Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.258228.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 6x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.34628\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.34628 | 1.93198 | 0.965988 | − | 0.258587i | \(-0.0832570\pi\) | ||||
0.965988 | + | 0.258587i | \(0.0832570\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.34628 | 1.04929 | 0.524644 | − | 0.851322i | \(-0.324198\pi\) | ||||
0.524644 | + | 0.851322i | \(0.324198\pi\) | |||||||
\(6\) | 3.34628 | 1.36611 | ||||||||
\(7\) | −4.77567 | −1.80503 | −0.902517 | − | 0.430654i | \(-0.858283\pi\) | ||||
−0.902517 | + | 0.430654i | \(0.858283\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.19759 | 2.73253 | ||||||||
\(10\) | 2.34628 | 0.741959 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.34628 | 0.965988 | ||||||||
\(13\) | 1.57808 | 0.437681 | 0.218840 | − | 0.975761i | \(-0.429773\pi\) | ||||
0.218840 | + | 0.975761i | \(0.429773\pi\) | |||||||
\(14\) | −4.77567 | −1.27635 | ||||||||
\(15\) | 7.85131 | 2.02720 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.77567 | 0.915735 | 0.457867 | − | 0.889020i | \(-0.348613\pi\) | ||||
0.457867 | + | 0.889020i | \(0.348613\pi\) | |||||||
\(18\) | 8.19759 | 1.93219 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.34628 | 0.524644 | ||||||||
\(21\) | −15.9807 | −3.48728 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.57808 | −0.537567 | −0.268784 | − | 0.963201i | \(-0.586622\pi\) | ||||
−0.268784 | + | 0.963201i | \(0.586622\pi\) | |||||||
\(24\) | 3.34628 | 0.683057 | ||||||||
\(25\) | 0.505030 | 0.101006 | ||||||||
\(26\) | 1.57808 | 0.309487 | ||||||||
\(27\) | 17.3926 | 3.34721 | ||||||||
\(28\) | −4.77567 | −0.902517 | ||||||||
\(29\) | −4.85131 | −0.900866 | −0.450433 | − | 0.892810i | \(-0.648730\pi\) | ||||
−0.450433 | + | 0.892810i | \(0.648730\pi\) | |||||||
\(30\) | 7.85131 | 1.43345 | ||||||||
\(31\) | 6.69256 | 1.20202 | 0.601010 | − | 0.799242i | \(-0.294765\pi\) | ||||
0.601010 | + | 0.799242i | \(0.294765\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.77567 | 0.647522 | ||||||||
\(35\) | −11.2051 | −1.89400 | ||||||||
\(36\) | 8.19759 | 1.36627 | ||||||||
\(37\) | −10.8976 | −1.79156 | −0.895779 | − | 0.444499i | \(-0.853382\pi\) | ||||
−0.895779 | + | 0.444499i | \(0.853382\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 5.28070 | 0.845589 | ||||||||
\(40\) | 2.34628 | 0.370979 | ||||||||
\(41\) | 7.00747 | 1.09438 | 0.547192 | − | 0.837007i | \(-0.315697\pi\) | ||||
0.547192 | + | 0.837007i | \(0.315697\pi\) | |||||||
\(42\) | −15.9807 | −2.46588 | ||||||||
\(43\) | 11.8487 | 1.80691 | 0.903457 | − | 0.428680i | \(-0.141021\pi\) | ||||
0.903457 | + | 0.428680i | \(0.141021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.2338 | 2.86721 | ||||||||
\(46\) | −2.57808 | −0.380117 | ||||||||
\(47\) | −7.19759 | −1.04988 | −0.524938 | − | 0.851140i | \(-0.675912\pi\) | ||||
−0.524938 | + | 0.851140i | \(0.675912\pi\) | |||||||
\(48\) | 3.34628 | 0.482994 | ||||||||
\(49\) | 15.8070 | 2.25815 | ||||||||
\(50\) | 0.505030 | 0.0714221 | ||||||||
\(51\) | 12.6345 | 1.76918 | ||||||||
\(52\) | 1.57808 | 0.218840 | ||||||||
\(53\) | −1.14869 | −0.157785 | −0.0788923 | − | 0.996883i | \(-0.525138\pi\) | ||||
−0.0788923 | + | 0.996883i | \(0.525138\pi\) | |||||||
\(54\) | 17.3926 | 2.36683 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.77567 | −0.638176 | ||||||||
\(57\) | 3.34628 | 0.443226 | ||||||||
\(58\) | −4.85131 | −0.637008 | ||||||||
\(59\) | 4.92436 | 0.641097 | 0.320549 | − | 0.947232i | \(-0.396133\pi\) | ||||
0.320549 | + | 0.947232i | \(0.396133\pi\) | |||||||
\(60\) | 7.85131 | 1.01360 | ||||||||
\(61\) | −4.04890 | −0.518409 | −0.259204 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259204 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(62\) | 6.69256 | 0.849956 | ||||||||
\(63\) | −39.1490 | −4.93231 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.70262 | 0.459254 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4369 | 1.27507 | 0.637533 | − | 0.770423i | \(-0.279955\pi\) | ||||
0.637533 | + | 0.770423i | \(0.279955\pi\) | |||||||
\(68\) | 3.77567 | 0.457867 | ||||||||
\(69\) | −8.62698 | −1.03857 | ||||||||
\(70\) | −11.2051 | −1.33926 | ||||||||
\(71\) | −2.31491 | −0.274730 | −0.137365 | − | 0.990521i | \(-0.543863\pi\) | ||||
−0.137365 | + | 0.990521i | \(0.543863\pi\) | |||||||
\(72\) | 8.19759 | 0.966095 | ||||||||
\(73\) | −7.77567 | −0.910074 | −0.455037 | − | 0.890473i | \(-0.650374\pi\) | ||||
−0.455037 | + | 0.890473i | \(0.650374\pi\) | |||||||
\(74\) | −10.8976 | −1.26682 | ||||||||
\(75\) | 1.68997 | 0.195141 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.28070 | 0.597922 | ||||||||
\(79\) | 0.992527 | 0.111668 | 0.0558340 | − | 0.998440i | \(-0.482218\pi\) | ||||
0.0558340 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(80\) | 2.34628 | 0.262322 | ||||||||
\(81\) | 33.6077 | 3.73419 | ||||||||
\(82\) | 7.00747 | 0.773846 | ||||||||
\(83\) | −8.34628 | −0.916123 | −0.458062 | − | 0.888920i | \(-0.651456\pi\) | ||||
−0.458062 | + | 0.888920i | \(0.651456\pi\) | |||||||
\(84\) | −15.9807 | −1.74364 | ||||||||
\(85\) | 8.85878 | 0.960870 | ||||||||
\(86\) | 11.8487 | 1.27768 | ||||||||
\(87\) | −16.2338 | −1.74045 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7000 | −1.24020 | −0.620101 | − | 0.784522i | \(-0.712908\pi\) | ||||
−0.620101 | + | 0.784522i | \(0.712908\pi\) | |||||||
\(90\) | 19.2338 | 2.02743 | ||||||||
\(91\) | −7.53640 | −0.790029 | ||||||||
\(92\) | −2.57808 | −0.268784 | ||||||||
\(93\) | 22.3952 | 2.32227 | ||||||||
\(94\) | −7.19759 | −0.742375 | ||||||||
\(95\) | 2.34628 | 0.240723 | ||||||||
\(96\) | 3.34628 | 0.341528 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 15.8070 | 1.59675 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.505030 | 0.0505030 | ||||||||
\(101\) | 1.35634 | 0.134961 | 0.0674805 | − | 0.997721i | \(-0.478504\pi\) | ||||
0.0674805 | + | 0.997721i | \(0.478504\pi\) | |||||||
\(102\) | 12.6345 | 1.25100 | ||||||||
\(103\) | 2.29997 | 0.226622 | 0.113311 | − | 0.993560i | \(-0.463854\pi\) | ||||
0.113311 | + | 0.993560i | \(0.463854\pi\) | |||||||
\(104\) | 1.57808 | 0.154744 | ||||||||
\(105\) | −37.4953 | −3.65916 | ||||||||
\(106\) | −1.14869 | −0.111571 | ||||||||
\(107\) | −14.6583 | −1.41708 | −0.708538 | − | 0.705673i | \(-0.750645\pi\) | ||||
−0.708538 | + | 0.705673i | \(0.750645\pi\) | |||||||
\(108\) | 17.3926 | 1.67360 | ||||||||
\(109\) | −2.92436 | −0.280103 | −0.140052 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140052 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −36.4665 | −3.46125 | ||||||||
\(112\) | −4.77567 | −0.451259 | ||||||||
\(113\) | −1.00747 | −0.0947751 | −0.0473875 | − | 0.998877i | \(-0.515090\pi\) | ||||
−0.0473875 | + | 0.998877i | \(0.515090\pi\) | |||||||
\(114\) | 3.34628 | 0.313408 | ||||||||
