Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.30998405.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 9x^{4} + 8x^{3} + 16x^{2} - 13x + 2 \) |
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 | \(0.516938\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.407480 | 0.182231 | 0.0911154 | − | 0.995840i | \(-0.470957\pi\) | ||||
0.0911154 | + | 0.995840i | \(0.470957\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.39127 | −1.28178 | −0.640890 | − | 0.767632i | \(-0.721435\pi\) | ||||
−0.640890 | + | 0.767632i | \(0.721435\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.407480 | −0.128857 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.190339 | −0.0527907 | −0.0263953 | − | 0.999652i | \(-0.508403\pi\) | ||||
−0.0263953 | + | 0.999652i | \(0.508403\pi\) | |||||||
\(14\) | 3.39127 | 0.906356 | ||||||||
\(15\) | −0.407480 | −0.105211 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.90821 | 0.947880 | 0.473940 | − | 0.880557i | \(-0.342831\pi\) | ||||
0.473940 | + | 0.880557i | \(0.342831\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.21451 | −0.966874 | −0.483437 | − | 0.875379i | \(-0.660612\pi\) | ||||
−0.483437 | + | 0.875379i | \(0.660612\pi\) | |||||||
\(20\) | 0.407480 | 0.0911154 | ||||||||
\(21\) | 3.39127 | 0.740036 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.09855 | 0.854607 | 0.427303 | − | 0.904108i | \(-0.359464\pi\) | ||||
0.427303 | + | 0.904108i | \(0.359464\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.83396 | −0.966792 | ||||||||
\(26\) | 0.190339 | 0.0373286 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.39127 | −0.640890 | ||||||||
\(29\) | 0.0390710 | 0.00725529 | 0.00362765 | − | 0.999993i | \(-0.498845\pi\) | ||||
0.00362765 | + | 0.999993i | \(0.498845\pi\) | |||||||
\(30\) | 0.407480 | 0.0743954 | ||||||||
\(31\) | −2.91932 | −0.524326 | −0.262163 | − | 0.965024i | \(-0.584436\pi\) | ||||
−0.262163 | + | 0.965024i | \(0.584436\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −3.90821 | −0.670253 | ||||||||
\(35\) | −1.38188 | −0.233580 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.51463 | 1.07100 | 0.535500 | − | 0.844536i | \(-0.320123\pi\) | ||||
0.535500 | + | 0.844536i | \(0.320123\pi\) | |||||||
\(38\) | 4.21451 | 0.683683 | ||||||||
\(39\) | 0.190339 | 0.0304787 | ||||||||
\(40\) | −0.407480 | −0.0644283 | ||||||||
\(41\) | 8.27278 | 1.29199 | 0.645996 | − | 0.763341i | \(-0.276442\pi\) | ||||
0.645996 | + | 0.763341i | \(0.276442\pi\) | |||||||
\(42\) | −3.39127 | −0.523285 | ||||||||
\(43\) | 2.67207 | 0.407487 | 0.203743 | − | 0.979024i | \(-0.434689\pi\) | ||||
0.203743 | + | 0.979024i | \(0.434689\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.407480 | 0.0607436 | ||||||||
\(46\) | −4.09855 | −0.604298 | ||||||||
\(47\) | −4.59990 | −0.670964 | −0.335482 | − | 0.942047i | \(-0.608899\pi\) | ||||
−0.335482 | + | 0.942047i | \(0.608899\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.50073 | 0.642961 | ||||||||
\(50\) | 4.83396 | 0.683625 | ||||||||
\(51\) | −3.90821 | −0.547259 | ||||||||
\(52\) | −0.190339 | −0.0263953 | ||||||||
\(53\) | −2.73918 | −0.376255 | −0.188127 | − | 0.982145i | \(-0.560242\pi\) | ||||
−0.188127 | + | 0.982145i | \(0.560242\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.407480 | 0.0549447 | ||||||||
\(56\) | 3.39127 | 0.453178 | ||||||||
\(57\) | 4.21451 | 0.558225 | ||||||||
\(58\) | −0.0390710 | −0.00513027 | ||||||||
\(59\) | −13.4343 | −1.74900 | −0.874501 | − | 0.485024i | \(-0.838811\pi\) | ||||
−0.874501 | + | 0.485024i | \(0.838811\pi\) | |||||||
\(60\) | −0.407480 | −0.0526055 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 2.91932 | 0.370754 | ||||||||
\(63\) | −3.39127 | −0.427260 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0775596 | −0.00962008 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 8.45198 | 1.03257 | 0.516287 | − | 0.856416i | \(-0.327314\pi\) | ||||
0.516287 | + | 0.856416i | \(0.327314\pi\) | |||||||
\(68\) | 3.90821 | 0.473940 | ||||||||
\(69\) | −4.09855 | −0.493407 | ||||||||
\(70\) | 1.38188 | 0.165166 | ||||||||
\(71\) | 1.56991 | 0.186314 | 0.0931571 | − | 0.995651i | \(-0.470304\pi\) | ||||
0.0931571 | + | 0.995651i | \(0.470304\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 11.6664 | 1.36545 | 0.682724 | − | 0.730677i | \(-0.260795\pi\) | ||||
0.682724 | + | 0.730677i | \(0.260795\pi\) | |||||||
\(74\) | −6.51463 | −0.757311 | ||||||||
\(75\) | 4.83396 | 0.558178 | ||||||||
\(76\) | −4.21451 | −0.483437 | ||||||||
\(77\) | −3.39127 | −0.386471 | ||||||||
\(78\) | −0.190339 | −0.0215517 | ||||||||
\(79\) | 9.38091 | 1.05543 | 0.527717 | − | 0.849420i | \(-0.323048\pi\) | ||||
0.527717 | + | 0.849420i | \(0.323048\pi\) | |||||||
\(80\) | 0.407480 | 0.0455577 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.27278 | −0.913576 | ||||||||
\(83\) | −11.5050 | −1.26284 | −0.631421 | − | 0.775441i | \(-0.717528\pi\) | ||||
−0.631421 | + | 0.775441i | \(0.717528\pi\) | |||||||
\(84\) | 3.39127 | 0.370018 | ||||||||
\(85\) | 1.59252 | 0.172733 | ||||||||
\(86\) | −2.67207 | −0.288137 | ||||||||
\(87\) | −0.0390710 | −0.00418885 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −3.26264 | −0.345839 | −0.172920 | − | 0.984936i | \(-0.555320\pi\) | ||||
−0.172920 | + | 0.984936i | \(0.555320\pi\) | |||||||
\(90\) | −0.407480 | −0.0429522 | ||||||||
\(91\) | 0.645493 | 0.0676660 | ||||||||
\(92\) | 4.09855 | 0.427303 | ||||||||
\(93\) | 2.91932 | 0.302720 | ||||||||
\(94\) | 4.59990 | 0.474443 | ||||||||
\(95\) | −1.71733 | −0.176194 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.20116 | −0.629633 | −0.314816 | − | 0.949153i | \(-0.601943\pi\) | ||||
−0.314816 | + | 0.949153i | \(0.601943\pi\) | |||||||
\(98\) | −4.50073 | −0.454642 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −4.83396 | −0.483396 | ||||||||
\(101\) | −5.66027 | −0.563218 | −0.281609 | − | 0.959529i | \(-0.590868\pi\) | ||||
−0.281609 | + | 0.959529i | \(0.590868\pi\) | |||||||
\(102\) | 3.90821 | 0.386971 | ||||||||
\(103\) | −11.6542 | −1.14833 | −0.574163 | − | 0.818741i | \(-0.694673\pi\) | ||||
−0.574163 | + | 0.818741i | \(0.694673\pi\) | |||||||
\(104\) | 0.190339 | 0.0186643 | ||||||||
\(105\) | 1.38188 | 0.134857 | ||||||||
\(106\) | 2.73918 | 0.266052 | ||||||||
\(107\) | 15.0109 | 1.45116 | 0.725578 | − | 0.688140i | \(-0.241572\pi\) | ||||
0.725578 | + | 0.688140i | \(0.241572\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 9.88750 | 0.947050 | 0.473525 | − | 0.880780i | \(-0.342981\pi\) | ||||
0.473525 | + | 0.880780i | \(0.342981\pi\) | |||||||
\(110\) | −0.407480 | −0.0388517 | ||||||||
\(111\) | −6.51463 | −0.618342 | ||||||||
\(112\) | −3.39127 | −0.320445 | ||||||||
\(113\) | −17.4789 | −1.64428 | −0.822139 | − | 0.569287i | \(-0.807219\pi\) | ||||
−0.822139 | + | 0.569287i | \(0.807219\pi\) | |||||||
\(114\) | −4.21451 | −0.394725 | ||||||||
\(115\) | 1.67008 | 0.155736 | ||||||||
\(116\) | 0.0390710 | 0.00362765 | ||||||||
\(117\) | −0.190339 | −0.0175969 | ||||||||
\(118\) | 13.4343 | 1.23673 | ||||||||
