Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.415881\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | −0.415881 | −0.240109 | −0.120055 | − | 0.992767i | \(-0.538307\pi\) | ||||
−0.120055 | + | 0.992767i | \(0.538307\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.24456 | −1.00380 | −0.501899 | − | 0.864926i | \(-0.667365\pi\) | ||||
−0.501899 | + | 0.864926i | \(0.667365\pi\) | |||||||
\(6\) | 0.415881 | 0.169783 | ||||||||
\(7\) | 1.94686 | 0.735842 | 0.367921 | − | 0.929857i | \(-0.380070\pi\) | ||||
0.367921 | + | 0.929857i | \(0.380070\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.82704 | −0.942348 | ||||||||
\(10\) | 2.24456 | 0.709793 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.415881 | −0.120055 | ||||||||
\(13\) | 1.65329 | 0.458541 | 0.229270 | − | 0.973363i | \(-0.426366\pi\) | ||||
0.229270 | + | 0.973363i | \(0.426366\pi\) | |||||||
\(14\) | −1.94686 | −0.520319 | ||||||||
\(15\) | 0.933471 | 0.241021 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.04145 | −0.980196 | −0.490098 | − | 0.871667i | \(-0.663039\pi\) | ||||
−0.490098 | + | 0.871667i | \(0.663039\pi\) | |||||||
\(18\) | 2.82704 | 0.666340 | ||||||||
\(19\) | −7.25266 | −1.66387 | −0.831937 | − | 0.554870i | \(-0.812768\pi\) | ||||
−0.831937 | + | 0.554870i | \(0.812768\pi\) | |||||||
\(20\) | −2.24456 | −0.501899 | ||||||||
\(21\) | −0.809661 | −0.176682 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 8.28397 | 1.72733 | 0.863663 | − | 0.504069i | \(-0.168164\pi\) | ||||
0.863663 | + | 0.504069i | \(0.168164\pi\) | |||||||
\(24\) | 0.415881 | 0.0848914 | ||||||||
\(25\) | 0.0380545 | 0.00761091 | ||||||||
\(26\) | −1.65329 | −0.324237 | ||||||||
\(27\) | 2.42336 | 0.466375 | ||||||||
\(28\) | 1.94686 | 0.367921 | ||||||||
\(29\) | 10.1950 | 1.89316 | 0.946581 | − | 0.322466i | \(-0.104512\pi\) | ||||
0.946581 | + | 0.322466i | \(0.104512\pi\) | |||||||
\(30\) | −0.933471 | −0.170428 | ||||||||
\(31\) | 2.78382 | 0.499989 | 0.249994 | − | 0.968247i | \(-0.419571\pi\) | ||||
0.249994 | + | 0.968247i | \(0.419571\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.415881 | −0.0723956 | ||||||||
\(34\) | 4.04145 | 0.693103 | ||||||||
\(35\) | −4.36984 | −0.738637 | ||||||||
\(36\) | −2.82704 | −0.471174 | ||||||||
\(37\) | −0.827167 | −0.135985 | −0.0679927 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679927 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(38\) | 7.25266 | 1.17654 | ||||||||
\(39\) | −0.687573 | −0.110100 | ||||||||
\(40\) | 2.24456 | 0.354896 | ||||||||
\(41\) | 5.69287 | 0.889077 | 0.444538 | − | 0.895760i | \(-0.353368\pi\) | ||||
0.444538 | + | 0.895760i | \(0.353368\pi\) | |||||||
\(42\) | 0.809661 | 0.124933 | ||||||||
\(43\) | 7.31501 | 1.11553 | 0.557764 | − | 0.830000i | \(-0.311659\pi\) | ||||
0.557764 | + | 0.830000i | \(0.311659\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 6.34547 | 0.945927 | ||||||||
\(46\) | −8.28397 | −1.22140 | ||||||||
\(47\) | −7.73976 | −1.12896 | −0.564480 | − | 0.825447i | \(-0.690923\pi\) | ||||
−0.564480 | + | 0.825447i | \(0.690923\pi\) | |||||||
\(48\) | −0.415881 | −0.0600273 | ||||||||
\(49\) | −3.20976 | −0.458536 | ||||||||
\(50\) | −0.0380545 | −0.00538172 | ||||||||
\(51\) | 1.68076 | 0.235354 | ||||||||
\(52\) | 1.65329 | 0.229270 | ||||||||
\(53\) | −7.74921 | −1.06444 | −0.532218 | − | 0.846607i | \(-0.678641\pi\) | ||||
−0.532218 | + | 0.846607i | \(0.678641\pi\) | |||||||
\(54\) | −2.42336 | −0.329777 | ||||||||
\(55\) | −2.24456 | −0.302657 | ||||||||
\(56\) | −1.94686 | −0.260159 | ||||||||
\(57\) | 3.01625 | 0.399512 | ||||||||
\(58\) | −10.1950 | −1.33867 | ||||||||
\(59\) | 7.99838 | 1.04130 | 0.520650 | − | 0.853770i | \(-0.325690\pi\) | ||||
0.520650 | + | 0.853770i | \(0.325690\pi\) | |||||||
\(60\) | 0.933471 | 0.120511 | ||||||||
\(61\) | −8.08683 | −1.03541 | −0.517706 | − | 0.855559i | \(-0.673214\pi\) | ||||
−0.517706 | + | 0.855559i | \(0.673214\pi\) | |||||||
\(62\) | −2.78382 | −0.353545 | ||||||||
\(63\) | −5.50384 | −0.693419 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.71092 | −0.460282 | ||||||||
\(66\) | 0.415881 | 0.0511915 | ||||||||
\(67\) | −11.4984 | −1.40475 | −0.702377 | − | 0.711805i | \(-0.747878\pi\) | ||||
−0.702377 | + | 0.711805i | \(0.747878\pi\) | |||||||
\(68\) | −4.04145 | −0.490098 | ||||||||
\(69\) | −3.44515 | −0.414747 | ||||||||
\(70\) | 4.36984 | 0.522295 | ||||||||
\(71\) | −3.83205 | −0.454781 | −0.227391 | − | 0.973804i | \(-0.573019\pi\) | ||||
−0.227391 | + | 0.973804i | \(0.573019\pi\) | |||||||
\(72\) | 2.82704 | 0.333170 | ||||||||
\(73\) | 0.425688 | 0.0498230 | 0.0249115 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249115 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(74\) | 0.827167 | 0.0961562 | ||||||||
\(75\) | −0.0158262 | −0.00182745 | ||||||||
\(76\) | −7.25266 | −0.831937 | ||||||||
\(77\) | 1.94686 | 0.221865 | ||||||||
\(78\) | 0.687573 | 0.0778524 | ||||||||
\(79\) | −13.8952 | −1.56333 | −0.781666 | − | 0.623698i | \(-0.785630\pi\) | ||||
−0.781666 | + | 0.623698i | \(0.785630\pi\) | |||||||
\(80\) | −2.24456 | −0.250950 | ||||||||
\(81\) | 7.47330 | 0.830367 | ||||||||
\(82\) | −5.69287 | −0.628672 | ||||||||
\(83\) | −2.39944 | −0.263373 | −0.131686 | − | 0.991291i | \(-0.542039\pi\) | ||||
−0.131686 | + | 0.991291i | \(0.542039\pi\) | |||||||
\(84\) | −0.809661 | −0.0883412 | ||||||||
\(85\) | 9.07128 | 0.983919 | ||||||||
\(86\) | −7.31501 | −0.788798 | ||||||||
\(87\) | −4.23991 | −0.454566 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 10.9318 | 1.15877 | 0.579387 | − | 0.815053i | \(-0.303292\pi\) | ||||
0.579387 | + | 0.815053i | \(0.303292\pi\) | |||||||
\(90\) | −6.34547 | −0.668871 | ||||||||
\(91\) | 3.21872 | 0.337414 | ||||||||
\(92\) | 8.28397 | 0.863663 | ||||||||
\(93\) | −1.15774 | −0.120052 | ||||||||
\(94\) | 7.73976 | 0.798295 | ||||||||
\(95\) | 16.2790 | 1.67019 | ||||||||
\(96\) | 0.415881 | 0.0424457 | ||||||||
\(97\) | 13.3160 | 1.35204 | 0.676020 | − | 0.736883i | \(-0.263703\pi\) | ||||
0.676020 | + | 0.736883i | \(0.263703\pi\) | |||||||
\(98\) | 3.20976 | 0.324234 | ||||||||
\(99\) | −2.82704 | −0.284128 | ||||||||
\(100\) | 0.0380545 | 0.00380545 | ||||||||
\(101\) | 8.43947 | 0.839758 | 0.419879 | − | 0.907580i | \(-0.362072\pi\) | ||||
0.419879 | + | 0.907580i | \(0.362072\pi\) | |||||||
\(102\) | −1.68076 | −0.166420 | ||||||||
\(103\) | −0.908357 | −0.0895031 | −0.0447516 | − | 0.998998i | \(-0.514250\pi\) | ||||
−0.0447516 | + | 0.998998i | \(0.514250\pi\) | |||||||
\(104\) | −1.65329 | −0.162119 | ||||||||
\(105\) | 1.81733 | 0.177354 | ||||||||
\(106\) | 7.74921 | 0.752670 | ||||||||
\(107\) | 14.1911 | 1.37190 | 0.685951 | − | 0.727647i | \(-0.259386\pi\) | ||||
0.685951 | + | 0.727647i | \(0.259386\pi\) | |||||||
\(108\) | 2.42336 | 0.233188 | ||||||||
\(109\) | 4.23544 | 0.405681 | 0.202841 | − | 0.979212i | \(-0.434983\pi\) | ||||
0.202841 | + | 0.979212i | \(0.434983\pi\) | |||||||
\(110\) | 2.24456 | 0.214011 | ||||||||
\(111\) | 0.344003 | 0.0326513 | ||||||||
\(112\) | 1.94686 | 0.183961 | ||||||||
\(113\) | −7.13396 | −0.671106 | −0.335553 | − | 0.942021i | \(-0.608923\pi\) | ||||