\(115\) | −6.04890 | −0.564063 | ||||||||
\(116\) | −4.85131 | −0.450433 | ||||||||
\(117\) | 12.9365 | 1.19598 | ||||||||
\(118\) | 4.92436 | 0.453324 | ||||||||
\(119\) | −18.0314 | −1.65293 | ||||||||
\(120\) | 7.85131 | 0.716723 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.04890 | −0.366570 | ||||||||
\(123\) | 23.4490 | 2.11432 | ||||||||
\(124\) | 6.69256 | 0.601010 | ||||||||
\(125\) | −10.5465 | −0.943304 | ||||||||
\(126\) | −39.1490 | −3.48767 | ||||||||
\(127\) | −1.14122 | −0.101267 | −0.0506333 | − | 0.998717i | \(-0.516124\pi\) | ||||
−0.0506333 | + | 0.998717i | \(0.516124\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 39.6491 | 3.49091 | ||||||||
\(130\) | 3.70262 | 0.324741 | ||||||||
\(131\) | 18.7075 | 1.63448 | 0.817241 | − | 0.576296i | \(-0.195502\pi\) | ||||
0.817241 | + | 0.576296i | \(0.195502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.77567 | −0.414103 | ||||||||
\(134\) | 10.4369 | 0.901608 | ||||||||
\(135\) | 40.8079 | 3.51218 | ||||||||
\(136\) | 3.77567 | 0.323761 | ||||||||
\(137\) | 12.0731 | 1.03147 | 0.515735 | − | 0.856748i | \(-0.327519\pi\) | ||||
0.515735 | + | 0.856748i | \(0.327519\pi\) | |||||||
\(138\) | −8.62698 | −0.734377 | ||||||||
\(139\) | −21.7803 | −1.84738 | −0.923691 | − | 0.383139i | \(-0.874843\pi\) | ||||
−0.923691 | + | 0.383139i | \(0.874843\pi\) | |||||||
\(140\) | −11.2051 | −0.947001 | ||||||||
\(141\) | −24.0852 | −2.02834 | ||||||||
\(142\) | −2.31491 | −0.194263 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.19759 | 0.683133 | ||||||||
\(145\) | −11.3825 | −0.945268 | ||||||||
\(146\) | −7.77567 | −0.643519 | ||||||||
\(147\) | 52.8948 | 4.36269 | ||||||||
\(148\) | −10.8976 | −0.895779 | ||||||||
\(149\) | −6.38024 | −0.522689 | −0.261345 | − | 0.965246i | \(-0.584166\pi\) | ||||
−0.261345 | + | 0.965246i | \(0.584166\pi\) | |||||||
\(150\) | 1.68997 | 0.137986 | ||||||||
\(151\) | 2.54387 | 0.207017 | 0.103509 | − | 0.994629i | \(-0.466993\pi\) | ||||
0.103509 | + | 0.994629i | \(0.466993\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 30.9514 | 2.50227 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.7026 | 1.26126 | ||||||||
\(156\) | 5.28070 | 0.422795 | ||||||||
\(157\) | −5.60024 | −0.446948 | −0.223474 | − | 0.974710i | \(-0.571740\pi\) | ||||
−0.223474 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(158\) | 0.992527 | 0.0789612 | ||||||||
\(159\) | −3.84384 | −0.304836 | ||||||||
\(160\) | 2.34628 | 0.185490 | ||||||||
\(161\) | 12.3121 | 0.970327 | ||||||||
\(162\) | 33.6077 | 2.64047 | ||||||||
\(163\) | 7.25396 | 0.568174 | 0.284087 | − | 0.958798i | \(-0.408309\pi\) | ||||
0.284087 | + | 0.958798i | \(0.408309\pi\) | |||||||
\(164\) | 7.00747 | 0.547192 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.34628 | −0.647797 | ||||||||
\(167\) | 2.85878 | 0.221219 | 0.110610 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110610 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(168\) | −15.9807 | −1.23294 | ||||||||
\(169\) | −10.5097 | −0.808435 | ||||||||
\(170\) | 8.85878 | 0.679438 | ||||||||
\(171\) | 8.19759 | 0.626885 | ||||||||
\(172\) | 11.8487 | 0.903457 | ||||||||
\(173\) | 12.8663 | 0.978203 | 0.489102 | − | 0.872227i | \(-0.337325\pi\) | ||||
0.489102 | + | 0.872227i | \(0.337325\pi\) | |||||||
\(174\) | −16.2338 | −1.23068 | ||||||||
\(175\) | −2.41186 | −0.182319 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.4783 | 1.23858 | ||||||||
\(178\) | −11.7000 | −0.876955 | ||||||||
\(179\) | −24.9290 | −1.86328 | −0.931640 | − | 0.363382i | \(-0.881622\pi\) | ||||
−0.931640 | + | 0.363382i | \(0.881622\pi\) | |||||||
\(180\) | 19.2338 | 1.43361 | ||||||||
\(181\) | −17.7952 | −1.32271 | −0.661355 | − | 0.750073i | \(-0.730018\pi\) | ||||
−0.661355 | + | 0.750073i | \(0.730018\pi\) | |||||||
\(182\) | −7.53640 | −0.558635 | ||||||||
\(183\) | −13.5488 | −1.00155 | ||||||||
\(184\) | −2.57808 | −0.190059 | ||||||||
\(185\) | −25.5689 | −1.87986 | ||||||||
\(186\) | 22.3952 | 1.64209 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.19759 | −0.524938 | ||||||||
\(189\) | −83.0613 | −6.04182 | ||||||||
\(190\) | 2.34628 | 0.170217 | ||||||||
\(191\) | −4.47829 | −0.324038 | −0.162019 | − | 0.986788i | \(-0.551801\pi\) | ||||
−0.162019 | + | 0.986788i | \(0.551801\pi\) | |||||||
\(192\) | 3.34628 | 0.241497 | ||||||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 12.3900 | 0.887267 | ||||||||
\(196\) | 15.8070 | 1.12907 | ||||||||
\(197\) | −12.5614 | −0.894963 | −0.447481 | − | 0.894293i | \(-0.647679\pi\) | ||||
−0.447481 | + | 0.894293i | \(0.647679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.750666 | −0.0532133 | −0.0266066 | − | 0.999646i | \(-0.508470\pi\) | ||||
−0.0266066 | + | 0.999646i | \(0.508470\pi\) | |||||||
\(200\) | 0.505030 | 0.0357110 | ||||||||
\(201\) | 34.9247 | 2.46340 | ||||||||
\(202\) | 1.35634 | 0.0954318 | ||||||||
\(203\) | 23.1683 | 1.62609 | ||||||||
\(204\) | 12.6345 | 0.884589 | ||||||||
\(205\) | 16.4415 | 1.14832 | ||||||||
\(206\) | 2.29997 | 0.160246 | ||||||||
\(207\) | −21.1341 | −1.46892 | ||||||||
\(208\) | 1.57808 | 0.109420 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −37.4953 | −2.58742 | ||||||||
\(211\) | 4.66867 | 0.321404 | 0.160702 | − | 0.987003i | \(-0.448624\pi\) | ||||
0.160702 | + | 0.987003i | \(0.448624\pi\) | |||||||
\(212\) | −1.14869 | −0.0788923 | ||||||||
\(213\) | −7.74635 | −0.530771 | ||||||||
\(214\) | −14.6583 | −1.00202 | ||||||||
\(215\) | 27.8004 | 1.89597 | ||||||||
\(216\) | 17.3926 | 1.18342 | ||||||||
\(217\) | −31.9615 | −2.16969 | ||||||||
\(218\) | −2.92436 | −0.198063 | ||||||||
\(219\) | −26.0196 | −1.75824 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.95832 | 0.400800 | ||||||||
\(222\) | −36.4665 | −2.44747 | ||||||||
\(223\) | 23.8663 | 1.59820 | 0.799101 | − | 0.601196i | \(-0.205309\pi\) | ||||
0.799101 | + | 0.601196i | \(0.205309\pi\) | |||||||
\(224\) | −4.77567 | −0.319088 | ||||||||
\(225\) | 4.14003 | 0.276002 | ||||||||
\(226\) | −1.00747 | −0.0670161 | ||||||||
\(227\) | 13.5097 | 0.896668 | 0.448334 | − | 0.893866i | \(-0.352018\pi\) | ||||
0.448334 | + | 0.893866i | \(0.352018\pi\) | |||||||
\(228\) | 3.34628 | 0.221613 | ||||||||
\(229\) | −8.22896 | −0.543785 | −0.271892 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271892 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(230\) | −6.04890 | −0.398853 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.85131 | −0.318504 | ||||||||
\(233\) | −0.490085 | −0.0321065 | −0.0160533 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160533 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(234\) | 12.9365 | 0.845683 | ||||||||
\(235\) | −16.8876 | −1.10162 | ||||||||
\(236\) | 4.92436 | 0.320549 | ||||||||
\(237\) | 3.32127 | 0.215740 | ||||||||
\(238\) | −18.0314 | −1.16880 | ||||||||
\(239\) | 20.5364 | 1.32839 | 0.664195 | − | 0.747560i | \(-0.268775\pi\) | ||||
0.664195 | + | 0.747560i | \(0.268775\pi\) | |||||||