\(119\) | −13.2538 | −1.21497 | ||||||||
\(120\) | 0.407480 | 0.0371977 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −8.27278 | −0.745931 | ||||||||
\(124\) | −2.91932 | −0.262163 | ||||||||
\(125\) | −4.00715 | −0.358410 | ||||||||
\(126\) | 3.39127 | 0.302119 | ||||||||
\(127\) | 13.0092 | 1.15438 | 0.577190 | − | 0.816610i | \(-0.304149\pi\) | ||||
0.577190 | + | 0.816610i | \(0.304149\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.67207 | −0.235263 | ||||||||
\(130\) | 0.0775596 | 0.00680243 | ||||||||
\(131\) | −21.9677 | −1.91933 | −0.959665 | − | 0.281145i | \(-0.909286\pi\) | ||||
−0.959665 | + | 0.281145i | \(0.909286\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 14.2925 | 1.23932 | ||||||||
\(134\) | −8.45198 | −0.730140 | ||||||||
\(135\) | −0.407480 | −0.0350703 | ||||||||
\(136\) | −3.90821 | −0.335126 | ||||||||
\(137\) | 9.51622 | 0.813025 | 0.406513 | − | 0.913645i | \(-0.366745\pi\) | ||||
0.406513 | + | 0.913645i | \(0.366745\pi\) | |||||||
\(138\) | 4.09855 | 0.348892 | ||||||||
\(139\) | −8.06367 | −0.683952 | −0.341976 | − | 0.939709i | \(-0.611096\pi\) | ||||
−0.341976 | + | 0.939709i | \(0.611096\pi\) | |||||||
\(140\) | −1.38188 | −0.116790 | ||||||||
\(141\) | 4.59990 | 0.387381 | ||||||||
\(142\) | −1.56991 | −0.131744 | ||||||||
\(143\) | −0.190339 | −0.0159170 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.0159206 | 0.00132214 | ||||||||
\(146\) | −11.6664 | −0.965517 | ||||||||
\(147\) | −4.50073 | −0.371214 | ||||||||
\(148\) | 6.51463 | 0.535500 | ||||||||
\(149\) | −1.61425 | −0.132245 | −0.0661223 | − | 0.997812i | \(-0.521063\pi\) | ||||
−0.0661223 | + | 0.997812i | \(0.521063\pi\) | |||||||
\(150\) | −4.83396 | −0.394691 | ||||||||
\(151\) | −11.6620 | −0.949040 | −0.474520 | − | 0.880245i | \(-0.657378\pi\) | ||||
−0.474520 | + | 0.880245i | \(0.657378\pi\) | |||||||
\(152\) | 4.21451 | 0.341842 | ||||||||
\(153\) | 3.90821 | 0.315960 | ||||||||
\(154\) | 3.39127 | 0.273277 | ||||||||
\(155\) | −1.18957 | −0.0955483 | ||||||||
\(156\) | 0.190339 | 0.0152394 | ||||||||
\(157\) | −15.5480 | −1.24087 | −0.620433 | − | 0.784259i | \(-0.713043\pi\) | ||||
−0.620433 | + | 0.784259i | \(0.713043\pi\) | |||||||
\(158\) | −9.38091 | −0.746305 | ||||||||
\(159\) | 2.73918 | 0.217231 | ||||||||
\(160\) | −0.407480 | −0.0322142 | ||||||||
\(161\) | −13.8993 | −1.09542 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.35200 | −0.340875 | −0.170437 | − | 0.985369i | \(-0.554518\pi\) | ||||
−0.170437 | + | 0.985369i | \(0.554518\pi\) | |||||||
\(164\) | 8.27278 | 0.645996 | ||||||||
\(165\) | −0.407480 | −0.0317223 | ||||||||
\(166\) | 11.5050 | 0.892963 | ||||||||
\(167\) | −11.0735 | −0.856895 | −0.428448 | − | 0.903567i | \(-0.640939\pi\) | ||||
−0.428448 | + | 0.903567i | \(0.640939\pi\) | |||||||
\(168\) | −3.39127 | −0.261642 | ||||||||
\(169\) | −12.9638 | −0.997213 | ||||||||
\(170\) | −1.59252 | −0.122141 | ||||||||
\(171\) | −4.21451 | −0.322291 | ||||||||
\(172\) | 2.67207 | 0.203743 | ||||||||
\(173\) | 2.93785 | 0.223361 | 0.111680 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111680 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(174\) | 0.0390710 | 0.00296196 | ||||||||
\(175\) | 16.3933 | 1.23922 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 13.4343 | 1.00979 | ||||||||
\(178\) | 3.26264 | 0.244545 | ||||||||
\(179\) | 0.675191 | 0.0504661 | 0.0252331 | − | 0.999682i | \(-0.491967\pi\) | ||||
0.0252331 | + | 0.999682i | \(0.491967\pi\) | |||||||
\(180\) | 0.407480 | 0.0303718 | ||||||||
\(181\) | −19.6035 | −1.45711 | −0.728557 | − | 0.684985i | \(-0.759809\pi\) | ||||
−0.728557 | + | 0.684985i | \(0.759809\pi\) | |||||||
\(182\) | −0.645493 | −0.0478471 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −4.09855 | −0.302149 | ||||||||
\(185\) | 2.65459 | 0.195169 | ||||||||
\(186\) | −2.91932 | −0.214055 | ||||||||
\(187\) | 3.90821 | 0.285797 | ||||||||
\(188\) | −4.59990 | −0.335482 | ||||||||
\(189\) | 3.39127 | 0.246679 | ||||||||
\(190\) | 1.71733 | 0.124588 | ||||||||
\(191\) | −1.78577 | −0.129214 | −0.0646069 | − | 0.997911i | \(-0.520579\pi\) | ||||
−0.0646069 | + | 0.997911i | \(0.520579\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.84397 | 0.636603 | 0.318301 | − | 0.947990i | \(-0.396888\pi\) | ||||
0.318301 | + | 0.947990i | \(0.396888\pi\) | |||||||
\(194\) | 6.20116 | 0.445218 | ||||||||
\(195\) | 0.0775596 | 0.00555416 | ||||||||
\(196\) | 4.50073 | 0.321481 | ||||||||
\(197\) | 15.8207 | 1.12718 | 0.563589 | − | 0.826055i | \(-0.309420\pi\) | ||||
0.563589 | + | 0.826055i | \(0.309420\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 2.49048 | 0.176545 | 0.0882727 | − | 0.996096i | \(-0.471865\pi\) | ||||
0.0882727 | + | 0.996096i | \(0.471865\pi\) | |||||||
\(200\) | 4.83396 | 0.341813 | ||||||||
\(201\) | −8.45198 | −0.596156 | ||||||||
\(202\) | 5.66027 | 0.398255 | ||||||||
\(203\) | −0.132500 | −0.00929969 | ||||||||
\(204\) | −3.90821 | −0.273629 | ||||||||
\(205\) | 3.37100 | 0.235441 | ||||||||
\(206\) | 11.6542 | 0.811990 | ||||||||
\(207\) | 4.09855 | 0.284869 | ||||||||
\(208\) | −0.190339 | −0.0131977 | ||||||||
\(209\) | −4.21451 | −0.291524 | ||||||||
\(210\) | −1.38188 | −0.0953586 | ||||||||
\(211\) | 6.86376 | 0.472520 | 0.236260 | − | 0.971690i | \(-0.424078\pi\) | ||||
0.236260 | + | 0.971690i | \(0.424078\pi\) | |||||||
\(212\) | −2.73918 | −0.188127 | ||||||||
\(213\) | −1.56991 | −0.107569 | ||||||||
\(214\) | −15.0109 | −1.02612 | ||||||||
\(215\) | 1.08882 | 0.0742567 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 9.90022 | 0.672071 | ||||||||
\(218\) | −9.88750 | −0.669666 | ||||||||
\(219\) | −11.6664 | −0.788341 | ||||||||
\(220\) | 0.407480 | 0.0274723 | ||||||||
\(221\) | −0.743887 | −0.0500392 | ||||||||
\(222\) | 6.51463 | 0.437234 | ||||||||
\(223\) | 0.569295 | 0.0381228 | 0.0190614 | − | 0.999818i | \(-0.493932\pi\) | ||||
0.0190614 | + | 0.999818i | \(0.493932\pi\) | |||||||
\(224\) | 3.39127 | 0.226589 | ||||||||
\(225\) | −4.83396 | −0.322264 | ||||||||
\(226\) | 17.4789 | 1.16268 | ||||||||
\(227\) | 10.8386 | 0.719381 | 0.359691 | − | 0.933072i | \(-0.382882\pi\) | ||||
0.359691 | + | 0.933072i | \(0.382882\pi\) | |||||||
\(228\) | 4.21451 | 0.279113 | ||||||||
\(229\) | −20.1015 | −1.32834 | −0.664171 | − | 0.747580i | \(-0.731215\pi\) | ||||
−0.664171 | + | 0.747580i | \(0.731215\pi\) | |||||||
\(230\) | −1.67008 | −0.110122 | ||||||||
\(231\) | 3.39127 | 0.223129 | ||||||||
\(232\) | −0.0390710 | −0.00256513 | ||||||||
\(233\) | −1.73528 | −0.113682 | −0.0568409 | − | 0.998383i | \(-0.518103\pi\) | ||||
−0.0568409 | + | 0.998383i | \(0.518103\pi\) | |||||||
\(234\) | 0.190339 | 0.0124429 | ||||||||
\(235\) | −1.87437 | −0.122270 | ||||||||
\(236\) | −13.4343 | −0.874501 | ||||||||
\(237\) | −9.38091 | −0.609355 | ||||||||
\(238\) | 13.2538 | 0.859117 | ||||||||
\(239\) | −4.90179 | −0.317070 | −0.158535 | − | 0.987353i | \(-0.550677\pi\) | ||||
−0.158535 | + | 0.987353i | \(0.550677\pi\) | |||||||
\(240\) | −0.407480 | −0.0263028 | ||||||||
\(241\) | 29.1570 | 1.87817 | 0.939084 | − | 0.343689i | \(-0.111677\pi\) | ||||