−0.335553 | + | 0.942021i | \(0.608923\pi\) | |||||||
\(114\) | −3.01625 | −0.282497 | ||||||||
\(115\) | −18.5939 | −1.73389 | ||||||||
\(116\) | 10.1950 | 0.946581 | ||||||||
\(117\) | −4.67393 | −0.432105 | ||||||||
\(118\) | −7.99838 | −0.736310 | ||||||||
\(119\) | −7.86812 | −0.721269 | ||||||||
\(120\) | −0.933471 | −0.0852139 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.08683 | 0.732147 | ||||||||
\(123\) | −2.36756 | −0.213476 | ||||||||
\(124\) | 2.78382 | 0.249994 | ||||||||
\(125\) | 11.1374 | 0.996158 | ||||||||
\(126\) | 5.50384 | 0.490321 | ||||||||
\(127\) | −17.6578 | −1.56687 | −0.783436 | − | 0.621472i | \(-0.786535\pi\) | ||||
−0.783436 | + | 0.621472i | \(0.786535\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.04217 | −0.267849 | ||||||||
\(130\) | 3.71092 | 0.325469 | ||||||||
\(131\) | −7.73493 | −0.675804 | −0.337902 | − | 0.941181i | \(-0.609717\pi\) | ||||
−0.337902 | + | 0.941181i | \(0.609717\pi\) | |||||||
\(132\) | −0.415881 | −0.0361978 | ||||||||
\(133\) | −14.1199 | −1.22435 | ||||||||
\(134\) | 11.4984 | 0.993312 | ||||||||
\(135\) | −5.43938 | −0.468147 | ||||||||
\(136\) | 4.04145 | 0.346551 | ||||||||
\(137\) | 1.28592 | 0.109864 | 0.0549319 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549319 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(138\) | 3.44515 | 0.293270 | ||||||||
\(139\) | −15.5538 | −1.31925 | −0.659627 | − | 0.751593i | \(-0.729286\pi\) | ||||
−0.659627 | + | 0.751593i | \(0.729286\pi\) | |||||||
\(140\) | −4.36984 | −0.369318 | ||||||||
\(141\) | 3.21882 | 0.271074 | ||||||||
\(142\) | 3.83205 | 0.321579 | ||||||||
\(143\) | 1.65329 | 0.138255 | ||||||||
\(144\) | −2.82704 | −0.235587 | ||||||||
\(145\) | −22.8833 | −1.90035 | ||||||||
\(146\) | −0.425688 | −0.0352302 | ||||||||
\(147\) | 1.33488 | 0.110099 | ||||||||
\(148\) | −0.827167 | −0.0679927 | ||||||||
\(149\) | −20.2290 | −1.65722 | −0.828611 | − | 0.559825i | \(-0.810868\pi\) | ||||
−0.828611 | + | 0.559825i | \(0.810868\pi\) | |||||||
\(150\) | 0.0158262 | 0.00129220 | ||||||||
\(151\) | 5.49776 | 0.447402 | 0.223701 | − | 0.974658i | \(-0.428186\pi\) | ||||
0.223701 | + | 0.974658i | \(0.428186\pi\) | |||||||
\(152\) | 7.25266 | 0.588269 | ||||||||
\(153\) | 11.4254 | 0.923685 | ||||||||
\(154\) | −1.94686 | −0.156882 | ||||||||
\(155\) | −6.24845 | −0.501888 | ||||||||
\(156\) | −0.687573 | −0.0550499 | ||||||||
\(157\) | 2.13019 | 0.170008 | 0.0850039 | − | 0.996381i | \(-0.472910\pi\) | ||||
0.0850039 | + | 0.996381i | \(0.472910\pi\) | |||||||
\(158\) | 13.8952 | 1.10544 | ||||||||
\(159\) | 3.22275 | 0.255581 | ||||||||
\(160\) | 2.24456 | 0.177448 | ||||||||
\(161\) | 16.1277 | 1.27104 | ||||||||
\(162\) | −7.47330 | −0.587158 | ||||||||
\(163\) | 20.4786 | 1.60401 | 0.802005 | − | 0.597317i | \(-0.203767\pi\) | ||||
0.802005 | + | 0.597317i | \(0.203767\pi\) | |||||||
\(164\) | 5.69287 | 0.444538 | ||||||||
\(165\) | 0.933471 | 0.0726706 | ||||||||
\(166\) | 2.39944 | 0.186233 | ||||||||
\(167\) | −2.86254 | −0.221510 | −0.110755 | − | 0.993848i | \(-0.535327\pi\) | ||||
−0.110755 | + | 0.993848i | \(0.535327\pi\) | |||||||
\(168\) | 0.809661 | 0.0624667 | ||||||||
\(169\) | −10.2666 | −0.789740 | ||||||||
\(170\) | −9.07128 | −0.695735 | ||||||||
\(171\) | 20.5036 | 1.56795 | ||||||||
\(172\) | 7.31501 | 0.557764 | ||||||||
\(173\) | −16.6986 | −1.26957 | −0.634784 | − | 0.772690i | \(-0.718911\pi\) | ||||
−0.634784 | + | 0.772690i | \(0.718911\pi\) | |||||||
\(174\) | 4.23991 | 0.321426 | ||||||||
\(175\) | 0.0740866 | 0.00560042 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −3.32637 | −0.250026 | ||||||||
\(178\) | −10.9318 | −0.819377 | ||||||||
\(179\) | −23.1531 | −1.73055 | −0.865273 | − | 0.501301i | \(-0.832855\pi\) | ||||
−0.865273 | + | 0.501301i | \(0.832855\pi\) | |||||||
\(180\) | 6.34547 | 0.472963 | ||||||||
\(181\) | 8.37604 | 0.622586 | 0.311293 | − | 0.950314i | \(-0.399238\pi\) | ||||
0.311293 | + | 0.950314i | \(0.399238\pi\) | |||||||
\(182\) | −3.21872 | −0.238587 | ||||||||
\(183\) | 3.36316 | 0.248612 | ||||||||
\(184\) | −8.28397 | −0.610702 | ||||||||
\(185\) | 1.85663 | 0.136502 | ||||||||
\(186\) | 1.15774 | 0.0848895 | ||||||||
\(187\) | −4.04145 | −0.295540 | ||||||||
\(188\) | −7.73976 | −0.564480 | ||||||||
\(189\) | 4.71793 | 0.343179 | ||||||||
\(190\) | −16.2790 | −1.18101 | ||||||||
\(191\) | 8.39612 | 0.607522 | 0.303761 | − | 0.952748i | \(-0.401758\pi\) | ||||
0.303761 | + | 0.952748i | \(0.401758\pi\) | |||||||
\(192\) | −0.415881 | −0.0300136 | ||||||||
\(193\) | −21.4162 | −1.54157 | −0.770784 | − | 0.637096i | \(-0.780135\pi\) | ||||
−0.770784 | + | 0.637096i | \(0.780135\pi\) | |||||||
\(194\) | −13.3160 | −0.956036 | ||||||||
\(195\) | 1.54330 | 0.110518 | ||||||||
\(196\) | −3.20976 | −0.229268 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 2.82704 | 0.200909 | ||||||||
\(199\) | 2.37949 | 0.168678 | 0.0843389 | − | 0.996437i | \(-0.473122\pi\) | ||||
0.0843389 | + | 0.996437i | \(0.473122\pi\) | |||||||
\(200\) | −0.0380545 | −0.00269086 | ||||||||
\(201\) | 4.78197 | 0.337294 | ||||||||
\(202\) | −8.43947 | −0.593799 | ||||||||
\(203\) | 19.8482 | 1.39307 | ||||||||
\(204\) | 1.68076 | 0.117677 | ||||||||
\(205\) | −12.7780 | −0.892454 | ||||||||
\(206\) | 0.908357 | 0.0632883 | ||||||||
\(207\) | −23.4191 | −1.62774 | ||||||||
\(208\) | 1.65329 | 0.114635 | ||||||||
\(209\) | −7.25266 | −0.501677 | ||||||||
\(210\) | −1.81733 | −0.125408 | ||||||||
\(211\) | 12.5858 | 0.866441 | 0.433220 | − | 0.901288i | \(-0.357377\pi\) | ||||
0.433220 | + | 0.901288i | \(0.357377\pi\) | |||||||
\(212\) | −7.74921 | −0.532218 | ||||||||
\(213\) | 1.59368 | 0.109197 | ||||||||
\(214\) | −14.1911 | −0.970082 | ||||||||
\(215\) | −16.4190 | −1.11977 | ||||||||
\(216\) | −2.42336 | −0.164889 | ||||||||
\(217\) | 5.41969 | 0.367913 | ||||||||
\(218\) | −4.23544 | −0.286860 | ||||||||
\(219\) | −0.177036 | −0.0119630 | ||||||||
\(220\) | −2.24456 | −0.151328 | ||||||||
\(221\) | −6.68170 | −0.449460 | ||||||||
\(222\) | −0.344003 | −0.0230880 | ||||||||
\(223\) | −17.6630 | −1.18280 | −0.591402 | − | 0.806377i | \(-0.701425\pi\) | ||||
−0.591402 | + | 0.806377i | \(0.701425\pi\) | |||||||
\(224\) | −1.94686 | −0.130080 | ||||||||
\(225\) | −0.107582 | −0.00717212 | ||||||||
\(226\) | 7.13396 | 0.474544 | ||||||||
\(227\) | −18.5462 | −1.23096 | −0.615478 | − | 0.788154i | \(-0.711037\pi\) | ||||
−0.615478 | + | 0.788154i | \(0.711037\pi\) | |||||||
\(228\) | 3.01625 | 0.199756 | ||||||||
\(229\) | −21.5774 | −1.42587 | −0.712936 | − | 0.701229i | \(-0.752635\pi\) | ||||
−0.712936 | + | 0.701229i | \(0.752635\pi\) | |||||||
\(230\) | 18.5939 | 1.22604 | ||||||||
\(231\) | −0.809661 | −0.0532718 | ||||||||
\(232\) | −10.1950 | −0.669334 | ||||||||
\(233\) | 22.8480 | 1.49682 | 0.748412 | − | 0.663234i | \(-0.230817\pi\) | ||||
0.748412 | + | 0.663234i | \(0.230817\pi\) | |||||||
\(234\) | 4.67393 | 0.305544 | ||||||||
\(235\) | 17.3724 | 1.13325 | ||||||||
\(236\) | 7.99838 | 0.520650 | ||||||||
\(237\) | 5.77875 | 0.375370 | ||||||||
\(238\) | 7.86812 | 0.510014 | ||||||||