\(240\) | 7.85131 | 0.506800 | ||||||||
\(241\) | −19.4654 | −1.25388 | −0.626938 | − | 0.779069i | \(-0.715692\pi\) | ||||
−0.626938 | + | 0.779069i | \(0.715692\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 60.2831 | 3.86716 | ||||||||
\(244\) | −4.04890 | −0.259204 | ||||||||
\(245\) | 37.0877 | 2.36945 | ||||||||
\(246\) | 23.4490 | 1.49505 | ||||||||
\(247\) | 1.57808 | 0.100411 | ||||||||
\(248\) | 6.69256 | 0.424978 | ||||||||
\(249\) | −27.9290 | −1.76993 | ||||||||
\(250\) | −10.5465 | −0.667017 | ||||||||
\(251\) | −9.84872 | −0.621646 | −0.310823 | − | 0.950468i | \(-0.600605\pi\) | ||||
−0.310823 | + | 0.950468i | \(0.600605\pi\) | |||||||
\(252\) | −39.1490 | −2.46616 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.14122 | −0.0716063 | ||||||||
\(255\) | 29.6440 | 1.85638 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.2540 | 0.702003 | 0.351001 | − | 0.936375i | \(-0.385841\pi\) | ||||
0.351001 | + | 0.936375i | \(0.385841\pi\) | |||||||
\(258\) | 39.6491 | 2.46845 | ||||||||
\(259\) | 52.0435 | 3.23382 | ||||||||
\(260\) | 3.70262 | 0.229627 | ||||||||
\(261\) | −39.7691 | −2.46164 | ||||||||
\(262\) | 18.7075 | 1.15575 | ||||||||
\(263\) | 3.49008 | 0.215208 | 0.107604 | − | 0.994194i | \(-0.465682\pi\) | ||||
0.107604 | + | 0.994194i | \(0.465682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.69515 | −0.165562 | ||||||||
\(266\) | −4.77567 | −0.292815 | ||||||||
\(267\) | −39.1516 | −2.39604 | ||||||||
\(268\) | 10.4369 | 0.637533 | ||||||||
\(269\) | −20.1737 | −1.23001 | −0.615006 | − | 0.788522i | \(-0.710846\pi\) | ||||
−0.615006 | + | 0.788522i | \(0.710846\pi\) | |||||||
\(270\) | 40.8079 | 2.48349 | ||||||||
\(271\) | 0.239274 | 0.0145349 | 0.00726743 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726743 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(272\) | 3.77567 | 0.228934 | ||||||||
\(273\) | −25.2189 | −1.52632 | ||||||||
\(274\) | 12.0731 | 0.729360 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.62698 | −0.519283 | ||||||||
\(277\) | −13.1901 | −0.792517 | −0.396259 | − | 0.918139i | \(-0.629692\pi\) | ||||
−0.396259 | + | 0.918139i | \(0.629692\pi\) | |||||||
\(278\) | −21.7803 | −1.30630 | ||||||||
\(279\) | 54.8629 | 3.28455 | ||||||||
\(280\) | −11.2051 | −0.669631 | ||||||||
\(281\) | 6.54387 | 0.390375 | 0.195187 | − | 0.980766i | \(-0.437469\pi\) | ||||
0.195187 | + | 0.980766i | \(0.437469\pi\) | |||||||
\(282\) | −24.0852 | −1.43425 | ||||||||
\(283\) | 9.08774 | 0.540210 | 0.270105 | − | 0.962831i | \(-0.412942\pi\) | ||||
0.270105 | + | 0.962831i | \(0.412942\pi\) | |||||||
\(284\) | −2.31491 | −0.137365 | ||||||||
\(285\) | 7.85131 | 0.465071 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.4654 | −1.97540 | ||||||||
\(288\) | 8.19759 | 0.483048 | ||||||||
\(289\) | −2.74430 | −0.161430 | ||||||||
\(290\) | −11.3825 | −0.668405 | ||||||||
\(291\) | −33.4628 | −1.96162 | ||||||||
\(292\) | −7.77567 | −0.455037 | ||||||||
\(293\) | 20.2051 | 1.18039 | 0.590196 | − | 0.807260i | \(-0.299050\pi\) | ||||
0.590196 | + | 0.807260i | \(0.299050\pi\) | |||||||
\(294\) | 52.8948 | 3.08489 | ||||||||
\(295\) | 11.5539 | 0.672696 | ||||||||
\(296\) | −10.8976 | −0.633411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.38024 | −0.369597 | ||||||||
\(299\) | −4.06842 | −0.235283 | ||||||||
\(300\) | 1.68997 | 0.0975706 | ||||||||
\(301\) | −56.5856 | −3.26154 | ||||||||
\(302\) | 2.54387 | 0.146383 | ||||||||
\(303\) | 4.53870 | 0.260741 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −9.49985 | −0.543960 | ||||||||
\(306\) | 30.9514 | 1.76937 | ||||||||
\(307\) | −20.2514 | −1.15581 | −0.577904 | − | 0.816105i | \(-0.696129\pi\) | ||||
−0.577904 | + | 0.816105i | \(0.696129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.69633 | 0.437829 | ||||||||
\(310\) | 15.7026 | 0.891849 | ||||||||
\(311\) | 29.3897 | 1.66654 | 0.833270 | − | 0.552866i | \(-0.186466\pi\) | ||||
0.833270 | + | 0.552866i | \(0.186466\pi\) | |||||||
\(312\) | 5.28070 | 0.298961 | ||||||||
\(313\) | −0.229213 | −0.0129559 | −0.00647796 | − | 0.999979i | \(-0.502062\pi\) | ||||
−0.00647796 | + | 0.999979i | \(0.502062\pi\) | |||||||
\(314\) | −5.60024 | −0.316040 | ||||||||
\(315\) | −91.8545 | −5.17542 | ||||||||
\(316\) | 0.992527 | 0.0558340 | ||||||||
\(317\) | −19.6908 | −1.10595 | −0.552974 | − | 0.833199i | \(-0.686507\pi\) | ||||
−0.552974 | + | 0.833199i | \(0.686507\pi\) | |||||||
\(318\) | −3.84384 | −0.215552 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.34628 | 0.131161 | ||||||||
\(321\) | −49.0509 | −2.73776 | ||||||||
\(322\) | 12.3121 | 0.686125 | ||||||||
\(323\) | 3.77567 | 0.210084 | ||||||||
\(324\) | 33.6077 | 1.86710 | ||||||||
\(325\) | 0.796979 | 0.0442084 | ||||||||
\(326\) | 7.25396 | 0.401760 | ||||||||
\(327\) | −9.78573 | −0.541152 | ||||||||
\(328\) | 7.00747 | 0.386923 | ||||||||
\(329\) | 34.3733 | 1.89506 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9707 | −0.932793 | −0.466396 | − | 0.884576i | \(-0.654448\pi\) | ||||
−0.466396 | + | 0.884576i | \(0.654448\pi\) | |||||||
\(332\) | −8.34628 | −0.458062 | ||||||||
\(333\) | −89.3343 | −4.89549 | ||||||||
\(334\) | 2.85878 | 0.156426 | ||||||||
\(335\) | 24.4878 | 1.33791 | ||||||||
\(336\) | −15.9807 | −0.871821 | ||||||||
\(337\) | −8.01236 | −0.436461 | −0.218230 | − | 0.975897i | \(-0.570028\pi\) | ||||
−0.218230 | + | 0.975897i | \(0.570028\pi\) | |||||||
\(338\) | −10.5097 | −0.571650 | ||||||||
\(339\) | −3.37129 | −0.183103 | ||||||||
\(340\) | 8.85878 | 0.480435 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.19759 | 0.443275 | ||||||||
\(343\) | −42.0595 | −2.27100 | ||||||||
\(344\) | 11.8487 | 0.638840 | ||||||||
\(345\) | −20.2413 | −1.08976 | ||||||||
\(346\) | 12.8663 | 0.691694 | ||||||||
\(347\) | −27.7613 | −1.49030 | −0.745152 | − | 0.666895i | \(-0.767623\pi\) | ||||
−0.745152 | + | 0.666895i | \(0.767623\pi\) | |||||||
\(348\) | −16.2338 | −0.870225 | ||||||||
\(349\) | −11.4886 | −0.614971 | −0.307486 | − | 0.951553i | \(-0.599488\pi\) | ||||
−0.307486 | + | 0.951553i | \(0.599488\pi\) | |||||||
\(350\) | −2.41186 | −0.128919 | ||||||||
\(351\) | 27.4469 | 1.46501 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.2853 | −1.39903 | −0.699514 | − | 0.714619i | \(-0.746600\pi\) | ||||
−0.699514 | + | 0.714619i | \(0.746600\pi\) | |||||||
\(354\) | 16.4783 | 0.875811 | ||||||||
\(355\) | −5.43143 | −0.288271 | ||||||||
\(356\) | −11.7000 | −0.620101 | ||||||||
\(357\) | −60.3380 | −3.19343 | ||||||||
\(358\) | −24.9290 | −1.31754 | ||||||||
\(359\) | 18.0731 | 0.953859 | 0.476930 | − | 0.878942i | \(-0.341750\pi\) | ||||
0.476930 | + | 0.878942i | \(0.341750\pi\) | |||||||
\(360\) | 19.2338 | 1.01371 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.7952 | −0.935297 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.53640 | −0.395015 | ||||||||
\(365\) | −18.2439 | −0.954930 | ||||||||