0.939084 | + | 0.343689i | \(0.111677\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 1.83396 | 0.117167 | ||||||||
\(246\) | 8.27278 | 0.527453 | ||||||||
\(247\) | 0.802187 | 0.0510419 | ||||||||
\(248\) | 2.91932 | 0.185377 | ||||||||
\(249\) | 11.5050 | 0.729102 | ||||||||
\(250\) | 4.00715 | 0.253434 | ||||||||
\(251\) | 2.69434 | 0.170066 | 0.0850328 | − | 0.996378i | \(-0.472901\pi\) | ||||
0.0850328 | + | 0.996378i | \(0.472901\pi\) | |||||||
\(252\) | −3.39127 | −0.213630 | ||||||||
\(253\) | 4.09855 | 0.257674 | ||||||||
\(254\) | −13.0092 | −0.816269 | ||||||||
\(255\) | −1.59252 | −0.0997274 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.10517 | −0.443209 | −0.221604 | − | 0.975137i | \(-0.571129\pi\) | ||||
−0.221604 | + | 0.975137i | \(0.571129\pi\) | |||||||
\(258\) | 2.67207 | 0.166356 | ||||||||
\(259\) | −22.0929 | −1.37279 | ||||||||
\(260\) | −0.0775596 | −0.00481004 | ||||||||
\(261\) | 0.0390710 | 0.00241843 | ||||||||
\(262\) | 21.9677 | 1.35717 | ||||||||
\(263\) | −19.9870 | −1.23245 | −0.616227 | − | 0.787569i | \(-0.711340\pi\) | ||||
−0.616227 | + | 0.787569i | \(0.711340\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −1.11616 | −0.0685652 | ||||||||
\(266\) | −14.2925 | −0.876332 | ||||||||
\(267\) | 3.26264 | 0.199670 | ||||||||
\(268\) | 8.45198 | 0.516287 | ||||||||
\(269\) | 18.3489 | 1.11875 | 0.559377 | − | 0.828914i | \(-0.311041\pi\) | ||||
0.559377 | + | 0.828914i | \(0.311041\pi\) | |||||||
\(270\) | 0.407480 | 0.0247985 | ||||||||
\(271\) | 7.27120 | 0.441694 | 0.220847 | − | 0.975308i | \(-0.429118\pi\) | ||||
0.220847 | + | 0.975308i | \(0.429118\pi\) | |||||||
\(272\) | 3.90821 | 0.236970 | ||||||||
\(273\) | −0.645493 | −0.0390670 | ||||||||
\(274\) | −9.51622 | −0.574896 | ||||||||
\(275\) | −4.83396 | −0.291499 | ||||||||
\(276\) | −4.09855 | −0.246704 | ||||||||
\(277\) | −9.48724 | −0.570033 | −0.285017 | − | 0.958523i | \(-0.591999\pi\) | ||||
−0.285017 | + | 0.958523i | \(0.591999\pi\) | |||||||
\(278\) | 8.06367 | 0.483627 | ||||||||
\(279\) | −2.91932 | −0.174775 | ||||||||
\(280\) | 1.38188 | 0.0825830 | ||||||||
\(281\) | −31.6176 | −1.88615 | −0.943073 | − | 0.332587i | \(-0.892078\pi\) | ||||
−0.943073 | + | 0.332587i | \(0.892078\pi\) | |||||||
\(282\) | −4.59990 | −0.273920 | ||||||||
\(283\) | −20.9491 | −1.24530 | −0.622648 | − | 0.782502i | \(-0.713943\pi\) | ||||
−0.622648 | + | 0.782502i | \(0.713943\pi\) | |||||||
\(284\) | 1.56991 | 0.0931571 | ||||||||
\(285\) | 1.71733 | 0.101726 | ||||||||
\(286\) | 0.190339 | 0.0112550 | ||||||||
\(287\) | −28.0553 | −1.65605 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.72589 | −0.101523 | ||||||||
\(290\) | −0.0159206 | −0.000934893 0 | ||||||||
\(291\) | 6.20116 | 0.363519 | ||||||||
\(292\) | 11.6664 | 0.682724 | ||||||||
\(293\) | −18.7636 | −1.09618 | −0.548091 | − | 0.836419i | \(-0.684645\pi\) | ||||
−0.548091 | + | 0.836419i | \(0.684645\pi\) | |||||||
\(294\) | 4.50073 | 0.262488 | ||||||||
\(295\) | −5.47423 | −0.318722 | ||||||||
\(296\) | −6.51463 | −0.378655 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 1.61425 | 0.0935111 | ||||||||
\(299\) | −0.780116 | −0.0451153 | ||||||||
\(300\) | 4.83396 | 0.279089 | ||||||||
\(301\) | −9.06172 | −0.522309 | ||||||||
\(302\) | 11.6620 | 0.671073 | ||||||||
\(303\) | 5.66027 | 0.325174 | ||||||||
\(304\) | −4.21451 | −0.241719 | ||||||||
\(305\) | 0.407480 | 0.0233323 | ||||||||
\(306\) | −3.90821 | −0.223418 | ||||||||
\(307\) | −12.8926 | −0.735818 | −0.367909 | − | 0.929862i | \(-0.619926\pi\) | ||||
−0.367909 | + | 0.929862i | \(0.619926\pi\) | |||||||
\(308\) | −3.39127 | −0.193236 | ||||||||
\(309\) | 11.6542 | 0.662987 | ||||||||
\(310\) | 1.18957 | 0.0675629 | ||||||||
\(311\) | −26.0626 | −1.47788 | −0.738938 | − | 0.673773i | \(-0.764673\pi\) | ||||
−0.738938 | + | 0.673773i | \(0.764673\pi\) | |||||||
\(312\) | −0.190339 | −0.0107758 | ||||||||
\(313\) | −9.41313 | −0.532062 | −0.266031 | − | 0.963964i | \(-0.585712\pi\) | ||||
−0.266031 | + | 0.963964i | \(0.585712\pi\) | |||||||
\(314\) | 15.5480 | 0.877425 | ||||||||
\(315\) | −1.38188 | −0.0778600 | ||||||||
\(316\) | 9.38091 | 0.527717 | ||||||||
\(317\) | 8.50811 | 0.477863 | 0.238931 | − | 0.971036i | \(-0.423203\pi\) | ||||
0.238931 | + | 0.971036i | \(0.423203\pi\) | |||||||
\(318\) | −2.73918 | −0.153605 | ||||||||
\(319\) | 0.0390710 | 0.00218755 | ||||||||
\(320\) | 0.407480 | 0.0227789 | ||||||||
\(321\) | −15.0109 | −0.837826 | ||||||||
\(322\) | 13.8993 | 0.774578 | ||||||||
\(323\) | −16.4712 | −0.916481 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.920093 | 0.0510376 | ||||||||
\(326\) | 4.35200 | 0.241035 | ||||||||
\(327\) | −9.88750 | −0.546780 | ||||||||
\(328\) | −8.27278 | −0.456788 | ||||||||
\(329\) | 15.5995 | 0.860028 | ||||||||
\(330\) | 0.407480 | 0.0224311 | ||||||||
\(331\) | −34.5824 | −1.90082 | −0.950409 | − | 0.311003i | \(-0.899335\pi\) | ||||
−0.950409 | + | 0.311003i | \(0.899335\pi\) | |||||||
\(332\) | −11.5050 | −0.631421 | ||||||||
\(333\) | 6.51463 | 0.357000 | ||||||||
\(334\) | 11.0735 | 0.605917 | ||||||||
\(335\) | 3.44402 | 0.188167 | ||||||||
\(336\) | 3.39127 | 0.185009 | ||||||||
\(337\) | 4.70730 | 0.256423 | 0.128212 | − | 0.991747i | \(-0.459076\pi\) | ||||
0.128212 | + | 0.991747i | \(0.459076\pi\) | |||||||
\(338\) | 12.9638 | 0.705136 | ||||||||
\(339\) | 17.4789 | 0.949324 | ||||||||
\(340\) | 1.59252 | 0.0863665 | ||||||||
\(341\) | −2.91932 | −0.158090 | ||||||||
\(342\) | 4.21451 | 0.227894 | ||||||||
\(343\) | 8.47571 | 0.457645 | ||||||||
\(344\) | −2.67207 | −0.144068 | ||||||||
\(345\) | −1.67008 | −0.0899140 | ||||||||
\(346\) | −2.93785 | −0.157940 | ||||||||
\(347\) | −22.0091 | −1.18151 | −0.590754 | − | 0.806851i | \(-0.701170\pi\) | ||||
−0.590754 | + | 0.806851i | \(0.701170\pi\) | |||||||
\(348\) | −0.0390710 | −0.00209442 | ||||||||
\(349\) | 18.4244 | 0.986236 | 0.493118 | − | 0.869963i | \(-0.335857\pi\) | ||||
0.493118 | + | 0.869963i | \(0.335857\pi\) | |||||||
\(350\) | −16.3933 | −0.876257 | ||||||||
\(351\) | 0.190339 | 0.0101596 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 12.4271 | 0.661429 | 0.330714 | − | 0.943731i | \(-0.392710\pi\) | ||||
0.330714 | + | 0.943731i | \(0.392710\pi\) | |||||||
\(354\) | −13.4343 | −0.714027 | ||||||||
\(355\) | 0.639708 | 0.0339522 | ||||||||
\(356\) | −3.26264 | −0.172920 | ||||||||
\(357\) | 13.2538 | 0.701466 | ||||||||
\(358\) | −0.675191 | −0.0356849 | ||||||||
\(359\) | −19.6443 | −1.03679 | −0.518393 | − | 0.855143i | \(-0.673469\pi\) | ||||
−0.518393 | + | 0.855143i | \(0.673469\pi\) | |||||||
\(360\) | −0.407480 | −0.0214761 | ||||||||
\(361\) | −1.23793 | −0.0651544 | ||||||||
\(362\) | 19.6035 | 1.03034 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0.645493 | 0.0338330 | ||||||||
\(365\) | 4.75382 | 0.248827 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −1.14405 | −0.0597188 | −0.0298594 | − | 0.999554i | \(-0.509506\pi\) | ||||
−0.0298594 | + | 0.999554i | \(0.509506\pi\) | |||||||
