Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.23864\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23864 | −1.58296 | −0.791478 | − | 0.611197i | \(-0.790688\pi\) | ||||
−0.791478 | + | 0.611197i | \(0.790688\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.01150 | 1.50575 | ||||||||
\(5\) | 2.46287 | 1.10143 | 0.550715 | − | 0.834693i | \(-0.314355\pi\) | ||||
0.550715 | + | 0.834693i | \(0.314355\pi\) | |||||||
\(6\) | −2.23864 | −0.913920 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.26439 | −0.800582 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.51348 | −1.74352 | ||||||||
\(11\) | 3.07123 | 0.926009 | 0.463005 | − | 0.886356i | \(-0.346771\pi\) | ||||
0.463005 | + | 0.886356i | \(0.346771\pi\) | |||||||
\(12\) | 3.01150 | 0.869346 | ||||||||
\(13\) | 3.08168 | 0.854705 | 0.427353 | − | 0.904085i | \(-0.359446\pi\) | ||||
0.427353 | + | 0.904085i | \(0.359446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.46287 | 0.635911 | ||||||||
\(16\) | −0.953860 | −0.238465 | ||||||||
\(17\) | −3.92563 | −0.952106 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(18\) | −2.23864 | −0.527652 | ||||||||
\(19\) | 2.23891 | 0.513642 | 0.256821 | − | 0.966459i | \(-0.417325\pi\) | ||||
0.256821 | + | 0.966459i | \(0.417325\pi\) | |||||||
\(20\) | 7.41695 | 1.65848 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.87536 | −1.46583 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −2.26439 | −0.462216 | ||||||||
\(25\) | 1.06575 | 0.213149 | ||||||||
\(26\) | −6.89878 | −1.35296 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.31559 | 0.801385 | 0.400693 | − | 0.916213i | \(-0.368770\pi\) | ||||
0.400693 | + | 0.916213i | \(0.368770\pi\) | |||||||
\(30\) | −5.51348 | −1.00662 | ||||||||
\(31\) | 3.47943 | 0.624925 | 0.312462 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312462 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(32\) | 6.66412 | 1.17806 | ||||||||
\(33\) | 3.07123 | 0.534632 | ||||||||
\(34\) | 8.78808 | 1.50714 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.01150 | 0.501917 | ||||||||
\(37\) | −3.10069 | −0.509751 | −0.254875 | − | 0.966974i | \(-0.582034\pi\) | ||||
−0.254875 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(38\) | −5.01212 | −0.813073 | ||||||||
\(39\) | 3.08168 | 0.493464 | ||||||||
\(40\) | −5.57690 | −0.881785 | ||||||||
\(41\) | 8.45567 | 1.32055 | 0.660277 | − | 0.751022i | \(-0.270439\pi\) | ||||
0.660277 | + | 0.751022i | \(0.270439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.01191 | −0.459312 | −0.229656 | − | 0.973272i | \(-0.573760\pi\) | ||||
−0.229656 | + | 0.973272i | \(0.573760\pi\) | |||||||
\(44\) | 9.24900 | 1.39434 | ||||||||
\(45\) | 2.46287 | 0.367144 | ||||||||
\(46\) | 2.23864 | 0.330069 | ||||||||
\(47\) | −9.63365 | −1.40521 | −0.702606 | − | 0.711579i | \(-0.747980\pi\) | ||||
−0.702606 | + | 0.711579i | \(0.747980\pi\) | |||||||
\(48\) | −0.953860 | −0.137678 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.38582 | −0.337406 | ||||||||
\(51\) | −3.92563 | −0.549699 | ||||||||
\(52\) | 9.28050 | 1.28697 | ||||||||
\(53\) | 3.32711 | 0.457014 | 0.228507 | − | 0.973542i | \(-0.426616\pi\) | ||||
0.228507 | + | 0.973542i | \(0.426616\pi\) | |||||||
\(54\) | −2.23864 | −0.304640 | ||||||||
\(55\) | 7.56404 | 1.01993 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.23891 | 0.296551 | ||||||||
\(58\) | −9.66105 | −1.26856 | ||||||||
\(59\) | 7.60292 | 0.989816 | 0.494908 | − | 0.868945i | \(-0.335202\pi\) | ||||
0.494908 | + | 0.868945i | \(0.335202\pi\) | |||||||
\(60\) | 7.41695 | 0.957524 | ||||||||
\(61\) | −1.60304 | −0.205249 | −0.102624 | − | 0.994720i | \(-0.532724\pi\) | ||||
−0.102624 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(62\) | −7.78919 | −0.989229 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0108 | −1.62635 | ||||||||
\(65\) | 7.58980 | 0.941398 | ||||||||
\(66\) | −6.87536 | −0.846299 | ||||||||
\(67\) | 13.7403 | 1.67865 | 0.839325 | − | 0.543631i | \(-0.182951\pi\) | ||||
0.839325 | + | 0.543631i | \(0.182951\pi\) | |||||||
\(68\) | −11.8221 | −1.43363 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7392 | 1.27451 | 0.637256 | − | 0.770652i | \(-0.280070\pi\) | ||||
0.637256 | + | 0.770652i | \(0.280070\pi\) | |||||||
\(72\) | −2.26439 | −0.266861 | ||||||||
\(73\) | −5.47869 | −0.641232 | −0.320616 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320616 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(74\) | 6.94133 | 0.806913 | ||||||||
\(75\) | 1.06575 | 0.123062 | ||||||||
\(76\) | 6.74249 | 0.773417 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.89878 | −0.781132 | ||||||||
\(79\) | −9.72680 | −1.09435 | −0.547175 | − | 0.837018i | \(-0.684297\pi\) | ||||
−0.547175 | + | 0.837018i | \(0.684297\pi\) | |||||||
\(80\) | −2.34924 | −0.262653 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −18.9292 | −2.09038 | ||||||||
\(83\) | −2.34134 | −0.256995 | −0.128498 | − | 0.991710i | \(-0.541015\pi\) | ||||
−0.128498 | + | 0.991710i | \(0.541015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.66834 | −1.04868 | ||||||||
\(86\) | 6.74257 | 0.727070 | ||||||||
\(87\) | 4.31559 | 0.462680 | ||||||||
\(88\) | −6.95444 | −0.741346 | ||||||||
\(89\) | 5.01990 | 0.532108 | 0.266054 | − | 0.963958i | \(-0.414280\pi\) | ||||
0.266054 | + | 0.963958i | \(0.414280\pi\) | |||||||
\(90\) | −5.51348 | −0.581172 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.01150 | −0.313971 | ||||||||
\(93\) | 3.47943 | 0.360800 | ||||||||
\(94\) | 21.5662 | 2.22439 | ||||||||
\(95\) | 5.51416 | 0.565741 | ||||||||
\(96\) | 6.66412 | 0.680154 | ||||||||
\(97\) | 5.86596 | 0.595598 | 0.297799 | − | 0.954629i | \(-0.403747\pi\) | ||||
0.297799 | + | 0.954629i | \(0.403747\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.07123 | 0.308670 | ||||||||
\(100\) | 3.20950 | 0.320950 | ||||||||
\(101\) | 0.968892 | 0.0964084 | 0.0482042 | − | 0.998838i | \(-0.484650\pi\) | ||||
0.0482042 | + | 0.998838i | \(0.484650\pi\) | |||||||
\(102\) | 8.78808 | 0.870149 | ||||||||
\(103\) | −6.40172 | −0.630781 | −0.315390 | − | 0.948962i | \(-0.602135\pi\) | ||||
−0.315390 | + | 0.948962i | \(0.602135\pi\) | |||||||
\(104\) | −6.97812 | −0.684261 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.44820 | −0.723434 | ||||||||
\(107\) | 16.1158 | 1.55798 | 0.778988 | − | 0.627039i | \(-0.215733\pi\) | ||||
0.778988 | + | 0.627039i | \(0.215733\pi\) | |||||||
\(108\) | 3.01150 | 0.289782 | ||||||||
\(109\) | 6.45532 | 0.618308 | 0.309154 | − | 0.951012i | \(-0.399954\pi\) | ||||
0.309154 | + | 0.951012i | \(0.399954\pi\) | |||||||
\(110\) | −16.9332 | −1.61451 | ||||||||
\(111\) | −3.10069 | −0.294305 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.50261 | 0.799858 | 0.399929 | − | 0.916546i | \(-0.369035\pi\) | ||||
0.399929 | + | 0.916546i | \(0.369035\pi\) | |||||||
