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 | 1.4 | ||
Root | \(0.334904\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74912 | 1.94392 | 0.971960 | − | 0.235147i | \(-0.0755571\pi\) | ||||
0.971960 | + | 0.235147i | \(0.0755571\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.55765 | 2.77882 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.74912 | −1.12232 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.78039 | 3.45789 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.74912 | 0.869347 | ||||||||
\(11\) | −4.44549 | −1.34036 | −0.670182 | − | 0.742197i | \(-0.733784\pi\) | ||||
−0.670182 | + | 0.742197i | \(0.733784\pi\) | |||||||
\(12\) | −5.55765 | −1.60435 | ||||||||
\(13\) | 3.61706 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332746\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 15.7721 | 3.94304 | ||||||||
\(17\) | −4.94725 | −1.19988 | −0.599942 | − | 0.800043i | \(-0.704810\pi\) | ||||
−0.599942 | + | 0.800043i | \(0.704810\pi\) | |||||||
\(18\) | 2.74912 | 0.647973 | ||||||||
\(19\) | 2.74441 | 0.629610 | 0.314805 | − | 0.949156i | \(-0.398061\pi\) | ||||
0.314805 | + | 0.949156i | \(0.398061\pi\) | |||||||
\(20\) | 5.55765 | 1.24273 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.2212 | −2.60556 | ||||||||
\(23\) | −4.36147 | −0.909428 | −0.454714 | − | 0.890637i | \(-0.650259\pi\) | ||||
−0.454714 | + | 0.890637i | \(0.650259\pi\) | |||||||
\(24\) | −9.78039 | −1.99641 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 9.94372 | 1.95012 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.660384 | 0.122630 | 0.0613151 | − | 0.998118i | \(-0.480471\pi\) | ||||
0.0613151 | + | 0.998118i | \(0.480471\pi\) | |||||||
\(30\) | −2.74912 | −0.501918 | ||||||||
\(31\) | 1.25559 | 0.225511 | 0.112756 | − | 0.993623i | \(-0.464032\pi\) | ||||
0.112756 | + | 0.993623i | \(0.464032\pi\) | |||||||
\(32\) | 23.7987 | 4.20706 | ||||||||
\(33\) | 4.44549 | 0.773860 | ||||||||
\(34\) | −13.6006 | −2.33248 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.55765 | 0.926275 | ||||||||
\(37\) | −2.16804 | −0.356424 | −0.178212 | − | 0.983992i | \(-0.557031\pi\) | ||||
−0.178212 | + | 0.983992i | \(0.557031\pi\) | |||||||
\(38\) | 7.54469 | 1.22391 | ||||||||
\(39\) | −3.61706 | −0.579193 | ||||||||
\(40\) | 9.78039 | 1.54642 | ||||||||
\(41\) | −5.77568 | −0.902009 | −0.451005 | − | 0.892522i | \(-0.648934\pi\) | ||||
−0.451005 | + | 0.892522i | \(0.648934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.11529 | −1.39007 | −0.695035 | − | 0.718976i | \(-0.744611\pi\) | ||||
−0.695035 | + | 0.718976i | \(0.744611\pi\) | |||||||
\(44\) | −24.7064 | −3.72464 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −11.9902 | −1.76786 | ||||||||
\(47\) | 6.48528 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(48\) | −15.7721 | −2.27651 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.74912 | 0.388784 | ||||||||
\(51\) | 4.94725 | 0.692754 | ||||||||
\(52\) | 20.1023 | 2.78769 | ||||||||
\(53\) | 7.03127 | 0.965820 | 0.482910 | − | 0.875670i | \(-0.339580\pi\) | ||||
0.482910 | + | 0.875670i | \(0.339580\pi\) | |||||||
\(54\) | −2.74912 | −0.374108 | ||||||||
\(55\) | −4.44549 | −0.599429 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.74441 | −0.363505 | ||||||||
\(58\) | 1.81547 | 0.238383 | ||||||||
\(59\) | −13.8249 | −1.79985 | −0.899924 | − | 0.436046i | \(-0.856378\pi\) | ||||
−0.899924 | + | 0.436046i | \(0.856378\pi\) | |||||||
\(60\) | −5.55765 | −0.717489 | ||||||||
\(61\) | 9.41421 | 1.20537 | 0.602683 | − | 0.797981i | \(-0.294098\pi\) | ||||
0.602683 | + | 0.797981i | \(0.294098\pi\) | |||||||
\(62\) | 3.45178 | 0.438376 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 33.8812 | 4.23514 | ||||||||
\(65\) | 3.61706 | 0.448641 | ||||||||
\(66\) | 12.2212 | 1.50432 | ||||||||
\(67\) | 3.06608 | 0.374581 | 0.187290 | − | 0.982305i | \(-0.440029\pi\) | ||||
0.187290 | + | 0.982305i | \(0.440029\pi\) | |||||||
\(68\) | −27.4951 | −3.33427 | ||||||||
\(69\) | 4.36147 | 0.525059 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.277444 | 0.0329265 | 0.0164632 | − | 0.999864i | \(-0.494759\pi\) | ||||
0.0164632 | + | 0.999864i | \(0.494759\pi\) | |||||||
\(72\) | 9.78039 | 1.15263 | ||||||||
\(73\) | −10.6135 | −1.24222 | −0.621110 | − | 0.783724i | \(-0.713318\pi\) | ||||
−0.621110 | + | 0.783724i | \(0.713318\pi\) | |||||||
\(74\) | −5.96021 | −0.692860 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 15.2524 | 1.74957 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.94372 | −1.12590 | ||||||||
\(79\) | −5.53803 | −0.623077 | −0.311539 | − | 0.950234i | \(-0.600844\pi\) | ||||
−0.311539 | + | 0.950234i | \(0.600844\pi\) | |||||||
\(80\) | 15.7721 | 1.76338 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.8780 | −1.75343 | ||||||||
\(83\) | −7.17157 | −0.787182 | −0.393591 | − | 0.919286i | \(-0.628767\pi\) | ||||
−0.393591 | + | 0.919286i | \(0.628767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.94725 | −0.536605 | ||||||||
\(86\) | −25.0590 | −2.70218 | ||||||||
\(87\) | −0.660384 | −0.0708006 | ||||||||
\(88\) | −43.4786 | −4.63483 | ||||||||
\(89\) | −0.828427 | −0.0878131 | −0.0439065 | − | 0.999036i | \(-0.513980\pi\) | ||||
−0.0439065 | + | 0.999036i | \(0.513980\pi\) | |||||||
\(90\) | 2.74912 | 0.289782 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −24.2395 | −2.52714 | ||||||||
\(93\) | −1.25559 | −0.130199 | ||||||||
\(94\) | 17.8288 | 1.83890 | ||||||||
\(95\) | 2.74441 | 0.281570 | ||||||||
\(96\) | −23.7987 | −2.42895 | ||||||||
\(97\) | 6.20784 | 0.630310 | 0.315155 | − | 0.949040i | \(-0.397943\pi\) | ||||
0.315155 | + | 0.949040i | \(0.397943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.44549 | −0.446788 | ||||||||
\(100\) | 5.55765 | 0.555765 | ||||||||
\(101\) | 4.11882 | 0.409838 | 0.204919 | − | 0.978779i | \(-0.434307\pi\) | ||||
0.204919 | + | 0.978779i | \(0.434307\pi\) | |||||||
\(102\) | 13.6006 | 1.34666 | ||||||||
\(103\) | −8.16804 | −0.804821 | −0.402411 | − | 0.915459i | \(-0.631828\pi\) | ||||
−0.402411 | + | 0.915459i | \(0.631828\pi\) | |||||||
\(104\) | 35.3763 | 3.46893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.3298 | 1.87748 | ||||||||
\(107\) | −8.52951 | −0.824579 | −0.412289 | − | 0.911053i | \(-0.635271\pi\) | ||||
−0.412289 | + | 0.911053i | \(0.635271\pi\) | |||||||
\(108\) | −5.55765 | −0.534785 | ||||||||
\(109\) | −3.65685 | −0.350263 | −0.175132 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175132 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(110\) | −12.2212 | −1.16524 | ||||||||
\(111\) | 2.16804 | 0.205782 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.6085 | 1.18611 | 0.593056 | − | 0.805161i | \(-0.297921\pi\) | ||||
0.593056 | + | 0.805161i | \(0.297921\pi\) | |||||||
\(114\) | −7.54469 | −0.706625 | ||||||||
\(115\) | −4.36147 | −0.406709 | ||||||||
\(116\) | 3.67018 | 0.340768 | ||||||||
\(117\) | 3.61706 | 0.334397 | ||||||||