\(368\) | 4.09855 | 0.213652 | ||||||||
\(369\) | 8.27278 | 0.430664 | ||||||||
\(370\) | −2.65459 | −0.138005 | ||||||||
\(371\) | 9.28929 | 0.482276 | ||||||||
\(372\) | 2.91932 | 0.151360 | ||||||||
\(373\) | −17.9312 | −0.928441 | −0.464220 | − | 0.885720i | \(-0.653665\pi\) | ||||
−0.464220 | + | 0.885720i | \(0.653665\pi\) | |||||||
\(374\) | −3.90821 | −0.202089 | ||||||||
\(375\) | 4.00715 | 0.206928 | ||||||||
\(376\) | 4.59990 | 0.237222 | ||||||||
\(377\) | −0.00743674 | −0.000383012 0 | ||||||||
\(378\) | −3.39127 | −0.174428 | ||||||||
\(379\) | −3.60125 | −0.184984 | −0.0924920 | − | 0.995713i | \(-0.529483\pi\) | ||||
−0.0924920 | + | 0.995713i | \(0.529483\pi\) | |||||||
\(380\) | −1.71733 | −0.0880971 | ||||||||
\(381\) | −13.0092 | −0.666481 | ||||||||
\(382\) | 1.78577 | 0.0913679 | ||||||||
\(383\) | −13.9835 | −0.714524 | −0.357262 | − | 0.934004i | \(-0.616290\pi\) | ||||
−0.357262 | + | 0.934004i | \(0.616290\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.38188 | −0.0704270 | ||||||||
\(386\) | −8.84397 | −0.450146 | ||||||||
\(387\) | 2.67207 | 0.135829 | ||||||||
\(388\) | −6.20116 | −0.314816 | ||||||||
\(389\) | −8.68005 | −0.440096 | −0.220048 | − | 0.975489i | \(-0.570621\pi\) | ||||
−0.220048 | + | 0.975489i | \(0.570621\pi\) | |||||||
\(390\) | −0.0775596 | −0.00392738 | ||||||||
\(391\) | 16.0180 | 0.810065 | ||||||||
\(392\) | −4.50073 | −0.227321 | ||||||||
\(393\) | 21.9677 | 1.10813 | ||||||||
\(394\) | −15.8207 | −0.797035 | ||||||||
\(395\) | 3.82254 | 0.192333 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 4.05936 | 0.203733 | 0.101867 | − | 0.994798i | \(-0.467519\pi\) | ||||
0.101867 | + | 0.994798i | \(0.467519\pi\) | |||||||
\(398\) | −2.49048 | −0.124836 | ||||||||
\(399\) | −14.2925 | −0.715522 | ||||||||
\(400\) | −4.83396 | −0.241698 | ||||||||
\(401\) | 2.25650 | 0.112684 | 0.0563422 | − | 0.998412i | \(-0.482056\pi\) | ||||
0.0563422 | + | 0.998412i | \(0.482056\pi\) | |||||||
\(402\) | 8.45198 | 0.421546 | ||||||||
\(403\) | 0.555662 | 0.0276795 | ||||||||
\(404\) | −5.66027 | −0.281609 | ||||||||
\(405\) | 0.407480 | 0.0202479 | ||||||||
\(406\) | 0.132500 | 0.00657588 | ||||||||
\(407\) | 6.51463 | 0.322918 | ||||||||
\(408\) | 3.90821 | 0.193485 | ||||||||
\(409\) | −4.93027 | −0.243786 | −0.121893 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121893 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(410\) | −3.37100 | −0.166482 | ||||||||
\(411\) | −9.51622 | −0.469400 | ||||||||
\(412\) | −11.6542 | −0.574163 | ||||||||
\(413\) | 45.5595 | 2.24184 | ||||||||
\(414\) | −4.09855 | −0.201433 | ||||||||
\(415\) | −4.68807 | −0.230129 | ||||||||
\(416\) | 0.190339 | 0.00933216 | ||||||||
\(417\) | 8.06367 | 0.394880 | ||||||||
\(418\) | 4.21451 | 0.206138 | ||||||||
\(419\) | −1.40235 | −0.0685094 | −0.0342547 | − | 0.999413i | \(-0.510906\pi\) | ||||
−0.0342547 | + | 0.999413i | \(0.510906\pi\) | |||||||
\(420\) | 1.38188 | 0.0674287 | ||||||||
\(421\) | −8.61008 | −0.419629 | −0.209815 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209815 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(422\) | −6.86376 | −0.334122 | ||||||||
\(423\) | −4.59990 | −0.223655 | ||||||||
\(424\) | 2.73918 | 0.133026 | ||||||||
\(425\) | −18.8921 | −0.916403 | ||||||||
\(426\) | 1.56991 | 0.0760625 | ||||||||
\(427\) | −3.39127 | −0.164115 | ||||||||
\(428\) | 15.0109 | 0.725578 | ||||||||
\(429\) | 0.190339 | 0.00918967 | ||||||||
\(430\) | −1.08882 | −0.0525074 | ||||||||
\(431\) | −35.2866 | −1.69969 | −0.849847 | − | 0.527029i | \(-0.823306\pi\) | ||||
−0.849847 | + | 0.527029i | \(0.823306\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −0.934742 | −0.0449208 | −0.0224604 | − | 0.999748i | \(-0.507150\pi\) | ||||
−0.0224604 | + | 0.999748i | \(0.507150\pi\) | |||||||
\(434\) | −9.90022 | −0.475226 | ||||||||
\(435\) | −0.0159206 | −0.000763337 0 | ||||||||
\(436\) | 9.88750 | 0.473525 | ||||||||
\(437\) | −17.2734 | −0.826297 | ||||||||
\(438\) | 11.6664 | 0.557441 | ||||||||
\(439\) | 0.742524 | 0.0354387 | 0.0177194 | − | 0.999843i | \(-0.494359\pi\) | ||||
0.0177194 | + | 0.999843i | \(0.494359\pi\) | |||||||
\(440\) | −0.407480 | −0.0194259 | ||||||||
\(441\) | 4.50073 | 0.214320 | ||||||||
\(442\) | 0.743887 | 0.0353831 | ||||||||
\(443\) | −22.5191 | −1.06991 | −0.534957 | − | 0.844879i | \(-0.679672\pi\) | ||||
−0.534957 | + | 0.844879i | \(0.679672\pi\) | |||||||
\(444\) | −6.51463 | −0.309171 | ||||||||
\(445\) | −1.32946 | −0.0630225 | ||||||||
\(446\) | −0.569295 | −0.0269569 | ||||||||
\(447\) | 1.61425 | 0.0763515 | ||||||||
\(448\) | −3.39127 | −0.160223 | ||||||||
\(449\) | −30.8487 | −1.45584 | −0.727920 | − | 0.685663i | \(-0.759513\pi\) | ||||
−0.727920 | + | 0.685663i | \(0.759513\pi\) | |||||||
\(450\) | 4.83396 | 0.227875 | ||||||||
\(451\) | 8.27278 | 0.389550 | ||||||||
\(452\) | −17.4789 | −0.822139 | ||||||||
\(453\) | 11.6620 | 0.547929 | ||||||||
\(454\) | −10.8386 | −0.508679 | ||||||||
\(455\) | 0.263026 | 0.0123308 | ||||||||
\(456\) | −4.21451 | −0.197362 | ||||||||
\(457\) | 11.1117 | 0.519785 | 0.259893 | − | 0.965638i | \(-0.416313\pi\) | ||||
0.259893 | + | 0.965638i | \(0.416313\pi\) | |||||||
\(458\) | 20.1015 | 0.939280 | ||||||||
\(459\) | −3.90821 | −0.182420 | ||||||||
\(460\) | 1.67008 | 0.0778678 | ||||||||
\(461\) | −1.71664 | −0.0799520 | −0.0399760 | − | 0.999201i | \(-0.512728\pi\) | ||||
−0.0399760 | + | 0.999201i | \(0.512728\pi\) | |||||||
\(462\) | −3.39127 | −0.157776 | ||||||||
\(463\) | 18.7085 | 0.869458 | 0.434729 | − | 0.900561i | \(-0.356844\pi\) | ||||
0.434729 | + | 0.900561i | \(0.356844\pi\) | |||||||
\(464\) | 0.0390710 | 0.00181382 | ||||||||
\(465\) | 1.18957 | 0.0551648 | ||||||||
\(466\) | 1.73528 | 0.0803852 | ||||||||
\(467\) | −15.4734 | −0.716023 | −0.358012 | − | 0.933717i | \(-0.616545\pi\) | ||||
−0.358012 | + | 0.933717i | \(0.616545\pi\) | |||||||
\(468\) | −0.190339 | −0.00879844 | ||||||||
\(469\) | −28.6630 | −1.32353 | ||||||||
\(470\) | 1.87437 | 0.0864581 | ||||||||
\(471\) | 15.5480 | 0.716415 | ||||||||
\(472\) | 13.4343 | 0.618366 | ||||||||
\(473\) | 2.67207 | 0.122862 | ||||||||
\(474\) | 9.38091 | 0.430879 | ||||||||
\(475\) | 20.3728 | 0.934766 | ||||||||
\(476\) | −13.2538 | −0.607487 | ||||||||
\(477\) | −2.73918 | −0.125418 | ||||||||
\(478\) | 4.90179 | 0.224202 | ||||||||
\(479\) | 6.51343 | 0.297606 | 0.148803 | − | 0.988867i | \(-0.452458\pi\) | ||||
0.148803 | + | 0.988867i | \(0.452458\pi\) | |||||||
\(480\) | 0.407480 | 0.0185989 | ||||||||
\(481\) | −1.23999 | −0.0565387 | ||||||||
\(482\) | −29.1570 | −1.32806 | ||||||||
\(483\) | 13.8993 | 0.632440 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.52685 | −0.114738 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −16.7789 | −0.760324 | −0.380162 | − | 0.924920i | \(-0.624132\pi\) | ||||
−0.380162 | + | 0.924920i | \(0.624132\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 4.35200 | 0.196804 | ||||||||
\(490\) | −1.83396 | −0.0828499 | ||||||||
\(491\) | −21.5232 | −0.971329 | −0.485665 | − | 0.874145i | \(-0.661422\pi\) | ||||