\(239\) | 15.0535 | 0.973733 | 0.486866 | − | 0.873476i | \(-0.338140\pi\) | ||||
0.486866 | + | 0.873476i | \(0.338140\pi\) | |||||||
\(240\) | 0.933471 | 0.0602553 | ||||||||
\(241\) | −5.12265 | −0.329979 | −0.164989 | − | 0.986295i | \(-0.552759\pi\) | ||||
−0.164989 | + | 0.986295i | \(0.552759\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −10.3781 | −0.665754 | ||||||||
\(244\) | −8.08683 | −0.517706 | ||||||||
\(245\) | 7.20449 | 0.460278 | ||||||||
\(246\) | 2.36756 | 0.150950 | ||||||||
\(247\) | −11.9908 | −0.762954 | ||||||||
\(248\) | −2.78382 | −0.176773 | ||||||||
\(249\) | 0.997882 | 0.0632382 | ||||||||
\(250\) | −11.1374 | −0.704390 | ||||||||
\(251\) | −7.34662 | −0.463715 | −0.231857 | − | 0.972750i | \(-0.574480\pi\) | ||||
−0.231857 | + | 0.972750i | \(0.574480\pi\) | |||||||
\(252\) | −5.50384 | −0.346709 | ||||||||
\(253\) | 8.28397 | 0.520808 | ||||||||
\(254\) | 17.6578 | 1.10795 | ||||||||
\(255\) | −3.77258 | −0.236248 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.0169 | −1.43576 | −0.717878 | − | 0.696169i | \(-0.754886\pi\) | ||||
−0.717878 | + | 0.696169i | \(0.754886\pi\) | |||||||
\(258\) | 3.04217 | 0.189398 | ||||||||
\(259\) | −1.61037 | −0.100064 | ||||||||
\(260\) | −3.71092 | −0.230141 | ||||||||
\(261\) | −28.8217 | −1.78402 | ||||||||
\(262\) | 7.73493 | 0.477865 | ||||||||
\(263\) | −12.3679 | −0.762636 | −0.381318 | − | 0.924444i | \(-0.624530\pi\) | ||||
−0.381318 | + | 0.924444i | \(0.624530\pi\) | |||||||
\(264\) | 0.415881 | 0.0255957 | ||||||||
\(265\) | 17.3936 | 1.06848 | ||||||||
\(266\) | 14.1199 | 0.865745 | ||||||||
\(267\) | −4.54635 | −0.278232 | ||||||||
\(268\) | −11.4984 | −0.702377 | ||||||||
\(269\) | 19.0593 | 1.16206 | 0.581032 | − | 0.813881i | \(-0.302649\pi\) | ||||
0.581032 | + | 0.813881i | \(0.302649\pi\) | |||||||
\(270\) | 5.43938 | 0.331030 | ||||||||
\(271\) | −27.2184 | −1.65340 | −0.826700 | − | 0.562643i | \(-0.809784\pi\) | ||||
−0.826700 | + | 0.562643i | \(0.809784\pi\) | |||||||
\(272\) | −4.04145 | −0.245049 | ||||||||
\(273\) | −1.33861 | −0.0810161 | ||||||||
\(274\) | −1.28592 | −0.0776854 | ||||||||
\(275\) | 0.0380545 | 0.00229477 | ||||||||
\(276\) | −3.44515 | −0.207373 | ||||||||
\(277\) | −9.80168 | −0.588926 | −0.294463 | − | 0.955663i | \(-0.595141\pi\) | ||||
−0.294463 | + | 0.955663i | \(0.595141\pi\) | |||||||
\(278\) | 15.5538 | 0.932854 | ||||||||
\(279\) | −7.86998 | −0.471163 | ||||||||
\(280\) | 4.36984 | 0.261148 | ||||||||
\(281\) | 10.1543 | 0.605753 | 0.302876 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302876 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(282\) | −3.21882 | −0.191678 | ||||||||
\(283\) | −9.36458 | −0.556667 | −0.278333 | − | 0.960485i | \(-0.589782\pi\) | ||||
−0.278333 | + | 0.960485i | \(0.589782\pi\) | |||||||
\(284\) | −3.83205 | −0.227391 | ||||||||
\(285\) | −6.77015 | −0.401029 | ||||||||
\(286\) | −1.65329 | −0.0977612 | ||||||||
\(287\) | 11.0832 | 0.654220 | ||||||||
\(288\) | 2.82704 | 0.166585 | ||||||||
\(289\) | −0.666685 | −0.0392167 | ||||||||
\(290\) | 22.8833 | 1.34375 | ||||||||
\(291\) | −5.53789 | −0.324637 | ||||||||
\(292\) | 0.425688 | 0.0249115 | ||||||||
\(293\) | −6.59187 | −0.385101 | −0.192550 | − | 0.981287i | \(-0.561676\pi\) | ||||
−0.192550 | + | 0.981287i | \(0.561676\pi\) | |||||||
\(294\) | −1.33488 | −0.0778516 | ||||||||
\(295\) | −17.9528 | −1.04525 | ||||||||
\(296\) | 0.827167 | 0.0480781 | ||||||||
\(297\) | 2.42336 | 0.140618 | ||||||||
\(298\) | 20.2290 | 1.17183 | ||||||||
\(299\) | 13.6958 | 0.792049 | ||||||||
\(300\) | −0.0158262 | −0.000913724 0 | ||||||||
\(301\) | 14.2413 | 0.820853 | ||||||||
\(302\) | −5.49776 | −0.316361 | ||||||||
\(303\) | −3.50982 | −0.201634 | ||||||||
\(304\) | −7.25266 | −0.415969 | ||||||||
\(305\) | 18.1514 | 1.03934 | ||||||||
\(306\) | −11.4254 | −0.653144 | ||||||||
\(307\) | −6.82122 | −0.389308 | −0.194654 | − | 0.980872i | \(-0.562358\pi\) | ||||
−0.194654 | + | 0.980872i | \(0.562358\pi\) | |||||||
\(308\) | 1.94686 | 0.110932 | ||||||||
\(309\) | 0.377769 | 0.0214905 | ||||||||
\(310\) | 6.24845 | 0.354888 | ||||||||
\(311\) | −12.7217 | −0.721384 | −0.360692 | − | 0.932685i | \(-0.617459\pi\) | ||||
−0.360692 | + | 0.932685i | \(0.617459\pi\) | |||||||
\(312\) | 0.687573 | 0.0389262 | ||||||||
\(313\) | −2.87908 | −0.162735 | −0.0813676 | − | 0.996684i | \(-0.525929\pi\) | ||||
−0.0813676 | + | 0.996684i | \(0.525929\pi\) | |||||||
\(314\) | −2.13019 | −0.120214 | ||||||||
\(315\) | 12.3537 | 0.696053 | ||||||||
\(316\) | −13.8952 | −0.781666 | ||||||||
\(317\) | 1.25368 | 0.0704135 | 0.0352067 | − | 0.999380i | \(-0.488791\pi\) | ||||
0.0352067 | + | 0.999380i | \(0.488791\pi\) | |||||||
\(318\) | −3.22275 | −0.180723 | ||||||||
\(319\) | 10.1950 | 0.570810 | ||||||||
\(320\) | −2.24456 | −0.125475 | ||||||||
\(321\) | −5.90180 | −0.329406 | ||||||||
\(322\) | −16.1277 | −0.898761 | ||||||||
\(323\) | 29.3113 | 1.63092 | ||||||||
\(324\) | 7.47330 | 0.415183 | ||||||||
\(325\) | 0.0629153 | 0.00348991 | ||||||||
\(326\) | −20.4786 | −1.13421 | ||||||||
\(327\) | −1.76144 | −0.0974078 | ||||||||
\(328\) | −5.69287 | −0.314336 | ||||||||
\(329\) | −15.0682 | −0.830736 | ||||||||
\(330\) | −0.933471 | −0.0513859 | ||||||||
\(331\) | −30.0110 | −1.64955 | −0.824777 | − | 0.565458i | \(-0.808700\pi\) | ||||
−0.824777 | + | 0.565458i | \(0.808700\pi\) | |||||||
\(332\) | −2.39944 | −0.131686 | ||||||||
\(333\) | 2.33844 | 0.128145 | ||||||||
\(334\) | 2.86254 | 0.156631 | ||||||||
\(335\) | 25.8089 | 1.41009 | ||||||||
\(336\) | −0.809661 | −0.0441706 | ||||||||
\(337\) | −17.6720 | −0.962654 | −0.481327 | − | 0.876541i | \(-0.659845\pi\) | ||||
−0.481327 | + | 0.876541i | \(0.659845\pi\) | |||||||
\(338\) | 10.2666 | 0.558431 | ||||||||
\(339\) | 2.96688 | 0.161139 | ||||||||
\(340\) | 9.07128 | 0.491959 | ||||||||
\(341\) | 2.78382 | 0.150752 | ||||||||
\(342\) | −20.5036 | −1.10871 | ||||||||
\(343\) | −19.8769 | −1.07325 | ||||||||
\(344\) | −7.31501 | −0.394399 | ||||||||
\(345\) | 7.73284 | 0.416322 | ||||||||
\(346\) | 16.6986 | 0.897720 | ||||||||
\(347\) | −0.243786 | −0.0130871 | −0.00654355 | − | 0.999979i | \(-0.502083\pi\) | ||||
−0.00654355 | + | 0.999979i | \(0.502083\pi\) | |||||||
\(348\) | −4.23991 | −0.227283 | ||||||||
\(349\) | −34.9736 | −1.87210 | −0.936048 | − | 0.351872i | \(-0.885545\pi\) | ||||
−0.936048 | + | 0.351872i | \(0.885545\pi\) | |||||||
\(350\) | −0.0740866 | −0.00396010 | ||||||||
\(351\) | 4.00652 | 0.213852 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 24.5306 | 1.30563 | 0.652816 | − | 0.757517i | \(-0.273588\pi\) | ||||
0.652816 | + | 0.757517i | \(0.273588\pi\) | |||||||
\(354\) | 3.32637 | 0.176795 | ||||||||
\(355\) | 8.60128 | 0.456508 | ||||||||
\(356\) | 10.9318 | 0.579387 | ||||||||
\(357\) | 3.27220 | 0.173183 | ||||||||
\(358\) | 23.1531 | 1.22368 | ||||||||
\(359\) | 34.5941 | 1.82581 | 0.912903 | − | 0.408177i | \(-0.133835\pi\) | ||||
0.912903 | + | 0.408177i | \(0.133835\pi\) | |||||||
\(360\) | −6.34547 | −0.334436 | ||||||||
\(361\) | 33.6011 | 1.76848 | ||||||||
\(362\) | −8.37604 | −0.440235 | ||||||||