\(118\) | −38.0063 | −3.49876 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.78039 | −0.892823 | ||||||||
\(121\) | 8.76235 | 0.796577 | ||||||||
\(122\) | 25.8808 | 2.34314 | ||||||||
\(123\) | 5.77568 | 0.520775 | ||||||||
\(124\) | 6.97815 | 0.626656 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0562783 | −0.00499389 | −0.00249695 | − | 0.999997i | \(-0.500795\pi\) | ||||
−0.00249695 | + | 0.999997i | \(0.500795\pi\) | |||||||
\(128\) | 45.5459 | 4.02572 | ||||||||
\(129\) | 9.11529 | 0.802557 | ||||||||
\(130\) | 9.94372 | 0.872122 | ||||||||
\(131\) | 19.6631 | 1.71797 | 0.858987 | − | 0.511997i | \(-0.171094\pi\) | ||||
0.858987 | + | 0.511997i | \(0.171094\pi\) | |||||||
\(132\) | 24.7064 | 2.15042 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.42900 | 0.728155 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −48.3861 | −4.14907 | ||||||||
\(137\) | −18.7507 | −1.60198 | −0.800989 | − | 0.598679i | \(-0.795693\pi\) | ||||
−0.800989 | + | 0.598679i | \(0.795693\pi\) | |||||||
\(138\) | 11.9902 | 1.02067 | ||||||||
\(139\) | −6.14657 | −0.521345 | −0.260673 | − | 0.965427i | \(-0.583944\pi\) | ||||
−0.260673 | + | 0.965427i | \(0.583944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.48528 | −0.546159 | ||||||||
\(142\) | 0.762725 | 0.0640065 | ||||||||
\(143\) | −16.0796 | −1.34464 | ||||||||
\(144\) | 15.7721 | 1.31435 | ||||||||
\(145\) | 0.660384 | 0.0548419 | ||||||||
\(146\) | −29.1778 | −2.41478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.0492 | −0.990440 | ||||||||
\(149\) | 20.2306 | 1.65735 | 0.828677 | − | 0.559727i | \(-0.189094\pi\) | ||||
0.828677 | + | 0.559727i | \(0.189094\pi\) | |||||||
\(150\) | −2.74912 | −0.224465 | ||||||||
\(151\) | 21.1082 | 1.71776 | 0.858882 | − | 0.512174i | \(-0.171160\pi\) | ||||
0.858882 | + | 0.512174i | \(0.171160\pi\) | |||||||
\(152\) | 26.8414 | 2.17712 | ||||||||
\(153\) | −4.94725 | −0.399962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.25559 | 0.100852 | ||||||||
\(156\) | −20.1023 | −1.60948 | ||||||||
\(157\) | 1.96021 | 0.156441 | 0.0782207 | − | 0.996936i | \(-0.475076\pi\) | ||||
0.0782207 | + | 0.996936i | \(0.475076\pi\) | |||||||
\(158\) | −15.2247 | −1.21121 | ||||||||
\(159\) | −7.03127 | −0.557616 | ||||||||
\(160\) | 23.7987 | 1.88145 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.74912 | 0.215991 | ||||||||
\(163\) | −8.18137 | −0.640814 | −0.320407 | − | 0.947280i | \(-0.603820\pi\) | ||||
−0.320407 | + | 0.947280i | \(0.603820\pi\) | |||||||
\(164\) | −32.0992 | −2.50653 | ||||||||
\(165\) | 4.44549 | 0.346081 | ||||||||
\(166\) | −19.7155 | −1.53022 | ||||||||
\(167\) | −3.76235 | −0.291139 | −0.145570 | − | 0.989348i | \(-0.546502\pi\) | ||||
−0.145570 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0831193 | 0.00639379 | ||||||||
\(170\) | −13.6006 | −1.04312 | ||||||||
\(171\) | 2.74441 | 0.209870 | ||||||||
\(172\) | −50.6596 | −3.86276 | ||||||||
\(173\) | −15.7061 | −1.19411 | −0.597055 | − | 0.802200i | \(-0.703663\pi\) | ||||
−0.597055 | + | 0.802200i | \(0.703663\pi\) | |||||||
\(174\) | −1.81547 | −0.137631 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −70.1149 | −5.28511 | ||||||||
\(177\) | 13.8249 | 1.03914 | ||||||||
\(178\) | −2.27744 | −0.170702 | ||||||||
\(179\) | −1.28097 | −0.0957444 | −0.0478722 | − | 0.998853i | \(-0.515244\pi\) | ||||
−0.0478722 | + | 0.998853i | \(0.515244\pi\) | |||||||
\(180\) | 5.55765 | 0.414243 | ||||||||
\(181\) | 16.5599 | 1.23089 | 0.615443 | − | 0.788181i | \(-0.288977\pi\) | ||||
0.615443 | + | 0.788181i | \(0.288977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.41421 | −0.695919 | ||||||||
\(184\) | −42.6568 | −3.14470 | ||||||||
\(185\) | −2.16804 | −0.159398 | ||||||||
\(186\) | −3.45178 | −0.253097 | ||||||||
\(187\) | 21.9929 | 1.60828 | ||||||||
\(188\) | 36.0429 | 2.62870 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.54469 | 0.547350 | ||||||||
\(191\) | 8.76272 | 0.634049 | 0.317024 | − | 0.948417i | \(-0.397316\pi\) | ||||
0.317024 | + | 0.948417i | \(0.397316\pi\) | |||||||
\(192\) | −33.8812 | −2.44516 | ||||||||
\(193\) | 26.4986 | 1.90741 | 0.953706 | − | 0.300741i | \(-0.0972340\pi\) | ||||
0.953706 | + | 0.300741i | \(0.0972340\pi\) | |||||||
\(194\) | 17.0661 | 1.22527 | ||||||||
\(195\) | −3.61706 | −0.259023 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.11439 | 0.293138 | 0.146569 | − | 0.989200i | \(-0.453177\pi\) | ||||
0.146569 | + | 0.989200i | \(0.453177\pi\) | |||||||
\(198\) | −12.2212 | −0.868520 | ||||||||
\(199\) | −7.63538 | −0.541258 | −0.270629 | − | 0.962684i | \(-0.587232\pi\) | ||||
−0.270629 | + | 0.962684i | \(0.587232\pi\) | |||||||
\(200\) | 9.78039 | 0.691578 | ||||||||
\(201\) | −3.06608 | −0.216264 | ||||||||
\(202\) | 11.3231 | 0.796693 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 27.4951 | 1.92504 | ||||||||
\(205\) | −5.77568 | −0.403391 | ||||||||
\(206\) | −22.4549 | −1.56451 | ||||||||
\(207\) | −4.36147 | −0.303143 | ||||||||
\(208\) | 57.0488 | 3.95562 | ||||||||
\(209\) | −12.2002 | −0.843907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.317238 | −0.0218396 | −0.0109198 | − | 0.999940i | \(-0.503476\pi\) | ||||
−0.0109198 | + | 0.999940i | \(0.503476\pi\) | |||||||
\(212\) | 39.0773 | 2.68384 | ||||||||
\(213\) | −0.277444 | −0.0190101 | ||||||||
\(214\) | −23.4486 | −1.60291 | ||||||||
\(215\) | −9.11529 | −0.621658 | ||||||||
\(216\) | −9.78039 | −0.665471 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0531 | −0.680883 | ||||||||
\(219\) | 10.6135 | 0.717196 | ||||||||
\(220\) | −24.7064 | −1.66571 | ||||||||
\(221\) | −17.8945 | −1.20371 | ||||||||
\(222\) | 5.96021 | 0.400023 | ||||||||
\(223\) | 29.0590 | 1.94594 | 0.972968 | − | 0.230941i | \(-0.0741803\pi\) | ||||
0.972968 | + | 0.230941i | \(0.0741803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 34.6624 | 2.30571 | ||||||||
\(227\) | −20.8910 | −1.38658 | −0.693291 | − | 0.720657i | \(-0.743840\pi\) | ||||
−0.693291 | + | 0.720657i | \(0.743840\pi\) | |||||||
\(228\) | −15.2524 | −1.01012 | ||||||||
\(229\) | 4.92893 | 0.325713 | 0.162857 | − | 0.986650i | \(-0.447929\pi\) | ||||
0.162857 | + | 0.986650i | \(0.447929\pi\) | |||||||
\(230\) | −11.9902 | −0.790609 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.45881 | 0.424042 | ||||||||
\(233\) | −1.09382 | −0.0716585 | −0.0358292 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358292 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(234\) | 9.94372 | 0.650041 | ||||||||
\(235\) | 6.48528 | 0.423053 | ||||||||
\(236\) | −76.8339 | −5.00146 | ||||||||
\(237\) | 5.53803 | 0.359734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6725 | 1.66062 | 0.830309 | − | 0.557303i | \(-0.188164\pi\) | ||||
0.830309 | + | 0.557303i | \(0.188164\pi\) | |||||||
\(240\) | −15.7721 | −1.01809 | ||||||||
\(241\) | 24.7468 | 1.59408 | 0.797040 | − | 0.603927i | \(-0.206398\pi\) | ||||
0.797040 | + | 0.603927i | \(0.206398\pi\) | |||||||