−0.485665 | + | 0.874145i | \(0.661422\pi\) | |||||||
\(492\) | −8.27278 | −0.372966 | ||||||||
\(493\) | 0.152698 | 0.00687715 | ||||||||
\(494\) | −0.802187 | −0.0360921 | ||||||||
\(495\) | 0.407480 | 0.0183149 | ||||||||
\(496\) | −2.91932 | −0.131081 | ||||||||
\(497\) | −5.32400 | −0.238814 | ||||||||
\(498\) | −11.5050 | −0.515553 | ||||||||
\(499\) | 20.7732 | 0.929936 | 0.464968 | − | 0.885327i | \(-0.346066\pi\) | ||||
0.464968 | + | 0.885327i | \(0.346066\pi\) | |||||||
\(500\) | −4.00715 | −0.179205 | ||||||||
\(501\) | 11.0735 | 0.494729 | ||||||||
\(502\) | −2.69434 | −0.120254 | ||||||||
\(503\) | −9.49556 | −0.423386 | −0.211693 | − | 0.977336i | \(-0.567898\pi\) | ||||
−0.211693 | + | 0.977336i | \(0.567898\pi\) | |||||||
\(504\) | 3.39127 | 0.151059 | ||||||||
\(505\) | −2.30645 | −0.102636 | ||||||||
\(506\) | −4.09855 | −0.182203 | ||||||||
\(507\) | 12.9638 | 0.575741 | ||||||||
\(508\) | 13.0092 | 0.577190 | ||||||||
\(509\) | −20.7252 | −0.918630 | −0.459315 | − | 0.888273i | \(-0.651905\pi\) | ||||
−0.459315 | + | 0.888273i | \(0.651905\pi\) | |||||||
\(510\) | 1.59252 | 0.0705180 | ||||||||
\(511\) | −39.5639 | −1.75020 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.21451 | 0.186075 | ||||||||
\(514\) | 7.10517 | 0.313396 | ||||||||
\(515\) | −4.74888 | −0.209261 | ||||||||
\(516\) | −2.67207 | −0.117631 | ||||||||
\(517\) | −4.59990 | −0.202303 | ||||||||
\(518\) | 22.0929 | 0.970706 | ||||||||
\(519\) | −2.93785 | −0.128957 | ||||||||
\(520\) | 0.0775596 | 0.00340121 | ||||||||
\(521\) | −3.13961 | −0.137549 | −0.0687745 | − | 0.997632i | \(-0.521909\pi\) | ||||
−0.0687745 | + | 0.997632i | \(0.521909\pi\) | |||||||
\(522\) | −0.0390710 | −0.00171009 | ||||||||
\(523\) | 14.6829 | 0.642037 | 0.321019 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321019 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(524\) | −21.9677 | −0.959665 | ||||||||
\(525\) | −16.3933 | −0.715461 | ||||||||
\(526\) | 19.9870 | 0.871476 | ||||||||
\(527\) | −11.4093 | −0.496998 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −6.20189 | −0.269647 | ||||||||
\(530\) | 1.11616 | 0.0484829 | ||||||||
\(531\) | −13.4343 | −0.583001 | ||||||||
\(532\) | 14.2925 | 0.619660 | ||||||||
\(533\) | −1.57464 | −0.0682051 | ||||||||
\(534\) | −3.26264 | −0.141188 | ||||||||
\(535\) | 6.11664 | 0.264445 | ||||||||
\(536\) | −8.45198 | −0.365070 | ||||||||
\(537\) | −0.675191 | −0.0291366 | ||||||||
\(538\) | −18.3489 | −0.791078 | ||||||||
\(539\) | 4.50073 | 0.193860 | ||||||||
\(540\) | −0.407480 | −0.0175352 | ||||||||
\(541\) | −17.2033 | −0.739629 | −0.369815 | − | 0.929106i | \(-0.620579\pi\) | ||||
−0.369815 | + | 0.929106i | \(0.620579\pi\) | |||||||
\(542\) | −7.27120 | −0.312325 | ||||||||
\(543\) | 19.6035 | 0.841266 | ||||||||
\(544\) | −3.90821 | −0.167563 | ||||||||
\(545\) | 4.02896 | 0.172582 | ||||||||
\(546\) | 0.645493 | 0.0276245 | ||||||||
\(547\) | 14.2728 | 0.610259 | 0.305130 | − | 0.952311i | \(-0.401300\pi\) | ||||
0.305130 | + | 0.952311i | \(0.401300\pi\) | |||||||
\(548\) | 9.51622 | 0.406513 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 4.83396 | 0.206121 | ||||||||
\(551\) | −0.164665 | −0.00701496 | ||||||||
\(552\) | 4.09855 | 0.174446 | ||||||||
\(553\) | −31.8132 | −1.35284 | ||||||||
\(554\) | 9.48724 | 0.403074 | ||||||||
\(555\) | −2.65459 | −0.112681 | ||||||||
\(556\) | −8.06367 | −0.341976 | ||||||||
\(557\) | −2.96521 | −0.125640 | −0.0628199 | − | 0.998025i | \(-0.520009\pi\) | ||||
−0.0628199 | + | 0.998025i | \(0.520009\pi\) | |||||||
\(558\) | 2.91932 | 0.123585 | ||||||||
\(559\) | −0.508600 | −0.0215115 | ||||||||
\(560\) | −1.38188 | −0.0583950 | ||||||||
\(561\) | −3.90821 | −0.165005 | ||||||||
\(562\) | 31.6176 | 1.33371 | ||||||||
\(563\) | 16.8136 | 0.708609 | 0.354304 | − | 0.935130i | \(-0.384718\pi\) | ||||
0.354304 | + | 0.935130i | \(0.384718\pi\) | |||||||
\(564\) | 4.59990 | 0.193691 | ||||||||
\(565\) | −7.12232 | −0.299638 | ||||||||
\(566\) | 20.9491 | 0.880558 | ||||||||
\(567\) | −3.39127 | −0.142420 | ||||||||
\(568\) | −1.56991 | −0.0658720 | ||||||||
\(569\) | −19.8262 | −0.831157 | −0.415579 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415579 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(570\) | −1.71733 | −0.0719310 | ||||||||
\(571\) | −31.9143 | −1.33557 | −0.667786 | − | 0.744353i | \(-0.732758\pi\) | ||||
−0.667786 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(572\) | −0.190339 | −0.00795849 | ||||||||
\(573\) | 1.78577 | 0.0746016 | ||||||||
\(574\) | 28.0553 | 1.17100 | ||||||||
\(575\) | −19.8122 | −0.826227 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.45364 | 0.227038 | 0.113519 | − | 0.993536i | \(-0.463788\pi\) | ||||
0.113519 | + | 0.993536i | \(0.463788\pi\) | |||||||
\(578\) | 1.72589 | 0.0717875 | ||||||||
\(579\) | −8.84397 | −0.367543 | ||||||||
\(580\) | 0.0159206 | 0.000661069 0 | ||||||||
\(581\) | 39.0167 | 1.61869 | ||||||||
\(582\) | −6.20116 | −0.257047 | ||||||||
\(583\) | −2.73918 | −0.113445 | ||||||||
\(584\) | −11.6664 | −0.482758 | ||||||||
\(585\) | −0.0775596 | −0.00320669 | ||||||||
\(586\) | 18.7636 | 0.775117 | ||||||||
\(587\) | 24.9575 | 1.03011 | 0.515054 | − | 0.857158i | \(-0.327772\pi\) | ||||
0.515054 | + | 0.857158i | \(0.327772\pi\) | |||||||
\(588\) | −4.50073 | −0.185607 | ||||||||
\(589\) | 12.3035 | 0.506957 | ||||||||
\(590\) | 5.47423 | 0.225371 | ||||||||
\(591\) | −15.8207 | −0.650776 | ||||||||
\(592\) | 6.51463 | 0.267750 | ||||||||
\(593\) | 4.75203 | 0.195143 | 0.0975713 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975713 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −5.40067 | −0.221406 | ||||||||
\(596\) | −1.61425 | −0.0661223 | ||||||||
\(597\) | −2.49048 | −0.101929 | ||||||||
\(598\) | 0.780116 | 0.0319013 | ||||||||
\(599\) | −28.7186 | −1.17341 | −0.586704 | − | 0.809801i | \(-0.699575\pi\) | ||||
−0.586704 | + | 0.809801i | \(0.699575\pi\) | |||||||
\(600\) | −4.83396 | −0.197346 | ||||||||
\(601\) | −33.1823 | −1.35353 | −0.676766 | − | 0.736198i | \(-0.736619\pi\) | ||||
−0.676766 | + | 0.736198i | \(0.736619\pi\) | |||||||
\(602\) | 9.06172 | 0.369328 | ||||||||
\(603\) | 8.45198 | 0.344191 | ||||||||
\(604\) | −11.6620 | −0.474520 | ||||||||
\(605\) | 0.407480 | 0.0165664 | ||||||||
\(606\) | −5.66027 | −0.229933 | ||||||||
\(607\) | 29.5058 | 1.19760 | 0.598802 | − | 0.800897i | \(-0.295644\pi\) | ||||
0.598802 | + | 0.800897i | \(0.295644\pi\) | |||||||
\(608\) | 4.21451 | 0.170921 | ||||||||
\(609\) | 0.132500 | 0.00536918 | ||||||||
\(610\) | −0.407480 | −0.0164984 | ||||||||
\(611\) | 0.875542 | 0.0354206 | ||||||||
\(612\) | 3.90821 | 0.157980 | ||||||||
\(613\) | −0.815836 | −0.0329513 | −0.0164756 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164756 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(614\) | 12.8926 | 0.520302 | ||||||||
\(615\) | −3.37100 | −0.135932 | ||||||||
\(616\) | 3.39127 | 0.136638 | ||||||||
\(617\) | 34.3165 | 1.38153 | 0.690764 | − | 0.723080i | \(-0.257274\pi\) | ||||
