) | −4.84547 | −0.179216 | ||||||||
\(732\) | 14.6640 | 0.541998 | ||||||||
\(733\) | −3.94316 | −0.145644 | −0.0728220 | − | 0.997345i | \(-0.523200\pi\) | ||||
−0.0728220 | + | 0.997345i | \(0.523200\pi\) | |||||||
\(734\) | −3.50506 | −0.129374 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.82668 | 0.325356 | ||||||||
\(737\) | −48.9972 | −1.80484 | ||||||||
\(738\) | −0.0790296 | −0.00290912 | ||||||||
\(739\) | −31.9859 | −1.17662 | −0.588310 | − | 0.808636i | \(-0.700206\pi\) | ||||
−0.588310 | + | 0.808636i | \(0.700206\pi\) | |||||||
\(740\) | 9.60764 | 0.353184 | ||||||||
\(741\) | −44.5541 | −1.63674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.4170 | 0.602280 | 0.301140 | − | 0.953580i | \(-0.402633\pi\) | ||||
0.301140 | + | 0.953580i | \(0.402633\pi\) | |||||||
\(744\) | −6.89137 | −0.252650 | ||||||||
\(745\) | 8.23059 | 0.301545 | ||||||||
\(746\) | −18.1615 | −0.664941 | ||||||||
\(747\) | 7.17157 | 0.262394 | ||||||||
\(748\) | 8.28788 | 0.303035 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.665096 | −0.0242859 | ||||||||
\(751\) | 11.5702 | 0.422203 | 0.211101 | − | 0.977464i | \(-0.432295\pi\) | ||||
0.211101 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(752\) | −9.99745 | −0.364569 | ||||||||
\(753\) | 19.7194 | 0.718615 | ||||||||
\(754\) | 38.5667 | 1.40452 | ||||||||
\(755\) | 9.79453 | 0.356459 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9178 | 0.433160 | 0.216580 | − | 0.976265i | \(-0.430510\pi\) | ||||
0.216580 | + | 0.976265i | \(0.430510\pi\) | |||||||
\(758\) | −8.11312 | −0.294682 | ||||||||
\(759\) | 8.61117 | 0.312566 | ||||||||
\(760\) | −16.3561 | −0.593297 | ||||||||
\(761\) | 14.1492 | 0.512908 | 0.256454 | − | 0.966556i | \(-0.417446\pi\) | ||||
0.256454 | + | 0.966556i | \(0.417446\pi\) | |||||||
\(762\) | −9.50214 | −0.344226 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.9600 | −0.396520 | ||||||||
\(765\) | 0.947252 | 0.0342480 | ||||||||
\(766\) | −8.96666 | −0.323979 | ||||||||
\(767\) | 35.3781 | 1.27743 | ||||||||
\(768\) | −8.82118 | −0.318307 | ||||||||
\(769\) | 40.2097 | 1.45000 | 0.724999 | − | 0.688750i | \(-0.241840\pi\) | ||||
0.724999 | + | 0.688750i | \(0.241840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.23412 | −0.332559 | ||||||||
\(772\) | −13.7308 | −0.494183 | ||||||||
\(773\) | 54.0618 | 1.94447 | 0.972233 | − | 0.234015i | \(-0.0751864\pi\) | ||||
0.972233 | + | 0.234015i | \(0.0751864\pi\) | |||||||
\(774\) | 3.40216 | 0.122288 | ||||||||
\(775\) | 2.91245 | 0.104618 | ||||||||
\(776\) | 18.7740 | 0.673946 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9702 | −0.787669 | ||||||||
\(779\) | 0.821368 | 0.0294285 | ||||||||
\(780\) | 10.0398 | 0.359482 | ||||||||
\(781\) | −8.13921 | −0.291244 | ||||||||
\(782\) | −0.965834 | −0.0345382 | ||||||||
\(783\) | 8.99647 | 0.321508 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.10234 | −0.289185 | ||||||||
\(786\) | 9.77196 | 0.348554 | ||||||||
\(787\) | −23.8775 | −0.851140 | −0.425570 | − | 0.904926i | \(-0.639926\pi\) | ||||
−0.425570 | + | 0.904926i | \(0.639926\pi\) | |||||||
\(788\) | −35.0674 | −1.24922 | ||||||||
\(789\) | −17.2524 | −0.614203 | ||||||||
\(790\) | 7.60373 | 0.270529 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.2910 | −0.472274 | ||||||||
\(793\) | −60.6792 | −2.15478 | ||||||||
\(794\) | 13.9911 | 0.496527 | ||||||||
\(795\) | 3.03127 | 0.107508 | ||||||||
\(796\) | 12.9622 | 0.459434 | ||||||||
\(797\) | 4.63001 | 0.164003 | 0.0820017 | − | 0.996632i | \(-0.473869\pi\) | ||||
0.0820017 | + | 0.996632i | \(0.473869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.14319 | 0.217331 | ||||||||
\(800\) | 5.75764 | 0.203563 | ||||||||
\(801\) | 0.828427 | 0.0292710 | ||||||||
\(802\) | 4.53686 | 0.160202 | ||||||||
\(803\) | −43.7294 | −1.54318 | ||||||||
\(804\) | 13.5872 | 0.479185 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4853 | 0.439775 | ||||||||
\(807\) | 11.5210 | 0.405558 | ||||||||
\(808\) | −4.20157 | −0.147811 | ||||||||
\(809\) | −0.908017 | −0.0319242 | −0.0159621 | − | 0.999873i | \(-0.505081\pi\) | ||||
−0.0159621 | + | 0.999873i | \(0.505081\pi\) | |||||||
\(810\) | −0.665096 | −0.0233691 | ||||||||
\(811\) | 3.39773 | 0.119310 | 0.0596552 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596552 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2958 | −0.641660 | ||||||||
\(814\) | 23.0431 | 0.807660 | ||||||||
\(815\) | −17.8382 | −0.624846 | ||||||||
\(816\) | −1.46024 | −0.0511188 | ||||||||
\(817\) | −35.3592 | −1.23706 | ||||||||
\(818\) | −9.16964 | −0.320609 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.185086 | −0.00646350 | ||||||||
\(821\) | 0.193951 | 0.00676892 | 0.00338446 | − | 0.999994i | \(-0.498923\pi\) | ||||
0.00338446 | + | 0.999994i | \(0.498923\pi\) | |||||||
\(822\) | 7.60668 | 0.265313 | ||||||||
\(823\) | −30.2869 | −1.05573 | −0.527867 | − | 0.849327i | \(-0.677008\pi\) | ||||
−0.527867 | + | 0.849327i | \(0.677008\pi\) | |||||||
\(824\) | 0.397620 | 0.0138517 | ||||||||
\(825\) | 5.61706 | 0.195561 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.23006 | 0.286187 | 0.143094 | − | 0.989709i | \(-0.454295\pi\) | ||||
0.143094 | + | 0.989709i | \(0.454295\pi\) | |||||||
\(828\) | −2.38793 | −0.0829864 | ||||||||
\(829\) | −7.80286 | −0.271005 | −0.135502 | − | 0.990777i | \(-0.543265\pi\) | ||||
−0.135502 | + | 0.990777i | \(0.543265\pi\) | |||||||
\(830\) | −4.76978 | −0.165562 | ||||||||
\(831\) | −14.8776 | −0.516100 | ||||||||
\(832\) | 4.81003 | 0.166758 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.0692 | −0.417923 | ||||||||
\(835\) | −15.5514 | −0.538177 | ||||||||
\(836\) | 60.4798 | 2.09174 | ||||||||
\(837\) | 2.91245 | 0.100669 | ||||||||
\(838\) | −1.26003 | −0.0435269 | ||||||||
\(839\) | 40.9409 | 1.41344 | 0.706719 | − | 0.707494i | \(-0.250174\pi\) | ||||
0.706719 | + | 0.707494i | \(0.250174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.9365 | 1.79091 | ||||||||
\(842\) | −3.20003 | −0.110280 | ||||||||
\(843\) | −15.5443 | −0.535374 | ||||||||
\(844\) | 13.4788 | 0.463960 | ||||||||
\(845\) | −28.5443 | −0.981954 | ||||||||