\(363\) | −0.415881 | −0.0218281 | ||||||||
\(364\) | 3.21872 | 0.168707 | ||||||||
\(365\) | −0.955483 | −0.0500123 | ||||||||
\(366\) | −3.36316 | −0.175795 | ||||||||
\(367\) | −16.5904 | −0.866013 | −0.433006 | − | 0.901391i | \(-0.642547\pi\) | ||||
−0.433006 | + | 0.901391i | \(0.642547\pi\) | |||||||
\(368\) | 8.28397 | 0.431832 | ||||||||
\(369\) | −16.0940 | −0.837819 | ||||||||
\(370\) | −1.85663 | −0.0965214 | ||||||||
\(371\) | −15.0866 | −0.783257 | ||||||||
\(372\) | −1.15774 | −0.0600259 | ||||||||
\(373\) | 31.2666 | 1.61892 | 0.809462 | − | 0.587172i | \(-0.199759\pi\) | ||||
0.809462 | + | 0.587172i | \(0.199759\pi\) | |||||||
\(374\) | 4.04145 | 0.208978 | ||||||||
\(375\) | −4.63183 | −0.239187 | ||||||||
\(376\) | 7.73976 | 0.399148 | ||||||||
\(377\) | 16.8553 | 0.868092 | ||||||||
\(378\) | −4.71793 | −0.242664 | ||||||||
\(379\) | −7.45385 | −0.382878 | −0.191439 | − | 0.981504i | \(-0.561315\pi\) | ||||
−0.191439 | + | 0.981504i | \(0.561315\pi\) | |||||||
\(380\) | 16.2790 | 0.835097 | ||||||||
\(381\) | 7.34353 | 0.376221 | ||||||||
\(382\) | −8.39612 | −0.429583 | ||||||||
\(383\) | −19.2295 | −0.982582 | −0.491291 | − | 0.870996i | \(-0.663475\pi\) | ||||
−0.491291 | + | 0.870996i | \(0.663475\pi\) | |||||||
\(384\) | 0.415881 | 0.0212229 | ||||||||
\(385\) | −4.36984 | −0.222707 | ||||||||
\(386\) | 21.4162 | 1.09005 | ||||||||
\(387\) | −20.6798 | −1.05122 | ||||||||
\(388\) | 13.3160 | 0.676020 | ||||||||
\(389\) | −18.3410 | −0.929926 | −0.464963 | − | 0.885330i | \(-0.653932\pi\) | ||||
−0.464963 | + | 0.885330i | \(0.653932\pi\) | |||||||
\(390\) | −1.54330 | −0.0781481 | ||||||||
\(391\) | −33.4792 | −1.69312 | ||||||||
\(392\) | 3.20976 | 0.162117 | ||||||||
\(393\) | 3.21681 | 0.162267 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 31.1886 | 1.56927 | ||||||||
\(396\) | −2.82704 | −0.142064 | ||||||||
\(397\) | −5.37974 | −0.270001 | −0.135001 | − | 0.990846i | \(-0.543104\pi\) | ||||
−0.135001 | + | 0.990846i | \(0.543104\pi\) | |||||||
\(398\) | −2.37949 | −0.119273 | ||||||||
\(399\) | 5.87219 | 0.293977 | ||||||||
\(400\) | 0.0380545 | 0.00190273 | ||||||||
\(401\) | −38.0579 | −1.90052 | −0.950261 | − | 0.311456i | \(-0.899183\pi\) | ||||
−0.950261 | + | 0.311456i | \(0.899183\pi\) | |||||||
\(402\) | −4.78197 | −0.238503 | ||||||||
\(403\) | 4.60247 | 0.229265 | ||||||||
\(404\) | 8.43947 | 0.419879 | ||||||||
\(405\) | −16.7743 | −0.833520 | ||||||||
\(406\) | −19.8482 | −0.985048 | ||||||||
\(407\) | −0.827167 | −0.0410011 | ||||||||
\(408\) | −1.68076 | −0.0832102 | ||||||||
\(409\) | 25.1927 | 1.24570 | 0.622850 | − | 0.782341i | \(-0.285975\pi\) | ||||
0.622850 | + | 0.782341i | \(0.285975\pi\) | |||||||
\(410\) | 12.7780 | 0.631060 | ||||||||
\(411\) | −0.534791 | −0.0263793 | ||||||||
\(412\) | −0.908357 | −0.0447516 | ||||||||
\(413\) | 15.5717 | 0.766232 | ||||||||
\(414\) | 23.4191 | 1.15099 | ||||||||
\(415\) | 5.38569 | 0.264373 | ||||||||
\(416\) | −1.65329 | −0.0810593 | ||||||||
\(417\) | 6.46853 | 0.316765 | ||||||||
\(418\) | 7.25266 | 0.354739 | ||||||||
\(419\) | 3.41451 | 0.166809 | 0.0834047 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834047 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(420\) | 1.81733 | 0.0886768 | ||||||||
\(421\) | 20.5210 | 1.00013 | 0.500067 | − | 0.865987i | \(-0.333309\pi\) | ||||
0.500067 | + | 0.865987i | \(0.333309\pi\) | |||||||
\(422\) | −12.5858 | −0.612666 | ||||||||
\(423\) | 21.8806 | 1.06387 | ||||||||
\(424\) | 7.74921 | 0.376335 | ||||||||
\(425\) | −0.153795 | −0.00746018 | ||||||||
\(426\) | −1.59368 | −0.0772140 | ||||||||
\(427\) | −15.7439 | −0.761900 | ||||||||
\(428\) | 14.1911 | 0.685951 | ||||||||
\(429\) | −0.687573 | −0.0331964 | ||||||||
\(430\) | 16.4190 | 0.791794 | ||||||||
\(431\) | 7.43175 | 0.357975 | 0.178987 | − | 0.983851i | \(-0.442718\pi\) | ||||
0.178987 | + | 0.983851i | \(0.442718\pi\) | |||||||
\(432\) | 2.42336 | 0.116594 | ||||||||
\(433\) | −32.3343 | −1.55389 | −0.776943 | − | 0.629571i | \(-0.783231\pi\) | ||||
−0.776943 | + | 0.629571i | \(0.783231\pi\) | |||||||
\(434\) | −5.41969 | −0.260154 | ||||||||
\(435\) | 9.51673 | 0.456292 | ||||||||
\(436\) | 4.23544 | 0.202841 | ||||||||
\(437\) | −60.0808 | −2.87405 | ||||||||
\(438\) | 0.177036 | 0.00845909 | ||||||||
\(439\) | 6.87171 | 0.327969 | 0.163984 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163984 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(440\) | 2.24456 | 0.107005 | ||||||||
\(441\) | 9.07412 | 0.432101 | ||||||||
\(442\) | 6.68170 | 0.317816 | ||||||||
\(443\) | −2.12632 | −0.101025 | −0.0505124 | − | 0.998723i | \(-0.516085\pi\) | ||||
−0.0505124 | + | 0.998723i | \(0.516085\pi\) | |||||||
\(444\) | 0.344003 | 0.0163257 | ||||||||
\(445\) | −24.5372 | −1.16317 | ||||||||
\(446\) | 17.6630 | 0.836369 | ||||||||
\(447\) | 8.41285 | 0.397914 | ||||||||
\(448\) | 1.94686 | 0.0919803 | ||||||||
\(449\) | −29.2391 | −1.37988 | −0.689939 | − | 0.723868i | \(-0.742363\pi\) | ||||
−0.689939 | + | 0.723868i | \(0.742363\pi\) | |||||||
\(450\) | 0.107582 | 0.00507145 | ||||||||
\(451\) | 5.69287 | 0.268067 | ||||||||
\(452\) | −7.13396 | −0.335553 | ||||||||
\(453\) | −2.28642 | −0.107425 | ||||||||
\(454\) | 18.5462 | 0.870417 | ||||||||
\(455\) | −7.22461 | −0.338695 | ||||||||
\(456\) | −3.01625 | −0.141249 | ||||||||
\(457\) | −26.0219 | −1.21725 | −0.608626 | − | 0.793458i | \(-0.708279\pi\) | ||||
−0.608626 | + | 0.793458i | \(0.708279\pi\) | |||||||
\(458\) | 21.5774 | 1.00824 | ||||||||
\(459\) | −9.79388 | −0.457139 | ||||||||
\(460\) | −18.5939 | −0.866944 | ||||||||
\(461\) | −22.1268 | −1.03055 | −0.515275 | − | 0.857025i | \(-0.672310\pi\) | ||||
−0.515275 | + | 0.857025i | \(0.672310\pi\) | |||||||
\(462\) | 0.809661 | 0.0376688 | ||||||||
\(463\) | −18.9937 | −0.882711 | −0.441356 | − | 0.897332i | \(-0.645502\pi\) | ||||
−0.441356 | + | 0.897332i | \(0.645502\pi\) | |||||||
\(464\) | 10.1950 | 0.473291 | ||||||||
\(465\) | 2.59861 | 0.120508 | ||||||||
\(466\) | −22.8480 | −1.05841 | ||||||||
\(467\) | 20.0636 | 0.928433 | 0.464217 | − | 0.885722i | \(-0.346336\pi\) | ||||
0.464217 | + | 0.885722i | \(0.346336\pi\) | |||||||
\(468\) | −4.67393 | −0.216052 | ||||||||
\(469\) | −22.3857 | −1.03368 | ||||||||
\(470\) | −17.3724 | −0.801327 | ||||||||
\(471\) | −0.885907 | −0.0408204 | ||||||||
\(472\) | −7.99838 | −0.368155 | ||||||||
\(473\) | 7.31501 | 0.336344 | ||||||||
\(474\) | −5.77875 | −0.265427 | ||||||||
\(475\) | −0.275997 | −0.0126636 | ||||||||
\(476\) | −7.86812 | −0.360635 | ||||||||
\(477\) | 21.9074 | 1.00307 | ||||||||
\(478\) | −15.0535 | −0.688533 | ||||||||
\(479\) | −30.9779 | −1.41542 | −0.707708 | − | 0.706505i | \(-0.750271\pi\) | ||||
−0.707708 | + | 0.706505i | \(0.750271\pi\) | |||||||
\(480\) | −0.933471 | −0.0426069 | ||||||||
\(481\) | −1.36755 | −0.0623548 | ||||||||
\(482\) | 5.12265 | 0.233330 | ||||||||
\(483\) | −6.70720 | −0.305188 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −29.8887 | −1.35717 | ||||||||
\(486\) | 10.3781 | 0.470759 | ||||||||
\(487\) | −40.2405 | −1.82347 | −0.911735 | − | 0.410778i | \(-0.865257\pi\) | ||||