0.690764 | + | 0.723080i | \(0.257274\pi\) | |||||||
\(618\) | −11.6542 | −0.468803 | ||||||||
\(619\) | −1.13167 | −0.0454855 | −0.0227427 | − | 0.999741i | \(-0.507240\pi\) | ||||
−0.0227427 | + | 0.999741i | \(0.507240\pi\) | |||||||
\(620\) | −1.18957 | −0.0477742 | ||||||||
\(621\) | −4.09855 | −0.164469 | ||||||||
\(622\) | 26.0626 | 1.04502 | ||||||||
\(623\) | 11.0645 | 0.443290 | ||||||||
\(624\) | 0.190339 | 0.00761968 | ||||||||
\(625\) | 22.5370 | 0.901479 | ||||||||
\(626\) | 9.41313 | 0.376225 | ||||||||
\(627\) | 4.21451 | 0.168311 | ||||||||
\(628\) | −15.5480 | −0.620433 | ||||||||
\(629\) | 25.4606 | 1.01518 | ||||||||
\(630\) | 1.38188 | 0.0550553 | ||||||||
\(631\) | 25.9961 | 1.03489 | 0.517445 | − | 0.855717i | \(-0.326883\pi\) | ||||
0.517445 | + | 0.855717i | \(0.326883\pi\) | |||||||
\(632\) | −9.38091 | −0.373152 | ||||||||
\(633\) | −6.86376 | −0.272810 | ||||||||
\(634\) | −8.50811 | −0.337900 | ||||||||
\(635\) | 5.30099 | 0.210363 | ||||||||
\(636\) | 2.73918 | 0.108615 | ||||||||
\(637\) | −0.856666 | −0.0339424 | ||||||||
\(638\) | −0.0390710 | −0.00154683 | ||||||||
\(639\) | 1.56991 | 0.0621047 | ||||||||
\(640\) | −0.407480 | −0.0161071 | ||||||||
\(641\) | −29.9358 | −1.18239 | −0.591196 | − | 0.806528i | \(-0.701344\pi\) | ||||
−0.591196 | + | 0.806528i | \(0.701344\pi\) | |||||||
\(642\) | 15.0109 | 0.592432 | ||||||||
\(643\) | 35.8982 | 1.41569 | 0.707844 | − | 0.706368i | \(-0.249668\pi\) | ||||
0.707844 | + | 0.706368i | \(0.249668\pi\) | |||||||
\(644\) | −13.8993 | −0.547709 | ||||||||
\(645\) | −1.08882 | −0.0428721 | ||||||||
\(646\) | 16.4712 | 0.648050 | ||||||||
\(647\) | 16.7452 | 0.658322 | 0.329161 | − | 0.944274i | \(-0.393234\pi\) | ||||
0.329161 | + | 0.944274i | \(0.393234\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −13.4343 | −0.527344 | ||||||||
\(650\) | −0.920093 | −0.0360890 | ||||||||
\(651\) | −9.90022 | −0.388020 | ||||||||
\(652\) | −4.35200 | −0.170437 | ||||||||
\(653\) | 22.5161 | 0.881122 | 0.440561 | − | 0.897723i | \(-0.354780\pi\) | ||||
0.440561 | + | 0.897723i | \(0.354780\pi\) | |||||||
\(654\) | 9.88750 | 0.386632 | ||||||||
\(655\) | −8.95143 | −0.349761 | ||||||||
\(656\) | 8.27278 | 0.322998 | ||||||||
\(657\) | 11.6664 | 0.455149 | ||||||||
\(658\) | −15.5995 | −0.608132 | ||||||||
\(659\) | −30.5059 | −1.18834 | −0.594170 | − | 0.804340i | \(-0.702519\pi\) | ||||
−0.594170 | + | 0.804340i | \(0.702519\pi\) | |||||||
\(660\) | −0.407480 | −0.0158612 | ||||||||
\(661\) | −13.7892 | −0.536338 | −0.268169 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268169 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(662\) | 34.5824 | 1.34408 | ||||||||
\(663\) | 0.743887 | 0.0288902 | ||||||||
\(664\) | 11.5050 | 0.446482 | ||||||||
\(665\) | 5.82393 | 0.225842 | ||||||||
\(666\) | −6.51463 | −0.252437 | ||||||||
\(667\) | 0.160134 | 0.00620042 | ||||||||
\(668\) | −11.0735 | −0.428448 | ||||||||
\(669\) | −0.569295 | −0.0220102 | ||||||||
\(670\) | −3.44402 | −0.133054 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −3.39127 | −0.130821 | ||||||||
\(673\) | 22.3861 | 0.862922 | 0.431461 | − | 0.902132i | \(-0.357998\pi\) | ||||
0.431461 | + | 0.902132i | \(0.357998\pi\) | |||||||
\(674\) | −4.70730 | −0.181319 | ||||||||
\(675\) | 4.83396 | 0.186059 | ||||||||
\(676\) | −12.9638 | −0.498607 | ||||||||
\(677\) | 45.6483 | 1.75441 | 0.877203 | − | 0.480120i | \(-0.159407\pi\) | ||||
0.877203 | + | 0.480120i | \(0.159407\pi\) | |||||||
\(678\) | −17.4789 | −0.671274 | ||||||||
\(679\) | 21.0298 | 0.807051 | ||||||||
\(680\) | −1.59252 | −0.0610703 | ||||||||
\(681\) | −10.8386 | −0.415335 | ||||||||
\(682\) | 2.91932 | 0.111787 | ||||||||
\(683\) | 27.5327 | 1.05351 | 0.526754 | − | 0.850018i | \(-0.323409\pi\) | ||||
0.526754 | + | 0.850018i | \(0.323409\pi\) | |||||||
\(684\) | −4.21451 | −0.161146 | ||||||||
\(685\) | 3.87767 | 0.148158 | ||||||||
\(686\) | −8.47571 | −0.323604 | ||||||||
\(687\) | 20.1015 | 0.766919 | ||||||||
\(688\) | 2.67207 | 0.101872 | ||||||||
\(689\) | 0.521373 | 0.0198627 | ||||||||
\(690\) | 1.67008 | 0.0635788 | ||||||||
\(691\) | 18.4860 | 0.703239 | 0.351619 | − | 0.936143i | \(-0.385631\pi\) | ||||
0.351619 | + | 0.936143i | \(0.385631\pi\) | |||||||
\(692\) | 2.93785 | 0.111680 | ||||||||
\(693\) | −3.39127 | −0.128824 | ||||||||
\(694\) | 22.0091 | 0.835453 | ||||||||
\(695\) | −3.28579 | −0.124637 | ||||||||
\(696\) | 0.0390710 | 0.00148098 | ||||||||
\(697\) | 32.3318 | 1.22465 | ||||||||
\(698\) | −18.4244 | −0.697374 | ||||||||
\(699\) | 1.73528 | 0.0656342 | ||||||||
\(700\) | 16.3933 | 0.619608 | ||||||||
\(701\) | 27.0939 | 1.02332 | 0.511661 | − | 0.859187i | \(-0.329030\pi\) | ||||
0.511661 | + | 0.859187i | \(0.329030\pi\) | |||||||
\(702\) | −0.190339 | −0.00718390 | ||||||||
\(703\) | −27.4560 | −1.03552 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 1.87437 | 0.0705928 | ||||||||
\(706\) | −12.4271 | −0.467701 | ||||||||
\(707\) | 19.1955 | 0.721922 | ||||||||
\(708\) | 13.4343 | 0.504893 | ||||||||
\(709\) | 44.8042 | 1.68266 | 0.841328 | − | 0.540525i | \(-0.181774\pi\) | ||||
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(710\) | −0.639708 | −0.0240078 | ||||||||
\(711\) | 9.38091 | 0.351812 | ||||||||
\(712\) | 3.26264 | 0.122273 | ||||||||
\(713\) | −11.9650 | −0.448092 | ||||||||
\(714\) | −13.2538 | −0.496011 | ||||||||
\(715\) | −0.0775596 | −0.00290056 | ||||||||
\(716\) | 0.675191 | 0.0252331 | ||||||||
\(717\) | 4.90179 | 0.183061 | ||||||||
\(718\) | 19.6443 | 0.733118 | ||||||||
\(719\) | −2.90008 | −0.108155 | −0.0540774 | − | 0.998537i | \(-0.517222\pi\) | ||||
−0.0540774 | + | 0.998537i | \(0.517222\pi\) | |||||||
\(720\) | 0.407480 | 0.0151859 | ||||||||
\(721\) | 39.5227 | 1.47190 | ||||||||
\(722\) | 1.23793 | 0.0460711 | ||||||||
\(723\) | −29.1570 | −1.08436 | ||||||||
\(724\) | −19.6035 | −0.728557 | ||||||||
\(725\) | −0.188867 | −0.00701436 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −17.2518 | −0.639836 | −0.319918 | − | 0.947445i | \(-0.603655\pi\) | ||||
−0.319918 | + | 0.947445i | \(0.603655\pi\) | |||||||
\(728\) | −0.645493 | −0.0239236 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.75382 | −0.175947 | ||||||||
\(731\) | 10.4430 | 0.386249 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 16.7611 | 0.619086 | 0.309543 | − | 0.950885i | \(-0.399824\pi\) | ||||
0.309543 | + | 0.950885i | \(0.399824\pi\) | |||||||
\(734\) | 1.14405 | 0.0422276 | ||||||||
\(735\) | −1.83396 | −0.0676466 | ||||||||
\(736\) | −4.09855 | −0.151075 | ||||||||
\(737\) | 8.45198 | 0.311333 | ||||||||
\(738\) | −8.27278 | −0.304525 | ||||||||
\(739\) | 36.8176 | 1.35436 | 0.677178 | − | 0.735819i | \(-0.263203\pi\) | ||||
0.677178 | + | 0.735819i | \(0.263203\pi\) | |||||||
\(740\) | 2.65459 | 0.0975845 | ||||||||
\(741\) | −0.802187 | −0.0294691 | ||||||||
\(742\) | −9.28929 | −0.341021 | ||||||||
\(743\) | 35.7438 | 1.31131 | 0.655657 | − | 0.755059i | \(-0.272392\pi\) | ||||
0.655657 | + | 0.755059i | \(0.272392\pi\) | |||||||
\(744\) | −2.91932 | −0.107028 | ||||||||