\(114\) | −5.01212 | −0.469428 | ||||||||
\(115\) | −2.46287 | −0.229664 | ||||||||
\(116\) | 12.9964 | 1.20669 | ||||||||
\(117\) | 3.08168 | 0.284902 | ||||||||
\(118\) | −17.0202 | −1.56684 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.57690 | −0.509099 | ||||||||
\(121\) | −1.56757 | −0.142507 | ||||||||
\(122\) | 3.58863 | 0.324900 | ||||||||
\(123\) | 8.45567 | 0.762422 | ||||||||
\(124\) | 10.4783 | 0.940981 | ||||||||
\(125\) | −9.68957 | −0.866661 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.69548 | −0.860334 | −0.430167 | − | 0.902749i | \(-0.641545\pi\) | ||||
−0.430167 | + | 0.902749i | \(0.641545\pi\) | |||||||
\(128\) | 15.7983 | 1.39639 | ||||||||
\(129\) | −3.01191 | −0.265184 | ||||||||
\(130\) | −16.9908 | −1.49019 | ||||||||
\(131\) | 18.2934 | 1.59830 | 0.799150 | − | 0.601132i | \(-0.205283\pi\) | ||||
0.799150 | + | 0.601132i | \(0.205283\pi\) | |||||||
\(132\) | 9.24900 | 0.805022 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −30.7596 | −2.65723 | ||||||||
\(135\) | 2.46287 | 0.211970 | ||||||||
\(136\) | 8.88916 | 0.762239 | ||||||||
\(137\) | 4.69464 | 0.401090 | 0.200545 | − | 0.979685i | \(-0.435729\pi\) | ||||
0.200545 | + | 0.979685i | \(0.435729\pi\) | |||||||
\(138\) | 2.23864 | 0.190566 | ||||||||
\(139\) | −9.69649 | −0.822446 | −0.411223 | − | 0.911535i | \(-0.634898\pi\) | ||||
−0.411223 | + | 0.911535i | \(0.634898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.63365 | −0.811299 | ||||||||
\(142\) | −24.0412 | −2.01750 | ||||||||
\(143\) | 9.46454 | 0.791465 | ||||||||
\(144\) | −0.953860 | −0.0794883 | ||||||||
\(145\) | 10.6288 | 0.882670 | ||||||||
\(146\) | 12.2648 | 1.01504 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.33774 | −0.767558 | ||||||||
\(149\) | −10.3636 | −0.849017 | −0.424509 | − | 0.905424i | \(-0.639553\pi\) | ||||
−0.424509 | + | 0.905424i | \(0.639553\pi\) | |||||||
\(150\) | −2.38582 | −0.194802 | ||||||||
\(151\) | 10.8567 | 0.883503 | 0.441752 | − | 0.897137i | \(-0.354357\pi\) | ||||
0.441752 | + | 0.897137i | \(0.354357\pi\) | |||||||
\(152\) | −5.06976 | −0.411212 | ||||||||
\(153\) | −3.92563 | −0.317369 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.56941 | 0.688311 | ||||||||
\(156\) | 9.28050 | 0.743034 | ||||||||
\(157\) | −2.52233 | −0.201304 | −0.100652 | − | 0.994922i | \(-0.532093\pi\) | ||||
−0.100652 | + | 0.994922i | \(0.532093\pi\) | |||||||
\(158\) | 21.7748 | 1.73231 | ||||||||
\(159\) | 3.32711 | 0.263857 | ||||||||
\(160\) | 16.4129 | 1.29755 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.23864 | −0.175884 | ||||||||
\(163\) | −14.4762 | −1.13386 | −0.566932 | − | 0.823765i | \(-0.691870\pi\) | ||||
−0.566932 | + | 0.823765i | \(0.691870\pi\) | |||||||
\(164\) | 25.4643 | 1.98842 | ||||||||
\(165\) | 7.56404 | 0.588860 | ||||||||
\(166\) | 5.24141 | 0.406812 | ||||||||
\(167\) | 15.6448 | 1.21063 | 0.605314 | − | 0.795987i | \(-0.293047\pi\) | ||||
0.605314 | + | 0.795987i | \(0.293047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.50323 | −0.269479 | ||||||||
\(170\) | 21.6439 | 1.66001 | ||||||||
\(171\) | 2.23891 | 0.171214 | ||||||||
\(172\) | −9.07037 | −0.691609 | ||||||||
\(173\) | −21.9908 | −1.67193 | −0.835963 | − | 0.548785i | \(-0.815091\pi\) | ||||
−0.835963 | + | 0.548785i | \(0.815091\pi\) | |||||||
\(174\) | −9.66105 | −0.732402 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.92952 | −0.220821 | ||||||||
\(177\) | 7.60292 | 0.571471 | ||||||||
\(178\) | −11.2377 | −0.842304 | ||||||||
\(179\) | −18.7258 | −1.39963 | −0.699815 | − | 0.714324i | \(-0.746734\pi\) | ||||
−0.699815 | + | 0.714324i | \(0.746734\pi\) | |||||||
\(180\) | 7.41695 | 0.552827 | ||||||||
\(181\) | −4.88885 | −0.363386 | −0.181693 | − | 0.983355i | \(-0.558158\pi\) | ||||
−0.181693 | + | 0.983355i | \(0.558158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.60304 | −0.118500 | ||||||||
\(184\) | 2.26439 | 0.166933 | ||||||||
\(185\) | −7.63661 | −0.561455 | ||||||||
\(186\) | −7.78919 | −0.571131 | ||||||||
\(187\) | −12.0565 | −0.881659 | ||||||||
\(188\) | −29.0117 | −2.11590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.3442 | −0.895543 | ||||||||
\(191\) | −13.3658 | −0.967118 | −0.483559 | − | 0.875312i | \(-0.660656\pi\) | ||||
−0.483559 | + | 0.875312i | \(0.660656\pi\) | |||||||
\(192\) | −13.0108 | −0.938976 | ||||||||
\(193\) | −11.0215 | −0.793344 | −0.396672 | − | 0.917960i | \(-0.629835\pi\) | ||||
−0.396672 | + | 0.917960i | \(0.629835\pi\) | |||||||
\(194\) | −13.1318 | −0.942806 | ||||||||
\(195\) | 7.58980 | 0.543517 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6336 | 1.18510 | 0.592549 | − | 0.805535i | \(-0.298122\pi\) | ||||
0.592549 | + | 0.805535i | \(0.298122\pi\) | |||||||
\(198\) | −6.87536 | −0.488611 | ||||||||
\(199\) | −14.7498 | −1.04559 | −0.522794 | − | 0.852459i | \(-0.675110\pi\) | ||||
−0.522794 | + | 0.852459i | \(0.675110\pi\) | |||||||
\(200\) | −2.41326 | −0.170644 | ||||||||
\(201\) | 13.7403 | 0.969169 | ||||||||
\(202\) | −2.16900 | −0.152610 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.8221 | −0.827709 | ||||||||
\(205\) | 20.8252 | 1.45450 | ||||||||
\(206\) | 14.3311 | 0.998498 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −2.93949 | −0.203817 | ||||||||
\(209\) | 6.87620 | 0.475637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.38157 | 0.508168 | 0.254084 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254084 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(212\) | 10.0196 | 0.688150 | ||||||||
\(213\) | 10.7392 | 0.735839 | ||||||||
\(214\) | −36.0775 | −2.46621 | ||||||||
\(215\) | −7.41795 | −0.505900 | ||||||||
\(216\) | −2.26439 | −0.154072 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.4511 | −0.978754 | ||||||||
\(219\) | −5.47869 | −0.370216 | ||||||||
\(220\) | 22.7791 | 1.53577 | ||||||||
\(221\) | −12.0976 | −0.813770 | ||||||||
\(222\) | 6.94133 | 0.465872 | ||||||||
\(223\) | −25.6512 | −1.71773 | −0.858865 | − | 0.512202i | \(-0.828830\pi\) | ||||
−0.858865 | + | 0.512202i | \(0.828830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.06575 | 0.0710498 | ||||||||
\(226\) | −19.0343 | −1.26614 | ||||||||
\(227\) | 9.34980 | 0.620568 | 0.310284 | − | 0.950644i | \(-0.399576\pi\) | ||||
0.310284 | + | 0.950644i | \(0.399576\pi\) | |||||||
\(228\) | 6.74249 | 0.446532 | ||||||||
\(229\) | 18.0873 | 1.19524 | 0.597621 | − | 0.801779i | \(-0.296113\pi\) | ||||
0.597621 | + | 0.801779i | \(0.296113\pi\) | |||||||
\(230\) | 5.51348 | 0.363548 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.77217 | −0.641574 | ||||||||
\(233\) | −17.8642 | −1.17033 | −0.585163 | − | 0.810916i | \(-0.698969\pi\) | ||||
−0.585163 | + | 0.810916i | \(0.698969\pi\) | |||||||
\(234\) | −6.89878 | −0.450987 | ||||||||
\(235\) | −23.7265 | −1.54774 | ||||||||
\(236\) | 22.8962 | 1.49042 | ||||||||