\(366\) | −13.5488 | −0.708205 | ||||||||
\(367\) | 33.9051 | 1.76983 | 0.884916 | − | 0.465751i | \(-0.154216\pi\) | ||||
0.884916 | + | 0.465751i | \(0.154216\pi\) | |||||||
\(368\) | −2.57808 | −0.134392 | ||||||||
\(369\) | 57.4444 | 2.99044 | ||||||||
\(370\) | −25.5689 | −1.32926 | ||||||||
\(371\) | 5.48576 | 0.284807 | ||||||||
\(372\) | 22.3952 | 1.16114 | ||||||||
\(373\) | 10.9342 | 0.566150 | 0.283075 | − | 0.959098i | \(-0.408646\pi\) | ||||
0.283075 | + | 0.959098i | \(0.408646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −35.2914 | −1.82244 | ||||||||
\(376\) | −7.19759 | −0.371187 | ||||||||
\(377\) | −7.65576 | −0.394292 | ||||||||
\(378\) | −83.0613 | −4.27221 | ||||||||
\(379\) | −24.8395 | −1.27592 | −0.637960 | − | 0.770069i | \(-0.720222\pi\) | ||||
−0.637960 | + | 0.770069i | \(0.720222\pi\) | |||||||
\(380\) | 2.34628 | 0.120362 | ||||||||
\(381\) | −3.81883 | −0.195645 | ||||||||
\(382\) | −4.47829 | −0.229129 | ||||||||
\(383\) | −2.82372 | −0.144285 | −0.0721426 | − | 0.997394i | \(-0.522984\pi\) | ||||
−0.0721426 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(384\) | 3.34628 | 0.170764 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 97.1310 | 4.93744 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −7.03884 | −0.356883 | −0.178442 | − | 0.983950i | \(-0.557106\pi\) | ||||
−0.178442 | + | 0.983950i | \(0.557106\pi\) | |||||||
\(390\) | 12.3900 | 0.627392 | ||||||||
\(391\) | −9.73399 | −0.492269 | ||||||||
\(392\) | 15.8070 | 0.798376 | ||||||||
\(393\) | 62.6006 | 3.15778 | ||||||||
\(394\) | −12.5614 | −0.632834 | ||||||||
\(395\) | 2.32875 | 0.117172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.67761 | 0.234763 | 0.117381 | − | 0.993087i | \(-0.462550\pi\) | ||||
0.117381 | + | 0.993087i | \(0.462550\pi\) | |||||||
\(398\) | −0.750666 | −0.0376275 | ||||||||
\(399\) | −15.9807 | −0.800037 | ||||||||
\(400\) | 0.505030 | 0.0252515 | ||||||||
\(401\) | 14.5588 | 0.727033 | 0.363516 | − | 0.931588i | \(-0.381576\pi\) | ||||
0.363516 | + | 0.931588i | \(0.381576\pi\) | |||||||
\(402\) | 34.9247 | 1.74188 | ||||||||
\(403\) | 10.5614 | 0.526101 | ||||||||
\(404\) | 1.35634 | 0.0674805 | ||||||||
\(405\) | 78.8531 | 3.91824 | ||||||||
\(406\) | 23.1683 | 1.14982 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12.6345 | 0.625499 | ||||||||
\(409\) | −9.71757 | −0.480503 | −0.240251 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240251 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(410\) | 16.4415 | 0.811987 | ||||||||
\(411\) | 40.3998 | 1.99278 | ||||||||
\(412\) | 2.29997 | 0.113311 | ||||||||
\(413\) | −23.5171 | −1.15720 | ||||||||
\(414\) | −21.1341 | −1.03868 | ||||||||
\(415\) | −19.5827 | −0.961277 | ||||||||
\(416\) | 1.57808 | 0.0773718 | ||||||||
\(417\) | −72.8830 | −3.56910 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.13227 | 0.299581 | 0.149790 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149790 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(420\) | −37.4953 | −1.82958 | ||||||||
\(421\) | −3.79957 | −0.185180 | −0.0925898 | − | 0.995704i | \(-0.529515\pi\) | ||||
−0.0925898 | + | 0.995704i | \(0.529515\pi\) | |||||||
\(422\) | 4.66867 | 0.227267 | ||||||||
\(423\) | −59.0029 | −2.86882 | ||||||||
\(424\) | −1.14869 | −0.0557853 | ||||||||
\(425\) | 1.90683 | 0.0924948 | ||||||||
\(426\) | −7.74635 | −0.375312 | ||||||||
\(427\) | 19.3362 | 0.935745 | ||||||||
\(428\) | −14.6583 | −0.708538 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.8004 | 1.34066 | ||||||||
\(431\) | 8.69515 | 0.418831 | 0.209415 | − | 0.977827i | \(-0.432844\pi\) | ||||
0.209415 | + | 0.977827i | \(0.432844\pi\) | |||||||
\(432\) | 17.3926 | 0.836802 | ||||||||
\(433\) | 3.30744 | 0.158945 | 0.0794727 | − | 0.996837i | \(-0.474676\pi\) | ||||
0.0794727 | + | 0.996837i | \(0.474676\pi\) | |||||||
\(434\) | −31.9615 | −1.53420 | ||||||||
\(435\) | −38.0891 | −1.82623 | ||||||||
\(436\) | −2.92436 | −0.140052 | ||||||||
\(437\) | −2.57808 | −0.123326 | ||||||||
\(438\) | −26.0196 | −1.24326 | ||||||||
\(439\) | 4.54128 | 0.216744 | 0.108372 | − | 0.994110i | \(-0.465436\pi\) | ||||
0.108372 | + | 0.994110i | \(0.465436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 129.580 | 6.17046 | ||||||||
\(442\) | 5.95832 | 0.283408 | ||||||||
\(443\) | 17.8637 | 0.848728 | 0.424364 | − | 0.905492i | \(-0.360498\pi\) | ||||
0.424364 | + | 0.905492i | \(0.360498\pi\) | |||||||
\(444\) | −36.4665 | −1.73062 | ||||||||
\(445\) | −27.4516 | −1.30133 | ||||||||
\(446\) | 23.8663 | 1.13010 | ||||||||
\(447\) | −21.3501 | −1.00982 | ||||||||
\(448\) | −4.77567 | −0.225629 | ||||||||
\(449\) | −21.8487 | −1.03110 | −0.515552 | − | 0.856858i | \(-0.672413\pi\) | ||||
−0.515552 | + | 0.856858i | \(0.672413\pi\) | |||||||
\(450\) | 4.14003 | 0.195163 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.00747 | −0.0473875 | ||||||||
\(453\) | 8.51250 | 0.399952 | ||||||||
\(454\) | 13.5097 | 0.634040 | ||||||||
\(455\) | −17.6825 | −0.828968 | ||||||||
\(456\) | 3.34628 | 0.156704 | ||||||||
\(457\) | −5.73424 | −0.268237 | −0.134118 | − | 0.990965i | \(-0.542820\pi\) | ||||
−0.134118 | + | 0.990965i | \(0.542820\pi\) | |||||||
\(458\) | −8.22896 | −0.384514 | ||||||||
\(459\) | 65.6687 | 3.06515 | ||||||||
\(460\) | −6.04890 | −0.282031 | ||||||||
\(461\) | 12.5752 | 0.585687 | 0.292844 | − | 0.956160i | \(-0.405398\pi\) | ||||
0.292844 | + | 0.956160i | \(0.405398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2853 | 0.896265 | 0.448133 | − | 0.893967i | \(-0.352089\pi\) | ||||
0.448133 | + | 0.893967i | \(0.352089\pi\) | |||||||
\(464\) | −4.85131 | −0.225216 | ||||||||
\(465\) | 52.5454 | 2.43673 | ||||||||
\(466\) | −0.490085 | −0.0227027 | ||||||||
\(467\) | 15.8004 | 0.731156 | 0.365578 | − | 0.930781i | \(-0.380871\pi\) | ||||
0.365578 | + | 0.930781i | \(0.380871\pi\) | |||||||
\(468\) | 12.9365 | 0.597988 | ||||||||
\(469\) | −49.8430 | −2.30154 | ||||||||
\(470\) | −16.8876 | −0.778965 | ||||||||
\(471\) | −18.7400 | −0.863493 | ||||||||
\(472\) | 4.92436 | 0.226662 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.32127 | 0.152551 | ||||||||
\(475\) | 0.505030 | 0.0231724 | ||||||||
\(476\) | −18.0314 | −0.826466 | ||||||||
\(477\) | −9.41649 | −0.431151 | ||||||||
\(478\) | 20.5364 | 0.939313 | ||||||||
\(479\) | −17.0149 | −0.777433 | −0.388716 | − | 0.921357i | \(-0.627081\pi\) | ||||
−0.388716 | + | 0.921357i | \(0.627081\pi\) | |||||||
\(480\) | 7.85131 | 0.358362 | ||||||||
\(481\) | −17.1973 | −0.784131 | ||||||||
\(482\) | −19.4654 | −0.886624 | ||||||||
\(483\) | 41.1996 | 1.87465 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.4628 | −1.06539 | ||||||||
\(486\) | 60.2831 | 2.73449 | ||||||||
\(487\) | 12.8387 | 0.581775 | 0.290888 | − | 0.956757i | \(-0.406049\pi\) | ||||
0.290888 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(488\) | −4.04890 | −0.183285 | ||||||||
\(489\) | 24.2738 | 1.09770 | ||||||||
