Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 16x^{4} + 49x^{3} - 53x^{2} - 44x + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.22542\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | −0.383827 | −0.221602 | −0.110801 | − | 0.993843i | \(-0.535342\pi\) | ||||
−0.110801 | + | 0.993843i | \(0.535342\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.15424 | 1.85783 | 0.928916 | − | 0.370291i | \(-0.120742\pi\) | ||||
0.928916 | + | 0.370291i | \(0.120742\pi\) | |||||||
\(6\) | −0.383827 | −0.156697 | ||||||||
\(7\) | 4.87818 | 1.84378 | 0.921890 | − | 0.387452i | \(-0.126645\pi\) | ||||
0.921890 | + | 0.387452i | \(0.126645\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.85268 | −0.950892 | ||||||||
\(10\) | 4.15424 | 1.31369 | ||||||||
\(11\) | −1.62910 | −0.491191 | −0.245596 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245596 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(12\) | −0.383827 | −0.110801 | ||||||||
\(13\) | −2.16682 | −0.600968 | −0.300484 | − | 0.953787i | \(-0.597148\pi\) | ||||
−0.300484 | + | 0.953787i | \(0.597148\pi\) | |||||||
\(14\) | 4.87818 | 1.30375 | ||||||||
\(15\) | −1.59451 | −0.411700 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.78448 | −1.64548 | −0.822739 | − | 0.568420i | \(-0.807555\pi\) | ||||
−0.822739 | + | 0.568420i | \(0.807555\pi\) | |||||||
\(18\) | −2.85268 | −0.672382 | ||||||||
\(19\) | −8.61766 | −1.97703 | −0.988513 | − | 0.151136i | \(-0.951707\pi\) | ||||
−0.988513 | + | 0.151136i | \(0.951707\pi\) | |||||||
\(20\) | 4.15424 | 0.928916 | ||||||||
\(21\) | −1.87238 | −0.408586 | ||||||||
\(22\) | −1.62910 | −0.347325 | ||||||||
\(23\) | 2.76765 | 0.577096 | 0.288548 | − | 0.957465i | \(-0.406828\pi\) | ||||
0.288548 | + | 0.957465i | \(0.406828\pi\) | |||||||
\(24\) | −0.383827 | −0.0783483 | ||||||||
\(25\) | 12.2577 | 2.45154 | ||||||||
\(26\) | −2.16682 | −0.424948 | ||||||||
\(27\) | 2.24641 | 0.432322 | ||||||||
\(28\) | 4.87818 | 0.921890 | ||||||||
\(29\) | 2.10510 | 0.390907 | 0.195454 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195454 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(30\) | −1.59451 | −0.291116 | ||||||||
\(31\) | −3.62414 | −0.650914 | −0.325457 | − | 0.945557i | \(-0.605518\pi\) | ||||
−0.325457 | + | 0.945557i | \(0.605518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.625290 | 0.108849 | ||||||||
\(34\) | −6.78448 | −1.16353 | ||||||||
\(35\) | 20.2651 | 3.42543 | ||||||||
\(36\) | −2.85268 | −0.475446 | ||||||||
\(37\) | 1.19760 | 0.196885 | 0.0984424 | − | 0.995143i | \(-0.468614\pi\) | ||||
0.0984424 | + | 0.995143i | \(0.468614\pi\) | |||||||
\(38\) | −8.61766 | −1.39797 | ||||||||
\(39\) | 0.831683 | 0.133176 | ||||||||
\(40\) | 4.15424 | 0.656843 | ||||||||
\(41\) | 5.43715 | 0.849140 | 0.424570 | − | 0.905395i | \(-0.360425\pi\) | ||||
0.424570 | + | 0.905395i | \(0.360425\pi\) | |||||||
\(42\) | −1.87238 | −0.288914 | ||||||||
\(43\) | −9.63402 | −1.46917 | −0.734587 | − | 0.678514i | \(-0.762624\pi\) | ||||
−0.734587 | + | 0.678514i | \(0.762624\pi\) | |||||||
\(44\) | −1.62910 | −0.245596 | ||||||||
\(45\) | −11.8507 | −1.76660 | ||||||||
\(46\) | 2.76765 | 0.408068 | ||||||||
\(47\) | −7.07613 | −1.03216 | −0.516080 | − | 0.856541i | \(-0.672609\pi\) | ||||
−0.516080 | + | 0.856541i | \(0.672609\pi\) | |||||||
\(48\) | −0.383827 | −0.0554006 | ||||||||
\(49\) | 16.7967 | 2.39952 | ||||||||
\(50\) | 12.2577 | 1.73350 | ||||||||
\(51\) | 2.60406 | 0.364642 | ||||||||
\(52\) | −2.16682 | −0.300484 | ||||||||
\(53\) | −3.03890 | −0.417425 | −0.208712 | − | 0.977977i | \(-0.566927\pi\) | ||||
−0.208712 | + | 0.977977i | \(0.566927\pi\) | |||||||
\(54\) | 2.24641 | 0.305698 | ||||||||
\(55\) | −6.76765 | −0.912550 | ||||||||
\(56\) | 4.87818 | 0.651875 | ||||||||
\(57\) | 3.30769 | 0.438114 | ||||||||
\(58\) | 2.10510 | 0.276413 | ||||||||
\(59\) | 4.21827 | 0.549172 | 0.274586 | − | 0.961563i | \(-0.411459\pi\) | ||||
0.274586 | + | 0.961563i | \(0.411459\pi\) | |||||||
\(60\) | −1.59451 | −0.205850 | ||||||||
\(61\) | 8.74744 | 1.11999 | 0.559997 | − | 0.828494i | \(-0.310802\pi\) | ||||
0.559997 | + | 0.828494i | \(0.310802\pi\) | |||||||
\(62\) | −3.62414 | −0.460266 | ||||||||
\(63\) | −13.9159 | −1.75324 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.00148 | −1.11650 | ||||||||
\(66\) | 0.625290 | 0.0769679 | ||||||||
\(67\) | −1.50761 | −0.184184 | −0.0920921 | − | 0.995750i | \(-0.529355\pi\) | ||||
−0.0920921 | + | 0.995750i | \(0.529355\pi\) | |||||||
\(68\) | −6.78448 | −0.822739 | ||||||||
\(69\) | −1.06230 | −0.127886 | ||||||||
\(70\) | 20.2651 | 2.42215 | ||||||||
\(71\) | 11.0270 | 1.30866 | 0.654331 | − | 0.756208i | \(-0.272950\pi\) | ||||
0.654331 | + | 0.756208i | \(0.272950\pi\) | |||||||
\(72\) | −2.85268 | −0.336191 | ||||||||
\(73\) | 1.37039 | 0.160391 | 0.0801957 | − | 0.996779i | \(-0.474445\pi\) | ||||
0.0801957 | + | 0.996779i | \(0.474445\pi\) | |||||||
\(74\) | 1.19760 | 0.139219 | ||||||||
\(75\) | −4.70482 | −0.543266 | ||||||||
\(76\) | −8.61766 | −0.988513 | ||||||||
\(77\) | −7.94703 | −0.905648 | ||||||||
\(78\) | 0.831683 | 0.0941695 | ||||||||
\(79\) | −14.9749 | −1.68480 | −0.842401 | − | 0.538850i | \(-0.818859\pi\) | ||||
−0.842401 | + | 0.538850i | \(0.818859\pi\) | |||||||
\(80\) | 4.15424 | 0.464458 | ||||||||
\(81\) | 7.69580 | 0.855089 | ||||||||
\(82\) | 5.43715 | 0.600432 | ||||||||
\(83\) | −8.08276 | −0.887198 | −0.443599 | − | 0.896225i | \(-0.646299\pi\) | ||||
−0.443599 | + | 0.896225i | \(0.646299\pi\) | |||||||
\(84\) | −1.87238 | −0.204293 | ||||||||
\(85\) | −28.1843 | −3.05702 | ||||||||
\(86\) | −9.63402 | −1.03886 | ||||||||
\(87\) | −0.807993 | −0.0866259 | ||||||||
\(88\) | −1.62910 | −0.173662 | ||||||||
\(89\) | 3.31299 | 0.351176 | 0.175588 | − | 0.984464i | \(-0.443817\pi\) | ||||
0.175588 | + | 0.984464i | \(0.443817\pi\) | |||||||
\(90\) | −11.8507 | −1.24917 | ||||||||
\(91\) | −10.5701 | −1.10805 | ||||||||
\(92\) | 2.76765 | 0.288548 | ||||||||
\(93\) | 1.39104 | 0.144244 | ||||||||
\(94\) | −7.07613 | −0.729847 | ||||||||
\(95\) | −35.7998 | −3.67298 | ||||||||
\(96\) | −0.383827 | −0.0391741 | ||||||||
\(97\) | 16.8474 | 1.71059 | 0.855296 | − | 0.518139i | \(-0.173375\pi\) | ||||
0.855296 | + | 0.518139i | \(0.173375\pi\) | |||||||
\(98\) | 16.7967 | 1.69672 | ||||||||
\(99\) | 4.64729 | 0.467070 | ||||||||
\(100\) | 12.2577 | 1.22577 | ||||||||
\(101\) | 2.93034 | 0.291580 | 0.145790 | − | 0.989316i | \(-0.453428\pi\) | ||||
0.145790 | + | 0.989316i | \(0.453428\pi\) | |||||||
\(102\) | 2.60406 | 0.257841 | ||||||||
\(103\) | 1.25819 | 0.123973 | 0.0619867 | − | 0.998077i | \(-0.480256\pi\) | ||||
0.0619867 | + | 0.998077i | \(0.480256\pi\) | |||||||
\(104\) | −2.16682 | −0.212474 | ||||||||
\(105\) | −7.77829 | −0.759084 | ||||||||
\(106\) | −3.03890 | −0.295164 | ||||||||
\(107\) | 9.35946 | 0.904813 | 0.452407 | − | 0.891812i | \(-0.350566\pi\) | ||||
0.452407 | + | 0.891812i | \(0.350566\pi\) | |||||||
\(108\) | 2.24641 | 0.216161 | ||||||||
\(109\) | 11.4192 | 1.09376 | 0.546882 | − | 0.837210i | \(-0.315815\pi\) | ||||
0.546882 | + | 0.837210i | \(0.315815\pi\) | |||||||
\(110\) | −6.76765 | −0.645270 | ||||||||
\(111\) | −0.459672 | −0.0436301 | ||||||||
\(112\) | 4.87818 | 0.460945 | ||||||||
\(113\) | 0.316816 | 0.0298036 | 0.0149018 | − | 0.999889i | \(-0.495256\pi\) | ||||
0.0149018 | + | 0.999889i | \(0.495256\pi\) | |||||||
\(114\) | 3.30769 | 0.309793 | ||||||||
\(115\) | 11.4975 | 1.07215 | ||||||||
\(116\) | 2.10510 | 0.195454 | ||||||||
\(117\) | 6.18124 | 0.571456 | ||||||||
\(118\) | 4.21827 | 0.388323 | ||||||||
\(119\) | −33.0959 | −3.03390 | ||||||||
\(120\) | −1.59451 | −0.145558 | ||||||||
\(121\) | −8.34604 | −0.758731 | ||||||||
\(122\) | 8.74744 | 0.791956 | ||||||||
\(123\) | −2.08692 | −0.188171 | ||||||||
\(124\) | −3.62414 | −0.325457 | ||||||||
\(125\) | 30.1501 | 2.69671 | ||||||||
\(126\) | −13.9159 | −1.23973 | ||||||||
\(127\) | −2.08772 | −0.185255 | −0.0926276 | − | 0.995701i | \(-0.529527\pi\) | ||||
−0.0926276 | + | 0.995701i | \(0.529527\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.69779 | 0.325572 | ||||||||
\(130\) | −9.00148 | −0.789482 | ||||||||
\(131\) | −5.17397 | −0.452052 | −0.226026 | − | 0.974121i | \(-0.572573\pi\) | ||||
−0.226026 | + | 0.974121i | \(0.572573\pi\) | |||||||
\(132\) | 0.625290 | 0.0544245 | ||||||||
\(133\) | −42.0385 | −3.64520 | ||||||||
\(134\) | −1.50761 | −0.130238 | ||||||||
\(135\) | 9.33213 | 0.803182 | ||||||||
\(136\) | −6.78448 | −0.581764 | ||||||||
\(137\) | 6.35949 | 0.543328 | 0.271664 | − | 0.962392i | \(-0.412426\pi\) | ||||
0.271664 | + | 0.962392i | \(0.412426\pi\) | |||||||
\(138\) | −1.06230 | −0.0904289 | ||||||||
\(139\) | −10.6786 | −0.905746 | −0.452873 | − | 0.891575i | \(-0.649601\pi\) | ||||
−0.452873 | + | 0.891575i | \(0.649601\pi\) | |||||||
\(140\) | 20.2651 | 1.71272 | ||||||||
\(141\) | 2.71601 | 0.228729 | ||||||||
\(142\) | 11.0270 | 0.925364 | ||||||||
\(143\) | 3.52996 | 0.295190 | ||||||||
\(144\) | −2.85268 | −0.237723 | ||||||||
\(145\) | 8.74508 | 0.726239 | ||||||||
\(146\) | 1.37039 | 0.113414 | ||||||||
\(147\) | −6.44701 | −0.531740 | ||||||||
\(148\) | 1.19760 | 0.0984424 | ||||||||
\(149\) | −3.47426 | −0.284622 | −0.142311 | − | 0.989822i | \(-0.545453\pi\) | ||||
−0.142311 | + | 0.989822i | \(0.545453\pi\) | |||||||
\(150\) | −4.70482 | −0.384147 | ||||||||
\(151\) | 11.2407 | 0.914752 | 0.457376 | − | 0.889273i | \(-0.348789\pi\) | ||||
0.457376 | + | 0.889273i | \(0.348789\pi\) | |||||||
\(152\) | −8.61766 | −0.698984 | ||||||||
\(153\) | 19.3539 | 1.56467 | ||||||||
\(154\) | −7.94703 | −0.640390 | ||||||||
\(155\) | −15.0555 | −1.20929 | ||||||||
\(156\) | 0.831683 | 0.0665879 | ||||||||
\(157\) | 8.59533 | 0.685982 | 0.342991 | − | 0.939339i | \(-0.388560\pi\) | ||||
0.342991 | + | 0.939339i | \(0.388560\pi\) | |||||||
\(158\) | −14.9749 | −1.19134 | ||||||||
\(159\) | 1.16641 | 0.0925024 | ||||||||
\(160\) | 4.15424 | 0.328421 | ||||||||
\(161\) | 13.5011 | 1.06404 | ||||||||
\(162\) | 7.69580 | 0.604639 | ||||||||
\(163\) | 10.1530 | 0.795241 | 0.397621 | − | 0.917550i | \(-0.369836\pi\) | ||||
0.397621 | + | 0.917550i | \(0.369836\pi\) | |||||||
\(164\) | 5.43715 | 0.424570 | ||||||||
\(165\) | 2.59760 | 0.202223 | ||||||||
\(166\) | −8.08276 | −0.627344 | ||||||||
\(167\) | 4.37572 | 0.338604 | 0.169302 | − | 0.985564i | \(-0.445849\pi\) | ||||
0.169302 | + | 0.985564i | \(0.445849\pi\) | |||||||
\(168\) | −1.87238 | −0.144457 | ||||||||
\(169\) | −8.30489 | −0.638838 | ||||||||
\(170\) | −28.1843 | −2.16164 | ||||||||
\(171\) | 24.5834 | 1.87994 | ||||||||
\(172\) | −9.63402 | −0.734587 | ||||||||
\(173\) | −22.7651 | −1.73080 | −0.865398 | − | 0.501085i | \(-0.832934\pi\) | ||||
−0.865398 | + | 0.501085i | \(0.832934\pi\) | |||||||
\(174\) | −0.807993 | −0.0612538 | ||||||||
\(175\) | 59.7952 | 4.52009 | ||||||||
\(176\) | −1.62910 | −0.122798 | ||||||||
\(177\) | −1.61908 | −0.121698 | ||||||||
\(178\) | 3.31299 | 0.248319 | ||||||||
\(179\) | 12.1634 | 0.909139 | 0.454569 | − | 0.890711i | \(-0.349793\pi\) | ||||
0.454569 | + | 0.890711i | \(0.349793\pi\) | |||||||
\(180\) | −11.8507 | −0.883299 | ||||||||
\(181\) | −4.61048 | −0.342694 | −0.171347 | − | 0.985211i | \(-0.554812\pi\) | ||||
−0.171347 | + | 0.985211i | \(0.554812\pi\) | |||||||
\(182\) | −10.5701 | −0.783511 | ||||||||
\(183\) | −3.35750 | −0.248193 | ||||||||
\(184\) | 2.76765 | 0.204034 | ||||||||
\(185\) | 4.97513 | 0.365779 | ||||||||
\(186\) | 1.39104 | 0.101996 | ||||||||
\(187\) | 11.0526 | 0.808244 | ||||||||
\(188\) | −7.07613 | −0.516080 | ||||||||
\(189\) | 10.9584 | 0.797107 | ||||||||
\(190\) | −35.7998 | −2.59719 | ||||||||
\(191\) | 3.30553 | 0.239180 | 0.119590 | − | 0.992823i | \(-0.461842\pi\) | ||||
0.119590 | + | 0.992823i | \(0.461842\pi\) | |||||||
\(192\) | −0.383827 | −0.0277003 | ||||||||
\(193\) | −18.5157 | −1.33279 | −0.666394 | − | 0.745600i | \(-0.732163\pi\) | ||||
−0.666394 | + | 0.745600i | \(0.732163\pi\) | |||||||
\(194\) | 16.8474 | 1.20957 | ||||||||
\(195\) | 3.45501 | 0.247418 | ||||||||
\(196\) | 16.7967 | 1.19976 | ||||||||
\(197\) | 8.78109 | 0.625627 | 0.312814 | − | 0.949815i | \(-0.398729\pi\) | ||||
0.312814 | + | 0.949815i | \(0.398729\pi\) | |||||||
\(198\) | 4.64729 | 0.330268 | ||||||||
\(199\) | −12.4370 | −0.881634 | −0.440817 | − | 0.897597i | \(-0.645311\pi\) | ||||
−0.440817 | + | 0.897597i | \(0.645311\pi\) | |||||||
\(200\) | 12.2577 | 0.866749 | ||||||||
\(201\) | 0.578661 | 0.0408156 | ||||||||
\(202\) | 2.93034 | 0.206178 | ||||||||
\(203\) | 10.2691 | 0.720746 | ||||||||
\(204\) | 2.60406 | 0.182321 | ||||||||
\(205\) | 22.5872 | 1.57756 | ||||||||
\(206\) | 1.25819 | 0.0876625 | ||||||||
\(207\) | −7.89522 | −0.548756 | ||||||||
\(208\) | −2.16682 | −0.150242 | ||||||||
\(209\) | 14.0390 | 0.971098 | ||||||||
\(210\) | −7.77829 | −0.536753 | ||||||||
\(211\) | −10.9290 | −0.752381 | −0.376191 | − | 0.926542i | \(-0.622766\pi\) | ||||
−0.376191 | + | 0.926542i | \(0.622766\pi\) | |||||||
\(212\) | −3.03890 | −0.208712 | ||||||||
\(213\) | −4.23245 | −0.290003 | ||||||||
\(214\) | 9.35946 | 0.639800 | ||||||||
\(215\) | −40.0220 | −2.72948 | ||||||||
\(216\) | 2.24641 | 0.152849 | ||||||||
\(217\) | −17.6792 | −1.20014 | ||||||||
\(218\) | 11.4192 | 0.773408 | ||||||||
\(219\) | −0.525990 | −0.0355431 | ||||||||
\(220\) | −6.76765 | −0.456275 | ||||||||
\(221\) | 14.7007 | 0.988879 | ||||||||
\(222\) | −0.459672 | −0.0308512 | ||||||||
\(223\) | 8.79372 | 0.588871 | 0.294436 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294436 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(224\) | 4.87818 | 0.325937 | ||||||||
\(225\) | −34.9672 | −2.33115 | ||||||||
\(226\) | 0.316816 | 0.0210743 | ||||||||
\(227\) | 6.74871 | 0.447928 | 0.223964 | − | 0.974597i | \(-0.428100\pi\) | ||||
0.223964 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(228\) | 3.30769 | 0.219057 | ||||||||
\(229\) | −23.2606 | −1.53711 | −0.768553 | − | 0.639787i | \(-0.779023\pi\) | ||||
−0.768553 | + | 0.639787i | \(0.779023\pi\) | |||||||
\(230\) | 11.4975 | 0.758122 | ||||||||
\(231\) | 3.05028 | 0.200694 | ||||||||
\(232\) | 2.10510 | 0.138206 | ||||||||
\(233\) | 11.0721 | 0.725357 | 0.362679 | − | 0.931914i | \(-0.381862\pi\) | ||||
0.362679 | + | 0.931914i | \(0.381862\pi\) | |||||||
\(234\) | 6.18124 | 0.404080 | ||||||||
\(235\) | −29.3959 | −1.91758 | ||||||||
\(236\) | 4.21827 | 0.274586 | ||||||||
\(237\) | 5.74775 | 0.373356 | ||||||||
\(238\) | −33.0959 | −2.14529 | ||||||||
\(239\) | −3.99072 | −0.258138 | −0.129069 | − | 0.991636i | \(-0.541199\pi\) | ||||
−0.129069 | + | 0.991636i | \(0.541199\pi\) | |||||||
\(240\) | −1.59451 | −0.102925 | ||||||||
\(241\) | −16.5408 | −1.06549 | −0.532745 | − | 0.846276i | \(-0.678839\pi\) | ||||
−0.532745 | + | 0.846276i | \(0.678839\pi\) | |||||||
\(242\) | −8.34604 | −0.536504 | ||||||||
\(243\) | −9.69309 | −0.621812 | ||||||||
\(244\) | 8.74744 | 0.559997 | ||||||||
\(245\) | 69.7773 | 4.45791 | ||||||||
\(246\) | −2.08692 | −0.133057 | ||||||||
\(247\) | 18.6729 | 1.18813 | ||||||||
\(248\) | −3.62414 | −0.230133 | ||||||||
\(249\) | 3.10238 | 0.196605 | ||||||||
\(250\) | 30.1501 | 1.90686 | ||||||||
\(251\) | 24.0533 | 1.51823 | 0.759117 | − | 0.650955i | \(-0.225631\pi\) | ||||
0.759117 | + | 0.650955i | \(0.225631\pi\) | |||||||
\(252\) | −13.9159 | −0.876618 | ||||||||
\(253\) | −4.50877 | −0.283464 | ||||||||
\(254\) | −2.08772 | −0.130995 | ||||||||
\(255\) | 10.8179 | 0.677443 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.6822 | −0.853470 | −0.426735 | − | 0.904377i | \(-0.640336\pi\) | ||||
−0.426735 | + | 0.904377i | \(0.640336\pi\) | |||||||
\(258\) | 3.69779 | 0.230214 | ||||||||
\(259\) | 5.84213 | 0.363012 | ||||||||
\(260\) | −9.00148 | −0.558248 | ||||||||
\(261\) | −6.00517 | −0.371711 | ||||||||
\(262\) | −5.17397 | −0.319649 | ||||||||
\(263\) | 11.3942 | 0.702596 | 0.351298 | − | 0.936264i | \(-0.385740\pi\) | ||||
0.351298 | + | 0.936264i | \(0.385740\pi\) | |||||||
\(264\) | 0.625290 | 0.0384840 | ||||||||
\(265\) | −12.6243 | −0.775505 | ||||||||
\(266\) | −42.0385 | −2.57755 | ||||||||
\(267\) | −1.27161 | −0.0778214 | ||||||||
\(268\) | −1.50761 | −0.0920921 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | 9.33213 | 0.567935 | ||||||||
\(271\) | −24.6167 | −1.49536 | −0.747679 | − | 0.664061i | \(-0.768832\pi\) | ||||
−0.747679 | + | 0.664061i | \(0.768832\pi\) | |||||||
\(272\) | −6.78448 | −0.411369 | ||||||||
\(273\) | 4.05710 | 0.245547 | ||||||||
\(274\) | 6.35949 | 0.384191 | ||||||||
\(275\) | −19.9690 | −1.20417 | ||||||||
\(276\) | −1.06230 | −0.0639429 | ||||||||
\(277\) | 4.70762 | 0.282853 | 0.141427 | − | 0.989949i | \(-0.454831\pi\) | ||||
0.141427 | + | 0.989949i | \(0.454831\pi\) | |||||||
\(278\) | −10.6786 | −0.640459 | ||||||||
\(279\) | 10.3385 | 0.618949 | ||||||||
\(280\) | 20.2651 | 1.21107 | ||||||||
\(281\) | 6.51540 | 0.388676 | 0.194338 | − | 0.980935i | \(-0.437744\pi\) | ||||
0.194338 | + | 0.980935i | \(0.437744\pi\) | |||||||
\(282\) | 2.71601 | 0.161736 | ||||||||
\(283\) | −8.67417 | −0.515626 | −0.257813 | − | 0.966195i | \(-0.583002\pi\) | ||||
−0.257813 | + | 0.966195i | \(0.583002\pi\) | |||||||
\(284\) | 11.0270 | 0.654331 | ||||||||
\(285\) | 13.7409 | 0.813941 | ||||||||
\(286\) | 3.52996 | 0.208731 | ||||||||
\(287\) | 26.5234 | 1.56563 | ||||||||
\(288\) | −2.85268 | −0.168096 | ||||||||
\(289\) | 29.0291 | 1.70760 | ||||||||
\(290\) | 8.74508 | 0.513529 | ||||||||
\(291\) | −6.46647 | −0.379071 | ||||||||
\(292\) | 1.37039 | 0.0801957 | ||||||||
\(293\) | 20.3798 | 1.19060 | 0.595300 | − | 0.803504i | \(-0.297033\pi\) | ||||
0.595300 | + | 0.803504i | \(0.297033\pi\) | |||||||
\(294\) | −6.44701 | −0.375997 | ||||||||
\(295\) | 17.5237 | 1.02027 | ||||||||
\(296\) | 1.19760 | 0.0696093 | ||||||||
\(297\) | −3.65962 | −0.212353 | ||||||||
\(298\) | −3.47426 | −0.201258 | ||||||||
\(299\) | −5.99701 | −0.346816 | ||||||||
\(300\) | −4.70482 | −0.271633 | ||||||||
\(301\) | −46.9965 | −2.70883 | ||||||||
\(302\) | 11.2407 | 0.646827 | ||||||||
\(303\) | −1.12474 | −0.0646147 | ||||||||
\(304\) | −8.61766 | −0.494256 | ||||||||
\(305\) | 36.3389 | 2.08076 | ||||||||
\(306\) | 19.3539 | 1.10639 | ||||||||
\(307\) | −17.5028 | −0.998939 | −0.499470 | − | 0.866331i | \(-0.666472\pi\) | ||||
−0.499470 | + | 0.866331i | \(0.666472\pi\) | |||||||
\(308\) | −7.94703 | −0.452824 | ||||||||
\(309\) | −0.482928 | −0.0274728 | ||||||||
\(310\) | −15.0555 | −0.855096 | ||||||||
\(311\) | 22.4715 | 1.27424 | 0.637120 | − | 0.770764i | \(-0.280125\pi\) | ||||
0.637120 | + | 0.770764i | \(0.280125\pi\) | |||||||
\(312\) | 0.831683 | 0.0470848 | ||||||||
\(313\) | −32.6321 | −1.84447 | −0.922236 | − | 0.386626i | \(-0.873640\pi\) | ||||
−0.922236 | + | 0.386626i | \(0.873640\pi\) | |||||||
\(314\) | 8.59533 | 0.485063 | ||||||||
\(315\) | −57.8099 | −3.25722 | ||||||||
\(316\) | −14.9749 | −0.842401 | ||||||||
\(317\) | −19.5532 | −1.09822 | −0.549110 | − | 0.835750i | \(-0.685033\pi\) | ||||
−0.549110 | + | 0.835750i | \(0.685033\pi\) | |||||||
\(318\) | 1.16641 | 0.0654090 | ||||||||
\(319\) | −3.42941 | −0.192010 | ||||||||
\(320\) | 4.15424 | 0.232229 | ||||||||
\(321\) | −3.59241 | −0.200509 | ||||||||
\(322\) | 13.5011 | 0.752388 | ||||||||
\(323\) | 58.4663 | 3.25315 | ||||||||
\(324\) | 7.69580 | 0.427544 | ||||||||
\(325\) | −26.5602 | −1.47329 | ||||||||
\(326\) | 10.1530 | 0.562321 | ||||||||
\(327\) | −4.38300 | −0.242381 | ||||||||
\(328\) | 5.43715 | 0.300216 | ||||||||
\(329\) | −34.5186 | −1.90307 | ||||||||
\(330\) | 2.59760 | 0.142993 | ||||||||
\(331\) | −20.1680 | −1.10853 | −0.554266 | − | 0.832340i | \(-0.687001\pi\) | ||||
−0.554266 | + | 0.832340i | \(0.687001\pi\) | |||||||
\(332\) | −8.08276 | −0.443599 | ||||||||
\(333\) | −3.41638 | −0.187216 | ||||||||
\(334\) | 4.37572 | 0.239429 | ||||||||
\(335\) | −6.26298 | −0.342183 | ||||||||
\(336\) | −1.87238 | −0.102146 | ||||||||
\(337\) | 29.1409 | 1.58741 | 0.793704 | − | 0.608305i | \(-0.208150\pi\) | ||||
0.793704 | + | 0.608305i | \(0.208150\pi\) | |||||||
\(338\) | −8.30489 | −0.451727 | ||||||||
\(339\) | −0.121603 | −0.00660454 | ||||||||
\(340\) | −28.1843 | −1.52851 | ||||||||
\(341\) | 5.90407 | 0.319723 | ||||||||
\(342\) | 24.5834 | 1.32932 | ||||||||
\(343\) | 47.7899 | 2.58041 | ||||||||
\(344\) | −9.63402 | −0.519432 | ||||||||
\(345\) | −4.41304 | −0.237590 | ||||||||
\(346\) | −22.7651 | −1.22386 | ||||||||
\(347\) | 12.2141 | 0.655686 | 0.327843 | − | 0.944732i | \(-0.393678\pi\) | ||||
0.327843 | + | 0.944732i | \(0.393678\pi\) | |||||||
\(348\) | −0.807993 | −0.0433130 | ||||||||
\(349\) | 15.3346 | 0.820843 | 0.410421 | − | 0.911896i | \(-0.365382\pi\) | ||||
0.410421 | + | 0.911896i | \(0.365382\pi\) | |||||||
\(350\) | 59.7952 | 3.19619 | ||||||||
\(351\) | −4.86757 | −0.259812 | ||||||||
\(352\) | −1.62910 | −0.0868311 | ||||||||
\(353\) | 30.6859 | 1.63324 | 0.816622 | − | 0.577173i | \(-0.195844\pi\) | ||||
0.816622 | + | 0.577173i | \(0.195844\pi\) | |||||||
\(354\) | −1.61908 | −0.0860533 | ||||||||
\(355\) | 45.8087 | 2.43127 | ||||||||
\(356\) | 3.31299 | 0.175588 | ||||||||
\(357\) | 12.7031 | 0.672319 | ||||||||
\(358\) | 12.1634 | 0.642858 | ||||||||
\(359\) | 0.344824 | 0.0181991 | 0.00909956 | − | 0.999959i | \(-0.497103\pi\) | ||||
0.00909956 | + | 0.999959i | \(0.497103\pi\) | |||||||
\(360\) | −11.8507 | −0.624587 | ||||||||
\(361\) | 55.2640 | 2.90863 | ||||||||
\(362\) | −4.61048 | −0.242322 | ||||||||
\(363\) | 3.20343 | 0.168137 | ||||||||
\(364\) | −10.5701 | −0.554026 | ||||||||
\(365\) | 5.69291 | 0.297980 | ||||||||
\(366\) | −3.35750 | −0.175499 | ||||||||
\(367\) | 22.3072 | 1.16443 | 0.582214 | − | 0.813035i | \(-0.302186\pi\) | ||||
0.582214 | + | 0.813035i | \(0.302186\pi\) | |||||||
\(368\) | 2.76765 | 0.144274 | ||||||||
\(369\) | −15.5104 | −0.807440 | ||||||||
\(370\) | 4.97513 | 0.258645 | ||||||||
\(371\) | −14.8243 | −0.769640 | ||||||||
\(372\) | 1.39104 | 0.0721220 | ||||||||
\(373\) | −5.92843 | −0.306962 | −0.153481 | − | 0.988152i | \(-0.549048\pi\) | ||||
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(374\) | 11.0526 | 0.571515 | ||||||||
\(375\) | −11.5724 | −0.597597 | ||||||||
\(376\) | −7.07613 | −0.364923 | ||||||||
\(377\) | −4.56137 | −0.234922 | ||||||||
\(378\) | 10.9584 | 0.563640 | ||||||||
\(379\) | −2.01119 | −0.103308 | −0.0516540 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516540 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(380\) | −35.7998 | −1.83649 | ||||||||
\(381\) | 0.801322 | 0.0410530 | ||||||||
\(382\) | 3.30553 | 0.169126 | ||||||||
\(383\) | 4.21696 | 0.215477 | 0.107738 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107738 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(384\) | −0.383827 | −0.0195871 | ||||||||
\(385\) | −33.0138 | −1.68254 | ||||||||
\(386\) | −18.5157 | −0.942423 | ||||||||
\(387\) | 27.4827 | 1.39703 | ||||||||
\(388\) | 16.8474 | 0.855296 | ||||||||
\(389\) | 4.54939 | 0.230663 | 0.115332 | − | 0.993327i | \(-0.463207\pi\) | ||||
0.115332 | + | 0.993327i | \(0.463207\pi\) | |||||||
\(390\) | 3.45501 | 0.174951 | ||||||||
\(391\) | −18.7771 | −0.949598 | ||||||||
\(392\) | 16.7967 | 0.848360 | ||||||||
\(393\) | 1.98591 | 0.100176 | ||||||||
\(394\) | 8.78109 | 0.442385 | ||||||||
\(395\) | −62.2091 | −3.13008 | ||||||||
\(396\) | 4.64729 | 0.233535 | ||||||||
\(397\) | −15.2162 | −0.763677 | −0.381839 | − | 0.924229i | \(-0.624709\pi\) | ||||
−0.381839 | + | 0.924229i | \(0.624709\pi\) | |||||||
\(398\) | −12.4370 | −0.623409 | ||||||||
\(399\) | 16.1355 | 0.807785 | ||||||||
\(400\) | 12.2577 | 0.612884 | ||||||||
\(401\) | 18.4280 | 0.920250 | 0.460125 | − | 0.887854i | \(-0.347805\pi\) | ||||
0.460125 | + | 0.887854i | \(0.347805\pi\) | |||||||
\(402\) | 0.578661 | 0.0288610 | ||||||||
\(403\) | 7.85285 | 0.391178 | ||||||||
\(404\) | 2.93034 | 0.145790 | ||||||||
\(405\) | 31.9702 | 1.58861 | ||||||||
\(406\) | 10.2691 | 0.509645 | ||||||||
\(407\) | −1.95101 | −0.0967081 | ||||||||
\(408\) | 2.60406 | 0.128920 | ||||||||
\(409\) | 36.3293 | 1.79637 | 0.898184 | − | 0.439619i | \(-0.144887\pi\) | ||||
0.898184 | + | 0.439619i | \(0.144887\pi\) | |||||||
\(410\) | 22.5872 | 1.11550 | ||||||||
\(411\) | −2.44094 | −0.120403 | ||||||||
\(412\) | 1.25819 | 0.0619867 | ||||||||
\(413\) | 20.5775 | 1.01255 | ||||||||
\(414\) | −7.89522 | −0.388029 | ||||||||
\(415\) | −33.5777 | −1.64826 | ||||||||
\(416\) | −2.16682 | −0.106237 | ||||||||
\(417\) | 4.09872 | 0.200715 | ||||||||
\(418\) | 14.0390 | 0.686670 | ||||||||
\(419\) | −6.63242 | −0.324015 | −0.162007 | − | 0.986790i | \(-0.551797\pi\) | ||||
−0.162007 | + | 0.986790i | \(0.551797\pi\) | |||||||
\(420\) | −7.77829 | −0.379542 | ||||||||
\(421\) | −33.1090 | −1.61363 | −0.806817 | − | 0.590801i | \(-0.798812\pi\) | ||||
−0.806817 | + | 0.590801i | \(0.798812\pi\) | |||||||
\(422\) | −10.9290 | −0.532014 | ||||||||
\(423\) | 20.1859 | 0.981472 | ||||||||
\(424\) | −3.03890 | −0.147582 | ||||||||
\(425\) | −83.1620 | −4.03395 | ||||||||
\(426\) | −4.23245 | −0.205063 | ||||||||
\(427\) | 42.6716 | 2.06502 | ||||||||
\(428\) | 9.35946 | 0.452407 | ||||||||
\(429\) | −1.35489 | −0.0654148 | ||||||||
\(430\) | −40.0220 | −1.93003 | ||||||||
\(431\) | −16.6498 | −0.801995 | −0.400997 | − | 0.916079i | \(-0.631336\pi\) | ||||
−0.400997 | + | 0.916079i | \(0.631336\pi\) | |||||||
\(432\) | 2.24641 | 0.108081 | ||||||||
\(433\) | 5.36131 | 0.257648 | 0.128824 | − | 0.991667i | \(-0.458880\pi\) | ||||
0.128824 | + | 0.991667i | \(0.458880\pi\) | |||||||
\(434\) | −17.6792 | −0.848629 | ||||||||
\(435\) | −3.35659 | −0.160936 | ||||||||
\(436\) | 11.4192 | 0.546882 | ||||||||
\(437\) | −23.8507 | −1.14093 | ||||||||
\(438\) | −0.525990 | −0.0251328 | ||||||||
\(439\) | −5.42961 | −0.259141 | −0.129571 | − | 0.991570i | \(-0.541360\pi\) | ||||
−0.129571 | + | 0.991570i | \(0.541360\pi\) | |||||||
\(440\) | −6.76765 | −0.322635 | ||||||||
\(441\) | −47.9155 | −2.28169 | ||||||||
\(442\) | 14.7007 | 0.699243 | ||||||||
\(443\) | 3.66946 | 0.174341 | 0.0871706 | − | 0.996193i | \(-0.472217\pi\) | ||||
0.0871706 | + | 0.996193i | \(0.472217\pi\) | |||||||
\(444\) | −0.459672 | −0.0218151 | ||||||||
\(445\) | 13.7629 | 0.652426 | ||||||||
\(446\) | 8.79372 | 0.416395 | ||||||||
\(447\) | 1.33351 | 0.0630729 | ||||||||
\(448\) | 4.87818 | 0.230472 | ||||||||
\(449\) | 6.43513 | 0.303693 | 0.151846 | − | 0.988404i | \(-0.451478\pi\) | ||||
0.151846 | + | 0.988404i | \(0.451478\pi\) | |||||||
\(450\) | −34.9672 | −1.64837 | ||||||||
\(451\) | −8.85764 | −0.417090 | ||||||||
\(452\) | 0.316816 | 0.0149018 | ||||||||
\(453\) | −4.31446 | −0.202711 | ||||||||
\(454\) | 6.74871 | 0.316733 | ||||||||
\(455\) | −43.9109 | −2.05857 | ||||||||
\(456\) | 3.30769 | 0.154897 | ||||||||
\(457\) | 2.97606 | 0.139214 | 0.0696071 | − | 0.997574i | \(-0.477825\pi\) | ||||
0.0696071 | + | 0.997574i | \(0.477825\pi\) | |||||||
\(458\) | −23.2606 | −1.08690 | ||||||||
\(459\) | −15.2407 | −0.711377 | ||||||||
\(460\) | 11.4975 | 0.536073 | ||||||||
\(461\) | 9.73958 | 0.453617 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(462\) | 3.05028 | 0.141912 | ||||||||
\(463\) | −19.9810 | −0.928598 | −0.464299 | − | 0.885679i | \(-0.653694\pi\) | ||||
−0.464299 | + | 0.885679i | \(0.653694\pi\) | |||||||
\(464\) | 2.10510 | 0.0977268 | ||||||||
\(465\) | 5.77871 | 0.267981 | ||||||||
\(466\) | 11.0721 | 0.512905 | ||||||||
\(467\) | −14.3949 | −0.666115 | −0.333057 | − | 0.942907i | \(-0.608080\pi\) | ||||
−0.333057 | + | 0.942907i | \(0.608080\pi\) | |||||||
\(468\) | 6.18124 | 0.285728 | ||||||||
\(469\) | −7.35441 | −0.339595 | ||||||||
\(470\) | −29.3959 | −1.35593 | ||||||||
\(471\) | −3.29912 | −0.152015 | ||||||||
\(472\) | 4.21827 | 0.194161 | ||||||||
\(473\) | 15.6947 | 0.721645 | ||||||||
\(474\) | 5.74775 | 0.264003 | ||||||||
\(475\) | −105.633 | −4.84675 | ||||||||
\(476\) | −33.0959 | −1.51695 | ||||||||
\(477\) | 8.66900 | 0.396926 | ||||||||
\(478\) | −3.99072 | −0.182531 | ||||||||
\(479\) | −22.4679 | −1.02659 | −0.513293 | − | 0.858213i | \(-0.671575\pi\) | ||||
−0.513293 | + | 0.858213i | \(0.671575\pi\) | |||||||
\(480\) | −1.59451 | −0.0727789 | ||||||||
\(481\) | −2.59499 | −0.118321 | ||||||||
\(482\) | −16.5408 | −0.753415 | ||||||||
\(483\) | −5.18209 | −0.235793 | ||||||||
\(484\) | −8.34604 | −0.379366 | ||||||||
\(485\) | 69.9880 | 3.17799 | ||||||||
\(486\) | −9.69309 | −0.439687 | ||||||||
\(487\) | −15.3289 | −0.694618 | −0.347309 | − | 0.937751i | \(-0.612904\pi\) | ||||
−0.347309 | + | 0.937751i | \(0.612904\pi\) | |||||||
\(488\) | 8.74744 | 0.395978 | ||||||||
\(489\) | −3.89698 | −0.176227 | ||||||||
\(490\) | 69.7773 | 3.15222 | ||||||||
\(491\) | −23.8945 | −1.07834 | −0.539172 | − | 0.842196i | \(-0.681263\pi\) | ||||
−0.539172 | + | 0.842196i | \(0.681263\pi\) | |||||||
\(492\) | −2.08692 | −0.0940857 | ||||||||
\(493\) | −14.2820 | −0.643229 | ||||||||
\(494\) | 18.6729 | 0.840134 | ||||||||
\(495\) | 19.3059 | 0.867737 | ||||||||
\(496\) | −3.62414 | −0.162729 | ||||||||
\(497\) | 53.7917 | 2.41289 | ||||||||
\(498\) | 3.10238 | 0.139021 | ||||||||
\(499\) | −15.7627 | −0.705635 | −0.352818 | − | 0.935692i | \(-0.614776\pi\) | ||||
−0.352818 | + | 0.935692i | \(0.614776\pi\) | |||||||
\(500\) | 30.1501 | 1.34836 | ||||||||
\(501\) | −1.67952 | −0.0750353 | ||||||||
\(502\) | 24.0533 | 1.07355 | ||||||||
\(503\) | 0.635388 | 0.0283305 | 0.0141653 | − | 0.999900i | \(-0.495491\pi\) | ||||
0.0141653 | + | 0.999900i | \(0.495491\pi\) | |||||||
\(504\) | −13.9159 | −0.619863 | ||||||||
\(505\) | 12.1733 | 0.541706 | ||||||||
\(506\) | −4.50877 | −0.200439 | ||||||||
\(507\) | 3.18764 | 0.141568 | ||||||||
\(508\) | −2.08772 | −0.0926276 | ||||||||
\(509\) | 1.74035 | 0.0771399 | 0.0385699 | − | 0.999256i | \(-0.487720\pi\) | ||||
0.0385699 | + | 0.999256i | \(0.487720\pi\) | |||||||
\(510\) | 10.8179 | 0.479024 | ||||||||
\(511\) | 6.68499 | 0.295727 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −19.3588 | −0.854712 | ||||||||
\(514\) | −13.6822 | −0.603495 | ||||||||
\(515\) | 5.22683 | 0.230322 | ||||||||
\(516\) | 3.69779 | 0.162786 | ||||||||
\(517\) | 11.5277 | 0.506987 | ||||||||
\(518\) | 5.84213 | 0.256688 | ||||||||
\(519\) | 8.73784 | 0.383548 | ||||||||
\(520\) | −9.00148 | −0.394741 | ||||||||
\(521\) | 10.5683 | 0.463004 | 0.231502 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(522\) | −6.00517 | −0.262839 | ||||||||
\(523\) | 10.5329 | 0.460572 | 0.230286 | − | 0.973123i | \(-0.426034\pi\) | ||||
0.230286 | + | 0.973123i | \(0.426034\pi\) | |||||||
\(524\) | −5.17397 | −0.226026 | ||||||||
\(525\) | −22.9510 | −1.00166 | ||||||||
\(526\) | 11.3942 | 0.496810 | ||||||||
\(527\) | 24.5879 | 1.07106 | ||||||||
\(528\) | 0.625290 | 0.0272123 | ||||||||
\(529\) | −15.3401 | −0.666961 | ||||||||
\(530\) | −12.6243 | −0.548365 | ||||||||
\(531\) | −12.0334 | −0.522203 | ||||||||
\(532\) | −42.0385 | −1.82260 | ||||||||
\(533\) | −11.7813 | −0.510305 | ||||||||
\(534\) | −1.27161 | −0.0550281 | ||||||||
\(535\) | 38.8814 | 1.68099 | ||||||||
\(536\) | −1.50761 | −0.0651189 | ||||||||
\(537\) | −4.66865 | −0.201467 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | −27.3634 | −1.17862 | ||||||||
\(540\) | 9.33213 | 0.401591 | ||||||||
\(541\) | −0.0839881 | −0.00361093 | −0.00180546 | − | 0.999998i | \(-0.500575\pi\) | ||||
−0.00180546 | + | 0.999998i | \(0.500575\pi\) | |||||||
\(542\) | −24.6167 | −1.05738 | ||||||||
\(543\) | 1.76963 | 0.0759419 | ||||||||
\(544\) | −6.78448 | −0.290882 | ||||||||
\(545\) | 47.4382 | 2.03203 | ||||||||
\(546\) | 4.05710 | 0.173628 | ||||||||
\(547\) | 1.38614 | 0.0592669 | 0.0296334 | − | 0.999561i | \(-0.490566\pi\) | ||||
0.0296334 | + | 0.999561i | \(0.490566\pi\) | |||||||
\(548\) | 6.35949 | 0.271664 | ||||||||
\(549\) | −24.9536 | −1.06499 | ||||||||
\(550\) | −19.9690 | −0.851479 | ||||||||
\(551\) | −18.1410 | −0.772833 | ||||||||
\(552\) | −1.06230 | −0.0452144 | ||||||||
\(553\) | −73.0501 | −3.10641 | ||||||||
\(554\) | 4.70762 | 0.200008 | ||||||||
\(555\) | −1.90959 | −0.0810575 | ||||||||
\(556\) | −10.6786 | −0.452873 | ||||||||
\(557\) | 17.1840 | 0.728111 | 0.364056 | − | 0.931377i | \(-0.381392\pi\) | ||||
0.364056 | + | 0.931377i | \(0.381392\pi\) | |||||||
\(558\) | 10.3385 | 0.437663 | ||||||||
\(559\) | 20.8752 | 0.882926 | ||||||||
\(560\) | 20.2651 | 0.856358 | ||||||||
\(561\) | −4.24227 | −0.179109 | ||||||||
\(562\) | 6.51540 | 0.274836 | ||||||||
\(563\) | −12.1968 | −0.514033 | −0.257017 | − | 0.966407i | \(-0.582740\pi\) | ||||
−0.257017 | + | 0.966407i | \(0.582740\pi\) | |||||||
\(564\) | 2.71601 | 0.114364 | ||||||||
\(565\) | 1.31613 | 0.0553700 | ||||||||
\(566\) | −8.67417 | −0.364602 | ||||||||
\(567\) | 37.5415 | 1.57660 | ||||||||
\(568\) | 11.0270 | 0.462682 | ||||||||
\(569\) | 23.4816 | 0.984401 | 0.492201 | − | 0.870482i | \(-0.336193\pi\) | ||||
0.492201 | + | 0.870482i | \(0.336193\pi\) | |||||||
\(570\) | 13.7409 | 0.575543 | ||||||||
\(571\) | −2.61940 | −0.109619 | −0.0548093 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548093 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(572\) | 3.52996 | 0.147595 | ||||||||
\(573\) | −1.26875 | −0.0530028 | ||||||||
\(574\) | 26.5234 | 1.10707 | ||||||||
\(575\) | 33.9250 | 1.41477 | ||||||||
\(576\) | −2.85268 | −0.118862 | ||||||||
\(577\) | 12.1035 | 0.503874 | 0.251937 | − | 0.967744i | \(-0.418932\pi\) | ||||
0.251937 | + | 0.967744i | \(0.418932\pi\) | |||||||
\(578\) | 29.0291 | 1.20745 | ||||||||
\(579\) | 7.10681 | 0.295349 | ||||||||
\(580\) | 8.74508 | 0.363120 | ||||||||
\(581\) | −39.4292 | −1.63580 | ||||||||
\(582\) | −6.46647 | −0.268044 | ||||||||
\(583\) | 4.95066 | 0.205035 | ||||||||
\(584\) | 1.37039 | 0.0567070 | ||||||||
\(585\) | 25.6783 | 1.06167 | ||||||||
\(586\) | 20.3798 | 0.841881 | ||||||||
\(587\) | −3.09578 | −0.127776 | −0.0638882 | − | 0.997957i | \(-0.520350\pi\) | ||||
−0.0638882 | + | 0.997957i | \(0.520350\pi\) | |||||||
\(588\) | −6.44701 | −0.265870 | ||||||||
\(589\) | 31.2316 | 1.28687 | ||||||||
\(590\) | 17.5237 | 0.721439 | ||||||||
\(591\) | −3.37042 | −0.138640 | ||||||||
\(592\) | 1.19760 | 0.0492212 | ||||||||
\(593\) | −24.1730 | −0.992666 | −0.496333 | − | 0.868132i | \(-0.665321\pi\) | ||||
−0.496333 | + | 0.868132i | \(0.665321\pi\) | |||||||
\(594\) | −3.65962 | −0.150156 | ||||||||
\(595\) | −137.488 | −5.63647 | ||||||||
\(596\) | −3.47426 | −0.142311 | ||||||||
\(597\) | 4.77364 | 0.195372 | ||||||||
\(598\) | −5.99701 | −0.245236 | ||||||||
\(599\) | 39.0984 | 1.59752 | 0.798759 | − | 0.601651i | \(-0.205490\pi\) | ||||
0.798759 | + | 0.601651i | \(0.205490\pi\) | |||||||
\(600\) | −4.70482 | −0.192074 | ||||||||
\(601\) | −29.5069 | −1.20361 | −0.601807 | − | 0.798642i | \(-0.705552\pi\) | ||||
−0.601807 | + | 0.798642i | \(0.705552\pi\) | |||||||
\(602\) | −46.9965 | −1.91543 | ||||||||
\(603\) | 4.30073 | 0.175139 | ||||||||
\(604\) | 11.2407 | 0.457376 | ||||||||
\(605\) | −34.6714 | −1.40959 | ||||||||
\(606\) | −1.12474 | −0.0456895 | ||||||||
\(607\) | 17.2674 | 0.700861 | 0.350431 | − | 0.936589i | \(-0.386035\pi\) | ||||
0.350431 | + | 0.936589i | \(0.386035\pi\) | |||||||
\(608\) | −8.61766 | −0.349492 | ||||||||
\(609\) | −3.94154 | −0.159719 | ||||||||
\(610\) | 36.3389 | 1.47132 | ||||||||
\(611\) | 15.3327 | 0.620294 | ||||||||
\(612\) | 19.3539 | 0.782336 | ||||||||
\(613\) | −7.94254 | −0.320796 | −0.160398 | − | 0.987052i | \(-0.551278\pi\) | ||||
−0.160398 | + | 0.987052i | \(0.551278\pi\) | |||||||
\(614\) | −17.5028 | −0.706357 | ||||||||
\(615\) | −8.66956 | −0.349591 | ||||||||
\(616\) | −7.94703 | −0.320195 | ||||||||
\(617\) | 18.0886 | 0.728218 | 0.364109 | − | 0.931356i | \(-0.381374\pi\) | ||||
0.364109 | + | 0.931356i | \(0.381374\pi\) | |||||||
\(618\) | −0.482928 | −0.0194262 | ||||||||
\(619\) | −33.4949 | −1.34627 | −0.673136 | − | 0.739518i | \(-0.735053\pi\) | ||||
−0.673136 | + | 0.739518i | \(0.735053\pi\) | |||||||
\(620\) | −15.0555 | −0.604644 | ||||||||
\(621\) | 6.21729 | 0.249491 | ||||||||
\(622\) | 22.4715 | 0.901024 | ||||||||
\(623\) | 16.1614 | 0.647491 | ||||||||
\(624\) | 0.831683 | 0.0332940 | ||||||||
\(625\) | 63.9624 | 2.55850 | ||||||||
\(626\) | −32.6321 | −1.30424 | ||||||||
\(627\) | −5.38854 | −0.215197 | ||||||||
\(628\) | 8.59533 | 0.342991 | ||||||||
\(629\) | −8.12512 | −0.323970 | ||||||||
\(630\) | −57.8099 | −2.30320 | ||||||||
\(631\) | 37.3162 | 1.48554 | 0.742768 | − | 0.669549i | \(-0.233512\pi\) | ||||
0.742768 | + | 0.669549i | \(0.233512\pi\) | |||||||
\(632\) | −14.9749 | −0.595668 | ||||||||
\(633\) | 4.19483 | 0.166729 | ||||||||
\(634\) | −19.5532 | −0.776559 | ||||||||
\(635\) | −8.67288 | −0.344173 | ||||||||
\(636\) | 1.16641 | 0.0462512 | ||||||||
\(637\) | −36.3954 | −1.44204 | ||||||||
\(638\) | −3.42941 | −0.135772 | ||||||||
\(639\) | −31.4564 | −1.24440 | ||||||||
\(640\) | 4.15424 | 0.164211 | ||||||||
\(641\) | −18.0393 | −0.712509 | −0.356254 | − | 0.934389i | \(-0.615946\pi\) | ||||
−0.356254 | + | 0.934389i | \(0.615946\pi\) | |||||||
\(642\) | −3.59241 | −0.141781 | ||||||||
\(643\) | −33.0496 | −1.30335 | −0.651675 | − | 0.758498i | \(-0.725933\pi\) | ||||
−0.651675 | + | 0.758498i | \(0.725933\pi\) | |||||||
\(644\) | 13.5011 | 0.532019 | ||||||||
\(645\) | 15.3615 | 0.604859 | ||||||||
\(646\) | 58.4663 | 2.30033 | ||||||||
\(647\) | −40.3067 | −1.58462 | −0.792310 | − | 0.610118i | \(-0.791122\pi\) | ||||
−0.792310 | + | 0.610118i | \(0.791122\pi\) | |||||||
\(648\) | 7.69580 | 0.302320 | ||||||||
\(649\) | −6.87196 | −0.269748 | ||||||||
\(650\) | −26.5602 | −1.04178 | ||||||||
\(651\) | 6.78575 | 0.265954 | ||||||||
\(652\) | 10.1530 | 0.397621 | ||||||||
\(653\) | −21.3784 | −0.836601 | −0.418300 | − | 0.908309i | \(-0.637374\pi\) | ||||
−0.418300 | + | 0.908309i | \(0.637374\pi\) | |||||||
\(654\) | −4.38300 | −0.171389 | ||||||||
\(655\) | −21.4939 | −0.839836 | ||||||||
\(656\) | 5.43715 | 0.212285 | ||||||||
\(657\) | −3.90927 | −0.152515 | ||||||||
\(658\) | −34.5186 | −1.34568 | ||||||||
\(659\) | 23.1777 | 0.902875 | 0.451438 | − | 0.892303i | \(-0.350911\pi\) | ||||
0.451438 | + | 0.892303i | \(0.350911\pi\) | |||||||
\(660\) | 2.59760 | 0.101112 | ||||||||
\(661\) | −3.96791 | −0.154334 | −0.0771669 | − | 0.997018i | \(-0.524587\pi\) | ||||
−0.0771669 | + | 0.997018i | \(0.524587\pi\) | |||||||
\(662\) | −20.1680 | −0.783850 | ||||||||
\(663\) | −5.64253 | −0.219138 | ||||||||
\(664\) | −8.08276 | −0.313672 | ||||||||
\(665\) | −174.638 | −6.77217 | ||||||||
\(666\) | −3.41638 | −0.132382 | ||||||||
\(667\) | 5.82618 | 0.225591 | ||||||||
\(668\) | 4.37572 | 0.169302 | ||||||||
\(669\) | −3.37526 | −0.130495 | ||||||||
\(670\) | −6.26298 | −0.241960 | ||||||||
\(671\) | −14.2504 | −0.550131 | ||||||||
\(672\) | −1.87238 | −0.0722285 | ||||||||
\(673\) | 32.9589 | 1.27047 | 0.635235 | − | 0.772319i | \(-0.280903\pi\) | ||||
0.635235 | + | 0.772319i | \(0.280903\pi\) | |||||||
\(674\) | 29.1409 | 1.12247 | ||||||||
\(675\) | 27.5358 | 1.05985 | ||||||||
\(676\) | −8.30489 | −0.319419 | ||||||||
\(677\) | 17.1159 | 0.657816 | 0.328908 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328908 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(678\) | −0.121603 | −0.00467012 | ||||||||
\(679\) | 82.1846 | 3.15396 | ||||||||
\(680\) | −28.1843 | −1.08082 | ||||||||
\(681\) | −2.59033 | −0.0992618 | ||||||||
\(682\) | 5.90407 | 0.226078 | ||||||||
\(683\) | 33.2813 | 1.27347 | 0.636736 | − | 0.771082i | \(-0.280284\pi\) | ||||
0.636736 | + | 0.771082i | \(0.280284\pi\) | |||||||
\(684\) | 24.5834 | 0.939969 | ||||||||
\(685\) | 26.4188 | 1.00941 | ||||||||
\(686\) | 47.7899 | 1.82463 | ||||||||
\(687\) | 8.92804 | 0.340626 | ||||||||
\(688\) | −9.63402 | −0.367294 | ||||||||
\(689\) | 6.58475 | 0.250859 | ||||||||
\(690\) | −4.41304 | −0.168002 | ||||||||
\(691\) | −21.3236 | −0.811189 | −0.405594 | − | 0.914053i | \(-0.632935\pi\) | ||||
−0.405594 | + | 0.914053i | \(0.632935\pi\) | |||||||
\(692\) | −22.7651 | −0.865398 | ||||||||
\(693\) | 22.6703 | 0.861174 | ||||||||
\(694\) | 12.2141 | 0.463640 | ||||||||
\(695\) | −44.3614 | −1.68272 | ||||||||
\(696\) | −0.807993 | −0.0306269 | ||||||||
\(697\) | −36.8882 | −1.39724 | ||||||||
\(698\) | 15.3346 | 0.580423 | ||||||||
\(699\) | −4.24976 | −0.160741 | ||||||||
\(700\) | 59.7952 | 2.26005 | ||||||||
\(701\) | −28.5333 | −1.07769 | −0.538844 | − | 0.842406i | \(-0.681139\pi\) | ||||
−0.538844 | + | 0.842406i | \(0.681139\pi\) | |||||||
\(702\) | −4.86757 | −0.183715 | ||||||||
\(703\) | −10.3205 | −0.389246 | ||||||||
\(704\) | −1.62910 | −0.0613989 | ||||||||
\(705\) | 11.2829 | 0.424940 | ||||||||
\(706\) | 30.6859 | 1.15488 | ||||||||
\(707\) | 14.2947 | 0.537609 | ||||||||
\(708\) | −1.61908 | −0.0608489 | ||||||||
\(709\) | 4.38294 | 0.164605 | 0.0823024 | − | 0.996607i | \(-0.473773\pi\) | ||||
0.0823024 | + | 0.996607i | \(0.473773\pi\) | |||||||
\(710\) | 45.8087 | 1.71917 | ||||||||
\(711\) | 42.7184 | 1.60207 | ||||||||
\(712\) | 3.31299 | 0.124159 | ||||||||
\(713\) | −10.0304 | −0.375640 | ||||||||
\(714\) | 12.7031 | 0.475401 | ||||||||
\(715\) | 14.6643 | 0.548413 | ||||||||
\(716\) | 12.1634 | 0.454569 | ||||||||
\(717\) | 1.53174 | 0.0572040 | ||||||||
\(718\) | 0.344824 | 0.0128687 | ||||||||
\(719\) | −36.1805 | −1.34930 | −0.674652 | − | 0.738136i | \(-0.735706\pi\) | ||||
−0.674652 | + | 0.738136i | \(0.735706\pi\) | |||||||
\(720\) | −11.8507 | −0.441649 | ||||||||
\(721\) | 6.13770 | 0.228580 | ||||||||
\(722\) | 55.2640 | 2.05671 | ||||||||
\(723\) | 6.34881 | 0.236115 | ||||||||
\(724\) | −4.61048 | −0.171347 | ||||||||
\(725\) | 25.8036 | 0.958323 | ||||||||
\(726\) | 3.20343 | 0.118891 | ||||||||
\(727\) | −23.0348 | −0.854312 | −0.427156 | − | 0.904178i | \(-0.640485\pi\) | ||||
−0.427156 | + | 0.904178i | \(0.640485\pi\) | |||||||
\(728\) | −10.5701 | −0.391756 | ||||||||
\(729\) | −19.3669 | −0.717294 | ||||||||
\(730\) | 5.69291 | 0.210704 | ||||||||
\(731\) | 65.3618 | 2.41749 | ||||||||
\(732\) | −3.35750 | −0.124097 | ||||||||
\(733\) | −41.3032 | −1.52557 | −0.762785 | − | 0.646652i | \(-0.776169\pi\) | ||||
−0.762785 | + | 0.646652i | \(0.776169\pi\) | |||||||
\(734\) | 22.3072 | 0.823375 | ||||||||
\(735\) | −26.7824 | −0.987884 | ||||||||
\(736\) | 2.76765 | 0.102017 | ||||||||
\(737\) | 2.45605 | 0.0904696 | ||||||||
\(738\) | −15.5104 | −0.570947 | ||||||||
\(739\) | −15.2014 | −0.559191 | −0.279596 | − | 0.960118i | \(-0.590200\pi\) | ||||
−0.279596 | + | 0.960118i | \(0.590200\pi\) | |||||||
\(740\) | 4.97513 | 0.182889 | ||||||||
\(741\) | −7.16716 | −0.263292 | ||||||||
\(742\) | −14.8243 | −0.544218 | ||||||||
\(743\) | 51.4130 | 1.88616 | 0.943079 | − | 0.332568i | \(-0.107915\pi\) | ||||
0.943079 | + | 0.332568i | \(0.107915\pi\) | |||||||
\(744\) | 1.39104 | 0.0509980 | ||||||||
\(745\) | −14.4329 | −0.528780 | ||||||||
\(746\) | −5.92843 | −0.217055 | ||||||||
\(747\) | 23.0575 | 0.843630 | ||||||||
\(748\) | 11.0526 | 0.404122 | ||||||||
\(749\) | 45.6572 | 1.66828 | ||||||||
\(750\) | −11.5724 | −0.422565 | ||||||||
\(751\) | 37.2197 | 1.35816 | 0.679082 | − | 0.734062i | \(-0.262378\pi\) | ||||
0.679082 | + | 0.734062i | \(0.262378\pi\) | |||||||
\(752\) | −7.07613 | −0.258040 | ||||||||
\(753\) | −9.23231 | −0.336444 | ||||||||
\(754\) | −4.56137 | −0.166115 | ||||||||
\(755\) | 46.6964 | 1.69945 | ||||||||
\(756\) | 10.9584 | 0.398554 | ||||||||
\(757\) | 51.7191 | 1.87976 | 0.939882 | − | 0.341499i | \(-0.110935\pi\) | ||||
0.939882 | + | 0.341499i | \(0.110935\pi\) | |||||||
\(758\) | −2.01119 | −0.0730499 | ||||||||
\(759\) | 1.73059 | 0.0628163 | ||||||||
\(760\) | −35.7998 | −1.29859 | ||||||||
\(761\) | 16.8448 | 0.610623 | 0.305312 | − | 0.952253i | \(-0.401239\pi\) | ||||
0.305312 | + | 0.952253i | \(0.401239\pi\) | |||||||
\(762\) | 0.801322 | 0.0290288 | ||||||||
\(763\) | 55.7051 | 2.01666 | ||||||||
\(764\) | 3.30553 | 0.119590 | ||||||||
\(765\) | 80.4008 | 2.90690 | ||||||||
\(766\) | 4.21696 | 0.152365 | ||||||||
\(767\) | −9.14022 | −0.330034 | ||||||||
\(768\) | −0.383827 | −0.0138501 | ||||||||
\(769\) | 10.2220 | 0.368614 | 0.184307 | − | 0.982869i | \(-0.440996\pi\) | ||||
0.184307 | + | 0.982869i | \(0.440996\pi\) | |||||||
\(770\) | −33.0138 | −1.18974 | ||||||||
\(771\) | 5.25158 | 0.189131 | ||||||||
\(772\) | −18.5157 | −0.666394 | ||||||||
\(773\) | −31.6879 | −1.13973 | −0.569867 | − | 0.821737i | \(-0.693005\pi\) | ||||
−0.569867 | + | 0.821737i | \(0.693005\pi\) | |||||||
\(774\) | 27.4827 | 0.987847 | ||||||||
\(775\) | −44.4235 | −1.59574 | ||||||||
\(776\) | 16.8474 | 0.604786 | ||||||||
\(777\) | −2.24236 | −0.0804444 | ||||||||
\(778\) | 4.54939 | 0.163103 | ||||||||
\(779\) | −46.8555 | −1.67877 | ||||||||
\(780\) | 3.45501 | 0.123709 | ||||||||
\(781\) | −17.9640 | −0.642803 | ||||||||
\(782\) | −18.7771 | −0.671467 | ||||||||
\(783\) | 4.72892 | 0.168998 | ||||||||
\(784\) | 16.7967 | 0.599881 | ||||||||
\(785\) | 35.7070 | 1.27444 | ||||||||
\(786\) | 1.98591 | 0.0708350 | ||||||||
\(787\) | 21.1252 | 0.753033 | 0.376516 | − | 0.926410i | \(-0.377122\pi\) | ||||
0.376516 | + | 0.926410i | \(0.377122\pi\) | |||||||
\(788\) | 8.78109 | 0.312814 | ||||||||
\(789\) | −4.37339 | −0.155697 | ||||||||
\(790\) | −62.2091 | −2.21330 | ||||||||
\(791\) | 1.54549 | 0.0549512 | ||||||||
\(792\) | 4.64729 | 0.165134 | ||||||||
\(793\) | −18.9541 | −0.673080 | ||||||||
\(794\) | −15.2162 | −0.540001 | ||||||||
\(795\) | 4.84554 | 0.171854 | ||||||||
\(796\) | −12.4370 | −0.440817 | ||||||||
\(797\) | −4.27630 | −0.151474 | −0.0757371 | − | 0.997128i | \(-0.524131\pi\) | ||||
−0.0757371 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(798\) | 16.1355 | 0.571190 | ||||||||
\(799\) | 48.0078 | 1.69839 | ||||||||
\(800\) | 12.2577 | 0.433375 | ||||||||
\(801\) | −9.45089 | −0.333931 | ||||||||
\(802\) | 18.4280 | 0.650715 | ||||||||
\(803\) | −2.23249 | −0.0787829 | ||||||||
\(804\) | 0.578661 | 0.0204078 | ||||||||
\(805\) | 56.0868 | 1.97680 | ||||||||
\(806\) | 7.85285 | 0.276605 | ||||||||
\(807\) | 0.383827 | 0.0135113 | ||||||||
\(808\) | 2.93034 | 0.103089 | ||||||||
\(809\) | 4.78386 | 0.168192 | 0.0840958 | − | 0.996458i | \(-0.473200\pi\) | ||||
0.0840958 | + | 0.996458i | \(0.473200\pi\) | |||||||
\(810\) | 31.9702 | 1.12332 | ||||||||
\(811\) | −34.4127 | −1.20839 | −0.604197 | − | 0.796835i | \(-0.706506\pi\) | ||||
−0.604197 | + | 0.796835i | \(0.706506\pi\) | |||||||
\(812\) | 10.2691 | 0.360373 | ||||||||
\(813\) | 9.44854 | 0.331375 | ||||||||
\(814\) | −1.95101 | −0.0683829 | ||||||||
\(815\) | 42.1778 | 1.47742 | ||||||||
\(816\) | 2.60406 | 0.0911604 | ||||||||
\(817\) | 83.0227 | 2.90460 | ||||||||
\(818\) | 36.3293 | 1.27022 | ||||||||
\(819\) | 30.1532 | 1.05364 | ||||||||
\(820\) | 22.5872 | 0.788779 | ||||||||
\(821\) | −38.7973 | −1.35404 | −0.677018 | − | 0.735967i | \(-0.736728\pi\) | ||||
−0.677018 | + | 0.735967i | \(0.736728\pi\) | |||||||
\(822\) | −2.44094 | −0.0851375 | ||||||||
\(823\) | −8.52567 | −0.297186 | −0.148593 | − | 0.988898i | \(-0.547474\pi\) | ||||
−0.148593 | + | 0.988898i | \(0.547474\pi\) | |||||||
\(824\) | 1.25819 | 0.0438312 | ||||||||
\(825\) | 7.66461 | 0.266848 | ||||||||
\(826\) | 20.5775 | 0.715982 | ||||||||
\(827\) | 3.84932 | 0.133854 | 0.0669271 | − | 0.997758i | \(-0.478681\pi\) | ||||
0.0669271 | + | 0.997758i | \(0.478681\pi\) | |||||||
\(828\) | −7.89522 | −0.274378 | ||||||||
\(829\) | 1.76719 | 0.0613771 | 0.0306886 | − | 0.999529i | \(-0.490230\pi\) | ||||
0.0306886 | + | 0.999529i | \(0.490230\pi\) | |||||||
\(830\) | −33.5777 | −1.16550 | ||||||||
\(831\) | −1.80691 | −0.0626810 | ||||||||
\(832\) | −2.16682 | −0.0751210 | ||||||||
\(833\) | −113.957 | −3.94836 | ||||||||
\(834\) | 4.09872 | 0.141927 | ||||||||
\(835\) | 18.1778 | 0.629068 | ||||||||
\(836\) | 14.0390 | 0.485549 | ||||||||
\(837\) | −8.14131 | −0.281405 | ||||||||
\(838\) | −6.63242 | −0.229113 | ||||||||
\(839\) | 48.4527 | 1.67277 | 0.836386 | − | 0.548141i | \(-0.184664\pi\) | ||||
0.836386 | + | 0.548141i | \(0.184664\pi\) | |||||||
\(840\) | −7.77829 | −0.268377 | ||||||||
\(841\) | −24.5686 | −0.847192 | ||||||||
\(842\) | −33.1090 | −1.14101 | ||||||||
\(843\) | −2.50078 | −0.0861315 | ||||||||
\(844\) | −10.9290 | −0.376191 | ||||||||
\(845\) | −34.5005 | −1.18685 | ||||||||
\(846\) | 20.1859 | 0.694006 | ||||||||
\(847\) | −40.7135 | −1.39893 | ||||||||
\(848\) | −3.03890 | −0.104356 | ||||||||
\(849\) | 3.32938 | 0.114264 | ||||||||
\(850\) | −83.1620 | −2.85243 | ||||||||
\(851\) | 3.31455 | 0.113621 | ||||||||
\(852\) | −4.23245 | −0.145001 | ||||||||
\(853\) | 35.2024 | 1.20531 | 0.602654 | − | 0.798002i | \(-0.294110\pi\) | ||||
0.602654 | + | 0.798002i | \(0.294110\pi\) | |||||||
\(854\) | 42.6716 | 1.46019 | ||||||||
\(855\) | 102.125 | 3.49261 | ||||||||
\(856\) | 9.35946 | 0.319900 | ||||||||
\(857\) | 8.30685 | 0.283757 | 0.141878 | − | 0.989884i | \(-0.454686\pi\) | ||||
0.141878 | + | 0.989884i | \(0.454686\pi\) | |||||||
\(858\) | −1.35489 | −0.0462552 | ||||||||
\(859\) | 48.5886 | 1.65782 | 0.828911 | − | 0.559381i | \(-0.188961\pi\) | ||||
0.828911 | + | 0.559381i | \(0.188961\pi\) | |||||||
\(860\) | −40.0220 | −1.36474 | ||||||||
\(861\) | −10.1804 | −0.346947 | ||||||||
\(862\) | −16.6498 | −0.567096 | ||||||||
\(863\) | 50.0516 | 1.70378 | 0.851888 | − | 0.523723i | \(-0.175457\pi\) | ||||
0.851888 | + | 0.523723i | \(0.175457\pi\) | |||||||
\(864\) | 2.24641 | 0.0764245 | ||||||||
\(865\) | −94.5715 | −3.21553 | ||||||||
\(866\) | 5.36131 | 0.182185 | ||||||||
\(867\) | −11.1421 | −0.378407 | ||||||||
\(868\) | −17.6792 | −0.600071 | ||||||||
\(869\) | 24.3955 | 0.827560 | ||||||||
\(870\) | −3.35659 | −0.113799 | ||||||||
\(871\) | 3.26672 | 0.110689 | ||||||||
\(872\) | 11.4192 | 0.386704 | ||||||||
\(873\) | −48.0601 | −1.62659 | ||||||||
\(874\) | −23.8507 | −0.806761 | ||||||||
\(875\) | 147.078 | 4.97214 | ||||||||
\(876\) | −0.525990 | −0.0177716 | ||||||||