\(237\) | −9.72680 | −0.631823 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.3433 | 0.992475 | 0.496237 | − | 0.868187i | \(-0.334715\pi\) | ||||
0.496237 | + | 0.868187i | \(0.334715\pi\) | |||||||
\(240\) | −2.34924 | −0.151643 | ||||||||
\(241\) | −3.96319 | −0.255292 | −0.127646 | − | 0.991820i | \(-0.540742\pi\) | ||||
−0.127646 | + | 0.991820i | \(0.540742\pi\) | |||||||
\(242\) | 3.50923 | 0.225582 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.82757 | −0.309053 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.9292 | −1.20688 | ||||||||
\(247\) | 6.89962 | 0.439012 | ||||||||
\(248\) | −7.87879 | −0.500303 | ||||||||
\(249\) | −2.34134 | −0.148376 | ||||||||
\(250\) | 21.6914 | 1.37189 | ||||||||
\(251\) | −5.68753 | −0.358994 | −0.179497 | − | 0.983759i | \(-0.557447\pi\) | ||||
−0.179497 | + | 0.983759i | \(0.557447\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.07123 | −0.193086 | ||||||||
\(254\) | 21.7047 | 1.36187 | ||||||||
\(255\) | −9.66834 | −0.605455 | ||||||||
\(256\) | −9.34505 | −0.584066 | ||||||||
\(257\) | −12.2060 | −0.761387 | −0.380693 | − | 0.924701i | \(-0.624315\pi\) | ||||
−0.380693 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(258\) | 6.74257 | 0.419774 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22.8567 | 1.41751 | ||||||||
\(261\) | 4.31559 | 0.267128 | ||||||||
\(262\) | −40.9522 | −2.53004 | ||||||||
\(263\) | −10.6450 | −0.656397 | −0.328199 | − | 0.944609i | \(-0.606442\pi\) | ||||
−0.328199 | + | 0.944609i | \(0.606442\pi\) | |||||||
\(264\) | −6.95444 | −0.428016 | ||||||||
\(265\) | 8.19426 | 0.503369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.01990 | 0.307213 | ||||||||
\(268\) | 41.3790 | 2.52763 | ||||||||
\(269\) | 24.8992 | 1.51813 | 0.759066 | − | 0.651014i | \(-0.225656\pi\) | ||||
0.759066 | + | 0.651014i | \(0.225656\pi\) | |||||||
\(270\) | −5.51348 | −0.335540 | ||||||||
\(271\) | −6.57668 | −0.399505 | −0.199752 | − | 0.979846i | \(-0.564014\pi\) | ||||
−0.199752 | + | 0.979846i | \(0.564014\pi\) | |||||||
\(272\) | 3.74451 | 0.227044 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.5096 | −0.634908 | ||||||||
\(275\) | 3.27315 | 0.197378 | ||||||||
\(276\) | −3.01150 | −0.181271 | ||||||||
\(277\) | −23.2474 | −1.39680 | −0.698400 | − | 0.715708i | \(-0.746104\pi\) | ||||
−0.698400 | + | 0.715708i | \(0.746104\pi\) | |||||||
\(278\) | 21.7069 | 1.30190 | ||||||||
\(279\) | 3.47943 | 0.208308 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7437 | 0.640913 | 0.320456 | − | 0.947263i | \(-0.396164\pi\) | ||||
0.320456 | + | 0.947263i | \(0.396164\pi\) | |||||||
\(282\) | 21.5662 | 1.28425 | ||||||||
\(283\) | 24.5170 | 1.45739 | 0.728694 | − | 0.684840i | \(-0.240128\pi\) | ||||
0.728694 | + | 0.684840i | \(0.240128\pi\) | |||||||
\(284\) | 32.3412 | 1.91910 | ||||||||
\(285\) | 5.51416 | 0.326631 | ||||||||
\(286\) | −21.1877 | −1.25285 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.66412 | 0.392687 | ||||||||
\(289\) | −1.58939 | −0.0934937 | ||||||||
\(290\) | −23.7939 | −1.39723 | ||||||||
\(291\) | 5.86596 | 0.343869 | ||||||||
\(292\) | −16.4991 | −0.965536 | ||||||||
\(293\) | 33.2732 | 1.94384 | 0.971920 | − | 0.235311i | \(-0.0756108\pi\) | ||||
0.971920 | + | 0.235311i | \(0.0756108\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.7250 | 1.09021 | ||||||||
\(296\) | 7.02117 | 0.408097 | ||||||||
\(297\) | 3.07123 | 0.178211 | ||||||||
\(298\) | 23.2003 | 1.34396 | ||||||||
\(299\) | −3.08168 | −0.178218 | ||||||||
\(300\) | 3.20950 | 0.185301 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −24.3042 | −1.39855 | ||||||||
\(303\) | 0.968892 | 0.0556614 | ||||||||
\(304\) | −2.13561 | −0.122486 | ||||||||
\(305\) | −3.94809 | −0.226067 | ||||||||
\(306\) | 8.78808 | 0.502381 | ||||||||
\(307\) | 20.2345 | 1.15485 | 0.577423 | − | 0.816445i | \(-0.304058\pi\) | ||||
0.577423 | + | 0.816445i | \(0.304058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.40172 | −0.364181 | ||||||||
\(310\) | −19.1838 | −1.08957 | ||||||||
\(311\) | 22.8603 | 1.29629 | 0.648145 | − | 0.761517i | \(-0.275545\pi\) | ||||
0.648145 | + | 0.761517i | \(0.275545\pi\) | |||||||
\(312\) | −6.97812 | −0.395059 | ||||||||
\(313\) | 23.6714 | 1.33798 | 0.668992 | − | 0.743269i | \(-0.266726\pi\) | ||||
0.668992 | + | 0.743269i | \(0.266726\pi\) | |||||||
\(314\) | 5.64659 | 0.318655 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.2923 | −1.64782 | ||||||||
\(317\) | 12.4283 | 0.698041 | 0.349021 | − | 0.937115i | \(-0.386514\pi\) | ||||
0.349021 | + | 0.937115i | \(0.386514\pi\) | |||||||
\(318\) | −7.44820 | −0.417675 | ||||||||
\(319\) | 13.2542 | 0.742090 | ||||||||
\(320\) | −32.0441 | −1.79132 | ||||||||
\(321\) | 16.1158 | 0.899497 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.78915 | −0.489042 | ||||||||
\(324\) | 3.01150 | 0.167306 | ||||||||
\(325\) | 3.28429 | 0.182180 | ||||||||
\(326\) | 32.4070 | 1.79486 | ||||||||
\(327\) | 6.45532 | 0.356980 | ||||||||
\(328\) | −19.1469 | −1.05721 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.9332 | −0.932139 | ||||||||
\(331\) | −7.30561 | −0.401553 | −0.200776 | − | 0.979637i | \(-0.564346\pi\) | ||||
−0.200776 | + | 0.979637i | \(0.564346\pi\) | |||||||
\(332\) | −7.05094 | −0.386971 | ||||||||
\(333\) | −3.10069 | −0.169917 | ||||||||
\(334\) | −35.0230 | −1.91637 | ||||||||
\(335\) | 33.8407 | 1.84892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.1798 | 1.69847 | 0.849235 | − | 0.528015i | \(-0.177063\pi\) | ||||
0.849235 | + | 0.528015i | \(0.177063\pi\) | |||||||
\(338\) | 7.84246 | 0.426574 | ||||||||
\(339\) | 8.50261 | 0.461798 | ||||||||
\(340\) | −29.1162 | −1.57905 | ||||||||
\(341\) | 10.6861 | 0.578686 | ||||||||
\(342\) | −5.01212 | −0.271024 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.82013 | 0.367717 | ||||||||
\(345\) | −2.46287 | −0.132597 | ||||||||
\(346\) | 49.2294 | 2.64659 | ||||||||
\(347\) | −6.98372 | −0.374906 | −0.187453 | − | 0.982274i | \(-0.560023\pi\) | ||||
−0.187453 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(348\) | 12.9964 | 0.696681 | ||||||||
\(349\) | 12.5064 | 0.669454 | 0.334727 | − | 0.942315i | \(-0.391356\pi\) | ||||
0.334727 | + | 0.942315i | \(0.391356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.08168 | 0.164488 | ||||||||
\(352\) | 20.4670 | 1.09090 | ||||||||
\(353\) | −19.9458 | −1.06161 | −0.530803 | − | 0.847495i | \(-0.678110\pi\) | ||||
−0.530803 | + | 0.847495i | \(0.678110\pi\) | |||||||
\(354\) | −17.0202 | −0.904613 | ||||||||
\(355\) | 26.4494 | 1.40379 | ||||||||
\(356\) | 15.1174 | 0.801222 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 41.9203 | 2.21555 | ||||||||
\(359\) | 31.2088 | 1.64714 | 0.823570 | − | 0.567215i | \(-0.191979\pi\) | ||||
0.823570 | + | 0.567215i | \(0.191979\pi\) | |||||||
\(360\) | −5.57690 | −0.293928 | ||||||||
\(361\) | −13.9873 | −0.736172 | ||||||||
\(362\) | 10.9444 | 0.575224 | ||||||||