\(745\) | −0.657776 | −0.0240990 | ||||||||
\(746\) | 17.9312 | 0.656507 | ||||||||
\(747\) | −11.5050 | −0.420947 | ||||||||
\(748\) | 3.90821 | 0.142898 | ||||||||
\(749\) | −50.9060 | −1.86006 | ||||||||
\(750\) | −4.00715 | −0.146320 | ||||||||
\(751\) | −0.0439324 | −0.00160312 | −0.000801558 | − | 1.00000i | \(-0.500255\pi\) | ||||
−0.000801558 | 1.00000i | \(0.500255\pi\) | ||||||||
\(752\) | −4.59990 | −0.167741 | ||||||||
\(753\) | −2.69434 | −0.0981874 | ||||||||
\(754\) | 0.00743674 | 0.000270830 0 | ||||||||
\(755\) | −4.75204 | −0.172944 | ||||||||
\(756\) | 3.39127 | 0.123339 | ||||||||
\(757\) | 23.2903 | 0.846501 | 0.423250 | − | 0.906013i | \(-0.360889\pi\) | ||||
0.423250 | + | 0.906013i | \(0.360889\pi\) | |||||||
\(758\) | 3.60125 | 0.130803 | ||||||||
\(759\) | −4.09855 | −0.148768 | ||||||||
\(760\) | 1.71733 | 0.0622941 | ||||||||
\(761\) | −14.8136 | −0.536994 | −0.268497 | − | 0.963281i | \(-0.586527\pi\) | ||||
−0.268497 | + | 0.963281i | \(0.586527\pi\) | |||||||
\(762\) | 13.0092 | 0.471273 | ||||||||
\(763\) | −33.5312 | −1.21391 | ||||||||
\(764\) | −1.78577 | −0.0646069 | ||||||||
\(765\) | 1.59252 | 0.0575777 | ||||||||
\(766\) | 13.9835 | 0.505245 | ||||||||
\(767\) | 2.55708 | 0.0923310 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −25.8876 | −0.933532 | −0.466766 | − | 0.884381i | \(-0.654581\pi\) | ||||
−0.466766 | + | 0.884381i | \(0.654581\pi\) | |||||||
\(770\) | 1.38188 | 0.0497994 | ||||||||
\(771\) | 7.10517 | 0.255887 | ||||||||
\(772\) | 8.84397 | 0.318301 | ||||||||
\(773\) | −21.7017 | −0.780556 | −0.390278 | − | 0.920697i | \(-0.627621\pi\) | ||||
−0.390278 | + | 0.920697i | \(0.627621\pi\) | |||||||
\(774\) | −2.67207 | −0.0960456 | ||||||||
\(775\) | 14.1119 | 0.506914 | ||||||||
\(776\) | 6.20116 | 0.222609 | ||||||||
\(777\) | 22.0929 | 0.792578 | ||||||||
\(778\) | 8.68005 | 0.311195 | ||||||||
\(779\) | −34.8657 | −1.24919 | ||||||||
\(780\) | 0.0775596 | 0.00277708 | ||||||||
\(781\) | 1.56991 | 0.0561758 | ||||||||
\(782\) | −16.0180 | −0.572802 | ||||||||
\(783\) | −0.0390710 | −0.00139628 | ||||||||
\(784\) | 4.50073 | 0.160740 | ||||||||
\(785\) | −6.33551 | −0.226124 | ||||||||
\(786\) | −21.9677 | −0.783563 | ||||||||
\(787\) | −25.9523 | −0.925100 | −0.462550 | − | 0.886593i | \(-0.653065\pi\) | ||||
−0.462550 | + | 0.886593i | \(0.653065\pi\) | |||||||
\(788\) | 15.8207 | 0.563589 | ||||||||
\(789\) | 19.9870 | 0.711557 | ||||||||
\(790\) | −3.82254 | −0.136000 | ||||||||
\(791\) | 59.2758 | 2.10760 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −0.190339 | −0.00675915 | ||||||||
\(794\) | −4.05936 | −0.144061 | ||||||||
\(795\) | 1.11616 | 0.0395861 | ||||||||
\(796\) | 2.49048 | 0.0882727 | ||||||||
\(797\) | 3.96050 | 0.140288 | 0.0701441 | − | 0.997537i | \(-0.477654\pi\) | ||||
0.0701441 | + | 0.997537i | \(0.477654\pi\) | |||||||
\(798\) | 14.2925 | 0.505950 | ||||||||
\(799\) | −17.9774 | −0.635993 | ||||||||
\(800\) | 4.83396 | 0.170906 | ||||||||
\(801\) | −3.26264 | −0.115280 | ||||||||
\(802\) | −2.25650 | −0.0796799 | ||||||||
\(803\) | 11.6664 | 0.411698 | ||||||||
\(804\) | −8.45198 | −0.298078 | ||||||||
\(805\) | −5.66369 | −0.199619 | ||||||||
\(806\) | −0.555662 | −0.0195724 | ||||||||
\(807\) | −18.3489 | −0.645913 | ||||||||
\(808\) | 5.66027 | 0.199128 | ||||||||
\(809\) | 42.6688 | 1.50016 | 0.750078 | − | 0.661350i | \(-0.230016\pi\) | ||||
0.750078 | + | 0.661350i | \(0.230016\pi\) | |||||||
\(810\) | −0.407480 | −0.0143174 | ||||||||
\(811\) | −5.56902 | −0.195555 | −0.0977774 | − | 0.995208i | \(-0.531173\pi\) | ||||
−0.0977774 | + | 0.995208i | \(0.531173\pi\) | |||||||
\(812\) | −0.132500 | −0.00464985 | ||||||||
\(813\) | −7.27120 | −0.255012 | ||||||||
\(814\) | −6.51463 | −0.228338 | ||||||||
\(815\) | −1.77335 | −0.0621179 | ||||||||
\(816\) | −3.90821 | −0.136815 | ||||||||
\(817\) | −11.2615 | −0.393989 | ||||||||
\(818\) | 4.93027 | 0.172383 | ||||||||
\(819\) | 0.645493 | 0.0225553 | ||||||||
\(820\) | 3.37100 | 0.117720 | ||||||||
\(821\) | −6.78716 | −0.236873 | −0.118437 | − | 0.992962i | \(-0.537788\pi\) | ||||
−0.118437 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(822\) | 9.51622 | 0.331916 | ||||||||
\(823\) | −2.74207 | −0.0955827 | −0.0477913 | − | 0.998857i | \(-0.515218\pi\) | ||||
−0.0477913 | + | 0.998857i | \(0.515218\pi\) | |||||||
\(824\) | 11.6542 | 0.405995 | ||||||||
\(825\) | 4.83396 | 0.168297 | ||||||||
\(826\) | −45.5595 | −1.58522 | ||||||||
\(827\) | −49.4575 | −1.71980 | −0.859902 | − | 0.510459i | \(-0.829476\pi\) | ||||
−0.859902 | + | 0.510459i | \(0.829476\pi\) | |||||||
\(828\) | 4.09855 | 0.142434 | ||||||||
\(829\) | 32.3937 | 1.12508 | 0.562540 | − | 0.826770i | \(-0.309824\pi\) | ||||
0.562540 | + | 0.826770i | \(0.309824\pi\) | |||||||
\(830\) | 4.68807 | 0.162725 | ||||||||
\(831\) | 9.48724 | 0.329109 | ||||||||
\(832\) | −0.190339 | −0.00659883 | ||||||||
\(833\) | 17.5898 | 0.609451 | ||||||||
\(834\) | −8.06367 | −0.279222 | ||||||||
\(835\) | −4.51225 | −0.156153 | ||||||||
\(836\) | −4.21451 | −0.145762 | ||||||||
\(837\) | 2.91932 | 0.100907 | ||||||||
\(838\) | 1.40235 | 0.0484435 | ||||||||
\(839\) | 53.0397 | 1.83113 | 0.915567 | − | 0.402166i | \(-0.131742\pi\) | ||||
0.915567 | + | 0.402166i | \(0.131742\pi\) | |||||||
\(840\) | −1.38188 | −0.0476793 | ||||||||
\(841\) | −28.9985 | −0.999947 | ||||||||
\(842\) | 8.61008 | 0.296723 | ||||||||
\(843\) | 31.6176 | 1.08897 | ||||||||
\(844\) | 6.86376 | 0.236260 | ||||||||
\(845\) | −5.28248 | −0.181723 | ||||||||
\(846\) | 4.59990 | 0.158148 | ||||||||
\(847\) | −3.39127 | −0.116526 | ||||||||
\(848\) | −2.73918 | −0.0940637 | ||||||||
\(849\) | 20.9491 | 0.718973 | ||||||||
\(850\) | 18.8921 | 0.647995 | ||||||||
\(851\) | 26.7005 | 0.915283 | ||||||||
\(852\) | −1.56991 | −0.0537843 | ||||||||
\(853\) | 33.5046 | 1.14718 | 0.573588 | − | 0.819144i | \(-0.305551\pi\) | ||||
0.573588 | + | 0.819144i | \(0.305551\pi\) | |||||||
\(854\) | 3.39127 | 0.116047 | ||||||||
\(855\) | −1.71733 | −0.0587314 | ||||||||
\(856\) | −15.0109 | −0.513061 | ||||||||
\(857\) | 16.7805 | 0.573210 | 0.286605 | − | 0.958049i | \(-0.407473\pi\) | ||||
0.286605 | + | 0.958049i | \(0.407473\pi\) | |||||||
\(858\) | −0.190339 | −0.00649808 | ||||||||
\(859\) | −22.2763 | −0.760057 | −0.380029 | − | 0.924975i | \(-0.624086\pi\) | ||||
−0.380029 | + | 0.924975i | \(0.624086\pi\) | |||||||
\(860\) | 1.08882 | 0.0371283 | ||||||||
\(861\) | 28.0553 | 0.956120 | ||||||||
\(862\) | 35.2866 | 1.20187 | ||||||||
\(863\) | 36.0948 | 1.22868 | 0.614341 | − | 0.789041i | \(-0.289422\pi\) | ||||
0.614341 | + | 0.789041i | \(0.289422\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.19712 | 0.0407032 | ||||||||
\(866\) | 0.934742 | 0.0317638 | ||||||||
\(867\) | 1.72589 | 0.0586143 | ||||||||
\(868\) | 9.90022 | 0.336035 | ||||||||
\(869\) | 9.38091 | 0.318225 | ||||||||
\(870\) | 0.0159206 | 0.000539761 0 | ||||||||
\(871\) | −1.60874 | −0.0545102 | ||||||||
\(872\) | −9.88750 | −0.334833 | ||||||||
\(873\) | −6.20116 | −0.209878 | ||||||||
\(874\) | 17.2734 | 0.584280 | ||||||||