−0.911735 | + | 0.410778i | \(0.865257\pi\) | |||||||
\(488\) | 8.08683 | 0.366073 | ||||||||
\(489\) | −8.51668 | −0.385137 | ||||||||
\(490\) | −7.20449 | −0.325466 | ||||||||
\(491\) | 23.9956 | 1.08291 | 0.541453 | − | 0.840731i | \(-0.317874\pi\) | ||||
0.541453 | + | 0.840731i | \(0.317874\pi\) | |||||||
\(492\) | −2.36756 | −0.106738 | ||||||||
\(493\) | −41.2025 | −1.85567 | ||||||||
\(494\) | 11.9908 | 0.539490 | ||||||||
\(495\) | 6.34547 | 0.285208 | ||||||||
\(496\) | 2.78382 | 0.124997 | ||||||||
\(497\) | −7.46045 | −0.334647 | ||||||||
\(498\) | −0.997882 | −0.0447162 | ||||||||
\(499\) | 10.6271 | 0.475733 | 0.237867 | − | 0.971298i | \(-0.423552\pi\) | ||||
0.237867 | + | 0.971298i | \(0.423552\pi\) | |||||||
\(500\) | 11.1374 | 0.498079 | ||||||||
\(501\) | 1.19048 | 0.0531866 | ||||||||
\(502\) | 7.34662 | 0.327896 | ||||||||
\(503\) | −12.7231 | −0.567297 | −0.283648 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283648 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(504\) | 5.50384 | 0.245161 | ||||||||
\(505\) | −18.9429 | −0.842948 | ||||||||
\(506\) | −8.28397 | −0.368267 | ||||||||
\(507\) | 4.26970 | 0.189624 | ||||||||
\(508\) | −17.6578 | −0.783436 | ||||||||
\(509\) | 1.21159 | 0.0537026 | 0.0268513 | − | 0.999639i | \(-0.491452\pi\) | ||||
0.0268513 | + | 0.999639i | \(0.491452\pi\) | |||||||
\(510\) | 3.77258 | 0.167052 | ||||||||
\(511\) | 0.828753 | 0.0366619 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.5758 | −0.775990 | ||||||||
\(514\) | 23.0169 | 1.01523 | ||||||||
\(515\) | 2.03886 | 0.0898431 | ||||||||
\(516\) | −3.04217 | −0.133924 | ||||||||
\(517\) | −7.73976 | −0.340394 | ||||||||
\(518\) | 1.61037 | 0.0707557 | ||||||||
\(519\) | 6.94462 | 0.304835 | ||||||||
\(520\) | 3.71092 | 0.162734 | ||||||||
\(521\) | 10.2745 | 0.450133 | 0.225067 | − | 0.974343i | \(-0.427740\pi\) | ||||
0.225067 | + | 0.974343i | \(0.427740\pi\) | |||||||
\(522\) | 28.8217 | 1.26149 | ||||||||
\(523\) | 38.8472 | 1.69867 | 0.849334 | − | 0.527855i | \(-0.177004\pi\) | ||||
0.849334 | + | 0.527855i | \(0.177004\pi\) | |||||||
\(524\) | −7.73493 | −0.337902 | ||||||||
\(525\) | −0.0308113 | −0.00134471 | ||||||||
\(526\) | 12.3679 | 0.539265 | ||||||||
\(527\) | −11.2507 | −0.490087 | ||||||||
\(528\) | −0.415881 | −0.0180989 | ||||||||
\(529\) | 45.6241 | 1.98366 | ||||||||
\(530\) | −17.3936 | −0.755529 | ||||||||
\(531\) | −22.6117 | −0.981266 | ||||||||
\(532\) | −14.1199 | −0.612174 | ||||||||
\(533\) | 9.41198 | 0.407678 | ||||||||
\(534\) | 4.54635 | 0.196740 | ||||||||
\(535\) | −31.8527 | −1.37711 | ||||||||
\(536\) | 11.4984 | 0.496656 | ||||||||
\(537\) | 9.62895 | 0.415520 | ||||||||
\(538\) | −19.0593 | −0.821703 | ||||||||
\(539\) | −3.20976 | −0.138254 | ||||||||
\(540\) | −5.43938 | −0.234073 | ||||||||
\(541\) | 14.0073 | 0.602221 | 0.301111 | − | 0.953589i | \(-0.402643\pi\) | ||||
0.301111 | + | 0.953589i | \(0.402643\pi\) | |||||||
\(542\) | 27.2184 | 1.16913 | ||||||||
\(543\) | −3.48344 | −0.149489 | ||||||||
\(544\) | 4.04145 | 0.173276 | ||||||||
\(545\) | −9.50670 | −0.407222 | ||||||||
\(546\) | 1.33861 | 0.0572870 | ||||||||
\(547\) | 41.4133 | 1.77070 | 0.885352 | − | 0.464922i | \(-0.153918\pi\) | ||||
0.885352 | + | 0.464922i | \(0.153918\pi\) | |||||||
\(548\) | 1.28592 | 0.0549319 | ||||||||
\(549\) | 22.8618 | 0.975718 | ||||||||
\(550\) | −0.0380545 | −0.00162265 | ||||||||
\(551\) | −73.9408 | −3.14998 | ||||||||
\(552\) | 3.44515 | 0.146635 | ||||||||
\(553\) | −27.0519 | −1.15036 | ||||||||
\(554\) | 9.80168 | 0.416433 | ||||||||
\(555\) | −0.772136 | −0.0327753 | ||||||||
\(556\) | −15.5538 | −0.659627 | ||||||||
\(557\) | 12.2680 | 0.519814 | 0.259907 | − | 0.965634i | \(-0.416308\pi\) | ||||
0.259907 | + | 0.965634i | \(0.416308\pi\) | |||||||
\(558\) | 7.86998 | 0.333163 | ||||||||
\(559\) | 12.0938 | 0.511515 | ||||||||
\(560\) | −4.36984 | −0.184659 | ||||||||
\(561\) | 1.68076 | 0.0709619 | ||||||||
\(562\) | −10.1543 | −0.428332 | ||||||||
\(563\) | 14.1117 | 0.594738 | 0.297369 | − | 0.954763i | \(-0.403891\pi\) | ||||
0.297369 | + | 0.954763i | \(0.403891\pi\) | |||||||
\(564\) | 3.21882 | 0.135537 | ||||||||
\(565\) | 16.0126 | 0.673655 | ||||||||
\(566\) | 9.36458 | 0.393623 | ||||||||
\(567\) | 14.5494 | 0.611019 | ||||||||
\(568\) | 3.83205 | 0.160789 | ||||||||
\(569\) | 1.27004 | 0.0532428 | 0.0266214 | − | 0.999646i | \(-0.491525\pi\) | ||||
0.0266214 | + | 0.999646i | \(0.491525\pi\) | |||||||
\(570\) | 6.77015 | 0.283570 | ||||||||
\(571\) | −29.1426 | −1.21958 | −0.609789 | − | 0.792564i | \(-0.708746\pi\) | ||||
−0.609789 | + | 0.792564i | \(0.708746\pi\) | |||||||
\(572\) | 1.65329 | 0.0691276 | ||||||||
\(573\) | −3.49179 | −0.145872 | ||||||||
\(574\) | −11.0832 | −0.462603 | ||||||||
\(575\) | 0.315242 | 0.0131465 | ||||||||
\(576\) | −2.82704 | −0.117793 | ||||||||
\(577\) | 17.4190 | 0.725164 | 0.362582 | − | 0.931952i | \(-0.381895\pi\) | ||||
0.362582 | + | 0.931952i | \(0.381895\pi\) | |||||||
\(578\) | 0.666685 | 0.0277304 | ||||||||
\(579\) | 8.90658 | 0.370145 | ||||||||
\(580\) | −22.8833 | −0.950177 | ||||||||
\(581\) | −4.67136 | −0.193801 | ||||||||
\(582\) | 5.53789 | 0.229553 | ||||||||
\(583\) | −7.74921 | −0.320940 | ||||||||
\(584\) | −0.425688 | −0.0176151 | ||||||||
\(585\) | 10.4909 | 0.433746 | ||||||||
\(586\) | 6.59187 | 0.272307 | ||||||||
\(587\) | 23.4923 | 0.969629 | 0.484815 | − | 0.874617i | \(-0.338887\pi\) | ||||
0.484815 | + | 0.874617i | \(0.338887\pi\) | |||||||
\(588\) | 1.33488 | 0.0550494 | ||||||||
\(589\) | −20.1901 | −0.831919 | ||||||||
\(590\) | 17.9528 | 0.739107 | ||||||||
\(591\) | −0.415881 | −0.0171071 | ||||||||
\(592\) | −0.827167 | −0.0339963 | ||||||||
\(593\) | −31.0519 | −1.27515 | −0.637575 | − | 0.770389i | \(-0.720062\pi\) | ||||
−0.637575 | + | 0.770389i | \(0.720062\pi\) | |||||||
\(594\) | −2.42336 | −0.0994316 | ||||||||
\(595\) | 17.6605 | 0.724009 | ||||||||
\(596\) | −20.2290 | −0.828611 | ||||||||
\(597\) | −0.989587 | −0.0405011 | ||||||||
\(598\) | −13.6958 | −0.560064 | ||||||||
\(599\) | 11.6353 | 0.475407 | 0.237703 | − | 0.971338i | \(-0.423605\pi\) | ||||
0.237703 | + | 0.971338i | \(0.423605\pi\) | |||||||
\(600\) | 0.0158262 | 0.000646101 0 | ||||||||
\(601\) | −21.8978 | −0.893230 | −0.446615 | − | 0.894726i | \(-0.647371\pi\) | ||||
−0.446615 | + | 0.894726i | \(0.647371\pi\) | |||||||
\(602\) | −14.2413 | −0.580430 | ||||||||
\(603\) | 32.5065 | 1.32377 | ||||||||
\(604\) | 5.49776 | 0.223701 | ||||||||
\(605\) | −2.24456 | −0.0912544 | ||||||||
\(606\) | 3.50982 | 0.142577 | ||||||||
\(607\) | −3.60391 | −0.146278 | −0.0731391 | − | 0.997322i | \(-0.523302\pi\) | ||||
−0.0731391 | + | 0.997322i | \(0.523302\pi\) | |||||||
\(608\) | 7.25266 | 0.294134 | ||||||||
\(609\) | −8.25448 | −0.334489 | ||||||||
\(610\) | −18.1514 | −0.734928 | ||||||||
\(611\) | −12.7961 | −0.517674 | ||||||||
\(612\) | 11.4254 | 0.461842 | ||||||||
\(613\) | −11.8355 | −0.478031 | −0.239016 | − | 0.971016i | \(-0.576825\pi\) | ||||
−0.239016 | + | 0.971016i | \(0.576825\pi\) | |||||||
\(614\) | 6.82122 | 0.275282 | ||||||||
\(615\) | 5.31413 | 0.214286 | ||||||||