\(242\) | 24.0887 | 1.54848 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 52.3209 | 3.34950 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.8780 | 1.01235 | ||||||||
\(247\) | 9.92668 | 0.631619 | ||||||||
\(248\) | 12.2802 | 0.779794 | ||||||||
\(249\) | 7.17157 | 0.454480 | ||||||||
\(250\) | 2.74912 | 0.173869 | ||||||||
\(251\) | 0.405692 | 0.0256070 | 0.0128035 | − | 0.999918i | \(-0.495924\pi\) | ||||
0.0128035 | + | 0.999918i | \(0.495924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3888 | 1.21897 | ||||||||
\(254\) | −0.154716 | −0.00970772 | ||||||||
\(255\) | 4.94725 | 0.309809 | ||||||||
\(256\) | 57.4486 | 3.59054 | ||||||||
\(257\) | −10.8910 | −0.679360 | −0.339680 | − | 0.940541i | \(-0.610319\pi\) | ||||
−0.339680 | + | 0.940541i | \(0.610319\pi\) | |||||||
\(258\) | 25.0590 | 1.56011 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 20.1023 | 1.24669 | ||||||||
\(261\) | 0.660384 | 0.0408767 | ||||||||
\(262\) | 54.0562 | 3.33961 | ||||||||
\(263\) | 8.76716 | 0.540606 | 0.270303 | − | 0.962775i | \(-0.412876\pi\) | ||||
0.270303 | + | 0.962775i | \(0.412876\pi\) | |||||||
\(264\) | 43.4786 | 2.67592 | ||||||||
\(265\) | 7.03127 | 0.431928 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.828427 | 0.0506989 | ||||||||
\(268\) | 17.0402 | 1.04089 | ||||||||
\(269\) | 22.8347 | 1.39226 | 0.696128 | − | 0.717918i | \(-0.254905\pi\) | ||||
0.696128 | + | 0.717918i | \(0.254905\pi\) | |||||||
\(270\) | −2.74912 | −0.167306 | ||||||||
\(271\) | 10.6748 | 0.648448 | 0.324224 | − | 0.945980i | \(-0.394897\pi\) | ||||
0.324224 | + | 0.945980i | \(0.394897\pi\) | |||||||
\(272\) | −78.0288 | −4.73119 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −51.5478 | −3.11412 | ||||||||
\(275\) | −4.44549 | −0.268073 | ||||||||
\(276\) | 24.2395 | 1.45905 | ||||||||
\(277\) | −12.4361 | −0.747211 | −0.373605 | − | 0.927588i | \(-0.621879\pi\) | ||||
−0.373605 | + | 0.927588i | \(0.621879\pi\) | |||||||
\(278\) | −16.8976 | −1.01345 | ||||||||
\(279\) | 1.25559 | 0.0751705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9169 | 0.770556 | 0.385278 | − | 0.922800i | \(-0.374105\pi\) | ||||
0.385278 | + | 0.922800i | \(0.374105\pi\) | |||||||
\(282\) | −17.8288 | −1.06169 | ||||||||
\(283\) | 25.6139 | 1.52259 | 0.761294 | − | 0.648407i | \(-0.224564\pi\) | ||||
0.761294 | + | 0.648407i | \(0.224564\pi\) | |||||||
\(284\) | 1.54193 | 0.0914969 | ||||||||
\(285\) | −2.74441 | −0.162565 | ||||||||
\(286\) | −44.2047 | −2.61388 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 23.7987 | 1.40235 | ||||||||
\(289\) | 7.47530 | 0.439723 | ||||||||
\(290\) | 1.81547 | 0.106608 | ||||||||
\(291\) | −6.20784 | −0.363910 | ||||||||
\(292\) | −58.9863 | −3.45191 | ||||||||
\(293\) | −1.68276 | −0.0983080 | −0.0491540 | − | 0.998791i | \(-0.515653\pi\) | ||||
−0.0491540 | + | 0.998791i | \(0.515653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.8249 | −0.804917 | ||||||||
\(296\) | −21.2043 | −1.23248 | ||||||||
\(297\) | 4.44549 | 0.257953 | ||||||||
\(298\) | 55.6163 | 3.22176 | ||||||||
\(299\) | −15.7757 | −0.912331 | ||||||||
\(300\) | −5.55765 | −0.320871 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 58.0290 | 3.33919 | ||||||||
\(303\) | −4.11882 | −0.236620 | ||||||||
\(304\) | 43.2852 | 2.48257 | ||||||||
\(305\) | 9.41421 | 0.539056 | ||||||||
\(306\) | −13.6006 | −0.777493 | ||||||||
\(307\) | −7.31371 | −0.417415 | −0.208708 | − | 0.977978i | \(-0.566926\pi\) | ||||
−0.208708 | + | 0.977978i | \(0.566926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.16804 | 0.464664 | ||||||||
\(310\) | 3.45178 | 0.196048 | ||||||||
\(311\) | 11.2019 | 0.635204 | 0.317602 | − | 0.948224i | \(-0.397122\pi\) | ||||
0.317602 | + | 0.948224i | \(0.397122\pi\) | |||||||
\(312\) | −35.3763 | −2.00279 | ||||||||
\(313\) | −31.4857 | −1.77967 | −0.889837 | − | 0.456278i | \(-0.849182\pi\) | ||||
−0.889837 | + | 0.456278i | \(0.849182\pi\) | |||||||
\(314\) | 5.38883 | 0.304110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.7784 | −1.73142 | ||||||||
\(317\) | 8.45048 | 0.474626 | 0.237313 | − | 0.971433i | \(-0.423733\pi\) | ||||
0.237313 | + | 0.971433i | \(0.423733\pi\) | |||||||
\(318\) | −19.3298 | −1.08396 | ||||||||
\(319\) | −2.93573 | −0.164369 | ||||||||
\(320\) | 33.8812 | 1.89401 | ||||||||
\(321\) | 8.52951 | 0.476071 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.5773 | −0.755459 | ||||||||
\(324\) | 5.55765 | 0.308758 | ||||||||
\(325\) | 3.61706 | 0.200638 | ||||||||
\(326\) | −22.4915 | −1.24569 | ||||||||
\(327\) | 3.65685 | 0.202225 | ||||||||
\(328\) | −56.4884 | −3.11905 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.2212 | 0.672753 | ||||||||
\(331\) | 16.6533 | 0.915349 | 0.457675 | − | 0.889120i | \(-0.348682\pi\) | ||||
0.457675 | + | 0.889120i | \(0.348682\pi\) | |||||||
\(332\) | −39.8571 | −2.18744 | ||||||||
\(333\) | −2.16804 | −0.118808 | ||||||||
\(334\) | −10.3431 | −0.565952 | ||||||||
\(335\) | 3.06608 | 0.167518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.9178 | 1.73867 | 0.869337 | − | 0.494220i | \(-0.164546\pi\) | ||||
0.869337 | + | 0.494220i | \(0.164546\pi\) | |||||||
\(338\) | 0.228505 | 0.0124290 | ||||||||
\(339\) | −12.6085 | −0.684802 | ||||||||
\(340\) | −27.4951 | −1.49113 | ||||||||
\(341\) | −5.58173 | −0.302268 | ||||||||
\(342\) | 7.54469 | 0.407970 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −89.1511 | −4.80671 | ||||||||
\(345\) | 4.36147 | 0.234813 | ||||||||
\(346\) | −43.1778 | −2.32126 | ||||||||
\(347\) | −7.91282 | −0.424783 | −0.212391 | − | 0.977185i | \(-0.568125\pi\) | ||||
−0.212391 | + | 0.977185i | \(0.568125\pi\) | |||||||
\(348\) | −3.67018 | −0.196742 | ||||||||
\(349\) | 25.1525 | 1.34638 | 0.673190 | − | 0.739469i | \(-0.264924\pi\) | ||||
0.673190 | + | 0.739469i | \(0.264924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.61706 | −0.193064 | ||||||||
\(352\) | −105.797 | −5.63899 | ||||||||
\(353\) | −20.5667 | −1.09465 | −0.547327 | − | 0.836919i | \(-0.684355\pi\) | ||||
−0.547327 | + | 0.836919i | \(0.684355\pi\) | |||||||
\(354\) | 38.0063 | 2.02001 | ||||||||
\(355\) | 0.277444 | 0.0147252 | ||||||||
\(356\) | −4.60411 | −0.244017 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.52155 | −0.186120 | ||||||||
\(359\) | −14.1023 | −0.744293 | −0.372147 | − | 0.928174i | \(-0.621378\pi\) | ||||
−0.372147 | + | 0.928174i | \(0.621378\pi\) | |||||||
\(360\) | 9.78039 | 0.515472 | ||||||||
\(361\) | −11.4682 | −0.603591 | ||||||||
\(362\) | 45.5251 | 2.39274 | ||||||||
\(363\) | −8.76235 | −0.459904 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6135 | −0.555538 | ||||||||
\(366\) | −25.8808 | −1.35281 | ||||||||
\(367\) | 0.386844 | 0.0201931 | 0.0100965 | − | 0.999949i | \(-0.496786\pi\) | ||||
0.0100965 | + | 0.999949i | \(0.496786\pi\) | |||||||
\(368\) | −68.7897 | −3.58591 | ||||||||
\(369\) | −5.77568 | −0.300670 | ||||||||