\(363\) | −1.56757 | −0.0822763 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4933 | −0.706273 | ||||||||
\(366\) | 3.58863 | 0.187581 | ||||||||
\(367\) | 15.0953 | 0.787966 | 0.393983 | − | 0.919118i | \(-0.371097\pi\) | ||||
0.393983 | + | 0.919118i | \(0.371097\pi\) | |||||||
\(368\) | 0.953860 | 0.0497234 | ||||||||
\(369\) | 8.45567 | 0.440184 | ||||||||
\(370\) | 17.0956 | 0.888759 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.4783 | 0.543276 | ||||||||
\(373\) | −27.2574 | −1.41134 | −0.705668 | − | 0.708543i | \(-0.749353\pi\) | ||||
−0.705668 | + | 0.708543i | \(0.749353\pi\) | |||||||
\(374\) | 26.9902 | 1.39563 | ||||||||
\(375\) | −9.68957 | −0.500367 | ||||||||
\(376\) | 21.8143 | 1.12499 | ||||||||
\(377\) | 13.2993 | 0.684948 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.6079 | −1.46949 | −0.734745 | − | 0.678344i | \(-0.762698\pi\) | ||||
−0.734745 | + | 0.678344i | \(0.762698\pi\) | |||||||
\(380\) | 16.6059 | 0.851865 | ||||||||
\(381\) | −9.69548 | −0.496714 | ||||||||
\(382\) | 29.9213 | 1.53091 | ||||||||
\(383\) | 18.3899 | 0.939682 | 0.469841 | − | 0.882751i | \(-0.344311\pi\) | ||||
0.469841 | + | 0.882751i | \(0.344311\pi\) | |||||||
\(384\) | 15.7983 | 0.806205 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.6731 | 1.25583 | ||||||||
\(387\) | −3.01191 | −0.153104 | ||||||||
\(388\) | 17.6654 | 0.896823 | ||||||||
\(389\) | −32.8984 | −1.66801 | −0.834007 | − | 0.551753i | \(-0.813959\pi\) | ||||
−0.834007 | + | 0.551753i | \(0.813959\pi\) | |||||||
\(390\) | −16.9908 | −0.860363 | ||||||||
\(391\) | 3.92563 | 0.198528 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.2934 | 0.922779 | ||||||||
\(394\) | −37.2367 | −1.87596 | ||||||||
\(395\) | −23.9559 | −1.20535 | ||||||||
\(396\) | 9.24900 | 0.464780 | ||||||||
\(397\) | 17.3815 | 0.872352 | 0.436176 | − | 0.899861i | \(-0.356332\pi\) | ||||
0.436176 | + | 0.899861i | \(0.356332\pi\) | |||||||
\(398\) | 33.0195 | 1.65512 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.01657 | −0.0508287 | ||||||||
\(401\) | −23.2849 | −1.16279 | −0.581396 | − | 0.813621i | \(-0.697493\pi\) | ||||
−0.581396 | + | 0.813621i | \(0.697493\pi\) | |||||||
\(402\) | −30.7596 | −1.53415 | ||||||||
\(403\) | 10.7225 | 0.534126 | ||||||||
\(404\) | 2.91782 | 0.145167 | ||||||||
\(405\) | 2.46287 | 0.122381 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.52293 | −0.472034 | ||||||||
\(408\) | 8.88916 | 0.440079 | ||||||||
\(409\) | 0.712227 | 0.0352174 | 0.0176087 | − | 0.999845i | \(-0.494395\pi\) | ||||
0.0176087 | + | 0.999845i | \(0.494395\pi\) | |||||||
\(410\) | −46.6202 | −2.30241 | ||||||||
\(411\) | 4.69464 | 0.231569 | ||||||||
\(412\) | −19.2788 | −0.949799 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.23864 | 0.110023 | ||||||||
\(415\) | −5.76642 | −0.283062 | ||||||||
\(416\) | 20.5367 | 1.00690 | ||||||||
\(417\) | −9.69649 | −0.474839 | ||||||||
\(418\) | −15.3933 | −0.752913 | ||||||||
\(419\) | −5.77916 | −0.282330 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.8487 | −0.723680 | −0.361840 | − | 0.932240i | \(-0.617851\pi\) | ||||
−0.361840 | + | 0.932240i | \(0.617851\pi\) | |||||||
\(422\) | −16.5247 | −0.804408 | ||||||||
\(423\) | −9.63365 | −0.468404 | ||||||||
\(424\) | −7.53387 | −0.365877 | ||||||||
\(425\) | −4.18373 | −0.202941 | ||||||||
\(426\) | −24.0412 | −1.16480 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 48.5328 | 2.34592 | ||||||||
\(429\) | 9.46454 | 0.456953 | ||||||||
\(430\) | 16.6061 | 0.800818 | ||||||||
\(431\) | 4.44128 | 0.213929 | 0.106964 | − | 0.994263i | \(-0.465887\pi\) | ||||
0.106964 | + | 0.994263i | \(0.465887\pi\) | |||||||
\(432\) | −0.953860 | −0.0458926 | ||||||||
\(433\) | −8.07973 | −0.388287 | −0.194143 | − | 0.980973i | \(-0.562193\pi\) | ||||
−0.194143 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.6288 | 0.509610 | ||||||||
\(436\) | 19.4402 | 0.931018 | ||||||||
\(437\) | −2.23891 | −0.107102 | ||||||||
\(438\) | 12.2648 | 0.586035 | ||||||||
\(439\) | 11.5837 | 0.552860 | 0.276430 | − | 0.961034i | \(-0.410849\pi\) | ||||
0.276430 | + | 0.961034i | \(0.410849\pi\) | |||||||
\(440\) | −17.1279 | −0.816541 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.0821 | 1.28816 | ||||||||
\(443\) | −36.6133 | −1.73955 | −0.869775 | − | 0.493448i | \(-0.835736\pi\) | ||||
−0.869775 | + | 0.493448i | \(0.835736\pi\) | |||||||
\(444\) | −9.33774 | −0.443150 | ||||||||
\(445\) | 12.3634 | 0.586080 | ||||||||
\(446\) | 57.4237 | 2.71909 | ||||||||
\(447\) | −10.3636 | −0.490180 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.72363 | 0.411694 | 0.205847 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205847 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(450\) | −2.38582 | −0.112469 | ||||||||
\(451\) | 25.9693 | 1.22284 | ||||||||
\(452\) | 25.6056 | 1.20439 | ||||||||
\(453\) | 10.8567 | 0.510091 | ||||||||
\(454\) | −20.9308 | −0.982332 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.06976 | −0.237413 | ||||||||
\(457\) | 22.5857 | 1.05651 | 0.528256 | − | 0.849085i | \(-0.322846\pi\) | ||||
0.528256 | + | 0.849085i | \(0.322846\pi\) | |||||||
\(458\) | −40.4909 | −1.89202 | ||||||||
\(459\) | −3.92563 | −0.183233 | ||||||||
\(460\) | −7.41695 | −0.345817 | ||||||||
\(461\) | 29.1463 | 1.35748 | 0.678740 | − | 0.734379i | \(-0.262526\pi\) | ||||
0.678740 | + | 0.734379i | \(0.262526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0153471 | −0.000713240 0 | −0.000356620 | − | 1.00000i | \(-0.500114\pi\) | ||||
−0.000356620 | 1.00000i | \(0.500114\pi\) | ||||||||
\(464\) | −4.11647 | −0.191102 | ||||||||
\(465\) | 8.56941 | 0.397397 | ||||||||
\(466\) | 39.9916 | 1.85257 | ||||||||
\(467\) | 16.3186 | 0.755135 | 0.377568 | − | 0.925982i | \(-0.376761\pi\) | ||||
0.377568 | + | 0.925982i | \(0.376761\pi\) | |||||||
\(468\) | 9.28050 | 0.428991 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 53.1149 | 2.45001 | ||||||||
\(471\) | −2.52233 | −0.116223 | ||||||||
\(472\) | −17.2160 | −0.792429 | ||||||||
\(473\) | −9.25025 | −0.425327 | ||||||||
\(474\) | 21.7748 | 1.00015 | ||||||||
\(475\) | 2.38611 | 0.109482 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.32711 | 0.152338 | ||||||||
\(478\) | −34.3481 | −1.57104 | ||||||||
\(479\) | 19.2029 | 0.877403 | 0.438701 | − | 0.898633i | \(-0.355439\pi\) | ||||
0.438701 | + | 0.898633i | \(0.355439\pi\) | |||||||
\(480\) | 16.4129 | 0.749143 | ||||||||
\(481\) | −9.55535 | −0.435687 | ||||||||
\(482\) | 8.87216 | 0.404116 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.72075 | −0.214580 | ||||||||
\(485\) | 14.4471 | 0.656010 | ||||||||
\(486\) | −2.23864 | −0.101547 | ||||||||
\(487\) | 38.5000 | 1.74460 | 0.872300 | − | 0.488971i | \(-0.162628\pi\) | ||||
0.872300 | + | 0.488971i | \(0.162628\pi\) | |||||||
\(488\) | 3.62991 | 0.164318 | ||||||||
