Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 3 x^{14} - 33 x^{13} + 101 x^{12} + 408 x^{11} - 1314 x^{10} - 2271 x^{9} + 8292 x^{8} + 4944 x^{7} - 26254 x^{6} + 1401 x^{5} + 39318 x^{4} - 19069 x^{3} + \cdots - 3592 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.75198\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.75198 | −1.01151 | −0.505754 | − | 0.862677i | \(-0.668786\pi\) | ||||
−0.505754 | + | 0.862677i | \(0.668786\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.75002 | 1.22985 | 0.614923 | − | 0.788588i | \(-0.289187\pi\) | ||||
0.614923 | + | 0.788588i | \(0.289187\pi\) | |||||||
\(6\) | −1.75198 | −0.715245 | ||||||||
\(7\) | 3.83483 | 1.44943 | 0.724714 | − | 0.689050i | \(-0.241972\pi\) | ||||
0.724714 | + | 0.689050i | \(0.241972\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0694508 | 0.0231503 | ||||||||
\(10\) | 2.75002 | 0.869632 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.75198 | −0.505754 | ||||||||
\(13\) | −2.99887 | −0.831737 | −0.415868 | − | 0.909425i | \(-0.636522\pi\) | ||||
−0.415868 | + | 0.909425i | \(0.636522\pi\) | |||||||
\(14\) | 3.83483 | 1.02490 | ||||||||
\(15\) | −4.81799 | −1.24400 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.94349 | 1.68404 | 0.842022 | − | 0.539444i | \(-0.181365\pi\) | ||||
0.842022 | + | 0.539444i | \(0.181365\pi\) | |||||||
\(18\) | 0.0694508 | 0.0163697 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.75002 | 0.614923 | ||||||||
\(21\) | −6.71856 | −1.46611 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.05872 | 0.220758 | 0.110379 | − | 0.993890i | \(-0.464794\pi\) | ||||
0.110379 | + | 0.993890i | \(0.464794\pi\) | |||||||
\(24\) | −1.75198 | −0.357622 | ||||||||
\(25\) | 2.56259 | 0.512519 | ||||||||
\(26\) | −2.99887 | −0.588127 | ||||||||
\(27\) | 5.13428 | 0.988092 | ||||||||
\(28\) | 3.83483 | 0.724714 | ||||||||
\(29\) | −6.97269 | −1.29480 | −0.647398 | − | 0.762152i | \(-0.724143\pi\) | ||||
−0.647398 | + | 0.762152i | \(0.724143\pi\) | |||||||
\(30\) | −4.81799 | −0.879640 | ||||||||
\(31\) | −5.40593 | −0.970933 | −0.485466 | − | 0.874255i | \(-0.661350\pi\) | ||||
−0.485466 | + | 0.874255i | \(0.661350\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.75198 | 0.304981 | ||||||||
\(34\) | 6.94349 | 1.19080 | ||||||||
\(35\) | 10.5458 | 1.78257 | ||||||||
\(36\) | 0.0694508 | 0.0115751 | ||||||||
\(37\) | 5.74381 | 0.944277 | 0.472139 | − | 0.881524i | \(-0.343482\pi\) | ||||
0.472139 | + | 0.881524i | \(0.343482\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.25398 | 0.841309 | ||||||||
\(40\) | 2.75002 | 0.434816 | ||||||||
\(41\) | 6.29831 | 0.983631 | 0.491816 | − | 0.870699i | \(-0.336333\pi\) | ||||
0.491816 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(42\) | −6.71856 | −1.03670 | ||||||||
\(43\) | −5.27048 | −0.803741 | −0.401870 | − | 0.915697i | \(-0.631640\pi\) | ||||
−0.401870 | + | 0.915697i | \(0.631640\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0.190991 | 0.0284712 | ||||||||
\(46\) | 1.05872 | 0.156099 | ||||||||
\(47\) | 9.76272 | 1.42404 | 0.712019 | − | 0.702160i | \(-0.247781\pi\) | ||||
0.712019 | + | 0.702160i | \(0.247781\pi\) | |||||||
\(48\) | −1.75198 | −0.252877 | ||||||||
\(49\) | 7.70590 | 1.10084 | ||||||||
\(50\) | 2.56259 | 0.362406 | ||||||||
\(51\) | −12.1649 | −1.70342 | ||||||||
\(52\) | −2.99887 | −0.415868 | ||||||||
\(53\) | −7.56179 | −1.03869 | −0.519346 | − | 0.854564i | \(-0.673824\pi\) | ||||
−0.519346 | + | 0.854564i | \(0.673824\pi\) | |||||||
\(54\) | 5.13428 | 0.698687 | ||||||||
\(55\) | −2.75002 | −0.370812 | ||||||||
\(56\) | 3.83483 | 0.512450 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.97269 | −0.915559 | ||||||||
\(59\) | 0.993331 | 0.129321 | 0.0646603 | − | 0.997907i | \(-0.479404\pi\) | ||||
0.0646603 | + | 0.997907i | \(0.479404\pi\) | |||||||
\(60\) | −4.81799 | −0.622000 | ||||||||
\(61\) | 6.30075 | 0.806729 | 0.403364 | − | 0.915039i | \(-0.367841\pi\) | ||||
0.403364 | + | 0.915039i | \(0.367841\pi\) | |||||||
\(62\) | −5.40593 | −0.686553 | ||||||||
\(63\) | 0.266332 | 0.0335547 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.24695 | −1.02291 | ||||||||
\(66\) | 1.75198 | 0.215654 | ||||||||
\(67\) | 1.99535 | 0.243771 | 0.121886 | − | 0.992544i | \(-0.461106\pi\) | ||||
0.121886 | + | 0.992544i | \(0.461106\pi\) | |||||||
\(68\) | 6.94349 | 0.842022 | ||||||||
\(69\) | −1.85486 | −0.223298 | ||||||||
\(70\) | 10.5458 | 1.26047 | ||||||||
\(71\) | 13.3663 | 1.58628 | 0.793142 | − | 0.609037i | \(-0.208444\pi\) | ||||
0.793142 | + | 0.609037i | \(0.208444\pi\) | |||||||
\(72\) | 0.0694508 | 0.00818485 | ||||||||
\(73\) | 8.55207 | 1.00094 | 0.500472 | − | 0.865753i | \(-0.333160\pi\) | ||||
0.500472 | + | 0.865753i | \(0.333160\pi\) | |||||||
\(74\) | 5.74381 | 0.667705 | ||||||||
\(75\) | −4.48963 | −0.518418 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.83483 | −0.437019 | ||||||||
\(78\) | 5.25398 | 0.594896 | ||||||||
\(79\) | 9.61507 | 1.08178 | 0.540890 | − | 0.841093i | \(-0.318087\pi\) | ||||
0.540890 | + | 0.841093i | \(0.318087\pi\) | |||||||
\(80\) | 2.75002 | 0.307461 | ||||||||
\(81\) | −9.20353 | −1.02261 | ||||||||
\(82\) | 6.29831 | 0.695532 | ||||||||
\(83\) | −9.86312 | −1.08262 | −0.541309 | − | 0.840824i | \(-0.682071\pi\) | ||||
−0.541309 | + | 0.840824i | \(0.682071\pi\) | |||||||
\(84\) | −6.71856 | −0.733055 | ||||||||
\(85\) | 19.0947 | 2.07111 | ||||||||
\(86\) | −5.27048 | −0.568331 | ||||||||
\(87\) | 12.2161 | 1.30970 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 13.1889 | 1.39802 | 0.699009 | − | 0.715113i | \(-0.253625\pi\) | ||||
0.699009 | + | 0.715113i | \(0.253625\pi\) | |||||||
\(90\) | 0.190991 | 0.0201322 | ||||||||
\(91\) | −11.5001 | −1.20554 | ||||||||
\(92\) | 1.05872 | 0.110379 | ||||||||
\(93\) | 9.47110 | 0.982107 | ||||||||
\(94\) | 9.76272 | 1.00695 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.75198 | −0.178811 | ||||||||
\(97\) | −6.09792 | −0.619150 | −0.309575 | − | 0.950875i | \(-0.600187\pi\) | ||||
−0.309575 | + | 0.950875i | \(0.600187\pi\) | |||||||
\(98\) | 7.70590 | 0.778413 | ||||||||
\(99\) | −0.0694508 | −0.00698007 | ||||||||
\(100\) | 2.56259 | 0.256259 | ||||||||
\(101\) | −17.8867 | −1.77979 | −0.889895 | − | 0.456166i | \(-0.849222\pi\) | ||||
−0.889895 | + | 0.456166i | \(0.849222\pi\) | |||||||
\(102\) | −12.1649 | −1.20450 | ||||||||
\(103\) | 1.63523 | 0.161124 | 0.0805620 | − | 0.996750i | \(-0.474329\pi\) | ||||
0.0805620 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(104\) | −2.99887 | −0.294063 | ||||||||
\(105\) | −18.4762 | −1.80309 | ||||||||
\(106\) | −7.56179 | −0.734466 | ||||||||
\(107\) | 6.69253 | 0.646991 | 0.323496 | − | 0.946230i | \(-0.395142\pi\) | ||||
0.323496 | + | 0.946230i | \(0.395142\pi\) | |||||||
\(108\) | 5.13428 | 0.494046 | ||||||||
\(109\) | 2.64617 | 0.253458 | 0.126729 | − | 0.991937i | \(-0.459552\pi\) | ||||
0.126729 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(110\) | −2.75002 | −0.262204 | ||||||||
\(111\) | −10.0631 | −0.955145 | ||||||||
\(112\) | 3.83483 | 0.362357 | ||||||||
\(113\) | 8.01087 | 0.753599 | 0.376800 | − | 0.926295i | \(-0.377025\pi\) | ||||
0.376800 | + | 0.926295i | \(0.377025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.91149 | 0.271498 | ||||||||
\(116\) | −6.97269 | −0.647398 | ||||||||
\(117\) | −0.208274 | −0.0192549 | ||||||||
\(118\) | 0.993331 | 0.0914435 | ||||||||
\(119\) | 26.6271 | 2.44090 | ||||||||
\(120\) | −4.81799 | −0.439820 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.30075 | 0.570443 | ||||||||
\(123\) | −11.0346 | −0.994952 | ||||||||
\(124\) | −5.40593 | −0.485466 | ||||||||
\(125\) | −6.70291 | −0.599526 | ||||||||
\(126\) | 0.266332 | 0.0237267 | ||||||||
\(127\) | 20.7918 | 1.84497 | 0.922487 | − | 0.386027i | \(-0.126153\pi\) | ||||
0.922487 | + | 0.386027i | \(0.126153\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.23380 | 0.812991 | ||||||||
\(130\) | −8.24695 | −0.723305 | ||||||||
\(131\) | −6.68860 | −0.584386 | −0.292193 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292193 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(132\) | 1.75198 | 0.152491 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.99535 | 0.172372 | ||||||||
\(135\) | 14.1194 | 1.21520 | ||||||||
\(136\) | 6.94349 | 0.595399 | ||||||||
\(137\) | 16.3981 | 1.40099 | 0.700494 | − | 0.713658i | \(-0.252963\pi\) | ||||
0.700494 | + | 0.713658i | \(0.252963\pi\) | |||||||
\(138\) | −1.85486 | −0.157896 | ||||||||
\(139\) | 13.1961 | 1.11928 | 0.559640 | − | 0.828736i | \(-0.310939\pi\) | ||||
0.559640 | + | 0.828736i | \(0.310939\pi\) | |||||||
\(140\) | 10.5458 | 0.891286 | ||||||||
\(141\) | −17.1041 | −1.44043 | ||||||||
\(142\) | 13.3663 | 1.12167 | ||||||||
\(143\) | 2.99887 | 0.250778 | ||||||||
\(144\) | 0.0694508 | 0.00578757 | ||||||||
\(145\) | −19.1750 | −1.59240 | ||||||||
\(146\) | 8.55207 | 0.707775 | ||||||||
\(147\) | −13.5006 | −1.11351 | ||||||||
\(148\) | 5.74381 | 0.472139 | ||||||||
\(149\) | 10.4264 | 0.854161 | 0.427080 | − | 0.904214i | \(-0.359542\pi\) | ||||
0.427080 | + | 0.904214i | \(0.359542\pi\) | |||||||
\(150\) | −4.48963 | −0.366577 | ||||||||
\(151\) | 0.887856 | 0.0722527 | 0.0361264 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361264 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.482231 | 0.0389860 | ||||||||
\(154\) | −3.83483 | −0.309019 | ||||||||
\(155\) | −14.8664 | −1.19410 | ||||||||
\(156\) | 5.25398 | 0.420655 | ||||||||
\(157\) | −7.69032 | −0.613755 | −0.306877 | − | 0.951749i | \(-0.599284\pi\) | ||||
−0.306877 | + | 0.951749i | \(0.599284\pi\) | |||||||
\(158\) | 9.61507 | 0.764934 | ||||||||
\(159\) | 13.2481 | 1.05065 | ||||||||
\(160\) | 2.75002 | 0.217408 | ||||||||
\(161\) | 4.06000 | 0.319973 | ||||||||
\(162\) | −9.20353 | −0.723098 | ||||||||
\(163\) | 0.977244 | 0.0765436 | 0.0382718 | − | 0.999267i | \(-0.487815\pi\) | ||||
0.0382718 | + | 0.999267i | \(0.487815\pi\) | |||||||
\(164\) | 6.29831 | 0.491816 | ||||||||
\(165\) | 4.81799 | 0.375080 | ||||||||
\(166\) | −9.86312 | −0.765526 | ||||||||
\(167\) | −14.4378 | −1.11723 | −0.558616 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558616 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(168\) | −6.71856 | −0.518348 | ||||||||
\(169\) | −4.00678 | −0.308214 | ||||||||
\(170\) | 19.0947 | 1.46450 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.27048 | −0.401870 | ||||||||
\(173\) | −20.7436 | −1.57711 | −0.788555 | − | 0.614965i | \(-0.789170\pi\) | ||||
−0.788555 | + | 0.614965i | \(0.789170\pi\) | |||||||
\(174\) | 12.2161 | 0.926096 | ||||||||
\(175\) | 9.82711 | 0.742860 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −1.74030 | −0.130809 | ||||||||
\(178\) | 13.1889 | 0.988547 | ||||||||
\(179\) | −19.5304 | −1.45977 | −0.729884 | − | 0.683571i | \(-0.760426\pi\) | ||||
−0.729884 | + | 0.683571i | \(0.760426\pi\) | |||||||
\(180\) | 0.190991 | 0.0142356 | ||||||||
\(181\) | 0.524440 | 0.0389813 | 0.0194906 | − | 0.999810i | \(-0.493796\pi\) | ||||
0.0194906 | + | 0.999810i | \(0.493796\pi\) | |||||||
\(182\) | −11.5001 | −0.852448 | ||||||||
\(183\) | −11.0388 | −0.816013 | ||||||||
\(184\) | 1.05872 | 0.0780497 | ||||||||
\(185\) | 15.7956 | 1.16131 | ||||||||
\(186\) | 9.47110 | 0.694455 | ||||||||
\(187\) | −6.94349 | −0.507758 | ||||||||
\(188\) | 9.76272 | 0.712019 | ||||||||
\(189\) | 19.6891 | 1.43217 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6960 | 1.42515 | 0.712576 | − | 0.701595i | \(-0.247528\pi\) | ||||
0.712576 | + | 0.701595i | \(0.247528\pi\) | |||||||
\(192\) | −1.75198 | −0.126439 | ||||||||
\(193\) | −0.558050 | −0.0401693 | −0.0200846 | − | 0.999798i | \(-0.506394\pi\) | ||||
−0.0200846 | + | 0.999798i | \(0.506394\pi\) | |||||||
\(194\) | −6.09792 | −0.437805 | ||||||||
\(195\) | 14.4485 | 1.03468 | ||||||||
\(196\) | 7.70590 | 0.550421 | ||||||||
\(197\) | −27.2349 | −1.94040 | −0.970202 | − | 0.242297i | \(-0.922099\pi\) | ||||
−0.970202 | + | 0.242297i | \(0.922099\pi\) | |||||||
\(198\) | −0.0694508 | −0.00493565 | ||||||||
\(199\) | −9.66076 | −0.684833 | −0.342417 | − | 0.939548i | \(-0.611245\pi\) | ||||
−0.342417 | + | 0.939548i | \(0.611245\pi\) | |||||||
\(200\) | 2.56259 | 0.181203 | ||||||||
\(201\) | −3.49583 | −0.246577 | ||||||||
\(202\) | −17.8867 | −1.25850 | ||||||||
\(203\) | −26.7391 | −1.87671 | ||||||||
\(204\) | −12.1649 | −0.851712 | ||||||||
\(205\) | 17.3205 | 1.20971 | ||||||||
\(206\) | 1.63523 | 0.113932 | ||||||||
\(207\) | 0.0735287 | 0.00511060 | ||||||||
\(208\) | −2.99887 | −0.207934 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −18.4762 | −1.27498 | ||||||||
\(211\) | 16.7285 | 1.15164 | 0.575819 | − | 0.817577i | \(-0.304683\pi\) | ||||
0.575819 | + | 0.817577i | \(0.304683\pi\) | |||||||
\(212\) | −7.56179 | −0.519346 | ||||||||
\(213\) | −23.4175 | −1.60454 | ||||||||
\(214\) | 6.69253 | 0.457492 | ||||||||
\(215\) | −14.4939 | −0.988477 | ||||||||
\(216\) | 5.13428 | 0.349343 | ||||||||
\(217\) | −20.7308 | −1.40730 | ||||||||
\(218\) | 2.64617 | 0.179222 | ||||||||
\(219\) | −14.9831 | −1.01246 | ||||||||
\(220\) | −2.75002 | −0.185406 | ||||||||
\(221\) | −20.8226 | −1.40068 | ||||||||
\(222\) | −10.0631 | −0.675389 | ||||||||
\(223\) | −9.83783 | −0.658790 | −0.329395 | − | 0.944192i | \(-0.606845\pi\) | ||||
−0.329395 | + | 0.944192i | \(0.606845\pi\) | |||||||
\(224\) | 3.83483 | 0.256225 | ||||||||
\(225\) | 0.177974 | 0.0118650 | ||||||||
\(226\) | 8.01087 | 0.532875 | ||||||||
\(227\) | 0.864686 | 0.0573913 | 0.0286956 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286956 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.33952 | 0.551091 | 0.275545 | − | 0.961288i | \(-0.411142\pi\) | ||||
0.275545 | + | 0.961288i | \(0.411142\pi\) | |||||||
\(230\) | 2.91149 | 0.191978 | ||||||||
\(231\) | 6.71856 | 0.442049 | ||||||||
\(232\) | −6.97269 | −0.457780 | ||||||||
\(233\) | 19.8575 | 1.30091 | 0.650455 | − | 0.759545i | \(-0.274578\pi\) | ||||
0.650455 | + | 0.759545i | \(0.274578\pi\) | |||||||
\(234\) | −0.208274 | −0.0136153 | ||||||||
\(235\) | 26.8476 | 1.75135 | ||||||||
\(236\) | 0.993331 | 0.0646603 | ||||||||
\(237\) | −16.8455 | −1.09423 | ||||||||
\(238\) | 26.6271 | 1.72598 | ||||||||
\(239\) | −15.7645 | −1.01972 | −0.509860 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509860 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(240\) | −4.81799 | −0.311000 | ||||||||
\(241\) | −22.0841 | −1.42256 | −0.711282 | − | 0.702907i | \(-0.751885\pi\) | ||||
−0.711282 | + | 0.702907i | \(0.751885\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0.721610 | 0.0462913 | ||||||||
\(244\) | 6.30075 | 0.403364 | ||||||||
\(245\) | 21.1914 | 1.35387 | ||||||||
\(246\) | −11.0346 | −0.703537 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.40593 | −0.343277 | ||||||||
\(249\) | 17.2800 | 1.09508 | ||||||||
\(250\) | −6.70291 | −0.423929 | ||||||||
\(251\) | 7.83629 | 0.494623 | 0.247311 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247311 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(252\) | 0.266332 | 0.0167773 | ||||||||
\(253\) | −1.05872 | −0.0665610 | ||||||||
\(254\) | 20.7918 | 1.30459 | ||||||||
\(255\) | −33.4536 | −2.09495 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.4912 | −1.27820 | −0.639102 | − | 0.769122i | \(-0.720694\pi\) | ||||
−0.639102 | + | 0.769122i | \(0.720694\pi\) | |||||||
\(258\) | 9.23380 | 0.574871 | ||||||||
\(259\) | 22.0265 | 1.36866 | ||||||||
\(260\) | −8.24695 | −0.511454 | ||||||||
\(261\) | −0.484259 | −0.0299749 | ||||||||
\(262\) | −6.68860 | −0.413223 | ||||||||
\(263\) | −26.8143 | −1.65344 | −0.826719 | − | 0.562614i | \(-0.809796\pi\) | ||||
−0.826719 | + | 0.562614i | \(0.809796\pi\) | |||||||
\(264\) | 1.75198 | 0.107827 | ||||||||
\(265\) | −20.7950 | −1.27743 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.1067 | −1.41411 | ||||||||
\(268\) | 1.99535 | 0.121886 | ||||||||
\(269\) | 10.9612 | 0.668316 | 0.334158 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334158 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(270\) | 14.1194 | 0.859276 | ||||||||
\(271\) | 1.86040 | 0.113011 | 0.0565057 | − | 0.998402i | \(-0.482004\pi\) | ||||
0.0565057 | + | 0.998402i | \(0.482004\pi\) | |||||||
\(272\) | 6.94349 | 0.421011 | ||||||||
\(273\) | 20.1481 | 1.21942 | ||||||||
\(274\) | 16.3981 | 0.990648 | ||||||||
\(275\) | −2.56259 | −0.154530 | ||||||||
\(276\) | −1.85486 | −0.111649 | ||||||||
\(277\) | 18.7769 | 1.12819 | 0.564097 | − | 0.825709i | \(-0.309225\pi\) | ||||
0.564097 | + | 0.825709i | \(0.309225\pi\) | |||||||
\(278\) | 13.1961 | 0.791451 | ||||||||
\(279\) | −0.375446 | −0.0224774 | ||||||||
\(280\) | 10.5458 | 0.630235 | ||||||||
\(281\) | 12.7105 | 0.758246 | 0.379123 | − | 0.925346i | \(-0.376226\pi\) | ||||
0.379123 | + | 0.925346i | \(0.376226\pi\) | |||||||
\(282\) | −17.1041 | −1.01854 | ||||||||
\(283\) | −10.9472 | −0.650741 | −0.325371 | − | 0.945587i | \(-0.605489\pi\) | ||||
−0.325371 | + | 0.945587i | \(0.605489\pi\) | |||||||
\(284\) | 13.3663 | 0.793142 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.99887 | 0.177327 | ||||||||
\(287\) | 24.1529 | 1.42570 | ||||||||
\(288\) | 0.0694508 | 0.00409243 | ||||||||
\(289\) | 31.2120 | 1.83600 | ||||||||
\(290\) | −19.1750 | −1.12600 | ||||||||
\(291\) | 10.6835 | 0.626275 | ||||||||
\(292\) | 8.55207 | 0.500472 | ||||||||
\(293\) | −4.29499 | −0.250916 | −0.125458 | − | 0.992099i | \(-0.540040\pi\) | ||||
−0.125458 | + | 0.992099i | \(0.540040\pi\) | |||||||
\(294\) | −13.5006 | −0.787372 | ||||||||
\(295\) | 2.73168 | 0.159044 | ||||||||
\(296\) | 5.74381 | 0.333852 | ||||||||
\(297\) | −5.13428 | −0.297921 | ||||||||
\(298\) | 10.4264 | 0.603983 | ||||||||
\(299\) | −3.17496 | −0.183612 | ||||||||
\(300\) | −4.48963 | −0.259209 | ||||||||
\(301\) | −20.2114 | −1.16496 | ||||||||
\(302\) | 0.887856 | 0.0510904 | ||||||||
\(303\) | 31.3372 | 1.80027 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.3272 | 0.992152 | ||||||||
\(306\) | 0.482231 | 0.0275673 | ||||||||
\(307\) | 33.2043 | 1.89507 | 0.947534 | − | 0.319656i | \(-0.103567\pi\) | ||||
0.947534 | + | 0.319656i | \(0.103567\pi\) | |||||||
\(308\) | −3.83483 | −0.218510 | ||||||||
\(309\) | −2.86490 | −0.162978 | ||||||||
\(310\) | −14.8664 | −0.844354 | ||||||||
\(311\) | 29.4236 | 1.66846 | 0.834230 | − | 0.551417i | \(-0.185913\pi\) | ||||
0.834230 | + | 0.551417i | \(0.185913\pi\) | |||||||
\(312\) | 5.25398 | 0.297448 | ||||||||
\(313\) | −8.73586 | −0.493780 | −0.246890 | − | 0.969044i | \(-0.579409\pi\) | ||||
−0.246890 | + | 0.969044i | \(0.579409\pi\) | |||||||
\(314\) | −7.69032 | −0.433990 | ||||||||
\(315\) | 0.732417 | 0.0412670 | ||||||||
\(316\) | 9.61507 | 0.540890 | ||||||||
\(317\) | 3.01863 | 0.169543 | 0.0847715 | − | 0.996400i | \(-0.472984\pi\) | ||||
0.0847715 | + | 0.996400i | \(0.472984\pi\) | |||||||
\(318\) | 13.2481 | 0.742919 | ||||||||
\(319\) | 6.97269 | 0.390396 | ||||||||
\(320\) | 2.75002 | 0.153731 | ||||||||
\(321\) | −11.7252 | −0.654437 | ||||||||
\(322\) | 4.06000 | 0.226255 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.20353 | −0.511307 | ||||||||
\(325\) | −7.68489 | −0.426281 | ||||||||
\(326\) | 0.977244 | 0.0541245 | ||||||||
\(327\) | −4.63606 | −0.256375 | ||||||||
\(328\) | 6.29831 | 0.347766 | ||||||||
\(329\) | 37.4383 | 2.06404 | ||||||||
\(330\) | 4.81799 | 0.265222 | ||||||||
\(331\) | 21.0483 | 1.15692 | 0.578461 | − | 0.815710i | \(-0.303654\pi\) | ||||
0.578461 | + | 0.815710i | \(0.303654\pi\) | |||||||
\(332\) | −9.86312 | −0.541309 | ||||||||
\(333\) | 0.398912 | 0.0218603 | ||||||||
\(334\) | −14.4378 | −0.790002 | ||||||||
\(335\) | 5.48725 | 0.299801 | ||||||||
\(336\) | −6.71856 | −0.366527 | ||||||||
\(337\) | 32.8578 | 1.78988 | 0.894938 | − | 0.446191i | \(-0.147220\pi\) | ||||
0.894938 | + | 0.446191i | \(0.147220\pi\) | |||||||
\(338\) | −4.00678 | −0.217940 | ||||||||
\(339\) | −14.0349 | −0.762272 | ||||||||
\(340\) | 19.0947 | 1.03556 | ||||||||
\(341\) | 5.40593 | 0.292747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.70700 | 0.146164 | ||||||||
\(344\) | −5.27048 | −0.284165 | ||||||||
\(345\) | −5.10089 | −0.274623 | ||||||||
\(346\) | −20.7436 | −1.11518 | ||||||||
\(347\) | −1.55590 | −0.0835252 | −0.0417626 | − | 0.999128i | \(-0.513297\pi\) | ||||
−0.0417626 | + | 0.999128i | \(0.513297\pi\) | |||||||
\(348\) | 12.2161 | 0.654849 | ||||||||
\(349\) | −7.35032 | −0.393454 | −0.196727 | − | 0.980458i | \(-0.563031\pi\) | ||||
−0.196727 | + | 0.980458i | \(0.563031\pi\) | |||||||
\(350\) | 9.82711 | 0.525281 | ||||||||
\(351\) | −15.3970 | −0.821833 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −19.3609 | −1.03048 | −0.515240 | − | 0.857046i | \(-0.672297\pi\) | ||||
−0.515240 | + | 0.857046i | \(0.672297\pi\) | |||||||
\(354\) | −1.74030 | −0.0924959 | ||||||||
\(355\) | 36.7575 | 1.95088 | ||||||||
\(356\) | 13.1889 | 0.699009 | ||||||||
\(357\) | −46.6502 | −2.46899 | ||||||||
\(358\) | −19.5304 | −1.03221 | ||||||||
\(359\) | −14.9074 | −0.786785 | −0.393392 | − | 0.919371i | \(-0.628699\pi\) | ||||
−0.393392 | + | 0.919371i | \(0.628699\pi\) | |||||||
\(360\) | 0.190991 | 0.0100661 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0.524440 | 0.0275639 | ||||||||
\(363\) | −1.75198 | −0.0919554 | ||||||||
\(364\) | −11.5001 | −0.602772 | ||||||||
\(365\) | 23.5184 | 1.23101 | ||||||||
\(366\) | −11.0388 | −0.577009 | ||||||||
\(367\) | −27.5633 | −1.43879 | −0.719397 | − | 0.694600i | \(-0.755582\pi\) | ||||
−0.719397 | + | 0.694600i | \(0.755582\pi\) | |||||||
\(368\) | 1.05872 | 0.0551894 | ||||||||
\(369\) | 0.437423 | 0.0227713 | ||||||||
\(370\) | 15.7956 | 0.821174 | ||||||||
\(371\) | −28.9982 | −1.50551 | ||||||||
\(372\) | 9.47110 | 0.491054 | ||||||||
\(373\) | −13.6882 | −0.708746 | −0.354373 | − | 0.935104i | \(-0.615306\pi\) | ||||
−0.354373 | + | 0.935104i | \(0.615306\pi\) | |||||||
\(374\) | −6.94349 | −0.359039 | ||||||||
\(375\) | 11.7434 | 0.606426 | ||||||||
\(376\) | 9.76272 | 0.503474 | ||||||||
\(377\) | 20.9102 | 1.07693 | ||||||||
\(378\) | 19.6891 | 1.01270 | ||||||||
\(379\) | −6.31554 | −0.324407 | −0.162204 | − | 0.986757i | \(-0.551860\pi\) | ||||
−0.162204 | + | 0.986757i | \(0.551860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.4269 | −1.86621 | ||||||||
\(382\) | 19.6960 | 1.00773 | ||||||||
\(383\) | 4.01015 | 0.204909 | 0.102455 | − | 0.994738i | \(-0.467330\pi\) | ||||
0.102455 | + | 0.994738i | \(0.467330\pi\) | |||||||
\(384\) | −1.75198 | −0.0894056 | ||||||||
\(385\) | −10.5458 | −0.537466 | ||||||||
\(386\) | −0.558050 | −0.0284040 | ||||||||
\(387\) | −0.366039 | −0.0186068 | ||||||||
\(388\) | −6.09792 | −0.309575 | ||||||||
\(389\) | −17.8884 | −0.906976 | −0.453488 | − | 0.891262i | \(-0.649820\pi\) | ||||
−0.453488 | + | 0.891262i | \(0.649820\pi\) | |||||||
\(390\) | 14.4485 | 0.731629 | ||||||||
\(391\) | 7.35119 | 0.371766 | ||||||||
\(392\) | 7.70590 | 0.389207 | ||||||||
\(393\) | 11.7183 | 0.591111 | ||||||||
\(394\) | −27.2349 | −1.37207 | ||||||||
\(395\) | 26.4416 | 1.33042 | ||||||||
\(396\) | −0.0694508 | −0.00349003 | ||||||||
\(397\) | −7.46337 | −0.374576 | −0.187288 | − | 0.982305i | \(-0.559970\pi\) | ||||
−0.187288 | + | 0.982305i | \(0.559970\pi\) | |||||||
\(398\) | −9.66076 | −0.484250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.56259 | 0.128130 | ||||||||
\(401\) | −16.9891 | −0.848396 | −0.424198 | − | 0.905569i | \(-0.639444\pi\) | ||||
−0.424198 | + | 0.905569i | \(0.639444\pi\) | |||||||
\(402\) | −3.49583 | −0.174356 | ||||||||
\(403\) | 16.2117 | 0.807561 | ||||||||
\(404\) | −17.8867 | −0.889895 | ||||||||
\(405\) | −25.3099 | −1.25766 | ||||||||
\(406\) | −26.7391 | −1.32704 | ||||||||
\(407\) | −5.74381 | −0.284710 | ||||||||
\(408\) | −12.1649 | −0.602252 | ||||||||
\(409\) | 3.76849 | 0.186340 | 0.0931698 | − | 0.995650i | \(-0.470300\pi\) | ||||
0.0931698 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(410\) | 17.3205 | 0.855397 | ||||||||
\(411\) | −28.7293 | −1.41711 | ||||||||
\(412\) | 1.63523 | 0.0805620 | ||||||||
\(413\) | 3.80925 | 0.187441 | ||||||||
\(414\) | 0.0735287 | 0.00361374 | ||||||||
\(415\) | −27.1237 | −1.33145 | ||||||||
\(416\) | −2.99887 | −0.147032 | ||||||||
\(417\) | −23.1194 | −1.13216 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.5461 | 1.58998 | 0.794990 | − | 0.606622i | \(-0.207476\pi\) | ||||
0.794990 | + | 0.606622i | \(0.207476\pi\) | |||||||
\(420\) | −18.4762 | −0.901544 | ||||||||
\(421\) | 3.97736 | 0.193845 | 0.0969223 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969223 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(422\) | 16.7285 | 0.814331 | ||||||||
\(423\) | 0.678029 | 0.0329669 | ||||||||
\(424\) | −7.56179 | −0.367233 | ||||||||
\(425\) | 17.7933 | 0.863104 | ||||||||
\(426\) | −23.4175 | −1.13458 | ||||||||
\(427\) | 24.1623 | 1.16930 | ||||||||
\(428\) | 6.69253 | 0.323496 | ||||||||
\(429\) | −5.25398 | −0.253664 | ||||||||
\(430\) | −14.4939 | −0.698959 | ||||||||
\(431\) | −4.18326 | −0.201501 | −0.100750 | − | 0.994912i | \(-0.532124\pi\) | ||||
−0.100750 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(432\) | 5.13428 | 0.247023 | ||||||||
\(433\) | 13.7414 | 0.660367 | 0.330184 | − | 0.943917i | \(-0.392889\pi\) | ||||
0.330184 | + | 0.943917i | \(0.392889\pi\) | |||||||
\(434\) | −20.7308 | −0.995110 | ||||||||
\(435\) | 33.5944 | 1.61073 | ||||||||
\(436\) | 2.64617 | 0.126729 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −14.9831 | −0.715920 | ||||||||
\(439\) | 27.4116 | 1.30828 | 0.654142 | − | 0.756372i | \(-0.273030\pi\) | ||||
0.654142 | + | 0.756372i | \(0.273030\pi\) | |||||||
\(440\) | −2.75002 | −0.131102 | ||||||||
\(441\) | 0.535181 | 0.0254848 | ||||||||
\(442\) | −20.8226 | −0.990431 | ||||||||
\(443\) | 34.5821 | 1.64304 | 0.821521 | − | 0.570178i | \(-0.193126\pi\) | ||||
0.821521 | + | 0.570178i | \(0.193126\pi\) | |||||||
\(444\) | −10.0631 | −0.477572 | ||||||||
\(445\) | 36.2696 | 1.71934 | ||||||||
\(446\) | −9.83783 | −0.465835 | ||||||||
\(447\) | −18.2668 | −0.863991 | ||||||||
\(448\) | 3.83483 | 0.181179 | ||||||||
\(449\) | 14.0064 | 0.661002 | 0.330501 | − | 0.943806i | \(-0.392782\pi\) | ||||
0.330501 | + | 0.943806i | \(0.392782\pi\) | |||||||
\(450\) | 0.177974 | 0.00838979 | ||||||||
\(451\) | −6.29831 | −0.296576 | ||||||||
\(452\) | 8.01087 | 0.376800 | ||||||||
\(453\) | −1.55551 | −0.0730843 | ||||||||
\(454\) | 0.864686 | 0.0405817 | ||||||||
\(455\) | −31.6256 | −1.48263 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.1525 | −1.59759 | −0.798793 | − | 0.601606i | \(-0.794528\pi\) | ||||
−0.798793 | + | 0.601606i | \(0.794528\pi\) | |||||||
\(458\) | 8.33952 | 0.389680 | ||||||||
\(459\) | 35.6498 | 1.66399 | ||||||||
\(460\) | 2.91149 | 0.135749 | ||||||||
\(461\) | 37.5791 | 1.75023 | 0.875117 | − | 0.483912i | \(-0.160784\pi\) | ||||
0.875117 | + | 0.483912i | \(0.160784\pi\) | |||||||
\(462\) | 6.71856 | 0.312576 | ||||||||
\(463\) | 5.53335 | 0.257157 | 0.128578 | − | 0.991699i | \(-0.458959\pi\) | ||||
0.128578 | + | 0.991699i | \(0.458959\pi\) | |||||||
\(464\) | −6.97269 | −0.323699 | ||||||||
\(465\) | 26.0457 | 1.20784 | ||||||||
\(466\) | 19.8575 | 0.919882 | ||||||||
\(467\) | 12.6215 | 0.584055 | 0.292027 | − | 0.956410i | \(-0.405670\pi\) | ||||
0.292027 | + | 0.956410i | \(0.405670\pi\) | |||||||
\(468\) | −0.208274 | −0.00962747 | ||||||||
\(469\) | 7.65183 | 0.353329 | ||||||||
\(470\) | 26.8476 | 1.23839 | ||||||||
\(471\) | 13.4733 | 0.620818 | ||||||||
\(472\) | 0.993331 | 0.0457217 | ||||||||
\(473\) | 5.27048 | 0.242337 | ||||||||
\(474\) | −16.8455 | −0.773738 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.6271 | 1.22045 | ||||||||
\(477\) | −0.525172 | −0.0240460 | ||||||||
\(478\) | −15.7645 | −0.721051 | ||||||||
\(479\) | −22.1665 | −1.01281 | −0.506407 | − | 0.862295i | \(-0.669026\pi\) | ||||
−0.506407 | + | 0.862295i | \(0.669026\pi\) | |||||||
\(480\) | −4.81799 | −0.219910 | ||||||||
\(481\) | −17.2250 | −0.785390 | ||||||||
\(482\) | −22.0841 | −1.00590 | ||||||||
\(483\) | −7.11305 | −0.323655 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −16.7694 | −0.761458 | ||||||||
\(486\) | 0.721610 | 0.0327329 | ||||||||
\(487\) | 8.56601 | 0.388163 | 0.194082 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(488\) | 6.30075 | 0.285222 | ||||||||
\(489\) | −1.71212 | −0.0774246 | ||||||||
\(490\) | 21.1914 | 0.957328 | ||||||||
\(491\) | 22.0937 | 0.997075 | 0.498537 | − | 0.866868i | \(-0.333871\pi\) | ||||
0.498537 | + | 0.866868i | \(0.333871\pi\) | |||||||
\(492\) | −11.0346 | −0.497476 | ||||||||
\(493\) | −48.4148 | −2.18049 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.190991 | −0.00858440 | ||||||||
\(496\) | −5.40593 | −0.242733 | ||||||||
\(497\) | 51.2573 | 2.29921 | ||||||||
\(498\) | 17.2800 | 0.774337 | ||||||||
\(499\) | −2.72781 | −0.122114 | −0.0610569 | − | 0.998134i | \(-0.519447\pi\) | ||||
−0.0610569 | + | 0.998134i | \(0.519447\pi\) | |||||||
\(500\) | −6.70291 | −0.299763 | ||||||||
\(501\) | 25.2948 | 1.13009 | ||||||||
\(502\) | 7.83629 | 0.349751 | ||||||||
\(503\) | 7.28006 | 0.324602 | 0.162301 | − | 0.986741i | \(-0.448108\pi\) | ||||
0.162301 | + | 0.986741i | \(0.448108\pi\) | |||||||
\(504\) | 0.266332 | 0.0118634 | ||||||||
\(505\) | −49.1886 | −2.18886 | ||||||||
\(506\) | −1.05872 | −0.0470657 | ||||||||
\(507\) | 7.01981 | 0.311761 | ||||||||
\(508\) | 20.7918 | 0.922487 | ||||||||
\(509\) | −24.1341 | −1.06973 | −0.534863 | − | 0.844939i | \(-0.679637\pi\) | ||||
−0.534863 | + | 0.844939i | \(0.679637\pi\) | |||||||
\(510\) | −33.4536 | −1.48135 | ||||||||
\(511\) | 32.7957 | 1.45080 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.4912 | −0.903827 | ||||||||
\(515\) | 4.49691 | 0.198157 | ||||||||
\(516\) | 9.23380 | 0.406496 | ||||||||
\(517\) | −9.76272 | −0.429364 | ||||||||
\(518\) | 22.0265 | 0.967790 | ||||||||
\(519\) | 36.3425 | 1.59526 | ||||||||
\(520\) | −8.24695 | −0.361652 | ||||||||
\(521\) | −12.8461 | −0.562800 | −0.281400 | − | 0.959591i | \(-0.590799\pi\) | ||||
−0.281400 | + | 0.959591i | \(0.590799\pi\) | |||||||
\(522\) | −0.484259 | −0.0211954 | ||||||||
\(523\) | −2.93950 | −0.128535 | −0.0642676 | − | 0.997933i | \(-0.520471\pi\) | ||||
−0.0642676 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(524\) | −6.68860 | −0.292193 | ||||||||
\(525\) | −17.2169 | −0.751409 | ||||||||
\(526\) | −26.8143 | −1.16916 | ||||||||
\(527\) | −37.5360 | −1.63509 | ||||||||
\(528\) | 1.75198 | 0.0762454 | ||||||||
\(529\) | −21.8791 | −0.951266 | ||||||||
\(530\) | −20.7950 | −0.903279 | ||||||||
\(531\) | 0.0689876 | 0.00299381 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.8878 | −0.818123 | ||||||||
\(534\) | −23.1067 | −0.999924 | ||||||||
\(535\) | 18.4046 | 0.795699 | ||||||||
\(536\) | 1.99535 | 0.0861861 | ||||||||
\(537\) | 34.2169 | 1.47657 | ||||||||
\(538\) | 10.9612 | 0.472571 | ||||||||
\(539\) | −7.70590 | −0.331917 | ||||||||
\(540\) | 14.1194 | 0.607600 | ||||||||
\(541\) | 29.2712 | 1.25847 | 0.629233 | − | 0.777217i | \(-0.283369\pi\) | ||||
0.629233 | + | 0.777217i | \(0.283369\pi\) | |||||||
\(542\) | 1.86040 | 0.0799112 | ||||||||
\(543\) | −0.918810 | −0.0394299 | ||||||||
\(544\) | 6.94349 | 0.297700 | ||||||||
\(545\) | 7.27703 | 0.311714 | ||||||||
\(546\) | 20.1481 | 0.862258 | ||||||||
\(547\) | −28.6335 | −1.22428 | −0.612140 | − | 0.790750i | \(-0.709691\pi\) | ||||
−0.612140 | + | 0.790750i | \(0.709691\pi\) | |||||||
\(548\) | 16.3981 | 0.700494 | ||||||||
\(549\) | 0.437592 | 0.0186760 | ||||||||
\(550\) | −2.56259 | −0.109269 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.85486 | −0.0789479 | ||||||||
\(553\) | 36.8721 | 1.56796 | ||||||||
\(554\) | 18.7769 | 0.797753 | ||||||||
\(555\) | −27.6736 | −1.17468 | ||||||||
\(556\) | 13.1961 | 0.559640 | ||||||||
\(557\) | 1.59398 | 0.0675390 | 0.0337695 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337695 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(558\) | −0.375446 | −0.0158939 | ||||||||
\(559\) | 15.8055 | 0.668501 | ||||||||
\(560\) | 10.5458 | 0.445643 | ||||||||
\(561\) | 12.1649 | 0.513602 | ||||||||
\(562\) | 12.7105 | 0.536161 | ||||||||
\(563\) | 34.4090 | 1.45017 | 0.725083 | − | 0.688662i | \(-0.241801\pi\) | ||||
0.725083 | + | 0.688662i | \(0.241801\pi\) | |||||||
\(564\) | −17.1041 | −0.720214 | ||||||||
\(565\) | 22.0300 | 0.926810 | ||||||||
\(566\) | −10.9472 | −0.460143 | ||||||||
\(567\) | −35.2939 | −1.48221 | ||||||||
\(568\) | 13.3663 | 0.560836 | ||||||||
\(569\) | 29.9011 | 1.25352 | 0.626760 | − | 0.779213i | \(-0.284381\pi\) | ||||
0.626760 | + | 0.779213i | \(0.284381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.80807 | 0.410455 | 0.205228 | − | 0.978714i | \(-0.434207\pi\) | ||||
0.205228 | + | 0.978714i | \(0.434207\pi\) | |||||||
\(572\) | 2.99887 | 0.125389 | ||||||||
\(573\) | −34.5071 | −1.44155 | ||||||||
\(574\) | 24.1529 | 1.00812 | ||||||||
\(575\) | 2.71306 | 0.113143 | ||||||||
\(576\) | 0.0694508 | 0.00289378 | ||||||||
\(577\) | −4.11896 | −0.171475 | −0.0857373 | − | 0.996318i | \(-0.527325\pi\) | ||||
−0.0857373 | + | 0.996318i | \(0.527325\pi\) | |||||||
\(578\) | 31.2120 | 1.29825 | ||||||||
\(579\) | 0.977694 | 0.0406316 | ||||||||
\(580\) | −19.1750 | −0.796200 | ||||||||
\(581\) | −37.8234 | −1.56918 | ||||||||
\(582\) | 10.6835 | 0.442844 | ||||||||
\(583\) | 7.56179 | 0.313177 | ||||||||
\(584\) | 8.55207 | 0.353887 | ||||||||
\(585\) | −0.572757 | −0.0236806 | ||||||||
\(586\) | −4.29499 | −0.177424 | ||||||||
\(587\) | 18.6749 | 0.770795 | 0.385397 | − | 0.922751i | \(-0.374064\pi\) | ||||
0.385397 | + | 0.922751i | \(0.374064\pi\) | |||||||
\(588\) | −13.5006 | −0.556756 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.73168 | 0.112461 | ||||||||
\(591\) | 47.7151 | 1.96274 | ||||||||
\(592\) | 5.74381 | 0.236069 | ||||||||
\(593\) | 8.40647 | 0.345212 | 0.172606 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172606 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(594\) | −5.13428 | −0.210662 | ||||||||
\(595\) | 73.2249 | 3.00193 | ||||||||
\(596\) | 10.4264 | 0.427080 | ||||||||
\(597\) | 16.9255 | 0.692715 | ||||||||
\(598\) | −3.17496 | −0.129834 | ||||||||
\(599\) | −35.2002 | −1.43824 | −0.719120 | − | 0.694886i | \(-0.755455\pi\) | ||||
−0.719120 | + | 0.694886i | \(0.755455\pi\) | |||||||
\(600\) | −4.48963 | −0.183288 | ||||||||
\(601\) | −25.9342 | −1.05788 | −0.528939 | − | 0.848660i | \(-0.677410\pi\) | ||||
−0.528939 | + | 0.848660i | \(0.677410\pi\) | |||||||
\(602\) | −20.2114 | −0.823755 | ||||||||
\(603\) | 0.138579 | 0.00564336 | ||||||||
\(604\) | 0.887856 | 0.0361264 | ||||||||
\(605\) | 2.75002 | 0.111804 | ||||||||
\(606\) | 31.3372 | 1.27298 | ||||||||
\(607\) | 14.6858 | 0.596079 | 0.298039 | − | 0.954554i | \(-0.403667\pi\) | ||||
0.298039 | + | 0.954554i | \(0.403667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 46.8464 | 1.89831 | ||||||||
\(610\) | 17.3272 | 0.701557 | ||||||||
\(611\) | −29.2771 | −1.18443 | ||||||||
\(612\) | 0.482231 | 0.0194930 | ||||||||
\(613\) | −13.9711 | −0.564287 | −0.282143 | − | 0.959372i | \(-0.591045\pi\) | ||||
−0.282143 | + | 0.959372i | \(0.591045\pi\) | |||||||
\(614\) | 33.2043 | 1.34002 | ||||||||
\(615\) | −30.3452 | −1.22364 | ||||||||
\(616\) | −3.83483 | −0.154510 | ||||||||
\(617\) | 25.2895 | 1.01812 | 0.509058 | − | 0.860732i | \(-0.329994\pi\) | ||||
0.509058 | + | 0.860732i | \(0.329994\pi\) | |||||||
\(618\) | −2.86490 | −0.115243 | ||||||||
\(619\) | −18.7851 | −0.755037 | −0.377518 | − | 0.926002i | \(-0.623222\pi\) | ||||
−0.377518 | + | 0.926002i | \(0.623222\pi\) | |||||||
\(620\) | −14.8664 | −0.597049 | ||||||||
\(621\) | 5.43575 | 0.218129 | ||||||||
\(622\) | 29.4236 | 1.17978 | ||||||||
\(623\) | 50.5770 | 2.02633 | ||||||||
\(624\) | 5.25398 | 0.210327 | ||||||||
\(625\) | −31.2461 | −1.24984 | ||||||||
\(626\) | −8.73586 | −0.349155 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.69032 | −0.306877 | ||||||||
\(629\) | 39.8821 | 1.59020 | ||||||||
\(630\) | 0.732417 | 0.0291802 | ||||||||
\(631\) | −12.4425 | −0.495327 | −0.247663 | − | 0.968846i | \(-0.579663\pi\) | ||||
−0.247663 | + | 0.968846i | \(0.579663\pi\) | |||||||
\(632\) | 9.61507 | 0.382467 | ||||||||
\(633\) | −29.3081 | −1.16489 | ||||||||
\(634\) | 3.01863 | 0.119885 | ||||||||
\(635\) | 57.1778 | 2.26903 | ||||||||
\(636\) | 13.2481 | 0.525323 | ||||||||
\(637\) | −23.1090 | −0.915611 | ||||||||
\(638\) | 6.97269 | 0.276052 | ||||||||
\(639\) | 0.928298 | 0.0367229 | ||||||||
\(640\) | 2.75002 | 0.108704 | ||||||||
\(641\) | −12.3531 | −0.487918 | −0.243959 | − | 0.969786i | \(-0.578446\pi\) | ||||
−0.243959 | + | 0.969786i | \(0.578446\pi\) | |||||||
\(642\) | −11.7252 | −0.462757 | ||||||||
\(643\) | 18.9417 | 0.746987 | 0.373494 | − | 0.927633i | \(-0.378160\pi\) | ||||
0.373494 | + | 0.927633i | \(0.378160\pi\) | |||||||
\(644\) | 4.06000 | 0.159986 | ||||||||
\(645\) | 25.3931 | 0.999853 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.99197 | −0.353511 | −0.176755 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176755 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(648\) | −9.20353 | −0.361549 | ||||||||
\(649\) | −0.993331 | −0.0389916 | ||||||||
\(650\) | −7.68489 | −0.301426 | ||||||||
\(651\) | 36.3200 | 1.42349 | ||||||||
\(652\) | 0.977244 | 0.0382718 | ||||||||
\(653\) | −42.3768 | −1.65833 | −0.829166 | − | 0.559002i | \(-0.811184\pi\) | ||||
−0.829166 | + | 0.559002i | \(0.811184\pi\) | |||||||
\(654\) | −4.63606 | −0.181284 | ||||||||
\(655\) | −18.3938 | −0.718704 | ||||||||
\(656\) | 6.29831 | 0.245908 | ||||||||
\(657\) | 0.593948 | 0.0231721 | ||||||||
\(658\) | 37.4383 | 1.45950 | ||||||||
\(659\) | −29.6322 | −1.15431 | −0.577153 | − | 0.816636i | \(-0.695837\pi\) | ||||
−0.577153 | + | 0.816636i | \(0.695837\pi\) | |||||||
\(660\) | 4.81799 | 0.187540 | ||||||||
\(661\) | −49.1859 | −1.91311 | −0.956554 | − | 0.291554i | \(-0.905828\pi\) | ||||
−0.956554 | + | 0.291554i | \(0.905828\pi\) | |||||||
\(662\) | 21.0483 | 0.818067 | ||||||||
\(663\) | 36.4809 | 1.41680 | ||||||||
\(664\) | −9.86312 | −0.382763 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.398912 | 0.0154575 | ||||||||
\(667\) | −7.38211 | −0.285836 | ||||||||
\(668\) | −14.4378 | −0.558616 | ||||||||
\(669\) | 17.2357 | 0.666372 | ||||||||
\(670\) | 5.48725 | 0.211991 | ||||||||
\(671\) | −6.30075 | −0.243238 | ||||||||
\(672\) | −6.71856 | −0.259174 | ||||||||
\(673\) | −31.4592 | −1.21266 | −0.606331 | − | 0.795212i | \(-0.707359\pi\) | ||||
−0.606331 | + | 0.795212i | \(0.707359\pi\) | |||||||
\(674\) | 32.8578 | 1.26563 | ||||||||
\(675\) | 13.1571 | 0.506416 | ||||||||
\(676\) | −4.00678 | −0.154107 | ||||||||
\(677\) | −5.95353 | −0.228813 | −0.114406 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114406 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(678\) | −14.0349 | −0.539008 | ||||||||
\(679\) | −23.3845 | −0.897413 | ||||||||
\(680\) | 19.0947 | 0.732249 | ||||||||
\(681\) | −1.51492 | −0.0580518 | ||||||||
\(682\) | 5.40593 | 0.207004 | ||||||||
\(683\) | 8.82659 | 0.337740 | 0.168870 | − | 0.985638i | \(-0.445988\pi\) | ||||
0.168870 | + | 0.985638i | \(0.445988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.0952 | 1.72300 | ||||||||
\(686\) | 2.70700 | 0.103354 | ||||||||
\(687\) | −14.6107 | −0.557433 | ||||||||
\(688\) | −5.27048 | −0.200935 | ||||||||
\(689\) | 22.6768 | 0.863918 | ||||||||
\(690\) | −5.10089 | −0.194187 | ||||||||
\(691\) | 0.0845197 | 0.00321528 | 0.00160764 | − | 0.999999i | \(-0.499488\pi\) | ||||
0.00160764 | + | 0.999999i | \(0.499488\pi\) | |||||||
\(692\) | −20.7436 | −0.788555 | ||||||||
\(693\) | −0.266332 | −0.0101171 | ||||||||
\(694\) | −1.55590 | −0.0590612 | ||||||||
\(695\) | 36.2896 | 1.37654 | ||||||||
\(696\) | 12.2161 | 0.463048 | ||||||||
\(697\) | 43.7323 | 1.65648 | ||||||||
\(698\) | −7.35032 | −0.278214 | ||||||||
\(699\) | −34.7901 | −1.31588 | ||||||||
\(700\) | 9.82711 | 0.371430 | ||||||||
\(701\) | −2.73246 | −0.103204 | −0.0516018 | − | 0.998668i | \(-0.516433\pi\) | ||||
−0.0516018 | + | 0.998668i | \(0.516433\pi\) | |||||||
\(702\) | −15.3970 | −0.581124 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −47.0367 | −1.77150 | ||||||||
\(706\) | −19.3609 | −0.728659 | ||||||||
\(707\) | −68.5922 | −2.57968 | ||||||||
\(708\) | −1.74030 | −0.0654045 | ||||||||
\(709\) | −5.26476 | −0.197722 | −0.0988611 | − | 0.995101i | \(-0.531520\pi\) | ||||
−0.0988611 | + | 0.995101i | \(0.531520\pi\) | |||||||
\(710\) | 36.7575 | 1.37948 | ||||||||
\(711\) | 0.667775 | 0.0250435 | ||||||||
\(712\) | 13.1889 | 0.494274 | ||||||||
\(713\) | −5.72335 | −0.214341 | ||||||||
\(714\) | −46.6502 | −1.74584 | ||||||||
\(715\) | 8.24695 | 0.308418 | ||||||||
\(716\) | −19.5304 | −0.729884 | ||||||||
\(717\) | 27.6191 | 1.03146 | ||||||||
\(718\) | −14.9074 | −0.556341 | ||||||||
\(719\) | 25.8897 | 0.965523 | 0.482762 | − | 0.875752i | \(-0.339634\pi\) | ||||
0.482762 | + | 0.875752i | \(0.339634\pi\) | |||||||
\(720\) | 0.190991 | 0.00711781 | ||||||||
\(721\) | 6.27082 | 0.233538 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 38.6911 | 1.43894 | ||||||||
\(724\) | 0.524440 | 0.0194906 | ||||||||
\(725\) | −17.8682 | −0.663608 | ||||||||
\(726\) | −1.75198 | −0.0650223 | ||||||||
\(727\) | 49.4783 | 1.83505 | 0.917525 | − | 0.397678i | \(-0.130184\pi\) | ||||
0.917525 | + | 0.397678i | \(0.130184\pi\) | |||||||
\(728\) | −11.5001 | −0.426224 | ||||||||
\(729\) | 26.3463 | 0.975790 | ||||||||
\(730\) | 23.5184 | 0.870453 | ||||||||
\(731\) | −36.5955 | −1.35353 | ||||||||
\(732\) | −11.0388 | −0.408007 | ||||||||
\(733\) | 31.3799 | 1.15904 | 0.579522 | − | 0.814957i | \(-0.303239\pi\) | ||||
0.579522 | + | 0.814957i | \(0.303239\pi\) | |||||||
\(734\) | −27.5633 | −1.01738 | ||||||||
\(735\) | −37.1269 | −1.36945 | ||||||||
\(736\) | 1.05872 | 0.0390248 | ||||||||
\(737\) | −1.99535 | −0.0734997 | ||||||||
\(738\) | 0.437423 | 0.0161018 | ||||||||
\(739\) | 33.1196 | 1.21832 | 0.609161 | − | 0.793046i | \(-0.291506\pi\) | ||||
0.609161 | + | 0.793046i | \(0.291506\pi\) | |||||||
\(740\) | 15.7956 | 0.580657 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.9982 | −1.06456 | ||||||||
\(743\) | 1.63951 | 0.0601477 | 0.0300738 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300738 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(744\) | 9.47110 | 0.347227 | ||||||||
\(745\) | 28.6727 | 1.05049 | ||||||||
\(746\) | −13.6882 | −0.501159 | ||||||||
\(747\) | −0.685001 | −0.0250629 | ||||||||
\(748\) | −6.94349 | −0.253879 | ||||||||
\(749\) | 25.6647 | 0.937768 | ||||||||
\(750\) | 11.7434 | 0.428808 | ||||||||
\(751\) | −28.0985 | −1.02533 | −0.512664 | − | 0.858589i | \(-0.671342\pi\) | ||||
−0.512664 | + | 0.858589i | \(0.671342\pi\) | |||||||
\(752\) | 9.76272 | 0.356010 | ||||||||
\(753\) | −13.7291 | −0.500315 | ||||||||
\(754\) | 20.9102 | 0.761505 | ||||||||
\(755\) | 2.44162 | 0.0888597 | ||||||||
\(756\) | 19.6891 | 0.716084 | ||||||||
\(757\) | −24.9320 | −0.906170 | −0.453085 | − | 0.891467i | \(-0.649677\pi\) | ||||
−0.453085 | + | 0.891467i | \(0.649677\pi\) | |||||||
\(758\) | −6.31554 | −0.229391 | ||||||||
\(759\) | 1.85486 | 0.0673270 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5854 | 0.419972 | 0.209986 | − | 0.977704i | \(-0.432658\pi\) | ||||
0.209986 | + | 0.977704i | \(0.432658\pi\) | |||||||
\(762\) | −36.4269 | −1.31961 | ||||||||
\(763\) | 10.1476 | 0.367369 | ||||||||
\(764\) | 19.6960 | 0.712576 | ||||||||
\(765\) | 1.32614 | 0.0479468 | ||||||||
\(766\) | 4.01015 | 0.144893 | ||||||||
\(767\) | −2.97887 | −0.107561 | ||||||||
\(768\) | −1.75198 | −0.0632193 | ||||||||
\(769\) | 4.99290 | 0.180049 | 0.0900243 | − | 0.995940i | \(-0.471306\pi\) | ||||
0.0900243 | + | 0.995940i | \(0.471306\pi\) | |||||||
\(770\) | −10.5458 | −0.380046 | ||||||||
\(771\) | 35.9002 | 1.29291 | ||||||||
\(772\) | −0.558050 | −0.0200846 | ||||||||
\(773\) | −4.30139 | −0.154710 | −0.0773550 | − | 0.997004i | \(-0.524647\pi\) | ||||
−0.0773550 | + | 0.997004i | \(0.524647\pi\) | |||||||
\(774\) | −0.366039 | −0.0131570 | ||||||||
\(775\) | −13.8532 | −0.497622 | ||||||||
\(776\) | −6.09792 | −0.218902 | ||||||||
\(777\) | −38.5902 | −1.38441 | ||||||||
\(778\) | −17.8884 | −0.641329 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 14.4485 | 0.517340 | ||||||||
\(781\) | −13.3663 | −0.478283 | ||||||||
\(782\) | 7.35119 | 0.262878 | ||||||||
\(783\) | −35.7997 | −1.27938 | ||||||||
\(784\) | 7.70590 | 0.275211 | ||||||||
\(785\) | −21.1485 | −0.754823 | ||||||||
\(786\) | 11.7183 | 0.417979 | ||||||||
\(787\) | 19.1746 | 0.683500 | 0.341750 | − | 0.939791i | \(-0.388980\pi\) | ||||
0.341750 | + | 0.939791i | \(0.388980\pi\) | |||||||
\(788\) | −27.2349 | −0.970202 | ||||||||
\(789\) | 46.9782 | 1.67247 | ||||||||
\(790\) | 26.4416 | 0.940751 | ||||||||
\(791\) | 30.7203 | 1.09229 | ||||||||
\(792\) | −0.0694508 | −0.00246783 | ||||||||
\(793\) | −18.8951 | −0.670986 | ||||||||
\(794\) | −7.46337 | −0.264865 | ||||||||
\(795\) | 36.4326 | 1.29213 | ||||||||
\(796\) | −9.66076 | −0.342417 | ||||||||
\(797\) | −26.0624 | −0.923179 | −0.461589 | − | 0.887094i | \(-0.652721\pi\) | ||||
−0.461589 | + | 0.887094i | \(0.652721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.7873 | 2.39814 | ||||||||
\(800\) | 2.56259 | 0.0906014 | ||||||||
\(801\) | 0.915977 | 0.0323645 | ||||||||
\(802\) | −16.9891 | −0.599907 | ||||||||
\(803\) | −8.55207 | −0.301796 | ||||||||
\(804\) | −3.49583 | −0.123288 | ||||||||
\(805\) | 11.1651 | 0.393517 | ||||||||
\(806\) | 16.2117 | 0.571032 | ||||||||
\(807\) | −19.2038 | −0.676007 | ||||||||
\(808\) | −17.8867 | −0.629250 | ||||||||
\(809\) | 14.0330 | 0.493374 | 0.246687 | − | 0.969095i | \(-0.420658\pi\) | ||||
0.246687 | + | 0.969095i | \(0.420658\pi\) | |||||||
\(810\) | −25.3099 | −0.889298 | ||||||||
\(811\) | 17.0976 | 0.600379 | 0.300190 | − | 0.953880i | \(-0.402950\pi\) | ||||
0.300190 | + | 0.953880i | \(0.402950\pi\) | |||||||
\(812\) | −26.7391 | −0.938357 | ||||||||
\(813\) | −3.25940 | −0.114312 | ||||||||
\(814\) | −5.74381 | −0.201321 | ||||||||
\(815\) | 2.68744 | 0.0941368 | ||||||||
\(816\) | −12.1649 | −0.425856 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 3.76849 | 0.131762 | ||||||||
\(819\) | −0.798694 | −0.0279086 | ||||||||
\(820\) | 17.3205 | 0.604857 | ||||||||
\(821\) | −38.3104 | −1.33704 | −0.668521 | − | 0.743693i | \(-0.733072\pi\) | ||||
−0.668521 | + | 0.743693i | \(0.733072\pi\) | |||||||
\(822\) | −28.7293 | −1.00205 | ||||||||
\(823\) | −45.4170 | −1.58314 | −0.791568 | − | 0.611081i | \(-0.790735\pi\) | ||||
−0.791568 | + | 0.611081i | \(0.790735\pi\) | |||||||
\(824\) | 1.63523 | 0.0569659 | ||||||||
\(825\) | 4.48963 | 0.156309 | ||||||||
\(826\) | 3.80925 | 0.132541 | ||||||||
\(827\) | −38.2328 | −1.32948 | −0.664742 | − | 0.747073i | \(-0.731459\pi\) | ||||
−0.664742 | + | 0.747073i | \(0.731459\pi\) | |||||||
\(828\) | 0.0735287 | 0.00255530 | ||||||||
\(829\) | −9.68698 | −0.336443 | −0.168221 | − | 0.985749i | \(-0.553802\pi\) | ||||
−0.168221 | + | 0.985749i | \(0.553802\pi\) | |||||||
\(830\) | −27.1237 | −0.941479 | ||||||||
\(831\) | −32.8968 | −1.14118 | ||||||||
\(832\) | −2.99887 | −0.103967 | ||||||||
\(833\) | 53.5058 | 1.85387 | ||||||||
\(834\) | −23.1194 | −0.800560 | ||||||||
\(835\) | −39.7042 | −1.37402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.7555 | −0.959371 | ||||||||
\(838\) | 32.5461 | 1.12429 | ||||||||
\(839\) | 18.0609 | 0.623531 | 0.311766 | − | 0.950159i | \(-0.399080\pi\) | ||||
0.311766 | + | 0.950159i | \(0.399080\pi\) | |||||||
\(840\) | −18.4762 | −0.637488 | ||||||||
\(841\) | 19.6184 | 0.676498 | ||||||||
\(842\) | 3.97736 | 0.137069 | ||||||||
\(843\) | −22.2686 | −0.766973 | ||||||||
\(844\) | 16.7285 | 0.575819 | ||||||||
\(845\) | −11.0187 | −0.379055 | ||||||||
\(846\) | 0.678029 | 0.0233111 | ||||||||
\(847\) | 3.83483 | 0.131766 | ||||||||
\(848\) | −7.56179 | −0.259673 | ||||||||
\(849\) | 19.1793 | 0.658230 | ||||||||
\(850\) | 17.7933 | 0.610307 | ||||||||
\(851\) | 6.08107 | 0.208457 | ||||||||
\(852\) | −23.4175 | −0.802270 | ||||||||
\(853\) | −52.2530 | −1.78911 | −0.894554 | − | 0.446961i | \(-0.852506\pi\) | ||||
−0.894554 | + | 0.446961i | \(0.852506\pi\) | |||||||
\(854\) | 24.1623 | 0.826817 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.69253 | 0.228746 | ||||||||
\(857\) | 9.26830 | 0.316599 | 0.158299 | − | 0.987391i | \(-0.449399\pi\) | ||||
0.158299 | + | 0.987391i | \(0.449399\pi\) | |||||||
\(858\) | −5.25398 | −0.179368 | ||||||||
\(859\) | 30.3995 | 1.03722 | 0.518609 | − | 0.855011i | \(-0.326450\pi\) | ||||
0.518609 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(860\) | −14.4939 | −0.494238 | ||||||||
\(861\) | −42.3156 | −1.44211 | ||||||||
\(862\) | −4.18326 | −0.142483 | ||||||||
\(863\) | 20.8169 | 0.708614 | 0.354307 | − | 0.935129i | \(-0.384717\pi\) | ||||
0.354307 | + | 0.935129i | \(0.384717\pi\) | |||||||
\(864\) | 5.13428 | 0.174672 | ||||||||
\(865\) | −57.0453 | −1.93960 | ||||||||
\(866\) | 13.7414 | 0.466950 | ||||||||
\(867\) | −54.6830 | −1.85713 | ||||||||
\(868\) | −20.7308 | −0.703649 | ||||||||
\(869\) | −9.61507 | −0.326169 | ||||||||
\(870\) | 33.5944 | 1.13896 | ||||||||
\(871\) | −5.98380 | −0.202753 | ||||||||
\(872\) | 2.64617 | 0.0896108 | ||||||||
\(873\) | −0.423505 | −0.0143335 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.7045 | −0.868970 | ||||||||
\(876\) | −14.9831 | −0.506232 | ||||||||
\(877\) | 38.3678 | 1.29559 | 0.647795 | − | 0.761815i | \(-0.275691\pi\) | ||||
0.647795 | + | 0.761815i | \(0.275691\pi\) | |||||||
\(878\) | 27.4116 | 0.925096 | ||||||||
\(879\) | 7.52476 | 0.253804 | ||||||||
\(880\) | −2.75002 | −0.0927031 | ||||||||
\(881\) | −11.9200 | −0.401595 | −0.200797 | − | 0.979633i | \(-0.564353\pi\) | ||||
−0.200797 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(882\) | 0.535181 | 0.0180205 | ||||||||
\(883\) | −8.10007 | −0.272589 | −0.136295 | − | 0.990668i | \(-0.543519\pi\) | ||||
−0.136295 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(884\) | −20.8226 | −0.700341 | ||||||||
\(885\) | −4.78586 | −0.160875 | ||||||||
\(886\) | 34.5821 | 1.16181 | ||||||||
\(887\) | −16.4058 | −0.550854 | −0.275427 | − | 0.961322i | \(-0.588819\pi\) | ||||
−0.275427 | + | 0.961322i | \(0.588819\pi\) | |||||||
\(888\) | −10.0631 | −0.337695 | ||||||||
\(889\) | 79.7330 | 2.67416 | ||||||||
\(890\) | 36.2696 | 1.21576 | ||||||||
\(891\) | 9.20353 | 0.308330 | ||||||||
\(892\) | −9.83783 | −0.329395 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −18.2668 | −0.610934 | ||||||||
\(895\) | −53.7088 | −1.79529 | ||||||||
\(896\) | 3.83483 | 0.128113 | ||||||||
\(897\) | 5.56247 | 0.185726 | ||||||||
\(898\) | 14.0064 | 0.467399 | ||||||||
\(899\) | 37.6939 | 1.25716 | ||||||||
\(900\) | 0.177974 | 0.00593248 | ||||||||
\(901\) | −52.5052 | −1.74920 | ||||||||
\(902\) | −6.29831 | −0.209711 | ||||||||
\(903\) | 35.4100 | 1.17837 | ||||||||
\(904\) | 8.01087 | 0.266438 | ||||||||
\(905\) | 1.44222 | 0.0479409 | ||||||||
\(906\) | −1.55551 | −0.0516784 | ||||||||
\(907\) | −3.06778 | −0.101864 | −0.0509320 | − | 0.998702i | \(-0.516219\pi\) | ||||
−0.0509320 | + | 0.998702i | \(0.516219\pi\) | |||||||
\(908\) | 0.864686 | 0.0286956 | ||||||||
\(909\) | −1.24224 | −0.0412026 | ||||||||
\(910\) | −31.6256 | −1.04838 | ||||||||
\(911\) | 32.5171 | 1.07734 | 0.538669 | − | 0.842517i | \(-0.318927\pi\) | ||||
0.538669 | + | 0.842517i | \(0.318927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.86312 | 0.326422 | ||||||||
\(914\) | −34.1525 | −1.12966 | ||||||||
\(915\) | −30.3570 | −1.00357 | ||||||||
\(916\) | 8.33952 | 0.275545 | ||||||||
\(917\) | −25.6496 | −0.847025 | ||||||||
\(918\) | 35.6498 | 1.17662 | ||||||||
\(919\) | −6.71906 | −0.221641 | −0.110821 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110821 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(920\) | 2.91149 | 0.0959890 | ||||||||
\(921\) | −58.1734 | −1.91688 | ||||||||
\(922\) | 37.5791 | 1.23760 | ||||||||
\(923\) | −40.0837 | −1.31937 | ||||||||
\(924\) | 6.71856 | 0.221024 | ||||||||
\(925\) | 14.7191 | 0.483960 | ||||||||
\(926\) | 5.53335 | 0.181837 | ||||||||
\(927\) | 0.113568 | 0.00373006 | ||||||||
\(928\) | −6.97269 | −0.228890 | ||||||||
\(929\) | 51.7217 | 1.69693 | 0.848466 | − | 0.529249i | \(-0.177526\pi\) | ||||
0.848466 | + | 0.529249i | \(0.177526\pi\) | |||||||
\(930\) | 26.0457 | 0.854072 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.8575 | 0.650455 | ||||||||
\(933\) | −51.5497 | −1.68766 | ||||||||
\(934\) | 12.6215 | 0.412989 | ||||||||
\(935\) | −19.0947 | −0.624464 | ||||||||
\(936\) | −0.208274 | −0.00680765 | ||||||||
\(937\) | −33.3287 | −1.08880 | −0.544401 | − | 0.838825i | \(-0.683243\pi\) | ||||
−0.544401 | + | 0.838825i | \(0.683243\pi\) | |||||||
\(938\) | 7.65183 | 0.249841 | ||||||||
\(939\) | 15.3051 | 0.499463 | ||||||||
\(940\) | 26.8476 | 0.875674 | ||||||||
\(941\) | 32.9924 | 1.07552 | 0.537761 | − | 0.843097i | \(-0.319270\pi\) | ||||
0.537761 | + | 0.843097i | \(0.319270\pi\) | |||||||
\(942\) | 13.4733 | 0.438985 | ||||||||
\(943\) | 6.66813 | 0.217144 | ||||||||
\(944\) | 0.993331 | 0.0323302 | ||||||||
\(945\) | 54.1453 | 1.76135 | ||||||||
\(946\) | 5.27048 | 0.171358 | ||||||||
\(947\) | 6.13812 | 0.199462 | 0.0997311 | − | 0.995014i | \(-0.468202\pi\) | ||||
0.0997311 | + | 0.995014i | \(0.468202\pi\) | |||||||
\(948\) | −16.8455 | −0.547115 | ||||||||
\(949\) | −25.6466 | −0.832523 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.28859 | −0.171494 | ||||||||
\(952\) | 26.6271 | 0.862988 | ||||||||
\(953\) | −12.0071 | −0.388948 | −0.194474 | − | 0.980908i | \(-0.562300\pi\) | ||||
−0.194474 | + | 0.980908i | \(0.562300\pi\) | |||||||
\(954\) | −0.525172 | −0.0170031 | ||||||||
\(955\) | 54.1643 | 1.75272 | ||||||||
\(956\) | −15.7645 | −0.509860 | ||||||||
\(957\) | −12.2161 | −0.394889 | ||||||||
\(958\) | −22.1665 | −0.716167 | ||||||||
\(959\) | 62.8841 | 2.03063 | ||||||||
\(960\) | −4.81799 | −0.155500 | ||||||||
\(961\) | −1.77597 | −0.0572894 | ||||||||
\(962\) | −17.2250 | −0.555355 | ||||||||
\(963\) | 0.464802 | 0.0149780 | ||||||||
\(964\) | −22.0841 | −0.711282 | ||||||||
\(965\) | −1.53465 | −0.0494020 | ||||||||
\(966\) | −7.11305 | −0.228859 | ||||||||
\(967\) | −48.3924 | −1.55619 | −0.778097 | − | 0.628144i | \(-0.783815\pi\) | ||||
−0.778097 | + | 0.628144i | \(0.783815\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.7694 | −0.538432 | ||||||||
\(971\) | 29.7309 | 0.954109 | 0.477054 | − | 0.878874i | \(-0.341704\pi\) | ||||
0.477054 | + | 0.878874i | \(0.341704\pi\) | |||||||
\(972\) | 0.721610 | 0.0231456 | ||||||||
\(973\) | 50.6049 | 1.62232 | ||||||||
\(974\) | 8.56601 | 0.274473 | ||||||||
\(975\) | 13.4638 | 0.431187 | ||||||||
\(976\) | 6.30075 | 0.201682 | ||||||||
\(977\) | −28.1112 | −0.899358 | −0.449679 | − | 0.893190i | \(-0.648462\pi\) | ||||
−0.449679 | + | 0.893190i | \(0.648462\pi\) | |||||||
\(978\) | −1.71212 | −0.0547474 | ||||||||
\(979\) | −13.1889 | −0.421518 | ||||||||
\(980\) | 21.1914 | 0.676933 | ||||||||
\(981\) | 0.183779 | 0.00586761 | ||||||||
\(982\) | 22.0937 | 0.705038 | ||||||||
\(983\) | −36.4985 | −1.16412 | −0.582061 | − | 0.813145i | \(-0.697753\pi\) | ||||
−0.582061 | + | 0.813145i | \(0.697753\pi\) | |||||||
\(984\) | −11.0346 | −0.351769 | ||||||||
\(985\) | −74.8964 | −2.38640 | ||||||||
\(986\) | −48.4148 | −1.54184 | ||||||||
\(987\) | −65.5914 | −2.08780 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.57995 | −0.177432 | ||||||||
\(990\) | −0.190991 | −0.00607009 | ||||||||
\(991\) | −54.1787 | −1.72104 | −0.860521 | − | 0.509415i | \(-0.829862\pi\) | ||||
−0.860521 | + | 0.509415i | \(0.829862\pi\) | |||||||
\(992\) | −5.40593 | −0.171638 | ||||||||
\(993\) | −36.8764 | −1.17024 | ||||||||
\(994\) | 51.2573 | 1.62578 | ||||||||
\(995\) | −26.5673 | −0.842239 | ||||||||
\(996\) | 17.2800 | 0.547539 | ||||||||
\(997\) | −56.3505 | −1.78464 | −0.892319 | − | 0.451406i | \(-0.850923\pi\) | ||||
−0.892319 | + | 0.451406i | \(0.850923\pi\) | |||||||
\(998\) | −2.72781 | −0.0863474 | ||||||||
\(999\) | 29.4903 | 0.933033 |
(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 | 7942.2.a.ca.1.4 | 15 | ||
19.4 | even | 9 | 418.2.j.d.111.4 | ✓ | 30 | ||
19.5 | even | 9 | 418.2.j.d.177.4 | yes | 30 | ||
19.18 | odd | 2 | 7942.2.a.by.1.12 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.j.d.111.4 | ✓ | 30 | 19.4 | even | 9 | ||
418.2.j.d.177.4 | yes | 30 | 19.5 | even | 9 | ||
7942.2.a.by.1.12 | 15 | 19.18 | odd | 2 | |||
7942.2.a.ca.1.4 | 15 | 1.1 | even | 1 | trivial |