\(846\) | −4.31333 | −0.148296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.67289 | −0.160468 | ||||||||
\(849\) | 6.30019 | 0.216222 | ||||||||
\(850\) | −0.630013 | −0.0216093 | ||||||||
\(851\) | 9.45584 | 0.324142 | ||||||||
\(852\) | 2.25706 | 0.0773255 | ||||||||
\(853\) | −45.0488 | −1.54244 | −0.771221 | − | 0.636568i | \(-0.780354\pi\) | ||||
−0.771221 | + | 0.636568i | \(0.780354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.91245 | 0.236401 | ||||||||
\(856\) | −13.4898 | −0.461071 | ||||||||
\(857\) | −34.4727 | −1.17757 | −0.588783 | − | 0.808291i | \(-0.700393\pi\) | ||||
−0.588783 | + | 0.808291i | \(0.700393\pi\) | |||||||
\(858\) | 24.0796 | 0.822064 | ||||||||
\(859\) | 6.43497 | 0.219558 | 0.109779 | − | 0.993956i | \(-0.464986\pi\) | ||||
0.109779 | + | 0.993956i | \(0.464986\pi\) | |||||||
\(860\) | 7.96782 | 0.271701 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.2508 | −0.417264 | ||||||||
\(863\) | −34.8663 | −1.18686 | −0.593432 | − | 0.804884i | \(-0.702227\pi\) | ||||
−0.593432 | + | 0.804884i | \(0.702227\pi\) | |||||||
\(864\) | 5.75764 | 0.195879 | ||||||||
\(865\) | −13.2645 | −0.451006 | ||||||||
\(866\) | 9.81863 | 0.333651 | ||||||||
\(867\) | −16.1027 | −0.546877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −64.2172 | −2.17842 | ||||||||
\(870\) | −5.98352 | −0.202860 | ||||||||
\(871\) | −56.2235 | −1.90506 | ||||||||
\(872\) | 8.65276 | 0.293020 | ||||||||
\(873\) | −7.93430 | −0.268535 | ||||||||
\(874\) | −7.04805 | −0.238404 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.1264 | 0.409715 | ||||||||
\(877\) | 21.6961 | 0.732625 | 0.366312 | − | 0.930492i | \(-0.380620\pi\) | ||||
0.366312 | + | 0.930492i | \(0.380620\pi\) | |||||||
\(878\) | −12.3331 | −0.416223 | ||||||||
\(879\) | −6.65332 | −0.224411 | ||||||||
\(880\) | −8.65903 | −0.291896 | ||||||||
\(881\) | 3.32077 | 0.111880 | 0.0559398 | − | 0.998434i | \(-0.482185\pi\) | ||||
0.0559398 | + | 0.998434i | \(0.482185\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.89450 | −0.332977 | −0.166488 | − | 0.986043i | \(-0.553243\pi\) | ||||
−0.166488 | + | 0.986043i | \(0.553243\pi\) | |||||||
\(884\) | 9.51021 | 0.319863 | ||||||||
\(885\) | −5.48881 | −0.184504 | ||||||||
\(886\) | −17.3635 | −0.583339 | ||||||||
\(887\) | 33.6864 | 1.13108 | 0.565540 | − | 0.824721i | \(-0.308668\pi\) | ||||
0.565540 | + | 0.824721i | \(0.308668\pi\) | |||||||
\(888\) | −14.5947 | −0.489765 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.550984 | −0.0184690 | ||||||||
\(891\) | 5.61706 | 0.188179 | ||||||||
\(892\) | 0.931221 | 0.0311796 | ||||||||
\(893\) | 44.8292 | 1.50015 | ||||||||
\(894\) | −5.47413 | −0.183082 | ||||||||
\(895\) | 7.89060 | 0.263754 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.88118 | 0.329923 | ||||||||
\(898\) | 26.4463 | 0.882524 | ||||||||
\(899\) | 26.2018 | 0.873878 | ||||||||
\(900\) | −1.55765 | −0.0519216 | ||||||||
\(901\) | 2.87138 | 0.0956595 | ||||||||
\(902\) | −0.443914 | −0.0147807 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.5953 | 1.38344 | ||||||||