\(489\) | −14.4762 | −0.654637 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.99057 | 0.270351 | 0.135175 | − | 0.990822i | \(-0.456840\pi\) | ||||
0.135175 | + | 0.990822i | \(0.456840\pi\) | |||||||
\(492\) | 25.4643 | 1.14802 | ||||||||
\(493\) | −16.9414 | −0.763004 | ||||||||
\(494\) | −15.4458 | −0.694937 | ||||||||
\(495\) | 7.56404 | 0.339978 | ||||||||
\(496\) | −3.31889 | −0.149023 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.24141 | 0.234873 | ||||||||
\(499\) | −12.3152 | −0.551302 | −0.275651 | − | 0.961258i | \(-0.588893\pi\) | ||||
−0.275651 | + | 0.961258i | \(0.588893\pi\) | |||||||
\(500\) | −29.1802 | −1.30498 | ||||||||
\(501\) | 15.6448 | 0.698957 | ||||||||
\(502\) | 12.7323 | 0.568271 | ||||||||
\(503\) | −12.8732 | −0.573990 | −0.286995 | − | 0.957932i | \(-0.592656\pi\) | ||||
−0.286995 | + | 0.957932i | \(0.592656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.38626 | 0.106187 | ||||||||
\(506\) | 6.87536 | 0.305647 | ||||||||
\(507\) | −3.50323 | −0.155584 | ||||||||
\(508\) | −29.1979 | −1.29545 | ||||||||
\(509\) | 6.75440 | 0.299383 | 0.149692 | − | 0.988733i | \(-0.452172\pi\) | ||||
0.149692 | + | 0.988733i | \(0.452172\pi\) | |||||||
\(510\) | 21.6439 | 0.958409 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.6765 | −0.471837 | ||||||||
\(513\) | 2.23891 | 0.0988504 | ||||||||
\(514\) | 27.3247 | 1.20524 | ||||||||
\(515\) | −15.7666 | −0.694761 | ||||||||
\(516\) | −9.07037 | −0.399301 | ||||||||
\(517\) | −29.5871 | −1.30124 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.9908 | −0.965288 | ||||||||
\(520\) | −17.1862 | −0.753666 | ||||||||
\(521\) | −13.1416 | −0.575745 | −0.287872 | − | 0.957669i | \(-0.592948\pi\) | ||||
−0.287872 | + | 0.957669i | \(0.592948\pi\) | |||||||
\(522\) | −9.66105 | −0.422853 | ||||||||
\(523\) | 29.6346 | 1.29583 | 0.647915 | − | 0.761713i | \(-0.275641\pi\) | ||||
0.647915 | + | 0.761713i | \(0.275641\pi\) | |||||||
\(524\) | 55.0905 | 2.40664 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.8302 | 1.03905 | ||||||||
\(527\) | −13.6590 | −0.594995 | ||||||||
\(528\) | −2.92952 | −0.127491 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −18.3440 | −0.796812 | ||||||||
\(531\) | 7.60292 | 0.329939 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.0577 | 1.12868 | ||||||||
\(534\) | −11.2377 | −0.486304 | ||||||||
\(535\) | 39.6912 | 1.71600 | ||||||||
\(536\) | −31.1134 | −1.34390 | ||||||||
\(537\) | −18.7258 | −0.808077 | ||||||||
\(538\) | −55.7403 | −2.40314 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.41695 | 0.319175 | ||||||||
\(541\) | −10.9740 | −0.471809 | −0.235904 | − | 0.971776i | \(-0.575805\pi\) | ||||
−0.235904 | + | 0.971776i | \(0.575805\pi\) | |||||||
\(542\) | 14.7228 | 0.632398 | ||||||||
\(543\) | −4.88885 | −0.209801 | ||||||||
\(544\) | −26.1609 | −1.12164 | ||||||||
\(545\) | 15.8986 | 0.681023 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8543 | 0.549609 | 0.274804 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274804 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(548\) | 14.1379 | 0.603941 | ||||||||
\(549\) | −1.60304 | −0.0684162 | ||||||||
\(550\) | −7.32740 | −0.312441 | ||||||||
\(551\) | 9.66223 | 0.411625 | ||||||||
\(552\) | 2.26439 | 0.0963787 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 52.0425 | 2.21107 | ||||||||
\(555\) | −7.63661 | −0.324156 | ||||||||
\(556\) | −29.2010 | −1.23840 | ||||||||
\(557\) | −27.4905 | −1.16481 | −0.582405 | − | 0.812899i | \(-0.697888\pi\) | ||||
−0.582405 | + | 0.812899i | \(0.697888\pi\) | |||||||
\(558\) | −7.78919 | −0.329743 | ||||||||
\(559\) | −9.28175 | −0.392576 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0565 | −0.509026 | ||||||||
\(562\) | −24.0512 | −1.01454 | ||||||||
\(563\) | −39.8365 | −1.67891 | −0.839455 | − | 0.543429i | \(-0.817126\pi\) | ||||
−0.839455 | + | 0.543429i | \(0.817126\pi\) | |||||||
\(564\) | −29.0117 | −1.22161 | ||||||||
\(565\) | 20.9408 | 0.880988 | ||||||||
\(566\) | −54.8848 | −2.30698 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.3178 | −1.02035 | ||||||||
\(569\) | 23.4654 | 0.983720 | 0.491860 | − | 0.870674i | \(-0.336317\pi\) | ||||
0.491860 | + | 0.870674i | \(0.336317\pi\) | |||||||
\(570\) | −12.3442 | −0.517042 | ||||||||
\(571\) | −0.958267 | −0.0401022 | −0.0200511 | − | 0.999799i | \(-0.506383\pi\) | ||||
−0.0200511 | + | 0.999799i | \(0.506383\pi\) | |||||||
\(572\) | 28.5025 | 1.19175 | ||||||||
\(573\) | −13.3658 | −0.558366 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.06575 | −0.0444447 | ||||||||
\(576\) | −13.0108 | −0.542118 | ||||||||
\(577\) | 36.0588 | 1.50115 | 0.750574 | − | 0.660786i | \(-0.229777\pi\) | ||||
0.750574 | + | 0.660786i | \(0.229777\pi\) | |||||||
\(578\) | 3.55808 | 0.147996 | ||||||||
\(579\) | −11.0215 | −0.458037 | ||||||||
\(580\) | 32.0085 | 1.32908 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.1318 | −0.544329 | ||||||||
\(583\) | 10.2183 | 0.423199 | ||||||||
\(584\) | 12.4059 | 0.513359 | ||||||||
\(585\) | 7.58980 | 0.313799 | ||||||||
\(586\) | −74.4866 | −3.07701 | ||||||||
\(587\) | −19.5627 | −0.807439 | −0.403720 | − | 0.914883i | \(-0.632283\pi\) | ||||
−0.403720 | + | 0.914883i | \(0.632283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.79015 | 0.320987 | ||||||||
\(590\) | −41.9186 | −1.72576 | ||||||||
\(591\) | 16.6336 | 0.684216 | ||||||||
\(592\) | 2.95763 | 0.121558 | ||||||||
\(593\) | −0.346580 | −0.0142324 | −0.00711618 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711618 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(594\) | −6.87536 | −0.282100 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.2099 | −1.27841 | ||||||||
\(597\) | −14.7498 | −0.603670 | ||||||||
\(598\) | 6.89878 | 0.282112 | ||||||||
\(599\) | −13.3827 | −0.546804 | −0.273402 | − | 0.961900i | \(-0.588149\pi\) | ||||
−0.273402 | + | 0.961900i | \(0.588149\pi\) | |||||||
\(600\) | −2.41326 | −0.0985211 | ||||||||
\(601\) | −19.1384 | −0.780670 | −0.390335 | − | 0.920673i | \(-0.627641\pi\) | ||||
−0.390335 | + | 0.920673i | \(0.627641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7403 | 0.559550 | ||||||||
\(604\) | 32.6949 | 1.33034 | ||||||||
\(605\) | −3.86074 | −0.156961 | ||||||||
\(606\) | −2.16900 | −0.0881096 | ||||||||
\(607\) | 26.2427 | 1.06516 | 0.532579 | − | 0.846381i | \(-0.321223\pi\) | ||||
0.532579 | + | 0.846381i | \(0.321223\pi\) | |||||||
\(608\) | 14.9204 | 0.605102 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.83835 | 0.357854 | ||||||||
\(611\) | −29.6878 | −1.20104 | ||||||||
\(612\) | −11.8221 | −0.477878 | ||||||||
\(613\) | −29.5838 | −1.19488 | −0.597440 | − | 0.801914i | \(-0.703815\pi\) | ||||
−0.597440 | + | 0.801914i | \(0.703815\pi\) | |||||||
\(614\) | −45.2978 | −1.82807 | ||||||||
\(615\) | 20.8252 | 0.839755 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.6171 | −1.71570 | −0.857851 | − | 0.513899i | \(-0.828201\pi\) | ||||