\(877\) | −35.1921 | −1.18835 | −0.594177 | − | 0.804334i | \(-0.702522\pi\) | ||||
−0.594177 | + | 0.804334i | \(0.702522\pi\) | |||||||
\(878\) | −5.42961 | −0.183240 | ||||||||
\(879\) | −7.82230 | −0.263840 | ||||||||
\(880\) | −6.76765 | −0.228138 | ||||||||
\(881\) | −29.4895 | −0.993527 | −0.496764 | − | 0.867886i | \(-0.665478\pi\) | ||||
−0.496764 | + | 0.867886i | \(0.665478\pi\) | |||||||
\(882\) | −47.9155 | −1.61340 | ||||||||
\(883\) | −28.1353 | −0.946829 | −0.473415 | − | 0.880840i | \(-0.656979\pi\) | ||||
−0.473415 | + | 0.880840i | \(0.656979\pi\) | |||||||
\(884\) | 14.7007 | 0.494439 | ||||||||
\(885\) | −6.72605 | −0.226094 | ||||||||
\(886\) | 3.66946 | 0.123278 | ||||||||
\(887\) | −12.3917 | −0.416072 | −0.208036 | − | 0.978121i | \(-0.566707\pi\) | ||||
−0.208036 | + | 0.978121i | \(0.566707\pi\) | |||||||
\(888\) | −0.459672 | −0.0154256 | ||||||||
\(889\) | −10.1843 | −0.341570 | ||||||||
\(890\) | 13.7629 | 0.461335 | ||||||||
\(891\) | −12.5372 | −0.420012 | ||||||||
\(892\) | 8.79372 | 0.294436 | ||||||||
\(893\) | 60.9796 | 2.04061 | ||||||||
\(894\) | 1.33351 | 0.0445993 | ||||||||
\(895\) | 50.5298 | 1.68903 | ||||||||
\(896\) | 4.87818 | 0.162969 | ||||||||
\(897\) | 2.30181 | 0.0768552 | ||||||||
\(898\) | 6.43513 | 0.214743 | ||||||||
\(899\) | −7.62916 | −0.254447 | ||||||||
\(900\) | −34.9672 | −1.16557 | ||||||||
\(901\) | 20.6173 | 0.686863 | ||||||||
\(902\) | −8.85764 | −0.294927 | ||||||||
\(903\) | 18.0385 | 0.600284 | ||||||||
\(904\) | 0.316816 | 0.0105372 | ||||||||
\(905\) | −19.1530 | −0.636669 | ||||||||
\(906\) | −4.31446 | −0.143338 | ||||||||
\(907\) | −14.9432 | −0.496181 | −0.248090 | − | 0.968737i | \(-0.579803\pi\) | ||||
−0.248090 | + | 0.968737i | \(0.579803\pi\) | |||||||
\(908\) | 6.74871 | 0.223964 | ||||||||
\(909\) | −8.35931 | −0.277261 | ||||||||
\(910\) | −43.9109 | −1.45563 | ||||||||
\(911\) | 29.3458 | 0.972269 | 0.486134 | − | 0.873884i | \(-0.338407\pi\) | ||||
0.486134 | + | 0.873884i | \(0.338407\pi\) | |||||||
\(912\) | 3.30769 | 0.109528 | ||||||||
\(913\) | 13.1676 | 0.435784 | ||||||||
\(914\) | 2.97606 | 0.0984393 | ||||||||
\(915\) | −13.9478 | −0.461101 | ||||||||
\(916\) | −23.2606 | −0.768553 | ||||||||
\(917\) | −25.2396 | −0.833485 | ||||||||
\(918\) | −15.2407 | −0.503019 | ||||||||
\(919\) | 24.7551 | 0.816595 | 0.408297 | − | 0.912849i | \(-0.366123\pi\) | ||||
0.408297 | + | 0.912849i | \(0.366123\pi\) | |||||||
\(920\) | 11.4975 | 0.379061 | ||||||||
\(921\) | 6.71805 | 0.221367 | ||||||||
\(922\) | 9.73958 | 0.320756 | ||||||||
\(923\) | −23.8935 | −0.786464 | ||||||||
\(924\) | 3.05028 | 0.100347 | ||||||||
\(925\) | 14.6799 | 0.482671 | ||||||||
\(926\) | −19.9810 | −0.656618 | ||||||||
\(927\) | −3.58922 | −0.117885 | ||||||||
\(928\) | 2.10510 | 0.0691032 | ||||||||
\(929\) | −27.1303 | −0.890117 | −0.445059 | − | 0.895501i | \(-0.646817\pi\) | ||||
−0.445059 | + | 0.895501i | \(0.646817\pi\) | |||||||
\(930\) | 5.77871 | 0.189491 | ||||||||
\(931\) | −144.748 | −4.74392 | ||||||||
\(932\) | 11.0721 | 0.362679 | ||||||||
\(933\) | −8.62515 | −0.282375 | ||||||||
\(934\) | −14.3949 | −0.471014 | ||||||||
\(935\) | 45.9150 | 1.50158 | ||||||||
\(936\) | 6.18124 | 0.202040 | ||||||||
\(937\) | 44.2931 | 1.44699 | 0.723496 | − | 0.690328i | \(-0.242534\pi\) | ||||
0.723496 | + | 0.690328i | \(0.242534\pi\) | |||||||
\(938\) | −7.35441 | −0.240130 | ||||||||
\(939\) | 12.5250 | 0.408740 | ||||||||
\(940\) | −29.3959 | −0.958789 | ||||||||
\(941\) | −27.0894 | −0.883090 | −0.441545 | − | 0.897239i | \(-0.645569\pi\) | ||||
−0.441545 | + | 0.897239i | \(0.645569\pi\) | |||||||
\(942\) | −3.29912 | −0.107491 | ||||||||
\(943\) | 15.0481 | 0.490035 | ||||||||
\(944\) | 4.21827 | 0.137293 | ||||||||
\(945\) | 45.5238 | 1.48089 | ||||||||
\(946\) | 15.6947 | 0.510280 | ||||||||
\(947\) | 44.9196 | 1.45969 | 0.729845 | − | 0.683613i | \(-0.239592\pi\) | ||||
0.729845 | + | 0.683613i | \(0.239592\pi\) | |||||||
\(948\) | 5.74775 | 0.186678 | ||||||||
\(949\) | −2.96938 | −0.0963901 | ||||||||
\(950\) | −105.633 | −3.42717 | ||||||||
\(951\) | 7.50505 | 0.243368 | ||||||||
\(952\) | −33.0959 | −1.07264 | ||||||||
\(953\) | −21.0858 | −0.683036 | −0.341518 | − | 0.939875i | \(-0.610941\pi\) | ||||
−0.341518 | + | 0.939875i | \(0.610941\pi\) | |||||||
\(954\) | 8.66900 | 0.280669 | ||||||||
\(955\) | 13.7320 | 0.444356 | ||||||||
\(956\) | −3.99072 | −0.129069 | ||||||||
\(957\) | 1.31630 | 0.0425499 | ||||||||
\(958\) | −22.4679 | −0.725906 | ||||||||
\(959\) | 31.0227 | 1.00178 | ||||||||
\(960\) | −1.59451 | −0.0514625 | ||||||||
\(961\) | −17.8656 | −0.576311 | ||||||||
\(962\) | −2.59499 | −0.0836659 | ||||||||
\(963\) | −26.6995 | −0.860380 | ||||||||
\(964\) | −16.5408 | −0.532745 | ||||||||
\(965\) | −76.9185 | −2.47609 | ||||||||
\(966\) | −5.18209 | −0.166731 | ||||||||
\(967\) | 25.2415 | 0.811711 | 0.405855 | − | 0.913937i | \(-0.366974\pi\) | ||||
0.405855 | + | 0.913937i | \(0.366974\pi\) | |||||||
\(968\) | −8.34604 | −0.268252 | ||||||||
\(969\) | −22.4409 | −0.720906 | ||||||||
\(970\) | 69.9880 | 2.24718 | ||||||||
\(971\) | −34.5382 | −1.10838 | −0.554192 | − | 0.832389i | \(-0.686973\pi\) | ||||
−0.554192 | + | 0.832389i | \(0.686973\pi\) | |||||||
\(972\) | −9.69309 | −0.310906 | ||||||||
\(973\) | −52.0921 | −1.67000 | ||||||||
\(974\) | −15.3289 | −0.491169 | ||||||||
\(975\) | 10.1945 | 0.326486 | ||||||||
\(976\) | 8.74744 | 0.279999 | ||||||||
\(977\) | 61.0213 | 1.95224 | 0.976122 | − | 0.217225i | \(-0.0697004\pi\) | ||||
0.976122 | + | 0.217225i | \(0.0697004\pi\) | |||||||
\(978\) | −3.89698 | −0.124612 | ||||||||
\(979\) | −5.39718 | −0.172495 | ||||||||
\(980\) | 69.7773 | 2.22896 | ||||||||
\(981\) | −32.5754 | −1.04005 | ||||||||
\(982\) | −23.8945 | −0.762504 | ||||||||
\(983\) | −47.5260 | −1.51585 | −0.757923 | − | 0.652345i | \(-0.773786\pi\) | ||||
−0.757923 | + | 0.652345i | \(0.773786\pi\) | |||||||
\(984\) | −2.08692 | −0.0665286 | ||||||||
\(985\) | 36.4787 | 1.16231 | ||||||||
\(986\) | −14.2820 | −0.454831 | ||||||||
\(987\) | 13.2492 | 0.421726 | ||||||||
\(988\) | 18.6729 | 0.594064 | ||||||||
\(989\) | −26.6636 | −0.847854 | ||||||||
\(990\) | 19.3059 | 0.613583 | ||||||||
\(991\) | −35.6855 | −1.13359 | −0.566794 | − | 0.823860i | \(-0.691816\pi\) | ||||
−0.566794 | + | 0.823860i | \(0.691816\pi\) | |||||||
\(992\) | −3.62414 | −0.115066 | ||||||||
\(993\) | 7.74100 | 0.245653 | ||||||||
\(994\) | 53.7917 | 1.70617 | ||||||||
\(995\) | −51.6662 | −1.63793 | ||||||||
\(996\) | 3.10238 | 0.0983026 | ||||||||
\(997\) | 12.2019 | 0.386438 | 0.193219 | − | 0.981156i | \(-0.438107\pi\) | ||||
0.193219 | + | 0.981156i | \(0.438107\pi\) | |||||||
\(998\) | −15.7627 | −0.498960 | ||||||||
\(999\) | 2.69031 | 0.0851177 |
(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 | 538.2.a.e.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 4842.2.a.n.1.1 | 7 | |||
4.3 | odd | 2 | 4304.2.a.h.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.e.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4304.2.a.h.1.5 | 7 | 4.3 | odd | 2 | |||
4842.2.a.n.1.1 | 7 | 3.2 | odd | 2 |