\(905\) | 24.8960 | 0.827570 | ||||||||
\(906\) | −6.51430 | −0.216423 | ||||||||
\(907\) | −17.2082 | −0.571389 | −0.285695 | − | 0.958321i | \(-0.592224\pi\) | ||||
−0.285695 | + | 0.958321i | \(0.592224\pi\) | |||||||
\(908\) | −1.19297 | −0.0395902 | ||||||||
\(909\) | 1.77568 | 0.0588955 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0551 | −0.763850 | −0.381925 | − | 0.924193i | \(-0.624739\pi\) | ||||
−0.381925 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(912\) | −10.6560 | −0.352854 | ||||||||
\(913\) | 40.2832 | 1.33318 | ||||||||
\(914\) | −5.46824 | −0.180873 | ||||||||
\(915\) | 9.41421 | 0.311224 | ||||||||
\(916\) | 7.67754 | 0.253673 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.630013 | −0.0207935 | ||||||||
\(919\) | 7.13568 | 0.235384 | 0.117692 | − | 0.993050i | \(-0.462450\pi\) | ||||
0.117692 | + | 0.993050i | \(0.462450\pi\) | |||||||
\(920\) | 3.62744 | 0.119593 | ||||||||
\(921\) | 7.31371 | 0.240995 | ||||||||
\(922\) | −6.59213 | −0.217100 | ||||||||
\(923\) | −9.33962 | −0.307417 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.16804 | 0.202804 | ||||||||
\(926\) | −11.1260 | −0.365624 | ||||||||
\(927\) | −0.168043 | −0.00551926 | ||||||||
\(928\) | 51.7984 | 1.70037 | ||||||||
\(929\) | 2.58372 | 0.0847691 | 0.0423845 | − | 0.999101i | \(-0.486505\pi\) | ||||
0.0423845 | + | 0.999101i | \(0.486505\pi\) | |||||||
\(930\) | −1.93706 | −0.0635186 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −45.3179 | −1.48444 | ||||||||
\(933\) | −33.7686 | −1.10553 | ||||||||
\(934\) | −19.1404 | −0.626293 | ||||||||
\(935\) | 5.32077 | 0.174008 | ||||||||
\(936\) | −15.2512 | −0.498500 | ||||||||
\(937\) | 6.03979 | 0.197311 | 0.0986557 | − | 0.995122i | \(-0.468546\pi\) | ||||
0.0986557 | + | 0.995122i | \(0.468546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.9702 | 0.586435 | ||||||||
\(940\) | −10.1018 | −0.329484 | ||||||||
\(941\) | −37.1027 | −1.20951 | −0.604757 | − | 0.796410i | \(-0.706730\pi\) | ||||
−0.604757 | + | 0.796410i | \(0.706730\pi\) | |||||||
\(942\) | 5.38883 | 0.175578 | ||||||||
\(943\) | −0.182162 | −0.00593202 | ||||||||
\(944\) | 8.46133 | 0.275393 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.1101 | 0.621324 | ||||||||
\(947\) | 17.6315 | 0.572946 | 0.286473 | − | 0.958088i | \(-0.407517\pi\) | ||||
0.286473 | + | 0.958088i | \(0.407517\pi\) | |||||||
\(948\) | 17.8079 | 0.578372 | ||||||||
\(949\) | −50.1788 | −1.62887 | ||||||||
\(950\) | −4.59744 | −0.149161 | ||||||||
\(951\) | 10.1769 | 0.330010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0366 | 0.713836 | 0.356918 | − | 0.934136i | \(-0.383828\pi\) | ||||
0.356918 | + | 0.934136i | \(0.383828\pi\) | |||||||
\(954\) | −2.01609 | −0.0652732 | ||||||||
\(955\) | −7.03626 | −0.227688 | ||||||||
\(956\) | 33.0023 | 1.06737 | ||||||||
\(957\) | 50.5337 | 1.63352 | ||||||||
\(958\) | 9.45584 | 0.305504 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.746264 | −0.0240856 | ||||||||
\(961\) | −22.5176 | −0.726376 | ||||||||