−0.857851 | + | 0.513899i | \(0.828201\pi\) | |||||||
\(618\) | 14.3311 | 0.576483 | ||||||||
\(619\) | 30.0740 | 1.20878 | 0.604389 | − | 0.796689i | \(-0.293417\pi\) | ||||
0.604389 | + | 0.796689i | \(0.293417\pi\) | |||||||
\(620\) | 25.8068 | 1.03643 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −51.1760 | −2.05197 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.93949 | −0.117674 | ||||||||
\(625\) | −29.1929 | −1.16772 | ||||||||
\(626\) | −52.9916 | −2.11797 | ||||||||
\(627\) | 6.87620 | 0.274609 | ||||||||
\(628\) | −7.59600 | −0.303114 | ||||||||
\(629\) | 12.1722 | 0.485337 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.5441 | 1.57423 | 0.787113 | − | 0.616809i | \(-0.211575\pi\) | ||||
0.787113 | + | 0.616809i | \(0.211575\pi\) | |||||||
\(632\) | 22.0252 | 0.876117 | ||||||||
\(633\) | 7.38157 | 0.293391 | ||||||||
\(634\) | −27.8224 | −1.10497 | ||||||||
\(635\) | −23.8787 | −0.947599 | ||||||||
\(636\) | 10.0196 | 0.397303 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.6713 | −1.17470 | ||||||||
\(639\) | 10.7392 | 0.424837 | ||||||||
\(640\) | 38.9093 | 1.53802 | ||||||||
\(641\) | 35.9145 | 1.41854 | 0.709269 | − | 0.704938i | \(-0.249025\pi\) | ||||
0.709269 | + | 0.704938i | \(0.249025\pi\) | |||||||
\(642\) | −36.0775 | −1.42387 | ||||||||
\(643\) | −16.2300 | −0.640049 | −0.320025 | − | 0.947409i | \(-0.603691\pi\) | ||||
−0.320025 | + | 0.947409i | \(0.603691\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.41795 | −0.292081 | ||||||||
\(646\) | 19.6757 | 0.774131 | ||||||||
\(647\) | −38.0710 | −1.49673 | −0.748364 | − | 0.663289i | \(-0.769160\pi\) | ||||
−0.748364 | + | 0.663289i | \(0.769160\pi\) | |||||||
\(648\) | −2.26439 | −0.0889535 | ||||||||
\(649\) | 23.3503 | 0.916579 | ||||||||
\(650\) | −7.35235 | −0.288383 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.5951 | −1.70732 | ||||||||
\(653\) | −8.45161 | −0.330737 | −0.165368 | − | 0.986232i | \(-0.552881\pi\) | ||||
−0.165368 | + | 0.986232i | \(0.552881\pi\) | |||||||
\(654\) | −14.4511 | −0.565084 | ||||||||
\(655\) | 45.0543 | 1.76042 | ||||||||
\(656\) | −8.06552 | −0.314906 | ||||||||
\(657\) | −5.47869 | −0.213744 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.3402 | 1.80516 | 0.902579 | − | 0.430523i | \(-0.141671\pi\) | ||||
0.902579 | + | 0.430523i | \(0.141671\pi\) | |||||||
\(660\) | 22.7791 | 0.886676 | ||||||||
\(661\) | 14.1551 | 0.550569 | 0.275285 | − | 0.961363i | \(-0.411228\pi\) | ||||
0.275285 | + | 0.961363i | \(0.411228\pi\) | |||||||
\(662\) | 16.3546 | 0.635641 | ||||||||
\(663\) | −12.0976 | −0.469830 | ||||||||
\(664\) | 5.30170 | 0.205746 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.94133 | 0.268971 | ||||||||
\(667\) | −4.31559 | −0.167100 | ||||||||
\(668\) | 47.1142 | 1.82290 | ||||||||
\(669\) | −25.6512 | −0.991732 | ||||||||
\(670\) | −75.7571 | −2.92675 | ||||||||
\(671\) | −4.92331 | −0.190062 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.1357 | −1.58567 | −0.792833 | − | 0.609439i | \(-0.791395\pi\) | ||||
−0.792833 | + | 0.609439i | \(0.791395\pi\) | |||||||
\(674\) | −69.8002 | −2.68860 | ||||||||
\(675\) | 1.06575 | 0.0410206 | ||||||||
\(676\) | −10.5500 | −0.405768 | ||||||||
\(677\) | −40.5057 | −1.55676 | −0.778380 | − | 0.627793i | \(-0.783958\pi\) | ||||
−0.778380 | + | 0.627793i | \(0.783958\pi\) | |||||||
\(678\) | −19.0343 | −0.731006 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 21.8929 | 0.839553 | ||||||||
\(681\) | 9.34980 | 0.358285 | ||||||||
\(682\) | −23.9224 | −0.916035 | ||||||||
\(683\) | −15.1819 | −0.580920 | −0.290460 | − | 0.956887i | \(-0.593808\pi\) | ||||
−0.290460 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(684\) | 6.74249 | 0.257806 | ||||||||
\(685\) | 11.5623 | 0.441773 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.0873 | 0.690073 | ||||||||
\(688\) | 2.87294 | 0.109530 | ||||||||
\(689\) | 10.2531 | 0.390612 | ||||||||
\(690\) | 5.51348 | 0.209895 | ||||||||
\(691\) | 35.8668 | 1.36444 | 0.682219 | − | 0.731148i | \(-0.261015\pi\) | ||||
0.682219 | + | 0.731148i | \(0.261015\pi\) | |||||||
\(692\) | −66.2252 | −2.51751 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6340 | 0.593460 | ||||||||
\(695\) | −23.8812 | −0.905867 | ||||||||
\(696\) | −9.77217 | −0.370413 | ||||||||
\(697\) | −33.1939 | −1.25731 | ||||||||
\(698\) | −27.9974 | −1.05972 | ||||||||
\(699\) | −17.8642 | −0.675688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.2118 | −1.78316 | −0.891582 | − | 0.452860i | \(-0.850404\pi\) | ||||
−0.891582 | + | 0.452860i | \(0.850404\pi\) | |||||||
\(702\) | −6.89878 | −0.260377 | ||||||||
\(703\) | −6.94218 | −0.261829 | ||||||||
\(704\) | −39.9592 | −1.50602 | ||||||||
\(705\) | −23.7265 | −0.893590 | ||||||||
\(706\) | 44.6514 | 1.68048 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.8962 | 0.860492 | ||||||||
\(709\) | 44.0818 | 1.65553 | 0.827764 | − | 0.561076i | \(-0.189612\pi\) | ||||
0.827764 | + | 0.561076i | \(0.189612\pi\) | |||||||
\(710\) | −59.2105 | −2.22213 | ||||||||
\(711\) | −9.72680 | −0.364783 | ||||||||
\(712\) | −11.3670 | −0.425996 | ||||||||
\(713\) | −3.47943 | −0.130306 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.3100 | 0.871744 | ||||||||
\(716\) | −56.3927 | −2.10750 | ||||||||
\(717\) | 15.3433 | 0.573006 | ||||||||
\(718\) | −69.8653 | −2.60735 | ||||||||
\(719\) | 36.8733 | 1.37514 | 0.687570 | − | 0.726118i | \(-0.258677\pi\) | ||||
0.687570 | + | 0.726118i | \(0.258677\pi\) | |||||||
\(720\) | −2.34924 | −0.0875509 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 31.3124 | 1.16533 | ||||||||
\(723\) | −3.96319 | −0.147393 | ||||||||
\(724\) | −14.7228 | −0.547168 | ||||||||
\(725\) | 4.59933 | 0.170815 | ||||||||
\(726\) | 3.50923 | 0.130240 | ||||||||
\(727\) | 1.06104 | 0.0393517 | 0.0196758 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196758 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.2067 | 1.11800 | ||||||||
\(731\) | 11.8237 | 0.437314 | ||||||||
\(732\) | −4.82757 | −0.178432 | ||||||||
\(733\) | −41.2144 | −1.52229 | −0.761144 | − | 0.648583i | \(-0.775362\pi\) | ||||
−0.761144 | + | 0.648583i | \(0.775362\pi\) | |||||||
\(734\) | −33.7928 | −1.24732 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.66412 | −0.245643 | ||||||||
\(737\) | 42.1997 | 1.55444 | ||||||||
\(738\) | −18.9292 | −0.696793 | ||||||||
\(739\) | 2.39486 | 0.0880964 | 0.0440482 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440482 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(740\) | −22.9977 | −0.845411 | ||||||||
\(741\) | 6.89962 | 0.253464 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.3260 | 1.11255 | 0.556277 | − | 0.830997i | \(-0.312229\pi\) | ||||
0.556277 | + | 0.830997i | \(0.312229\pi\) | |||||||
\(744\) | −7.87879 | −0.288850 | ||||||||