\(370\) | −5.96021 | −0.309856 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.97815 | −0.361800 | ||||||||
\(373\) | −10.6345 | −0.550632 | −0.275316 | − | 0.961354i | \(-0.588783\pi\) | ||||
−0.275316 | + | 0.961354i | \(0.588783\pi\) | |||||||
\(374\) | 60.4612 | 3.12637 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 63.4286 | 3.27108 | ||||||||
\(377\) | 2.38865 | 0.123022 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4290 | −1.35757 | −0.678783 | − | 0.734339i | \(-0.737492\pi\) | ||||
−0.678783 | + | 0.734339i | \(0.737492\pi\) | |||||||
\(380\) | 15.2524 | 0.782434 | ||||||||
\(381\) | 0.0562783 | 0.00288322 | ||||||||
\(382\) | 24.0898 | 1.23254 | ||||||||
\(383\) | 5.14567 | 0.262931 | 0.131466 | − | 0.991321i | \(-0.458032\pi\) | ||||
0.131466 | + | 0.991321i | \(0.458032\pi\) | |||||||
\(384\) | −45.5459 | −2.32425 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 72.8478 | 3.70785 | ||||||||
\(387\) | −9.11529 | −0.463356 | ||||||||
\(388\) | 34.5010 | 1.75152 | ||||||||
\(389\) | −12.9080 | −0.654462 | −0.327231 | − | 0.944944i | \(-0.606116\pi\) | ||||
−0.327231 | + | 0.944944i | \(0.606116\pi\) | |||||||
\(390\) | −9.94372 | −0.503520 | ||||||||
\(391\) | 21.5773 | 1.09121 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.6631 | −0.991873 | ||||||||
\(394\) | 11.3109 | 0.569837 | ||||||||
\(395\) | −5.53803 | −0.278649 | ||||||||
\(396\) | −24.7064 | −1.24155 | ||||||||
\(397\) | −22.7627 | −1.14243 | −0.571214 | − | 0.820801i | \(-0.693527\pi\) | ||||
−0.571214 | + | 0.820801i | \(0.693527\pi\) | |||||||
\(398\) | −20.9906 | −1.05216 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.7721 | 0.788607 | ||||||||
\(401\) | −9.85080 | −0.491926 | −0.245963 | − | 0.969279i | \(-0.579104\pi\) | ||||
−0.245963 | + | 0.969279i | \(0.579104\pi\) | |||||||
\(402\) | −8.42900 | −0.420400 | ||||||||
\(403\) | 4.54156 | 0.226231 | ||||||||
\(404\) | 22.8910 | 1.13887 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.63801 | 0.477738 | ||||||||
\(408\) | 48.3861 | 2.39547 | ||||||||
\(409\) | −14.6742 | −0.725594 | −0.362797 | − | 0.931868i | \(-0.618178\pi\) | ||||
−0.362797 | + | 0.931868i | \(0.618178\pi\) | |||||||
\(410\) | −15.8780 | −0.784159 | ||||||||
\(411\) | 18.7507 | 0.924903 | ||||||||
\(412\) | −45.3951 | −2.23646 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.9902 | −0.589285 | ||||||||
\(415\) | −7.17157 | −0.352039 | ||||||||
\(416\) | 86.0813 | 4.22049 | ||||||||
\(417\) | 6.14657 | 0.300999 | ||||||||
\(418\) | −33.5398 | −1.64049 | ||||||||
\(419\) | −9.89450 | −0.483378 | −0.241689 | − | 0.970354i | \(-0.577701\pi\) | ||||
−0.241689 | + | 0.970354i | \(0.577701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.4388 | 1.72718 | 0.863591 | − | 0.504193i | \(-0.168210\pi\) | ||||
0.863591 | + | 0.504193i | \(0.168210\pi\) | |||||||
\(422\) | −0.872125 | −0.0424544 | ||||||||
\(423\) | 6.48528 | 0.315325 | ||||||||
\(424\) | 68.7686 | 3.33970 | ||||||||
\(425\) | −4.94725 | −0.239977 | ||||||||
\(426\) | −0.762725 | −0.0369541 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −47.4040 | −2.29136 | ||||||||
\(429\) | 16.0796 | 0.776330 | ||||||||
\(430\) | −25.0590 | −1.20845 | ||||||||
\(431\) | −16.6931 | −0.804079 | −0.402040 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402040 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(432\) | −15.7721 | −0.758838 | ||||||||
\(433\) | −13.0363 | −0.626483 | −0.313241 | − | 0.949674i | \(-0.601415\pi\) | ||||
−0.313241 | + | 0.949674i | \(0.601415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.660384 | −0.0316630 | ||||||||
\(436\) | −20.3235 | −0.973319 | ||||||||
\(437\) | −11.9696 | −0.572585 | ||||||||
\(438\) | 29.1778 | 1.39417 | ||||||||
\(439\) | 22.7114 | 1.08396 | 0.541979 | − | 0.840392i | \(-0.317675\pi\) | ||||
0.541979 | + | 0.840392i | \(0.317675\pi\) | |||||||
\(440\) | −43.4786 | −2.07276 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −49.1941 | −2.33992 | ||||||||
\(443\) | 8.24891 | 0.391917 | 0.195959 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195959 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(444\) | 12.0492 | 0.571831 | ||||||||
\(445\) | −0.828427 | −0.0392712 | ||||||||
\(446\) | 79.8867 | 3.78274 | ||||||||
\(447\) | −20.2306 | −0.956874 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5212 | 1.15723 | 0.578613 | − | 0.815602i | \(-0.303594\pi\) | ||||
0.578613 | + | 0.815602i | \(0.303594\pi\) | |||||||
\(450\) | 2.74912 | 0.129595 | ||||||||
\(451\) | 25.6757 | 1.20902 | ||||||||
\(452\) | 70.0738 | 3.29599 | ||||||||
\(453\) | −21.1082 | −0.991751 | ||||||||
\(454\) | −57.4317 | −2.69541 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26.8414 | −1.25696 | ||||||||
\(457\) | −28.3468 | −1.32601 | −0.663004 | − | 0.748616i | \(-0.730719\pi\) | ||||
−0.663004 | + | 0.748616i | \(0.730719\pi\) | |||||||
\(458\) | 13.5502 | 0.633160 | ||||||||
\(459\) | 4.94725 | 0.230918 | ||||||||
\(460\) | −24.2395 | −1.13017 | ||||||||
\(461\) | 38.3727 | 1.78720 | 0.893598 | − | 0.448868i | \(-0.148173\pi\) | ||||
0.893598 | + | 0.448868i | \(0.148173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.38530 | 0.110855 | 0.0554273 | − | 0.998463i | \(-0.482348\pi\) | ||||
0.0554273 | + | 0.998463i | \(0.482348\pi\) | |||||||
\(464\) | 10.4157 | 0.483536 | ||||||||
\(465\) | −1.25559 | −0.0582268 | ||||||||
\(466\) | −3.00704 | −0.139298 | ||||||||
\(467\) | −19.8079 | −0.916598 | −0.458299 | − | 0.888798i | \(-0.651541\pi\) | ||||
−0.458299 | + | 0.888798i | \(0.651541\pi\) | |||||||
\(468\) | 20.1023 | 0.929231 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.8288 | 0.822381 | ||||||||
\(471\) | −1.96021 | −0.0903215 | ||||||||
\(472\) | −135.213 | −6.22368 | ||||||||
\(473\) | 40.5219 | 1.86320 | ||||||||
\(474\) | 15.2247 | 0.699293 | ||||||||
\(475\) | 2.74441 | 0.125922 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.03127 | 0.321940 | ||||||||
\(478\) | 70.5768 | 3.22811 | ||||||||
\(479\) | −3.43959 | −0.157159 | −0.0785795 | − | 0.996908i | \(-0.525038\pi\) | ||||
−0.0785795 | + | 0.996908i | \(0.525038\pi\) | |||||||
\(480\) | −23.7987 | −1.08626 | ||||||||
\(481\) | −7.84194 | −0.357562 | ||||||||
\(482\) | 68.0318 | 3.09876 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 48.6981 | 2.21355 | ||||||||
\(485\) | 6.20784 | 0.281883 | ||||||||
\(486\) | −2.74912 | −0.124703 | ||||||||
\(487\) | −7.12235 | −0.322745 | −0.161372 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161372 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(488\) | 92.0747 | 4.16803 | ||||||||
\(489\) | 8.18137 | 0.369974 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.6896 | −1.43013 | −0.715066 | − | 0.699057i | \(-0.753603\pi\) | ||||
−0.715066 | + | 0.699057i | \(0.753603\pi\) | |||||||
\(492\) | 32.0992 | 1.44714 | ||||||||
\(493\) | −3.26709 | −0.147142 | ||||||||
\(494\) | 27.2896 | 1.22782 | ||||||||
\(495\) | −4.44549 | −0.199810 | ||||||||