\(962\) | 26.4416 | 0.852511 | ||||||||
\(963\) | 5.70108 | 0.183715 | ||||||||
\(964\) | −0.407307 | −0.0131185 | ||||||||
\(965\) | −8.81510 | −0.283768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.7088 | −1.05184 | −0.525922 | − | 0.850533i | \(-0.676280\pi\) | ||||
−0.525922 | + | 0.850533i | \(0.676280\pi\) | |||||||
\(968\) | −48.6281 | −1.56297 | ||||||||
\(969\) | 6.54783 | 0.210347 | ||||||||
\(970\) | 5.27707 | 0.169437 | ||||||||
\(971\) | −11.4684 | −0.368039 | −0.184020 | − | 0.982923i | \(-0.558911\pi\) | ||||
−0.184020 | + | 0.982923i | \(0.558911\pi\) | |||||||
\(972\) | −1.55765 | −0.0499616 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.36094 | −0.203818 | ||||||||
\(975\) | 6.44549 | 0.206421 | ||||||||
\(976\) | −14.5126 | −0.464536 | ||||||||
\(977\) | 61.1404 | 1.95606 | 0.978028 | − | 0.208474i | \(-0.0668495\pi\) | ||||
0.978028 | + | 0.208474i | \(0.0668495\pi\) | |||||||
\(978\) | 11.8641 | 0.379373 | ||||||||
\(979\) | 4.65332 | 0.148721 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65685 | −0.116754 | ||||||||
\(982\) | −16.6806 | −0.532299 | ||||||||
\(983\) | −14.0259 | −0.447357 | −0.223678 | − | 0.974663i | \(-0.571807\pi\) | ||||
−0.223678 | + | 0.974663i | \(0.571807\pi\) | |||||||
\(984\) | 0.281160 | 0.00896304 | ||||||||
\(985\) | −22.5130 | −0.717325 | ||||||||
\(986\) | −5.66790 | −0.180503 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 69.3996 | 2.20789 | ||||||||
\(989\) | 7.84194 | 0.249359 | ||||||||
\(990\) | −3.73588 | −0.118734 | ||||||||
\(991\) | 10.5353 | 0.334665 | 0.167332 | − | 0.985901i | \(-0.446485\pi\) | ||||
0.167332 | + | 0.985901i | \(0.446485\pi\) | |||||||
\(992\) | 16.7688 | 0.532411 | ||||||||
\(993\) | 8.31724 | 0.263940 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.32167 | 0.263815 | ||||||||
\(996\) | −11.1708 | −0.353960 | ||||||||
\(997\) | 36.8971 | 1.16854 | 0.584271 | − | 0.811559i | \(-0.301381\pi\) | ||||
0.584271 | + | 0.811559i | \(0.301381\pi\) | |||||||
\(998\) | 2.45356 | 0.0776660 | ||||||||
\(999\) | 6.16804 | 0.195148 |
(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 | 735.2.a.o.1.2 | yes | 4 | |
3.2 | odd | 2 | 2205.2.a.bg.1.3 | 4 | |||
5.4 | even | 2 | 3675.2.a.bk.1.3 | 4 | |||
7.2 | even | 3 | 735.2.i.m.361.3 | 8 | |||
7.3 | odd | 6 | 735.2.i.n.226.3 | 8 | |||
7.4 | even | 3 | 735.2.i.m.226.3 | 8 | |||
7.5 | odd | 6 | 735.2.i.n.361.3 | 8 | |||
7.6 | odd | 2 | 735.2.a.n.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 2205.2.a.bf.1.3 | 4 | |||
35.34 | odd | 2 | 3675.2.a.bl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.a.n.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
735.2.a.o.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
735.2.i.m.226.3 | 8 | 7.4 | even | 3 | |||
735.2.i.m.361.3 | 8 | 7.2 | even | 3 | |||
735.2.i.n.226.3 | 8 | 7.3 | odd | 6 | |||
735.2.i.n.361.3 | 8 | 7.5 | odd | 6 | |||
2205.2.a.bf.1.3 | 4 | 21.20 | even | 2 | |||
2205.2.a.bg.1.3 | 4 | 3.2 | odd | 2 | |||
3675.2.a.bk.1.3 | 4 | 5.4 | even | 2 | |||
3675.2.a.bl.1.3 | 4 | 35.34 | odd | 2 |