\(745\) | −25.5242 | −0.935134 | ||||||||
\(746\) | 61.0195 | 2.23408 | ||||||||
\(747\) | −2.34134 | −0.0856651 | ||||||||
\(748\) | −36.3082 | −1.32756 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.6914 | 0.792059 | ||||||||
\(751\) | −36.2501 | −1.32278 | −0.661392 | − | 0.750041i | \(-0.730034\pi\) | ||||
−0.661392 | + | 0.750041i | \(0.730034\pi\) | |||||||
\(752\) | 9.18915 | 0.335094 | ||||||||
\(753\) | −5.68753 | −0.207265 | ||||||||
\(754\) | −29.7723 | −1.08424 | ||||||||
\(755\) | 26.7386 | 0.973117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3390 | 0.666543 | 0.333272 | − | 0.942831i | \(-0.391847\pi\) | ||||
0.333272 | + | 0.942831i | \(0.391847\pi\) | |||||||
\(758\) | 64.0428 | 2.32614 | ||||||||
\(759\) | −3.07123 | −0.111478 | ||||||||
\(760\) | −12.4862 | −0.452922 | ||||||||
\(761\) | −10.9230 | −0.395958 | −0.197979 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197979 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(762\) | 21.7047 | 0.786277 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −40.2512 | −1.45624 | ||||||||
\(765\) | −9.66834 | −0.349560 | ||||||||
\(766\) | −41.1684 | −1.48748 | ||||||||
\(767\) | 23.4298 | 0.846001 | ||||||||
\(768\) | −9.34505 | −0.337210 | ||||||||
\(769\) | −38.2640 | −1.37983 | −0.689917 | − | 0.723888i | \(-0.742353\pi\) | ||||
−0.689917 | + | 0.723888i | \(0.742353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.2060 | −0.439587 | ||||||||
\(772\) | −33.1912 | −1.19458 | ||||||||
\(773\) | −48.7903 | −1.75486 | −0.877432 | − | 0.479701i | \(-0.840745\pi\) | ||||
−0.877432 | + | 0.479701i | \(0.840745\pi\) | |||||||
\(774\) | 6.74257 | 0.242357 | ||||||||
\(775\) | 3.70820 | 0.133202 | ||||||||
\(776\) | −13.2828 | −0.476825 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 73.6476 | 2.64039 | ||||||||
\(779\) | 18.9315 | 0.678291 | ||||||||
\(780\) | 22.8567 | 0.818401 | ||||||||
\(781\) | 32.9826 | 1.18021 | ||||||||
\(782\) | −8.78808 | −0.314261 | ||||||||
\(783\) | 4.31559 | 0.154227 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.21218 | −0.221722 | ||||||||
\(786\) | −40.9522 | −1.46072 | ||||||||
\(787\) | 11.3998 | 0.406358 | 0.203179 | − | 0.979142i | \(-0.434873\pi\) | ||||
0.203179 | + | 0.979142i | \(0.434873\pi\) | |||||||
\(788\) | 50.0922 | 1.78446 | ||||||||
\(789\) | −10.6450 | −0.378971 | ||||||||
\(790\) | 53.6285 | 1.90802 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.95444 | −0.247115 | ||||||||
\(793\) | −4.94007 | −0.175427 | ||||||||
\(794\) | −38.9109 | −1.38090 | ||||||||
\(795\) | 8.19426 | 0.290620 | ||||||||
\(796\) | −44.4191 | −1.57439 | ||||||||
\(797\) | −38.3621 | −1.35886 | −0.679428 | − | 0.733742i | \(-0.737772\pi\) | ||||
−0.679428 | + | 0.733742i | \(0.737772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.8182 | 1.33791 | ||||||||
\(800\) | 7.10227 | 0.251103 | ||||||||
\(801\) | 5.01990 | 0.177369 | ||||||||
\(802\) | 52.1264 | 1.84065 | ||||||||
\(803\) | −16.8263 | −0.593787 | ||||||||
\(804\) | 41.3790 | 1.45933 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.0038 | −0.845499 | ||||||||
\(807\) | 24.8992 | 0.876494 | ||||||||
\(808\) | −2.19395 | −0.0771828 | ||||||||
\(809\) | 5.33756 | 0.187659 | 0.0938293 | − | 0.995588i | \(-0.470089\pi\) | ||||
0.0938293 | + | 0.995588i | \(0.470089\pi\) | |||||||
\(810\) | −5.51348 | −0.193724 | ||||||||
\(811\) | 15.5586 | 0.546335 | 0.273168 | − | 0.961966i | \(-0.411929\pi\) | ||||
0.273168 | + | 0.961966i | \(0.411929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.57668 | −0.230654 | ||||||||
\(814\) | 21.3184 | 0.747209 | ||||||||
\(815\) | −35.6531 | −1.24887 | ||||||||
\(816\) | 3.74451 | 0.131084 | ||||||||
\(817\) | −6.74340 | −0.235922 | ||||||||
\(818\) | −1.59442 | −0.0557476 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 62.7153 | 2.19011 | ||||||||
\(821\) | 46.1313 | 1.60999 | 0.804997 | − | 0.593279i | \(-0.202167\pi\) | ||||
0.804997 | + | 0.593279i | \(0.202167\pi\) | |||||||
\(822\) | −10.5096 | −0.366564 | ||||||||
\(823\) | −0.0521219 | −0.00181685 | −0.000908427 | − | 1.00000i | \(-0.500289\pi\) | ||||
−0.000908427 | 1.00000i | \(0.500289\pi\) | ||||||||
\(824\) | 14.4960 | 0.504991 | ||||||||
\(825\) | 3.27315 | 0.113956 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.4334 | −1.61465 | −0.807324 | − | 0.590109i | \(-0.799085\pi\) | ||||
−0.807324 | + | 0.590109i | \(0.799085\pi\) | |||||||
\(828\) | −3.01150 | −0.104657 | ||||||||
\(829\) | −25.8592 | −0.898127 | −0.449063 | − | 0.893500i | \(-0.648242\pi\) | ||||
−0.449063 | + | 0.893500i | \(0.648242\pi\) | |||||||
\(830\) | 12.9089 | 0.448076 | ||||||||
\(831\) | −23.2474 | −0.806443 | ||||||||
\(832\) | −40.0953 | −1.39005 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.7069 | 0.751650 | ||||||||
\(835\) | 38.5311 | 1.33342 | ||||||||
\(836\) | 20.7077 | 0.716191 | ||||||||
\(837\) | 3.47943 | 0.120267 | ||||||||
\(838\) | 12.9374 | 0.446917 | ||||||||
\(839\) | −41.4474 | −1.43092 | −0.715462 | − | 0.698652i | \(-0.753784\pi\) | ||||
−0.715462 | + | 0.698652i | \(0.753784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3757 | −0.357782 | ||||||||
\(842\) | 33.2408 | 1.14555 | ||||||||
\(843\) | 10.7437 | 0.370031 | ||||||||
\(844\) | 22.2296 | 0.765175 | ||||||||
\(845\) | −8.62801 | −0.296812 | ||||||||
\(846\) | 21.5662 | 0.741463 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.17360 | −0.108982 | ||||||||
\(849\) | 24.5170 | 0.841423 | ||||||||
\(850\) | 9.36587 | 0.321247 | ||||||||
\(851\) | 3.10069 | 0.106290 | ||||||||
\(852\) | 32.3412 | 1.10799 | ||||||||
\(853\) | −17.6926 | −0.605782 | −0.302891 | − | 0.953025i | \(-0.597952\pi\) | ||||
−0.302891 | + | 0.953025i | \(0.597952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.51416 | 0.188580 | ||||||||
\(856\) | −36.4925 | −1.24729 | ||||||||
\(857\) | −32.5992 | −1.11357 | −0.556784 | − | 0.830657i | \(-0.687965\pi\) | ||||
−0.556784 | + | 0.830657i | \(0.687965\pi\) | |||||||
\(858\) | −21.1877 | −0.723336 | ||||||||
\(859\) | −2.57341 | −0.0878036 | −0.0439018 | − | 0.999036i | \(-0.513979\pi\) | ||||
−0.0439018 | + | 0.999036i | \(0.513979\pi\) | |||||||
\(860\) | −22.3392 | −0.761759 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.94242 | −0.338640 | ||||||||
\(863\) | 6.05407 | 0.206083 | 0.103041 | − | 0.994677i | \(-0.467143\pi\) | ||||
0.103041 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(864\) | 6.66412 | 0.226718 | ||||||||
\(865\) | −54.1605 | −1.84151 | ||||||||
\(866\) | 18.0876 | 0.614641 | ||||||||
\(867\) | −1.58939 | −0.0539786 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.8732 | −1.01338 | ||||||||
\(870\) | −23.7939 | −0.806690 | ||||||||
\(871\) | 42.3434 | 1.43475 | ||||||||
\(872\) | −14.6173 | −0.495006 | ||||||||
\(873\) | 5.86596 | 0.198533 | ||||||||
\(874\) | 5.01212 | 0.169537 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.4991 | −0.557453 | ||||||||