\(875\) | 13.5893 | 0.459403 | ||||||||
\(876\) | −11.6664 | −0.394171 | ||||||||
\(877\) | −0.184201 | −0.00622003 | −0.00311001 | − | 0.999995i | \(-0.500990\pi\) | ||||
−0.00311001 | + | 0.999995i | \(0.500990\pi\) | |||||||
\(878\) | −0.742524 | −0.0250590 | ||||||||
\(879\) | 18.7636 | 0.632881 | ||||||||
\(880\) | 0.407480 | 0.0137362 | ||||||||
\(881\) | −37.7832 | −1.27295 | −0.636474 | − | 0.771298i | \(-0.719608\pi\) | ||||
−0.636474 | + | 0.771298i | \(0.719608\pi\) | |||||||
\(882\) | −4.50073 | −0.151547 | ||||||||
\(883\) | −40.5121 | −1.36334 | −0.681671 | − | 0.731659i | \(-0.738746\pi\) | ||||
−0.681671 | + | 0.731659i | \(0.738746\pi\) | |||||||
\(884\) | −0.743887 | −0.0250196 | ||||||||
\(885\) | 5.47423 | 0.184014 | ||||||||
\(886\) | 22.5191 | 0.756543 | ||||||||
\(887\) | −12.4836 | −0.419158 | −0.209579 | − | 0.977792i | \(-0.567209\pi\) | ||||
−0.209579 | + | 0.977792i | \(0.567209\pi\) | |||||||
\(888\) | 6.51463 | 0.218617 | ||||||||
\(889\) | −44.1177 | −1.47966 | ||||||||
\(890\) | 1.32946 | 0.0445637 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0.569295 | 0.0190614 | ||||||||
\(893\) | 19.3863 | 0.648738 | ||||||||
\(894\) | −1.61425 | −0.0539886 | ||||||||
\(895\) | 0.275127 | 0.00919648 | ||||||||
\(896\) | 3.39127 | 0.113294 | ||||||||
\(897\) | 0.780116 | 0.0260473 | ||||||||
\(898\) | 30.8487 | 1.02943 | ||||||||
\(899\) | −0.114061 | −0.00380414 | ||||||||
\(900\) | −4.83396 | −0.161132 | ||||||||
\(901\) | −10.7053 | −0.356644 | ||||||||
\(902\) | −8.27278 | −0.275453 | ||||||||
\(903\) | 9.06172 | 0.301555 | ||||||||
\(904\) | 17.4789 | 0.581340 | ||||||||
\(905\) | −7.98803 | −0.265531 | ||||||||
\(906\) | −11.6620 | −0.387444 | ||||||||
\(907\) | 31.8018 | 1.05596 | 0.527980 | − | 0.849257i | \(-0.322949\pi\) | ||||
0.527980 | + | 0.849257i | \(0.322949\pi\) | |||||||
\(908\) | 10.8386 | 0.359691 | ||||||||
\(909\) | −5.66027 | −0.187739 | ||||||||
\(910\) | −0.263026 | −0.00871922 | ||||||||
\(911\) | 43.8225 | 1.45190 | 0.725952 | − | 0.687745i | \(-0.241399\pi\) | ||||
0.725952 | + | 0.687745i | \(0.241399\pi\) | |||||||
\(912\) | 4.21451 | 0.139556 | ||||||||
\(913\) | −11.5050 | −0.380761 | ||||||||
\(914\) | −11.1117 | −0.367544 | ||||||||
\(915\) | −0.407480 | −0.0134709 | ||||||||
\(916\) | −20.1015 | −0.664171 | ||||||||
\(917\) | 74.4986 | 2.46016 | ||||||||
\(918\) | 3.90821 | 0.128990 | ||||||||
\(919\) | 38.8641 | 1.28201 | 0.641004 | − | 0.767537i | \(-0.278518\pi\) | ||||
0.641004 | + | 0.767537i | \(0.278518\pi\) | |||||||
\(920\) | −1.67008 | −0.0550609 | ||||||||
\(921\) | 12.8926 | 0.424825 | ||||||||
\(922\) | 1.71664 | 0.0565346 | ||||||||
\(923\) | −0.298816 | −0.00983565 | ||||||||
\(924\) | 3.39127 | 0.111565 | ||||||||
\(925\) | −31.4915 | −1.03543 | ||||||||
\(926\) | −18.7085 | −0.614800 | ||||||||
\(927\) | −11.6542 | −0.382776 | ||||||||
\(928\) | −0.0390710 | −0.00128257 | ||||||||
\(929\) | 47.7171 | 1.56555 | 0.782774 | − | 0.622306i | \(-0.213804\pi\) | ||||
0.782774 | + | 0.622306i | \(0.213804\pi\) | |||||||
\(930\) | −1.18957 | −0.0390074 | ||||||||
\(931\) | −18.9684 | −0.621663 | ||||||||
\(932\) | −1.73528 | −0.0568409 | ||||||||
\(933\) | 26.0626 | 0.853253 | ||||||||
\(934\) | 15.4734 | 0.506305 | ||||||||
\(935\) | 1.59252 | 0.0520810 | ||||||||
\(936\) | 0.190339 | 0.00622144 | ||||||||
\(937\) | 37.2358 | 1.21644 | 0.608220 | − | 0.793769i | \(-0.291884\pi\) | ||||
0.608220 | + | 0.793769i | \(0.291884\pi\) | |||||||
\(938\) | 28.6630 | 0.935879 | ||||||||
\(939\) | 9.41313 | 0.307186 | ||||||||
\(940\) | −1.87437 | −0.0611351 | ||||||||
\(941\) | −19.9915 | −0.651704 | −0.325852 | − | 0.945421i | \(-0.605651\pi\) | ||||
−0.325852 | + | 0.945421i | \(0.605651\pi\) | |||||||
\(942\) | −15.5480 | −0.506582 | ||||||||
\(943\) | 33.9064 | 1.10414 | ||||||||
\(944\) | −13.4343 | −0.437251 | ||||||||
\(945\) | 1.38188 | 0.0449525 | ||||||||
\(946\) | −2.67207 | −0.0868765 | ||||||||
\(947\) | −10.9948 | −0.357283 | −0.178642 | − | 0.983914i | \(-0.557170\pi\) | ||||
−0.178642 | + | 0.983914i | \(0.557170\pi\) | |||||||
\(948\) | −9.38091 | −0.304678 | ||||||||
\(949\) | −2.22057 | −0.0720828 | ||||||||
\(950\) | −20.3728 | −0.660979 | ||||||||
\(951\) | −8.50811 | −0.275894 | ||||||||
\(952\) | 13.2538 | 0.429558 | ||||||||
\(953\) | 30.4978 | 0.987920 | 0.493960 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493960 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(954\) | 2.73918 | 0.0886841 | ||||||||
\(955\) | −0.727666 | −0.0235467 | ||||||||
\(956\) | −4.90179 | −0.158535 | ||||||||
\(957\) | −0.0390710 | −0.00126298 | ||||||||
\(958\) | −6.51343 | −0.210439 | ||||||||
\(959\) | −32.2721 | −1.04212 | ||||||||
\(960\) | −0.407480 | −0.0131514 | ||||||||
\(961\) | −22.4776 | −0.725083 | ||||||||
\(962\) | 1.23999 | 0.0399789 | ||||||||
\(963\) | 15.0109 | 0.483719 | ||||||||
\(964\) | 29.1570 | 0.939084 | ||||||||
\(965\) | 3.60375 | 0.116009 | ||||||||
\(966\) | −13.8993 | −0.447203 | ||||||||
\(967\) | 16.1826 | 0.520396 | 0.260198 | − | 0.965555i | \(-0.416212\pi\) | ||||
0.260198 | + | 0.965555i | \(0.416212\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 16.4712 | 0.529131 | ||||||||
\(970\) | 2.52685 | 0.0811324 | ||||||||
\(971\) | −3.85576 | −0.123737 | −0.0618687 | − | 0.998084i | \(-0.519706\pi\) | ||||
−0.0618687 | + | 0.998084i | \(0.519706\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 27.3461 | 0.876676 | ||||||||
\(974\) | 16.7789 | 0.537630 | ||||||||
\(975\) | −0.920093 | −0.0294666 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | 40.7503 | 1.30372 | 0.651860 | − | 0.758340i | \(-0.273989\pi\) | ||||
0.651860 | + | 0.758340i | \(0.273989\pi\) | |||||||
\(978\) | −4.35200 | −0.139162 | ||||||||
\(979\) | −3.26264 | −0.104274 | ||||||||
\(980\) | 1.83396 | 0.0585837 | ||||||||
\(981\) | 9.88750 | 0.315683 | ||||||||
\(982\) | 21.5232 | 0.686833 | ||||||||
\(983\) | 34.8851 | 1.11266 | 0.556331 | − | 0.830960i | \(-0.312209\pi\) | ||||
0.556331 | + | 0.830960i | \(0.312209\pi\) | |||||||
\(984\) | 8.27278 | 0.263727 | ||||||||
\(985\) | 6.44662 | 0.205407 | ||||||||
\(986\) | −0.152698 | −0.00486288 | ||||||||
\(987\) | −15.5995 | −0.496538 | ||||||||
\(988\) | 0.802187 | 0.0255210 | ||||||||
\(989\) | 10.9516 | 0.348241 | ||||||||
\(990\) | −0.407480 | −0.0129506 | ||||||||
\(991\) | −12.8931 | −0.409564 | −0.204782 | − | 0.978808i | \(-0.565649\pi\) | ||||
−0.204782 | + | 0.978808i | \(0.565649\pi\) | |||||||
\(992\) | 2.91932 | 0.0926886 | ||||||||
\(993\) | 34.5824 | 1.09744 | ||||||||
\(994\) | 5.32400 | 0.168867 | ||||||||
\(995\) | 1.01482 | 0.0321720 | ||||||||
\(996\) | 11.5050 | 0.364551 | ||||||||
\(997\) | −58.4476 | −1.85105 | −0.925527 | − | 0.378682i | \(-0.876377\pi\) | ||||
−0.925527 | + | 0.378682i | \(0.876377\pi\) | |||||||
\(998\) | −20.7732 | −0.657564 | ||||||||
\(999\) | −6.51463 | −0.206114 |
(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 | 4026.2.a.w.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.w.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial |