Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.580017.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 4x^{2} + 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.74137\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74137 | −1.93844 | −0.969221 | − | 0.246193i | \(-0.920820\pi\) | ||||
−0.969221 | + | 0.246193i | \(0.920820\pi\) | |||||||
\(3\) | −3.04102 | −1.75574 | −0.877868 | − | 0.478902i | \(-0.841035\pi\) | ||||
−0.877868 | + | 0.478902i | \(0.841035\pi\) | |||||||
\(4\) | 5.51511 | 2.75756 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 8.33658 | 3.40339 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.63623 | −3.40692 | ||||||||
\(9\) | 6.24783 | 2.08261 | ||||||||
\(10\) | 2.74137 | 0.866898 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −16.7716 | −4.84154 | ||||||||
\(13\) | −6.59521 | −1.82918 | −0.914591 | − | 0.404381i | \(-0.867487\pi\) | ||||
−0.914591 | + | 0.404381i | \(0.867487\pi\) | |||||||
\(14\) | −2.74137 | −0.732662 | ||||||||
\(15\) | 3.04102 | 0.785189 | ||||||||
\(16\) | 15.3863 | 3.84656 | ||||||||
\(17\) | 4.86249 | 1.17933 | 0.589663 | − | 0.807649i | \(-0.299260\pi\) | ||||
0.589663 | + | 0.807649i | \(0.299260\pi\) | |||||||
\(18\) | −17.1276 | −4.03702 | ||||||||
\(19\) | −0.907153 | −0.208115 | −0.104058 | − | 0.994571i | \(-0.533183\pi\) | ||||
−0.104058 | + | 0.994571i | \(0.533183\pi\) | |||||||
\(20\) | −5.51511 | −1.23322 | ||||||||
\(21\) | −3.04102 | −0.663606 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.01425 | 0.628515 | 0.314257 | − | 0.949338i | \(-0.398245\pi\) | ||||
0.314257 | + | 0.949338i | \(0.398245\pi\) | |||||||
\(24\) | 29.3040 | 5.98166 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 18.0799 | 3.54576 | ||||||||
\(27\) | −9.87674 | −1.90078 | ||||||||
\(28\) | 5.51511 | 1.04226 | ||||||||
\(29\) | 0.914310 | 0.169783 | 0.0848915 | − | 0.996390i | \(-0.472946\pi\) | ||||
0.0848915 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(30\) | −8.33658 | −1.52204 | ||||||||
\(31\) | −5.33352 | −0.957929 | −0.478964 | − | 0.877834i | \(-0.658988\pi\) | ||||
−0.478964 | + | 0.877834i | \(0.658988\pi\) | |||||||
\(32\) | −22.9070 | −4.04942 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.3299 | −2.28606 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 34.4575 | 5.74292 | ||||||||
\(37\) | −2.76947 | −0.455299 | −0.227649 | − | 0.973743i | \(-0.573104\pi\) | ||||
−0.227649 | + | 0.973743i | \(0.573104\pi\) | |||||||
\(38\) | 2.48684 | 0.403419 | ||||||||
\(39\) | 20.0562 | 3.21156 | ||||||||
\(40\) | 9.63623 | 1.52362 | ||||||||
\(41\) | 5.06780 | 0.791457 | 0.395729 | − | 0.918368i | \(-0.370492\pi\) | ||||
0.395729 | + | 0.918368i | \(0.370492\pi\) | |||||||
\(42\) | 8.33658 | 1.28636 | ||||||||
\(43\) | −1.67940 | −0.256106 | −0.128053 | − | 0.991767i | \(-0.540873\pi\) | ||||
−0.128053 | + | 0.991767i | \(0.540873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.24783 | −0.931372 | ||||||||
\(46\) | −8.26318 | −1.21834 | ||||||||
\(47\) | 9.45037 | 1.37848 | 0.689239 | − | 0.724534i | \(-0.257945\pi\) | ||||
0.689239 | + | 0.724534i | \(0.257945\pi\) | |||||||
\(48\) | −46.7900 | −6.75355 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.74137 | −0.387688 | ||||||||
\(51\) | −14.7869 | −2.07059 | ||||||||
\(52\) | −36.3733 | −5.04407 | ||||||||
\(53\) | −3.38280 | −0.464663 | −0.232332 | − | 0.972637i | \(-0.574635\pi\) | ||||
−0.232332 | + | 0.972637i | \(0.574635\pi\) | |||||||
\(54\) | 27.0758 | 3.68455 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.63623 | −1.28770 | ||||||||
\(57\) | 2.75868 | 0.365396 | ||||||||
\(58\) | −2.50646 | −0.329115 | ||||||||
\(59\) | −1.13751 | −0.148091 | −0.0740457 | − | 0.997255i | \(-0.523591\pi\) | ||||
−0.0740457 | + | 0.997255i | \(0.523591\pi\) | |||||||
\(60\) | 16.7716 | 2.16520 | ||||||||
\(61\) | −10.4208 | −1.33424 | −0.667122 | − | 0.744949i | \(-0.732474\pi\) | ||||
−0.667122 | + | 0.744949i | \(0.732474\pi\) | |||||||
\(62\) | 14.6212 | 1.85689 | ||||||||
\(63\) | 6.24783 | 0.787153 | ||||||||
\(64\) | 32.0240 | 4.00300 | ||||||||
\(65\) | 6.59521 | 0.818035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.50236 | 0.916559 | 0.458280 | − | 0.888808i | \(-0.348466\pi\) | ||||
0.458280 | + | 0.888808i | \(0.348466\pi\) | |||||||
\(68\) | 26.8172 | 3.25206 | ||||||||
\(69\) | −9.16641 | −1.10351 | ||||||||
\(70\) | 2.74137 | 0.327656 | ||||||||
\(71\) | 3.74697 | 0.444683 | 0.222342 | − | 0.974969i | \(-0.428630\pi\) | ||||
0.222342 | + | 0.974969i | \(0.428630\pi\) | |||||||
\(72\) | −60.2056 | −7.09529 | ||||||||
\(73\) | −15.8983 | −1.86076 | −0.930378 | − | 0.366600i | \(-0.880522\pi\) | ||||
−0.930378 | + | 0.366600i | \(0.880522\pi\) | |||||||
\(74\) | 7.59215 | 0.882570 | ||||||||
\(75\) | −3.04102 | −0.351147 | ||||||||
\(76\) | −5.00305 | −0.573890 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −54.9814 | −6.22542 | ||||||||
\(79\) | −13.6658 | −1.53753 | −0.768763 | − | 0.639534i | \(-0.779127\pi\) | ||||
−0.768763 | + | 0.639534i | \(0.779127\pi\) | |||||||
\(80\) | −15.3863 | −1.72024 | ||||||||
\(81\) | 11.2919 | 1.25466 | ||||||||
\(82\) | −13.8927 | −1.53419 | ||||||||
\(83\) | −10.1635 | −1.11559 | −0.557793 | − | 0.829980i | \(-0.688352\pi\) | ||||
−0.557793 | + | 0.829980i | \(0.688352\pi\) | |||||||
\(84\) | −16.7716 | −1.82993 | ||||||||
\(85\) | −4.86249 | −0.527411 | ||||||||
\(86\) | 4.60386 | 0.496447 | ||||||||
\(87\) | −2.78044 | −0.298094 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.76964 | 0.823580 | 0.411790 | − | 0.911279i | \(-0.364904\pi\) | ||||
0.411790 | + | 0.911279i | \(0.364904\pi\) | |||||||
\(90\) | 17.1276 | 1.80541 | ||||||||
\(91\) | −6.59521 | −0.691365 | ||||||||
\(92\) | 16.6239 | 1.73317 | ||||||||
\(93\) | 16.2194 | 1.68187 | ||||||||
\(94\) | −25.9070 | −2.67210 | ||||||||
\(95\) | 0.907153 | 0.0930720 | ||||||||
\(96\) | 69.6607 | 7.10971 | ||||||||
\(97\) | 11.3919 | 1.15667 | 0.578334 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578334 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(98\) | −2.74137 | −0.276920 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.51511 | 0.551511 | ||||||||
\(101\) | −1.17248 | −0.116666 | −0.0583329 | − | 0.998297i | \(-0.518578\pi\) | ||||
−0.0583329 | + | 0.998297i | \(0.518578\pi\) | |||||||
\(102\) | 40.5365 | 4.01371 | ||||||||
\(103\) | −8.97905 | −0.884732 | −0.442366 | − | 0.896834i | \(-0.645861\pi\) | ||||
−0.442366 | + | 0.896834i | \(0.645861\pi\) | |||||||
\(104\) | 63.5529 | 6.23188 | ||||||||
\(105\) | 3.04102 | 0.296774 | ||||||||
\(106\) | 9.27351 | 0.900723 | ||||||||
\(107\) | 6.26036 | 0.605211 | 0.302606 | − | 0.953116i | \(-0.402143\pi\) | ||||
0.302606 | + | 0.953116i | \(0.402143\pi\) | |||||||
\(108\) | −54.4713 | −5.24151 | ||||||||
\(109\) | 1.70340 | 0.163156 | 0.0815781 | − | 0.996667i | \(-0.474004\pi\) | ||||
0.0815781 | + | 0.996667i | \(0.474004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.42204 | 0.799384 | ||||||||
\(112\) | 15.3863 | 1.45386 | ||||||||
\(113\) | −0.107727 | −0.0101341 | −0.00506706 | − | 0.999987i | \(-0.501613\pi\) | ||||
−0.00506706 | + | 0.999987i | \(0.501613\pi\) | |||||||
\(114\) | −7.56255 | −0.708298 | ||||||||
\(115\) | −3.01425 | −0.281080 | ||||||||
\(116\) | 5.04252 | 0.468186 | ||||||||
\(117\) | −41.2057 | −3.80947 | ||||||||
\(118\) | 3.11834 | 0.287067 | ||||||||
\(119\) | 4.86249 | 0.445744 | ||||||||
\(120\) | −29.3040 | −2.67508 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 28.5672 | 2.58635 | ||||||||
\(123\) | −15.4113 | −1.38959 | ||||||||
\(124\) | −29.4150 | −2.64154 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −17.1276 | −1.52585 | ||||||||
\(127\) | 14.1131 | 1.25234 | 0.626170 | − | 0.779687i | \(-0.284622\pi\) | ||||
0.626170 | + | 0.779687i | \(0.284622\pi\) | |||||||
\(128\) | −41.9757 | −3.71016 | ||||||||
\(129\) | 5.10710 | 0.449655 | ||||||||
\(130\) | −18.0799 | −1.58571 | ||||||||
\(131\) | 10.3314 | 0.902662 | 0.451331 | − | 0.892357i | \(-0.350949\pi\) | ||||
0.451331 | + | 0.892357i | \(0.350949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.907153 | −0.0786602 | ||||||||
\(134\) | −20.5667 | −1.77670 | ||||||||
\(135\) | 9.87674 | 0.850054 | ||||||||
\(136\) | −46.8561 | −4.01787 | ||||||||
\(137\) | 21.6579 | 1.85036 | 0.925180 | − | 0.379528i | \(-0.123913\pi\) | ||||
0.925180 | + | 0.379528i | \(0.123913\pi\) | |||||||
\(138\) | 25.1285 | 2.13908 | ||||||||
\(139\) | 14.7057 | 1.24732 | 0.623660 | − | 0.781695i | \(-0.285645\pi\) | ||||
0.623660 | + | 0.781695i | \(0.285645\pi\) | |||||||
\(140\) | −5.51511 | −0.466112 | ||||||||
\(141\) | −28.7388 | −2.42024 | ||||||||
\(142\) | −10.2718 | −0.861993 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 96.1307 | 8.01089 | ||||||||
\(145\) | −0.914310 | −0.0759293 | ||||||||
\(146\) | 43.5832 | 3.60697 | ||||||||
\(147\) | −3.04102 | −0.250820 | ||||||||
\(148\) | −15.2740 | −1.25551 | ||||||||
\(149\) | −4.62867 | −0.379196 | −0.189598 | − | 0.981862i | \(-0.560718\pi\) | ||||
−0.189598 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(150\) | 8.33658 | 0.680679 | ||||||||
\(151\) | −7.04541 | −0.573347 | −0.286674 | − | 0.958028i | \(-0.592550\pi\) | ||||
−0.286674 | + | 0.958028i | \(0.592550\pi\) | |||||||
\(152\) | 8.74154 | 0.709032 | ||||||||
\(153\) | 30.3800 | 2.45608 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.33352 | 0.428399 | ||||||||
\(156\) | 110.612 | 8.85606 | ||||||||
\(157\) | 6.56589 | 0.524015 | 0.262007 | − | 0.965066i | \(-0.415615\pi\) | ||||
0.262007 | + | 0.965066i | \(0.415615\pi\) | |||||||
\(158\) | 37.4631 | 2.98040 | ||||||||
\(159\) | 10.2872 | 0.815826 | ||||||||
\(160\) | 22.9070 | 1.81095 | ||||||||
\(161\) | 3.01425 | 0.237556 | ||||||||
\(162\) | −30.9553 | −2.43208 | ||||||||
\(163\) | 12.3470 | 0.967088 | 0.483544 | − | 0.875320i | \(-0.339349\pi\) | ||||
0.483544 | + | 0.875320i | \(0.339349\pi\) | |||||||
\(164\) | 27.9495 | 2.18249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.8618 | 2.16250 | ||||||||
\(167\) | −3.90433 | −0.302126 | −0.151063 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151063 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(168\) | 29.3040 | 2.26085 | ||||||||
\(169\) | 30.4967 | 2.34590 | ||||||||
\(170\) | 13.3299 | 1.02236 | ||||||||
\(171\) | −5.66774 | −0.433423 | ||||||||
\(172\) | −9.26208 | −0.706227 | ||||||||
\(173\) | −5.70167 | −0.433490 | −0.216745 | − | 0.976228i | \(-0.569544\pi\) | ||||
−0.216745 | + | 0.976228i | \(0.569544\pi\) | |||||||
\(174\) | 7.62221 | 0.577838 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.45920 | 0.260010 | ||||||||
\(178\) | −21.2995 | −1.59646 | ||||||||
\(179\) | −19.6283 | −1.46708 | −0.733542 | − | 0.679644i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679644i | \(0.762134\pi\) | |||||||
\(180\) | −34.4575 | −2.56831 | ||||||||
\(181\) | 15.4408 | 1.14770 | 0.573852 | − | 0.818959i | \(-0.305448\pi\) | ||||
0.573852 | + | 0.818959i | \(0.305448\pi\) | |||||||
\(182\) | 18.0799 | 1.34017 | ||||||||
\(183\) | 31.6898 | 2.34258 | ||||||||
\(184\) | −29.0460 | −2.14130 | ||||||||
\(185\) | 2.76947 | 0.203616 | ||||||||
\(186\) | −44.4633 | −3.26021 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 52.1199 | 3.80123 | ||||||||
\(189\) | −9.87674 | −0.718427 | ||||||||
\(190\) | −2.48684 | −0.180415 | ||||||||
\(191\) | −6.21529 | −0.449723 | −0.224861 | − | 0.974391i | \(-0.572193\pi\) | ||||
−0.224861 | + | 0.974391i | \(0.572193\pi\) | |||||||
\(192\) | −97.3857 | −7.02821 | ||||||||
\(193\) | 21.9778 | 1.58200 | 0.790999 | − | 0.611817i | \(-0.209561\pi\) | ||||
0.790999 | + | 0.611817i | \(0.209561\pi\) | |||||||
\(194\) | −31.2293 | −2.24213 | ||||||||
\(195\) | −20.0562 | −1.43625 | ||||||||
\(196\) | 5.51511 | 0.393937 | ||||||||
\(197\) | 2.95573 | 0.210587 | 0.105294 | − | 0.994441i | \(-0.466422\pi\) | ||||
0.105294 | + | 0.994441i | \(0.466422\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6335 | −0.824674 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(200\) | −9.63623 | −0.681384 | ||||||||
\(201\) | −22.8149 | −1.60924 | ||||||||
\(202\) | 3.21420 | 0.226150 | ||||||||
\(203\) | 0.914310 | 0.0641719 | ||||||||
\(204\) | −81.5517 | −5.70976 | ||||||||
\(205\) | −5.06780 | −0.353950 | ||||||||
\(206\) | 24.6149 | 1.71500 | ||||||||
\(207\) | 18.8325 | 1.30895 | ||||||||
\(208\) | −101.476 | −7.03606 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −8.33658 | −0.575278 | ||||||||
\(211\) | 26.2090 | 1.80430 | 0.902152 | − | 0.431419i | \(-0.141987\pi\) | ||||
0.902152 | + | 0.431419i | \(0.141987\pi\) | |||||||
\(212\) | −18.6565 | −1.28134 | ||||||||
\(213\) | −11.3946 | −0.780747 | ||||||||
\(214\) | −17.1620 | −1.17317 | ||||||||
\(215\) | 1.67940 | 0.114534 | ||||||||
\(216\) | 95.1745 | 6.47581 | ||||||||
\(217\) | −5.33352 | −0.362063 | ||||||||
\(218\) | −4.66965 | −0.316269 | ||||||||
\(219\) | 48.3472 | 3.26700 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.0691 | −2.15720 | ||||||||
\(222\) | −23.0879 | −1.54956 | ||||||||
\(223\) | 4.57357 | 0.306269 | 0.153134 | − | 0.988205i | \(-0.451063\pi\) | ||||
0.153134 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(224\) | −22.9070 | −1.53054 | ||||||||
\(225\) | 6.24783 | 0.416522 | ||||||||
\(226\) | 0.295320 | 0.0196444 | ||||||||
\(227\) | 8.22365 | 0.545823 | 0.272911 | − | 0.962039i | \(-0.412013\pi\) | ||||
0.272911 | + | 0.962039i | \(0.412013\pi\) | |||||||
\(228\) | 15.2144 | 1.00760 | ||||||||
\(229\) | −1.84824 | −0.122135 | −0.0610675 | − | 0.998134i | \(-0.519450\pi\) | ||||
−0.0610675 | + | 0.998134i | \(0.519450\pi\) | |||||||
\(230\) | 8.26318 | 0.544858 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.81050 | −0.578438 | ||||||||
\(233\) | −23.2023 | −1.52003 | −0.760016 | − | 0.649904i | \(-0.774809\pi\) | ||||
−0.760016 | + | 0.649904i | \(0.774809\pi\) | |||||||
\(234\) | 112.960 | 7.38444 | ||||||||
\(235\) | −9.45037 | −0.616474 | ||||||||
\(236\) | −6.27351 | −0.408371 | ||||||||
\(237\) | 41.5581 | 2.69949 | ||||||||
\(238\) | −13.3299 | −0.864048 | ||||||||
\(239\) | 26.4737 | 1.71244 | 0.856222 | − | 0.516608i | \(-0.172806\pi\) | ||||
0.856222 | + | 0.516608i | \(0.172806\pi\) | |||||||
\(240\) | 46.7900 | 3.02028 | ||||||||
\(241\) | −10.7031 | −0.689449 | −0.344724 | − | 0.938704i | \(-0.612028\pi\) | ||||
−0.344724 | + | 0.938704i | \(0.612028\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.70877 | −0.302068 | ||||||||
\(244\) | −57.4717 | −3.67925 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 42.2481 | 2.69364 | ||||||||
\(247\) | 5.98286 | 0.380680 | ||||||||
\(248\) | 51.3951 | 3.26359 | ||||||||
\(249\) | 30.9074 | 1.95867 | ||||||||
\(250\) | 2.74137 | 0.173380 | ||||||||
\(251\) | −16.9313 | −1.06870 | −0.534348 | − | 0.845265i | \(-0.679443\pi\) | ||||
−0.534348 | + | 0.845265i | \(0.679443\pi\) | |||||||
\(252\) | 34.4575 | 2.17062 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −38.6894 | −2.42759 | ||||||||
\(255\) | 14.7869 | 0.925994 | ||||||||
\(256\) | 51.0229 | 3.18893 | ||||||||
\(257\) | −12.5126 | −0.780513 | −0.390256 | − | 0.920706i | \(-0.627614\pi\) | ||||
−0.390256 | + | 0.920706i | \(0.627614\pi\) | |||||||
\(258\) | −14.0004 | −0.871630 | ||||||||
\(259\) | −2.76947 | −0.172087 | ||||||||
\(260\) | 36.3733 | 2.25578 | ||||||||
\(261\) | 5.71245 | 0.353592 | ||||||||
\(262\) | −28.3223 | −1.74976 | ||||||||
\(263\) | 22.4525 | 1.38448 | 0.692240 | − | 0.721667i | \(-0.256624\pi\) | ||||
0.692240 | + | 0.721667i | \(0.256624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.38280 | 0.207804 | ||||||||
\(266\) | 2.48684 | 0.152478 | ||||||||
\(267\) | −23.6277 | −1.44599 | ||||||||
\(268\) | 41.3764 | 2.52746 | ||||||||
\(269\) | −13.7295 | −0.837101 | −0.418551 | − | 0.908194i | \(-0.637462\pi\) | ||||
−0.418551 | + | 0.908194i | \(0.637462\pi\) | |||||||
\(270\) | −27.0758 | −1.64778 | ||||||||
\(271\) | 1.95141 | 0.118540 | 0.0592700 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592700 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(272\) | 74.8155 | 4.53635 | ||||||||
\(273\) | 20.0562 | 1.21386 | ||||||||
\(274\) | −59.3724 | −3.58682 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.5538 | −3.04298 | ||||||||
\(277\) | −6.52545 | −0.392076 | −0.196038 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196038 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(278\) | −40.3138 | −2.41786 | ||||||||
\(279\) | −33.3230 | −1.99499 | ||||||||
\(280\) | 9.63623 | 0.575875 | ||||||||
\(281\) | 2.41881 | 0.144294 | 0.0721472 | − | 0.997394i | \(-0.477015\pi\) | ||||
0.0721472 | + | 0.997394i | \(0.477015\pi\) | |||||||
\(282\) | 78.7837 | 4.69150 | ||||||||
\(283\) | 0.799239 | 0.0475099 | 0.0237549 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237549 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(284\) | 20.6650 | 1.22624 | ||||||||
\(285\) | −2.75868 | −0.163410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.06780 | 0.299143 | ||||||||
\(288\) | −143.119 | −8.43336 | ||||||||
\(289\) | 6.64379 | 0.390811 | ||||||||
\(290\) | 2.50646 | 0.147184 | ||||||||
\(291\) | −34.6429 | −2.03080 | ||||||||
\(292\) | −87.6810 | −5.13114 | ||||||||
\(293\) | −23.9733 | −1.40053 | −0.700267 | − | 0.713881i | \(-0.746936\pi\) | ||||
−0.700267 | + | 0.713881i | \(0.746936\pi\) | |||||||
\(294\) | 8.33658 | 0.486199 | ||||||||
\(295\) | 1.13751 | 0.0662285 | ||||||||
\(296\) | 26.6873 | 1.55117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.6889 | 0.735049 | ||||||||
\(299\) | −19.8796 | −1.14967 | ||||||||
\(300\) | −16.7716 | −0.968309 | ||||||||
\(301\) | −1.67940 | −0.0967990 | ||||||||
\(302\) | 19.3141 | 1.11140 | ||||||||
\(303\) | 3.56553 | 0.204835 | ||||||||
\(304\) | −13.9577 | −0.800529 | ||||||||
\(305\) | 10.4208 | 0.596692 | ||||||||
\(306\) | −83.2829 | −4.76096 | ||||||||
\(307\) | 19.0748 | 1.08865 | 0.544327 | − | 0.838873i | \(-0.316785\pi\) | ||||
0.544327 | + | 0.838873i | \(0.316785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.3055 | 1.55336 | ||||||||
\(310\) | −14.6212 | −0.830426 | ||||||||
\(311\) | 9.18049 | 0.520578 | 0.260289 | − | 0.965531i | \(-0.416182\pi\) | ||||
0.260289 | + | 0.965531i | \(0.416182\pi\) | |||||||
\(312\) | −193.266 | −10.9415 | ||||||||
\(313\) | −13.7670 | −0.778160 | −0.389080 | − | 0.921204i | \(-0.627207\pi\) | ||||
−0.389080 | + | 0.921204i | \(0.627207\pi\) | |||||||
\(314\) | −17.9995 | −1.01577 | ||||||||
\(315\) | −6.24783 | −0.352025 | ||||||||
\(316\) | −75.3686 | −4.23982 | ||||||||
\(317\) | 22.9456 | 1.28875 | 0.644376 | − | 0.764709i | \(-0.277117\pi\) | ||||
0.644376 | + | 0.764709i | \(0.277117\pi\) | |||||||
\(318\) | −28.2010 | −1.58143 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −32.0240 | −1.79019 | ||||||||
\(321\) | −19.0379 | −1.06259 | ||||||||
\(322\) | −8.26318 | −0.460489 | ||||||||
\(323\) | −4.41102 | −0.245436 | ||||||||
\(324\) | 62.2762 | 3.45979 | ||||||||
\(325\) | −6.59521 | −0.365836 | ||||||||
\(326\) | −33.8476 | −1.87464 | ||||||||
\(327\) | −5.18008 | −0.286459 | ||||||||
\(328\) | −48.8345 | −2.69643 | ||||||||
\(329\) | 9.45037 | 0.521016 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.44016 | −0.189088 | −0.0945441 | − | 0.995521i | \(-0.530139\pi\) | ||||
−0.0945441 | + | 0.995521i | \(0.530139\pi\) | |||||||
\(332\) | −56.0527 | −3.07629 | ||||||||
\(333\) | −17.3032 | −0.948210 | ||||||||
\(334\) | 10.7032 | 0.585654 | ||||||||
\(335\) | −7.50236 | −0.409898 | ||||||||
\(336\) | −46.7900 | −2.55260 | ||||||||
\(337\) | −30.2961 | −1.65033 | −0.825166 | − | 0.564891i | \(-0.808918\pi\) | ||||
−0.825166 | + | 0.564891i | \(0.808918\pi\) | |||||||
\(338\) | −83.6029 | −4.54740 | ||||||||
\(339\) | 0.327601 | 0.0177929 | ||||||||
\(340\) | −26.8172 | −1.45437 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 15.5374 | 0.840165 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 16.1831 | 0.872534 | ||||||||
\(345\) | 9.16641 | 0.493503 | ||||||||
\(346\) | 15.6304 | 0.840296 | ||||||||
\(347\) | −3.88350 | −0.208477 | −0.104239 | − | 0.994552i | \(-0.533241\pi\) | ||||
−0.104239 | + | 0.994552i | \(0.533241\pi\) | |||||||
\(348\) | −15.3344 | −0.822012 | ||||||||
\(349\) | −19.2489 | −1.03037 | −0.515184 | − | 0.857080i | \(-0.672276\pi\) | ||||
−0.515184 | + | 0.857080i | \(0.672276\pi\) | |||||||
\(350\) | −2.74137 | −0.146532 | ||||||||
\(351\) | 65.1391 | 3.47687 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.3031 | −1.39997 | −0.699986 | − | 0.714156i | \(-0.746811\pi\) | ||||
−0.699986 | + | 0.714156i | \(0.746811\pi\) | |||||||
\(354\) | −9.48296 | −0.504014 | ||||||||
\(355\) | −3.74697 | −0.198868 | ||||||||
\(356\) | 42.8505 | 2.27107 | ||||||||
\(357\) | −14.7869 | −0.782608 | ||||||||
\(358\) | 53.8083 | 2.84386 | ||||||||
\(359\) | 21.4912 | 1.13426 | 0.567131 | − | 0.823627i | \(-0.308053\pi\) | ||||
0.567131 | + | 0.823627i | \(0.308053\pi\) | |||||||
\(360\) | 60.2056 | 3.17311 | ||||||||
\(361\) | −18.1771 | −0.956688 | ||||||||
\(362\) | −42.3289 | −2.22476 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −36.3733 | −1.90648 | ||||||||
\(365\) | 15.8983 | 0.832156 | ||||||||
\(366\) | −86.8736 | −4.54095 | ||||||||
\(367\) | −5.20635 | −0.271769 | −0.135885 | − | 0.990725i | \(-0.543388\pi\) | ||||
−0.135885 | + | 0.990725i | \(0.543388\pi\) | |||||||
\(368\) | 46.3780 | 2.41762 | ||||||||
\(369\) | 31.6628 | 1.64830 | ||||||||
\(370\) | −7.59215 | −0.394697 | ||||||||
\(371\) | −3.38280 | −0.175626 | ||||||||
\(372\) | 89.4517 | 4.63785 | ||||||||
\(373\) | −15.6505 | −0.810354 | −0.405177 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405177 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.04102 | 0.157038 | ||||||||
\(376\) | −91.0659 | −4.69637 | ||||||||
\(377\) | −6.03006 | −0.310564 | ||||||||
\(378\) | 27.0758 | 1.39263 | ||||||||
\(379\) | 19.0890 | 0.980537 | 0.490269 | − | 0.871571i | \(-0.336899\pi\) | ||||
0.490269 | + | 0.871571i | \(0.336899\pi\) | |||||||
\(380\) | 5.00305 | 0.256651 | ||||||||
\(381\) | −42.9184 | −2.19878 | ||||||||
\(382\) | 17.0384 | 0.871761 | ||||||||
\(383\) | 23.3917 | 1.19526 | 0.597629 | − | 0.801773i | \(-0.296110\pi\) | ||||
0.597629 | + | 0.801773i | \(0.296110\pi\) | |||||||
\(384\) | 127.649 | 6.51406 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −60.2494 | −3.06661 | ||||||||
\(387\) | −10.4926 | −0.533369 | ||||||||
\(388\) | 62.8274 | 3.18958 | ||||||||
\(389\) | 11.3746 | 0.576715 | 0.288358 | − | 0.957523i | \(-0.406891\pi\) | ||||
0.288358 | + | 0.957523i | \(0.406891\pi\) | |||||||
\(390\) | 54.9814 | 2.78409 | ||||||||
\(391\) | 14.6568 | 0.741224 | ||||||||
\(392\) | −9.63623 | −0.486703 | ||||||||
\(393\) | −31.4182 | −1.58484 | ||||||||
\(394\) | −8.10276 | −0.408211 | ||||||||
\(395\) | 13.6658 | 0.687602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2708 | −0.766418 | −0.383209 | − | 0.923662i | \(-0.625181\pi\) | ||||
−0.383209 | + | 0.923662i | \(0.625181\pi\) | |||||||
\(398\) | 31.8916 | 1.59858 | ||||||||
\(399\) | 2.75868 | 0.138107 | ||||||||
\(400\) | 15.3863 | 0.769313 | ||||||||
\(401\) | 9.66663 | 0.482728 | 0.241364 | − | 0.970435i | \(-0.422405\pi\) | ||||
0.241364 | + | 0.970435i | \(0.422405\pi\) | |||||||
\(402\) | 62.5440 | 3.11941 | ||||||||
\(403\) | 35.1757 | 1.75223 | ||||||||
\(404\) | −6.46635 | −0.321713 | ||||||||
\(405\) | −11.2919 | −0.561100 | ||||||||
\(406\) | −2.50646 | −0.124394 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 142.490 | 7.05433 | ||||||||
\(409\) | −14.2142 | −0.702849 | −0.351425 | − | 0.936216i | \(-0.614303\pi\) | ||||
−0.351425 | + | 0.936216i | \(0.614303\pi\) | |||||||
\(410\) | 13.8927 | 0.686112 | ||||||||
\(411\) | −65.8623 | −3.24875 | ||||||||
\(412\) | −49.5205 | −2.43970 | ||||||||
\(413\) | −1.13751 | −0.0559733 | ||||||||
\(414\) | −51.6270 | −2.53733 | ||||||||
\(415\) | 10.1635 | 0.498905 | ||||||||
\(416\) | 151.076 | 7.40712 | ||||||||
\(417\) | −44.7204 | −2.18997 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2832 | 0.746633 | 0.373317 | − | 0.927704i | \(-0.378221\pi\) | ||||
0.373317 | + | 0.927704i | \(0.378221\pi\) | |||||||
\(420\) | 16.7716 | 0.818370 | ||||||||
\(421\) | 8.10283 | 0.394908 | 0.197454 | − | 0.980312i | \(-0.436733\pi\) | ||||
0.197454 | + | 0.980312i | \(0.436733\pi\) | |||||||
\(422\) | −71.8487 | −3.49754 | ||||||||
\(423\) | 59.0443 | 2.87083 | ||||||||
\(424\) | 32.5974 | 1.58307 | ||||||||
\(425\) | 4.86249 | 0.235865 | ||||||||
\(426\) | 31.2369 | 1.51343 | ||||||||
\(427\) | −10.4208 | −0.504296 | ||||||||
\(428\) | 34.5266 | 1.66890 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.60386 | −0.222018 | ||||||||
\(431\) | 16.6282 | 0.800953 | 0.400476 | − | 0.916307i | \(-0.368845\pi\) | ||||
0.400476 | + | 0.916307i | \(0.368845\pi\) | |||||||
\(432\) | −151.966 | −7.31147 | ||||||||
\(433\) | 35.0842 | 1.68604 | 0.843019 | − | 0.537884i | \(-0.180776\pi\) | ||||
0.843019 | + | 0.537884i | \(0.180776\pi\) | |||||||
\(434\) | 14.6212 | 0.701838 | ||||||||
\(435\) | 2.78044 | 0.133312 | ||||||||
\(436\) | 9.39445 | 0.449912 | ||||||||
\(437\) | −2.73439 | −0.130804 | ||||||||
\(438\) | −132.538 | −6.33289 | ||||||||
\(439\) | −24.3254 | −1.16099 | −0.580493 | − | 0.814265i | \(-0.697140\pi\) | ||||
−0.580493 | + | 0.814265i | \(0.697140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.24783 | 0.297516 | ||||||||
\(442\) | 87.9133 | 4.18161 | ||||||||
\(443\) | 5.08137 | 0.241423 | 0.120712 | − | 0.992688i | \(-0.461482\pi\) | ||||
0.120712 | + | 0.992688i | \(0.461482\pi\) | |||||||
\(444\) | 46.4485 | 2.20435 | ||||||||
\(445\) | −7.76964 | −0.368316 | ||||||||
\(446\) | −12.5378 | −0.593684 | ||||||||
\(447\) | 14.0759 | 0.665768 | ||||||||
\(448\) | 32.0240 | 1.51299 | ||||||||
\(449\) | −31.8906 | −1.50501 | −0.752504 | − | 0.658588i | \(-0.771154\pi\) | ||||
−0.752504 | + | 0.658588i | \(0.771154\pi\) | |||||||
\(450\) | −17.1276 | −0.807404 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.594128 | −0.0279454 | ||||||||
\(453\) | 21.4253 | 1.00665 | ||||||||
\(454\) | −22.5441 | −1.05805 | ||||||||
\(455\) | 6.59521 | 0.309188 | ||||||||
\(456\) | −26.5832 | −1.24487 | ||||||||
\(457\) | 6.92579 | 0.323975 | 0.161987 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161987 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(458\) | 5.06671 | 0.236752 | ||||||||
\(459\) | −48.0255 | −2.24164 | ||||||||
\(460\) | −16.6239 | −0.775095 | ||||||||
\(461\) | 26.9670 | 1.25598 | 0.627989 | − | 0.778222i | \(-0.283878\pi\) | ||||
0.627989 | + | 0.778222i | \(0.283878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.4519 | −1.64759 | −0.823795 | − | 0.566888i | \(-0.808147\pi\) | ||||
−0.823795 | + | 0.566888i | \(0.808147\pi\) | |||||||
\(464\) | 14.0678 | 0.653081 | ||||||||
\(465\) | −16.2194 | −0.752156 | ||||||||
\(466\) | 63.6061 | 2.94649 | ||||||||
\(467\) | −32.4914 | −1.50352 | −0.751762 | − | 0.659434i | \(-0.770796\pi\) | ||||
−0.751762 | + | 0.659434i | \(0.770796\pi\) | |||||||
\(468\) | −227.254 | −10.5048 | ||||||||
\(469\) | 7.50236 | 0.346427 | ||||||||
\(470\) | 25.9070 | 1.19500 | ||||||||
\(471\) | −19.9670 | −0.920032 | ||||||||
\(472\) | 10.9613 | 0.504536 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −113.926 | −5.23281 | ||||||||
\(475\) | −0.907153 | −0.0416231 | ||||||||
\(476\) | 26.8172 | 1.22916 | ||||||||
\(477\) | −21.1352 | −0.967713 | ||||||||
\(478\) | −72.5743 | −3.31947 | ||||||||
\(479\) | −20.7343 | −0.947375 | −0.473687 | − | 0.880693i | \(-0.657077\pi\) | ||||
−0.473687 | + | 0.880693i | \(0.657077\pi\) | |||||||
\(480\) | −69.6607 | −3.17956 | ||||||||
\(481\) | 18.2652 | 0.832823 | ||||||||
\(482\) | 29.3412 | 1.33646 | ||||||||
\(483\) | −9.16641 | −0.417086 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.3919 | −0.517277 | ||||||||
\(486\) | 12.9085 | 0.585540 | ||||||||
\(487\) | 3.50987 | 0.159047 | 0.0795236 | − | 0.996833i | \(-0.474660\pi\) | ||||
0.0795236 | + | 0.996833i | \(0.474660\pi\) | |||||||
\(488\) | 100.417 | 4.54566 | ||||||||
\(489\) | −37.5474 | −1.69795 | ||||||||
\(490\) | 2.74137 | 0.123843 | ||||||||
\(491\) | 0.148819 | 0.00671611 | 0.00335805 | − | 0.999994i | \(-0.498931\pi\) | ||||
0.00335805 | + | 0.999994i | \(0.498931\pi\) | |||||||
\(492\) | −84.9951 | −3.83187 | ||||||||
\(493\) | 4.44582 | 0.200230 | ||||||||
\(494\) | −16.4012 | −0.737927 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −82.0629 | −3.68473 | ||||||||
\(497\) | 3.74697 | 0.168075 | ||||||||
\(498\) | −84.7285 | −3.79678 | ||||||||
\(499\) | 3.48032 | 0.155800 | 0.0779002 | − | 0.996961i | \(-0.475178\pi\) | ||||
0.0779002 | + | 0.996961i | \(0.475178\pi\) | |||||||
\(500\) | −5.51511 | −0.246643 | ||||||||
\(501\) | 11.8732 | 0.530454 | ||||||||
\(502\) | 46.4150 | 2.07160 | ||||||||
\(503\) | 18.0097 | 0.803012 | 0.401506 | − | 0.915856i | \(-0.368487\pi\) | ||||
0.401506 | + | 0.915856i | \(0.368487\pi\) | |||||||
\(504\) | −60.2056 | −2.68177 | ||||||||
\(505\) | 1.17248 | 0.0521746 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −92.7414 | −4.11879 | ||||||||
\(508\) | 77.8356 | 3.45340 | ||||||||
\(509\) | −35.1540 | −1.55818 | −0.779088 | − | 0.626915i | \(-0.784317\pi\) | ||||
−0.779088 | + | 0.626915i | \(0.784317\pi\) | |||||||
\(510\) | −40.5365 | −1.79499 | ||||||||
\(511\) | −15.8983 | −0.703300 | ||||||||
\(512\) | −55.9214 | −2.47140 | ||||||||
\(513\) | 8.95972 | 0.395581 | ||||||||
\(514\) | 34.3016 | 1.51298 | ||||||||
\(515\) | 8.97905 | 0.395664 | ||||||||
\(516\) | 28.1662 | 1.23995 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.59215 | 0.333580 | ||||||||
\(519\) | 17.3389 | 0.761095 | ||||||||
\(520\) | −63.5529 | −2.78698 | ||||||||
\(521\) | −24.5834 | −1.07702 | −0.538509 | − | 0.842620i | \(-0.681012\pi\) | ||||
−0.538509 | + | 0.842620i | \(0.681012\pi\) | |||||||
\(522\) | −15.6600 | −0.685417 | ||||||||
\(523\) | −16.0636 | −0.702411 | −0.351205 | − | 0.936298i | \(-0.614228\pi\) | ||||
−0.351205 | + | 0.936298i | \(0.614228\pi\) | |||||||
\(524\) | 56.9791 | 2.48914 | ||||||||
\(525\) | −3.04102 | −0.132721 | ||||||||
\(526\) | −61.5506 | −2.68373 | ||||||||
\(527\) | −25.9342 | −1.12971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.9143 | −0.604969 | ||||||||
\(530\) | −9.27351 | −0.402816 | ||||||||
\(531\) | −7.10699 | −0.308417 | ||||||||
\(532\) | −5.00305 | −0.216910 | ||||||||
\(533\) | −33.4232 | −1.44772 | ||||||||
\(534\) | 64.7722 | 2.80297 | ||||||||
\(535\) | −6.26036 | −0.270659 | ||||||||
\(536\) | −72.2945 | −3.12265 | ||||||||
\(537\) | 59.6900 | 2.57581 | ||||||||
\(538\) | 37.6376 | 1.62267 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 54.4713 | 2.34407 | ||||||||
\(541\) | −24.6520 | −1.05987 | −0.529937 | − | 0.848037i | \(-0.677784\pi\) | ||||
−0.529937 | + | 0.848037i | \(0.677784\pi\) | |||||||
\(542\) | −5.34955 | −0.229783 | ||||||||
\(543\) | −46.9558 | −2.01507 | ||||||||
\(544\) | −111.385 | −4.77559 | ||||||||
\(545\) | −1.70340 | −0.0729656 | ||||||||
\(546\) | −54.9814 | −2.35299 | ||||||||
\(547\) | 24.6864 | 1.05552 | 0.527758 | − | 0.849395i | \(-0.323033\pi\) | ||||
0.527758 | + | 0.849395i | \(0.323033\pi\) | |||||||
\(548\) | 119.446 | 5.10248 | ||||||||
\(549\) | −65.1072 | −2.77871 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.829419 | −0.0353344 | ||||||||
\(552\) | 88.3297 | 3.75956 | ||||||||
\(553\) | −13.6658 | −0.581130 | ||||||||
\(554\) | 17.8887 | 0.760017 | ||||||||
\(555\) | −8.42204 | −0.357496 | ||||||||
\(556\) | 81.1036 | 3.43956 | ||||||||
\(557\) | −20.2912 | −0.859766 | −0.429883 | − | 0.902885i | \(-0.641445\pi\) | ||||
−0.429883 | + | 0.902885i | \(0.641445\pi\) | |||||||
\(558\) | 91.3506 | 3.86718 | ||||||||
\(559\) | 11.0760 | 0.468464 | ||||||||
\(560\) | −15.3863 | −0.650188 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.63086 | −0.279706 | ||||||||
\(563\) | 11.9397 | 0.503200 | 0.251600 | − | 0.967831i | \(-0.419043\pi\) | ||||
0.251600 | + | 0.967831i | \(0.419043\pi\) | |||||||
\(564\) | −158.498 | −6.67396 | ||||||||
\(565\) | 0.107727 | 0.00453212 | ||||||||
\(566\) | −2.19101 | −0.0920951 | ||||||||
\(567\) | 11.2919 | 0.474216 | ||||||||
\(568\) | −36.1067 | −1.51500 | ||||||||
\(569\) | −18.0100 | −0.755017 | −0.377509 | − | 0.926006i | \(-0.623219\pi\) | ||||
−0.377509 | + | 0.926006i | \(0.623219\pi\) | |||||||
\(570\) | 7.56255 | 0.316761 | ||||||||
\(571\) | −0.0419420 | −0.00175522 | −0.000877610 | − | 1.00000i | \(-0.500279\pi\) | ||||
−0.000877610 | 1.00000i | \(0.500279\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.9009 | 0.789595 | ||||||||
\(574\) | −13.8927 | −0.579871 | ||||||||
\(575\) | 3.01425 | 0.125703 | ||||||||
\(576\) | 200.080 | 8.33669 | ||||||||
\(577\) | −12.9887 | −0.540726 | −0.270363 | − | 0.962758i | \(-0.587144\pi\) | ||||
−0.270363 | + | 0.962758i | \(0.587144\pi\) | |||||||
\(578\) | −18.2131 | −0.757564 | ||||||||
\(579\) | −66.8351 | −2.77757 | ||||||||
\(580\) | −5.04252 | −0.209379 | ||||||||
\(581\) | −10.1635 | −0.421652 | ||||||||
\(582\) | 94.9691 | 3.93659 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 153.200 | 6.33945 | ||||||||
\(585\) | 41.2057 | 1.70365 | ||||||||
\(586\) | 65.7196 | 2.71485 | ||||||||
\(587\) | 4.44817 | 0.183596 | 0.0917979 | − | 0.995778i | \(-0.470739\pi\) | ||||
0.0917979 | + | 0.995778i | \(0.470739\pi\) | |||||||
\(588\) | −16.7716 | −0.691649 | ||||||||
\(589\) | 4.83832 | 0.199360 | ||||||||
\(590\) | −3.11834 | −0.128380 | ||||||||
\(591\) | −8.98846 | −0.369736 | ||||||||
\(592\) | −42.6118 | −1.75133 | ||||||||
\(593\) | 25.1551 | 1.03300 | 0.516498 | − | 0.856288i | \(-0.327235\pi\) | ||||
0.516498 | + | 0.856288i | \(0.327235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.86249 | −0.199343 | ||||||||
\(596\) | −25.5277 | −1.04565 | ||||||||
\(597\) | 35.3776 | 1.44791 | ||||||||
\(598\) | 54.4974 | 2.22856 | ||||||||
\(599\) | −41.3234 | −1.68843 | −0.844215 | − | 0.536004i | \(-0.819933\pi\) | ||||
−0.844215 | + | 0.536004i | \(0.819933\pi\) | |||||||
\(600\) | 29.3040 | 1.19633 | ||||||||
\(601\) | 36.8476 | 1.50305 | 0.751523 | − | 0.659707i | \(-0.229320\pi\) | ||||
0.751523 | + | 0.659707i | \(0.229320\pi\) | |||||||
\(602\) | 4.60386 | 0.187639 | ||||||||
\(603\) | 46.8735 | 1.90884 | ||||||||
\(604\) | −38.8562 | −1.58104 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.77445 | −0.397060 | ||||||||
\(607\) | −9.84153 | −0.399455 | −0.199728 | − | 0.979851i | \(-0.564006\pi\) | ||||
−0.199728 | + | 0.979851i | \(0.564006\pi\) | |||||||
\(608\) | 20.7801 | 0.842746 | ||||||||
\(609\) | −2.78044 | −0.112669 | ||||||||
\(610\) | −28.5672 | −1.15665 | ||||||||
\(611\) | −62.3271 | −2.52149 | ||||||||
\(612\) | 167.549 | 6.77278 | ||||||||
\(613\) | −27.7360 | −1.12025 | −0.560123 | − | 0.828409i | \(-0.689246\pi\) | ||||
−0.560123 | + | 0.828409i | \(0.689246\pi\) | |||||||
\(614\) | −52.2910 | −2.11029 | ||||||||
\(615\) | 15.4113 | 0.621444 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.34939 | −0.255617 | −0.127808 | − | 0.991799i | \(-0.540794\pi\) | ||||
−0.127808 | + | 0.991799i | \(0.540794\pi\) | |||||||
\(618\) | −74.8546 | −3.01109 | ||||||||
\(619\) | 21.7248 | 0.873192 | 0.436596 | − | 0.899658i | \(-0.356184\pi\) | ||||
0.436596 | + | 0.899658i | \(0.356184\pi\) | |||||||
\(620\) | 29.4150 | 1.18133 | ||||||||
\(621\) | −29.7710 | −1.19467 | ||||||||
\(622\) | −25.1671 | −1.00911 | ||||||||
\(623\) | 7.76964 | 0.311284 | ||||||||
\(624\) | 308.590 | 12.3535 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 37.7406 | 1.50842 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.2116 | 1.44500 | ||||||||
\(629\) | −13.4665 | −0.536946 | ||||||||
\(630\) | 17.1276 | 0.682381 | ||||||||
\(631\) | −46.9428 | −1.86876 | −0.934382 | − | 0.356272i | \(-0.884048\pi\) | ||||
−0.934382 | + | 0.356272i | \(0.884048\pi\) | |||||||
\(632\) | 131.687 | 5.23823 | ||||||||
\(633\) | −79.7023 | −3.16788 | ||||||||
\(634\) | −62.9023 | −2.49817 | ||||||||
\(635\) | −14.1131 | −0.560063 | ||||||||
\(636\) | 56.7350 | 2.24969 | ||||||||
\(637\) | −6.59521 | −0.261312 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.4104 | 0.926103 | ||||||||
\(640\) | 41.9757 | 1.65923 | ||||||||
\(641\) | −34.5237 | −1.36361 | −0.681803 | − | 0.731536i | \(-0.738804\pi\) | ||||
−0.681803 | + | 0.731536i | \(0.738804\pi\) | |||||||
\(642\) | 52.1899 | 2.05977 | ||||||||
\(643\) | −0.0386672 | −0.00152489 | −0.000762443 | − | 1.00000i | \(-0.500243\pi\) | ||||
−0.000762443 | 1.00000i | \(0.500243\pi\) | ||||||||
\(644\) | 16.6239 | 0.655075 | ||||||||
\(645\) | −5.10710 | −0.201092 | ||||||||
\(646\) | 12.0922 | 0.475763 | ||||||||
\(647\) | 3.77288 | 0.148327 | 0.0741636 | − | 0.997246i | \(-0.476371\pi\) | ||||
0.0741636 | + | 0.997246i | \(0.476371\pi\) | |||||||
\(648\) | −108.811 | −4.27452 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 18.0799 | 0.709152 | ||||||||
\(651\) | 16.2194 | 0.635687 | ||||||||
\(652\) | 68.0949 | 2.66680 | ||||||||
\(653\) | −47.8327 | −1.87184 | −0.935918 | − | 0.352217i | \(-0.885428\pi\) | ||||
−0.935918 | + | 0.352217i | \(0.885428\pi\) | |||||||
\(654\) | 14.2005 | 0.555284 | ||||||||
\(655\) | −10.3314 | −0.403683 | ||||||||
\(656\) | 77.9744 | 3.04439 | ||||||||
\(657\) | −99.3300 | −3.87523 | ||||||||
\(658\) | −25.9070 | −1.00996 | ||||||||
\(659\) | −19.7418 | −0.769030 | −0.384515 | − | 0.923119i | \(-0.625631\pi\) | ||||
−0.384515 | + | 0.923119i | \(0.625631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6196 | −0.607530 | −0.303765 | − | 0.952747i | \(-0.598244\pi\) | ||||
−0.303765 | + | 0.952747i | \(0.598244\pi\) | |||||||
\(662\) | 9.43075 | 0.366536 | ||||||||
\(663\) | 97.5230 | 3.78748 | ||||||||
\(664\) | 97.9375 | 3.80071 | ||||||||
\(665\) | 0.907153 | 0.0351779 | ||||||||
\(666\) | 47.4345 | 1.83805 | ||||||||
\(667\) | 2.75596 | 0.106711 | ||||||||
\(668\) | −21.5328 | −0.833130 | ||||||||
\(669\) | −13.9083 | −0.537727 | ||||||||
\(670\) | 20.5667 | 0.794563 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 69.6607 | 2.68722 | ||||||||
\(673\) | 3.27724 | 0.126328 | 0.0631642 | − | 0.998003i | \(-0.479881\pi\) | ||||
0.0631642 | + | 0.998003i | \(0.479881\pi\) | |||||||
\(674\) | 83.0527 | 3.19907 | ||||||||
\(675\) | −9.87674 | −0.380156 | ||||||||
\(676\) | 168.193 | 6.46896 | ||||||||
\(677\) | −31.4726 | −1.20959 | −0.604795 | − | 0.796381i | \(-0.706745\pi\) | ||||
−0.604795 | + | 0.796381i | \(0.706745\pi\) | |||||||
\(678\) | −0.898076 | −0.0344904 | ||||||||
\(679\) | 11.3919 | 0.437179 | ||||||||
\(680\) | 46.8561 | 1.79685 | ||||||||
\(681\) | −25.0083 | −0.958321 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.0569 | 1.34142 | 0.670708 | − | 0.741721i | \(-0.265990\pi\) | ||||
0.670708 | + | 0.741721i | \(0.265990\pi\) | |||||||
\(684\) | −31.2582 | −1.19519 | ||||||||
\(685\) | −21.6579 | −0.827507 | ||||||||
\(686\) | −2.74137 | −0.104666 | ||||||||
\(687\) | 5.62054 | 0.214437 | ||||||||
\(688\) | −25.8397 | −0.985128 | ||||||||
\(689\) | 22.3103 | 0.849953 | ||||||||
\(690\) | −25.1285 | −0.956627 | ||||||||
\(691\) | 36.2261 | 1.37810 | 0.689052 | − | 0.724712i | \(-0.258027\pi\) | ||||
0.689052 | + | 0.724712i | \(0.258027\pi\) | |||||||
\(692\) | −31.4454 | −1.19537 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.6461 | 0.404121 | ||||||||
\(695\) | −14.7057 | −0.557819 | ||||||||
\(696\) | 26.7929 | 1.01558 | ||||||||
\(697\) | 24.6421 | 0.933386 | ||||||||
\(698\) | 52.7683 | 1.99731 | ||||||||
\(699\) | 70.5587 | 2.66878 | ||||||||
\(700\) | 5.51511 | 0.208452 | ||||||||
\(701\) | 32.4214 | 1.22454 | 0.612269 | − | 0.790649i | \(-0.290257\pi\) | ||||
0.612269 | + | 0.790649i | \(0.290257\pi\) | |||||||
\(702\) | −178.571 | −6.73971 | ||||||||
\(703\) | 2.51234 | 0.0947546 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.7388 | 1.08237 | ||||||||
\(706\) | 72.1065 | 2.71377 | ||||||||
\(707\) | −1.17248 | −0.0440955 | ||||||||
\(708\) | 19.0779 | 0.716991 | ||||||||
\(709\) | 38.9574 | 1.46308 | 0.731538 | − | 0.681801i | \(-0.238803\pi\) | ||||
0.731538 | + | 0.681801i | \(0.238803\pi\) | |||||||
\(710\) | 10.2718 | 0.385495 | ||||||||
\(711\) | −85.3818 | −3.20207 | ||||||||
\(712\) | −74.8701 | −2.80587 | ||||||||
\(713\) | −16.0766 | −0.602073 | ||||||||
\(714\) | 40.5365 | 1.51704 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −108.252 | −4.04557 | ||||||||
\(717\) | −80.5073 | −3.00660 | ||||||||
\(718\) | −58.9154 | −2.19870 | ||||||||
\(719\) | −21.0902 | −0.786531 | −0.393266 | − | 0.919425i | \(-0.628655\pi\) | ||||
−0.393266 | + | 0.919425i | \(0.628655\pi\) | |||||||
\(720\) | −96.1307 | −3.58258 | ||||||||
\(721\) | −8.97905 | −0.334397 | ||||||||
\(722\) | 49.8301 | 1.85448 | ||||||||
\(723\) | 32.5485 | 1.21049 | ||||||||
\(724\) | 85.1577 | 3.16486 | ||||||||
\(725\) | 0.914310 | 0.0339566 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.1383 | −1.78535 | −0.892675 | − | 0.450702i | \(-0.851174\pi\) | ||||
−0.892675 | + | 0.450702i | \(0.851174\pi\) | |||||||
\(728\) | 63.5529 | 2.35543 | ||||||||
\(729\) | −19.5563 | −0.724306 | ||||||||
\(730\) | −43.5832 | −1.61309 | ||||||||
\(731\) | −8.16606 | −0.302033 | ||||||||
\(732\) | 174.773 | 6.45980 | ||||||||
\(733\) | 48.4595 | 1.78989 | 0.894946 | − | 0.446174i | \(-0.147214\pi\) | ||||
0.894946 | + | 0.446174i | \(0.147214\pi\) | |||||||
\(734\) | 14.2725 | 0.526809 | ||||||||
\(735\) | 3.04102 | 0.112170 | ||||||||
\(736\) | −69.0473 | −2.54512 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −86.7994 | −3.19513 | ||||||||
\(739\) | −13.6252 | −0.501211 | −0.250606 | − | 0.968089i | \(-0.580630\pi\) | ||||
−0.250606 | + | 0.968089i | \(0.580630\pi\) | |||||||
\(740\) | 15.2740 | 0.561482 | ||||||||
\(741\) | −18.1940 | −0.668375 | ||||||||
\(742\) | 9.27351 | 0.340441 | ||||||||
\(743\) | −15.5807 | −0.571602 | −0.285801 | − | 0.958289i | \(-0.592260\pi\) | ||||
−0.285801 | + | 0.958289i | \(0.592260\pi\) | |||||||
\(744\) | −156.294 | −5.73000 | ||||||||
\(745\) | 4.62867 | 0.169582 | ||||||||
\(746\) | 42.9039 | 1.57082 | ||||||||
\(747\) | −63.4997 | −2.32333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.26036 | 0.228748 | ||||||||
\(750\) | −8.33658 | −0.304409 | ||||||||
\(751\) | −30.0749 | −1.09745 | −0.548725 | − | 0.836003i | \(-0.684887\pi\) | ||||
−0.548725 | + | 0.836003i | \(0.684887\pi\) | |||||||
\(752\) | 145.406 | 5.30240 | ||||||||
\(753\) | 51.4886 | 1.87635 | ||||||||
\(754\) | 16.5306 | 0.602010 | ||||||||
\(755\) | 7.04541 | 0.256409 | ||||||||
\(756\) | −54.4713 | −1.98110 | ||||||||
\(757\) | 20.9610 | 0.761840 | 0.380920 | − | 0.924608i | \(-0.375607\pi\) | ||||
0.380920 | + | 0.924608i | \(0.375607\pi\) | |||||||
\(758\) | −52.3301 | −1.90071 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.74154 | −0.317089 | ||||||||
\(761\) | 48.0504 | 1.74182 | 0.870912 | − | 0.491439i | \(-0.163529\pi\) | ||||
0.870912 | + | 0.491439i | \(0.163529\pi\) | |||||||
\(762\) | 117.655 | 4.26220 | ||||||||
\(763\) | 1.70340 | 0.0616672 | ||||||||
\(764\) | −34.2780 | −1.24014 | ||||||||
\(765\) | −30.3800 | −1.09839 | ||||||||
\(766\) | −64.1252 | −2.31694 | ||||||||
\(767\) | 7.50213 | 0.270886 | ||||||||
\(768\) | −155.162 | −5.59893 | ||||||||
\(769\) | 22.9234 | 0.826638 | 0.413319 | − | 0.910586i | \(-0.364370\pi\) | ||||
0.413319 | + | 0.910586i | \(0.364370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0510 | 1.37037 | ||||||||
\(772\) | 121.210 | 4.36245 | ||||||||
\(773\) | −31.4722 | −1.13198 | −0.565988 | − | 0.824413i | \(-0.691505\pi\) | ||||
−0.565988 | + | 0.824413i | \(0.691505\pi\) | |||||||
\(774\) | 28.7641 | 1.03391 | ||||||||
\(775\) | −5.33352 | −0.191586 | ||||||||
\(776\) | −109.775 | −3.94068 | ||||||||
\(777\) | 8.42204 | 0.302139 | ||||||||
\(778\) | −31.1820 | −1.11793 | ||||||||
\(779\) | −4.59727 | −0.164714 | ||||||||
\(780\) | −110.612 | −3.96055 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −40.1796 | −1.43682 | ||||||||
\(783\) | −9.03040 | −0.322720 | ||||||||
\(784\) | 15.3863 | 0.549509 | ||||||||
\(785\) | −6.56589 | −0.234347 | ||||||||
\(786\) | 86.1288 | 3.07211 | ||||||||
\(787\) | −44.9445 | −1.60210 | −0.801049 | − | 0.598598i | \(-0.795725\pi\) | ||||
−0.801049 | + | 0.598598i | \(0.795725\pi\) | |||||||
\(788\) | 16.3012 | 0.580707 | ||||||||
\(789\) | −68.2786 | −2.43078 | ||||||||
\(790\) | −37.4631 | −1.33288 | ||||||||
\(791\) | −0.107727 | −0.00383034 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.7271 | 2.44057 | ||||||||
\(794\) | 41.8629 | 1.48566 | ||||||||
\(795\) | −10.2872 | −0.364849 | ||||||||
\(796\) | −64.1598 | −2.27409 | ||||||||
\(797\) | 29.7898 | 1.05521 | 0.527605 | − | 0.849490i | \(-0.323090\pi\) | ||||
0.527605 | + | 0.849490i | \(0.323090\pi\) | |||||||
\(798\) | −7.56255 | −0.267711 | ||||||||
\(799\) | 45.9523 | 1.62568 | ||||||||
\(800\) | −22.9070 | −0.809884 | ||||||||
\(801\) | 48.5434 | 1.71520 | ||||||||
\(802\) | −26.4998 | −0.935741 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −125.827 | −4.43756 | ||||||||
\(805\) | −3.01425 | −0.106238 | ||||||||
\(806\) | −96.4296 | −3.39659 | ||||||||
\(807\) | 41.7517 | 1.46973 | ||||||||
\(808\) | 11.2983 | 0.397471 | ||||||||
\(809\) | 28.3849 | 0.997961 | 0.498980 | − | 0.866613i | \(-0.333708\pi\) | ||||
0.498980 | + | 0.866613i | \(0.333708\pi\) | |||||||
\(810\) | 30.9553 | 1.08766 | ||||||||
\(811\) | 1.22401 | 0.0429807 | 0.0214904 | − | 0.999769i | \(-0.493159\pi\) | ||||
0.0214904 | + | 0.999769i | \(0.493159\pi\) | |||||||
\(812\) | 5.04252 | 0.176958 | ||||||||
\(813\) | −5.93430 | −0.208125 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3470 | −0.432495 | ||||||||
\(816\) | −227.516 | −7.96464 | ||||||||
\(817\) | 1.52347 | 0.0532996 | ||||||||
\(818\) | 38.9665 | 1.36243 | ||||||||
\(819\) | −41.2057 | −1.43985 | ||||||||
\(820\) | −27.9495 | −0.976038 | ||||||||
\(821\) | 9.87864 | 0.344767 | 0.172383 | − | 0.985030i | \(-0.444853\pi\) | ||||
0.172383 | + | 0.985030i | \(0.444853\pi\) | |||||||
\(822\) | 180.553 | 6.29751 | ||||||||
\(823\) | 13.9342 | 0.485714 | 0.242857 | − | 0.970062i | \(-0.421915\pi\) | ||||
0.242857 | + | 0.970062i | \(0.421915\pi\) | |||||||
\(824\) | 86.5242 | 3.01421 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.11834 | 0.108501 | ||||||||
\(827\) | −30.9317 | −1.07560 | −0.537801 | − | 0.843072i | \(-0.680745\pi\) | ||||
−0.537801 | + | 0.843072i | \(0.680745\pi\) | |||||||
\(828\) | 103.864 | 3.60951 | ||||||||
\(829\) | −39.1431 | −1.35950 | −0.679749 | − | 0.733445i | \(-0.737911\pi\) | ||||
−0.679749 | + | 0.733445i | \(0.737911\pi\) | |||||||
\(830\) | −27.8618 | −0.967099 | ||||||||
\(831\) | 19.8441 | 0.688383 | ||||||||
\(832\) | −211.205 | −7.32221 | ||||||||
\(833\) | 4.86249 | 0.168475 | ||||||||
\(834\) | 122.595 | 4.24512 | ||||||||
\(835\) | 3.90433 | 0.135115 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.6778 | 1.82081 | ||||||||
\(838\) | −41.8969 | −1.44730 | ||||||||
\(839\) | 8.38642 | 0.289531 | 0.144766 | − | 0.989466i | \(-0.453757\pi\) | ||||
0.144766 | + | 0.989466i | \(0.453757\pi\) | |||||||
\(840\) | −29.3040 | −1.01108 | ||||||||
\(841\) | −28.1640 | −0.971174 | ||||||||
\(842\) | −22.2129 | −0.765506 | ||||||||
\(843\) | −7.35567 | −0.253343 | ||||||||
\(844\) | 144.546 | 4.97547 | ||||||||
\(845\) | −30.4967 | −1.04912 | ||||||||
\(846\) | −161.862 | −5.56494 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −52.0486 | −1.78736 | ||||||||
\(849\) | −2.43051 | −0.0834148 | ||||||||
\(850\) | −13.3299 | −0.457211 | ||||||||
\(851\) | −8.34789 | −0.286162 | ||||||||
\(852\) | −62.8427 | −2.15295 | ||||||||
\(853\) | 6.41870 | 0.219772 | 0.109886 | − | 0.993944i | \(-0.464951\pi\) | ||||
0.109886 | + | 0.993944i | \(0.464951\pi\) | |||||||
\(854\) | 28.5672 | 0.977549 | ||||||||
\(855\) | 5.66774 | 0.193833 | ||||||||
\(856\) | −60.3262 | −2.06191 | ||||||||
\(857\) | −42.0950 | −1.43794 | −0.718968 | − | 0.695043i | \(-0.755385\pi\) | ||||
−0.718968 | + | 0.695043i | \(0.755385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4518 | −0.970763 | −0.485381 | − | 0.874303i | \(-0.661319\pi\) | ||||
−0.485381 | + | 0.874303i | \(0.661319\pi\) | |||||||
\(860\) | 9.26208 | 0.315834 | ||||||||
\(861\) | −15.4113 | −0.525216 | ||||||||
\(862\) | −45.5841 | −1.55260 | ||||||||
\(863\) | 49.5170 | 1.68558 | 0.842789 | − | 0.538245i | \(-0.180912\pi\) | ||||
0.842789 | + | 0.538245i | \(0.180912\pi\) | |||||||
\(864\) | 226.246 | 7.69705 | ||||||||
\(865\) | 5.70167 | 0.193863 | ||||||||
\(866\) | −96.1787 | −3.26829 | ||||||||
\(867\) | −20.2039 | −0.686161 | ||||||||
\(868\) | −29.4150 | −0.998410 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −7.62221 | −0.258417 | ||||||||
\(871\) | −49.4796 | −1.67655 | ||||||||
\(872\) | −16.4144 | −0.555860 | ||||||||
\(873\) | 71.1744 | 2.40889 | ||||||||
\(874\) | 7.49597 | 0.253555 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 266.640 | 9.00894 | ||||||||
\(877\) | 30.9398 | 1.04476 | 0.522381 | − | 0.852712i | \(-0.325044\pi\) | ||||
0.522381 | + | 0.852712i | \(0.325044\pi\) | |||||||
\(878\) | 66.6848 | 2.25050 | ||||||||
\(879\) | 72.9033 | 2.45897 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.9677 | −0.605348 | −0.302674 | − | 0.953094i | \(-0.597879\pi\) | ||||
−0.302674 | + | 0.953094i | \(0.597879\pi\) | |||||||
\(882\) | −17.1276 | −0.576717 | ||||||||
\(883\) | 4.90553 | 0.165084 | 0.0825421 | − | 0.996588i | \(-0.473696\pi\) | ||||
0.0825421 | + | 0.996588i | \(0.473696\pi\) | |||||||
\(884\) | −176.865 | −5.94861 | ||||||||
\(885\) | −3.45920 | −0.116280 | ||||||||
\(886\) | −13.9299 | −0.467985 | ||||||||
\(887\) | 24.4188 | 0.819902 | 0.409951 | − | 0.912107i | \(-0.365546\pi\) | ||||
0.409951 | + | 0.912107i | \(0.365546\pi\) | |||||||
\(888\) | −81.1567 | −2.72344 | ||||||||
\(889\) | 14.1131 | 0.473340 | ||||||||
\(890\) | 21.2995 | 0.713960 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.2238 | 0.844554 | ||||||||
\(893\) | −8.57293 | −0.286882 | ||||||||
\(894\) | −38.5873 | −1.29055 | ||||||||
\(895\) | 19.6283 | 0.656100 | ||||||||
\(896\) | −41.9757 | −1.40231 | ||||||||
\(897\) | 60.4544 | 2.01851 | ||||||||
\(898\) | 87.4238 | 2.91737 | ||||||||
\(899\) | −4.87649 | −0.162640 | ||||||||
\(900\) | 34.4575 | 1.14858 | ||||||||
\(901\) | −16.4488 | −0.547990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.10710 | 0.169954 | ||||||||
\(904\) | 1.03808 | 0.0345262 | ||||||||
\(905\) | −15.4408 | −0.513269 | ||||||||
\(906\) | −58.7346 | −1.95133 | ||||||||
\(907\) | −33.4445 | −1.11051 | −0.555253 | − | 0.831682i | \(-0.687378\pi\) | ||||
−0.555253 | + | 0.831682i | \(0.687378\pi\) | |||||||
\(908\) | 45.3544 | 1.50514 | ||||||||
\(909\) | −7.32544 | −0.242970 | ||||||||
\(910\) | −18.0799 | −0.599343 | ||||||||
\(911\) | −20.8102 | −0.689474 | −0.344737 | − | 0.938699i | \(-0.612032\pi\) | ||||
−0.344737 | + | 0.938699i | \(0.612032\pi\) | |||||||
\(912\) | 42.4457 | 1.40552 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −18.9861 | −0.628006 | ||||||||
\(915\) | −31.6898 | −1.04763 | ||||||||
\(916\) | −10.1932 | −0.336794 | ||||||||
\(917\) | 10.3314 | 0.341174 | ||||||||
\(918\) | 131.656 | 4.34529 | ||||||||
\(919\) | 11.8322 | 0.390308 | 0.195154 | − | 0.980773i | \(-0.437479\pi\) | ||||
0.195154 | + | 0.980773i | \(0.437479\pi\) | |||||||
\(920\) | 29.0460 | 0.957619 | ||||||||
\(921\) | −58.0068 | −1.91139 | ||||||||
\(922\) | −73.9265 | −2.43464 | ||||||||
\(923\) | −24.7120 | −0.813407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.76947 | −0.0910597 | ||||||||
\(926\) | 97.1868 | 3.19376 | ||||||||
\(927\) | −56.0996 | −1.84255 | ||||||||
\(928\) | −20.9441 | −0.687522 | ||||||||
\(929\) | 57.2642 | 1.87878 | 0.939388 | − | 0.342855i | \(-0.111394\pi\) | ||||
0.939388 | + | 0.342855i | \(0.111394\pi\) | |||||||
\(930\) | 44.4633 | 1.45801 | ||||||||
\(931\) | −0.907153 | −0.0297308 | ||||||||
\(932\) | −127.963 | −4.19158 | ||||||||
\(933\) | −27.9181 | −0.913998 | ||||||||
\(934\) | 89.0711 | 2.91449 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 397.068 | 12.9786 | ||||||||
\(937\) | −49.7345 | −1.62476 | −0.812378 | − | 0.583131i | \(-0.801827\pi\) | ||||
−0.812378 | + | 0.583131i | \(0.801827\pi\) | |||||||
\(938\) | −20.5667 | −0.671528 | ||||||||
\(939\) | 41.8659 | 1.36624 | ||||||||
\(940\) | −52.1199 | −1.69996 | ||||||||
\(941\) | −47.0701 | −1.53444 | −0.767221 | − | 0.641383i | \(-0.778361\pi\) | ||||
−0.767221 | + | 0.641383i | \(0.778361\pi\) | |||||||
\(942\) | 54.7370 | 1.78343 | ||||||||
\(943\) | 15.2756 | 0.497443 | ||||||||
\(944\) | −17.5021 | −0.569643 | ||||||||
\(945\) | 9.87674 | 0.321290 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.1208 | 0.523855 | 0.261927 | − | 0.965088i | \(-0.415642\pi\) | ||||
0.261927 | + | 0.965088i | \(0.415642\pi\) | |||||||
\(948\) | 229.198 | 7.44400 | ||||||||
\(949\) | 104.853 | 3.40366 | ||||||||
\(950\) | 2.48684 | 0.0806839 | ||||||||
\(951\) | −69.7780 | −2.26271 | ||||||||
\(952\) | −46.8561 | −1.51861 | ||||||||
\(953\) | 17.5288 | 0.567813 | 0.283907 | − | 0.958852i | \(-0.408369\pi\) | ||||
0.283907 | + | 0.958852i | \(0.408369\pi\) | |||||||
\(954\) | 57.9393 | 1.87586 | ||||||||
\(955\) | 6.21529 | 0.201122 | ||||||||
\(956\) | 146.006 | 4.72216 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56.8404 | 1.83643 | ||||||||
\(959\) | 21.6579 | 0.699371 | ||||||||
\(960\) | 97.3857 | 3.14311 | ||||||||
\(961\) | −2.55354 | −0.0823721 | ||||||||
\(962\) | −50.0718 | −1.61438 | ||||||||
\(963\) | 39.1136 | 1.26042 | ||||||||
\(964\) | −59.0289 | −1.90119 | ||||||||
\(965\) | −21.9778 | −0.707491 | ||||||||
\(966\) | 25.1285 | 0.808497 | ||||||||
\(967\) | −11.5858 | −0.372575 | −0.186287 | − | 0.982495i | \(-0.559646\pi\) | ||||
−0.186287 | + | 0.982495i | \(0.559646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.4140 | 0.430921 | ||||||||
\(970\) | 31.2293 | 1.00271 | ||||||||
\(971\) | 30.6243 | 0.982782 | 0.491391 | − | 0.870939i | \(-0.336489\pi\) | ||||
0.491391 | + | 0.870939i | \(0.336489\pi\) | |||||||
\(972\) | −25.9694 | −0.832968 | ||||||||
\(973\) | 14.7057 | 0.471443 | ||||||||
\(974\) | −9.62184 | −0.308304 | ||||||||
\(975\) | 20.0562 | 0.642312 | ||||||||
\(976\) | −160.337 | −5.13225 | ||||||||
\(977\) | 1.44818 | 0.0463314 | 0.0231657 | − | 0.999732i | \(-0.492625\pi\) | ||||
0.0231657 | + | 0.999732i | \(0.492625\pi\) | |||||||
\(978\) | 102.931 | 3.29138 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.51511 | −0.176174 | ||||||||
\(981\) | 10.6426 | 0.339791 | ||||||||
\(982\) | −0.407968 | −0.0130188 | ||||||||
\(983\) | −60.3589 | −1.92515 | −0.962574 | − | 0.271018i | \(-0.912640\pi\) | ||||
−0.962574 | + | 0.271018i | \(0.912640\pi\) | |||||||
\(984\) | 148.507 | 4.73423 | ||||||||
\(985\) | −2.95573 | −0.0941775 | ||||||||
\(986\) | −12.1876 | −0.388133 | ||||||||
\(987\) | −28.7388 | −0.914766 | ||||||||
\(988\) | 32.9962 | 1.04975 | ||||||||
\(989\) | −5.06213 | −0.160966 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9689 | 0.888460 | 0.444230 | − | 0.895913i | \(-0.353477\pi\) | ||||
0.444230 | + | 0.895913i | \(0.353477\pi\) | |||||||
\(992\) | 122.175 | 3.87905 | ||||||||
\(993\) | 10.4616 | 0.331989 | ||||||||
\(994\) | −10.2718 | −0.325803 | ||||||||
\(995\) | 11.6335 | 0.368805 | ||||||||
\(996\) | 170.458 | 5.40116 | ||||||||
\(997\) | −4.12371 | −0.130599 | −0.0652996 | − | 0.997866i | \(-0.520800\pi\) | ||||
−0.0652996 | + | 0.997866i | \(0.520800\pi\) | |||||||
\(998\) | −9.54084 | −0.302010 | ||||||||
\(999\) | 27.3534 | 0.865422 |
(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 | 4235.2.a.bb.1.1 | yes | 5 | |
11.10 | odd | 2 | 4235.2.a.ba.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.ba.1.5 | ✓ | 5 | 11.10 | odd | 2 | ||
4235.2.a.bb.1.1 | yes | 5 | 1.1 | even | 1 | trivial |