\(496\) | 19.8034 | 0.889200 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.7155 | 0.883473 | ||||||||
\(499\) | −39.0027 | −1.74600 | −0.873001 | − | 0.487718i | \(-0.837829\pi\) | ||||
−0.873001 | + | 0.487718i | \(0.837829\pi\) | |||||||
\(500\) | 5.55765 | 0.248546 | ||||||||
\(501\) | 3.76235 | 0.168089 | ||||||||
\(502\) | 1.11529 | 0.0497780 | ||||||||
\(503\) | −18.5308 | −0.826247 | −0.413123 | − | 0.910675i | \(-0.635562\pi\) | ||||
−0.413123 | + | 0.910675i | \(0.635562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.11882 | 0.183285 | ||||||||
\(506\) | 53.3022 | 2.36957 | ||||||||
\(507\) | −0.0831193 | −0.00369146 | ||||||||
\(508\) | −0.312775 | −0.0138771 | ||||||||
\(509\) | −39.8053 | −1.76434 | −0.882169 | − | 0.470934i | \(-0.843917\pi\) | ||||
−0.882169 | + | 0.470934i | \(0.843917\pi\) | |||||||
\(510\) | 13.6006 | 0.602244 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 66.8412 | 2.95399 | ||||||||
\(513\) | −2.74441 | −0.121168 | ||||||||
\(514\) | −29.9406 | −1.32062 | ||||||||
\(515\) | −8.16804 | −0.359927 | ||||||||
\(516\) | 50.6596 | 2.23016 | ||||||||
\(517\) | −28.8302 | −1.26795 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.7061 | 0.689420 | ||||||||
\(520\) | 35.3763 | 1.55135 | ||||||||
\(521\) | 26.3594 | 1.15483 | 0.577413 | − | 0.816452i | \(-0.304062\pi\) | ||||
0.577413 | + | 0.816452i | \(0.304062\pi\) | |||||||
\(522\) | 1.81547 | 0.0794611 | ||||||||
\(523\) | −24.3727 | −1.06574 | −0.532872 | − | 0.846196i | \(-0.678887\pi\) | ||||
−0.532872 | + | 0.846196i | \(0.678887\pi\) | |||||||
\(524\) | 109.281 | 4.77395 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1019 | 1.05089 | ||||||||
\(527\) | −6.21174 | −0.270588 | ||||||||
\(528\) | 70.1149 | 3.05136 | ||||||||
\(529\) | −3.97762 | −0.172940 | ||||||||
\(530\) | 19.3298 | 0.839633 | ||||||||
\(531\) | −13.8249 | −0.599949 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.8910 | −0.904888 | ||||||||
\(534\) | 2.27744 | 0.0985546 | ||||||||
\(535\) | −8.52951 | −0.368763 | ||||||||
\(536\) | 29.9874 | 1.29526 | ||||||||
\(537\) | 1.28097 | 0.0552781 | ||||||||
\(538\) | 62.7753 | 2.70643 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.55765 | −0.239163 | ||||||||
\(541\) | 24.3627 | 1.04744 | 0.523718 | − | 0.851892i | \(-0.324545\pi\) | ||||
0.523718 | + | 0.851892i | \(0.324545\pi\) | |||||||
\(542\) | 29.3463 | 1.26053 | ||||||||
\(543\) | −16.5599 | −0.710652 | ||||||||
\(544\) | −117.738 | −5.04798 | ||||||||
\(545\) | −3.65685 | −0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1421 | 0.433646 | 0.216823 | − | 0.976211i | \(-0.430430\pi\) | ||||
0.216823 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(548\) | −104.210 | −4.45161 | ||||||||
\(549\) | 9.41421 | 0.401789 | ||||||||
\(550\) | −12.2212 | −0.521112 | ||||||||
\(551\) | 1.81236 | 0.0772092 | ||||||||
\(552\) | 42.6568 | 1.81560 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −34.1882 | −1.45252 | ||||||||
\(555\) | 2.16804 | 0.0920283 | ||||||||
\(556\) | −34.1605 | −1.44873 | ||||||||
\(557\) | −14.5560 | −0.616756 | −0.308378 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308378 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(558\) | 3.45178 | 0.146125 | ||||||||
\(559\) | −32.9706 | −1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.9929 | −0.928543 | ||||||||
\(562\) | 35.5100 | 1.49790 | ||||||||
\(563\) | −36.5845 | −1.54185 | −0.770926 | − | 0.636925i | \(-0.780206\pi\) | ||||
−0.770926 | + | 0.636925i | \(0.780206\pi\) | |||||||
\(564\) | −36.0429 | −1.51768 | ||||||||
\(565\) | 12.6085 | 0.530445 | ||||||||
\(566\) | 70.4156 | 2.95979 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.71351 | 0.113856 | ||||||||
\(569\) | −3.64687 | −0.152885 | −0.0764424 | − | 0.997074i | \(-0.524356\pi\) | ||||
−0.0764424 | + | 0.997074i | \(0.524356\pi\) | |||||||
\(570\) | −7.54469 | −0.316012 | ||||||||
\(571\) | −38.5933 | −1.61508 | −0.807540 | − | 0.589812i | \(-0.799202\pi\) | ||||
−0.807540 | + | 0.589812i | \(0.799202\pi\) | |||||||
\(572\) | −89.3647 | −3.73653 | ||||||||
\(573\) | −8.76272 | −0.366068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.36147 | −0.181886 | ||||||||
\(576\) | 33.8812 | 1.41171 | ||||||||
\(577\) | 14.0523 | 0.585006 | 0.292503 | − | 0.956265i | \(-0.405512\pi\) | ||||
0.292503 | + | 0.956265i | \(0.405512\pi\) | |||||||
\(578\) | 20.5505 | 0.854787 | ||||||||
\(579\) | −26.4986 | −1.10124 | ||||||||
\(580\) | 3.67018 | 0.152396 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17.0661 | −0.707412 | ||||||||
\(583\) | −31.2574 | −1.29455 | ||||||||
\(584\) | −103.804 | −4.29546 | ||||||||
\(585\) | 3.61706 | 0.149547 | ||||||||
\(586\) | −4.62611 | −0.191103 | ||||||||
\(587\) | −27.0402 | −1.11607 | −0.558034 | − | 0.829818i | \(-0.688444\pi\) | ||||
−0.558034 | + | 0.829818i | \(0.688444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.44586 | 0.141984 | ||||||||
\(590\) | −38.0063 | −1.56469 | ||||||||
\(591\) | −4.11439 | −0.169243 | ||||||||
\(592\) | −34.1947 | −1.40539 | ||||||||
\(593\) | 21.6764 | 0.890145 | 0.445073 | − | 0.895495i | \(-0.353178\pi\) | ||||
0.445073 | + | 0.895495i | \(0.353178\pi\) | |||||||
\(594\) | 12.2212 | 0.501440 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 112.434 | 4.60550 | ||||||||
\(597\) | 7.63538 | 0.312495 | ||||||||
\(598\) | −43.3692 | −1.77350 | ||||||||
\(599\) | 25.9898 | 1.06191 | 0.530957 | − | 0.847399i | \(-0.321833\pi\) | ||||
0.530957 | + | 0.847399i | \(0.321833\pi\) | |||||||
\(600\) | −9.78039 | −0.399283 | ||||||||
\(601\) | 12.0746 | 0.492533 | 0.246267 | − | 0.969202i | \(-0.420796\pi\) | ||||
0.246267 | + | 0.969202i | \(0.420796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.06608 | 0.124860 | ||||||||
\(604\) | 117.312 | 4.77336 | ||||||||
\(605\) | 8.76235 | 0.356240 | ||||||||
\(606\) | −11.3231 | −0.459971 | ||||||||
\(607\) | 41.7390 | 1.69413 | 0.847067 | − | 0.531486i | \(-0.178366\pi\) | ||||
0.847067 | + | 0.531486i | \(0.178366\pi\) | |||||||
\(608\) | 65.3133 | 2.64880 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.8808 | 1.04788 | ||||||||
\(611\) | 23.4576 | 0.948995 | ||||||||
\(612\) | −27.4951 | −1.11142 | ||||||||
\(613\) | −11.8016 | −0.476662 | −0.238331 | − | 0.971184i | \(-0.576600\pi\) | ||||
−0.238331 | + | 0.971184i | \(0.576600\pi\) | |||||||
\(614\) | −20.1062 | −0.811422 | ||||||||
\(615\) | 5.77568 | 0.232898 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.2913 | 0.494829 | 0.247415 | − | 0.968910i | \(-0.420419\pi\) | ||||
0.247415 | + | 0.968910i | \(0.420419\pi\) | |||||||
\(618\) | 22.4549 | 0.903269 | ||||||||
\(619\) | 24.3772 | 0.979801 | 0.489900 | − | 0.871778i | \(-0.337033\pi\) | ||||
0.489900 | + | 0.871778i | \(0.337033\pi\) | |||||||
\(620\) | 6.97815 | 0.280249 | ||||||||
\(621\) | 4.36147 | 0.175020 | ||||||||
\(622\) | 30.7955 | 1.23479 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −57.0488 | −2.28378 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −86.5578 | −3.45954 | ||||||||