\(616\) | −1.94686 | −0.0784410 | ||||||||
\(617\) | −11.4542 | −0.461129 | −0.230564 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230564 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(618\) | −0.377769 | −0.0151961 | ||||||||
\(619\) | −26.2561 | −1.05532 | −0.527660 | − | 0.849455i | \(-0.676931\pi\) | ||||
−0.527660 | + | 0.849455i | \(0.676931\pi\) | |||||||
\(620\) | −6.24845 | −0.250944 | ||||||||
\(621\) | 20.0750 | 0.805583 | ||||||||
\(622\) | 12.7217 | 0.510095 | ||||||||
\(623\) | 21.2827 | 0.852674 | ||||||||
\(624\) | −0.687573 | −0.0275250 | ||||||||
\(625\) | −25.1888 | −1.00755 | ||||||||
\(626\) | 2.87908 | 0.115071 | ||||||||
\(627\) | 3.01625 | 0.120457 | ||||||||
\(628\) | 2.13019 | 0.0850039 | ||||||||
\(629\) | 3.34295 | 0.133292 | ||||||||
\(630\) | −12.3537 | −0.492184 | ||||||||
\(631\) | 11.1616 | 0.444336 | 0.222168 | − | 0.975008i | \(-0.428687\pi\) | ||||
0.222168 | + | 0.975008i | \(0.428687\pi\) | |||||||
\(632\) | 13.8952 | 0.552721 | ||||||||
\(633\) | −5.23419 | −0.208040 | ||||||||
\(634\) | −1.25368 | −0.0497899 | ||||||||
\(635\) | 39.6339 | 1.57282 | ||||||||
\(636\) | 3.22275 | 0.127790 | ||||||||
\(637\) | −5.30666 | −0.210258 | ||||||||
\(638\) | −10.1950 | −0.403624 | ||||||||
\(639\) | 10.8334 | 0.428562 | ||||||||
\(640\) | 2.24456 | 0.0887241 | ||||||||
\(641\) | 43.2448 | 1.70807 | 0.854033 | − | 0.520219i | \(-0.174150\pi\) | ||||
0.854033 | + | 0.520219i | \(0.174150\pi\) | |||||||
\(642\) | 5.90180 | 0.232926 | ||||||||
\(643\) | 49.6160 | 1.95666 | 0.978332 | − | 0.207040i | \(-0.0663830\pi\) | ||||
0.978332 | + | 0.207040i | \(0.0663830\pi\) | |||||||
\(644\) | 16.1277 | 0.635520 | ||||||||
\(645\) | 6.82835 | 0.268866 | ||||||||
\(646\) | −29.3113 | −1.15324 | ||||||||
\(647\) | −28.2651 | −1.11121 | −0.555607 | − | 0.831445i | \(-0.687514\pi\) | ||||
−0.555607 | + | 0.831445i | \(0.687514\pi\) | |||||||
\(648\) | −7.47330 | −0.293579 | ||||||||
\(649\) | 7.99838 | 0.313964 | ||||||||
\(650\) | −0.0629153 | −0.00246774 | ||||||||
\(651\) | −2.25395 | −0.0883392 | ||||||||
\(652\) | 20.4786 | 0.802005 | ||||||||
\(653\) | −15.1579 | −0.593175 | −0.296588 | − | 0.955006i | \(-0.595849\pi\) | ||||
−0.296588 | + | 0.955006i | \(0.595849\pi\) | |||||||
\(654\) | 1.76144 | 0.0688777 | ||||||||
\(655\) | 17.3615 | 0.678371 | ||||||||
\(656\) | 5.69287 | 0.222269 | ||||||||
\(657\) | −1.20344 | −0.0469506 | ||||||||
\(658\) | 15.0682 | 0.587419 | ||||||||
\(659\) | −9.71715 | −0.378526 | −0.189263 | − | 0.981926i | \(-0.560610\pi\) | ||||
−0.189263 | + | 0.981926i | \(0.560610\pi\) | |||||||
\(660\) | 0.933471 | 0.0363353 | ||||||||
\(661\) | 31.9873 | 1.24416 | 0.622080 | − | 0.782953i | \(-0.286288\pi\) | ||||
0.622080 | + | 0.782953i | \(0.286288\pi\) | |||||||
\(662\) | 30.0110 | 1.16641 | ||||||||
\(663\) | 2.77879 | 0.107919 | ||||||||
\(664\) | 2.39944 | 0.0931164 | ||||||||
\(665\) | 31.6929 | 1.22900 | ||||||||
\(666\) | −2.33844 | −0.0906125 | ||||||||
\(667\) | 84.4550 | 3.27011 | ||||||||
\(668\) | −2.86254 | −0.110755 | ||||||||
\(669\) | 7.34572 | 0.284002 | ||||||||
\(670\) | −25.8089 | −0.997084 | ||||||||
\(671\) | −8.08683 | −0.312188 | ||||||||
\(672\) | 0.809661 | 0.0312333 | ||||||||
\(673\) | −1.26061 | −0.0485930 | −0.0242965 | − | 0.999705i | \(-0.507735\pi\) | ||||
−0.0242965 | + | 0.999705i | \(0.507735\pi\) | |||||||
\(674\) | 17.6720 | 0.680699 | ||||||||
\(675\) | 0.0922197 | 0.00354954 | ||||||||
\(676\) | −10.2666 | −0.394870 | ||||||||
\(677\) | −4.77936 | −0.183686 | −0.0918428 | − | 0.995774i | \(-0.529276\pi\) | ||||
−0.0918428 | + | 0.995774i | \(0.529276\pi\) | |||||||
\(678\) | −2.96688 | −0.113942 | ||||||||
\(679\) | 25.9244 | 0.994888 | ||||||||
\(680\) | −9.07128 | −0.347868 | ||||||||
\(681\) | 7.71302 | 0.295564 | ||||||||
\(682\) | −2.78382 | −0.106598 | ||||||||
\(683\) | 29.3451 | 1.12286 | 0.561430 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561430 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(684\) | 20.5036 | 0.783974 | ||||||||
\(685\) | −2.88633 | −0.110281 | ||||||||
\(686\) | 19.8769 | 0.758904 | ||||||||
\(687\) | 8.97362 | 0.342365 | ||||||||
\(688\) | 7.31501 | 0.278882 | ||||||||
\(689\) | −12.8117 | −0.488087 | ||||||||
\(690\) | −7.73284 | −0.294384 | ||||||||
\(691\) | −34.2141 | −1.30157 | −0.650783 | − | 0.759263i | \(-0.725559\pi\) | ||||
−0.650783 | + | 0.759263i | \(0.725559\pi\) | |||||||
\(692\) | −16.6986 | −0.634784 | ||||||||
\(693\) | −5.50384 | −0.209074 | ||||||||
\(694\) | 0.243786 | 0.00925398 | ||||||||
\(695\) | 34.9114 | 1.32427 | ||||||||
\(696\) | 4.23991 | 0.160713 | ||||||||
\(697\) | −23.0074 | −0.871469 | ||||||||
\(698\) | 34.9736 | 1.32377 | ||||||||
\(699\) | −9.50207 | −0.359401 | ||||||||
\(700\) | 0.0740866 | 0.00280021 | ||||||||
\(701\) | −11.5370 | −0.435745 | −0.217873 | − | 0.975977i | \(-0.569912\pi\) | ||||
−0.217873 | + | 0.975977i | \(0.569912\pi\) | |||||||
\(702\) | −4.00652 | −0.151216 | ||||||||
\(703\) | 5.99916 | 0.226263 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −7.22484 | −0.272103 | ||||||||
\(706\) | −24.5306 | −0.923221 | ||||||||
\(707\) | 16.4304 | 0.617929 | ||||||||
\(708\) | −3.32637 | −0.125013 | ||||||||
\(709\) | −21.8738 | −0.821489 | −0.410745 | − | 0.911750i | \(-0.634731\pi\) | ||||
−0.410745 | + | 0.911750i | \(0.634731\pi\) | |||||||
\(710\) | −8.60128 | −0.322800 | ||||||||
\(711\) | 39.2823 | 1.47320 | ||||||||
\(712\) | −10.9318 | −0.409688 | ||||||||
\(713\) | 23.0611 | 0.863644 | ||||||||
\(714\) | −3.27220 | −0.122459 | ||||||||
\(715\) | −3.71092 | −0.138780 | ||||||||
\(716\) | −23.1531 | −0.865273 | ||||||||
\(717\) | −6.26049 | −0.233802 | ||||||||
\(718\) | −34.5941 | −1.29104 | ||||||||
\(719\) | −13.8885 | −0.517953 | −0.258976 | − | 0.965884i | \(-0.583385\pi\) | ||||
−0.258976 | + | 0.965884i | \(0.583385\pi\) | |||||||
\(720\) | 6.34547 | 0.236482 | ||||||||
\(721\) | −1.76844 | −0.0658601 | ||||||||
\(722\) | −33.6011 | −1.25050 | ||||||||
\(723\) | 2.13041 | 0.0792309 | ||||||||
\(724\) | 8.37604 | 0.311293 | ||||||||
\(725\) | 0.387966 | 0.0144087 | ||||||||
\(726\) | 0.415881 | 0.0154348 | ||||||||
\(727\) | 13.0964 | 0.485720 | 0.242860 | − | 0.970061i | \(-0.421914\pi\) | ||||
0.242860 | + | 0.970061i | \(0.421914\pi\) | |||||||
\(728\) | −3.21872 | −0.119294 | ||||||||
\(729\) | −18.1038 | −0.670513 | ||||||||
\(730\) | 0.955483 | 0.0353640 | ||||||||
\(731\) | −29.5632 | −1.09344 | ||||||||
\(732\) | 3.36316 | 0.124306 | ||||||||
\(733\) | 13.6829 | 0.505388 | 0.252694 | − | 0.967546i | \(-0.418683\pi\) | ||||
0.252694 | + | 0.967546i | \(0.418683\pi\) | |||||||
\(734\) | 16.5904 | 0.612364 | ||||||||
\(735\) | −2.99621 | −0.110517 | ||||||||
\(736\) | −8.28397 | −0.305351 | ||||||||
\(737\) | −11.4984 | −0.423549 | ||||||||
\(738\) | 16.0940 | 0.592428 | ||||||||
\(739\) | −24.5625 | −0.903545 | −0.451773 | − | 0.892133i | \(-0.649208\pi\) | ||||
−0.451773 | + | 0.892133i | \(0.649208\pi\) | |||||||
\(740\) | 1.85663 | 0.0682509 | ||||||||
\(741\) | 4.98674 | 0.183192 | ||||||||
\(742\) | 15.0866 | 0.553846 | ||||||||