\(877\) | −10.5887 | −0.357556 | −0.178778 | − | 0.983889i | \(-0.557214\pi\) | ||||
−0.178778 | + | 0.983889i | \(0.557214\pi\) | |||||||
\(878\) | −25.9317 | −0.875153 | ||||||||
\(879\) | 33.2732 | 1.12228 | ||||||||
\(880\) | −7.21503 | −0.243219 | ||||||||
\(881\) | 37.2400 | 1.25465 | 0.627323 | − | 0.778759i | \(-0.284151\pi\) | ||||
0.627323 | + | 0.778759i | \(0.284151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.3648 | −1.56030 | −0.780150 | − | 0.625592i | \(-0.784857\pi\) | ||||
−0.780150 | + | 0.625592i | \(0.784857\pi\) | |||||||
\(884\) | −36.4318 | −1.22534 | ||||||||
\(885\) | 18.7250 | 0.629435 | ||||||||
\(886\) | 81.9639 | 2.75363 | ||||||||
\(887\) | 23.4809 | 0.788410 | 0.394205 | − | 0.919023i | \(-0.371020\pi\) | ||||
0.394205 | + | 0.919023i | \(0.371020\pi\) | |||||||
\(888\) | 7.02117 | 0.235615 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.6771 | −0.927739 | ||||||||
\(891\) | 3.07123 | 0.102890 | ||||||||
\(892\) | −77.2486 | −2.58647 | ||||||||
\(893\) | −21.5689 | −0.721775 | ||||||||
\(894\) | 23.2003 | 0.775934 | ||||||||
\(895\) | −46.1192 | −1.54160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.08168 | −0.102894 | ||||||||
\(898\) | −19.5291 | −0.651693 | ||||||||
\(899\) | 15.0158 | 0.500805 | ||||||||
\(900\) | 3.20950 | 0.106983 | ||||||||
\(901\) | −13.0610 | −0.435126 | ||||||||
\(902\) | −58.1358 | −1.93571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.2532 | −0.640352 | ||||||||
\(905\) | −12.0406 | −0.400244 | ||||||||
\(906\) | −24.3042 | −0.807451 | ||||||||
\(907\) | −13.4392 | −0.446241 | −0.223120 | − | 0.974791i | \(-0.571624\pi\) | ||||
−0.223120 | + | 0.974791i | \(0.571624\pi\) | |||||||
\(908\) | 28.1569 | 0.934420 | ||||||||
\(909\) | 0.968892 | 0.0321361 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.86837 | −0.293822 | −0.146911 | − | 0.989150i | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(912\) | −2.13561 | −0.0707171 | ||||||||
\(913\) | −7.19078 | −0.237980 | ||||||||
\(914\) | −50.5611 | −1.67241 | ||||||||
\(915\) | −3.94809 | −0.130520 | ||||||||
\(916\) | 54.4699 | 1.79974 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.78808 | 0.290050 | ||||||||
\(919\) | −14.9225 | −0.492249 | −0.246124 | − | 0.969238i | \(-0.579157\pi\) | ||||
−0.246124 | + | 0.969238i | \(0.579157\pi\) | |||||||
\(920\) | 5.57690 | 0.183865 | ||||||||
\(921\) | 20.2345 | 0.666750 | ||||||||
\(922\) | −65.2481 | −2.14883 | ||||||||
\(923\) | 33.0949 | 1.08933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.30455 | −0.108653 | ||||||||
\(926\) | 0.0343566 | 0.00112903 | ||||||||
\(927\) | −6.40172 | −0.210260 | ||||||||
\(928\) | 28.7596 | 0.944081 | ||||||||
\(929\) | −50.2999 | −1.65029 | −0.825143 | − | 0.564924i | \(-0.808906\pi\) | ||||
−0.825143 | + | 0.564924i | \(0.808906\pi\) | |||||||
\(930\) | −19.1838 | −0.629062 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −53.7982 | −1.76222 | ||||||||
\(933\) | 22.8603 | 0.748414 | ||||||||
\(934\) | −36.5315 | −1.19535 | ||||||||
\(935\) | −29.6937 | −0.971086 | ||||||||
\(936\) | −6.97812 | −0.228087 | ||||||||
\(937\) | 19.5619 | 0.639060 | 0.319530 | − | 0.947576i | \(-0.396475\pi\) | ||||
0.319530 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.6714 | 0.772486 | ||||||||
\(940\) | −71.4523 | −2.33052 | ||||||||
\(941\) | −10.1938 | −0.332307 | −0.166154 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166154 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(942\) | 5.64659 | 0.183976 | ||||||||
\(943\) | −8.45567 | −0.275354 | ||||||||
\(944\) | −7.25212 | −0.236036 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.7080 | 0.673274 | ||||||||
\(947\) | −0.762412 | −0.0247751 | −0.0123875 | − | 0.999923i | \(-0.503943\pi\) | ||||
−0.0123875 | + | 0.999923i | \(0.503943\pi\) | |||||||
\(948\) | −29.2923 | −0.951369 | ||||||||
\(949\) | −16.8836 | −0.548065 | ||||||||
\(950\) | −5.34165 | −0.173306 | ||||||||
\(951\) | 12.4283 | 0.403014 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.06240 | 0.163987 | 0.0819936 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819936 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(954\) | −7.44820 | −0.241145 | ||||||||
\(955\) | −32.9184 | −1.06521 | ||||||||
\(956\) | 46.2063 | 1.49442 | ||||||||
\(957\) | 13.2542 | 0.428446 | ||||||||
\(958\) | −42.9883 | −1.38889 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −32.0441 | −1.03422 | ||||||||
\(961\) | −18.8935 | −0.609469 | ||||||||
\(962\) | 21.3910 | 0.689673 | ||||||||
\(963\) | 16.1158 | 0.519325 | ||||||||
\(964\) | −11.9352 | −0.384406 | ||||||||
\(965\) | −27.1445 | −0.873813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.7637 | −0.699872 | −0.349936 | − | 0.936774i | \(-0.613797\pi\) | ||||
−0.349936 | + | 0.936774i | \(0.613797\pi\) | |||||||
\(968\) | 3.54960 | 0.114088 | ||||||||
\(969\) | −8.78915 | −0.282348 | ||||||||
\(970\) | −32.3419 | −1.03844 | ||||||||
\(971\) | 60.0563 | 1.92730 | 0.963649 | − | 0.267173i | \(-0.0860895\pi\) | ||||
0.963649 | + | 0.267173i | \(0.0860895\pi\) | |||||||
\(972\) | 3.01150 | 0.0965940 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −86.1875 | −2.76163 | ||||||||
\(975\) | 3.28429 | 0.105182 | ||||||||
\(976\) | 1.52908 | 0.0489446 | ||||||||
\(977\) | 22.6281 | 0.723936 | 0.361968 | − | 0.932190i | \(-0.382105\pi\) | ||||
0.361968 | + | 0.932190i | \(0.382105\pi\) | |||||||
\(978\) | 32.4070 | 1.03626 | ||||||||
\(979\) | 15.4172 | 0.492737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.45532 | 0.206103 | ||||||||
\(982\) | −13.4107 | −0.427954 | ||||||||
\(983\) | −3.29349 | −0.105046 | −0.0525230 | − | 0.998620i | \(-0.516726\pi\) | ||||
−0.0525230 | + | 0.998620i | \(0.516726\pi\) | |||||||
\(984\) | −19.1469 | −0.610381 | ||||||||
\(985\) | 40.9665 | 1.30530 | ||||||||
\(986\) | 37.9257 | 1.20780 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.7782 | 0.661043 | ||||||||
\(989\) | 3.01191 | 0.0957731 | ||||||||
\(990\) | −16.9332 | −0.538171 | ||||||||
\(991\) | −43.6326 | −1.38604 | −0.693018 | − | 0.720920i | \(-0.743719\pi\) | ||||
−0.693018 | + | 0.720920i | \(0.743719\pi\) | |||||||
\(992\) | 23.1874 | 0.736200 | ||||||||
\(993\) | −7.30561 | −0.231837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.3270 | −1.15164 | ||||||||
\(996\) | −7.05094 | −0.223418 | ||||||||
\(997\) | 0.571973 | 0.0181146 | 0.00905728 | − | 0.999959i | \(-0.497117\pi\) | ||||
0.00905728 | + | 0.999959i | \(0.497117\pi\) | |||||||
\(998\) | 27.5692 | 0.872687 | ||||||||
\(999\) | −3.10069 | −0.0981016 |
(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 | 3381.2.a.bl.1.1 | yes | 10 | |
7.6 | odd | 2 | 3381.2.a.bk.1.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3381.2.a.bk.1.1 | ✓ | 10 | 7.6 | odd | 2 | ||
3381.2.a.bl.1.1 | yes | 10 | 1.1 | even | 1 | trivial |