\(490\) | 37.0877 | 1.67545 | ||||||||
\(491\) | −21.1654 | −0.955182 | −0.477591 | − | 0.878582i | \(-0.658490\pi\) | ||||
−0.477591 | + | 0.878582i | \(0.658490\pi\) | |||||||
\(492\) | 23.4490 | 1.05716 | ||||||||
\(493\) | −18.3170 | −0.824954 | ||||||||
\(494\) | 1.57808 | 0.0710012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.69256 | 0.300505 | ||||||||
\(497\) | 11.0553 | 0.495896 | ||||||||
\(498\) | −27.9290 | −1.25153 | ||||||||
\(499\) | −5.35634 | −0.239783 | −0.119891 | − | 0.992787i | \(-0.538255\pi\) | ||||
−0.119891 | + | 0.992787i | \(0.538255\pi\) | |||||||
\(500\) | −10.5465 | −0.471652 | ||||||||
\(501\) | 9.56629 | 0.427390 | ||||||||
\(502\) | −9.84872 | −0.439570 | ||||||||
\(503\) | −13.8634 | −0.618139 | −0.309070 | − | 0.951039i | \(-0.600018\pi\) | ||||
−0.309070 | + | 0.951039i | \(0.600018\pi\) | |||||||
\(504\) | −39.1490 | −1.74384 | ||||||||
\(505\) | 3.18235 | 0.141613 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.1683 | −1.56188 | ||||||||
\(508\) | −1.14122 | −0.0506333 | ||||||||
\(509\) | 28.9902 | 1.28497 | 0.642485 | − | 0.766298i | \(-0.277903\pi\) | ||||
0.642485 | + | 0.766298i | \(0.277903\pi\) | |||||||
\(510\) | 29.6440 | 1.31266 | ||||||||
\(511\) | 37.1341 | 1.64271 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.3926 | 0.767902 | ||||||||
\(514\) | 11.2540 | 0.496391 | ||||||||
\(515\) | 5.39637 | 0.237792 | ||||||||
\(516\) | 39.6491 | 1.74546 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 52.0435 | 2.28666 | ||||||||
\(519\) | 43.0541 | 1.88987 | ||||||||
\(520\) | 3.70262 | 0.162371 | ||||||||
\(521\) | 24.3417 | 1.06643 | 0.533215 | − | 0.845980i | \(-0.320984\pi\) | ||||
0.533215 | + | 0.845980i | \(0.320984\pi\) | |||||||
\(522\) | −39.7691 | −1.74064 | ||||||||
\(523\) | 37.2347 | 1.62816 | 0.814080 | − | 0.580753i | \(-0.197242\pi\) | ||||
0.814080 | + | 0.580753i | \(0.197242\pi\) | |||||||
\(524\) | 18.7075 | 0.817241 | ||||||||
\(525\) | −8.07075 | −0.352237 | ||||||||
\(526\) | 3.49008 | 0.152175 | ||||||||
\(527\) | 25.2689 | 1.10073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3535 | −0.711022 | ||||||||
\(530\) | −2.69515 | −0.117070 | ||||||||
\(531\) | 40.3679 | 1.75182 | ||||||||
\(532\) | −4.77567 | −0.207052 | ||||||||
\(533\) | 11.0584 | 0.478991 | ||||||||
\(534\) | −39.1516 | −1.69425 | ||||||||
\(535\) | −34.3926 | −1.48692 | ||||||||
\(536\) | 10.4369 | 0.450804 | ||||||||
\(537\) | −83.4194 | −3.59981 | ||||||||
\(538\) | −20.1737 | −0.869750 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 40.8079 | 1.75609 | ||||||||
\(541\) | −4.31750 | −0.185624 | −0.0928119 | − | 0.995684i | \(-0.529586\pi\) | ||||
−0.0928119 | + | 0.995684i | \(0.529586\pi\) | |||||||
\(542\) | 0.239274 | 0.0102777 | ||||||||
\(543\) | −59.5479 | −2.55544 | ||||||||
\(544\) | 3.77567 | 0.161881 | ||||||||
\(545\) | −6.86137 | −0.293909 | ||||||||
\(546\) | −25.2189 | −1.07927 | ||||||||
\(547\) | −25.0104 | −1.06937 | −0.534683 | − | 0.845053i | \(-0.679569\pi\) | ||||
−0.534683 | + | 0.845053i | \(0.679569\pi\) | |||||||
\(548\) | 12.0731 | 0.515735 | ||||||||
\(549\) | −33.1912 | −1.41657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.85131 | −0.206673 | ||||||||
\(552\) | −8.62698 | −0.367189 | ||||||||
\(553\) | −4.73998 | −0.201565 | ||||||||
\(554\) | −13.1901 | −0.560394 | ||||||||
\(555\) | −85.5606 | −3.63185 | ||||||||
\(556\) | −21.7803 | −0.923691 | ||||||||
\(557\) | −31.3667 | −1.32905 | −0.664525 | − | 0.747266i | \(-0.731366\pi\) | ||||
−0.664525 | + | 0.747266i | \(0.731366\pi\) | |||||||
\(558\) | 54.8629 | 2.32253 | ||||||||
\(559\) | 18.6982 | 0.790852 | ||||||||
\(560\) | −11.2051 | −0.473500 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.54387 | 0.276037 | ||||||||
\(563\) | 11.4924 | 0.484346 | 0.242173 | − | 0.970233i | \(-0.422140\pi\) | ||||
0.242173 | + | 0.970233i | \(0.422140\pi\) | |||||||
\(564\) | −24.0852 | −1.01417 | ||||||||
\(565\) | −2.36381 | −0.0994464 | ||||||||
\(566\) | 9.08774 | 0.381986 | ||||||||
\(567\) | −160.499 | −6.74034 | ||||||||
\(568\) | −2.31491 | −0.0971316 | ||||||||
\(569\) | −18.5614 | −0.778135 | −0.389067 | − | 0.921209i | \(-0.627203\pi\) | ||||
−0.389067 | + | 0.921209i | \(0.627203\pi\) | |||||||
\(570\) | 7.85131 | 0.328855 | ||||||||
\(571\) | −36.2099 | −1.51534 | −0.757670 | − | 0.652638i | \(-0.773662\pi\) | ||||
−0.757670 | + | 0.652638i | \(0.773662\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.9856 | −0.626033 | ||||||||
\(574\) | −33.4654 | −1.39682 | ||||||||
\(575\) | −1.30201 | −0.0542975 | ||||||||
\(576\) | 8.19759 | 0.341566 | ||||||||
\(577\) | 29.5560 | 1.23043 | 0.615216 | − | 0.788359i | \(-0.289069\pi\) | ||||
0.615216 | + | 0.788359i | \(0.289069\pi\) | |||||||
\(578\) | −2.74430 | −0.114148 | ||||||||
\(579\) | 26.7702 | 1.11253 | ||||||||
\(580\) | −11.3825 | −0.472634 | ||||||||
\(581\) | 39.8591 | 1.65363 | ||||||||
\(582\) | −33.4628 | −1.38708 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.77567 | −0.321760 | ||||||||
\(585\) | 30.3526 | 1.25492 | ||||||||
\(586\) | 20.2051 | 0.834663 | ||||||||
\(587\) | −33.4340 | −1.37997 | −0.689985 | − | 0.723824i | \(-0.742383\pi\) | ||||
−0.689985 | + | 0.723824i | \(0.742383\pi\) | |||||||
\(588\) | 52.8948 | 2.18134 | ||||||||
\(589\) | 6.69256 | 0.275762 | ||||||||
\(590\) | 11.5539 | 0.475668 | ||||||||
\(591\) | −42.0340 | −1.72905 | ||||||||
\(592\) | −10.8976 | −0.447890 | ||||||||
\(593\) | 15.2753 | 0.627280 | 0.313640 | − | 0.949542i | \(-0.398451\pi\) | ||||
0.313640 | + | 0.949542i | \(0.398451\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.3066 | −1.73440 | ||||||||
\(596\) | −6.38024 | −0.261345 | ||||||||
\(597\) | −2.51194 | −0.102807 | ||||||||
\(598\) | −4.06842 | −0.166370 | ||||||||
\(599\) | 13.3316 | 0.544716 | 0.272358 | − | 0.962196i | \(-0.412196\pi\) | ||||
0.272358 | + | 0.962196i | \(0.412196\pi\) | |||||||
\(600\) | 1.68997 | 0.0689928 | ||||||||
\(601\) | 48.4729 | 1.97725 | 0.988625 | − | 0.150404i | \(-0.0480574\pi\) | ||||
0.988625 | + | 0.150404i | \(0.0480574\pi\) | |||||||
\(602\) | −56.5856 | −2.30626 | ||||||||
\(603\) | 85.5571 | 3.48416 | ||||||||
\(604\) | 2.54387 | 0.103509 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.53870 | 0.184372 | ||||||||
\(607\) | 43.4176 | 1.76227 | 0.881133 | − | 0.472869i | \(-0.156781\pi\) | ||||
0.881133 | + | 0.472869i | \(0.156781\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 77.5275 | 3.14157 | ||||||||
\(610\) | −9.49985 | −0.384638 | ||||||||
\(611\) | −11.3584 | −0.459511 | ||||||||
\(612\) | 30.9514 | 1.25114 | ||||||||
\(613\) | −44.8876 | −1.81299 | −0.906496 | − | 0.422215i | \(-0.861253\pi\) | ||||
−0.906496 | + | 0.422215i | \(0.861253\pi\) | |||||||
\(614\) | −20.2514 | −0.817279 | ||||||||
\(615\) | 55.0178 | 2.21853 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2275 | −0.693552 | −0.346776 | − | 0.937948i | \(-0.612724\pi\) | ||||
−0.346776 | + | 0.937948i | \(0.612724\pi\) | |||||||
\(618\) | 7.69633 | 0.309592 | ||||||||
\(619\) | 17.8004 | 0.715459 | 0.357730 | − | 0.933825i | \(-0.383551\pi\) | ||||
0.357730 | + | 0.933825i | \(0.383551\pi\) | |||||||
\(620\) | 15.7026 | 0.630632 | ||||||||
\(621\) | −44.8395 | −1.79935 | ||||||||
\(622\) | 29.3897 | 1.17842 | ||||||||
\(623\) | 55.8755 | 2.23861 | ||||||||
\(624\) | 5.28070 | 0.211397 | ||||||||
\(625\) | −27.2701 | −1.09080 | ||||||||
\(626\) | −0.229213 | −0.00916121 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.60024 | −0.223474 | ||||||||
\(629\) | −41.1458 | −1.64059 | ||||||||
\(630\) | −91.8545 | −3.65957 | ||||||||
\(631\) | 14.4202 | 0.574059 | 0.287029 | − | 0.957922i | \(-0.407332\pi\) | ||||
0.287029 | + | 0.957922i | \(0.407332\pi\) | |||||||
\(632\) | 0.992527 | 0.0394806 | ||||||||
\(633\) | 15.6227 | 0.620945 | ||||||||
\(634\) | −19.6908 | −0.782023 | ||||||||
\(635\) | −2.67761 | −0.106258 | ||||||||
\(636\) | −3.84384 | −0.152418 | ||||||||
\(637\) | 24.9448 | 0.988349 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.9767 | −0.750707 | ||||||||
\(640\) | 2.34628 | 0.0927449 | ||||||||
\(641\) | −29.1386 | −1.15091 | −0.575453 | − | 0.817835i | \(-0.695174\pi\) | ||||
−0.575453 | + | 0.817835i | \(0.695174\pi\) | |||||||
\(642\) | −49.0509 | −1.93589 | ||||||||
\(643\) | 37.4979 | 1.47877 | 0.739386 | − | 0.673282i | \(-0.235116\pi\) | ||||
0.739386 | + | 0.673282i | \(0.235116\pi\) | |||||||
\(644\) | 12.3121 | 0.485163 | ||||||||
\(645\) | 93.0280 | 3.66297 | ||||||||
\(646\) | 3.77567 | 0.148552 | ||||||||
\(647\) | 40.4294 | 1.58945 | 0.794723 | − | 0.606973i | \(-0.207616\pi\) | ||||
0.794723 | + | 0.606973i | \(0.207616\pi\) | |||||||
\(648\) | 33.6077 | 1.32024 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.796979 | 0.0312601 | ||||||||
\(651\) | −106.952 | −4.19178 | ||||||||
\(652\) | 7.25396 | 0.284087 | ||||||||
\(653\) | 33.8102 | 1.32310 | 0.661548 | − | 0.749903i | \(-0.269900\pi\) | ||||
0.661548 | + | 0.749903i | \(0.269900\pi\) | |||||||
\(654\) | −9.78573 | −0.382652 | ||||||||
\(655\) | 43.8930 | 1.71504 | ||||||||
\(656\) | 7.00747 | 0.273596 | ||||||||
\(657\) | −63.7418 | −2.48680 | ||||||||
\(658\) | 34.3733 | 1.34001 | ||||||||
\(659\) | −25.2586 | −0.983935 | −0.491968 | − | 0.870614i | \(-0.663722\pi\) | ||||
−0.491968 | + | 0.870614i | \(0.663722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.42965 | −0.133398 | −0.0666989 | − | 0.997773i | \(-0.521247\pi\) | ||||
−0.0666989 | + | 0.997773i | \(0.521247\pi\) | |||||||
\(662\) | −16.9707 | −0.659584 | ||||||||
\(663\) | 19.9382 | 0.774335 | ||||||||
\(664\) | −8.34628 | −0.323898 | ||||||||
\(665\) | −11.2051 | −0.434514 | ||||||||
\(666\) | −89.3343 | −3.46163 | ||||||||
\(667\) | 12.5071 | 0.484276 | ||||||||
\(668\) | 2.85878 | 0.110610 | ||||||||
\(669\) | 79.8632 | 3.08769 | ||||||||
\(670\) | 24.4878 | 0.946047 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −15.9807 | −0.616470 | ||||||||
\(673\) | 21.4855 | 0.828206 | 0.414103 | − | 0.910230i | \(-0.364095\pi\) | ||||
0.414103 | + | 0.910230i | \(0.364095\pi\) | |||||||
\(674\) | −8.01236 | −0.308624 | ||||||||
\(675\) | 8.78378 | 0.338088 | ||||||||
\(676\) | −10.5097 | −0.404218 | ||||||||
\(677\) | 33.2825 | 1.27915 | 0.639575 | − | 0.768729i | \(-0.279110\pi\) | ||||
0.639575 | + | 0.768729i | \(0.279110\pi\) | |||||||
\(678\) | −3.37129 | −0.129473 | ||||||||
\(679\) | 47.7567 | 1.83273 | ||||||||
\(680\) | 8.85878 | 0.339719 | ||||||||
\(681\) | 45.2071 | 1.73234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.1176 | −1.11416 | −0.557078 | − | 0.830460i | \(-0.688077\pi\) | ||||
−0.557078 | + | 0.830460i | \(0.688077\pi\) | |||||||
\(684\) | 8.19759 | 0.313443 | ||||||||
\(685\) | 28.3268 | 1.08231 | ||||||||
\(686\) | −42.0595 | −1.60584 | ||||||||
\(687\) | −27.5364 | −1.05058 | ||||||||
\(688\) | 11.8487 | 0.451728 | ||||||||
\(689\) | −1.81273 | −0.0690593 | ||||||||
\(690\) | −20.2413 | −0.770574 | ||||||||
\(691\) | −43.2143 | −1.64395 | −0.821975 | − | 0.569523i | \(-0.807128\pi\) | ||||
−0.821975 | + | 0.569523i | \(0.807128\pi\) | |||||||
\(692\) | 12.8663 | 0.489102 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.7613 | −1.05380 | ||||||||
\(695\) | −51.1027 | −1.93844 | ||||||||
\(696\) | −16.2338 | −0.615342 | ||||||||
\(697\) | 26.4579 | 1.00217 | ||||||||
\(698\) | −11.4886 | −0.434850 | ||||||||
\(699\) | −1.63996 | −0.0620290 | ||||||||
\(700\) | −2.41186 | −0.0911597 | ||||||||
\(701\) | 30.8680 | 1.16587 | 0.582935 | − | 0.812519i | \(-0.301904\pi\) | ||||
0.582935 | + | 0.812519i | \(0.301904\pi\) | |||||||
\(702\) | 27.4469 | 1.03592 | ||||||||
\(703\) | −10.8976 | −0.411012 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −56.5105 | −2.12831 | ||||||||
\(706\) | −26.2853 | −0.989261 | ||||||||
\(707\) | −6.47744 | −0.243609 | ||||||||
\(708\) | 16.4783 | 0.619292 | ||||||||
\(709\) | 8.14610 | 0.305933 | 0.152967 | − | 0.988231i | \(-0.451117\pi\) | ||||
0.152967 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(710\) | −5.43143 | −0.203838 | ||||||||
\(711\) | 8.13633 | 0.305136 | ||||||||
\(712\) | −11.7000 | −0.438477 | ||||||||
\(713\) | −17.2540 | −0.646166 | ||||||||
\(714\) | −60.3380 | −2.25809 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.9290 | −0.931640 | ||||||||
\(717\) | 68.7205 | 2.56642 | ||||||||
\(718\) | 18.0731 | 0.674480 | ||||||||
\(719\) | 43.5545 | 1.62431 | 0.812154 | − | 0.583443i | \(-0.198295\pi\) | ||||
0.812154 | + | 0.583443i | \(0.198295\pi\) | |||||||
\(720\) | 19.2338 | 0.716803 | ||||||||
\(721\) | −10.9839 | −0.409061 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −65.1366 | −2.42246 | ||||||||
\(724\) | −17.7952 | −0.661355 | ||||||||
\(725\) | −2.45006 | −0.0909929 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.4415 | −1.31445 | −0.657226 | − | 0.753693i | \(-0.728270\pi\) | ||||
−0.657226 | + | 0.753693i | \(0.728270\pi\) | |||||||
\(728\) | −7.53640 | −0.279317 | ||||||||
\(729\) | 100.901 | 3.73707 | ||||||||
\(730\) | −18.2439 | −0.675237 | ||||||||
\(731\) | 44.7369 | 1.65465 | ||||||||
\(732\) | −13.5488 | −0.500776 | ||||||||
\(733\) | −4.60970 | −0.170263 | −0.0851317 | − | 0.996370i | \(-0.527131\pi\) | ||||
−0.0851317 | + | 0.996370i | \(0.527131\pi\) | |||||||
\(734\) | 33.9051 | 1.25146 | ||||||||
\(735\) | 124.106 | 4.57772 | ||||||||
\(736\) | −2.57808 | −0.0950293 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 57.4444 | 2.11456 | ||||||||
\(739\) | 19.1423 | 0.704162 | 0.352081 | − | 0.935970i | \(-0.385474\pi\) | ||||
0.352081 | + | 0.935970i | \(0.385474\pi\) | |||||||
\(740\) | −25.5689 | −0.939931 | ||||||||
\(741\) | 5.28070 | 0.193991 | ||||||||
\(742\) | 5.48576 | 0.201389 | ||||||||
\(743\) | −41.0970 | −1.50770 | −0.753851 | − | 0.657045i | \(-0.771806\pi\) | ||||
−0.753851 | + | 0.657045i | \(0.771806\pi\) | |||||||
\(744\) | 22.3952 | 0.821047 | ||||||||
\(745\) | −14.9698 | −0.548452 | ||||||||
\(746\) | 10.9342 | 0.400328 | ||||||||
\(747\) | −68.4194 | −2.50333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 70.0035 | 2.55787 | ||||||||
\(750\) | −35.2914 | −1.28866 | ||||||||
\(751\) | −38.8882 | −1.41905 | −0.709525 | − | 0.704681i | \(-0.751090\pi\) | ||||
−0.709525 | + | 0.704681i | \(0.751090\pi\) | |||||||
\(752\) | −7.19759 | −0.262469 | ||||||||
\(753\) | −32.9566 | −1.20100 | ||||||||
\(754\) | −7.65576 | −0.278806 | ||||||||
\(755\) | 5.96863 | 0.217221 | ||||||||
\(756\) | −83.0613 | −3.02091 | ||||||||
\(757\) | 25.2051 | 0.916094 | 0.458047 | − | 0.888928i | \(-0.348549\pi\) | ||||
0.458047 | + | 0.888928i | \(0.348549\pi\) | |||||||
\(758\) | −24.8395 | −0.902212 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.34628 | 0.0851085 | ||||||||
\(761\) | 17.9247 | 0.649769 | 0.324884 | − | 0.945754i | \(-0.394675\pi\) | ||||
0.324884 | + | 0.945754i | \(0.394675\pi\) | |||||||
\(762\) | −3.81883 | −0.138342 | ||||||||
\(763\) | 13.9658 | 0.505596 | ||||||||
\(764\) | −4.47829 | −0.162019 | ||||||||
\(765\) | 72.6207 | 2.62561 | ||||||||
\(766\) | −2.82372 | −0.102025 | ||||||||
\(767\) | 7.77104 | 0.280596 | ||||||||
\(768\) | 3.34628 | 0.120748 | ||||||||
\(769\) | −17.4101 | −0.627825 | −0.313913 | − | 0.949452i | \(-0.601640\pi\) | ||||
−0.313913 | + | 0.949452i | \(0.601640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.6589 | 1.35625 | ||||||||
\(772\) | 8.00000 | 0.287926 | ||||||||
\(773\) | 42.5071 | 1.52887 | 0.764437 | − | 0.644699i | \(-0.223017\pi\) | ||||
0.764437 | + | 0.644699i | \(0.223017\pi\) | |||||||
\(774\) | 97.1310 | 3.49130 | ||||||||
\(775\) | 3.37994 | 0.121411 | ||||||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 174.152 | 6.24767 | ||||||||
\(778\) | −7.03884 | −0.252355 | ||||||||
\(779\) | 7.00747 | 0.251069 | ||||||||
\(780\) | 12.3900 | 0.443633 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.73399 | −0.348087 | ||||||||
\(783\) | −84.3769 | −3.01538 | ||||||||
\(784\) | 15.8070 | 0.564537 | ||||||||
\(785\) | −13.1397 | −0.468977 | ||||||||
\(786\) | 62.6006 | 2.23289 | ||||||||
\(787\) | 0.289907 | 0.0103341 | 0.00516703 | − | 0.999987i | \(-0.498355\pi\) | ||||
0.00516703 | + | 0.999987i | \(0.498355\pi\) | |||||||
\(788\) | −12.5614 | −0.447481 | ||||||||
\(789\) | 11.6788 | 0.415776 | ||||||||
\(790\) | 2.32875 | 0.0828531 | ||||||||
\(791\) | 4.81136 | 0.171072 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.38949 | −0.226898 | ||||||||
\(794\) | 4.67761 | 0.166002 | ||||||||
\(795\) | −9.01872 | −0.319861 | ||||||||
\(796\) | −0.750666 | −0.0266066 | ||||||||
\(797\) | 20.2557 | 0.717494 | 0.358747 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358747 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(798\) | −15.9807 | −0.565712 | ||||||||
\(799\) | −27.1757 | −0.961408 | ||||||||
\(800\) | 0.505030 | 0.0178555 | ||||||||
\(801\) | −95.9121 | −3.38889 | ||||||||
\(802\) | 14.5588 | 0.514090 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 34.9247 | 1.23170 | ||||||||
\(805\) | 28.8876 | 1.01815 | ||||||||
\(806\) | 10.5614 | 0.372010 | ||||||||
\(807\) | −67.5068 | −2.37635 | ||||||||
\(808\) | 1.35634 | 0.0477159 | ||||||||
\(809\) | 11.8902 | 0.418035 | 0.209018 | − | 0.977912i | \(-0.432973\pi\) | ||||
0.209018 | + | 0.977912i | \(0.432973\pi\) | |||||||
\(810\) | 78.8531 | 2.77062 | ||||||||
\(811\) | −37.3725 | −1.31232 | −0.656162 | − | 0.754620i | \(-0.727821\pi\) | ||||
−0.656162 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(812\) | 23.1683 | 0.813047 | ||||||||
\(813\) | 0.800677 | 0.0280810 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.0198 | 0.596179 | ||||||||
\(816\) | 12.6345 | 0.442294 | ||||||||
\(817\) | 11.8487 | 0.414534 | ||||||||
\(818\) | −9.71757 | −0.339767 | ||||||||
\(819\) | −61.7803 | −2.15878 | ||||||||
\(820\) | 16.4415 | 0.574162 | ||||||||
\(821\) | 15.7165 | 0.548508 | 0.274254 | − | 0.961657i | \(-0.411569\pi\) | ||||
0.274254 | + | 0.961657i | \(0.411569\pi\) | |||||||
\(822\) | 40.3998 | 1.40911 | ||||||||
\(823\) | 41.3066 | 1.43986 | 0.719929 | − | 0.694047i | \(-0.244174\pi\) | ||||
0.719929 | + | 0.694047i | \(0.244174\pi\) | |||||||
\(824\) | 2.29997 | 0.0801232 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.5171 | −0.818266 | ||||||||
\(827\) | 15.7406 | 0.547354 | 0.273677 | − | 0.961822i | \(-0.411760\pi\) | ||||
0.273677 | + | 0.961822i | \(0.411760\pi\) | |||||||
\(828\) | −21.1341 | −0.734459 | ||||||||
\(829\) | −0.255696 | −0.00888069 | −0.00444034 | − | 0.999990i | \(-0.501413\pi\) | ||||
−0.00444034 | + | 0.999990i | \(0.501413\pi\) | |||||||
\(830\) | −19.5827 | −0.679726 | ||||||||
\(831\) | −44.1378 | −1.53112 | ||||||||
\(832\) | 1.57808 | 0.0547101 | ||||||||
\(833\) | 59.6822 | 2.06787 | ||||||||
\(834\) | −72.8830 | −2.52373 | ||||||||
\(835\) | 6.70751 | 0.232123 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 116.401 | 4.02341 | ||||||||
\(838\) | 6.13227 | 0.211836 | ||||||||
\(839\) | −14.2764 | −0.492875 | −0.246438 | − | 0.969159i | \(-0.579260\pi\) | ||||
−0.246438 | + | 0.969159i | \(0.579260\pi\) | |||||||
\(840\) | −37.4953 | −1.29371 | ||||||||
\(841\) | −5.46479 | −0.188441 | ||||||||
\(842\) | −3.79957 | −0.130942 | ||||||||
\(843\) | 21.8976 | 0.754194 | ||||||||
\(844\) | 4.66867 | 0.160702 | ||||||||
\(845\) | −24.6586 | −0.848282 | ||||||||
\(846\) | −59.0029 | −2.02856 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.14869 | −0.0394462 | ||||||||
\(849\) | 30.4101 | 1.04367 | ||||||||
\(850\) | 1.90683 | 0.0654037 | ||||||||
\(851\) | 28.0950 | 0.963083 | ||||||||
\(852\) | −7.74635 | −0.265385 | ||||||||
\(853\) | −31.1027 | −1.06494 | −0.532468 | − | 0.846450i | \(-0.678735\pi\) | ||||
−0.532468 | + | 0.846450i | \(0.678735\pi\) | |||||||
\(854\) | 19.3362 | 0.661672 | ||||||||
\(855\) | 19.2338 | 0.657784 | ||||||||
\(856\) | −14.6583 | −0.501012 | ||||||||
\(857\) | 16.9715 | 0.579736 | 0.289868 | − | 0.957067i | \(-0.406389\pi\) | ||||
0.289868 | + | 0.957067i | \(0.406389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.5169 | 1.34830 | 0.674149 | − | 0.738595i | \(-0.264510\pi\) | ||||
0.674149 | + | 0.738595i | \(0.264510\pi\) | |||||||
\(860\) | 27.8004 | 0.947987 | ||||||||
\(861\) | −111.985 | −3.81642 | ||||||||
\(862\) | 8.69515 | 0.296158 | ||||||||
\(863\) | 55.4294 | 1.88684 | 0.943420 | − | 0.331600i | \(-0.107588\pi\) | ||||
0.943420 | + | 0.331600i | \(0.107588\pi\) | |||||||
\(864\) | 17.3926 | 0.591708 | ||||||||
\(865\) | 30.1878 | 1.02642 | ||||||||
\(866\) | 3.30744 | 0.112391 | ||||||||
\(867\) | −9.18321 | −0.311878 | ||||||||
\(868\) | −31.9615 | −1.08484 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −38.0891 | −1.29134 | ||||||||
\(871\) | 16.4702 | 0.558072 | ||||||||
\(872\) | −2.92436 | −0.0990314 | ||||||||
\(873\) | −81.9759 | −2.77446 | ||||||||
\(874\) | −2.57808 | −0.0872049 | ||||||||
\(875\) | 50.3664 | 1.70270 | ||||||||
\(876\) | −26.0196 | −0.879120 | ||||||||
\(877\) | −23.3069 | −0.787018 | −0.393509 | − | 0.919321i | \(-0.628739\pi\) | ||||
−0.393509 | + | 0.919321i | \(0.628739\pi\) | |||||||
\(878\) | 4.54128 | 0.153261 | ||||||||
\(879\) | 67.6118 | 2.28049 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.8830 | 1.81536 | 0.907682 | − | 0.419659i | \(-0.137850\pi\) | ||||
0.907682 | + | 0.419659i | \(0.137850\pi\) | |||||||
\(882\) | 129.580 | 4.36317 | ||||||||
\(883\) | 46.0638 | 1.55017 | 0.775086 | − | 0.631856i | \(-0.217707\pi\) | ||||
0.775086 | + | 0.631856i | \(0.217707\pi\) | |||||||
\(884\) | 5.95832 | 0.200400 | ||||||||
\(885\) | 38.6627 | 1.29963 | ||||||||
\(886\) | 17.8637 | 0.600142 | ||||||||
\(887\) | 14.9246 | 0.501120 | 0.250560 | − | 0.968101i | \(-0.419385\pi\) | ||||
0.250560 | + | 0.968101i | \(0.419385\pi\) | |||||||
\(888\) | −36.4665 | −1.22374 | ||||||||
\(889\) | 5.45008 | 0.182790 | ||||||||
\(890\) | −27.4516 | −0.920178 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.8663 | 0.799101 | ||||||||
\(893\) | −7.19759 | −0.240858 | ||||||||
\(894\) | −21.3501 | −0.714053 | ||||||||
\(895\) | −58.4904 | −1.95512 | ||||||||
\(896\) | −4.77567 | −0.159544 | ||||||||
\(897\) | −13.6141 | −0.454561 | ||||||||
\(898\) | −21.8487 | −0.729101 | ||||||||
\(899\) | −32.4677 | −1.08286 | ||||||||
\(900\) | 4.14003 | 0.138001 | ||||||||
\(901\) | −4.33708 | −0.144489 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −189.351 | −6.30122 | ||||||||
\(904\) | −1.00747 | −0.0335080 | ||||||||
\(905\) | −41.7526 | −1.38790 | ||||||||
\(906\) | 8.51250 | 0.282809 | ||||||||
\(907\) | −14.6419 | −0.486177 | −0.243089 | − | 0.970004i | \(-0.578161\pi\) | ||||
−0.243089 | + | 0.970004i | \(0.578161\pi\) | |||||||
\(908\) | 13.5097 | 0.448334 | ||||||||
\(909\) | 11.1187 | 0.368785 | ||||||||
\(910\) | −17.6825 | −0.586169 | ||||||||
\(911\) | −5.41760 | −0.179493 | −0.0897465 | − | 0.995965i | \(-0.528606\pi\) | ||||
−0.0897465 | + | 0.995965i | \(0.528606\pi\) | |||||||
\(912\) | 3.34628 | 0.110806 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.73424 | −0.189672 | ||||||||
\(915\) | −31.7892 | −1.05092 | ||||||||
\(916\) | −8.22896 | −0.271892 | ||||||||
\(917\) | −89.3409 | −2.95030 | ||||||||
\(918\) | 65.6687 | 2.16739 | ||||||||
\(919\) | 33.1536 | 1.09364 | 0.546819 | − | 0.837251i | \(-0.315839\pi\) | ||||
0.546819 | + | 0.837251i | \(0.315839\pi\) | |||||||
\(920\) | −6.04890 | −0.199426 | ||||||||
\(921\) | −67.7668 | −2.23299 | ||||||||
\(922\) | 12.5752 | 0.414143 | ||||||||
\(923\) | −3.65312 | −0.120244 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.50363 | −0.180958 | ||||||||
\(926\) | 19.2853 | 0.633755 | ||||||||
\(927\) | 18.8542 | 0.619253 | ||||||||
\(928\) | −4.85131 | −0.159252 | ||||||||
\(929\) | −0.322385 | −0.0105771 | −0.00528856 | − | 0.999986i | \(-0.501683\pi\) | ||||
−0.00528856 | + | 0.999986i | \(0.501683\pi\) | |||||||
\(930\) | 52.5454 | 1.72303 | ||||||||
\(931\) | 15.8070 | 0.518055 | ||||||||
\(932\) | −0.490085 | −0.0160533 | ||||||||
\(933\) | 98.3463 | 3.21971 | ||||||||
\(934\) | 15.8004 | 0.517006 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.9365 | 0.422842 | ||||||||
\(937\) | −2.64545 | −0.0864229 | −0.0432115 | − | 0.999066i | \(-0.513759\pi\) | ||||
−0.0432115 | + | 0.999066i | \(0.513759\pi\) | |||||||
\(938\) | −49.8430 | −1.62743 | ||||||||
\(939\) | −0.767013 | −0.0250305 | ||||||||
\(940\) | −16.8876 | −0.550812 | ||||||||
\(941\) | −11.1772 | −0.364367 | −0.182183 | − | 0.983265i | \(-0.558316\pi\) | ||||
−0.182183 | + | 0.983265i | \(0.558316\pi\) | |||||||
\(942\) | −18.7400 | −0.610582 | ||||||||
\(943\) | −18.0658 | −0.588304 | ||||||||
\(944\) | 4.92436 | 0.160274 | ||||||||
\(945\) | −194.885 | −6.33961 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.6693 | 0.379200 | 0.189600 | − | 0.981861i | \(-0.439281\pi\) | ||||
0.189600 | + | 0.981861i | \(0.439281\pi\) | |||||||
\(948\) | 3.32127 | 0.107870 | ||||||||
\(949\) | −12.2706 | −0.398322 | ||||||||
\(950\) | 0.505030 | 0.0163853 | ||||||||
\(951\) | −65.8910 | −2.13666 | ||||||||
\(952\) | −18.0314 | −0.584400 | ||||||||
\(953\) | 42.6900 | 1.38286 | 0.691432 | − | 0.722442i | \(-0.256980\pi\) | ||||
0.691432 | + | 0.722442i | \(0.256980\pi\) | |||||||
\(954\) | −9.41649 | −0.304870 | ||||||||
\(955\) | −10.5073 | −0.340009 | ||||||||
\(956\) | 20.5364 | 0.664195 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.0149 | −0.549728 | ||||||||
\(959\) | −57.6569 | −1.86184 | ||||||||
\(960\) | 7.85131 | 0.253400 | ||||||||
\(961\) | 13.7904 | 0.444850 | ||||||||
\(962\) | −17.1973 | −0.554464 | ||||||||
\(963\) | −120.163 | −3.87220 | ||||||||
\(964\) | −19.4654 | −0.626938 | ||||||||
\(965\) | 18.7702 | 0.604235 | ||||||||
\(966\) | 41.1996 | 1.32558 | ||||||||
\(967\) | −15.6705 | −0.503928 | −0.251964 | − | 0.967737i | \(-0.581076\pi\) | ||||
−0.251964 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.6345 | 0.405877 | ||||||||
\(970\) | −23.4628 | −0.753345 | ||||||||
\(971\) | −36.0369 | −1.15648 | −0.578239 | − | 0.815868i | \(-0.696260\pi\) | ||||
−0.578239 | + | 0.815868i | \(0.696260\pi\) | |||||||
\(972\) | 60.2831 | 1.93358 | ||||||||
\(973\) | 104.016 | 3.33459 | ||||||||
\(974\) | 12.8387 | 0.411377 | ||||||||
\(975\) | 2.66691 | 0.0854096 | ||||||||
\(976\) | −4.04890 | −0.129602 | ||||||||
\(977\) | −6.06273 | −0.193964 | −0.0969820 | − | 0.995286i | \(-0.530919\pi\) | ||||
−0.0969820 | + | 0.995286i | \(0.530919\pi\) | |||||||
\(978\) | 24.2738 | 0.776190 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 37.0877 | 1.18472 | ||||||||
\(981\) | −23.9727 | −0.765390 | ||||||||
\(982\) | −21.1654 | −0.675416 | ||||||||
\(983\) | −8.49608 | −0.270983 | −0.135491 | − | 0.990779i | \(-0.543261\pi\) | ||||
−0.135491 | + | 0.990779i | \(0.543261\pi\) | |||||||
\(984\) | 23.4490 | 0.747526 | ||||||||
\(985\) | −29.4726 | −0.939074 | ||||||||
\(986\) | −18.3170 | −0.583331 | ||||||||
\(987\) | 115.023 | 3.66122 | ||||||||
\(988\) | 1.57808 | 0.0502055 | ||||||||
\(989\) | −30.5470 | −0.971337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2663 | −0.802611 | −0.401306 | − | 0.915944i | \(-0.631443\pi\) | ||||
−0.401306 | + | 0.915944i | \(0.631443\pi\) | |||||||
\(992\) | 6.69256 | 0.212489 | ||||||||
\(993\) | −56.7886 | −1.80213 | ||||||||
\(994\) | 11.0553 | 0.350652 | ||||||||
\(995\) | −1.76127 | −0.0558361 | ||||||||
\(996\) | −27.9290 | −0.884964 | ||||||||
\(997\) | −45.5853 | −1.44370 | −0.721850 | − | 0.692049i | \(-0.756708\pi\) | ||||
−0.721850 | + | 0.692049i | \(0.756708\pi\) | |||||||
\(998\) | −5.35634 | −0.169552 | ||||||||
\(999\) | −189.538 | −5.99671 |
(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 | 4598.2.a.bv.1.4 | yes | 4 | |
11.10 | odd | 2 | 4598.2.a.bs.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bs.1.4 | ✓ | 4 | 11.10 | odd | 2 | ||
4598.2.a.bv.1.4 | yes | 4 | 1.1 | even | 1 | trivial |