\(743\) | 31.4640 | 1.15430 | 0.577151 | − | 0.816637i | \(-0.304164\pi\) | ||||
0.577151 | + | 0.816637i | \(0.304164\pi\) | |||||||
\(744\) | 1.15774 | 0.0424448 | ||||||||
\(745\) | 45.4051 | 1.66352 | ||||||||
\(746\) | −31.2666 | −1.14475 | ||||||||
\(747\) | 6.78332 | 0.248189 | ||||||||
\(748\) | −4.04145 | −0.147770 | ||||||||
\(749\) | 27.6280 | 1.00950 | ||||||||
\(750\) | 4.63183 | 0.169131 | ||||||||
\(751\) | 1.88471 | 0.0687740 | 0.0343870 | − | 0.999409i | \(-0.489052\pi\) | ||||
0.0343870 | + | 0.999409i | \(0.489052\pi\) | |||||||
\(752\) | −7.73976 | −0.282240 | ||||||||
\(753\) | 3.05532 | 0.111342 | ||||||||
\(754\) | −16.8553 | −0.613834 | ||||||||
\(755\) | −12.3401 | −0.449101 | ||||||||
\(756\) | 4.71793 | 0.171589 | ||||||||
\(757\) | 9.73585 | 0.353856 | 0.176928 | − | 0.984224i | \(-0.443384\pi\) | ||||
0.176928 | + | 0.984224i | \(0.443384\pi\) | |||||||
\(758\) | 7.45385 | 0.270736 | ||||||||
\(759\) | −3.44515 | −0.125051 | ||||||||
\(760\) | −16.2790 | −0.590503 | ||||||||
\(761\) | −3.78408 | −0.137173 | −0.0685863 | − | 0.997645i | \(-0.521849\pi\) | ||||
−0.0685863 | + | 0.997645i | \(0.521849\pi\) | |||||||
\(762\) | −7.34353 | −0.266028 | ||||||||
\(763\) | 8.24578 | 0.298517 | ||||||||
\(764\) | 8.39612 | 0.303761 | ||||||||
\(765\) | −25.6449 | −0.927193 | ||||||||
\(766\) | 19.2295 | 0.694790 | ||||||||
\(767\) | 13.2237 | 0.477478 | ||||||||
\(768\) | −0.415881 | −0.0150068 | ||||||||
\(769\) | 22.9503 | 0.827608 | 0.413804 | − | 0.910366i | \(-0.364200\pi\) | ||||
0.413804 | + | 0.910366i | \(0.364200\pi\) | |||||||
\(770\) | 4.36984 | 0.157478 | ||||||||
\(771\) | 9.57231 | 0.344738 | ||||||||
\(772\) | −21.4162 | −0.770784 | ||||||||
\(773\) | −24.2586 | −0.872523 | −0.436261 | − | 0.899820i | \(-0.643698\pi\) | ||||
−0.436261 | + | 0.899820i | \(0.643698\pi\) | |||||||
\(774\) | 20.6798 | 0.743321 | ||||||||
\(775\) | 0.105937 | 0.00380537 | ||||||||
\(776\) | −13.3160 | −0.478018 | ||||||||
\(777\) | 0.669724 | 0.0240262 | ||||||||
\(778\) | 18.3410 | 0.657557 | ||||||||
\(779\) | −41.2885 | −1.47931 | ||||||||
\(780\) | 1.54330 | 0.0552590 | ||||||||
\(781\) | −3.83205 | −0.137122 | ||||||||
\(782\) | 33.4792 | 1.19721 | ||||||||
\(783\) | 24.7061 | 0.882925 | ||||||||
\(784\) | −3.20976 | −0.114634 | ||||||||
\(785\) | −4.78135 | −0.170654 | ||||||||
\(786\) | −3.21681 | −0.114740 | ||||||||
\(787\) | −46.0669 | −1.64211 | −0.821054 | − | 0.570850i | \(-0.806614\pi\) | ||||
−0.821054 | + | 0.570850i | \(0.806614\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 5.14357 | 0.183116 | ||||||||
\(790\) | −31.1886 | −1.10964 | ||||||||
\(791\) | −13.8888 | −0.493828 | ||||||||
\(792\) | 2.82704 | 0.100455 | ||||||||
\(793\) | −13.3699 | −0.474779 | ||||||||
\(794\) | 5.37974 | 0.190920 | ||||||||
\(795\) | −7.23366 | −0.256552 | ||||||||
\(796\) | 2.37949 | 0.0843389 | ||||||||
\(797\) | 43.5713 | 1.54337 | 0.771687 | − | 0.636003i | \(-0.219413\pi\) | ||||
0.771687 | + | 0.636003i | \(0.219413\pi\) | |||||||
\(798\) | −5.87219 | −0.207873 | ||||||||
\(799\) | 31.2798 | 1.10660 | ||||||||
\(800\) | −0.0380545 | −0.00134543 | ||||||||
\(801\) | −30.9048 | −1.09197 | ||||||||
\(802\) | 38.0579 | 1.34387 | ||||||||
\(803\) | 0.425688 | 0.0150222 | ||||||||
\(804\) | 4.78197 | 0.168647 | ||||||||
\(805\) | −36.1996 | −1.27587 | ||||||||
\(806\) | −4.60247 | −0.162115 | ||||||||
\(807\) | −7.92639 | −0.279022 | ||||||||
\(808\) | −8.43947 | −0.296899 | ||||||||
\(809\) | −15.7310 | −0.553071 | −0.276536 | − | 0.961004i | \(-0.589186\pi\) | ||||
−0.276536 | + | 0.961004i | \(0.589186\pi\) | |||||||
\(810\) | 16.7743 | 0.589388 | ||||||||
\(811\) | 20.9510 | 0.735689 | 0.367845 | − | 0.929887i | \(-0.380096\pi\) | ||||
0.367845 | + | 0.929887i | \(0.380096\pi\) | |||||||
\(812\) | 19.8482 | 0.696534 | ||||||||
\(813\) | 11.3196 | 0.396996 | ||||||||
\(814\) | 0.827167 | 0.0289922 | ||||||||
\(815\) | −45.9655 | −1.61010 | ||||||||
\(816\) | 1.68076 | 0.0588385 | ||||||||
\(817\) | −53.0533 | −1.85610 | ||||||||
\(818\) | −25.1927 | −0.880843 | ||||||||
\(819\) | −9.09946 | −0.317961 | ||||||||
\(820\) | −12.7780 | −0.446227 | ||||||||
\(821\) | 21.6596 | 0.755924 | 0.377962 | − | 0.925821i | \(-0.376625\pi\) | ||||
0.377962 | + | 0.925821i | \(0.376625\pi\) | |||||||
\(822\) | 0.534791 | 0.0186530 | ||||||||
\(823\) | 51.1991 | 1.78469 | 0.892344 | − | 0.451355i | \(-0.149059\pi\) | ||||
0.892344 | + | 0.451355i | \(0.149059\pi\) | |||||||
\(824\) | 0.908357 | 0.0316441 | ||||||||
\(825\) | −0.0158262 | −0.000550996 0 | ||||||||
\(826\) | −15.5717 | −0.541808 | ||||||||
\(827\) | 39.9638 | 1.38968 | 0.694839 | − | 0.719166i | \(-0.255476\pi\) | ||||
0.694839 | + | 0.719166i | \(0.255476\pi\) | |||||||
\(828\) | −23.4191 | −0.813871 | ||||||||
\(829\) | 8.72748 | 0.303118 | 0.151559 | − | 0.988448i | \(-0.451571\pi\) | ||||
0.151559 | + | 0.988448i | \(0.451571\pi\) | |||||||
\(830\) | −5.38569 | −0.186940 | ||||||||
\(831\) | 4.07634 | 0.141406 | ||||||||
\(832\) | 1.65329 | 0.0573176 | ||||||||
\(833\) | 12.9721 | 0.449455 | ||||||||
\(834\) | −6.46853 | −0.223987 | ||||||||
\(835\) | 6.42514 | 0.222351 | ||||||||
\(836\) | −7.25266 | −0.250839 | ||||||||
\(837\) | 6.74619 | 0.233183 | ||||||||
\(838\) | −3.41451 | −0.117952 | ||||||||
\(839\) | −28.0173 | −0.967265 | −0.483632 | − | 0.875271i | \(-0.660683\pi\) | ||||
−0.483632 | + | 0.875271i | \(0.660683\pi\) | |||||||
\(840\) | −1.81733 | −0.0627039 | ||||||||
\(841\) | 74.9378 | 2.58406 | ||||||||
\(842\) | −20.5210 | −0.707202 | ||||||||
\(843\) | −4.22297 | −0.145447 | ||||||||
\(844\) | 12.5858 | 0.433220 | ||||||||
\(845\) | 23.0441 | 0.792740 | ||||||||
\(846\) | −21.8806 | −0.752271 | ||||||||
\(847\) | 1.94686 | 0.0668947 | ||||||||
\(848\) | −7.74921 | −0.266109 | ||||||||
\(849\) | 3.89456 | 0.133661 | ||||||||
\(850\) | 0.153795 | 0.00527514 | ||||||||
\(851\) | −6.85222 | −0.234891 | ||||||||
\(852\) | 1.59368 | 0.0545985 | ||||||||
\(853\) | 35.2276 | 1.20617 | 0.603085 | − | 0.797677i | \(-0.293938\pi\) | ||||
0.603085 | + | 0.797677i | \(0.293938\pi\) | |||||||
\(854\) | 15.7439 | 0.538744 | ||||||||
\(855\) | −46.0215 | −1.57390 | ||||||||
\(856\) | −14.1911 | −0.485041 | ||||||||
\(857\) | −17.6481 | −0.602848 | −0.301424 | − | 0.953490i | \(-0.597462\pi\) | ||||
−0.301424 | + | 0.953490i | \(0.597462\pi\) | |||||||
\(858\) | 0.687573 | 0.0234734 | ||||||||
\(859\) | −0.698490 | −0.0238322 | −0.0119161 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119161 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(860\) | −16.4190 | −0.559883 | ||||||||
\(861\) | −4.60929 | −0.157084 | ||||||||
\(862\) | −7.43175 | −0.253126 | ||||||||
\(863\) | 5.07840 | 0.172871 | 0.0864354 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864354 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(864\) | −2.42336 | −0.0824443 | ||||||||
\(865\) | 37.4809 | 1.27439 | ||||||||
\(866\) | 32.3343 | 1.09876 | ||||||||
\(867\) | 0.277262 | 0.00941630 | ||||||||
\(868\) | 5.41969 | 0.183956 | ||||||||
\(869\) | −13.8952 | −0.471362 | ||||||||
\(870\) | −9.51673 | −0.322647 | ||||||||
\(871\) | −19.0102 | −0.644137 | ||||||||