\(627\) | 12.2002 | 0.487230 | ||||||||
\(628\) | 10.8941 | 0.434723 | ||||||||
\(629\) | 10.7259 | 0.427668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.3200 | −1.72454 | −0.862271 | − | 0.506448i | \(-0.830958\pi\) | ||||
−0.862271 | + | 0.506448i | \(0.830958\pi\) | |||||||
\(632\) | −54.1641 | −2.15453 | ||||||||
\(633\) | 0.317238 | 0.0126091 | ||||||||
\(634\) | 23.2314 | 0.922635 | ||||||||
\(635\) | −0.0562783 | −0.00223334 | ||||||||
\(636\) | −39.0773 | −1.54952 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.07066 | −0.319521 | ||||||||
\(639\) | 0.277444 | 0.0109755 | ||||||||
\(640\) | 45.5459 | 1.80036 | ||||||||
\(641\) | 18.5408 | 0.732316 | 0.366158 | − | 0.930553i | \(-0.380673\pi\) | ||||
0.366158 | + | 0.930553i | \(0.380673\pi\) | |||||||
\(642\) | 23.4486 | 0.925443 | ||||||||
\(643\) | 8.55489 | 0.337372 | 0.168686 | − | 0.985670i | \(-0.446048\pi\) | ||||
0.168686 | + | 0.985670i | \(0.446048\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.11529 | 0.358914 | ||||||||
\(646\) | −37.3255 | −1.46855 | ||||||||
\(647\) | 43.0886 | 1.69399 | 0.846994 | − | 0.531603i | \(-0.178410\pi\) | ||||
0.846994 | + | 0.531603i | \(0.178410\pi\) | |||||||
\(648\) | 9.78039 | 0.384210 | ||||||||
\(649\) | 61.4584 | 2.41245 | ||||||||
\(650\) | 9.94372 | 0.390025 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.4692 | −1.78071 | ||||||||
\(653\) | −14.0277 | −0.548948 | −0.274474 | − | 0.961595i | \(-0.588504\pi\) | ||||
−0.274474 | + | 0.961595i | \(0.588504\pi\) | |||||||
\(654\) | 10.0531 | 0.393108 | ||||||||
\(655\) | 19.6631 | 0.768302 | ||||||||
\(656\) | −91.0949 | −3.55666 | ||||||||
\(657\) | −10.6135 | −0.414073 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1488 | −0.745932 | −0.372966 | − | 0.927845i | \(-0.621659\pi\) | ||||
−0.372966 | + | 0.927845i | \(0.621659\pi\) | |||||||
\(660\) | 24.7064 | 0.961697 | ||||||||
\(661\) | −26.5717 | −1.03352 | −0.516759 | − | 0.856131i | \(-0.672862\pi\) | ||||
−0.516759 | + | 0.856131i | \(0.672862\pi\) | |||||||
\(662\) | 45.7819 | 1.77937 | ||||||||
\(663\) | 17.8945 | 0.694965 | ||||||||
\(664\) | −70.1408 | −2.72199 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.96021 | −0.230953 | ||||||||
\(667\) | −2.88024 | −0.111523 | ||||||||
\(668\) | −20.9098 | −0.809025 | ||||||||
\(669\) | −29.0590 | −1.12349 | ||||||||
\(670\) | 8.42900 | 0.325641 | ||||||||
\(671\) | −41.8508 | −1.61563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.6900 | 1.79977 | 0.899883 | − | 0.436132i | \(-0.143652\pi\) | ||||
0.899883 | + | 0.436132i | \(0.143652\pi\) | |||||||
\(674\) | 87.7458 | 3.37984 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0.461948 | 0.0177672 | ||||||||
\(677\) | 41.6953 | 1.60248 | 0.801240 | − | 0.598343i | \(-0.204174\pi\) | ||||
0.801240 | + | 0.598343i | \(0.204174\pi\) | |||||||
\(678\) | −34.6624 | −1.33120 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −48.3861 | −1.85552 | ||||||||
\(681\) | 20.8910 | 0.800544 | ||||||||
\(682\) | −15.3448 | −0.587584 | ||||||||
\(683\) | −21.5430 | −0.824321 | −0.412160 | − | 0.911111i | \(-0.635226\pi\) | ||||
−0.412160 | + | 0.911111i | \(0.635226\pi\) | |||||||
\(684\) | 15.2524 | 0.583192 | ||||||||
\(685\) | −18.7507 | −0.716426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.92893 | −0.188050 | ||||||||
\(688\) | −143.768 | −5.48110 | ||||||||
\(689\) | 25.4325 | 0.968902 | ||||||||
\(690\) | 11.9902 | 0.456458 | ||||||||
\(691\) | 22.9224 | 0.872010 | 0.436005 | − | 0.899944i | \(-0.356393\pi\) | ||||
0.436005 | + | 0.899944i | \(0.356393\pi\) | |||||||
\(692\) | −87.2888 | −3.31822 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7533 | −0.825743 | ||||||||
\(695\) | −6.14657 | −0.233153 | ||||||||
\(696\) | −6.45881 | −0.244821 | ||||||||
\(697\) | 28.5737 | 1.08231 | ||||||||
\(698\) | 69.1471 | 2.61726 | ||||||||
\(699\) | 1.09382 | 0.0413720 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.4317 | −1.94255 | −0.971275 | − | 0.237960i | \(-0.923521\pi\) | ||||
−0.971275 | + | 0.237960i | \(0.923521\pi\) | |||||||
\(702\) | −9.94372 | −0.375302 | ||||||||
\(703\) | −5.94999 | −0.224408 | ||||||||
\(704\) | −150.618 | −5.67664 | ||||||||
\(705\) | −6.48528 | −0.244250 | ||||||||
\(706\) | −56.5402 | −2.12792 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 76.8339 | 2.88759 | ||||||||
\(709\) | −34.4682 | −1.29448 | −0.647241 | − | 0.762286i | \(-0.724077\pi\) | ||||
−0.647241 | + | 0.762286i | \(0.724077\pi\) | |||||||
\(710\) | 0.762725 | 0.0286246 | ||||||||
\(711\) | −5.53803 | −0.207692 | ||||||||
\(712\) | −8.10234 | −0.303648 | ||||||||
\(713\) | −5.47623 | −0.205086 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0796 | −0.601343 | ||||||||
\(716\) | −7.11920 | −0.266057 | ||||||||
\(717\) | −25.6725 | −0.958759 | ||||||||
\(718\) | −38.7690 | −1.44685 | ||||||||
\(719\) | 42.0751 | 1.56914 | 0.784568 | − | 0.620043i | \(-0.212885\pi\) | ||||
0.784568 | + | 0.620043i | \(0.212885\pi\) | |||||||
\(720\) | 15.7721 | 0.587793 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −31.5275 | −1.17333 | ||||||||
\(723\) | −24.7468 | −0.920342 | ||||||||
\(724\) | 92.0340 | 3.42042 | ||||||||
\(725\) | 0.660384 | 0.0245260 | ||||||||
\(726\) | −24.0887 | −0.894017 | ||||||||
\(727\) | 36.6722 | 1.36010 | 0.680048 | − | 0.733168i | \(-0.261959\pi\) | ||||
0.680048 | + | 0.733168i | \(0.261959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −29.1778 | −1.07992 | ||||||||
\(731\) | 45.0957 | 1.66792 | ||||||||
\(732\) | −52.3209 | −1.93384 | ||||||||
\(733\) | −46.3696 | −1.71270 | −0.856350 | − | 0.516397i | \(-0.827273\pi\) | ||||
−0.856350 | + | 0.516397i | \(0.827273\pi\) | |||||||
\(734\) | 1.06348 | 0.0392538 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −103.797 | −3.82602 | ||||||||
\(737\) | −13.6302 | −0.502075 | ||||||||
\(738\) | −15.8780 | −0.584478 | ||||||||
\(739\) | 1.35846 | 0.0499719 | 0.0249859 | − | 0.999688i | \(-0.492046\pi\) | ||||
0.0249859 | + | 0.999688i | \(0.492046\pi\) | |||||||
\(740\) | −12.0492 | −0.442938 | ||||||||
\(741\) | −9.92668 | −0.364666 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.2748 | −0.963930 | −0.481965 | − | 0.876191i | \(-0.660077\pi\) | ||||
−0.481965 | + | 0.876191i | \(0.660077\pi\) | |||||||
\(744\) | −12.2802 | −0.450214 | ||||||||
\(745\) | 20.2306 | 0.741191 | ||||||||
\(746\) | −29.2354 | −1.07039 | ||||||||
\(747\) | −7.17157 | −0.262394 | ||||||||
\(748\) | 122.229 | 4.46914 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.74912 | −0.100384 | ||||||||
\(751\) | −25.2271 | −0.920548 | −0.460274 | − | 0.887777i | \(-0.652249\pi\) | ||||
−0.460274 | + | 0.887777i | \(0.652249\pi\) | |||||||
\(752\) | 102.287 | 3.73002 | ||||||||
\(753\) | −0.405692 | −0.0147842 | ||||||||
\(754\) | 6.56668 | 0.239144 | ||||||||
\(755\) | 21.1082 | 0.768207 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.02331 | 0.218921 | 0.109460 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109460 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(758\) | −72.6564 | −2.63900 | ||||||||
\(759\) | −19.3888 | −0.703770 | ||||||||
\(760\) | 26.8414 | 0.973638 | ||||||||
\(761\) | −30.8214 | −1.11727 | −0.558637 | − | 0.829412i | \(-0.688675\pi\) | ||||
−0.558637 | + | 0.829412i | \(0.688675\pi\) | |||||||
\(762\) | 0.154716 | 0.00560476 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 48.7001 | 1.76191 | ||||||||
\(765\) | −4.94725 | −0.178868 | ||||||||
\(766\) | 14.1460 | 0.511117 | ||||||||
\(767\) | −50.0055 | −1.80559 | ||||||||
\(768\) | −57.4486 | −2.07300 | ||||||||
\(769\) | −31.8736 | −1.14939 | −0.574695 | − | 0.818367i | \(-0.694879\pi\) | ||||
−0.574695 | + | 0.818367i | \(0.694879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8910 | 0.392229 | ||||||||
\(772\) | 147.270 | 5.30036 | ||||||||
\(773\) | 17.0912 | 0.614727 | 0.307364 | − | 0.951592i | \(-0.400553\pi\) | ||||
0.307364 | + | 0.951592i | \(0.400553\pi\) | |||||||
\(774\) | −25.0590 | −0.900728 | ||||||||
\(775\) | 1.25559 | 0.0451023 | ||||||||
\(776\) | 60.7151 | 2.17954 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.4857 | −1.27222 | ||||||||
\(779\) | −15.8508 | −0.567914 | ||||||||
\(780\) | −20.1023 | −0.719779 | ||||||||
\(781\) | −1.23337 | −0.0441335 | ||||||||
\(782\) | 59.3184 | 2.12122 | ||||||||
\(783\) | −0.660384 | −0.0236002 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.96021 | 0.0699627 | ||||||||
\(786\) | −54.0562 | −1.92812 | ||||||||
\(787\) | −28.1617 | −1.00386 | −0.501929 | − | 0.864909i | \(-0.667376\pi\) | ||||
−0.501929 | + | 0.864909i | \(0.667376\pi\) | |||||||
\(788\) | 22.8663 | 0.814580 | ||||||||
\(789\) | −8.76716 | −0.312119 | ||||||||
\(790\) | −15.2247 | −0.541670 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −43.4786 | −1.54494 | ||||||||
\(793\) | 34.0518 | 1.20921 | ||||||||
\(794\) | −62.5774 | −2.22079 | ||||||||
\(795\) | −7.03127 | −0.249374 | ||||||||
\(796\) | −42.4347 | −1.50406 | ||||||||
\(797\) | 9.60058 | 0.340070 | 0.170035 | − | 0.985438i | \(-0.445612\pi\) | ||||
0.170035 | + | 0.985438i | \(0.445612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0843 | −1.13506 | ||||||||
\(800\) | 23.7987 | 0.841411 | ||||||||
\(801\) | −0.828427 | −0.0292710 | ||||||||
\(802\) | −27.0810 | −0.956264 | ||||||||
\(803\) | 47.1823 | 1.66503 | ||||||||
\(804\) | −17.0402 | −0.600960 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4853 | 0.439775 | ||||||||
\(807\) | −22.8347 | −0.803819 | ||||||||
\(808\) | 40.2837 | 1.41718 | ||||||||
\(809\) | −21.0331 | −0.739485 | −0.369742 | − | 0.929134i | \(-0.620554\pi\) | ||||
−0.369742 | + | 0.929134i | \(0.620554\pi\) | |||||||
\(810\) | 2.74912 | 0.0965941 | ||||||||
\(811\) | 0.770313 | 0.0270493 | 0.0135247 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135247 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.6748 | −0.374382 | ||||||||
\(814\) | 26.4960 | 0.928685 | ||||||||
\(815\) | −8.18137 | −0.286581 | ||||||||
\(816\) | 78.0288 | 2.73155 | ||||||||
\(817\) | −25.0161 | −0.875201 | ||||||||
\(818\) | −40.3412 | −1.41050 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −32.0992 | −1.12095 | ||||||||
\(821\) | −16.4782 | −0.575094 | −0.287547 | − | 0.957767i | \(-0.592840\pi\) | ||||
−0.287547 | + | 0.957767i | \(0.592840\pi\) | |||||||
\(822\) | 51.5478 | 1.79794 | ||||||||
\(823\) | −16.0563 | −0.559687 | −0.279843 | − | 0.960046i | \(-0.590283\pi\) | ||||
−0.279843 | + | 0.960046i | \(0.590283\pi\) | |||||||
\(824\) | −79.8867 | −2.78298 | ||||||||
\(825\) | 4.44549 | 0.154772 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.11736 | −0.0388545 | −0.0194272 | − | 0.999811i | \(-0.506184\pi\) | ||||
−0.0194272 | + | 0.999811i | \(0.506184\pi\) | |||||||
\(828\) | −24.2395 | −0.842380 | ||||||||
\(829\) | −52.5724 | −1.82592 | −0.912958 | − | 0.408054i | \(-0.866207\pi\) | ||||
−0.912958 | + | 0.408054i | \(0.866207\pi\) | |||||||
\(830\) | −19.7155 | −0.684335 | ||||||||
\(831\) | 12.4361 | 0.431402 | ||||||||
\(832\) | 122.550 | 4.24866 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.8976 | 0.585117 | ||||||||
\(835\) | −3.76235 | −0.130202 | ||||||||
\(836\) | −67.8045 | −2.34507 | ||||||||
\(837\) | −1.25559 | −0.0433997 | ||||||||
\(838\) | −27.2012 | −0.939648 | ||||||||
\(839\) | 8.65667 | 0.298861 | 0.149431 | − | 0.988772i | \(-0.452256\pi\) | ||||
0.149431 | + | 0.988772i | \(0.452256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5639 | −0.984962 | ||||||||
\(842\) | 97.4254 | 3.35750 | ||||||||
\(843\) | −12.9169 | −0.444881 | ||||||||
\(844\) | −1.76310 | −0.0606884 | ||||||||
\(845\) | 0.0831193 | 0.00285939 | ||||||||
\(846\) | 17.8288 | 0.612967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 110.898 | 3.80826 | ||||||||
\(849\) | −25.6139 | −0.879067 | ||||||||
\(850\) | −13.6006 | −0.466496 | ||||||||
\(851\) | 9.45584 | 0.324142 | ||||||||
\(852\) | −1.54193 | −0.0528258 | ||||||||
\(853\) | −21.9361 | −0.751078 | −0.375539 | − | 0.926807i | \(-0.622542\pi\) | ||||
−0.375539 | + | 0.926807i | \(0.622542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.74441 | 0.0938567 | ||||||||
\(856\) | −83.4219 | −2.85130 | ||||||||
\(857\) | 25.1253 | 0.858263 | 0.429132 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429132 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(858\) | 44.2047 | 1.50912 | ||||||||
\(859\) | 8.09183 | 0.276090 | 0.138045 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138045 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(860\) | −50.6596 | −1.72748 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45.8913 | −1.56307 | ||||||||
\(863\) | 23.0674 | 0.785222 | 0.392611 | − | 0.919705i | \(-0.371572\pi\) | ||||
0.392611 | + | 0.919705i | \(0.371572\pi\) | |||||||
\(864\) | −23.7987 | −0.809649 | ||||||||
\(865\) | −15.7061 | −0.534023 | ||||||||
\(866\) | −35.8382 | −1.21783 | ||||||||
\(867\) | −7.47530 | −0.253874 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.6192 | 0.835150 | ||||||||
\(870\) | −1.81547 | −0.0615503 | ||||||||
\(871\) | 11.0902 | 0.375776 | ||||||||
\(872\) | −35.7655 | −1.21117 | ||||||||
\(873\) | 6.20784 | 0.210103 | ||||||||
\(874\) | −32.9059 | −1.11306 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 58.9863 | 1.99296 | ||||||||
\(877\) | −4.32351 | −0.145994 | −0.0729972 | − | 0.997332i | \(-0.523256\pi\) | ||||
−0.0729972 | + | 0.997332i | \(0.523256\pi\) | |||||||
\(878\) | 62.4364 | 2.10713 | ||||||||
\(879\) | 1.68276 | 0.0567581 | ||||||||
\(880\) | −70.1149 | −2.36357 | ||||||||
\(881\) | −19.9929 | −0.673579 | −0.336790 | − | 0.941580i | \(-0.609341\pi\) | ||||
−0.336790 | + | 0.941580i | \(0.609341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.89450 | 0.0637551 | 0.0318776 | − | 0.999492i | \(-0.489851\pi\) | ||||
0.0318776 | + | 0.999492i | \(0.489851\pi\) | |||||||
\(884\) | −99.4513 | −3.34491 | ||||||||
\(885\) | 13.8249 | 0.464719 | ||||||||
\(886\) | 22.6772 | 0.761856 | ||||||||
\(887\) | −5.22525 | −0.175447 | −0.0877234 | − | 0.996145i | \(-0.527959\pi\) | ||||
−0.0877234 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(888\) | 21.2043 | 0.711570 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.27744 | −0.0763401 | ||||||||
\(891\) | −4.44549 | −0.148929 | ||||||||
\(892\) | 161.500 | 5.40741 | ||||||||
\(893\) | 17.7982 | 0.595595 | ||||||||
\(894\) | −55.6163 | −1.86009 | ||||||||
\(895\) | −1.28097 | −0.0428182 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.7757 | 0.526735 | ||||||||
\(898\) | 67.4116 | 2.24955 | ||||||||
\(899\) | 0.829175 | 0.0276545 | ||||||||
\(900\) | 5.55765 | 0.185255 | ||||||||
\(901\) | −34.7855 | −1.15887 | ||||||||
\(902\) | 70.5855 | 2.35024 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 123.316 | 4.10144 | ||||||||
\(905\) | 16.5599 | 0.550469 | ||||||||
\(906\) | −58.0290 | −1.92789 | ||||||||
\(907\) | −5.41921 | −0.179942 | −0.0899709 | − | 0.995944i | \(-0.528677\pi\) | ||||
−0.0899709 | + | 0.995944i | \(0.528677\pi\) | |||||||
\(908\) | −116.105 | −3.85307 | ||||||||
\(909\) | 4.11882 | 0.136613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.226686 | 0.00751043 | 0.00375522 | − | 0.999993i | \(-0.498805\pi\) | ||||
0.00375522 | + | 0.999993i | \(0.498805\pi\) | |||||||
\(912\) | −43.2852 | −1.43332 | ||||||||
\(913\) | 31.8811 | 1.05511 | ||||||||
\(914\) | −77.9287 | −2.57765 | ||||||||
\(915\) | −9.41421 | −0.311224 | ||||||||
\(916\) | 27.3933 | 0.905099 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.6006 | 0.448886 | ||||||||
\(919\) | −8.10624 | −0.267400 | −0.133700 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133700 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(920\) | −42.6568 | −1.40635 | ||||||||
\(921\) | 7.31371 | 0.240995 | ||||||||
\(922\) | 105.491 | 3.47417 | ||||||||
\(923\) | 1.00353 | 0.0330316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.16804 | −0.0712848 | ||||||||
\(926\) | 6.55748 | 0.215492 | ||||||||
\(927\) | −8.16804 | −0.268274 | ||||||||
\(928\) | 15.7163 | 0.515912 | ||||||||
\(929\) | 2.29945 | 0.0754424 | 0.0377212 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377212 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(930\) | −3.45178 | −0.113188 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.07906 | −0.199126 | ||||||||
\(933\) | −11.2019 | −0.366735 | ||||||||
\(934\) | −54.4541 | −1.78179 | ||||||||
\(935\) | 21.9929 | 0.719246 | ||||||||
\(936\) | 35.3763 | 1.15631 | ||||||||
\(937\) | −16.1023 | −0.526041 | −0.263020 | − | 0.964790i | \(-0.584719\pi\) | ||||
−0.263020 | + | 0.964790i | \(0.584719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.4857 | 1.02750 | ||||||||
\(940\) | 36.0429 | 1.17559 | ||||||||
\(941\) | 13.5247 | 0.440893 | 0.220446 | − | 0.975399i | \(-0.429249\pi\) | ||||
0.220446 | + | 0.975399i | \(0.429249\pi\) | |||||||
\(942\) | −5.38883 | −0.175578 | ||||||||
\(943\) | 25.1904 | 0.820313 | ||||||||
\(944\) | −218.048 | −7.09687 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 111.400 | 3.62191 | ||||||||
\(947\) | 6.85381 | 0.222719 | 0.111359 | − | 0.993780i | \(-0.464480\pi\) | ||||
0.111359 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(948\) | 30.7784 | 0.999637 | ||||||||
\(949\) | −38.3898 | −1.24618 | ||||||||
\(950\) | 7.54469 | 0.244782 | ||||||||
\(951\) | −8.45048 | −0.274026 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.9483 | −1.45602 | −0.728009 | − | 0.685568i | \(-0.759554\pi\) | ||||
−0.728009 | + | 0.685568i | \(0.759554\pi\) | |||||||
\(954\) | 19.3298 | 0.625825 | ||||||||
\(955\) | 8.76272 | 0.283555 | ||||||||
\(956\) | 142.679 | 4.61457 | ||||||||
\(957\) | 2.93573 | 0.0948986 | ||||||||
\(958\) | −9.45584 | −0.305504 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −33.8812 | −1.09351 | ||||||||
\(961\) | −29.4235 | −0.949145 | ||||||||
\(962\) | −21.5584 | −0.695071 | ||||||||
\(963\) | −8.52951 | −0.274860 | ||||||||
\(964\) | 137.534 | 4.42967 | ||||||||
\(965\) | 26.4986 | 0.853020 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.4245 | 0.399546 | 0.199773 | − | 0.979842i | \(-0.435979\pi\) | ||||
0.199773 | + | 0.979842i | \(0.435979\pi\) | |||||||
\(968\) | 85.6992 | 2.75448 | ||||||||
\(969\) | 13.5773 | 0.436165 | ||||||||
\(970\) | 17.0661 | 0.547959 | ||||||||
\(971\) | 20.8158 | 0.668012 | 0.334006 | − | 0.942571i | \(-0.391599\pi\) | ||||
0.334006 | + | 0.942571i | \(0.391599\pi\) | |||||||
\(972\) | −5.55765 | −0.178262 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.5802 | −0.627390 | ||||||||
\(975\) | −3.61706 | −0.115839 | ||||||||
\(976\) | 148.482 | 4.75281 | ||||||||
\(977\) | 42.7418 | 1.36743 | 0.683716 | − | 0.729748i | \(-0.260363\pi\) | ||||
0.683716 | + | 0.729748i | \(0.260363\pi\) | |||||||
\(978\) | 22.4915 | 0.719200 | ||||||||
\(979\) | 3.68276 | 0.117702 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65685 | −0.116754 | ||||||||
\(982\) | −87.1184 | −2.78006 | ||||||||
\(983\) | 5.68982 | 0.181477 | 0.0907386 | − | 0.995875i | \(-0.471077\pi\) | ||||
0.0907386 | + | 0.995875i | \(0.471077\pi\) | |||||||
\(984\) | 56.4884 | 1.80078 | ||||||||
\(985\) | 4.11439 | 0.131095 | ||||||||
\(986\) | −8.98160 | −0.286033 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 55.1690 | 1.75516 | ||||||||
\(989\) | 39.7560 | 1.26417 | ||||||||
\(990\) | −12.2212 | −0.388414 | ||||||||
\(991\) | 59.1216 | 1.87806 | 0.939029 | − | 0.343838i | \(-0.111727\pi\) | ||||
0.939029 | + | 0.343838i | \(0.111727\pi\) | |||||||
\(992\) | 29.8815 | 0.948739 | ||||||||
\(993\) | −16.6533 | −0.528477 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.63538 | −0.242058 | ||||||||
\(996\) | 39.8571 | 1.26292 | ||||||||
\(997\) | −45.5294 | −1.44193 | −0.720965 | − | 0.692972i | \(-0.756301\pi\) | ||||
−0.720965 | + | 0.692972i | \(0.756301\pi\) | |||||||
\(998\) | −107.223 | −3.39409 | ||||||||
\(999\) | 2.16804 | 0.0685938 |
(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.n.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 2205.2.a.bf.1.1 | 4 | |||
5.4 | even | 2 | 3675.2.a.bl.1.1 | 4 | |||
7.2 | even | 3 | 735.2.i.n.361.1 | 8 | |||
7.3 | odd | 6 | 735.2.i.m.226.1 | 8 | |||
7.4 | even | 3 | 735.2.i.n.226.1 | 8 | |||
7.5 | odd | 6 | 735.2.i.m.361.1 | 8 | |||
7.6 | odd | 2 | 735.2.a.o.1.4 | yes | 4 | ||
21.20 | even | 2 | 2205.2.a.bg.1.1 | 4 | |||
35.34 | odd | 2 | 3675.2.a.bk.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.a.n.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
735.2.a.o.1.4 | yes | 4 | 7.6 | odd | 2 | ||
735.2.i.m.226.1 | 8 | 7.3 | odd | 6 | |||
735.2.i.m.361.1 | 8 | 7.5 | odd | 6 | |||
735.2.i.n.226.1 | 8 | 7.4 | even | 3 | |||
735.2.i.n.361.1 | 8 | 7.2 | even | 3 | |||
2205.2.a.bf.1.1 | 4 | 3.2 | odd | 2 | |||
2205.2.a.bg.1.1 | 4 | 21.20 | even | 2 | |||
3675.2.a.bk.1.1 | 4 | 35.34 | odd | 2 | |||
3675.2.a.bl.1.1 | 4 | 5.4 | even | 2 |