\(872\) | −4.23544 | −0.143430 | ||||||||
\(873\) | −37.6450 | −1.27409 | ||||||||
\(874\) | 60.0808 | 2.03226 | ||||||||
\(875\) | 21.6829 | 0.733015 | ||||||||
\(876\) | −0.177036 | −0.00598148 | ||||||||
\(877\) | 3.11728 | 0.105263 | 0.0526315 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526315 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(878\) | −6.87171 | −0.231909 | ||||||||
\(879\) | 2.74143 | 0.0924663 | ||||||||
\(880\) | −2.24456 | −0.0756641 | ||||||||
\(881\) | −54.2647 | −1.82822 | −0.914112 | − | 0.405462i | \(-0.867111\pi\) | ||||
−0.914112 | + | 0.405462i | \(0.867111\pi\) | |||||||
\(882\) | −9.07412 | −0.305541 | ||||||||
\(883\) | 43.3020 | 1.45723 | 0.728614 | − | 0.684924i | \(-0.240165\pi\) | ||||
0.728614 | + | 0.684924i | \(0.240165\pi\) | |||||||
\(884\) | −6.68170 | −0.224730 | ||||||||
\(885\) | 7.46625 | 0.250975 | ||||||||
\(886\) | 2.12632 | 0.0714353 | ||||||||
\(887\) | 3.68238 | 0.123642 | 0.0618210 | − | 0.998087i | \(-0.480309\pi\) | ||||
0.0618210 | + | 0.998087i | \(0.480309\pi\) | |||||||
\(888\) | −0.344003 | −0.0115440 | ||||||||
\(889\) | −34.3771 | −1.15297 | ||||||||
\(890\) | 24.5372 | 0.822489 | ||||||||
\(891\) | 7.47330 | 0.250365 | ||||||||
\(892\) | −17.6630 | −0.591402 | ||||||||
\(893\) | 56.1338 | 1.87845 | ||||||||
\(894\) | −8.41285 | −0.281368 | ||||||||
\(895\) | 51.9686 | 1.73712 | ||||||||
\(896\) | −1.94686 | −0.0650399 | ||||||||
\(897\) | −5.69583 | −0.190178 | ||||||||
\(898\) | 29.2391 | 0.975721 | ||||||||
\(899\) | 28.3810 | 0.946560 | ||||||||
\(900\) | −0.107582 | −0.00358606 | ||||||||
\(901\) | 31.3180 | 1.04336 | ||||||||
\(902\) | −5.69287 | −0.189552 | ||||||||
\(903\) | −5.92267 | −0.197094 | ||||||||
\(904\) | 7.13396 | 0.237272 | ||||||||
\(905\) | −18.8005 | −0.624951 | ||||||||
\(906\) | 2.28642 | 0.0759611 | ||||||||
\(907\) | −9.34926 | −0.310437 | −0.155218 | − | 0.987880i | \(-0.549608\pi\) | ||||
−0.155218 | + | 0.987880i | \(0.549608\pi\) | |||||||
\(908\) | −18.5462 | −0.615478 | ||||||||
\(909\) | −23.8587 | −0.791344 | ||||||||
\(910\) | 7.22461 | 0.239494 | ||||||||
\(911\) | −2.06437 | −0.0683955 | −0.0341977 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341977 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(912\) | 3.01625 | 0.0998779 | ||||||||
\(913\) | −2.39944 | −0.0794099 | ||||||||
\(914\) | 26.0219 | 0.860727 | ||||||||
\(915\) | −7.54882 | −0.249556 | ||||||||
\(916\) | −21.5774 | −0.712936 | ||||||||
\(917\) | −15.0588 | −0.497285 | ||||||||
\(918\) | 9.79388 | 0.323246 | ||||||||
\(919\) | 38.7581 | 1.27851 | 0.639256 | − | 0.768994i | \(-0.279242\pi\) | ||||
0.639256 | + | 0.768994i | \(0.279242\pi\) | |||||||
\(920\) | 18.5939 | 0.613022 | ||||||||
\(921\) | 2.83682 | 0.0934764 | ||||||||
\(922\) | 22.1268 | 0.728708 | ||||||||
\(923\) | −6.33550 | −0.208536 | ||||||||
\(924\) | −0.809661 | −0.0266359 | ||||||||
\(925\) | −0.0314774 | −0.00103497 | ||||||||
\(926\) | 18.9937 | 0.624171 | ||||||||
\(927\) | 2.56796 | 0.0843430 | ||||||||
\(928\) | −10.1950 | −0.334667 | ||||||||
\(929\) | −22.1175 | −0.725653 | −0.362826 | − | 0.931857i | \(-0.618188\pi\) | ||||
−0.362826 | + | 0.931857i | \(0.618188\pi\) | |||||||
\(930\) | −2.59861 | −0.0852119 | ||||||||
\(931\) | 23.2793 | 0.762947 | ||||||||
\(932\) | 22.8480 | 0.748412 | ||||||||
\(933\) | 5.29073 | 0.173211 | ||||||||
\(934\) | −20.0636 | −0.656502 | ||||||||
\(935\) | 9.07128 | 0.296663 | ||||||||
\(936\) | 4.67393 | 0.152772 | ||||||||
\(937\) | 36.0675 | 1.17828 | 0.589138 | − | 0.808033i | \(-0.299468\pi\) | ||||
0.589138 | + | 0.808033i | \(0.299468\pi\) | |||||||
\(938\) | 22.3857 | 0.730920 | ||||||||
\(939\) | 1.19736 | 0.0390742 | ||||||||
\(940\) | 17.3724 | 0.566624 | ||||||||
\(941\) | −45.9104 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(942\) | 0.885907 | 0.0288644 | ||||||||
\(943\) | 47.1595 | 1.53573 | ||||||||
\(944\) | 7.99838 | 0.260325 | ||||||||
\(945\) | −10.5897 | −0.344482 | ||||||||
\(946\) | −7.31501 | −0.237831 | ||||||||
\(947\) | −29.7380 | −0.966356 | −0.483178 | − | 0.875522i | \(-0.660518\pi\) | ||||
−0.483178 | + | 0.875522i | \(0.660518\pi\) | |||||||
\(948\) | 5.77875 | 0.187685 | ||||||||
\(949\) | 0.703787 | 0.0228459 | ||||||||
\(950\) | 0.275997 | 0.00895451 | ||||||||
\(951\) | −0.521381 | −0.0169069 | ||||||||
\(952\) | 7.86812 | 0.255007 | ||||||||
\(953\) | −17.7427 | −0.574741 | −0.287370 | − | 0.957820i | \(-0.592781\pi\) | ||||
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(954\) | −21.9074 | −0.709277 | ||||||||
\(955\) | −18.8456 | −0.609829 | ||||||||
\(956\) | 15.0535 | 0.486866 | ||||||||
\(957\) | −4.23991 | −0.137057 | ||||||||
\(958\) | 30.9779 | 1.00085 | ||||||||
\(959\) | 2.50351 | 0.0808424 | ||||||||
\(960\) | 0.933471 | 0.0301276 | ||||||||
\(961\) | −23.2503 | −0.750011 | ||||||||
\(962\) | 1.36755 | 0.0440915 | ||||||||
\(963\) | −40.1188 | −1.29281 | ||||||||
\(964\) | −5.12265 | −0.164989 | ||||||||
\(965\) | 48.0699 | 1.54742 | ||||||||
\(966\) | 6.70720 | 0.215801 | ||||||||
\(967\) | 56.9254 | 1.83060 | 0.915299 | − | 0.402774i | \(-0.131954\pi\) | ||||
0.915299 | + | 0.402774i | \(0.131954\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −12.1900 | −0.391599 | ||||||||
\(970\) | 29.8887 | 0.959668 | ||||||||
\(971\) | −14.3546 | −0.460662 | −0.230331 | − | 0.973112i | \(-0.573981\pi\) | ||||
−0.230331 | + | 0.973112i | \(0.573981\pi\) | |||||||
\(972\) | −10.3781 | −0.332877 | ||||||||
\(973\) | −30.2810 | −0.970763 | ||||||||
\(974\) | 40.2405 | 1.28939 | ||||||||
\(975\) | −0.0261653 | −0.000837960 0 | ||||||||
\(976\) | −8.08683 | −0.258853 | ||||||||
\(977\) | −9.26264 | −0.296338 | −0.148169 | − | 0.988962i | \(-0.547338\pi\) | ||||
−0.148169 | + | 0.988962i | \(0.547338\pi\) | |||||||
\(978\) | 8.51668 | 0.272333 | ||||||||
\(979\) | 10.9318 | 0.349383 | ||||||||
\(980\) | 7.20449 | 0.230139 | ||||||||
\(981\) | −11.9738 | −0.382293 | ||||||||
\(982\) | −23.9956 | −0.765731 | ||||||||
\(983\) | −25.0803 | −0.799938 | −0.399969 | − | 0.916529i | \(-0.630979\pi\) | ||||
−0.399969 | + | 0.916529i | \(0.630979\pi\) | |||||||
\(984\) | 2.36756 | 0.0754750 | ||||||||
\(985\) | −2.24456 | −0.0715177 | ||||||||
\(986\) | 41.2025 | 1.31216 | ||||||||
\(987\) | 6.26658 | 0.199467 | ||||||||
\(988\) | −11.9908 | −0.381477 | ||||||||
\(989\) | 60.5973 | 1.92688 | ||||||||
\(990\) | −6.34547 | −0.201672 | ||||||||
\(991\) | −22.6092 | −0.718206 | −0.359103 | − | 0.933298i | \(-0.616917\pi\) | ||||
−0.359103 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(992\) | −2.78382 | −0.0883864 | ||||||||
\(993\) | 12.4810 | 0.396073 | ||||||||
\(994\) | 7.46045 | 0.236631 | ||||||||
\(995\) | −5.34092 | −0.169318 | ||||||||
\(996\) | 0.997882 | 0.0316191 | ||||||||
\(997\) | −15.6951 | −0.497070 | −0.248535 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248535 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(998\) | −10.6271 | −0.336394 | ||||||||
\(999\) | −2.00452 | −0.0634202 |
(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 | 4334.2.a.a.1.7 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.7 | ✓ | 15 | 1.1 | even | 1 | trivial |